Since I served in the military I am well aware of how it works.
No, they do not produce their own ships, their own engines, their own guidance systems, their own aircraft, their own clothing, their own food, their own housing... for the most part.
1. Lockheed Martin Corp.
2. Boeing Co.
3. General Dynamics Corp.
4. Raytheon Co.
5. Northrop Grumman Corp
6. United Technologies Corp.
7. Huntington Ingalls Industries Inc.
8. Humana Inc.
9. Harris Corp.
10. BAE Systems PLC
Just to name a few private contractors.