Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1540 conjugacy classes of subgroups; only the 805 normal subgroups are shown.
This group has 1540 conjugacy classes of subgroups — too many to draw. Only its 805 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 | C24×D31 |
| commutator | C2×C31 | C24×C4 |
| Fitting | C31×#519 | C2 |
| socle, cosocle | C22×C31 | C25 |
| prime radical | C22×#92499 | C2 |
| hypercenter | #519 | D31 |
| hypocenter | C31 | #3428 |
| LCS | G ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C22 ◁ #519 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14521531 | C2 | semidirect |
| 3. #14521527 | C2 | semidirect |
| 4. #14521523 | C2 | semidirect |
| 5. C4×#92499 | C2 | semidirect |
| 6. #117×D31 | C2 | semidirect |
| 7. C31×#519 | C2 | semidirect |
| 9. C2×#92499 | C4 | semidirect |
| 14. C4×Q8×C31 | C22 | semidirect |
| 16. Q8×Dic31 | C22 | semidirect |
| 18. #11758470 | C22 | semidirect |
| 19. #11758469 | C22 | semidirect |
| 20. C4⋊C4×D31 | C22 | semidirect |
| 23. C4×D124 | C22 | semidirect |
| 24. #11758449 | C22 | semidirect |
| 25. C42×D31 | C22 | semidirect |
| 27. C2×Q8×C31 | C2×C4 | semidirect |
| 31. #92499 | C2×C4 | semidirect |
| 32. #92499 | C2×C4 | semidirect |
| 33. C2×D124 | C2×C4 | semidirect |
| 35. C2×C4×D31 | C2×C4 | semidirect |
| 79. #519 | D31 | semidirect |
| 94. C4×Q8 | C2×D31 | semidirect |
| 105. C31 | #3428 | semidirect |
| 109. C2×Q8 | C4×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92499 | 2 |
| #14521531 | 2 |
| #14521527 | 2 |
| #14521523 | 2 |
| C4×#92499 | 2 |
| #117×D31 | 2 |
| C31×#519 | 2 |
| #3428 | 31 |