Finite Group DatabasebetaFinite Group DatabasebetaOrder 16448.
250 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D257 |
| commutator, socle, cosocle | C22×C257 | C24 |
| Fitting | #124×C257 | C2 |
| hypercenter | #124 | D257 |
| hypocenter | C257 | #538 |
| LCS | G ▷ C22×C257 ▷ C257 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22551586 | C2 | semidirect |
| 2. #22551585 | C2 | semidirect |
| 3. #22551581 | C2 | semidirect |
| 4. #22551576 | C2 | semidirect |
| 5. #22551574 | C2 | semidirect |
| 6. #22551568 | C2 | semidirect |
| 7. #22551565 | C2 | semidirect |
| 8. #22551565 | C2 | semidirect |
| 9. #22551564 | C2 | semidirect |
| 10. #22551562 | C2 | semidirect |
| 11. #22551560 | C2 | semidirect |
| 12. C4×D1028 | C2 | semidirect |
| 13. #22551552 | C2 | semidirect |
| 14. C22⋊C4×D257 | C2 | semidirect |
| 15. #124×C257 | C2 | semidirect |
| 22. C2×C22⋊D257 | C22 | semidirect |
| 23. C22×Dic257 | C22 | semidirect |
| 26. C2×C4×D257 | C22 | semidirect |
| 27. C4⋊Dic257 | C22 | semidirect |
| 28. C4⋊Dic257 | C22 | semidirect |
| 29. #16861597 | C22 | semidirect |
| 30. #16861597 | C22 | semidirect |
| 31. #16861597 | C22 | semidirect |
| 32. #16861597 | C22 | semidirect |
| 41. #16861595 | C22 | semidirect |
| 42. #16861595 | C22 | semidirect |
| 43. C4×Dic257 | C22 | semidirect |
| 44. C2×Q8×C257 | C22 | semidirect |
| 48. C22⋊C4×C257 | C22 | semidirect |
| 49. C22⋊C4×C257 | C22 | semidirect |
| 50. C42×C257 | C22 | semidirect |
| 116. C257 | #538 | semidirect |
| 121. #124 | D257 | semidirect |
| 134. C2×Q8 | C2×D257 | semidirect |
| 164. C22⋊C4 | C2×D257 | semidirect |
| 165. C22⋊C4 | C2×D257 | semidirect |
| 167. C42 | C2×D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22551586 | 2 |
| #22551585 | 2 |
| #22551581 | 2 |
| #22551576 | 2 |
| #22551574 | 2 |
| #22551568 | 2 |
| #22551565 | 2 |
| #22551564 | 2 |
| #22551562 | 2 |
| #22551560 | 2 |
| C4×D1028 | 2 |
| #22551552 | 2 |
| C22⋊C4×D257 | 2 |
| #124×C257 | 2 |
| #538 | 257 |