Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
1635 conjugacy classes of subgroups; only the 455 normal subgroups are shown.
This group has 1635 conjugacy classes of subgroups — too many to draw. Only its 455 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 | C26 | 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. #2480 | C2 | semidirect |
| 2. #2315 | C2 | semidirect |
| 4. #2273 | C2 | semidirect |
| 6. C2×#126 | C22 | semidirect |
| 10. #397 | C22 | semidirect |
| 11. #396 | C22 | semidirect |
| 12. #388 | C22 | semidirect |
| 13. #385 | C22 | semidirect |
| 14. #385 | C22 | semidirect |
| 15. #380 | C22 | semidirect |
| 18. C4×C22⋊C4 | C22 | semidirect |
| 26. C2×C4⋊C4 | C23 | semidirect |
| 36. C2×C42 | C23 | semidirect |
| 37. #95 | C23 | semidirect |
| 38. #95 | C23 | semidirect |
| 74. C23 | #126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2480 | 2 |
| #2315 | 2 |
| C2×#379 | 2 |
| #2273 | 2 |