Does the Monarchy in Canada have a military responsible to the governor general or to the prime minister?

Command-in-chief of the Canadian Forces is vested in Her Majesty the Queen pursuant to section 15 of the Constitution Act, 1867. However, letters patent have delegated this authority to the Governor General of Canada, who carries the title "Commander-in-Chief in and over Canada."

However, as the executive powers of the Crown are exercised only on the advice of the Queen's Privy Council for Canada (in practice, ministers responsible to the elected House of Commons), operational authority for the Canadian Forces is exercised by the Prime Minister of Canada, and the Minister of National Defence.

Therefore, while members of the Canadian Forces swear oaths of allegiance to the Queen, and the Governor General is the Commander-in-Chief of the Canadian Forces, the Canadian Forces are responsible to the Prime Minister and Cabinet for performance and conduct.