References:
Dyer's Compendium of the War of the Rebellion, 1959 Edition, Pages 37-38, Volume Unknown.

Note: I have modified the formatting from the original text in Dyers'; to make it more legible and eliminate his “Wall of Text”. I have also corrected a counting error in the New York entry. Dyer's lists the total units for N.Y. as 393, but if you add up all the specific types he lists, it comes out as 403.

ALABAMA

Cavalry: 1 Regiment
Heavy Artillery: 1 Regiment.
Infantry: 4 Regiments.
Total: 6 Units (6 Regiments)

ARKANSAS

Cavalry: 4 Regiments
Light Artillery: 2 Batteries
Infantry: 10 Regiments; 1 Battalion
Total: 17 Units (14 Regiments, 1 Battalion and 2 Batteries)

CALIFORNIA

Cavalry: 2 Regiments; 1 Battalion.
Infantry: 8 Regiments; 1 Battalion.
Total: 12 Units (10 Regiments and 2 Battalions)

COLORADO

Cavalry: 3 Regiments.
Light Artillery: 1 Battery.
Infantry: 3 Regiments; 1 Company.
Total: 8 Units (6 Regiments, 1 Battery, and 1 Company)

CONNECTICUT

Cavalry: 1 Regiment
Heavy Artillery: 2 Regiments
Light Artillery: 3 Batteries
Infantry: 30 Regiments
Total: 36 Units (33 Regiments and 3 Batteries)

DAKOTA TERRITORY

Cavalry: 1 Battalion
Total: 1 Unit (1 Battalion)

DELAWARE

Cavalry: 1 Regiment; 1 Company
Heavy Artillery: 1 Company
Light Artillery: 1 Battery
Infantry: 10 Regiments; 1 Company
Total: 15 Units (11 Regiments, 1 Battery, and 3 Companies)

DISTRICT OF COLUMBIA

Cavalry: 1 Regiment; 1 Company
Infantry: 2 Regiments.; 4 Battalions; 33 Companies
Total: 41 Units (3 Regiments, 4 Battalions and 34 Companies)

FLORIDA

Cavalry: 2 Regiments
Total: 2 Units (2 Regiments)

GEORGIA

Infantry: 1 Battalion
Total: 1 Unit (1 Battalion)

ILLINOIS

Cavalry: 17 Regiments; 3 Battalions; 17 Companies
Light Artillery: 35 Batteries
Infantry: 156 Regiments; 11 Companies
Total: 239 Units (173 Regiments, 3 Battalions, 35 Batteries and 28 Companies)

INDIANA

Cavalry: 13 Regiments; 3 Companies.
Heavy Artillery: 1 Regiment
Light Artillery: 26 Batteries
Infantry: 152 Regiments
Total: 195 Units (166 Regiments, 26 Batteries and 3 Companies)

IOWA

Cavalry: 9 Regiments
Light Artillery: 4 Batteries
Infantry: 51 Regiments
Total: 64 Units (60 Regiments and 4 Batteries)

KANSAS

Cavalry: 9 Regiments
Light Artillery: 8 Batteries
Infantry, 35 Regiments; 2 Companies
Total: 54 Units (44 Regiments, 8 Batteries and 2 Companies)

KENTUCKY

Cavalry: 17 Regiments.; 1 Battalion
Light Artillery: 6 Batteries
Engineers: 1 Company
Infantry: 55 Regiments.
Total: 80 Units (72 Regiments, 1 Battalion, 6 Batteries and 1 Company)

LOUISIANA

Cavalry: 2 Regiments
Heavy Artillery: 1 Regiment
Light Artillery: 3 Batteries
Infantry: 18 Regiments
Total: 24 Units (21 Regiments and 3 Batteries)

MAINE

Cavalry: 2 Regiments
Heavy Artillery: 1 Regiment
Light Artillery: 7 Batteries
Sharpshooters: 1 Battalion; 1 Company
Infantry: 33 Regiments; 1 Battalion; 7 Companies
Total: 53 Units (36 Regiments 1 Battalion, 7 Batteries and 8 Companies)

