Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
923 conjugacy classes of subgroups; only the 231 normal subgroups are shown.
This group has 923 conjugacy classes of subgroups — too many to draw. Only its 231 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C24 | C24 |
| prime radical | C23×D4 | C22 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ G | |
| LECS | G ▷ C24 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#397 | C2 | semidirect |
| 4. C2×#384 | C2 | semidirect |
| 5. #1439 | C2 | semidirect |
| 6. C4⋊#95 | C2 | semidirect |
| 7. C4×#95 | C2 | semidirect |
| 60. #95 | D4 | semidirect |
| 201. C4 | #397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#397 | 2 |
| C2×#390 | 2 |
| C2×#384 | 2 |
| #1439 | 2 |
| C4⋊#95 | 2 |
| C4×#95 | 2 |