Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
319 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 319 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #1276 |
| commutator | C42 | C4×C8 |
| Frattini, cosocle | C4×#117 | C22 |
| socle | C2 | #7017 |
| prime radical | C24 | #99 |
| LCS | G ▷ C42 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4 ◁ #376 ◁ C4×#117 ◁ G | |
| LECS | G ▷ C4×#117 ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. #1276 | C4 | semidirect |
| 18. C2×C4×C8 | C8 | semidirect |
| 26. C43 | C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×H(3,ℤ/4) | 2 |
| #8730 | 2 |