Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
670 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 670 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 | C2×C43 | #1782 |
| commutator | C22×C4 | C22×C4×C43 |
| Frattini, cosocle | C2×#41 | C23×C43 |
| prime radical | C2×#41×C43 | C23 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C43 ◁ C2×C4×C43 ◁ C4×#41×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 13. C43×#533 | C4 | semidirect |
| 14. C2×C4⋊Q8×C43 | C4 | semidirect |
| 15. C43×#519 | C4 | semidirect |
| 16. C43×#519 | C4 | semidirect |
| 153. #12724 | C43 | direct (N × H) |
| 186. #533 | C4×C43 | semidirect |
| 187. C2×C4⋊Q8 | C4×C43 | semidirect |
| 188. #519 | C4×C43 | semidirect |
| 189. #519 | C4×C43 | semidirect |
| 198. C43 | #12724 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#3509 | 2 |
| C43×#2135 | 2 |
| C43×#2129 | 2 |
| C43×#2123 | 2 |
| C43×#1827 | 2 |
| #12724 | 43 |