Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
568 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C41 | #469 |
| commutator, Frattini, cosocle | C22×C8 | C23×C41 |
| socle | C2×C41 | #1999 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C41 ◁ C22×C4×C41 ◁ C23×C8×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C41×#3414 | C2 | semidirect |
| 2. C41×#3050 | C2 | semidirect |
| 3. C41×#2145 | C2 | semidirect |
| 4. C41×#2112 | C2 | semidirect |
| 5. C41×#1384 | C2 | semidirect |
| 27. C2×Q16×C41 | D4 | semidirect |
| 29. C2×D8×C41 | D4 | semidirect |
| 48. C2×C16×C41 | D4 | semidirect |
| 50. #106×C41 | D4 | semidirect |
| 121. #13309 | C41 | direct (N × H) |
| 138. #3414 | C2×C41 | semidirect |
| 139. #3050 | C2×C41 | semidirect |
| 140. #2145 | C2×C41 | semidirect |
| 141. #2112 | C2×C41 | semidirect |
| 142. #1384 | C2×C41 | semidirect |
| 163. C41 | #13309 | direct (N × H) |
| 170. C2×Q16 | D4×C41 | semidirect |
| 172. C2×D8 | D4×C41 | semidirect |
| 191. C2×C16 | D4×C41 | semidirect |
| 193. #106 | D4×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#3414 | 2 |
| C41×#3050 | 2 |
| C41×#2145 | 2 |
| C41×#2112 | 2 |
| C41×#1384 | 2 |
| #13309 | 41 |