Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
1222 conjugacy classes of subgroups; only the 318 normal subgroups are shown.
This group has 1222 conjugacy classes of subgroups — too many to draw. Only its 318 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C41 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C41 |
| prime radical | C41×#2867 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ C43×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C41×#486 | C2 | semidirect |
| 3. C41×#2862 | C2 | semidirect |
| 4. C41×#1961 | C2 | semidirect |
| 5. C4×#97×C41 | C2 | semidirect |
| 33. C4×C8×C41 | D4 | semidirect |
| 72. #33235 | C41 | direct (N × H) |
| 83. C2×#486 | C2×C41 | semidirect |
| 85. #2862 | C2×C41 | semidirect |
| 86. #1961 | C2×C41 | semidirect |
| 87. C4×#97 | C2×C41 | semidirect |
| 103. C41 | #33235 | direct (N × H) |
| 120. C4×C8 | D4×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C41×#486 | 2 |
| C41×#2867 | 2 |
| C41×#2862 | 2 |
| C41×#1961 | 2 |
| C4×#97×C41 | 2 |
| #33235 | 41 |