Finite Group DatabasebetaFinite Group DatabasebetaOrder 4864.
278 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #1390 |
| commutator | C2×Q8 | C42×C19 |
| Frattini, cosocle | #532 | C22×C19 |
| prime radical | C19×#532 | C22 |
| LCS | G ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×C4×C19 ◁ C22×C4×C19 ◁ C19×#532 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C19×#568 | C4 | semidirect |
| 9. C19×#410 | C4 | semidirect |
| 10. C19×#354 | C4 | semidirect |
| 13. C19×#333 | C4 | semidirect |
| 70. #7482 | C19 | direct (N × H) |
| 120. #568 | C4×C19 | semidirect |
| 125. #410 | C4×C19 | semidirect |
| 126. #354 | C4×C19 | semidirect |
| 129. #333 | C4×C19 | semidirect |
| 157. C19 | #7482 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19×#2126 | 2 |
| C19×#1884 | 2 |
| C19×#1560 | 2 |
| #7482 | 19 |