Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
662 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 146 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C43 | C2×D8 |
| commutator, Frattini, cosocle | C22×C8 | C23×C43 |
| prime radical | C2×C43×#493 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C43 ◁ C2×C42×C43 ◁ C2×C4×C8×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×SD32×C43 | C2 | semidirect |
| 3. C2×C43×#357 | C2 | semidirect |
| 4. C43×#1969 | C2 | semidirect |
| 5. C43×#1374 | C2 | semidirect |
| 26. C2×Q16×C43 | D4 | semidirect |
| 45. C2×C16×C43 | D4 | semidirect |
| 111. C2×C4×C43 | SD32 | semidirect |
| 121. #13328 | C43 | direct (N × H) |
| 139. C22×SD32 | C2×C43 | semidirect |
| 141. C2×#357 | C2×C43 | semidirect |
| 142. #1969 | C2×C43 | semidirect |
| 143. #1374 | C2×C43 | semidirect |
| 164. C43 | #13328 | direct (N × H) |
| 171. C2×Q16 | D4×C43 | semidirect |
| 190. C2×C16 | D4×C43 | semidirect |
| 256. C2×C4 | SD32×C43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×SD32×C43 | 2 |
| C2×C43×#493 | 2 |
| C2×C43×#357 | 2 |
| C43×#1969 | 2 |
| C43×#1374 | 2 |
| #13328 | 43 |