It really depends on which military you're looking at -like navy, airforce, army, etc - and also what country, but a captain is always higher than a lieutenant. Here's a basic, generic list that ususually doesn't change in different countries (army)
Army General
General
Lieutenant General
Major General
Brigadier General
Colonel
Lieutenant Colonel
Major
Captain
1st Lieutenant
2nd Lieutenant
Cadet
I'm pretty sure private is the lowest rank you can get, but it also could be just below lieutenant and above cadet. Hope this helps
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