Here’s my second subgroup lattice post: Subgroup Lattices with Sage – Coloring Vertices. It shows how to color a poset according to properties that you’d like to highlight.
At the bottom of that post, you’ll also find a nice interactive section where you can play around with various groups and their subgroups. It looks like this:
These posts are pretty time-consuming to write, so the next post might be quite a while later. Have fun playing with the interactive subgroup demo!