Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
533 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 533 conjugacy classes of subgroups — too many to draw. Only its 156 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #2605 |
| commutator, Frattini, cosocle | C23×C4 | C24 |
| socle | C2 | #17054 |
| prime radical | C24 | 2−1+4 |
| LCS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4 ◁ C23×C4 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11368 | 2 |
| #11360 | 2 |
| #11349 | 2 |
| #11247 | 2 |
| #11235 | 2 |
| #11218 | 2 |
| #10817 | 2 |
| #10815 | 2 |
| #10799 | 2 |