Finite Group DatabasebetaFinite Group DatabasebetaOrder 4864.
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×C19 | #120 |
| commutator, Frattini, cosocle | C23 | C25×C19 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C25×C19 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C19×H(5,𝔽2) | C2 | semidirect |
| 2. C22×C19×#120 | C2 | semidirect |
| 3. C2×C19×B(4,𝔽2) | C2 | direct (N × H) |
| 4. C22×C19×#99 | C2 | semidirect |
| 5. C26×C19 | C22 | semidirect |
| 7. C2×C19×H(5,𝔽2) | C22 | semidirect |
| 13. C2×C19×#120 | C22 | semidirect |
| 15. C22×C22⋊C4×C19 | C22 | semidirect |
| 16. C19×B(4,𝔽2) | C22 | direct (N × H) |
| 17. C2×C19×#99 | C22 | semidirect |
| 22. C25×C19 | D4 | semidirect |
| 24. C25×C19 | C23 | semidirect |
| 27. C19×H(5,𝔽2) | C23 | semidirect |
| 38. C22×D4×C19 | D4 | semidirect |
| 42. C23×C4×C19 | D4 | semidirect |
| 44. C19×#120 | C23 | semidirect |
| 47. C2×C22⋊C4×C19 | C23 | semidirect |
| 48. C19×#99 | C23 | semidirect |
| 66. C24×C19 | C2×D4 | semidirect |
| 68. C24×C19 | C24 | semidirect |
| 81. C2×D4×C19 | C2×D4 | semidirect |
| 88. C22×C4×C19 | C2×D4 | semidirect |
| 91. C22⋊C4×C19 | C24 | semidirect |
| 92. C22×B(4,𝔽2) | C19 | direct (N × H) |
| 118. C23×C19 | C22×D4 | semidirect |
| 130. C2×C4×C19 | C22×D4 | semidirect |
| 131. C22×H(5,𝔽2) | C2×C19 | semidirect |
| 132. C22×#120 | C2×C19 | semidirect |
| 133. C2×B(4,𝔽2) | C2×C19 | direct (N × H) |
| 134. C22×#99 | C2×C19 | semidirect |
| 150. C22×C19 | B(4,𝔽2) | direct (N × H) |
| 156. C26 | C22×C19 | semidirect |
| 158. C2×H(5,𝔽2) | C22×C19 | semidirect |
| 164. C2×#120 | C22×C19 | semidirect |
| 166. C22×C22⋊C4 | C22×C19 | semidirect |
| 167. B(4,𝔽2) | C22×C19 | direct (N × H) |
| 168. C2×#99 | C22×C19 | semidirect |
| 173. C2×C19 | C2×B(4,𝔽2) | direct (N × H) |
| 179. C25 | D4×C19 | semidirect |
| 181. C25 | C23×C19 | semidirect |
| 184. H(5,𝔽2) | C23×C19 | semidirect |
| 195. C22×D4 | D4×C19 | semidirect |
| 199. C23×C4 | D4×C19 | semidirect |
| 201. #120 | C23×C19 | semidirect |
| 204. C2×C22⋊C4 | C23×C19 | semidirect |
| 205. #99 | C23×C19 | semidirect |
| 206. C19 | C22×B(4,𝔽2) | direct (N × H) |
| 224. C24 | C2×D4×C19 | semidirect |
| 226. C24 | C24×C19 | semidirect |
| 239. C2×D4 | C2×D4×C19 | semidirect |
| 246. C22×C4 | C2×D4×C19 | semidirect |
| 249. C22⋊C4 | C24×C19 | semidirect |
| 275. C23 | C22×D4×C19 | semidirect |
| 287. C2×C4 | C22×D4×C19 | semidirect |
| 303. C22 | C19×B(4,𝔽2) | direct (N × H) |
| 313. C2 | C2×C19×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×C19×H(5,𝔽2) | 2 |
| C22×C19×#120 | 2 |
| C2×C19×B(4,𝔽2) | 2 |
| C22×C19×#99 | 2 |
| C22×B(4,𝔽2) | 19 |