Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
1026 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 1026 conjugacy classes of subgroups — too many to draw. Only its 154 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 | #379 |
| commutator | C22×C4 | C22×C4×C41 |
| Frattini, cosocle | C2×C42 | C23×C41 |
| prime radical | C41×#3496 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ 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×#1955 | C2 | semidirect |
| 3. C41×#1551 | C2 | semidirect |
| 4. C41×#1530 | C2 | semidirect |
| 5. C41×#1466 | C2 | semidirect |
| 15. C41×#432 | C22 | semidirect |
| 16. C2×C4⋊C8×C41 | C22 | semidirect |
| 18. C2×#97×C41 | C22 | semidirect |
| 142. #8456 | C41 | direct (N × H) |
| 164. #1955 | C2×C41 | semidirect |
| 165. #1551 | C2×C41 | semidirect |
| 166. #1530 | C2×C41 | semidirect |
| 167. #1466 | C2×C41 | semidirect |
| 183. #432 | C22×C41 | semidirect |
| 184. C2×C4⋊C8 | C22×C41 | semidirect |
| 186. C2×#97 | C22×C41 | semidirect |
| 191. C41 | #8456 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#3496 | 2 |
| C41×#1955 | 2 |
| C41×#1551 | 2 |
| C41×#1530 | 2 |
| C41×#1466 | 2 |
| #8456 | 41 |