Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
936 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 230 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×#120 |
| commutator, Frattini, cosocle | C42 | C24×C41 |
| prime radical | C41×#3548 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C2×C42×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C41×#3141 | C2 | semidirect |
| 3. C41×#3139 | C2 | semidirect |
| 4. C41×#1662 | C2 | semidirect |
| 5. C41×#1526 | C2 | semidirect |
| 6. C41×#1525 | C2 | semidirect |
| 128. #19080 | C41 | direct (N × H) |
| 143. #3141 | C2×C41 | semidirect |
| 144. #3139 | C2×C41 | semidirect |
| 145. #1662 | C2×C41 | semidirect |
| 146. #1526 | C2×C41 | semidirect |
| 147. #1525 | C2×C41 | semidirect |
| 172. C41 | #19080 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#3548 | 2 |
| C41×#3141 | 2 |
| C41×#3139 | 2 |
| C41×#1662 | 2 |
| C41×#1526 | 2 |
| C41×#1525 | 2 |
| #19080 | 41 |