Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
608 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 186 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C2×#95 |
| commutator, prime radical | C24 | C2×C42 |
| Frattini, cosocle | C22×C42 | C23 |
| LCS | G ▷ C24 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C2×C43 ◁ G | |
| LECS | G ▷ C22×C42 ▷ C23 ▷ C1 | |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20810 | 2 |
| C4×#423 | 2 |
| #7034 | 2 |