Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
566 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 138 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 | C24×C43 | D8 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C43 ◁ C23×C4×C43 ◁ C23×C8×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Q32×C43 | C2 | semidirect |
| 3. C2×C43×#358 | C2 | semidirect |
| 5. C43×#1380 | C2 | semidirect |
| 84. C23×C43 | Q32 | semidirect |
| 109. #13306 | C43 | direct (N × H) |
| 126. C22×Q32 | C2×C43 | semidirect |
| 128. C2×#358 | C2×C43 | semidirect |
| 130. #1380 | C2×C43 | semidirect |
| 150. C43 | #13306 | direct (N × H) |
| 216. C23 | Q32×C43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q32×C43 | 2 |
| C2×C43×#467 | 2 |
| C2×C43×#358 | 2 |
| C2×C43×C22⋊C16 | 2 |
| C43×#1380 | 2 |
| #13306 | 43 |