  At the level of the bosonic fields, we construct consistent Kaluza--Klein
reductions of D=11 supergravity on $\Sigma_3\times S^4$, where
$\Sigma_3=H^3/\Gamma,S^3/\Gamma$ or $R^3/\Gamma$ where $\Gamma$ is a discrete
group of isometries.
  The result is the bosonic content of an N=2 D=4 gauged supergravity with a
single vector multiplet and two hypermultiplets, whose scalar fields
parametrise $SU(1,1)/U(1)\times G_{2(2)}/SO(4)$. %, and the gauging is only in
the hypermultiplet When $\Sigma_3=H^3/\Gamma$ the D=4 theory has an $AdS_4$
vacuum which uplifts to the known supersymmetric $AdS_4\times H^3/\Gamma\times
S^4$ solution of D=11 supergravity that describes the N=2 $d=3$ SCFT arising
when M5-branes wrap SLag 3-cycles $H^3/\Gamma$ in Calabi-Yau three-folds. We
use the KK reduction for $\Sigma_3=H^3/\Gamma$ to construct D=11 black hole
solutions that describe these d=3 SCFTs at finite temperature and charge
density and show that there is a superconducting instability involving a
charged scalar field, and another instability involving involving neutral
fields including both scalar and vector fields. We also use this KK reduction
to construct a D=11 Lifshitz solution that is dual to a d=3 field theory with
dynamical exponent $z\sim 39$.
