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You will be amazed at the number of specialties it takes to build aerospace components. Some of them are not, to my knowledge, even taught in universities. Virtually all engineering fields except civil and architectural engineering are sought after by aerospace firms. You would be amazed at the amount of documentation that are associated with the certification with the FAA. Other specialties include configuration management, quality assurance, environmental sciences, system engineering, verification, certification, parts obsolescence, program engineering etc. Most of these careers require a degree that is heavy in math and science (Although I once hired a software engineer that had her degree in music. She did great.). Math degrees, hard science (physics, chemistry). I would be remiss if I omitted management (although many of these positions are filled by people promoted from design fields) and, finance.
One piece of advice, a degree from some schools will open more doors than others. Just about any large state university or schools nationally recognized for strong technological programs are more likely to get you invited for an interview. You might find it more difficult if your degree comes from a school less well known.
If you would refine your question to be more specific I might be able to be of more assistance.