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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).
Here is a weaker question:

Question: Can the reversed lattice of $[H,G]$ be represented?
("reversed" means $180^{\circ}$ rotation)

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Yes, it can apparently. See the bottom of page 6 (of 13) of this pdf file. The result is due to Kurzweil:

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