Finite Group DatabasebetaFinite Group DatabasebetaOrder 24644.
20 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | D6161 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C61×D101 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C101×D61 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C61×C101 | C22 | 1 | 1 | yes | characteristic, complemented, Hall |
| 5 | C2×D101 | — | 61 | 1 | no | maximal, Hall |
| 6 | C2×D61 | — | 101 | 1 | no | maximal, Hall |
| 7 | C2×C101 | — | 61 | 1 | no | — |
| 8 | D101 | — | 61 | 1 | no | — |
| 9 | D101 | D61 | 1 | 1 | yes | characteristic, direct product factor |
| 10 | C2×C61 | — | 101 | 1 | no | — |
| 11 | D61 | — | 101 | 1 | no | — |
| 12 | D61 | D101 | 1 | 1 | yes | characteristic, direct product factor |
| 13 | C101 | C2×D61 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 14 | C61 | C2×D101 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 15 | C22 | — | 6161 | 1 | no | Sylow |
| 16 | C2 | — | 6161 | 1 | no | — |
| 17 | C2 | — | 61 | 1 | no | — |
| 18 | C2 | — | 101 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C61×C101 | C22 |
| LCS | G ▷ C61×C101 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D6161 | C2 | semidirect |
| 2. C61×D101 | C2 | semidirect |
| 3. C101×D61 | C2 | semidirect |
| 4. C61×C101 | C22 | semidirect |
| 9. D101 | D61 | direct (N × H) |
| 12. D61 | D101 | direct (N × H) |
| 13. C101 | C2×D61 | semidirect |
| 14. C61 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D6161 | 2 |
| C61×D101 | 2 |
| C101×D61 | 2 |
| C2×D101 | 61 |
| C2×D61 | 101 |