Supreme Commander

Supreme Commander is a high Covenant Elite (Sangheili) and Brute (Jiralhanae) rank.

Background
For most of the Covenant's history, this rank was held solely by the Elite race, but was gradually mixed then replaced completely by Brutes after the Great Schism. They command fleets, and armadas.

Rank
The Supreme Commander is indeed placed in the position of a high rank generally organized within the sophisticated and complex Covenant Empire. It is certain to say that this particular commander has the rightful purpose of commandeering a fleet of a possibly unknown amount of the Covenant's well-built and advanced warships.

It would be incorrect to say that the Supreme Commander is below in rank structure in comparison to Imperial Admirals as apparently the beginning "supreme" indicates top notch among individuals,thus allowing the situation to become unsure of who is higher and who isn't.It may even be possible that they are in different sects of the covenant similar to that of how the UNSC separates into different sects such as the navy,marines,the army,etc.

Physical Appearance
When commanding a fleet, Supreme Commanders wore violet armor with a cloak that wraps around and over the armor piece of their shoulders.

However, when the Arbiter was being tried for the destruction of Halo, he wore golden Zealot armor. Which could signify that Supreme Commander is one of several Zealot ranks, although this has yet to be confirmed.

The fact that the Arbiter wore the golden armor of a Zealot yet wore an unknown violet pigmented armor is quite odd. It could also prove that the creators/creator of that particular story part were exaggerating the Supreme Commander's appearance to allow the story to become a bit more interesting.

To prove this theory generally in Second Sunrise Over New Mombasa, the Elites (Sangheili) and their weapons appear to be exaggerated also. The Sangheili Energy Swords are pink along with the fact that Plasma Rifles shoot green beams opposing to the fact that the original plasma rifles seen shoot cyan repeater-type bolts.

In the Halo Graphic Novel (main article)
The particular Supreme Commander in the aforementioned text was a friend of and yet superior to Rtas 'Vadumee, and would later become the Arbiter. During the Civil War of the Covenant, it is possible the Brutes usurped these positions from the Elites. But even so some Supreme Commanders escaped to fight the Brutes.

Trivia

 * The future Arbiter was a Supreme Commander, yet he wore Zealot armour when questioned by the Prophets, however, he could have been demote in that time.