Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
524 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 154 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23 | C22×D8 |
| commutator, Frattini, cosocle | C22×C8 | C24 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×C8×Q8 ◁ 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 |
|---|---|
| C2×Q8×C16 | 2 |
| C2×C4×Q32 | 2 |
| #28268 | 2 |
| #13514 | 2 |
| #13450 | 2 |
| #13148 | 2 |
| #12889 | 2 |
| #12814 | 2 |