Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
476 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D44 |
| commutator, cosocle | C2×C4×C11 | C24 |
| Frattini | C2×C4 | C23×D11 |
| Fitting | C11×#443 | C2 |
| socle | C2×C11 | D42 |
| hypercenter | #443 | D11 |
| hypocenter | C11 | #3292 |
| LCS | G ▷ C2×C4×C11 ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #443 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10623300 | C2 | semidirect |
| 2. #10623283 | C2 | semidirect |
| 3. C11×#443 | C2 | semidirect |
| 4. #10622755 | C2 | semidirect |
| 5. #10622510 | C2 | semidirect |
| 6. #10622435 | C2 | semidirect |
| 7. #10622313 | C2 | semidirect |
| 8. #10622308 | C2 | semidirect |
| 9. #67042 | C22 | semidirect |
| 11. C11×#131 | C22 | semidirect |
| 12. #67002 | C22 | semidirect |
| 17. #66961 | C22 | semidirect |
| 21. C2×D88 | C22 | semidirect |
| 22. C2×D88 | C22 | semidirect |
| 23. #66954 | C22 | semidirect |
| 24. #66927 | C22 | semidirect |
| 25. C11×#108 | C22 | semidirect |
| 26. C11×#104 | C22 | semidirect |
| 27. C4×C8×C11 | C22 | semidirect |
| 28. #66887 | C22 | semidirect |
| 29. #66883 | C22 | semidirect |
| 30. #66869 | C22 | semidirect |
| 40. C11×Q16 | D4 | semidirect |
| 41. C11×SD16 | D4 | semidirect |
| 42. C11×D8 | D4 | semidirect |
| 52. Dic44 | D4 | semidirect |
| 58. D88 | D4 | semidirect |
| 60. #4314 | D4 | semidirect |
| 95. #443 | D11 | semidirect |
| 121. #131 | C2×D11 | semidirect |
| 124. #108 | C2×D11 | semidirect |
| 126. #104 | C2×D11 | semidirect |
| 128. C4×C8 | C2×D11 | semidirect |
| 144. Q16 | D44 | semidirect |
| 148. SD16 | D44 | semidirect |
| 156. D8 | D44 | semidirect |
| 166. C11 | #3292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10623300 | 2 |
| #10623283 | 2 |
| C11×#443 | 2 |
| #10622755 | 2 |
| #10622510 | 2 |
| #10622435 | 2 |
| #10622313 | 2 |
| #10622308 | 2 |
| #3292 | 11 |