↑

Learn more

Note: Search results may be incomplete due to uncomputed quantities: Subgroup label (103813812 objects)

Refine search

Subgroup label Subgroup order Cyclic Abelian Solvable
Normal Characteristic Perfect Maximal Central
Ambient label Ambient order Direct product Semidirect product
Quotient label Subgroup index Cyclic quotient Abelian quotient Solvable quotient
Maximal quotient Non-trivial proper Hall subgroup Sylow subgroup
Sort order Select

Results (46 matches)

  displayed columns for results
Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
128.162.2.b1.a1 $Q_{64}$ $2^{6}$ ✓ ✓ ✓ $\SD_{128}$ $2^{7}$ $C_2$ $2$ ✓
128.163.2.a1.a1 $Q_{64}$ $2^{6}$ ✓ ✓ $Q_{128}$ $2^{7}$ $C_2$ $2$ ✓
128.163.2.a1.b1 $Q_{64}$ $2^{6}$ ✓ ✓ $Q_{128}$ $2^{7}$ $C_2$ $2$ ✓
128.993.2.c1.a1 $Q_{64}$ $2^{6}$ ✓ ✓ $C_2\times Q_{64}$ $2^{7}$ $C_2$ $2$ ✓
128.993.2.c1.b1 $Q_{64}$ $2^{6}$ ✓ ✓ $C_2\times Q_{64}$ $2^{7}$ $C_2$ $2$ ✓
128.993.2.c1.c1 $Q_{64}$ $2^{6}$ ✓ ✓ $C_2\times Q_{64}$ $2^{7}$ $C_2$ $2$ ✓
128.993.2.c1.d1 $Q_{64}$ $2^{6}$ ✓ ✓ $C_2\times Q_{64}$ $2^{7}$ $C_2$ $2$ ✓
128.994.2.e1.a1 $Q_{64}$ $2^{6}$ ✓ ✓ ✓ $D_{32}:C_2$ $2^{7}$ $C_2$ $2$ ✓
128.996.2.e1.a1 $Q_{64}$ $2^{6}$ ✓ ✓ $Q_{64}:C_2$ $2^{7}$ $C_2$ $2$ ✓
128.996.2.e1.b1 $Q_{64}$ $2^{6}$ ✓ ✓ $Q_{64}:C_2$ $2^{7}$ $C_2$ $2$ ✓
192.9.3.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ $C_3:Q_{64}$ $2^{6} \cdot 3$ $3$ $-$
192.81.3.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ $C_3:Q_{64}$ $2^{6} \cdot 3$ $3$ $-$
192.179.3.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ ✓ ✓ $C_3\times Q_{64}$ $2^{6} \cdot 3$ $C_3$ $3$ ✓
320.8.5.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ $C_5:Q_{64}$ $2^{6} \cdot 5$ $5$ $-$
320.80.5.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ $C_5:Q_{64}$ $2^{6} \cdot 5$ $5$ $-$
320.178.5.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ ✓ ✓ $C_5\times Q_{64}$ $2^{6} \cdot 5$ $C_5$ $5$ ✓
448.7.7.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ $C_7:Q_{64}$ $2^{6} \cdot 7$ $7$ $-$
448.79.7.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ $C_7:Q_{64}$ $2^{6} \cdot 7$ $7$ $-$
448.177.7.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ ✓ ✓ $C_7\times Q_{64}$ $2^{6} \cdot 7$ $C_7$ $7$ ✓
576.1908.9.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ $C_3^2:Q_{64}$ $2^{6} \cdot 3^{2}$ $3^{2}$ $-$
704.7.11.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ $C_{11}:Q_{64}$ $2^{6} \cdot 11$ $11$ $-$
704.79.11.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ $C_{11}:Q_{64}$ $2^{6} \cdot 11$ $11$ $-$
704.177.11.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ ✓ ✓ $C_{11}\times Q_{64}$ $2^{6} \cdot 11$ $C_{11}$ $11$ ✓
832.8.13.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ $C_{13}:Q_{64}$ $2^{6} \cdot 13$ $13$ $-$
832.80.13.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ $C_{13}:Q_{64}$ $2^{6} \cdot 13$ $13$ $-$
832.178.13.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ ✓ ✓ $C_{13}\times Q_{64}$ $2^{6} \cdot 13$ $C_{13}$ $13$ ✓
1088.54.17.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ ✓ ✓ $C_{17}\times Q_{64}$ $2^{6} \cdot 17$ $C_{17}$ $17$ ✓
1088.389.17.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ $C_{17}:Q_{64}$ $2^{6} \cdot 17$ $17$ $-$
1088.390.17.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ $C_{17}:Q_{64}$ $2^{6} \cdot 17$ $17$ $-$
1216.54.19.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ ✓ ✓ $C_{19}\times Q_{64}$ $2^{6} \cdot 19$ $C_{19}$ $19$ ✓
1216.389.19.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ $C_{19}:Q_{64}$ $2^{6} \cdot 19$ $19$ $-$
1216.390.19.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ $C_{19}:Q_{64}$ $2^{6} \cdot 19$ $19$ $-$
1472.54.23.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ ✓ ✓ $C_{23}\times Q_{64}$ $2^{6} \cdot 23$ $C_{23}$ $23$ ✓
1472.389.23.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ $C_{23}:Q_{64}$ $2^{6} \cdot 23$ $23$ $-$
1472.390.23.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ $C_{23}:Q_{64}$ $2^{6} \cdot 23$ $23$ $-$
1600.2310.25.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ $C_5^2:Q_{64}$ $2^{6} \cdot 5^{2}$ $5^{2}$ $-$
1856.54.29.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ ✓ ✓ $C_{29}\times Q_{64}$ $2^{6} \cdot 29$ $C_{29}$ $29$ ✓
1856.389.29.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ $C_{29}:Q_{64}$ $2^{6} \cdot 29$ $29$ $-$
1856.390.29.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ $C_{29}:Q_{64}$ $2^{6} \cdot 29$ $29$ $-$
1984.54.31.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ ✓ ✓ $C_{31}\times Q_{64}$ $2^{6} \cdot 31$ $C_{31}$ $31$ ✓
1984.389.31.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ $C_{31}:Q_{64}$ $2^{6} \cdot 31$ $31$ $-$
1984.390.31.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ $C_{31}:Q_{64}$ $2^{6} \cdot 31$ $31$ $-$
2368.54.37.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ ✓ ✓ $C_{37}\times Q_{64}$ $2^{6} \cdot 37$ $C_{37}$ $37$ ✓
9792.b.153.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ $C_2.\PGL(2,17)$ $2^{6} \cdot 3^{2} \cdot 17$ $3^{2} \cdot 17$ $-$
12224.54.191.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ ✓ ✓ $Q_{64}\times C_{191}$ $2^{6} \cdot 191$ $C_{191}$ $191$ ✓
15296.54.239.a1.a1 $Q_{64}$ $2^{6}$ $2$ ✓ ✓ ✓ $Q_{64}\times C_{239}$ $2^{6} \cdot 239$ $C_{239}$ $239$ ✓
  displayed columns for results