Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
224 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 88 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 | #127 |
| commutator, Frattini, cosocle | C42 | C23×C41 |
| prime radical | C41×#493 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C42×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C41×#500 | C2 | semidirect |
| 3. C41×#492 | C2 | semidirect |
| 4. C41×#486 | C2 | semidirect |
| 5. C82×C41 | C2 | semidirect |
| 37. C8×C41 | D8 | semidirect |
| 38. C8×C41 | SD16 | semidirect |
| 47. #1706 | C41 | direct (N × H) |
| 52. #500 | C2×C41 | semidirect |
| 54. #492 | C2×C41 | semidirect |
| 55. #486 | C2×C41 | semidirect |
| 56. C82 | C2×C41 | semidirect |
| 57. C41 | #1706 | direct (N × H) |
| 89. C8 | D8×C41 | semidirect |
| 90. C8 | SD16×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#500 | 2 |
| C41×#493 | 2 |
| C41×#492 | 2 |
| C41×#486 | 2 |
| C82×C41 | 2 |
| #1706 | 41 |