Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
670 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C43 | #2021 |
| commutator, Frattini, cosocle | C2×#41 | C23×C43 |
| prime radical | C43×#585 | C22 |
| LCS | G ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C43 ◁ C2×C4×C43 ◁ C2×#41×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C43×#3202 | C2 | semidirect |
| 3. C43×#2123 | C2 | semidirect |
| 5. C43×#1392 | C2 | semidirect |
| 153. #13362 | C43 | direct (N × H) |
| 170. #3202 | C2×C43 | semidirect |
| 172. #2123 | C2×C43 | semidirect |
| 174. #1392 | C2×C43 | semidirect |
| 196. C43 | #13362 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#3202 | 2 |
| C43×#3022 | 2 |
| C43×#2123 | 2 |
| C43×#1794 | 2 |
| C43×#1392 | 2 |
| #13362 | 43 |