Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
372 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C41 | #127 |
| commutator, Frattini, cosocle | C2×C42 | C23×C41 |
| socle | C22×C41 | #399 |
| prime radical | C22×D4×C41 | Q8 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C41 ◁ C2×C42×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C41×#1849 | C2 | semidirect |
| 3. C41×#1570 | C2 | semidirect |
| 5. C41×#1275 | C2 | semidirect |
| 82. #10661 | C41 | direct (N × H) |
| 99. #1849 | C2×C41 | semidirect |
| 100. #1570 | C2×C41 | semidirect |
| 102. #1275 | C2×C41 | semidirect |
| 117. C41 | #10661 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#1955 | 2 |
| C41×#1849 | 2 |
| C41×#1570 | 2 |
| C41×#1486 | 2 |
| C41×#1275 | 2 |
| #10661 | 41 |