Do cockroaches fly?

This is no gag. I never studied any but I didn’t think cockroaches could fly.
Yesterday I was crossing a parking lot at the grocery store. A bug flew right in front of me, and landed on a car. It looked like a cockroach. It seemed a little lighter brown, and the wings were a bit longer than the body. It walked a few inches across the hood of the car, then flew away. When it did, I noticed that I could see through its papery brown wings. Seeing it gave me the hee bee gee bees.
If it wasn’t a cockroach, does anybody know what it would be?