Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
216 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C16 | D31 |
| commutator, hypocenter | C31 | C2×C4×C16 |
| Frattini | C2×C8 | C22×D31 |
| Fitting | C4×C16×C31 | C2 |
| socle | C22×C31 | C22×C8 |
| prime radical | C22×D31 | C2×C8 |
| cosocle | C2×C8×C31 | C23 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C4×C16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C4×C31⋊C16 | C2 | semidirect |
| 4. C16×Dic31 | C2 | semidirect |
| 5. C4×C16×C31 | C2 | semidirect |
| 15. C16×D31 | C4 | direct (N × H) |
| 27. C16×C31 | C2×C4 | semidirect |
| 28. C31⋊C16 | C2×C4 | semidirect |
| 34. C4×D31 | C16 | direct (N × H) |
| 45. C4×C31 | C2×C16 | semidirect |
| 49. Dic31 | C2×C16 | semidirect |
| 54. C4×C16 | D31 | direct (N × H) |
| 57. D31 | C4×C16 | direct (N × H) |
| 68. C31 | C2×C4×C16 | semidirect |
| 81. C16 | C4×D31 | direct (N × H) |
| 99. C4 | C16×D31 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C16×D31 | 2 |
| C4×C8×D31 | 2 |
| C4×C31⋊C16 | 2 |
| C16×Dic31 | 2 |
| C4×C16×C31 | 2 |
| C2×C4×C16 | 31 |