Finite Group DatabasebetaFinite Group DatabasebetaOrder 32596.
12 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C29×D281 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C29×C281 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 3 | #11765499 | C29 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 4 | D281 | C2×C29 | 1 | 1 | yes | characteristic |
| 5 | C281 | C4×C29 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 6 | C4×C29 | — | 281 | 1 | no | maximal, Hall |
| 7 | C2×C29 | — | 281 | 1 | no | — |
| 8 | C29 | #11765499 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 9 | C4 | — | 281 | 1 | no | Sylow |
| 10 | C2 | — | 281 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | #11765499 |
| commutator, hypocenter | C281 | C4×C29 |
| Frattini | C1 | G |
| Fitting, socle | C29×C281 | C4 |
| prime radical | C29×D281 | C2 |
| cosocle | D281 | C2×C29 |
| LCS | G ▷ C281 | |
| UCS | C1 ◁ C29 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×C281 | C4 | semidirect |
| 3. #11765499 | C29 | direct (N × H) |
| 5. C281 | C4×C29 | semidirect |
| 8. C29 | #11765499 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×D281 | 2 |
| #11765499 | 29 |
| C4×C29 | 281 |