Finite Group DatabasebetaFinite Group DatabasebetaOrder 4864.
2598 conjugacy classes of subgroups; only the 1374 normal subgroups are shown.
This group has 2598 conjugacy classes of subgroups — too many to draw. Only its 1374 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C19 | C24 |
| commutator | C2 | C2×C43×C19 |
| Frattini, cosocle | C24 | C24×C19 |
| prime radical | C25×C19 | C23 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C19 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C4×C19×#95 | C2 | semidirect |
| 7. C4×C22⋊C4×C19 | C4 | semidirect |
| 8. C2×C19×#95 | C4 | semidirect |
| 19. C2×C42×C19 | C2×C4 | semidirect |
| 21. C19×#95 | C2×C4 | semidirect |
| 32. C22×C4×C19 | C42 | semidirect |
| 37. C22⋊C4×C19 | C42 | semidirect |
| 39. #13749 | C19 | direct (N × H) |
| 60. C4×#95 | C2×C19 | semidirect |
| 76. C4×C22⋊C4 | C4×C19 | semidirect |
| 77. C2×#95 | C4×C19 | semidirect |
| 93. C2×C42 | C2×C4×C19 | semidirect |
| 95. #95 | C2×C4×C19 | semidirect |
| 96. C19 | #13749 | direct (N × H) |
| 107. C22×C4 | C42×C19 | semidirect |
| 112. C22⋊C4 | C42×C19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊C4×C19 | 2 |
| C22×C19×#95 | 2 |
| C4×C19×#95 | 2 |
| #13749 | 19 |