Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
1062 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 1062 conjugacy classes of subgroups — too many to draw. Only its 226 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C41 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C41 |
| prime radical | C41×#2847 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ C24×C4×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C41×#2848 | C2 | semidirect |
| 3. C41×#2077 | C2 | semidirect |
| 4. C41×#2035 | C2 | semidirect |
| 5. C41×#2034 | C2 | semidirect |
| 6. C41×#2000 | C2 | semidirect |
| 7. C41×#1779 | C2 | semidirect |
| 9. C22×SD16×C41 | C22 | semidirect |
| 13. C2×#106×C41 | C22 | semidirect |
| 14. C2×#103×C41 | C22 | semidirect |
| 15. C2×#102×C41 | C22 | semidirect |
| 23. C41×#340 | C22 | semidirect |
| 24. C41×#340 | C22 | semidirect |
| 58. C24×C41 | SD16 | semidirect |
| 134. #32708 | C41 | direct (N × H) |
| 155. #2848 | C2×C41 | semidirect |
| 157. #2077 | C2×C41 | semidirect |
| 158. #2035 | C2×C41 | semidirect |
| 159. #2034 | C2×C41 | semidirect |
| 160. #2000 | C2×C41 | semidirect |
| 161. #1779 | C2×C41 | semidirect |
| 168. C22×SD16 | C22×C41 | semidirect |
| 172. C2×#106 | C22×C41 | semidirect |
| 173. C2×#103 | C22×C41 | semidirect |
| 174. C2×#102 | C22×C41 | semidirect |
| 182. #340 | C22×C41 | semidirect |
| 183. #340 | C22×C41 | semidirect |
| 184. C41 | #32708 | direct (N × H) |
| 218. C24 | SD16×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#2848 | 2 |
| C41×#2847 | 2 |
| C41×#2077 | 2 |
| C41×#2035 | 2 |
| C41×#2034 | 2 |
| C41×#2000 | 2 |
| C41×#1779 | 2 |
| #32708 | 41 |