Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
560 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 560 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 | #386 |
| commutator | C22×C4 | C22×C4×C43 |
| Frattini, cosocle | C2×C42 | C23×C43 |
| prime radical | C43×#2631 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C43×#2973 | C2 | semidirect |
| 3. C4×#100×C43 | C2 | semidirect |
| 4. C43×#1527 | C2 | semidirect |
| 5. C43×#1288 | C2 | semidirect |
| 55. #97×C43 | D4 | semidirect |
| 161. #9187 | C43 | direct (N × H) |
| 193. #2973 | C2×C43 | semidirect |
| 195. C4×#100 | C2×C43 | semidirect |
| 196. #1527 | C2×C43 | semidirect |
| 197. #1288 | C2×C43 | semidirect |
| 225. C43 | #9187 | direct (N × H) |
| 256. #97 | D4×C43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#2973 | 2 |
| C43×#2631 | 2 |
| C4×#100×C43 | 2 |
| C43×#1527 | 2 |
| C43×#1288 | 2 |
| #9187 | 43 |