Finite Group DatabasebetaFinite Group DatabasebetaOrder 16448.
248 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 95 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 | #126×C257 | C2 |
| prime radical | #22551562 | C2 |
| hypercenter | #126 | D257 |
| hypocenter | C257 | #551 |
| LCS | G ▷ C22×C257 ▷ C257 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22551585 | C2 | semidirect |
| 2. #22551578 | C2 | semidirect |
| 3. #22551577 | C2 | semidirect |
| 4. #22551577 | C2 | semidirect |
| 5. #22551574 | C2 | semidirect |
| 6. #22551572 | C2 | semidirect |
| 7. #22551570 | C2 | semidirect |
| 9. C4×D1028 | C2 | semidirect |
| 10. #22551554 | C2 | semidirect |
| 11. #22551550 | C2 | semidirect |
| 12. #22551549 | C2 | semidirect |
| 13. C22⋊C4×D257 | C2 | semidirect |
| 14. C22⋊C4×D257 | C2 | semidirect |
| 15. #126×C257 | C2 | semidirect |
| 17. C2×Dic514 | C22 | semidirect |
| 25. C2×C4×D257 | C22 | semidirect |
| 26. C4⋊Dic257 | C22 | semidirect |
| 27. C4⋊Dic257 | C22 | semidirect |
| 28. #16861597 | C22 | semidirect |
| 29. #16861597 | C22 | semidirect |
| 30. #16861597 | C22 | semidirect |
| 39. #16861595 | C22 | semidirect |
| 40. #16861595 | C22 | semidirect |
| 41. #16861595 | C22 | semidirect |
| 42. C4×Dic257 | C22 | semidirect |
| 43. C4×Dic257 | C22 | semidirect |
| 44. C4⋊C4×C257 | C22 | semidirect |
| 45. C4⋊C4×C257 | C22 | semidirect |
| 46. C4⋊C4×C257 | C22 | semidirect |
| 50. C42×C257 | C22 | semidirect |
| 110. C257 | #551 | semidirect |
| 113. #126 | D257 | semidirect |
| 142. C4⋊C4 | C2×D257 | semidirect |
| 143. C4⋊C4 | C2×D257 | semidirect |
| 144. C4⋊C4 | C2×D257 | semidirect |
| 161. C42 | C2×D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22551585 | 2 |
| #22551578 | 2 |
| #22551577 | 2 |
| #22551574 | 2 |
| #22551572 | 2 |
| #22551570 | 2 |
| #22551562 | 2 |
| C4×D1028 | 2 |
| #22551554 | 2 |
| #22551550 | 2 |
| #22551549 | 2 |
| C22⋊C4×D257 | 2 |
| #126×C257 | 2 |
| #551 | 257 |