Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
1146 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 1146 conjugacy classes of subgroups — too many to draw. Only its 158 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 | C22×Q8 | C23×C41 |
| prime radical | C23×D4×C41 | C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C24×C41 ◁ C23×Q8×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C41×#355 | C2 | semidirect |
| 3. C41×#1784 | C2 | semidirect |
| 13. C2×#101×C41 | C22 | semidirect |
| 129. #12699 | C41 | direct (N × H) |
| 140. C22×C41 | #355 | semidirect |
| 150. C2×#355 | C2×C41 | semidirect |
| 151. #1784 | C2×C41 | semidirect |
| 167. C2×#101 | C22×C41 | semidirect |
| 170. C41 | #12699 | direct (N × H) |
| 294. C22 | C41×#355 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#124×C41 | 2 |
| C2×C41×#355 | 2 |
| C41×#1784 | 2 |
| #12699 | 41 |