Let $G$ be a finite group and $H$ a subgroup.  
Let $\mathcal{L}(H \subset G )$ be  the lattice of all the intermediate subgroups between $H$ and $G$.   

**Question:** Can any finite [complete lattice][1] be realized as an intermediate subgroups lattice? 


  [1]: http://en.wikipedia.org/wiki/Complete_lattice