Find the inner and outermorphisms of a particular dihedral group

Find the inner and outermorphisms of a particular dihedral group

Given that |Inn($D_8$)| = 8 and |Out($D_8$)| = 2 where Out($D_8$) =
Aut($D_8$)/Inn($D_8$) and $D_8$ = {e,r,$r^2$,..,$r^7$,s,sr,...,$sr^7$} we
want to find Inn($D_8$) and Out($D_8$).
We know that Out($D_8$) is a cyclic group (prime order) and we can let
Out($D_8$) = {f Inn($D_8$):$f \in $Aut($D_8$)}. We kow the identity
element must be in Out($D_8$) and also another element of order 2. I get
stuck here and not sure how to proceed to find Inn($D_8$) and Out($D_8$).