MARYLAND

Cavalry: 4 Regiments; 1 Battalion; 1 Company
Heavy Artillery: 1 Regiment
Light Artillery: 6 Batteries
Infantry: 20 Regiments; 2 Companies
Total: 35 Units (25 Regiments, 1 Battalion, 6 Batteries, and 3 Companies)

MASSACHUSETTS

Cavalry: 5 Regiments.; 3 Battalions
Heavy Artillery: 4 Regiments; 1 Battalion; 30 Companies
Light Artillery: 18 Batteries
Sharpshooters: 2 Companies
Infantry: 71 Regiments; 3 Battalions; 28 Unattached Companies
Total: 165 Units (80 Regiments, 7 Battalions, 18 Batteries, and 60 Companies)

MICHIGAN

Cavalry: 11 Regiments; 2 Companies
Heavy Artillery: 1 Regiment
Light Artillery: 14 Batteries
Engineers: 1 Regiment; 1 Company
Sharpshooters: 1 Regiment; 8 Companies
Infantry: 35 Regiments; 2 Companies
Total: 76 Units (49 Regiments, 14 Batteries and 13 Companies)

MINNESOTA

Cavalry: 2 Regiments; 2 Battalions
Heavy Artillery: 1 Regiment
Light Artillery: 3 Batteries
Sharpshooters: 2 Companies
Infantry: 11 Regiments
Total: 21 Units (14 Regiments, 2 Battalions, 3 Batteries and 2 Companies)

MISSOURI

Cavalry: 32 Regiments; 16 Battalions; 10 Companies
Light Artillery: 2 Battalions; 39 Batteries
Engineers: 2 Regiments; 4 Companies
Sharpshooters: 1 Regiment; 1 Battalion
Infantry: 266 Regiments; 40 Battalions; 34 Companies
Total: 447 Units (301 Regiments, 59 Battalions, 39 Batteries and 48 Companies)

MISSISSIPPI

Cavalry: 2 Regiments
Heavy Artillery: 2 Regiments
Infantry: 6 Regiments
Total: 10 Units (10 Regiments)

NEBRASKA

Cavalry: 2 Regiments; 1 Battalion; 2 Companies.
Total: 6 Units (2 Regiments, 1 Battalion, and 2 Companies)

NEVADA

Cavalry: 1 Battalion
Infantry: 1 Battalion
Total: 2 Units (2 Battalions)

NEW HAMPSHIRE

Cavalry: 2 Regiments
Heavy Artillery: 1 Regiment; 1 Company
Light Artillery: 1 Battery
Sharpshooters: 3 Companies
Infantry: 18 Regiments; 3 Companies
Total: 29 (21 Regiments, 1 Battery and 7 Companies)

NEW JERSEY

Cavalry: 3 Regiments
Light Artillery: 5 Batteries
Infantry: 41 Regiments.
Total: 49 Units (44 Regiments; 5 Batteries)

NEW MEXICO

Cavalry: 1 Regiment; 1 Battalion; 6 Companies
Infantry: 7 Regiments; 5 Companies
Total: 19 Units (8 Regiments, 1 Battalion and 11 Companies)

NEW YORK

Cavalry: 32 Regiments; 1 Battalion; 3 Companies
Heavy Artillery: 26 Regiments; 5 Battalions
Light Artillery: 6 Battalions; 66 Batteries
Engineers: 4 Regiments
Sharpshooters: 1 Battalion; 4 Companies
Infantry: 254 Regiments; 1 Battalion
Total: 403 Units (316 Regiments, 14 Battalions, 66 Batteries and 7 Companies)

NORTH CAROLINA

Heavy Artillery: 1 Regiment.
Infantry: 7 Regiments.
Total: 8 Units (8 Regiments)

OHIO

Cavalry: 13 Regiments; 5 Battalions; 10 Companies
Heavy Artillery: 2 Regiments
Light Artillery: 42 Batteries
Sharpshooters: 10 Companies
Infantry: 227 Regiments; 1 Battalion; 5 Companies
Total: 315 Units (242 Regiments, 6 Battalions, 42 Batteries and 25 Companies)

OREGON

Cavalry: 1 Regiment
Infantry: 1 Regiment
Total: 2 Units (2 Regiments)

