Finite Group DatabasebetaFinite Group DatabasebetaOrder 12224.
426 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 121 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×D191 |
| commutator, socle, cosocle | C22×C191 | C24 |
| Fitting | #121×C191 | C2 |
| hypercenter | #121 | D191 |
| hypocenter | C191 | C2×#121 |
| LCS | G ▷ C22×C191 ▷ C191 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D4×D191 | C2 | semidirect |
| 2. C2×D4×D191 | C2 | semidirect |
| 3. C22×C4×D191 | C2 | semidirect |
| 4. #20259297 | C2 | semidirect |
| 5. #20259296 | C2 | semidirect |
| 6. #20259295 | C2 | semidirect |
| 7. #20259294 | C2 | semidirect |
| 8. #20259293 | C2 | semidirect |
| 9. C4⋊C4×D191 | C2 | semidirect |
| 10. C22⋊C4×D191 | C2 | semidirect |
| 11. #121×C191 | C2 | semidirect |
| 14. C2×D764 | C22 | semidirect |
| 15. C2×D764 | C22 | semidirect |
| 16. C2×C22⋊D191 | C22 | semidirect |
| 17. C2×C22⋊D191 | C22 | semidirect |
| 18. C2×C22⋊D191 | C22 | semidirect |
| 21. C22×Dic191 | C22 | semidirect |
| 26. C2×C4×D191 | C22 | semidirect |
| 27. C2×C4×D191 | C22 | semidirect |
| 28. C4⋊Dic191 | C22 | semidirect |
| 29. Dic191⋊C4 | C22 | semidirect |
| 30. C22⋊Dic191 | C22 | semidirect |
| 31. (C2×D191)⋊C4 | C22 | semidirect |
| 32. (C2×D191)⋊C4 | C22 | semidirect |
| 33. C2×D4×C191 | C22 | semidirect |
| 34. C2×D4×C191 | C22 | semidirect |
| 35. C22×C4×C191 | C22 | semidirect |
| 36. C4⋊C4×C191 | C22 | semidirect |
| 37. C22⋊C4×C191 | C22 | semidirect |
| 43. C22×D191 | D4 | semidirect |
| 60. C4×D191 | D4 | semidirect |
| 74. C22×C191 | C2×D4 | semidirect |
| 85. C2×D191 | C2×D4 | semidirect |
| 89. C4×C191 | C2×D4 | semidirect |
| 92. Dic191 | C2×D4 | semidirect |
| 100. D191 | #121 | direct (N × H) |
| 101. C191 | C2×#121 | semidirect |
| 111. #121 | D191 | direct (N × H) |
| 123. C2×D4 | C2×D191 | semidirect |
| 124. C2×D4 | C2×D191 | semidirect |
| 132. C22×C4 | C2×D191 | semidirect |
| 135. C4⋊C4 | C2×D191 | semidirect |
| 139. C22⋊C4 | C2×D191 | semidirect |
| 187. C22 | D4×D191 | semidirect |
| 194. C4 | D4×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D191 | 2 |
| C22×C4×D191 | 2 |
| #20259297 | 2 |
| #20259296 | 2 |
| #20259295 | 2 |
| #20259294 | 2 |
| #20259293 | 2 |
| C4⋊C4×D191 | 2 |
| C22⋊C4×D191 | 2 |
| #121×C191 | 2 |
| C2×#121 | 191 |