Supreme Dalek
The Dalek Supreme, also known as the Supreme Dalek, Black Dalek, and the Dalek Controller, served in the role of an elite or commander Dalek, however occasionally a Gold Dalek was used for similar purposes. (DW: The Dalek Invasion of Earth, Day of the Daleks)
The Dalek Emperor also similarly used Black-domed Daleks as lieutenants. (DW: The Evil of the Daleks, The Parting of the Ways)
History
Dalek invasion of Earth
During the 22nd century Dalek invasion of Earth (2157 - 2167) 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. A black and silver coloured Dalek referred to as the Saucer Commander was also used during this invasion. (DW: The Dalek Invasion of Earth)
Alternative timeline of the 22nd century
The Black Dalek appeared to have been replaced by a Gold Dalek in an alternative timeline in which World War III had occured in the 1970s, enabling the Daleks to take over. (DW: Day of the Daleks)
- Though the World War III timeline did get "erased", the Gold Dalek may have come from the main timeline, via time travel.
Dalek invasion of Spiridon
On the planet Spiridon, a Dalek Supreme in black and gold trim was used to represent a member of the Supreme Council of Daleks, with an eye-stalk that lit up when it was speaking. (DW: Planet of the Daleks)
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A Dalek Supreme also led the Daleks on the planet Kembel, as well as dispatching a Dalek execution squad. (DW: The Daleks' Master Plan, The Chase).
Later, the Black Dalek was replaced by the Dalek Emperor, which used black-domed Daleks as lieutenants. (DW: The Evil of the Daleks)
Dalek-Movellan War
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 instead of the usual grey ones, and a more hollow voice. (DW: Resurrection of the Daleks)
Imperial-Renegade Dalek Civil War
A schism developed between the Daleks led by the Dalek Supreme and those still loyal to their creator Davros. ((DW: Resurrection of the Daleks, DW: Revelation of the Daleks, DW: Remembrance 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 on Earth. 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)
Last Great Time War
During and after the Last Great Time War, the Dalek Supreme had once again been replaced by the Emperor who used black-domed Daleks as lieutenants, however the Cult of Skaro had Sec, a Black Dalek, as a leader. (DW: The Parting of the Ways, Doomsday)
Note
In the TV 21 comic strips 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 audio plays, 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.