PENNSYLVANIA

Cavalry: 28 Regiments; 3 Battalions; 22 Companies
Heavy Artillery: 5 Regiments; 2 Battalions; 3 Companies
Light Artillery: 1 Battalion; 29 Batteries
Engineers: 1 Company
Sharpshooters: 1 Company
Infantry: 258 Regiments; 5 Battalions, 25 Companies.
Total: 383 Units (291 Regiments, 11 Battalions, 29 Batteries, and 52 Companies)

RHODE ISLAND

Cavalry: 3 Regiments; 1 Battalion
Heavy Artillery: 3 Regiments
Light Artillery: 10 Batteries
Infantry. 12 Regiments; 1 Company
Total: 30 Units (18 Regiments, 1 Battalion, 10 Batteries and 1 Company)

SOUTH CAROLINA

Infantry: 5 Regiments
Total: 5 Units (5 Regiments)

TENNESSEE

Cavalry: 20 Regiments; 1 Battalion
Heavy Artillery: 2 Regiments
Light Artillery: 9 Batteries
Infantry: 23 Regiments; 1 Company
Total: 56 Units (45 Regiments, 1 Battalion, 9 Batteries and 1 Company)

TEXAS

Cavalry: 2 Regiments; 2 Battalions
Total: 4 Units (2 Regiments, 2 Battalions)

VERMONT

Cavalry: 1 Regiment
Heavy Artillery: 1 Regiment; 1 Company
Light Artillery: 3 Batteries
Sharpshooters: 3 Companies
Infantry: 18 Regiments
Total: 27 Units (20 Regiments, 3 Batteries and 4 Companies)

VIRGINIA

Cavalry: 1 Battalion
Total: 1 Unit (1 Battalion)

WASHINGTON TERRITORY

Infantry: 1 Battalion
Total: 1 Unit (1 Battalion)

WEST VIRGINIA

Cavalry: 7 Regiments.
Light Artillery: 8 Batteries
Infantry: 20 Regiments; 1 Battalion; 1 Company
Total: 37 Units (27 Regiments, 1 Battalion, 8 Batteries and 1 Company)

WISCONSIN

Cavalry: 4 Regiments
Heavy Artillery: 1 Regiment
Light Artillery: 13 Batteries
Sharpshooters: 1 Company
Infantry: 54 Regiments
Total: 73 Units (59 Regiments, 13 Batteries and 1 Company)

U. S. REGULAR ARMY

Cavalry: 6 Regiments
Artillery: 60 Batteries
Engineers: 1 Battalion
Infantry: 19 Regiments
Total: 86 Units (25 Regiments, 1 Battalion and 60 Batteries)

U. S. VOLUNTEERS

Sharpshooters, 2 Regiments
Pontoneers: 1 Company
Infantry: 6 Regiments; 1 Company
Total: 10 Units (8 Regiments and 2 Companies)

U. S. VETERAN VOLUNTEERS

Engineers: 1 Regiment
Infantry: 9 Regiments
Total: 10 Units (10 Regiments)

CORPS DE AFRIQUE

Cavalry: 1 Regiment
Heavy Artillery: 1 Regiment
Engineers: 5 Regiments
Infantry: 22 Regiments
Total: 29 Units (29 Regiments)

U. S. COLORED TROOPS

Cavalry: 6 Regiments
Heavy Artillery: 13 Regiments
Light Artillery: 10 Batteries
Infantry: 137 Regiments
Total: 167 Units (156 Regiments and 10 Batteries)

U. S. VOLUNTEERS; INDIAN TROOPS

Infantry: 4 Regiments
Total: 4 Units (4 Regiments)

U. S. VETERAN RESERVE CORPS

Infantry: 24 Regiments; 188 Companies
Total: 212 Units (24 Regiments and 188 Companies)

RECAPITULATION

Cavalry:

272 Regiments
45 Battalions
78 Companies

Heavy Artillery:

61 Regiments
8 Battalions
36 Companies

Light Artillery:

9 Battalions
432 Batteries (Includes the Batteries of all Light Artillery Regiments, their service for the most part being as separate organizations.)

Engineers:

13 Regiments
1 Battalion
7 Companies

Sharpshooters:

4 Regiments
3 Battalions
35 Companies

Infantry:

2,144 Regiments
60 Battalions
351 Companies

Total Independent Units: 3,559