Finite Group DatabasebetaFinite Group DatabasebetaOrder 1984.
292 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 105 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 | #547 |
| 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. C2×#92497 | C2 | semidirect |
| 2. C2×#92495 | C2 | semidirect |
| 3. C31×#123 | C2 | semidirect |
| 4. #11758516 | C2 | semidirect |
| 5. C2×Dic31⋊C4 | C2 | semidirect |
| 6. #11758473 | C2 | semidirect |
| 7. #11758471 | C2 | semidirect |
| 8. C4⋊C4×D31 | C2 | semidirect |
| 9. #11758465 | C2 | semidirect |
| 10. #11758463 | C2 | semidirect |
| 11. #11758461 | C2 | semidirect |
| 12. #11758460 | C2 | semidirect |
| 13. (C22⋊D31)⋊C4 | C2 | semidirect |
| 14. (C22⋊D31)⋊C4 | C2 | semidirect |
| 15. #11758455 | C2 | semidirect |
| 67. C22⋊D31 | D4 | semidirect |
| 107. Dic31 | #41 | semidirect |
| 122. #123 | D31 | semidirect |
| 131. C31 | #547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#92497 | 2 |
| C2×#92495 | 2 |
| C31×#123 | 2 |
| #11758516 | 2 |
| C2×Dic31⋊C4 | 2 |
| #11758473 | 2 |
| #11758471 | 2 |
| C4⋊C4×D31 | 2 |
| #11758465 | 2 |
| #11758463 | 2 |
| #11758461 | 2 |
| #11758460 | 2 |
| (C22⋊D31)⋊C4 | 2 |
| #11758455 | 2 |
| #547 | 31 |