Finite Group DatabasebetaFinite Group DatabasebetaOrder 4864.
1062 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 1062 conjugacy classes of subgroups — too many to draw. Only its 226 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 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#2847 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C24×C4×C19 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C19×#2848 | C2 | semidirect |
| 3. C19×#2077 | C2 | semidirect |
| 4. C19×#2035 | C2 | semidirect |
| 5. C19×#2034 | C2 | semidirect |
| 6. C19×#2000 | C2 | semidirect |
| 7. C19×#1779 | C2 | semidirect |
| 9. C22×SD16×C19 | C22 | semidirect |
| 13. C2×C19×#106 | C22 | semidirect |
| 14. C2×C19×#103 | C22 | semidirect |
| 15. C2×C19×#102 | C22 | semidirect |
| 23. C19×#340 | C22 | semidirect |
| 24. C19×#340 | C22 | semidirect |
| 58. C24×C19 | SD16 | semidirect |
| 97. #32708 | C19 | direct (N × H) |
| 135. #2848 | C2×C19 | semidirect |
| 137. #2077 | C2×C19 | semidirect |
| 138. #2035 | C2×C19 | semidirect |
| 139. #2034 | C2×C19 | semidirect |
| 140. #2000 | C2×C19 | semidirect |
| 141. #1779 | C2×C19 | semidirect |
| 163. C22×SD16 | C22×C19 | semidirect |
| 167. C2×#106 | C22×C19 | semidirect |
| 168. C2×#103 | C22×C19 | semidirect |
| 169. C2×#102 | C22×C19 | semidirect |
| 177. #340 | C22×C19 | semidirect |
| 178. #340 | C22×C19 | semidirect |
| 214. C19 | #32708 | direct (N × H) |
| 218. C24 | SD16×C19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19×#2848 | 2 |
| C19×#2847 | 2 |
| C19×#2077 | 2 |
| C19×#2035 | 2 |
| C19×#2034 | 2 |
| C19×#2000 | 2 |
| C19×#1779 | 2 |
| #32708 | 19 |