  We consider symmetries of K3 manifolds. Holomorphic symplectic automorphisms
of K3 surfaces have been classified, and observed to be subgroups of the
Mathieu group $M_{23}$. More recently, automorphisms of K3 sigma models
commuting with $SU(2)\times SU(2)$ $R$-symmetry have been classified by
Gaberdiel, Hohenegger, and Volpato. These groups are all subgroups of the
Conway group. We fill in a small gap in the literature and classify the
possible hyperk\"ahler isometry groups of K3 manifolds. There is an explicit
list of $40$ possible groups, all of which are realized in the moduli space.
The groups are all subgroups of $M_{23}$.
