Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
2055 conjugacy classes of subgroups; only the 759 normal subgroups are shown.
This group has 2055 conjugacy classes of subgroups — too many to draw. Only its 759 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 | C26 | C22 |
| 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. #2342 | C2 | semidirect |
| 3. #2315 | C2 | semidirect |
| 4. #2312 | C2 | semidirect |
| 5. #2280 | C2 | semidirect |
| 7. #2273 | C2 | semidirect |
| 10. C2×#117 | C22 | semidirect |
| 11. C22×C22⋊C4 | C4 | semidirect |
| 18. #388 | C22 | semidirect |
| 19. #385 | C22 | semidirect |
| 20. #381 | C22 | semidirect |
| 21. #380 | C22 | semidirect |
| 22. #380 | C22 | semidirect |
| 26. C4×C22⋊C4 | C22 | semidirect |
| 27. C4×C22⋊C4 | C22 | semidirect |
| 28. C4×C22⋊C4 | C22 | semidirect |
| 37. C23×C4 | C2×C4 | semidirect |
| 44. C2×C4⋊C4 | C23 | semidirect |
| 49. C2×C22⋊C4 | C2×C4 | semidirect |
| 50. C2×C22⋊C4 | C2×C4 | semidirect |
| 58. C2×C42 | C23 | semidirect |
| 59. #95 | C23 | semidirect |
| 60. #95 | C23 | semidirect |
| 123. C23 | #117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊C4 | 2 |
| #2342 | 2 |
| #2315 | 2 |
| #2312 | 2 |
| #2280 | 2 |
| C2×#379 | 2 |
| #2273 | 2 |