This is an open problem. See

 - Wikipedia article: http://en.m.wikipedia.org/wiki/Finite_lattice_representation_problem

 - [Palfy and Pudlak][1]'s result (see open-source description in Palfy's article [Intervals in subgroup lattices of finite groups][2])

 - This MO question from 2012: http://mathoverflow.net/questions/85724/given-a-lattice-l-with-n-elements-are-there-finite-groups-h-g-such-that-l-c


  [1]: http://www.ams.org/mathscinet-getitem?mr=593011
  [2]: http://www.math.hawaii.edu/~williamdemeo/latticetheory/Palfy-IntervalsInSubgroupLattices-GStA-1993.pdf