Prove that the quaternions $\displaystyle \bold Q$ and the Dihedral group $\displaystyle D_8$ are non-isomorphic groups of order 8.
The dihedral group of order 8 can be seen as the group of symmetries of the square. There are two diagonal symetries, which are involutions, therefore $\displaystyle D_8$ (with your notation) contains at least 2 elements of order 2; that is sufficient to prove what you want.
$\displaystyle D_8$ has exactly 5 elements of order 2 (two diagonal symmetries, 2 lateral symmetries and one central symmetry) and 2 elements of order 4 (one rotation of $\displaystyle \frac{\pi}{2}$ and its inverse).