While trying to come up with a coloring scheme to organize all the complex interactions of the D8×C2 lattice, I realized I can make a much simpler lattice like structure of the kind of subgroups related by outer automorphisms. I don't know if this is a lattice or not. However, it has been really useful for me while trying to understand the actual subgroup lattice. The blue subgroups are all normal cores. The green subgroups are all 2-subnormal subgroups. The yellow subgroups are related to conjugate closure. The grey subgroups are all central. Does anyone know terms for this kind of thing, or could point me in the direction of resources related to this? Assume each point on the larger lattice is a unique subgroup of D8xC2
