Finite Group DatabasebetaFinite Group DatabasebetaOrder 18722.
16 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C11×C23×C37 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | D851 | — | 11 | 1 | no | maximal, Hall |
| 3 | C23×C37 | D11 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | D407 | — | 23 | 1 | no | maximal, Hall |
| 5 | D253 | — | 37 | 1 | no | maximal, Hall |
| 6 | C11×C37 | D23 | 1 | 1 | yes | characteristic, complemented, Hall |
| 7 | C11×C23 | D37 | 1 | 1 | yes | characteristic, complemented, Hall |
| 8 | D37 | — | 253 | 1 | no | Hall |
| 9 | D23 | — | 407 | 1 | no | Hall |
| 10 | C37 | D253 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 11 | C23 | D407 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 12 | D11 | — | 851 | 1 | no | Hall |
| 13 | C11 | D851 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 14 | C2 | — | 9361 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C23×C37 | C2 |
| LCS | G ▷ C11×C23×C37 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C11×C23×C37 | C2 | semidirect |
| 3. C23×C37 | D11 | semidirect |
| 6. C11×C37 | D23 | semidirect |
| 7. C11×C23 | D37 | semidirect |
| 10. C37 | D253 | semidirect |
| 11. C23 | D407 | semidirect |
| 13. C11 | D851 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×C23×C37 | 2 |
| D851 | 11 |
| D407 | 23 |
| D253 | 37 |