Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
1144 conjugacy classes of subgroups; only the 440 normal subgroups are shown.
This group has 1144 conjugacy classes of subgroups — too many to draw. Only its 440 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×C41 | C23 |
| commutator | C22 | C23×C4×C41 |
| Frattini, cosocle | C23 | C24×C41 |
| prime radical | C25×C41 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C41×#381 | C2 | direct (N × H) |
| 4. C2×#95×C41 | C2 | semidirect |
| 7. C23×C4×C41 | C4 | semidirect |
| 13. #95×C41 | C22 | semidirect |
| 25. C22×C4×C41 | C2×C4 | semidirect |
| 58. C2×#381 | C41 | direct (N × H) |
| 60. C2×C41 | #381 | direct (N × H) |
| 66. #381 | C2×C41 | direct (N × H) |
| 67. C2×#95 | C2×C41 | semidirect |
| 68. C41 | C2×#381 | direct (N × H) |
| 71. C23×C4 | C4×C41 | semidirect |
| 77. #95 | C22×C41 | semidirect |
| 89. C22×C4 | C2×C4×C41 | semidirect |
| 123. C2 | C41×#381 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C4×C41 | 2 |
| C22×C22⋊C4×C41 | 2 |
| C41×#381 | 2 |
| C2×#95×C41 | 2 |
| C2×#381 | 41 |