Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
440 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 102 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 | C2×#99 |
| commutator | C22×C4 | C22×C4×C41 |
| Frattini, cosocle | C2×C4⋊C4 | C23×C41 |
| prime radical | C2×#121×C41 | C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C24×C41 ◁ C22×C4⋊C4×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C41×#1463 | C2 | semidirect |
| 3. C2×C41×#324 | C2 | semidirect |
| 4. C41×#1324 | C2 | semidirect |
| 5. C41×#1318 | C2 | semidirect |
| 149. #11553 | C41 | direct (N × H) |
| 180. #1463 | C2×C41 | semidirect |
| 181. C2×#324 | C2×C41 | semidirect |
| 182. #1324 | C2×C41 | semidirect |
| 183. #1318 | C2×C41 | semidirect |
| 209. C41 | #11553 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#2504 | 2 |
| C41×#1463 | 2 |
| C2×C41×#324 | 2 |
| C41×#1324 | 2 |
| C41×#1318 | 2 |
| #11553 | 41 |