Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
348 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 78 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 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C41 |
| prime radical | C41×#3191 | C2 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C22×C4×C41 ◁ C2×C22⋊C8×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C41×#2235 | C2 | semidirect |
| 3. C41×#2232 | C2 | semidirect |
| 4. C41×#2075 | C2 | semidirect |
| 5. C41×#1348 | C2 | semidirect |
| 6. C41×#1347 | C2 | semidirect |
| 7. C41×#1314 | C2 | semidirect |
| 139. #12280 | C41 | direct (N × H) |
| 163. #2235 | C2×C41 | semidirect |
| 164. #2232 | C2×C41 | semidirect |
| 165. #2075 | C2×C41 | semidirect |
| 166. #1348 | C2×C41 | semidirect |
| 167. #1347 | C2×C41 | semidirect |
| 168. #1314 | C2×C41 | semidirect |
| 195. C41 | #12280 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#3191 | 2 |
| C41×#2235 | 2 |
| C41×#2232 | 2 |
| C41×#2075 | 2 |
| C41×#1348 | 2 |
| C41×#1347 | 2 |
| C41×#1314 | 2 |
| #12280 | 41 |