Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
792 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 214 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 | C2×#127 |
| commutator, Frattini, cosocle | C2×C42 | C24 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C43 ◁ 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 |
|---|---|
| #33313 | 2 |
| #28653 | 2 |
| C4×#494 | 2 |
| C2×#1707 | 2 |
| #10317 | 2 |
| #10316 | 2 |
| #9823 | 2 |
| C8×C4⋊C8 | 2 |