Finite Group DatabasebetaFinite Group DatabasebetaOrder 16448.
334 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 107 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 | C2×C22⋊C4×C257 | C2 |
| hypercenter | C2×C22⋊C4 | D257 |
| hypocenter | C257 | #546 |
| LCS | G ▷ C22×C257 ▷ C257 | |
| UCS | C1 ◁ C22 ◁ C2×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#16861618 | C2 | semidirect |
| 2. C22×C22⋊D257 | C2 | semidirect |
| 3. #22551578 | C2 | semidirect |
| 4. #22551575 | C2 | semidirect |
| 5. #22551574 | C2 | semidirect |
| 6. #22551569 | C2 | semidirect |
| 7. #22551566 | C2 | semidirect |
| 8. #22551565 | C2 | semidirect |
| 9. #22551565 | C2 | semidirect |
| 10. #22551562 | C2 | semidirect |
| 11. #22551561 | C2 | semidirect |
| 12. C4×C22⋊D257 | C2 | semidirect |
| 13. #22551552 | C2 | semidirect |
| 14. C22⋊C4×D257 | C2 | semidirect |
| 15. C2×C22⋊C4×C257 | C2 | semidirect |
| 18. C2×Dic514 | C22 | semidirect |
| 19. C2×D1028 | C22 | semidirect |
| 20. C2×D1028 | C22 | semidirect |
| 27. C2×C22⋊D257 | C22 | semidirect |
| 28. C2×C22⋊D257 | C22 | semidirect |
| 30. C2×C4×D257 | C22 | semidirect |
| 31. C2×C4×D257 | C22 | semidirect |
| 32. C2×C4×D257 | C22 | semidirect |
| 33. C4⋊Dic257 | C22 | semidirect |
| 34. #16861597 | C22 | semidirect |
| 35. #16861597 | C22 | semidirect |
| 36. #16861597 | C22 | semidirect |
| 38. C22⋊Dic257 | C22 | semidirect |
| 39. C22⋊Dic257 | C22 | semidirect |
| 40. #16861595 | C22 | semidirect |
| 41. #16861595 | C22 | semidirect |
| 42. #16861595 | C22 | semidirect |
| 43. #16861595 | C22 | semidirect |
| 44. #16861595 | C22 | semidirect |
| 45. C4×Dic257 | C22 | semidirect |
| 47. C22×C4×C257 | C22 | semidirect |
| 48. C22×C4×C257 | C22 | semidirect |
| 51. C22⋊C4×C257 | C22 | semidirect |
| 52. C22⋊C4×C257 | C22 | semidirect |
| 68. C22⋊D257 | D4 | semidirect |
| 99. C22×C257 | #41 | semidirect |
| 129. C257 | #546 | semidirect |
| 145. C2×C22⋊C4 | D257 | semidirect |
| 164. C22×C4 | C2×D257 | semidirect |
| 165. C22×C4 | C2×D257 | semidirect |
| 180. C22⋊C4 | C2×D257 | semidirect |
| 181. C22⋊C4 | C2×D257 | semidirect |
| 239. C22 | #16861618 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861618 | 2 |
| C22×C22⋊D257 | 2 |
| #22551578 | 2 |
| #22551575 | 2 |
| #22551574 | 2 |
| #22551569 | 2 |
| #22551566 | 2 |
| #22551565 | 2 |
| #22551562 | 2 |
| #22551561 | 2 |
| C4×C22⋊D257 | 2 |
| #22551552 | 2 |
| C22⋊C4×D257 | 2 |
| C2×C22⋊C4×C257 | 2 |
| #546 | 257 |