Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
650 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C43 | #459 |
| commutator, Frattini, cosocle | C22×C8 | C23×C43 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C43 ◁ C22×C4×C43 ◁ C2×C4×C8×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C43×#509 | C2 | semidirect |
| 2. C2×C43×#493 | C2 | semidirect |
| 3. C2×C43×#361 | C2 | semidirect |
| 4. C43×#1974 | C2 | semidirect |
| 5. C43×#1376 | C2 | semidirect |
| 26. C2×Q16×C43 | D4 | semidirect |
| 37. C2×D8×C43 | D4 | semidirect |
| 47. M32×C43 | D4 | semidirect |
| 125. #13331 | C43 | direct (N × H) |
| 142. C2×#509 | C2×C43 | semidirect |
| 143. C2×#493 | C2×C43 | semidirect |
| 144. C2×#361 | C2×C43 | semidirect |
| 145. #1974 | C2×C43 | semidirect |
| 146. #1376 | C2×C43 | semidirect |
| 168. C43 | #13331 | direct (N × H) |
| 174. C2×Q16 | D4×C43 | semidirect |
| 185. C2×D8 | D4×C43 | semidirect |
| 195. M32 | D4×C43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C43×#509 | 2 |
| C2×C43×#493 | 2 |
| C2×C43×#361 | 2 |
| C43×#1974 | 2 |
| C43×#1376 | 2 |
| #13331 | 43 |