Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
552 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 166 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×D8 |
| commutator, Frattini, cosocle | C22×C8 | C24 |
| socle, prime radical | C23 | C22×D8 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C43 ◁ C42×C8 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#499 | 2 |
| C4×#494 | 2 |
| #13537 | 2 |
| #13483 | 2 |
| #13409 | 2 |
| #13366 | 2 |
| C4×#358 | 2 |
| #12590 | 2 |