# Finding conjugacy classes and normal subgroups of $D_8$, the dihedral group of order $16$ [duplicate]

What are the conjugacy classes for the dihedral group $D_8$ of order 16?

What are its subgroups of order $4$, and which of them are normal subgroups?

I know that $\{e\} ,\{r^2,r^6\},\{r,r^7\},\{r^3,r^5\},\{r^4\},\{s,r^2s,r^4s,r^6s\}, \{rs,r^3s,r^5s,r^7s\}$ are the conjugacy classes, but I don't understand how they derived these in my book; they just mentioned it without explanation.

## marked as duplicate by Dietrich Burde, Najib Idrissi, user147263, Travis Willse, Jonas MeyerDec 13 '14 at 21:09

• @M alrantisi A first possible try could be to separate elements according to their orders, as conjugate elements have the same order. This doesn't seem hard at all to do with a group of order $\;16\;$ , though it can be a little time consuming. – Timbuc Dec 13 '14 at 13:24