Finite Group DatabasebetaFinite Group DatabasebetaOrder 23548.
25 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #26044462 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #19154636 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 3 | #16809859 | C7 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 4 | C29×D29 | C2×C7 | 1 | 1 | yes | characteristic |
| 5 | C292 | C4×C7 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 6 | AGL(1,𝔽29) | — | 29 | 1 | no | maximal |
| 7 | Dic29⋊C7 | — | 29 | 1 | no | maximal |
| 8 | C2×C29⋊C7 | — | 29 | 1 | no | — |
| 9 | D29⋊C7 | — | 29 | 1 | no | — |
| 10 | C29⋊C7 | — | 29 | 1 | no | — |
| 11 | C29⋊C7 | — | 29 | 1 | no | — |
| 12 | #1181 | — | 203 | 1 | no | — |
| 13 | Dic29 | — | 203 | 1 | no | — |
| 14 | C2×C29 | — | 203 | 1 | no | — |
| 15 | D29 | D29⋊C7 | 1 | 1 | yes | characteristic |
| 16 | C29 | — | 28 | 1 | no | — |
| 17 | C29 | Dic29⋊C7 | 1 | 1 | yes | characteristic, complemented |
| 18 | C29 | AGL(1,𝔽29) | 1 | 1 | yes | characteristic, complemented |
| 19 | C4×C7 | — | 841 | 1 | no | Hall |
| 20 | C2×C7 | — | 841 | 1 | no | — |
| 21 | C7 | — | 841 | 1 | no | Sylow |
| 22 | C4 | — | 5887 | 1 | no | Sylow |
| 23 | C2 | — | 203 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C292 | C4×C7 |
| prime radical | #26044462 | C2 |
| cosocle | C29×D29 | C2×C7 |
| LCS | G ▷ C292 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #19154636 | C4 | semidirect |
| 3. #16809859 | C7 | semidirect |
| 5. C292 | C4×C7 | semidirect |
| 17. C29 | Dic29⋊C7 | semidirect |
| 18. C29 | AGL(1,𝔽29) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26044462 | 2 |
| #16809859 | 7 |
| AGL(1,𝔽29) | 29 |
| Dic29⋊C7 | 29 |