Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
454 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 90 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 | C2×#353 |
| commutator | C42 | C22×C4×C43 |
| Frattini, cosocle | #124 | C23×C43 |
| prime radical | C43×#3151 | C2 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C43 ◁ C2×C4×C43 ◁ C22×C4×C43 ◁ C43×#532 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C43×#2132 | C2 | semidirect |
| 3. C43×#2126 | C2 | semidirect |
| 4. C43×#1406 | C2 | semidirect |
| 8. C2×#127×C43 | C4 | semidirect |
| 9. C43×#496 | C4 | semidirect |
| 15. C4×M16×C43 | C4 | semidirect |
| 17. C43×#355 | C22 | semidirect |
| 18. C43×#354 | C22 | semidirect |
| 131. #13579 | C43 | direct (N × H) |
| 152. #2132 | C2×C43 | semidirect |
| 153. #2126 | C2×C43 | semidirect |
| 154. #1406 | C2×C43 | semidirect |
| 164. C2×#127 | C4×C43 | semidirect |
| 165. #496 | C4×C43 | semidirect |
| 171. C4×M16 | C4×C43 | semidirect |
| 173. #355 | C22×C43 | semidirect |
| 174. #354 | C22×C43 | semidirect |
| 176. C43 | #13579 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#3151 | 2 |
| C43×#2132 | 2 |
| C43×#2126 | 2 |
| C43×#1406 | 2 |
| #13579 | 43 |