Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
1464 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 545 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C23×C22⋊D11 |
| commutator, cosocle | C4×C11 | C25 |
| Frattini | C4 | C24×D11 |
| Fitting | C11×#585 | C2 |
| socle | C2×C11 | C23×D4 |
| hypercenter | #585 | D11 |
| hypocenter | C11 | #3585 |
| LCS | G ▷ C4×C11 ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C2 ◁ C2×#41 ◁ #585 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C11×#585 | C2 | semidirect |
| 2. C2×#67042 | C2 | semidirect |
| 3. #10623368 | C2 | semidirect |
| 4. #10623366 | C2 | semidirect |
| 5. #10623353 | C2 | semidirect |
| 6. C2×#67002 | C2 | semidirect |
| 7. #10623350 | C2 | semidirect |
| 9. C11×2−1+4 | C22 | semidirect |
| 11. C11×H(5,𝔽2) | C22 | semidirect |
| 14. C2×C11×#41 | C22 | semidirect |
| 16. #67042 | C22 | semidirect |
| 19. C2×#4339 | C22 | semidirect |
| 20. C22×D44 | C22 | semidirect |
| 21. #67004 | C22 | semidirect |
| 22. #67003 | C22 | semidirect |
| 23. #67002 | C22 | semidirect |
| 24. #67002 | C22 | semidirect |
| 25. #67001 | C22 | semidirect |
| 26. #66995 | C22 | semidirect |
| 27. C2×#4325 | C22 | semidirect |
| 28. #66985 | C22 | semidirect |
| 29. C2×#4323 | C22 | semidirect |
| 30. C2×#4318 | C22 | semidirect |
| 39. C11×#41 | C23 | semidirect |
| 42. C2×Q8×C11 | C23 | semidirect |
| 46. C2×D4×C11 | C23 | semidirect |
| 60. #4326 | C23 | semidirect |
| 61. #4325 | C23 | semidirect |
| 62. #4324 | C23 | semidirect |
| 63. #4323 | C23 | semidirect |
| 65. #4318 | C23 | semidirect |
| 66. C2×C11⋊C8 | C23 | semidirect |
| 97. #585 | D11 | semidirect |
| 118. 2−1+4 | C2×D11 | semidirect |
| 122. H(5,𝔽2) | C2×D11 | semidirect |
| 127. C2×#41 | C2×D11 | semidirect |
| 156. #41 | C22×D11 | semidirect |
| 160. C2×Q8 | C22×D11 | semidirect |
| 170. C2×D4 | C22×D11 | semidirect |
| 181. C11 | #3585 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#585 | 2 |
| C2×#67042 | 2 |
| #10623368 | 2 |
| #10623366 | 2 |
| #10623353 | 2 |
| C2×#67002 | 2 |
| #10623350 | 2 |
| #3585 | 11 |