Let $G$ be a finite group and $H$ a subgroup. The interval $[H,G]$ is the lattice of overgroups of $H$.  

It is an open problem to know if every finite lattice can be represented by such an interval (see [here](https://en.wikipedia.org/wiki/Finite_lattice_representation_problem)).  

Here is a weaker question: 


*Question*: Can the reversed lattice of $[H,G]$ be represented?  

("reversed" means $180^{\circ}$ rotation)



Can the reversed lattice of a subgroups interval be represented?
Yes, it can apparently. See the bottom of page 6 (of 13) of this [pdf file](http://www.math.hawaii.edu/~williamdemeo/latticetheory/Palfy-IntervalsInSubgroupLattices-GStA-1993.pdf). The result is due to Kurzweil: 


* H. Kurzweil, *Endliche Gruppen mit vielen Untergruppen*, J. reine angew. Math. 356 (1985), 140-160.


