NR $CFT_3$ duals in M-theory

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.