United States Navy (USN)

Task Force 38 (TF 38)
    Commanded by Admiral William F. Halsey & Vice Admiral J. S. McCain

TF 38.1
    Rear Admiral T. L. Sprague
CV Bennington     CAPT B. L. Braun
    CVG-1 – 37 Hellcats, 37 Corsairs, 15 Helldivers, 15 Avengers
CV Lexington     CAPT T. H. Robbins, Jr.
    CVG-94
CV Hancock      CAPT R. F. Hickey
    CVG-6 – 72 Hellcats, 12 Helldivers, 10 Avengers
CVL  Belleau Wood
    Air Group 30 – 25 Hellcats, 9 Avengers
CVL San Jacinto    CAPT M. H. Kernodle
    CVG-49 – 25 Hellcats, 9 Avengers
CVL Bataan     CAPT W. G. Tomlinson
    CVG-49 – 24 Hellcats, 12 Avengers

BB Indiana
BB Massachusetts
BB Alabama
CL Topeka
CL Duluth
CL  Dayton
CL  Atlanta
CL San Diego

Desron 61
De Haven
Mansfield
Lyman K Swenson
Collett
Maddox
Blue
Brush
Taussig

Desron 25
John Rogers
Harrison
McKee
Murray
Ringgold
Schroeder
Dashiell

Desron 100
Capeton
Cogswell
Ingersoll
Knapp
 

TF 38.3
    Rear Admiral Bogan
CV Wasp    CAPT W. G. Switzer
    CVG-86 (joined 26 July after Wake strike enroute from US)
CV Ticonderoga    CAPT W. Swinton
    CVG-87 (joined 21 July after three weeks at Guam)
CV Randolph    CAPT F. L. Baker
    CVG-16 – 57 Hellcats, 15 Helldivers, 15 Avengers
CV Essex    CAPT R. L. Bowman
    CVG-83 – 36 Hellcats, 36 Corsairs, 15 Helldivers, 15 Avengers
CVL Monterey    CAPT J. B. Lyon
    CVG-34 – 25 Hellcats, 9 Avengers
CVL Bataan    CAPT W. C. Gilbert
    CVG-47

BB North Carolina  Battleship Division 6     Rear Admiral T. R. Cooley – Div. Comdr.
BB South Dakota
CL  Pasadena
CL Springfield
CL Wilkes-Barre
CL Astoria
CL Oakland

Desron 48
Erben
Walker
Hale
Abbot
Strembel
Bullard
Black
Chauncey
Heerman

Desron 62
English
Charles S. Sperry
Ault
Waldron
John W. Weeks
Hank
Wallace L. Lind
Borie
 

TF 38.4
    Rear Admiral Radford
CV Yorktown    CAPT W. F. Boone
    CVG-88 – 40 Hellcats, 33 Hellcat (Fighter-Bombers), 15 Helldivers, 7 Avengers
CV Shangri-La    CAPT J. D. Barner
    Vice Admiral J. S. McCain
    CVG-85
CV Bon Homme Richard    CAPT A. O. Rule, Jr.
    CVG(N)-91 – 37 Hellcats, 18 Avengers (Night Carrier Group)
CVL Independence    CAPT N. M. Kindell
    CVG-27 – 25 Hellcats, 8 Avengers
CVL Cowpens    CAPT G. H. DeBaun
    CVG-50 – 25 Hellcats, 9 Avengers

BB Iowa
BB Missouri      Admiral William F. Halsey
BB Wisconsin
CA Quincy
CA Chicago
CA Boston
CA St. Paul
CL San Juan

Desron 53
Cushing
Colahan
Uhlmann
Benham
Stockham
Wedderburn

Desron 54
Remey
Norman Scott
Mertz
Monssen
McGowan
McNair

Desron 113
Rowe
Smalley
Stoddard
Watts
Wren

DD Frank Knox  Radar Picket

Also attached to TF 38, but my sources do not denote to which particular  task group:

CL Oklahoma City
CL Amsterdam
CL Tuscon
CL Flint
DD Samuel N. Moore
DD Twining
DD Wadleigh
DD Franks
DD Higbee  Radar Picket
DD Southerland Radar Picket
DD Benner  Radar Picket

Task Force 37
Vice-Admiral Rawlings & Vice-Admiral Philip Vian
CV Formidable
Air Group: 1841 Sq. (18 Corsair IV), 1842 Sq. (18 Corsair IV), 1848 Sq. (4 Hellcat II, 2 Hellcat PRII), 848 Sq. (12 Avenger II)
CV Victorious
Air Group: 1834 Sq. (19 Corsair II & IV), 1836 Sq. (18 Corsair II & IV), 849 Sq. (16 Avenger II), Ship’s flight (2 Walrus)
CV Implacable
Air Group: 801 Sq. (24 Seafire LIII), 880 Sq. (24 Seafire LIII & FRIII), 1771 Sq. (12 Firefly I), 828 Sq. (21 Avenger II)
CV Indefatigable
Air Group: 887 Sq. (15 Seafire FIII & 9 Seafire LIII), 894 Sq. (16 Seafire LIII), 1772 Sq. (12 Firefly I), 820 Sq. (21 Avenger II)
BB  King George V
CL Newfoundland (RCN)
CL Achilles (RNZN)
CL  Uganda (RCN) relieved by Argonaut on July 27th, 1945
CL Euryalus
CL  Gambia
CL Black Prince
DD Quiberon
DD Quickmatch
DD Quality
DD Quadrant
DD Troubridge
DD Tenacious
DD Termagant
DD Teazer
DD Terpsichore
DD Grenville
DD Undaunted
DD Undine
DD Urania
DD Urchin
DD Ulysses
DD Barfleur
DD Wrangler
DD Wakeful

Sunk
CV Amagi
BB Ise
BB Hyuga
BB Haruna
CA Tone
CA  Aoba
CL Oyodo
TC Iwate (Training Cruiser)
TC Izumo (Training Cruiser)
DE Nashi
SS I-404
Numerous other auxiliary warships and merchant ships are also sunk.

Damaged
CV Katsuragi
CVL Ryuho
CVL Hosho
CVE Kaiyo
CL Kitakami
DD Yoitsuki
DD Yukikaze
SS I-205
SS I-202
SS I-153
DE Hagi
DE Kaba
DE Tsubaki
TS Settsu (Target Ship)
Corvette Kaibokan 2
Corvette Kaibokan 4
Corvette Kaibokan 6
Corvette Kaibokan 30
Corvette Kaibokan 44
Corvette Kaibokan 45
Corvette Kaibokan 190
Frigate Habushi
Frigate Takane
Frigate Okinawa
SC Kusentai Ch.14 (Sub-chaser)
SC Kusentai Ch.26
SC Kusen T-T Cha.182
ML Tojima (Minelayer)
SDS Komahashi (Sub depot ship)
SDS Chogei

Sources:
1. Chronology of the War at Sea 1939-1945 by J. Rohwer & G. Hummelchen
2. Carrier Operations of WWII Vol. 1: The Royal Navy by D. Brown
3. Ships Data 1, USS North Carolina (BB55) by A. Lott & R. Sumrall
4. The Fast Carriers by Clark G. Reynolds
5. U.S. Navy Fighter Squadrons of World War II by Barrett Tillman