Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
316 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 78 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 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C41 |
| prime radical | C41×#466 | C22 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C22×C4×C41 ◁ C2×C4⋊C8×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C41×#2235 | C2 | semidirect |
| 4. C41×#2086 | C2 | semidirect |
| 5. C41×#1348 | C2 | semidirect |
| 7. C41×#1322 | C2 | semidirect |
| 128. #12290 | C41 | direct (N × H) |
| 148. #2235 | C2×C41 | semidirect |
| 150. #2086 | C2×C41 | semidirect |
| 151. #1348 | C2×C41 | semidirect |
| 153. #1322 | C2×C41 | semidirect |
| 179. C41 | #12290 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#3250 | 2 |
| C41×#2235 | 2 |
| C41×#2232 | 2 |
| C41×#2086 | 2 |
| C41×#1348 | 2 |
| C41×#1347 | 2 |
| C41×#1322 | 2 |
| #12290 | 41 |