Finite Group DatabasebetaFinite Group DatabasebetaOrder 8416.
26 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | D2104 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C263⋊C16 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | Q16×C263 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | D1052 | — | 2 | 1 | no | — |
| 5 | Q8×C263 | — | 2 | 1 | no | — |
| 6 | C8×C263 | C22 | 1 | 1 | yes | characteristic |
| 7 | C2×D263 | — | 4 | 1 | no | — |
| 8 | C4×C263 | — | 4 | 1 | no | — |
| 9 | C4×C263 | D4 | 1 | 1 | yes | characteristic |
| 10 | C2×C263 | D8 | 1 | 1 | yes | characteristic |
| 11 | D263 | — | 8 | 1 | no | — |
| 12 | C263 | SD32 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 13 | SD32 | — | 263 | 1 | no | maximal, Sylow |
| 14 | Q16 | D263 | 1 | 1 | yes | characteristic, complemented |
| 15 | D8 | — | 263 | 1 | no | — |
| 16 | C16 | — | 263 | 1 | no | — |
| 17 | Q8 | — | 2 | 1 | no | — |
| 18 | D4 | — | 526 | 1 | no | — |
| 19 | C8 | C2×D263 | 1 | 1 | yes | characteristic |
| 20 | C22 | — | 1052 | 1 | no | — |
| 21 | C4 | — | 4 | 1 | no | — |
| 22 | C4 | C22⋊D263 | 1 | 1 | yes | characteristic |
| 23 | C2 | — | 2104 | 1 | no | — |
| 24 | C2 | #16862361 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #16862361 |
| commutator | C8×C263 | C22 |
| Frattini | C8 | C2×D263 |
| Fitting | Q16×C263 | C2 |
| socle | C2×C263 | D8 |
| hypercenter | Q16 | D263 |
| hypocenter | C263 | SD32 |
| LCS | G ▷ C8×C263 ▷ C4×C263 ▷ C2×C263 ▷ C263 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ Q16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C263⋊C16 | C2 | semidirect |
| 3. Q16×C263 | C2 | semidirect |
| 12. C263 | SD32 | semidirect |
| 14. Q16 | D263 | semidirect |