Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
410 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C8×C41 | #127 |
| commutator | C22×C4 | C22×C4×C41 |
| Frattini, cosocle | C22×C8 | C23×C41 |
| socle | C2×C41 | #1955 |
| prime radical | C41×#575 | C4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C41 ◁ C22×C8×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C41×#2151 | C2 | semidirect |
| 3. C41×#2117 | C2 | semidirect |
| 4. C41×#2113 | C2 | semidirect |
| 5. C41×#2110 | C2 | semidirect |
| 97. #13198 | C41 | direct (N × H) |
| 109. #2151 | C2×C41 | semidirect |
| 110. #2117 | C2×C41 | semidirect |
| 111. #2113 | C2×C41 | semidirect |
| 112. #2110 | C2×C41 | semidirect |
| 131. C41 | #13198 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#2955 | 2 |
| C41×#2151 | 2 |
| C41×#2117 | 2 |
| C41×#2113 | 2 |
| C41×#2110 | 2 |
| #13198 | 41 |