In the US Army and Airforce, a Major is one rank higher than a Captain. In the US Navy a Rear Admiral lower half (1 Star) is one rank higher than a Captain.
Major
There is no such rank in civiailan life. A captain is a military rank
captain
The term "captain" is generally used for the leader of a military unit. So in the Army, a captain is the leader of a company, and the next lower rank is "Lieutenant". At sea, the "military unit" is a ship, so the captain is the captain of a ship, which is a much larger military unit. The next lower rank may be commander (generally used for smaller ships) or lieutenant.
The next rank above Captaine in the French army is Major.
Major and Lieutenant Colonel
In the Navy, a Captian is an O-6, and the rank below a Captain is a Commander. In each of the other branches of the US Military, a Captain is an O-3, and the rank below is a 1st Lieutenant.
The next rank above Corporal in most military forces would be Sergeant.
Captain is an officer, Corporal is an enlisted man.
The correct spelling for the ship commander or military rank is "captain."
In US military Major is above the captain.