Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
288 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C41 | #447 |
| commutator, Frattini, cosocle | C4×C8 | C23×C41 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C42×C41 ◁ C8×Q8×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 90. Q8×C41 | Q32 | semidirect |
| 105. #12358 | C41 | direct (N × H) |
| 145. C41 | #12358 | direct (N × H) |
| 211. Q8 | Q32×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Q16×C41 | 2 |
| C41×#2241 | 2 |
| C41×#2209 | 2 |
| C41×#1670 | 2 |
| C41×#1365 | 2 |
| C41×Q8⋊C16 | 2 |
| C41×#1332 | 2 |
| #12358 | 41 |