Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
336 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 124 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 | C2×C22⋊C4 |
| commutator | C23 | C22×C4×C41 |
| Frattini, cosocle | C22×C4 | C23×C41 |
| prime radical | C22×D4×C41 | C22 |
| LCS | G ▷ C23 ▷ 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 |
|---|---|---|
| 2. C41×#423 | C2 | semidirect |
| 4. C41×#343 | C2 | semidirect |
| 70. C4×C41 | #100 | semidirect |
| 73. #1800 | C41 | direct (N × H) |
| 81. #423 | C2×C41 | semidirect |
| 83. #343 | C2×C41 | semidirect |
| 84. C41 | #1800 | direct (N × H) |
| 150. C4 | #100×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D4×C41 | 2 |
| C41×#423 | 2 |
| C2×#100×C41 | 2 |
| C41×#343 | 2 |
| #1800 | 41 |