Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
328 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C41 | #1613 |
| commutator, Frattini, cosocle | C2×M16 | C23×C41 |
| prime radical | C41×#3197 | C2 |
| LCS | G ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C41 ◁ C2×C4×C41 ◁ C2×M16×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C41×#2239 | C2 | semidirect |
| 3. C41×#2238 | C2 | semidirect |
| 4. C41×#2091 | C2 | semidirect |
| 5. C41×#1342 | C2 | semidirect |
| 6. C41×#1341 | C2 | semidirect |
| 7. C41×#1320 | C2 | semidirect |
| 131. #12300 | C41 | direct (N × H) |
| 151. #2239 | C2×C41 | semidirect |
| 152. #2238 | C2×C41 | semidirect |
| 153. #2091 | C2×C41 | semidirect |
| 154. #1342 | C2×C41 | semidirect |
| 155. #1341 | C2×C41 | semidirect |
| 156. #1320 | C2×C41 | semidirect |
| 181. C41 | #12300 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#3197 | 2 |
| C41×#2239 | 2 |
| C41×#2238 | 2 |
| C41×#2091 | 2 |
| C41×#1342 | 2 |
| C41×#1341 | 2 |
| C41×#1320 | 2 |
| #12300 | 41 |