Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
32 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #15690860 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C16×D97 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C8×D97 | C4 | 1 | 1 | yes | characteristic |
| 4 | #13095486 | C22 | 1 | 1 | yes | characteristic |
| 5 | C16×C97 | C4 | 1 | 1 | yes | characteristic |
| 6 | C4×D97 | C8 | 1 | 1 | yes | characteristic |
| 7 | C8×C97 | C2×C4 | 1 | 1 | yes | characteristic |
| 8 | #11715895 | C8 | 1 | 1 | yes | characteristic |
| 9 | C2×D97 | C16 | 1 | 1 | yes | characteristic |
| 10 | C4×C97 | C2×C8 | 1 | 1 | yes | characteristic |
| 11 | Dic97 | C16 | 1 | 1 | yes | characteristic |
| 12 | C2×C97 | C2×C16 | 1 | 1 | yes | characteristic |
| 13 | D97 | — | 2 | 1 | no | — |
| 14 | C97 | M64 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 15 | M64 | — | 97 | 1 | no | maximal, Sylow |
| 16 | C2×C16 | — | 97 | 1 | no | — |
| 17 | C32 | — | 97 | 2 | no | — |
| 18 | C2×C8 | — | 97 | 1 | no | — |
| 19 | C16 | — | 97 | 1 | no | — |
| 20 | C16 | #87604 | 1 | 1 | yes | characteristic |
| 21 | C2×C4 | — | 97 | 1 | no | — |
| 22 | C8 | — | 97 | 1 | no | — |
| 23 | C8 | C2×#87604 | 1 | 1 | yes | characteristic |
| 24 | C22 | — | 97 | 1 | no | — |
| 25 | C4 | — | 97 | 1 | no | — |
| 26 | C4 | #13095519 | 1 | 1 | yes | characteristic |
| 27 | C2 | — | 194 | 1 | no | — |
| 28 | C2 | #15690883 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C2×#87604 |
| commutator, socle | C2×C97 | C2×C16 |
| Fitting | C16×C97 | C4 |
| hypercenter | C16 | #87604 |
| hypocenter | C97 | M64 |
| LCS | G ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C8 ◁ C16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15690860 | C2 | semidirect |
| 14. C97 | M64 | semidirect |