↑

Learn more

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 (41 matches)

  displayed columns for results
Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
216.66.108.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $\He_3:Q_8$ $2^{3} \cdot 3^{3}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
216.67.108.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4\times C_3^2:S_3$ $2^{3} \cdot 3^{3}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
216.68.108.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_3^2:D_{12}$ $2^{3} \cdot 3^{3}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
216.71.108.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6^2.S_3$ $2^{3} \cdot 3^{3}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
216.72.108.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6^2:S_3$ $2^{3} \cdot 3^{3}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
216.113.108.a1 $C_2$ $2$ ✓ ✓ ✓ $C_6^2:S_3$ $2^{3} \cdot 3^{3}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
324.75.108.b1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_3^2:D_{18}$ $2^{2} \cdot 3^{4}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
324.77.108.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_3^3:D_6$ $2^{2} \cdot 3^{4}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
324.78.108.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $\He_3.D_6$ $2^{2} \cdot 3^{4}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
324.79.108.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $\He_3:D_6$ $2^{2} \cdot 3^{4}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
324.80.108.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $(C_3\times C_{18}).S_3$ $2^{2} \cdot 3^{4}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
324.122.108.b1 $C_3$ $3$ ✓ ✓ ✓ $C_3^2:S_3^2$ $2^{2} \cdot 3^{4}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
324.145.108.b1 $C_3$ $3$ ✓ ✓ ✓ $C_3^3:D_6$ $2^{2} \cdot 3^{4}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
324.150.108.b1 $C_3$ $3$ ✓ ✓ ✓ $C_3^3:D_6$ $2^{2} \cdot 3^{4}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
432.538.108.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
540.49.108.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $\He_3:D_{10}$ $2^{2} \cdot 3^{3} \cdot 5$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
540.74.108.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ ✓ $C_3^2:S_3\times C_{10}$ $2^{2} \cdot 3^{3} \cdot 5$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
540.76.108.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $C_3^2:D_{30}$ $2^{2} \cdot 3^{3} \cdot 5$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
756.93.108.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $\He_3:D_{14}$ $2^{2} \cdot 3^{3} \cdot 7$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
756.130.108.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ ✓ $C_3^2:S_3\times C_{14}$ $2^{2} \cdot 3^{3} \cdot 7$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
756.132.108.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $C_3^2:D_{42}$ $2^{2} \cdot 3^{3} \cdot 7$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
1188.36.108.a1.a1 $C_{11}$ $11$ $11$ ✓ ✓ ✓ $\He_3:D_{22}$ $2^{2} \cdot 3^{3} \cdot 11$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
1188.61.108.a1.a1 $C_{11}$ $11$ $11$ ✓ ✓ ✓ ✓ $C_3^2:S_3\times C_{22}$ $2^{2} \cdot 3^{3} \cdot 11$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
1188.63.108.a1.a1 $C_{11}$ $11$ $11$ ✓ ✓ ✓ $C_3^2:D_{66}$ $2^{2} \cdot 3^{3} \cdot 11$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
1404.117.108.a1.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ $\He_3:D_{26}$ $2^{2} \cdot 3^{3} \cdot 13$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
1404.154.108.a1.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ ✓ $C_3^2:D_6\times C_{13}$ $2^{2} \cdot 3^{3} \cdot 13$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
1404.156.108.a1.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ $C_3^2:D_{78}$ $2^{2} \cdot 3^{3} \cdot 13$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
1836.48.108.a1.a1 $C_{17}$ $17$ $17$ ✓ ✓ ✓ $\He_3:D_{34}$ $2^{2} \cdot 3^{3} \cdot 17$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
1836.73.108.a1.a1 $C_{17}$ $17$ $17$ ✓ ✓ ✓ ✓ $C_3^2:D_6\times C_{17}$ $2^{2} \cdot 3^{3} \cdot 17$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
1836.75.108.a1.a1 $C_{17}$ $17$ $17$ ✓ ✓ ✓ $C_3^2:D_{102}$ $2^{2} \cdot 3^{3} \cdot 17$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
2700.q.108.a1.a1 $C_5^2$ $5^{2}$ $5$ ✓ ✓ ✓ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
6480.cn.108.a1 $A_5$ $2^{2} \cdot 3 \cdot 5$ ✓ ✓ $C_3^2:S_3\times S_5$ $2^{4} \cdot 3^{4} \cdot 5$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
6912.bn.108.a1 $C_2^6$ $2^{6}$ ✓ ✓ ✓ $C_2^2:A_4^2:D_6$ $2^{8} \cdot 3^{3}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
18144.f.108.a1 $\PSL(2,7)$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ $C_3^2:D_6\times \GL(3,2)$ $2^{5} \cdot 3^{4} \cdot 7$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
37044.r.108.a1 $C_7^3$ $7^{3}$ $7$ ✓ ✓ ✓ $C_7^3:C_3^2:D_6$ $2^{2} \cdot 3^{3} \cdot 7^{3}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
37044.x.108.a1 $C_7^3$ $7^{3}$ $7$ ✓ ✓ ✓ $C_7^3:C_3^2:D_6$ $2^{2} \cdot 3^{3} \cdot 7^{3}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
37044.y.108.a1 $C_7^3$ $7^{3}$ $7$ ✓ ✓ ✓ $C_7^3:C_3^2:D_6$ $2^{2} \cdot 3^{3} \cdot 7^{3}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
38880.bf.108.a1 $A_6$ $2^{3} \cdot 3^{2} \cdot 5$ ✓ ✓ $C_3^2:S_3\times S_6$ $2^{5} \cdot 3^{5} \cdot 5$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
237276.f.108.a1 $C_{13}^3$ $13^{3}$ $13$ ✓ ✓ ✓ $C_{13}^3:C_3^2:D_6$ $2^{2} \cdot 3^{3} \cdot 13^{3}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
1687500.i.108.a1 $C_5^6$ $5^{6}$ $5$ ✓ ✓ ✓ $C_5^6:\He_3:C_2^2$ $2^{2} \cdot 3^{3} \cdot 5^{6}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
23328000.d.108.A $A_5^3$ $2^{6} \cdot 3^{3} \cdot 5^{3}$ ✓ ✓ $A_5^3.C_3^2:D_6$ $2^{8} \cdot 3^{6} \cdot 5^{3}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
  displayed columns for results