Finite Group DatabasebetaFinite Group DatabasebetaOrder 4864.
4360 conjugacy classes of subgroups; only the 370 normal subgroups are shown.
This group has 4360 conjugacy classes of subgroups — too many to draw. Only its 370 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×C19 | C2×#120 |
| commutator, Frattini, cosocle | C24 | C24×C19 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×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. C2×C19×B(4,𝔽2) | C2 | semidirect |
| 3. C19×#2403 | C2 | semidirect |
| 4. C19×#1790 | C2 | semidirect |
| 5. C19×#1781 | C2 | semidirect |
| 12. C23×D4×C19 | C22 | semidirect |
| 14. C2×C19×#120 | C22 | semidirect |
| 16. C2×C19×#99 | C22 | semidirect |
| 19. C19×#386 | C22 | semidirect |
| 20. C19×#379 | C22 | semidirect |
| 22. C25×C19 | D4 | semidirect |
| 24. C25×C19 | C23 | semidirect |
| 28. C19×H(5,𝔽2) | D4 | semidirect |
| 44. C22×D4×C19 | D4 | semidirect |
| 47. C23×C4×C19 | D4 | semidirect |
| 48. C23×C4×C19 | C23 | semidirect |
| 55. C2×C22⋊C4×C19 | C23 | semidirect |
| 119. #32898 | C19 | direct (N × H) |
| 152. C23×C19 | #120 | semidirect |
| 173. C2×C4×C19 | #120 | semidirect |
| 174. C22×H(5,𝔽2) | C2×C19 | semidirect |
| 175. C2×B(4,𝔽2) | C2×C19 | semidirect |
| 176. #2403 | C2×C19 | semidirect |
| 177. #1790 | C2×C19 | semidirect |
| 178. #1781 | C2×C19 | semidirect |
| 202. C22×C19 | B(4,𝔽2) | semidirect |
| 214. C23×D4 | C22×C19 | semidirect |
| 216. C2×#120 | C22×C19 | semidirect |
| 218. C2×#99 | C22×C19 | semidirect |
| 221. #386 | C22×C19 | semidirect |
| 222. #379 | C22×C19 | semidirect |
| 232. C25 | D4×C19 | semidirect |
| 234. C25 | C23×C19 | semidirect |
| 238. H(5,𝔽2) | D4×C19 | semidirect |
| 254. C22×D4 | D4×C19 | semidirect |
| 257. C23×C4 | D4×C19 | semidirect |
| 258. C23×C4 | C23×C19 | semidirect |
| 265. C2×C22⋊C4 | C23×C19 | semidirect |
| 268. C19 | #32898 | direct (N × H) |
| 362. C23 | C19×#120 | semidirect |
| 383. C2×C4 | C19×#120 | semidirect |
| 407. C22 | C19×B(4,𝔽2) | semidirect |
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 |
| C2×C19×B(4,𝔽2) | 2 |
| C19×#2403 | 2 |
| C19×#1790 | 2 |
| C19×#1781 | 2 |
| #32898 | 19 |