A Black Dalek known as a Supreme Controller directed the Bedfordshire operation. It had a terrifying pet called the Slyther which it used to let roam free around the mines at night killing those it found. Its voice was considerably higher than the other Daleks. A black and silver coloured Dalek referred to as the Saucer Commander was also used during this invasion. (DW: The Dalek Invasion of Earth)
During the 26th century, Dalek Supremes were gold with black trim. The Master liased with one after he'd been hired to start a human-Draconian war. (DW: Frontier in Space) Another, a member of the Dalek's Supreme Council, arrived to take command of operations on the planetSpiridon. The second supreme had an eye-stalk that lit up when it was speaking. (DW: Planet of the Daleks) The Dalek Tapes feature presented all golden Dalek Supremes as members of the Council.
The Dalek Supreme was the supreme commander of the Daleks during the war with the Movellans. A Dalek lieutenant, a Dalek of a darker shade of grey than the rest, was also of an intermediate rank at that time. (DW: Destiny of the Daleks)
Following the Dalek-Movellan war, the Supreme Dalek was a fully black Dalek, with white bumps and a more hollow voice. He was destroyed when the prison station holding Davros self-destructed taking the Dalek ship with it. (DW: Resurrection of the Daleks)
During the civil war, the Dalek Supreme was the leader of the Renegade Daleks that opposed the Imperial Daleks commanded by Davros, now calling himself the Dalek Emperor. The Dalek Supreme ended up as the last surviving Dalek . The Doctor convinced it that it had no purpose, at which point, in a state of confusion and distress, it destroyed itself. (DW: Remembrance of the Daleks)
After the return of Davros and the reestablishment of the Dalek race, a red Supreme Dalek took charge of the New Dalek Empire. His casing had gold ridges (similar in appearance to the Genesis Ark) around it, and its spheres are also golden. The Supreme Dalek speaks in a deep voice similar to that of the Emperor. He is killed by Jack Harkness who shoots him, blowing him up. (DW: The Stolen Earth/Journey's End)
The Doctor faces the new legion of Daleks, led by the Supreme in the middle.
The survivors of the New Dalek Empire, a bare three in a damaged saucer, located a Progenitor device, capable of restoring the Dalek race, which refused to activate for them due to their Davros-based genetics. The Daleks decided to lure the Doctor to them by posing as man-made machines in World War II. Gaining the Doctor's "testimony" that they were truly Daleks, the Progenitor finally activated for them, creating a new faction of improved Daleks who thought themselves as superior. These Daleks were led by a white Dalek Supreme. Under the Supreme's orders, the old Daleks were destroyed by the new ones. The Supreme Dalek then threatened to destroy the Earth using an Oblivion Continuum. While the Doctor rushed to Earth to disarm the device, the Supreme Dalek and his subordinates departed the era in a time corridor. (DW: Victory of the Daleks)
Behind the scenes
In the Dalek Chronicles the Black Dalek acts as overall second-in-command of the Daleks, ranking below only the Dalek Emperor. John Peel's BBC Books Doctor Who novel War of the Daleks the Daleks are led by the Dalek Prime, whose description matches that of the TV 21 Dalek Emperor. In the novel, the Dalek Prime is the judge at Davros's trial on Skaro and is stated to be the last survivor of the original Daleks created by Davros. As this was how Peel referred to the Dalek Emperor in his novelisation of The Evil of the Daleks, this suggests that they are the same Dalek at different points in its history. The novel also mentions Black Daleks as being high in the Dalek chain-of-command and being in charge of all lower ranks, being subordinate only to Gold Daleks and the Dalek Prime. The Dalek Prime is also mentioned in Peel's BBC Eighth Doctor Adventures novel Legacy of the Daleks.
In the Big Finish Productions series of Dalek Empire stories, the rank of Supreme Dalek is equivalent to an Army General, subordinate to the Emperor Dalek on Skaro, and eventually rises to command the Daleks in the Emperor's absence, with a different Dalek Supreme taking over in the third series.