Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
152 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 104 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×C41 | #106 |
| commutator | C8 | C22×C4×C41 |
| Frattini, cosocle | C2×C8 | C23×C41 |
| prime radical | C23×C41 | SD16 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C22×C4×C41 ◁ C22×C8×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C41×#365 | C2 | direct (N × H) |
| 8. M32×C41 | C4 | semidirect |
| 10. C2×C16×C41 | C4 | semidirect |
| 28. C16×C41 | C2×C4 | semidirect |
| 52. C2×#365 | C41 | direct (N × H) |
| 55. C2×C41 | #365 | direct (N × H) |
| 60. #365 | C2×C41 | direct (N × H) |
| 61. C41 | C2×#365 | direct (N × H) |
| 65. M32 | C4×C41 | semidirect |
| 67. C2×C16 | C4×C41 | semidirect |
| 85. C16 | C2×C4×C41 | semidirect |
| 111. C2 | C41×#365 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M32×C41 | 2 |
| C2×#108×C41 | 2 |
| C2×#106×C41 | 2 |
| C41×#365 | 2 |
| C2×#365 | 41 |