Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
836 conjugacy classes of subgroups; only the 447 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 447 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 | C23 | C25 |
| prime radical | C22×#41 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #2644 | C2 | semidirect |
| 2. #2513 | C2 | semidirect |
| 3. #2495 | C2 | semidirect |
| 4. #2401 | C2 | semidirect |
| 5. #2351 | C2 | semidirect |
| 7. #2276 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2644 | 2 |
| #2513 | 2 |
| #2495 | 2 |
| #2401 | 2 |
| #2351 | 2 |
| #2341 | 2 |
| #2276 | 2 |