  We investigate special compactifications of the heterotic string for which
the space of half-BPS states is, in a natural way, a representation of various
subgroups of the Conway group. These compactifications provide a useful
framework for analyzing the action of some of the large symmetry groups
appearing in discussions of Moonshine in the physics literature. We investigate
toroidal compactifications of heterotic string with sixteen supersymmetries as
well as asymmetric toroidal orbifolds with $N=2$ supersymmetry in four
dimensions that arise as $K3 \times T^2$ compactifications. The latter Conway
subgroup symmetric compactifications of the heterotic string might have some
interesting implications for D-brane bound states on Calabi-Yau manifolds.
