Finite Group DatabasebetaFinite Group DatabasebetaOrder 26158.
16 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C11×C29×C41 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | C41×D29 | — | 11 | 1 | no | maximal, Hall |
| 3 | C29×C41 | D11 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | D11×C41 | — | 29 | 1 | no | maximal, Hall |
| 5 | D319 | C41 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 6 | C11×C41 | D29 | 1 | 1 | yes | characteristic, complemented, Hall |
| 7 | C11×C29 | C2×C41 | 1 | 1 | yes | characteristic, complemented, Hall |
| 8 | C2×C41 | — | 319 | 1 | no | Hall |
| 9 | D29 | — | 11 | 1 | no | Hall |
| 10 | C41 | D319 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 11 | C29 | D11×C41 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 12 | D11 | — | 29 | 1 | no | Hall |
| 13 | C11 | C41×D29 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 14 | C2 | — | 319 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | D319 |
| commutator, cosocle, hypocenter | C11×C29 | C2×C41 |
| Frattini | C1 | G |
| Fitting, socle | C11×C29×C41 | C2 |
| LCS | G ▷ C11×C29 | |
| UCS | C1 ◁ C41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C11×C29×C41 | C2 | semidirect |
| 3. C29×C41 | D11 | semidirect |
| 5. D319 | C41 | direct (N × H) |
| 6. C11×C41 | D29 | semidirect |
| 7. C11×C29 | C2×C41 | semidirect |
| 10. C41 | D319 | direct (N × H) |
| 11. C29 | D11×C41 | semidirect |
| 13. C11 | C41×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×C29×C41 | 2 |
| C41×D29 | 11 |
| D11×C41 | 29 |
| D319 | 41 |