Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
1460 conjugacy classes of subgroups.
The subgroup lattice has 132 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C47 | C24 |
| commutator | C2 | C24×C4×C47 |
| Frattini, cosocle | C4 | C25×C47 |
| socle | C22×C47 | C23×C4 |
| prime radical | C22×#41×C47 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C47×#568 | C2 | direct (N × H) |
| 3. C2×#131×C47 | C2 | semidirect |
| 4. C22×M16×C47 | C2 | semidirect |
| 12. #131×C47 | C22 | semidirect |
| 14. C2×M16×C47 | C22 | semidirect |
| 15. C2×M16×C47 | C22 | semidirect |
| 16. C22×C8×C47 | C22 | semidirect |
| 32. M16×C47 | C23 | semidirect |
| 34. C2×C8×C47 | C23 | semidirect |
| 61. C2×#568 | C47 | direct (N × H) |
| 64. C2×C47 | #568 | direct (N × H) |
| 67. #568 | C2×C47 | direct (N × H) |
| 68. C2×#131 | C2×C47 | semidirect |
| 69. C22×M16 | C2×C47 | semidirect |
| 70. C47 | C2×#568 | direct (N × H) |
| 78. #131 | C22×C47 | semidirect |
| 80. C2×M16 | C22×C47 | semidirect |
| 81. C2×M16 | C22×C47 | semidirect |
| 82. C22×C8 | C22×C47 | semidirect |
| 98. M16 | C23×C47 | semidirect |
| 100. C2×C8 | C23×C47 | semidirect |
| 129. C2 | C47×#568 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#41×C47 | 2 |
| C47×#568 | 2 |
| C2×#131×C47 | 2 |
| C22×M16×C47 | 2 |
| C2×#568 | 47 |