Finite Group DatabasebetaFinite Group DatabasebetaOrder 4864.
390 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 82 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 | #447 |
| commutator, Frattini, cosocle | C4×C8 | C23×C19 |
| prime radical | C19×#3273 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C42×C19 ◁ C19×#436 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C19×#2251 | C2 | semidirect |
| 3. C19×#2208 | C2 | semidirect |
| 4. C19×#1689 | C2 | semidirect |
| 5. C19×#1360 | C2 | semidirect |
| 6. C19×#1333 | C2 | semidirect |
| 7. C19×#1330 | C2 | semidirect |
| 14. C19×#494 | C22 | semidirect |
| 22. C19×C4⋊C16 | C22 | semidirect |
| 24. C19×#346 | C22 | semidirect |
| 25. C19×#334 | C22 | semidirect |
| 113. #12326 | C19 | direct (N × H) |
| 149. #2251 | C2×C19 | semidirect |
| 150. #2208 | C2×C19 | semidirect |
| 151. #1689 | C2×C19 | semidirect |
| 152. #1360 | C2×C19 | semidirect |
| 153. #1333 | C2×C19 | semidirect |
| 154. #1330 | C2×C19 | semidirect |
| 180. #494 | C22×C19 | semidirect |
| 188. C4⋊C16 | C22×C19 | semidirect |
| 190. #346 | C22×C19 | semidirect |
| 191. #334 | C22×C19 | semidirect |
| 237. C19 | #12326 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19×#3273 | 2 |
| C19×#2251 | 2 |
| C19×#2208 | 2 |
| C19×#1689 | 2 |
| C19×#1360 | 2 |
| C19×#1333 | 2 |
| C19×#1330 | 2 |
| #12326 | 19 |