  We study black hole solutions of $D=4$ Einstein-Maxwell theory coupled to a
charged scalar field that are holographically dual to a $d=3$ conformal field
theory with a non-vanishing chemical potential and constant magnetic field. We
numerically construct black hole solutions that are dual to a superfluid phase
with a periodic lattice of vortices. For the specific model we investigate, we
find that the thermodynamically preferred configuration is given by a
triangular lattice and moreover the vortices are associated with the lowest
Landau level. We also construct black holes describing a lattice of vortices
associated with the next to lowest Landau level and while theses are not
thermodynamically preferred they exhibit some interesting features that could
be realised for other holographic models.
