Finite Group DatabasebetaFinite Group DatabasebetaOrder 23548.
18 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×C841⋊C7 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C841⋊C7 | C4 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 3 | C4×C841 | C7 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 4 | C2×C841 | C2×C7 | 1 | 1 | yes | characteristic |
| 5 | C841 | C4×C7 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 6 | C4×C29⋊C7 | — | 29 | 1 | no | maximal |
| 7 | C2×C29⋊C7 | — | 29 | 1 | no | — |
| 8 | C29⋊C7 | — | 29 | 1 | no | — |
| 9 | C4×C29 | C29⋊C7 | 1 | 1 | yes | characteristic |
| 10 | C2×C29 | C2×C29⋊C7 | 1 | 1 | yes | characteristic |
| 11 | C29 | C4×C29⋊C7 | 1 | 1 | yes | characteristic |
| 12 | C4×C7 | — | 841 | 1 | no | Hall |
| 13 | C2×C7 | — | 841 | 1 | no | — |
| 14 | C7 | — | 841 | 1 | no | Sylow |
| 15 | C4 | C841⋊C7 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 16 | C2 | C2×C841⋊C7 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C841⋊C7 |
| commutator, hypocenter | C841 | C4×C7 |
| Frattini, socle | C2×C29 | C2×C29⋊C7 |
| Fitting | C4×C841 | C7 |
| prime radical | C2×C841⋊C7 | C2 |
| cosocle | C2×C841 | C2×C7 |
| LCS | G ▷ C841 | |
| UCS | C1 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C841⋊C7 | C4 | direct (N × H) |
| 3. C4×C841 | C7 | semidirect |
| 5. C841 | C4×C7 | semidirect |
| 15. C4 | C841⋊C7 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C841⋊C7 | 2 |
| C4×C841 | 7 |
| C4×C29⋊C7 | 29 |