Fast Carrier Task Force 58 (and 38) was created as an Offensive Strategy for the Central Pacific War, based on a fleet of fast aircraft carriers that travelled in groups  (Task Groups).  Carriers were surrounded by capital ships (battleships and cruisers) which were surrounded by a ring of destroyers.  Each type of ship had it’s own command structure:  Divisions – two or more ships of the same type, and Squadrons – two or more divisions of the same type.  Each squadron and each division had a Commander (eg. USS Boston, a heavy cruiser, had an Admiral on board, because it was the lead (Flag) ship of Cruiser Division 10.)  Note:  the ship’s Captain was always the Boss of the ship, even when there was an Admiral aboard.

The Command Structure of Task Force 58:

Chester Nimitz (Admiral)  at Pearl Harbor (Guam, after 1/45)
Commander-in-Chief, United States Pacific Fleet (Cincpac)

Raymond Spruance  (Admiral)  on USS Indianapolis (heavy cruiser) *
Commander, Central Pacific Force

Marc Mitscher (Admiral) on USS Lexington (heavy carrier)
Commander, Task Force 58

The Command Structure of Task Force 38:

Chester Nimitz (Admiral)  Pearl Harbor (Guam, after 1/45)
Commander-in-Chief, United States Pacific Fleet (Cincpac)

William Halsey (Admiral) on USS New Jersey (battleship)
Commander, Central Pacific Force

Marc Mitscher (Admiral) on USS Lexington (heavy carrier)
Commander, Task Force 38 –  until Oct 30, 1944

John S. McCain Sr. (Admiral) on USS Lexington (heavy carrier)
Commander, Task Force 58 –  from Oct 30, 1944

(photos: wikimedia).       *Indianapolis was torpedoed and sank 7/30/45.