The group that supported the king are Cavaliers and Royalist. For instance: during English Civil War, Royalists (or Cavaliers) supported King Charles.
A royalist supports a particular monarch as head of state for a particular kingdom, or of a particular dynastic claim.
he term Cavalier was first used by Roundheads as a term of abuse for the wealthier Royalist supporters of King Charles I and his son Charles II of England during the English Civil War.