Finite Group DatabasebetaFinite Group DatabasebetaOrder 7936.
1550 conjugacy classes of subgroups; only the 298 normal subgroups are shown.
This group has 1550 conjugacy classes of subgroups — too many to draw. Only its 298 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C31 | C2×#120 |
| commutator, Frattini, cosocle | C24 | C24×C31 |
| prime radical | C2×C31×H(5,𝔽2) | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C31×#2409 | C2 | semidirect |
| 3. C31×#1867 | C2 | semidirect |
| 4. C31×#1799 | C2 | semidirect |
| 7. C23×Q8×C31 | C22 | semidirect |
| 20. C31×#385 | C22 | semidirect |
| 21. C31×#380 | C22 | semidirect |
| 22. C31×#342 | C22 | semidirect |
| 24. C31×H(5,𝔽2) | Q8 | semidirect |
| 110. #32975 | C31 | direct (N × H) |
| 120. C23×C31 | C22⋊Q8 | semidirect |
| 151. C2×C4×C31 | C22⋊Q8 | semidirect |
| 153. #2409 | C2×C31 | semidirect |
| 154. #1867 | C2×C31 | semidirect |
| 155. #1799 | C2×C31 | semidirect |
| 178. C23×Q8 | C22×C31 | semidirect |
| 191. #385 | C22×C31 | semidirect |
| 192. #380 | C22×C31 | semidirect |
| 193. #342 | C22×C31 | semidirect |
| 201. H(5,𝔽2) | Q8×C31 | semidirect |
| 240. C31 | #32975 | direct (N × H) |
| 297. C23 | C31×C22⋊Q8 | semidirect |
| 328. C2×C4 | C31×C22⋊Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C31×H(5,𝔽2) | 2 |
| C31×#2409 | 2 |
| C31×#1867 | 2 |
| C31×#1799 | 2 |
| C31×#1790 | 2 |
| #32975 | 31 |