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This is an open problem. See

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

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

• This MO question from 2012: Given a lattice L with n elements, are there finite groups H < G such that L $\cong$ the lattice of subgroups between H and G?

This is an open problem. See

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

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

• This MO question from 2012: Given a lattice L with n elements, are there finite groups H < G such that L $\cong$ the lattice of subgroups between H and G?

This is an open problem. See

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

• Palfy and Pudlak's result here: http://www.math.hawaii.edu/~williamdemeo/latticetheory/Palfy-IntervalsInSubgroupLattices-GStA-1993.pdf

• This MO question from 2012: Given a lattice L with n elements, are there finite groups H < G such that L $\cong$ the lattice of subgroups between H and G?

This is an open problem. See

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

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

• This MO question from 2012: Given a lattice L with n elements, are there finite groups H < G such that L $\cong$ the lattice of subgroups between H and G?

This is an open problem, see Palfy and Pudlak's result here:http://www.math.hawaii.edu/~williamdemeo/latticetheory/Palfy-IntervalsInSubgroupLattices-GStA-1993.pdf

This is an open problem. See

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

• Palfy and Pudlak's result here: http://www.math.hawaii.edu/~williamdemeo/latticetheory/Palfy-IntervalsInSubgroupLattices-GStA-1993.pdf

• This MO question from 2012: Given a lattice L with n elements, are there finite groups H < G such that L $\cong$ the lattice of subgroups between H and G?