It would make some of that real good sense stuff for Tom Lasky to be at least a one-star admiral (Rear Admiral, Commodore, etc.) rather than a captain. His command consists of upwards of 17,000 Sailors, Marines, and Spartans aboard Infinity, and thousands more aboard the attached frigate squadron. However, it's hard to tell what the present-day UNSC rank insignia even means nowadays. Lasky's collar insignia, consisting of four gold bars, apparently denotes him as a captain even though it suggests to me that he's a super ensign or something. Halo 4 saw Lasky as a Commander, yet had insignia suggesting he was a Lieutenant Commander according to the gold oak leaf on his collar and shoulders. Lord Hood has insignia, that while being a Fleet Admiral, would identify him simultaneously as a four-star admiral, a captain, and a super ensign.
UNSC uniforms have a lot of rank insignia for no good reason as evident by the provided screenshot. Lasky has four gold bars denoting him as an ensign (collar), four stars denoting him as an admiral (shoulder, top), four downward chevrons suggesting he's some super chief petty officer (shoulder, bottom), and finally four gold sleeve stripes correctly denoting him as a captain (cuffs).