Finite Group DatabasebetaFinite Group DatabasebetaOrder 4864.
442 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 106 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×#99 |
| commutator | C24 | C22×C4×C19 |
| Frattini, cosocle | C2×C22⋊C4 | C23×C19 |
| prime radical | C22×D4×C19 | C2×C4 |
| LCS | G ▷ C24 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ C2×C4×D4×C19 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C19×#1326 | C2 | semidirect |
| 5. C19×#1317 | C2 | semidirect |
| 82. C22×C4×C19 | M16 | semidirect |
| 100. C22⋊C4×C19 | M16 | semidirect |
| 104. #11528 | C19 | direct (N × H) |
| 155. #1326 | C2×C19 | semidirect |
| 156. #1317 | C2×C19 | semidirect |
| 244. C19 | #11528 | direct (N × H) |
| 269. C22×C4 | M16×C19 | semidirect |
| 287. C22⋊C4 | M16×C19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19×#2322 | 2 |
| C19×#1466 | 2 |
| C19×#1465 | 2 |
| C19×#1326 | 2 |
| C19×#1317 | 2 |
| #11528 | 19 |