Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
5956 conjugacy classes of subgroups; only the 3203 normal subgroups are shown.
This group has 5956 conjugacy classes of subgroups — too many to draw. Only its 3203 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | C24×D11 |
| commutator, socle, cosocle | C2×C11 | C26 |
| Frattini | C2 | C25×D11 |
| Fitting | C11×#585 | C2 |
| hypercenter | #585 | D11 |
| hypocenter | C11 | C2×#585 |
| LCS | G ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C4 ◁ #585 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C11×#585 | C2 | semidirect |
| 2. #10623457 | C2 | semidirect |
| 3. D11×2−1+4 | C2 | semidirect |
| 4. #10623455 | C2 | semidirect |
| 5. D11×H(5,𝔽2) | C2 | semidirect |
| 6. #10623453 | C2 | semidirect |
| 7. C2×#41×D11 | C2 | semidirect |
| 8. C11×2−1+4 | C22 | semidirect |
| 9. C11×H(5,𝔽2) | C22 | semidirect |
| 10. C2×C11×#41 | C22 | semidirect |
| 11. #67043 | C22 | semidirect |
| 12. #67042 | C22 | semidirect |
| 13. #41×D11 | C22 | semidirect |
| 14. #41×D11 | C22 | semidirect |
| 15. #41×D11 | C22 | semidirect |
| 16. #41×D11 | C22 | semidirect |
| 17. #67040 | C22 | semidirect |
| 18. C2×#4343 | C22 | semidirect |
| 19. C2×Q8×D11 | C22 | semidirect |
| 20. #67037 | C22 | semidirect |
| 21. C2×#4341 | C22 | semidirect |
| 22. C2×D4×D11 | C22 | semidirect |
| 23. C2×#4339 | C22 | semidirect |
| 24. C22×C4×D11 | C22 | semidirect |
| 26. C11×#41 | C23 | semidirect |
| 27. C11×#41 | C23 | semidirect |
| 28. C2×Q8×C11 | C23 | semidirect |
| 29. C2×D4×C11 | C23 | semidirect |
| 30. C22×C4×C11 | C23 | semidirect |
| 31. C2×C22⋊D11 | C23 | semidirect |
| 32. C22×Dic11 | C23 | semidirect |
| 33. #4343 | C23 | semidirect |
| 34. #4343 | C23 | semidirect |
| 36. Q8×D11 | C23 | semidirect |
| 37. #4341 | C23 | semidirect |
| 38. #4341 | C23 | semidirect |
| 40. D4×D11 | C23 | semidirect |
| 41. #4339 | C23 | semidirect |
| 42. #4339 | C23 | semidirect |
| 43. C2×D44 | C23 | semidirect |
| 46. C2×C4×D11 | C23 | semidirect |
| 47. C2×C4×D11 | C23 | semidirect |
| 48. C2×Dic22 | C23 | semidirect |
| 71. #585 | D11 | direct (N × H) |
| 87. 2−1+4 | C2×D11 | semidirect |
| 90. H(5,𝔽2) | C2×D11 | semidirect |
| 98. C2×#41 | C2×D11 | semidirect |
| 105. D11 | #585 | direct (N × H) |
| 113. #41 | C22×D11 | semidirect |
| 114. #41 | C22×D11 | semidirect |
| 118. C2×Q8 | C22×D11 | semidirect |
| 123. C2×D4 | C22×D11 | semidirect |
| 129. C22×C4 | C22×D11 | semidirect |
| 130. C11 | C2×#585 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#585 | 2 |
| #10623457 | 2 |
| D11×2−1+4 | 2 |
| #10623455 | 2 |
| D11×H(5,𝔽2) | 2 |
| #10623453 | 2 |
| C2×#41×D11 | 2 |
| C2×#585 | 11 |