Finite Group DatabasebetaFinite Group DatabasebetaOrder 26818.
16 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C53×C23⋊C11 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | D1219 | C11 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 3 | C23×C53 | C2×C11 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | C11×D53 | — | 23 | 1 | no | maximal, Hall |
| 5 | C11×C53 | — | 23 | 1 | no | Hall |
| 6 | AGL(1,𝔽23) | — | 53 | 1 | no | maximal, Hall |
| 7 | C23⋊C11 | D53 | 1 | 1 | yes | characteristic, complemented, Hall |
| 8 | D53 | — | 253 | 1 | no | Hall |
| 9 | C53 | AGL(1,𝔽23) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 10 | D23 | — | 53 | 1 | no | Hall |
| 11 | C23 | C11×D53 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 12 | C2×C11 | — | 1219 | 1 | no | Hall |
| 13 | C11 | — | 23 | 1 | no | Sylow |
| 14 | C2 | — | 13409 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C23×C53 | C2×C11 |
| LCS | G ▷ C23×C53 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C53×C23⋊C11 | C2 | semidirect |
| 2. D1219 | C11 | semidirect |
| 3. C23×C53 | C2×C11 | semidirect |
| 7. C23⋊C11 | D53 | semidirect |
| 9. C53 | AGL(1,𝔽23) | semidirect |
| 11. C23 | C11×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×C23⋊C11 | 2 |
| D1219 | 11 |
| C11×D53 | 23 |
| AGL(1,𝔽23) | 53 |