Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
182 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 65 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 | #12067 |
| commutator | C2×C16 | C22×C8 |
| Frattini, cosocle | #1311 | C23 |
| prime radical | C2×D16 | C2×C8 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ C82 ◁ #7053 ◁ G | |
| LECS | G ▷ #1311 ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #122962 | C2 | semidirect |
| 4. #93877 | C2 | semidirect |
| 5. #93758 | C2 | semidirect |
| 7. #93668 | C2 | semidirect |
| 83. Q32 | M32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #151083 | 2 |
| #122966 | 2 |
| #122962 | 2 |
| #93877 | 2 |
| #93758 | 2 |
| #93757 | 2 |
| #93668 | 2 |