So here’s a list of traditional royal dukedoms.
First, those for the monarch and heir:
Duke of Lancaster: dates back to Edward III’s third son in the 14th century; figured largely in the Wars of the Roses in the 15th century; since Henry VII’s accession, has been held by the monarch.
Duke of Cornwall: held by the monarch’s heir, which is why Prince Charles’ wife, Camilla, is referred to as the Duchess of Cornwall. Dates back to the 13th century; first English dukedom.
Duke of Rothesay: Scottish title, awarded to the monarch’s oldest son, so currently held by Prince Charles.
Second, those for younger sons of the monarch:
Duke of York: traditionally awarded to the monarch’s second son; currently held by Prince Andrew; dates back to Edward III in the 14th century who had numerous sons; figured prominently in the Wars of the Roses in the 15th century.
Duke of Edinburgh: currently held by Prince Phillip; will likely go to Prince Edward eventually; first granted to Frederick, Prince of Wales, son of George II and father of George III.
Duke of Cambridge: first granted during the Stuart period in the 17th century; revived for Adolphus, one of George III’s younger sons; revived for Prince William.
Duke of Sussex: first conferred on the sixth son of George III; revived for Prince Harry.
Duke of Gloucester: granted by George V to his third son; currently held by his son, first cousin to the Queen; also dates back to the Edward III and the Wars of the Roses; Richard III was Duke of Gloucester before becoming king.
Duke of Kent: first used as a royal dukedom for Edward, fourth son of George III and father of Queen Victoria; revived for George V’s fourth son, who died in WWII at a young age; currently held by his eldest son, cousin to the Queen.
Third, the ones that aren’t currently in use are :
Duke of Clarence: also dates back to Edward III; created a number of times; William IV, third son of George III was Duke of Clarence before ascending the throne; last created for Prince Edward Albert, the eldest son of Edward VII, who died before his father.
Duke of Albany: a traditional Scottish royal title for sons of the Scottish kings; created several times in Scotland, then in England during the Stuart period, then in Britain during the Hanoverian period. Last held by one of Victoria’s sons, a haemophiliac who died relatively young, without issue.
Duke of Connaught: first awarded to one of Victoria’s sons; extinct; unlikely to be awarded again, since Connaught is now in the Republic of Ireland.
Duke of Cumberland: first conferred on Prince Rupert, cousin to Charles I; later conferred on Prince George of Denmark, husband of Queen Anne; revived during the Hanoverian period, most recently for Ernest, fifth son of George III, who became King of Hanover; suspended by Act of Parliament during WWI, because the then-Duke of Cumberland was fighting for the German Empire; technically, the current Head of the House of Hanover could apply to have it revived, but has shown no interest in doing so.