Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
118 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 118 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C41 | #1333 |
| commutator | C16 | C2×C8×C41 |
| Frattini, cosocle | #346 | C22×C41 |
| prime radical | C41×#508 | C4 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C41 ◁ C2×C4×C41 ◁ C4×C8×C41 ◁ C41×#346 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C41×#1398 | C2 | semidirect |
| 3. C41×#1368 | C2 | semidirect |
| 13. Q32×C41 | C8 | semidirect |
| 15. D16×C41 | C8 | semidirect |
| 48. #7389 | C41 | direct (N × H) |
| 56. #1398 | C2×C41 | semidirect |
| 57. #1368 | C2×C41 | semidirect |
| 68. C41 | #7389 | direct (N × H) |
| 71. Q32 | C8×C41 | semidirect |
| 73. D16 | C8×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#2179 | 2 |
| C41×#1398 | 2 |
| C41×#1368 | 2 |
| #7389 | 41 |