Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
1429 conjugacy classes of subgroups; only the 1003 normal subgroups are shown.
This group has 1429 conjugacy classes of subgroups — too many to draw. Only its 1003 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, cosocle | C23 | C25 |
| commutator | C22 | C24×C4 |
| prime radical | C24 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #2351 | C2 | semidirect |
| 5. Q8×C4⋊C4 | C2 | semidirect |
| 10. #519 | C4 | semidirect |
| 38. C4×Q8 | C2×C4 | semidirect |
| 57. C2×Q8 | C4⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#519 | 2 |
| C22×C4×Q8 | 2 |
| #2351 | 2 |
| Q8×C4⋊C4 | 2 |
| #2317 | 2 |
| #2296 | 2 |