According to the 1st Naval District Port Director Files; the fleet diagram (shown above) indicates that the US Atlantic Fleet as of 10/17/1945 was technically the parent organizational force for the much of the entire Navy at that time to includ the Second,Fourth,Eighth and Tenth active fleets. Keep in mind this was at least two months after the surrender of the Japanese on V-J Day.
Looking more closely though, the chart also indicates how much of a role the Chief of Naval Operations (CNO) still had in the operational control of a large portion of the Navy, to include the Eastern, Gulf and Caribeean Sea Frontiers as well as the Sixteenth (Inactive) Fleet; all control entities for the units involved in the Flight-19 training and search and rescue missions.
The Chief of Naval Operations at that time and up to the day he was relieved of command December 15th, 1945 was Fleet Admiral Ernest King. Coincidentally his tour of duty ended just four days prior to the Court Martial of Captain James McVay of the USS Indianapolis was completed and just five days after the search and rescue of Flight-19 ended.