Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
400 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 184 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 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C41 |
| prime radical | C22×D4×C41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C2×C42×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C41×#533 | C2 | semidirect |
| 3. C41×#489 | C2 | semidirect |
| 4. C41×#488 | C2 | semidirect |
| 5. C41×#419 | C2 | semidirect |
| 7. C4×M16×C41 | C2 | semidirect |
| 11. C4⋊Q8×C41 | C22 | semidirect |
| 12. #125×C41 | C22 | semidirect |
| 21. #103×C41 | C22 | semidirect |
| 23. #97×C41 | C22 | semidirect |
| 24. C4×C8×C41 | C22 | semidirect |
| 79. #3140 | C41 | direct (N × H) |
| 84. #533 | C2×C41 | semidirect |
| 86. #489 | C2×C41 | semidirect |
| 87. #488 | C2×C41 | semidirect |
| 88. #419 | C2×C41 | semidirect |
| 90. C4×M16 | C2×C41 | semidirect |
| 91. C41 | #3140 | direct (N × H) |
| 95. C4⋊Q8 | C22×C41 | semidirect |
| 96. #125 | C22×C41 | semidirect |
| 105. #103 | C22×C41 | semidirect |
| 107. #97 | C22×C41 | semidirect |
| 108. C4×C8 | C22×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#533 | 2 |
| C2×#124×C41 | 2 |
| C41×#489 | 2 |
| C41×#488 | 2 |
| C41×#419 | 2 |
| C41×#418 | 2 |
| C4×M16×C41 | 2 |
| #3140 | 41 |