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 | C4×D4×C257 | C2 |
| hypercenter | C4×D4 | D257 |
| hypocenter | C257 | #546 |
| LCS | G ▷ C22×C257 ▷ C257 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#16861618 | C2 | semidirect |
| 2. C22×D1028 | C2 | semidirect |
| 3. #22551580 | C2 | semidirect |
| 4. #22551577 | C2 | semidirect |
| 5. #22551571 | C2 | semidirect |
| 6. #22551566 | C2 | semidirect |
| 7. #22551565 | C2 | semidirect |
| 8. #22551560 | C2 | semidirect |
| 9. C4×D1028 | C2 | semidirect |
| 10. C22⋊C4×D257 | C2 | semidirect |
| 11. C4×D4×C257 | C2 | semidirect |
| 14. C2×Dic514 | C22 | semidirect |
| 19. C2×C22⋊D257 | C22 | semidirect |
| 20. C2×C22⋊D257 | C22 | semidirect |
| 21. C2×C4×D257 | C22 | semidirect |
| 22. C2×C4×D257 | C22 | semidirect |
| 23. C4⋊Dic257 | C22 | semidirect |
| 24. #16861597 | C22 | semidirect |
| 26. #16861595 | C22 | semidirect |
| 27. #16861595 | C22 | semidirect |
| 28. #16861595 | C22 | semidirect |
| 29. #16861595 | C22 | semidirect |
| 32. C22×C4×C257 | C22 | semidirect |
| 33. C4⋊C4×C257 | C22 | semidirect |
| 35. C22⋊C4×C257 | C22 | semidirect |
| 36. C42×C257 | C22 | semidirect |
| 45. D1028 | D4 | semidirect |
| 67. C22×C257 | #41 | semidirect |
| 90. C257 | #546 | semidirect |
| 101. C4×D4 | D257 | semidirect |
| 116. C22×C4 | C2×D257 | semidirect |
| 119. C4⋊C4 | C2×D257 | semidirect |
| 126. C22⋊C4 | C2×D257 | semidirect |
| 127. C42 | C2×D257 | semidirect |
| 165. 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×D1028 | 2 |
| #22551580 | 2 |
| #22551577 | 2 |
| #22551571 | 2 |
| #22551566 | 2 |
| #22551565 | 2 |
| #22551560 | 2 |
| C4×D1028 | 2 |
| C22⋊C4×D257 | 2 |
| C4×D4×C257 | 2 |
| #546 | 257 |