  We extend the search for supergravity solution duals of non-relativistic
$d=3$ CFTs to $d=11$ supergravity. We consider the internal space to be an
$S^2$ bundle over a product base: $S^2 \times S^2$ and $S^2 \times T^2$. For
purely M-theoretic $S^2 \times S^2$, we find only magnetic fluxes preserving
two supersymmetries. $S^2 \times T^2$ is far richer admitting in addition to
magnetic fluxes, various non-trivial electric fluxes which break all
supersymmetry.
