Finite Group DatabasebetaFinite Group DatabasebetaOrder 1984.
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×D31 |
| commutator, socle, cosocle | C22×C31 | C24 |
| Fitting | C31×#123 | C2 |
| prime radical | #11758514 | C2 |
| hypercenter | #123 | D31 |
| hypocenter | C31 | #551 |
| LCS | G ▷ C22×C31 ▷ C31 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C31×#123 | C2 | semidirect |
| 3. D4×Dic31 | C2 | semidirect |
| 4. C2×(C2×D31)⋊C4 | C2 | semidirect |
| 5. #11758503 | C2 | semidirect |
| 6. #11758475 | C2 | semidirect |
| 7. #11758475 | C2 | semidirect |
| 8. #11758474 | C2 | semidirect |
| 9. #11758469 | C2 | semidirect |
| 10. #11758463 | C2 | semidirect |
| 11. #11758462 | C2 | semidirect |
| 12. #11758460 | C2 | semidirect |
| 13. (C22⋊D31)⋊C4 | C2 | semidirect |
| 14. C22⋊C4×D31 | C2 | semidirect |
| 15. #11758455 | C2 | semidirect |
| 22. C22×Dic31 | C22 | semidirect |
| 25. C2×Dic62 | C22 | semidirect |
| 26. C4⋊C4×C31 | C22 | semidirect |
| 27. C4⋊C4×C31 | C22 | semidirect |
| 29. C22⋊C4×C31 | C22 | semidirect |
| 30. C22⋊C4×C31 | C22 | semidirect |
| 33. C22⋊Dic31 | C22 | semidirect |
| 42. C4⋊Dic31 | C22 | semidirect |
| 43. C4⋊Dic31 | C22 | semidirect |
| 44. C4⋊Dic31 | C22 | semidirect |
| 45. C4⋊Dic31 | C22 | semidirect |
| 46. Dic31⋊C4 | C22 | semidirect |
| 47. Dic31⋊C4 | C22 | semidirect |
| 48. C4×Dic31 | C22 | semidirect |
| 49. C4×Dic31 | C22 | semidirect |
| 50. C4×Dic31 | C22 | semidirect |
| 116. #123 | D31 | semidirect |
| 126. C31 | #551 | semidirect |
| 143. C4⋊C4 | C2×D31 | semidirect |
| 144. C4⋊C4 | C2×D31 | semidirect |
| 157. C22⋊C4 | C2×D31 | semidirect |
| 158. C22⋊C4 | C2×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C31×#123 | 2 |
| #11758514 | 2 |
| D4×Dic31 | 2 |
| C2×(C2×D31)⋊C4 | 2 |
| #11758503 | 2 |
| #11758475 | 2 |
| #11758474 | 2 |
| #11758469 | 2 |
| #11758463 | 2 |
| #11758462 | 2 |
| #11758460 | 2 |
| (C22⋊D31)⋊C4 | 2 |
| C22⋊C4×D31 | 2 |
| #11758455 | 2 |
| #551 | 31 |