Finite Group DatabasebetaFinite Group DatabasebetaOrder 4864.
720 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 166 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #99 |
| commutator | C2×C4 | C2×C42×C19 |
| Frattini, cosocle | C22×D4 | C23×C19 |
| socle | C22×C19 | C2×#99 |
| prime radical | C2×C19×#127 | C22 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C22×C4×C19 ◁ C2×C4×D4×C19 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C4×C19×#99 | C2 | semidirect |
| 4. C19×#1393 | C2 | semidirect |
| 7. C2×C4×D4×C19 | C4 | semidirect |
| 11. C19×#390 | C4 | semidirect |
| 13. C19×#384 | C4 | semidirect |
| 15. C43×C19 | C4 | semidirect |
| 16. C19×#353 | C4 | direct (N × H) |
| 45. C19×#99 | C2×C4 | semidirect |
| 57. C2×D4×C19 | C42 | semidirect |
| 90. C42×C19 | C42 | semidirect |
| 91. C4×#353 | C19 | direct (N × H) |
| 136. C4×#99 | C2×C19 | semidirect |
| 137. #1393 | C2×C19 | semidirect |
| 162. C4×C19 | #353 | direct (N × H) |
| 165. C2×C4×D4 | C4×C19 | semidirect |
| 169. #390 | C4×C19 | semidirect |
| 171. #384 | C4×C19 | semidirect |
| 173. C43 | C4×C19 | semidirect |
| 174. #353 | C4×C19 | direct (N × H) |
| 210. #99 | C2×C4×C19 | semidirect |
| 212. C19 | C4×#353 | direct (N × H) |
| 223. C2×D4 | C42×C19 | semidirect |
| 256. C42 | C42×C19 | semidirect |
| 323. C4 | C19×#353 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C19×#127 | 2 |
| C2×C19×#353 | 2 |
| C4×C19×#99 | 2 |
| C19×#1393 | 2 |
| C4×#353 | 19 |