Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
547 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 547 conjugacy classes of subgroups — too many to draw. Only its 178 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #2328 |
| commutator | C22×C4 | C23×C4 |
| Frattini, cosocle | C2×C42 | C24 |
| prime radical | C23 | #518 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ G | |
| LECS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21698 | 2 |
| #17897 | 2 |
| #9669 | 2 |
| #9104 | 2 |
| #9092 | 2 |
| #8780 | 2 |
| #8137 | 2 |