Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
879 conjugacy classes of subgroups; only the 457 normal subgroups are shown.
This group has 879 conjugacy classes of subgroups — too many to draw. Only its 457 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. #2860 | C2 | semidirect |
| 2. #2513 | C2 | semidirect |
| 3. #2494 | C2 | semidirect |
| 4. #2351 | C2 | semidirect |
| 6. C4×#126 | C2 | semidirect |
| 7. C42×Q8 | C2 | semidirect |
| 73. C42 | #41 | semidirect |
| 78. Q8 | #126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2860 | 2 |
| #2513 | 2 |
| #2494 | 2 |
| #2351 | 2 |
| #2341 | 2 |
| C4×#126 | 2 |
| C42×Q8 | 2 |