Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
702 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 200 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×#120×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 |
|---|---|---|
| 2. C22×C22⋊C4×C41 | C2 | semidirect |
| 3. C41×#397 | C2 | semidirect |
| 4. C41×#394 | C2 | semidirect |
| 5. C41×#386 | C2 | semidirect |
| 6. C41×#385 | C2 | semidirect |
| 7. C41×#379 | C2 | semidirect |
| 13. C2×C4⋊C4×C41 | C22 | semidirect |
| 20. C2×C22⋊C4×C41 | C22 | semidirect |
| 21. #95×C41 | C22 | semidirect |
| 22. #95×C41 | C22 | semidirect |
| 91. #2622 | C41 | direct (N × H) |
| 99. C22×C22⋊C4 | C2×C41 | semidirect |
| 100. #397 | C2×C41 | semidirect |
| 101. #394 | C2×C41 | semidirect |
| 102. #386 | C2×C41 | semidirect |
| 103. #385 | C2×C41 | semidirect |
| 104. #379 | C2×C41 | semidirect |
| 105. C41 | #2622 | direct (N × H) |
| 111. C2×C4⋊C4 | C22×C41 | semidirect |
| 118. C2×C22⋊C4 | C22×C41 | semidirect |
| 119. #95 | C22×C41 | semidirect |
| 120. #95 | C22×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#120×C41 | 2 |
| C22×C22⋊C4×C41 | 2 |
| C41×#397 | 2 |
| C41×#394 | 2 |
| C41×#386 | 2 |
| C41×#385 | 2 |
| C41×#379 | 2 |
| #2622 | 41 |