Finite Group DatabasebetaFinite Group DatabasebetaOrder 1984.
252 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
| hypercenter | #123 | D31 |
| hypocenter | C31 | #560 |
| 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 |
| 2. #11758517 | C2 | semidirect |
| 3. #11758514 | C2 | semidirect |
| 4. #11758507 | C2 | semidirect |
| 5. #11758475 | C2 | semidirect |
| 6. #11758472 | C2 | semidirect |
| 7. #11758461 | C2 | semidirect |
| 8. #11758460 | C2 | semidirect |
| 9. #11758459 | C2 | semidirect |
| 12. C22×C4×C31 | C22 | semidirect |
| 15. C2×C22⋊D31 | C22 | semidirect |
| 18. C2×D124 | C22 | semidirect |
| 19. C2×C4×D31 | C22 | semidirect |
| 20. C4⋊C4×C31 | C22 | semidirect |
| 22. C22⋊C4×C31 | C22 | semidirect |
| 27. (C2×D31)⋊C4 | C22 | semidirect |
| 28. C4⋊Dic31 | C22 | semidirect |
| 29. Dic31⋊C4 | C22 | semidirect |
| 30. C4×Dic31 | C22 | semidirect |
| 78. #123 | D31 | semidirect |
| 84. C31 | #560 | semidirect |
| 94. C22×C4 | C2×D31 | semidirect |
| 97. C4⋊C4 | C2×D31 | semidirect |
| 104. 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 |
| #11758517 | 2 |
| #11758514 | 2 |
| #11758507 | 2 |
| #11758475 | 2 |
| #11758472 | 2 |
| #11758461 | 2 |
| #11758460 | 2 |
| #11758459 | 2 |
| #560 | 31 |