Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
498 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 174 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×#121 |
| 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 |
|---|---|
| #33258 | 2 |
| #29210 | 2 |
| #21673 | 2 |
| #10651 | 2 |
| #10649 | 2 |
| #9897 | 2 |
| #9622 | 2 |
| C4×#334 | 2 |