Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
520 conjugacy classes of subgroups; only the 264 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 264 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 | C22 | C23×C4×C41 |
| Frattini, cosocle | C23 | C24×C41 |
| prime radical | C22×D4×C41 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C41×#391 | C2 | semidirect |
| 3. C41×#388 | C2 | semidirect |
| 5. C41×#385 | C2 | semidirect |
| 6. C41×#382 | C2 | semidirect |
| 10. #124×C41 | C4 | semidirect |
| 25. C2×Q8×C41 | C2×C4 | semidirect |
| 41. C22⋊C4×C41 | C2×C4 | semidirect |
| 43. C42×C41 | C2×C4 | semidirect |
| 83. #2379 | C41 | direct (N × H) |
| 91. #391 | C2×C41 | semidirect |
| 92. #388 | C2×C41 | semidirect |
| 94. #385 | C2×C41 | semidirect |
| 95. #382 | C2×C41 | semidirect |
| 96. C41 | #2379 | direct (N × H) |
| 100. #124 | C4×C41 | semidirect |
| 115. C2×Q8 | C2×C4×C41 | semidirect |
| 131. C22⋊C4 | C2×C4×C41 | semidirect |
| 133. C42 | C2×C4×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#124×C41 | 2 |
| C41×#391 | 2 |
| C41×#388 | 2 |
| C41×#386 | 2 |
| C41×#385 | 2 |
| C41×#382 | 2 |
| #2379 | 41 |