I am trying to work out all the subgroups of $\displaystyle D_8$, the dihedral group, i.e. the symmetry group of the square.

I am not sure how to do this. I know of course they must have order 1,2,4,8, so the only real problem is working out the subgroups of order 4. Is there a quick way to do this? Thanks for any help with this :)