Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
496 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 102 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 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C41 |
| prime radical | C41×#532 | C22 |
| LCS | G ▷ C2×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 |
|---|---|---|
| 3. C41×#2660 | C2 | semidirect |
| 4. C41×#1556 | C2 | semidirect |
| 5. C41×#1528 | C2 | semidirect |
| 7. C41×#1300 | C2 | semidirect |
| 150. #10093 | C41 | direct (N × H) |
| 171. #2660 | C2×C41 | semidirect |
| 172. #1556 | C2×C41 | semidirect |
| 173. #1528 | C2×C41 | semidirect |
| 175. #1300 | C2×C41 | semidirect |
| 204. C41 | #10093 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#3234 | 2 |
| C41×#3141 | 2 |
| C41×#2660 | 2 |
| C41×#1556 | 2 |
| C41×#1528 | 2 |
| C41×#1505 | 2 |
| C41×#1300 | 2 |
| #10093 | 41 |