Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
703 conjugacy classes of subgroups; only the 327 normal subgroups are shown.
This group has 703 conjugacy classes of subgroups — too many to draw. Only its 327 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, prime radical, cosocle | C24 | C24 |
| commutator | C22 | C22×C42 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ G | |
| LECS | G ▷ C24 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 14. #383 | C4 | semidirect |
| 15. #382 | C4 | semidirect |
| 16. C4×C4⋊C4 | C4 | semidirect |
| 100. C42 | C42 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#383 | 2 |
| C2×#382 | 2 |
| C2×C4×C4⋊C4 | 2 |
| #1436 | 2 |
| #1434 | 2 |
| C4×#95 | 2 |