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If you use your favorite search engine, you may come accross this site.

There you can see that

P = SetPartitions(3)
f = lambda q,p: q in p.refinements()
Po = Poset((P,f))

constructs the associated poset Po. Then you can simply use the subposet method together to get the desired subposet Q. Getting the Hasse diagram for Q is just a matter of using