Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
576 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 118 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 | #386 |
| commutator | C42 | C22×C4×C41 |
| Frattini, cosocle | C2×C42 | C23×C41 |
| prime radical | C41×#3153 | C2 |
| LCS | G ▷ C42 ▷ 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×#2372 | C2 | semidirect |
| 3. C41×#1533 | C2 | semidirect |
| 4. C41×#1505 | C2 | semidirect |
| 5. C41×#1300 | C2 | semidirect |
| 10. C41×#497 | C4 | semidirect |
| 11. C41×#496 | C4 | semidirect |
| 36. C4⋊Q8×C41 | C2×C4 | semidirect |
| 37. #127×C41 | C2×C4 | semidirect |
| 54. #97×C41 | C2×C4 | semidirect |
| 145. #9441 | C41 | direct (N × H) |
| 166. #2372 | C2×C41 | semidirect |
| 167. #1533 | C2×C41 | semidirect |
| 168. #1505 | C2×C41 | semidirect |
| 169. #1300 | C2×C41 | semidirect |
| 180. #497 | C4×C41 | semidirect |
| 181. #496 | C4×C41 | semidirect |
| 193. C41 | #9441 | direct (N × H) |
| 207. C4⋊Q8 | C2×C4×C41 | semidirect |
| 208. #127 | C2×C4×C41 | semidirect |
| 225. #97 | C2×C4×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#3153 | 2 |
| C41×#2372 | 2 |
| C41×#1533 | 2 |
| C41×#1505 | 2 |
| C41×#1300 | 2 |
| #9441 | 41 |