Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
878 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 878 conjugacy classes of subgroups — too many to draw. Only its 126 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 | C24 | C22×C4×C41 |
| Frattini, cosocle | C23×C4 | C23×C41 |
| prime radical | C41×#2408 | C2 |
| LCS | G ▷ C24 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C23×C4×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C41×#2975 | C2 | semidirect |
| 3. C41×#1783 | C2 | semidirect |
| 4. C41×#1465 | C2 | semidirect |
| 5. C41×#1305 | C2 | semidirect |
| 35. C2×M16×C41 | D4 | semidirect |
| 152. C2×C4×C41 | #100 | semidirect |
| 158. #9504 | C41 | direct (N × H) |
| 190. #2975 | C2×C41 | semidirect |
| 192. #1783 | C2×C41 | semidirect |
| 193. #1465 | C2×C41 | semidirect |
| 194. #1305 | C2×C41 | semidirect |
| 220. C41 | #9504 | direct (N × H) |
| 233. C2×M16 | D4×C41 | semidirect |
| 350. C2×C4 | #100×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#2975 | 2 |
| C41×#2408 | 2 |
| C41×#1783 | 2 |
| C41×#1465 | 2 |
| C41×#1305 | 2 |
| #9504 | 41 |