Are the Ministry of National Defense and the War Department (Admiralty) subordinate?

The situation in each country is different.

The U.S. Department of Defense is a government department, which belongs to the War Department, the Navy Department and the Air Force Department. All four ministers are civilians. The highest military decision-making bodies are the Joint Chiefs of Staff of the Army, the Joint Chiefs of Staff of the Air Force, the Joint Chiefs of Naval Operations and the Joint Chiefs of Marine Corps.

During the Soviet period, the Ministry of National Defense was the highest military institution, and its subordinate services such as army, navy and air force and other military departments were all served as ministers and commanders by soldiers. However, in the early days, the Ministry of National Defense and the Ministry of the Navy coexisted for a short time, managing the army (when the air force belonged to the army) and naval affairs respectively.

Now the Russian defense minister is a civilian.

China's Ministry of Defence is actually a "shelf". The real military decision-making body is the Central Military Commission, which manages the navy, air force and other military departments through four headquarters.