Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
230 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C41 | #333 |
| commutator | C42 | C2×C8×C41 |
| Frattini, cosocle | C43 | C22×C41 |
| socle | C2×C41 | #1272 |
| prime radical | C23×C41 | #99 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C41 ◁ C22×C4×C41 ◁ C43×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 10. #125×C41 | C8 | semidirect |
| 55. #7134 | C41 | direct (N × H) |
| 77. C41 | #7134 | direct (N × H) |
| 80. #125 | C8×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#1994 | 2 |
| C41×#1276 | 2 |
| #7134 | 41 |