Correct. CAG reported to the CV's CO.
In the 70s during my four cruises, I had both 0-5 and 0-6 CAGs. Never had a Super CAG. Not sure what a DCAG is. Also, my RAG COs were O-6s.
Right Cat, remember in
"The Bridges at Toko Ri" , CAG-19 "bypassing" his CV CO, doing his tapdance with with the Admiral, in regard to the ship using his Spads to Pinwheel while berthing at Yokosuka.
BTW, using pinwheel to aid tugs while berthing at Yoko in heavy winds, while rare, was actually done several times by RANGER on our '60 WestPac. Only jets (F-8s/F-3Hs & A-4s) were used, as they were not prone to damage like the recips. Actually it was kinda' fun, & even some of our senior E maintainers & a few sharp P/Cs got to participate, in the cockpit!
BzB