one gets the impression that the was the Adelantado or Governor general, the Camp Master, a few royal officials, and a bunch of 'Captains'. In Europe the Spanish Tercio system had been well developed by the mid-sixteenth century. Many of the conquistadors were veterans of the Italian campaigns and its probably safe to assume that at least some of this organization and ranks carried over into the New World.
The best overview that I've come across is here:
Organisation of the Spanish army
As even the largest conquistador expeditions were tiny compared to armies in Europe the Company breakdown is probably closest to what might expect here in La Florida.
"All the companies have the same staff: 1 captain and his page,
1 alférez (lieutenant),
1 abanderado (ensign),
1 chaplain and 1 barber, in total 11 officers
Each Spanish company was divided in "escuadra " or group of a maximum of 25 men commanded by a "cabo". A 250 men company had 10 cabos and a 300 men company had 12 cabos. The Spanish had also an unofficial structure of half dozen of men called las camaradas, it was not a combat structure but a group of men from the same company sharing the food, the bed, the training, the friend ship. The camaradas were important to maintain the moral and the famous esprit de corps of the Spanish soldiers."
I have one small quibble the size of the camarada seems large compared to that which of come across. Hernando de Soto was a member of a three person group and the gentleman of Elvas states "...a mess of every three or four built a small house in which they were lodged."