Ingress fields within fields

If I were to make a larger field that entirely encompassed one or more smaller fields of the other faction, what happens?

Do the smaller fields "break" ? If they do, do I get AP for that? Can the other faction still own the portals inside my field?

I'm going to try this eventually but I'm relatively new and don't have enough higher level resonators to set up a field large enough to do this right now. So I ask you.

Thanks