Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
2659 conjugacy classes of subgroups; only the 999 normal subgroups are shown.
This group has 2659 conjugacy classes of subgroups — too many to draw. Only its 999 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 | C23×#41 | C2 |
| 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 |
|---|---|---|
| 2. C2×#519 | C2 | semidirect |
| 3. #2341 | C2 | semidirect |
| 4. #2309 | C2 | semidirect |
| 5. #2280 | C2 | semidirect |
| 7. C22×#41 | C4 | semidirect |
| 13. C2×C4×Q8 | C22 | semidirect |
| 15. #390 | C22 | semidirect |
| 17. #380 | C22 | semidirect |
| 19. C4×C22⋊C4 | C22 | semidirect |
| 48. C2×Q8 | C22⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#41 | 2 |
| C2×#519 | 2 |
| #2341 | 2 |
| #2309 | 2 |
| #2280 | 2 |