Finite Group DatabasebetaFinite Group DatabasebetaOrder 7936.
1810 conjugacy classes of subgroups.
The subgroup lattice has 170 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C31 | C24 |
| commutator | C22 | C24×C4×C31 |
| Frattini, cosocle | C2×C4 | C25×C31 |
| socle | C22×C31 | C24×C4 |
| prime radical | C24×C31 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C31 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C31×#2961 | C2 | semidirect |
| 3. C31×#2960 | C2 | semidirect |
| 12. C31×#446 | C22 | semidirect |
| 13. C8×Q8×C31 | C22 | semidirect |
| 23. C22×C8×C31 | Q8 | semidirect |
| 59. #60191 | C31 | direct (N × H) |
| 75. #2961 | C2×C31 | semidirect |
| 76. #2960 | C2×C31 | semidirect |
| 93. #446 | C22×C31 | semidirect |
| 94. C8×Q8 | C22×C31 | semidirect |
| 107. C22×C8 | Q8×C31 | semidirect |
| 124. C31 | #60191 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C31×#3458 | 2 |
| C31×#2961 | 2 |
| C31×#2960 | 2 |
| C31×#2905 | 2 |
| C2×C31×#405 | 2 |
| #60191 | 31 |