Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
248 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 97 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×D29 |
| commutator, socle, cosocle | C22×C29 | C24 |
| Fitting | C29×#123 | C2 |
| prime radical | #11745299 | C2 |
| hypercenter | #123 | D29 |
| hypocenter | C29 | #551 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C29×#123 | C2 | semidirect |
| 3. D4×Dic29 | C2 | semidirect |
| 4. C2×#90781 | C2 | semidirect |
| 5. #11745288 | C2 | semidirect |
| 6. #11745260 | C2 | semidirect |
| 7. #11745260 | C2 | semidirect |
| 8. #11745259 | C2 | semidirect |
| 9. #11745254 | C2 | semidirect |
| 10. #11745248 | C2 | semidirect |
| 11. #11745247 | C2 | semidirect |
| 12. #11745245 | C2 | semidirect |
| 13. #11745243 | C2 | semidirect |
| 14. C22⋊C4×D29 | C2 | semidirect |
| 15. #11745240 | C2 | semidirect |
| 22. C22×Dic29 | C22 | semidirect |
| 25. C2×Dic58 | C22 | semidirect |
| 26. C4⋊C4×C29 | C22 | semidirect |
| 27. C4⋊C4×C29 | C22 | semidirect |
| 29. C22⋊C4×C29 | C22 | semidirect |
| 30. C22⋊C4×C29 | C22 | semidirect |
| 33. C22⋊Dic29 | C22 | semidirect |
| 42. C4⋊Dic29 | C22 | semidirect |
| 43. C4⋊Dic29 | C22 | semidirect |
| 44. C4⋊Dic29 | C22 | semidirect |
| 45. C4⋊Dic29 | C22 | semidirect |
| 46. #90779 | C22 | semidirect |
| 47. #90779 | C22 | semidirect |
| 48. C4×Dic29 | C22 | semidirect |
| 49. C4×Dic29 | C22 | semidirect |
| 50. C4×Dic29 | C22 | semidirect |
| 116. #123 | D29 | semidirect |
| 126. C29 | #551 | semidirect |
| 143. C4⋊C4 | C2×D29 | semidirect |
| 144. C4⋊C4 | C2×D29 | semidirect |
| 157. C22⋊C4 | C2×D29 | semidirect |
| 158. C22⋊C4 | C2×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#123 | 2 |
| #11745299 | 2 |
| D4×Dic29 | 2 |
| C2×#90781 | 2 |
| #11745288 | 2 |
| #11745260 | 2 |
| #11745259 | 2 |
| #11745254 | 2 |
| #11745248 | 2 |
| #11745247 | 2 |
| #11745245 | 2 |
| #11745243 | 2 |
| C22⋊C4×D29 | 2 |
| #11745240 | 2 |
| #551 | 29 |