Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1488 conjugacy classes of subgroups; only the 813 normal subgroups are shown.
This group has 1488 conjugacy classes of subgroups — too many to draw. Only its 813 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 | C23×D31 | C23 |
| hypercenter | #519 | D31 |
| hypocenter | C31 | C2×#519 |
| 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. #14521527 | C2 | semidirect |
| 3. #14521526 | C2 | semidirect |
| 4. #14521525 | C2 | semidirect |
| 5. C4×Q8×D31 | C2 | semidirect |
| 7. C31×#519 | C2 | semidirect |
| 9. C2×Q8×D31 | C4 | semidirect |
| 14. C4×Q8×C31 | C22 | semidirect |
| 16. Q8×Dic31 | C22 | semidirect |
| 20. #11758464 | C22 | semidirect |
| 25. C4×Dic62 | C22 | semidirect |
| 27. C2×Q8×C31 | C2×C4 | semidirect |
| 32. Q8×D31 | C2×C4 | semidirect |
| 37. C2×Dic62 | C2×C4 | semidirect |
| 81. #519 | D31 | direct (N × H) |
| 88. D31 | #519 | direct (N × H) |
| 98. C4×Q8 | C2×D31 | semidirect |
| 107. C31 | C2×#519 | semidirect |
| 113. 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×Q8×D31 | 2 |
| #14521527 | 2 |
| #14521526 | 2 |
| #14521525 | 2 |
| C4×Q8×D31 | 2 |
| #117×D31 | 2 |
| C31×#519 | 2 |
| C2×#519 | 31 |