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Suppose G is a finitely generated group and for any 3 subgroups of G at least 2 of them are comparable. Find all Groups with this property.

I was found this problem on web today and It seems nice to me to think about. I know that the only finite groups where any two subgroups are comparable are the trivial group and the cyclic groups of prime power order and so they are some answers but what about other answers? Has any body an idea for hint?

A.F.23
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  • What have you researched on this problem so far? For example, cyclic groups of order a power of a prime fulfill this ( why? ) . Can you think of other ones? – Timbuc Dec 13 '14 at 13:23

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