Finite Group DatabasebetaFinite Group DatabasebetaOrder 4864.
1922 conjugacy classes of subgroups; only the 298 normal subgroups are shown.
This group has 1922 conjugacy classes of subgroups — too many to draw. Only its 298 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 ◁ C23×C4×C19 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C4×C19×H(5,𝔽2) | C2 | semidirect |
| 2. C2×C19×B(4,𝔽2) | C2 | semidirect |
| 3. C19×#2408 | C2 | semidirect |
| 4. C19×#1889 | C2 | semidirect |
| 5. C19×#1799 | C2 | semidirect |
| 7. C23×D4×C19 | C22 | semidirect |
| 21. C19×#380 | C22 | semidirect |
| 22. C19×#379 | C22 | semidirect |
| 23. C19×#342 | C22 | semidirect |
| 26. C19×H(5,𝔽2) | D4 | semidirect |
| 35. C23×C4×C19 | D4 | semidirect |
| 53. C2×C4⋊C4×C19 | D4 | semidirect |
| 59. C2×C22⋊C4×C19 | D4 | semidirect |
| 63. C2×C42×C19 | D4 | semidirect |
| 121. #32926 | C19 | direct (N × H) |
| 140. C23×C19 | #121 | semidirect |
| 169. C2×C4×C19 | #121 | semidirect |
| 170. C4×H(5,𝔽2) | C2×C19 | semidirect |
| 171. C2×B(4,𝔽2) | C2×C19 | semidirect |
| 172. #2408 | C2×C19 | semidirect |
| 173. #1889 | C2×C19 | semidirect |
| 174. #1799 | C2×C19 | semidirect |
| 200. C4×C19 | B(4,𝔽2) | semidirect |
| 202. C23×D4 | C22×C19 | semidirect |
| 216. #380 | C22×C19 | semidirect |
| 217. #379 | C22×C19 | semidirect |
| 218. #342 | C22×C19 | semidirect |
| 228. H(5,𝔽2) | D4×C19 | semidirect |
| 237. C23×C4 | D4×C19 | semidirect |
| 255. C2×C4⋊C4 | D4×C19 | semidirect |
| 261. C2×C22⋊C4 | D4×C19 | semidirect |
| 265. C2×C42 | D4×C19 | semidirect |
| 268. C19 | #32926 | direct (N × H) |
| 342. C23 | C19×#121 | semidirect |
| 371. C2×C4 | C19×#121 | semidirect |
| 397. C4 | C19×B(4,𝔽2) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C19×H(5,𝔽2) | 2 |
| C2×C19×B(4,𝔽2) | 2 |
| C19×#2408 | 2 |
| C19×#1889 | 2 |
| C19×#1799 | 2 |
| #32926 | 19 |