Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
992 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 222 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×#120 |
| commutator, Frattini, cosocle | C42 | C24×C41 |
| prime radical | C41×#3549 | 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×#3216 | C2 | semidirect |
| 3. C41×#3135 | C2 | semidirect |
| 4. C41×#1659 | C2 | semidirect |
| 5. C41×#1536 | C2 | semidirect |
| 6. C41×#1530 | C2 | semidirect |
| 14. C41×#533 | C22 | semidirect |
| 17. C41×#497 | C22 | semidirect |
| 20. C41×#489 | C22 | semidirect |
| 21. C41×#489 | C22 | semidirect |
| 25. C41×#432 | C22 | semidirect |
| 27. C2×#97×C41 | C22 | semidirect |
| 28. C41×#329 | C22 | semidirect |
| 29. C41×#329 | C22 | semidirect |
| 149. #19056 | C41 | direct (N × H) |
| 167. #3216 | C2×C41 | semidirect |
| 168. #3135 | C2×C41 | semidirect |
| 169. #1659 | C2×C41 | semidirect |
| 170. #1536 | C2×C41 | semidirect |
| 171. #1530 | C2×C41 | semidirect |
| 184. #533 | C22×C41 | semidirect |
| 187. #497 | C22×C41 | semidirect |
| 190. #489 | C22×C41 | semidirect |
| 191. #489 | C22×C41 | semidirect |
| 195. #432 | C22×C41 | semidirect |
| 197. C2×#97 | C22×C41 | semidirect |
| 198. #329 | C22×C41 | semidirect |
| 199. #329 | C22×C41 | semidirect |
| 200. C41 | #19056 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#3549 | 2 |
| C41×#3216 | 2 |
| C41×#3135 | 2 |
| C41×#1659 | 2 |
| C41×#1536 | 2 |
| C41×#1530 | 2 |
| #19056 | 41 |