Finite Group DatabasebetaFinite Group DatabasebetaOrder 4864.
33214 conjugacy classes of subgroups; only the 3614 normal subgroups are shown.
This group has 33214 conjugacy classes of subgroups — too many to draw. Only its 3614 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C25×C19 | C23 |
| commutator | C22 | C24×C4×C19 |
| Frattini, cosocle | C23 | C25×C19 |
| prime radical | C27×C19 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C25×C19 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×C22⋊C4×C19 | C2 | semidirect |
| 3. C2×C19×#379 | C2 | direct (N × H) |
| 5. C26×C19 | C4 | semidirect |
| 8. C24×C4×C19 | C22 | semidirect |
| 10. C22×C22⋊C4×C19 | C22 | semidirect |
| 11. C19×#379 | C22 | direct (N × H) |
| 17. C25×C19 | C2×C4 | semidirect |
| 23. C23×C4×C19 | C23 | semidirect |
| 25. C2×C22⋊C4×C19 | C23 | semidirect |
| 33. C24×C19 | C22⋊C4 | semidirect |
| 36. C24×C19 | C22×C4 | semidirect |
| 43. C22×C4×C19 | C24 | semidirect |
| 45. C22×#379 | C19 | direct (N × H) |
| 54. C23×C19 | C2×C22⋊C4 | semidirect |
| 64. C23×C22⋊C4 | C2×C19 | semidirect |
| 65. C2×#379 | C2×C19 | direct (N × H) |
| 70. C22×C19 | #379 | direct (N × H) |
| 72. C22×C19 | C22×C22⋊C4 | semidirect |
| 78. C26 | C4×C19 | semidirect |
| 81. C24×C4 | C22×C19 | semidirect |
| 83. C22×C22⋊C4 | C22×C19 | semidirect |
| 84. #379 | C22×C19 | direct (N × H) |
| 86. C2×C19 | C2×#379 | direct (N × H) |
| 94. C25 | C2×C4×C19 | semidirect |
| 100. C23×C4 | C23×C19 | semidirect |
| 102. C2×C22⋊C4 | C23×C19 | semidirect |
| 103. C19 | C22×#379 | direct (N × H) |
| 111. C24 | C22⋊C4×C19 | semidirect |
| 114. C24 | C22×C4×C19 | semidirect |
| 121. C22×C4 | C24×C19 | semidirect |
| 131. C23 | C2×C22⋊C4×C19 | semidirect |
| 144. C22 | C19×#379 | direct (N × H) |
| 146. C22 | C22×C22⋊C4×C19 | semidirect |
| 152. C2 | C2×C19×#379 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C27×C19 | 2 |
| C23×C22⋊C4×C19 | 2 |
| C2×C19×#379 | 2 |
| C22×#379 | 19 |