Schrodinger invariant solutions of M-theory with Enhanced Supersymmetry

We find the most general solution of 11-dimensional supergravity compatible with N=2 super-Schrodinger symmetry with six supercharges and SU(2) x SU(2) x U(1) x Z_2 global symmetry. It can be viewed as a one-parameter extension of a recently constructed solution by Ooguri and Park. Our original motivation was to find the gravity dual of the non-relativistic ABJM theory. But, our analysis shows that no such solution exists within the reach of our assumptions. We discuss possible reasons for the non-existence of the desired solution. We also uplift a super-Schrodinger solution in IIB supergravity of Donos and Gauntlett to 11-dimension and comment on its properties.