Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
7014 conjugacy classes of subgroups; only the 1134 normal subgroups are shown.
This group has 7014 conjugacy classes of subgroups — too many to draw. Only its 1134 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C43 | #120 |
| commutator, Frattini, cosocle | C23 | C25×C43 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C43 ◁ C25×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×H(5,𝔽2)×C43 | C2 | semidirect |
| 2. C22×#120×C43 | C2 | semidirect |
| 3. C2×C43×B(4,𝔽2) | C2 | direct (N × H) |
| 4. C22×#99×C43 | C2 | semidirect |
| 5. C26×C43 | C22 | semidirect |
| 7. C2×H(5,𝔽2)×C43 | C22 | semidirect |
| 13. C2×#120×C43 | C22 | semidirect |
| 15. C22×C22⋊C4×C43 | C22 | semidirect |
| 16. C43×B(4,𝔽2) | C22 | direct (N × H) |
| 17. C2×#99×C43 | C22 | semidirect |
| 22. C25×C43 | D4 | semidirect |
| 24. C25×C43 | C23 | semidirect |
| 27. H(5,𝔽2)×C43 | C23 | semidirect |
| 38. C22×D4×C43 | D4 | semidirect |
| 42. C23×C4×C43 | D4 | semidirect |
| 44. #120×C43 | C23 | semidirect |
| 47. C2×C22⋊C4×C43 | C23 | semidirect |
| 48. #99×C43 | C23 | semidirect |
| 66. C24×C43 | C2×D4 | semidirect |
| 68. C24×C43 | C24 | semidirect |
| 81. C2×D4×C43 | C2×D4 | semidirect |
| 88. C22×C4×C43 | C2×D4 | semidirect |
| 91. C22⋊C4×C43 | C24 | semidirect |
| 117. C23×C43 | C22×D4 | semidirect |
| 129. C2×C4×C43 | C22×D4 | semidirect |
| 130. C22×B(4,𝔽2) | C43 | direct (N × H) |
| 146. C22×C43 | B(4,𝔽2) | direct (N × H) |
| 152. C22×H(5,𝔽2) | C2×C43 | semidirect |
| 153. C22×#120 | C2×C43 | semidirect |
| 154. C2×B(4,𝔽2) | C2×C43 | direct (N × H) |
| 155. C22×#99 | C2×C43 | semidirect |
| 160. C2×C43 | C2×B(4,𝔽2) | direct (N × H) |
| 162. C26 | C22×C43 | semidirect |
| 164. C2×H(5,𝔽2) | C22×C43 | semidirect |
| 170. C2×#120 | C22×C43 | semidirect |
| 172. C22×C22⋊C4 | C22×C43 | semidirect |
| 173. B(4,𝔽2) | C22×C43 | direct (N × H) |
| 174. C2×#99 | C22×C43 | semidirect |
| 175. C43 | C22×B(4,𝔽2) | direct (N × H) |
| 180. C25 | D4×C43 | semidirect |
| 182. C25 | C23×C43 | semidirect |
| 185. H(5,𝔽2) | C23×C43 | semidirect |
| 196. C22×D4 | D4×C43 | semidirect |
| 200. C23×C4 | D4×C43 | semidirect |
| 202. #120 | C23×C43 | semidirect |
| 205. C2×C22⋊C4 | C23×C43 | semidirect |
| 206. #99 | C23×C43 | semidirect |
| 224. C24 | C2×D4×C43 | semidirect |
| 226. C24 | C24×C43 | semidirect |
| 239. C2×D4 | C2×D4×C43 | semidirect |
| 246. C22×C4 | C2×D4×C43 | semidirect |
| 249. C22⋊C4 | C24×C43 | semidirect |
| 275. C23 | C22×D4×C43 | semidirect |
| 287. C2×C4 | C22×D4×C43 | semidirect |
| 303. C22 | C43×B(4,𝔽2) | direct (N × H) |
| 313. C2 | C2×C43×B(4,𝔽2) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×H(5,𝔽2)×C43 | 2 |
| C22×#120×C43 | 2 |
| C2×C43×B(4,𝔽2) | 2 |
| C22×#99×C43 | 2 |
| C22×B(4,𝔽2) | 43 |