The old war canoe Melbourne [ +15 aircraft+ 1400 sailors] had a Commodore while the USS Midway sailed by with 80+ air vehicles + 6000 sailors driven by a Captain [4 bar].....
And a current Nimitz class CVN will be driven by one USN Captain and have another on board as CAG. So that's two four-bars to command ~4500 personnel and ~100 front-line combat aircraft.