Finite Group DatabasebetaFinite Group DatabasebetaOrder 1984.
216 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 93 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 | #11758516 | C2 |
| hypercenter | #123 | D31 |
| hypocenter | C31 | #542 |
| 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. #11758513 | C2 | semidirect |
| 4. C4×C22⋊D31 | C2 | semidirect |
| 5. #11758501 | C2 | semidirect |
| 6. #11758475 | C2 | semidirect |
| 7. #11758473 | C2 | semidirect |
| 8. #11758465 | C2 | semidirect |
| 9. #11758464 | C2 | semidirect |
| 10. #11758462 | C2 | semidirect |
| 11. #11758462 | C2 | semidirect |
| 12. #11758460 | C2 | semidirect |
| 13. #11758456 | C2 | semidirect |
| 14. #11758455 | C2 | semidirect |
| 15. #11758454 | C2 | semidirect |
| 111. #123 | D31 | semidirect |
| 119. C31 | #542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C31×#123 | 2 |
| #11758516 | 2 |
| #11758513 | 2 |
| C4×C22⋊D31 | 2 |
| #11758501 | 2 |
| #11758475 | 2 |
| #11758473 | 2 |
| #11758465 | 2 |
| #11758464 | 2 |
| #11758462 | 2 |
| #11758460 | 2 |
| #11758456 | 2 |
| #11758455 | 2 |
| #11758454 | 2 |
| #542 | 31 |