Hi. I'm stuck on a university level algebra question in my textbook and I was hoping to receive some help on it.

The problem is: Let G be a group and let H1, H2 be subgroups of G. Prove that if H1 union H2 is a subgroup then either H1 is a subset of H2 or H2 is a subset of H1. Sorry about the notation or lack thereof. I don't know all the programming stuff.

Plus I'm just reading something and I was wondering. Are the symbols S3, Q8, and D4 notations for specific groups? I have never seen them before and a problem I have seems to assume I should know them. Anyway, all the numbers after the letters are subscripts.

Thanks for any help. Pvt Bill Pilgrim.