Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
266 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | #99 |
| commutator | C23 | C82 |
| Frattini, cosocle | C2×#405 | C22 |
| socle | C22 | #1282 |
| prime radical | C24 | C4×C8 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#405 ◁ G | |
| LECS | G ▷ C2×#405 ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 22. C2×M32 | C8 | semidirect |
| 28. C22×C16 | C8 | semidirect |
| 37. #349 | C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #12602 | 2 |
| #12545 | 2 |
| #8156 | 2 |