Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
708 conjugacy classes of subgroups; only the 248 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 248 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C41 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C41 |
| prime radical | C2×#121×C41 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#123×C41 | C2 | semidirect |
| 3. C22×C4⋊C4×C41 | C2 | semidirect |
| 4. C41×#399 | C2 | semidirect |
| 5. C41×#390 | C2 | semidirect |
| 6. C41×#384 | C2 | semidirect |
| 7. C4×C22⋊C4×C41 | C2 | semidirect |
| 45. C22⋊C4×C41 | D4 | semidirect |
| 87. C4×C41 | #123 | semidirect |
| 88. #2501 | C41 | direct (N × H) |
| 95. C2×#123 | C2×C41 | semidirect |
| 97. C22×C4⋊C4 | C2×C41 | semidirect |
| 98. #399 | C2×C41 | semidirect |
| 99. #390 | C2×C41 | semidirect |
| 100. #384 | C2×C41 | semidirect |
| 101. C4×C22⋊C4 | C2×C41 | semidirect |
| 102. C41 | #2501 | direct (N × H) |
| 140. C22⋊C4 | D4×C41 | semidirect |
| 182. C4 | #123×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#123×C41 | 2 |
| C2×#121×C41 | 2 |
| C22×C4⋊C4×C41 | 2 |
| C41×#399 | 2 |
| C41×#390 | 2 |
| C41×#384 | 2 |
| C4×C22⋊C4×C41 | 2 |
| #2501 | 41 |