Order 10496.
708 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 254 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 | C22×D4×C41 | C23 |
| 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. C41×#2864 | C2 | semidirect |
| 3. C41×#1991 | C2 | semidirect |
| 6. C41×#1933 | C2 | semidirect |
| 7. C42×C8×C41 | C2 | semidirect |
| 87. #33279 | C41 | direct (N × H) |
| 100. #2864 | C2×C41 | semidirect |
| 102. #1991 | C2×C41 | semidirect |
| 105. #1933 | C2×C41 | semidirect |
| 106. C42×C8 | C2×C41 | semidirect |
| 125. C41 | #33279 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#2864 | 2 |
| C41×#2861 | 2 |
| C41×#1991 | 2 |
| C41×#1958 | 2 |
| C41×#1934 | 2 |
| C41×#1933 | 2 |
| C42×C8×C41 | 2 |
| #33279 | 41 |