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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
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Results (1-50 of 53 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
216.49.108.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $\He_3:Q_8$ $2^{3} \cdot 3^{3}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
216.50.108.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4\times C_3^2:C_6$ $2^{3} \cdot 3^{3}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
216.51.108.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_3^2:D_{12}$ $2^{3} \cdot 3^{3}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
216.59.108.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6^2.C_6$ $2^{3} \cdot 3^{3}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
216.60.108.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6^2:C_6$ $2^{3} \cdot 3^{3}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
216.110.108.a1.a1 $C_2$ $2$ ✓ ✓ ✓ $C_6^2:C_6$ $2^{3} \cdot 3^{3}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
216.110.108.a1.b1 $C_2$ $2$ ✓ ✓ ✓ $C_6^2:C_6$ $2^{3} \cdot 3^{3}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
216.110.108.a1.c1 $C_2$ $2$ ✓ ✓ ✓ $C_6^2:C_6$ $2^{3} \cdot 3^{3}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
324.62.108.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_2\times C_3^2:C_{18}$ $2^{2} \cdot 3^{4}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
324.63.108.c1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_3^2:D_{18}$ $2^{2} \cdot 3^{4}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
324.68.108.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_3^3:D_6$ $2^{2} \cdot 3^{4}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
324.69.108.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $\He_3:D_6$ $2^{2} \cdot 3^{4}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
324.70.108.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $(C_3\times C_{18}):S_3$ $2^{2} \cdot 3^{4}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
324.71.108.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $\He_3.D_6$ $2^{2} \cdot 3^{4}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
324.72.108.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $(C_3\times C_{18}):S_3$ $2^{2} \cdot 3^{4}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
324.73.108.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $\He_3.D_6$ $2^{2} \cdot 3^{4}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
324.116.108.b1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_3^2:S_3^2$ $2^{2} \cdot 3^{4}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
324.138.108.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_3^2:C_6^2$ $2^{2} \cdot 3^{4}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
324.144.108.a1 $C_3$ $3$ ✓ ✓ $C_3^3:D_6$ $2^{2} \cdot 3^{4}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
432.535.108.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
432.542.108.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2\times C_6^2:C_6$ $2^{4} \cdot 3^{3}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
540.46.108.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $\He_3:D_{10}$ $2^{2} \cdot 3^{3} \cdot 5$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
540.67.108.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ ✓ $C_2\times C_3^2:C_{30}$ $2^{2} \cdot 3^{3} \cdot 5$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
540.71.108.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $C_3^2:D_{30}$ $2^{2} \cdot 3^{3} \cdot 5$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
756.60.108.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $(C_3\times F_7):S_3$ $2^{2} \cdot 3^{3} \cdot 7$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
756.80.108.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $(C_3\times C_{42}):C_6$ $2^{2} \cdot 3^{3} \cdot 7$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
756.85.108.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $C_2\times C_3^2:F_7$ $2^{2} \cdot 3^{3} \cdot 7$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
756.90.108.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $\He_3:D_{14}$ $2^{2} \cdot 3^{3} \cdot 7$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
756.123.108.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ ✓ $C_2\times C_3^2:C_{42}$ $2^{2} \cdot 3^{3} \cdot 7$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
756.127.108.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $C_3^2:D_{42}$ $2^{2} \cdot 3^{3} \cdot 7$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
1188.33.108.a1.a1 $C_{11}$ $11$ $11$ ✓ ✓ ✓ $\He_3:D_{22}$ $2^{2} \cdot 3^{3} \cdot 11$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
1188.54.108.a1.a1 $C_{11}$ $11$ $11$ ✓ ✓ ✓ ✓ $C_2\times C_3^2:C_{66}$ $2^{2} \cdot 3^{3} \cdot 11$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
1188.58.108.a1.a1 $C_{11}$ $11$ $11$ ✓ ✓ ✓ $C_3^2:D_{66}$ $2^{2} \cdot 3^{3} \cdot 11$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
1404.74.108.a1.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ $(C_3^2\times D_{13}):C_6$ $2^{2} \cdot 3^{3} \cdot 13$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
1404.94.108.a1.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ $(C_3\times C_{78}):C_6$ $2^{2} \cdot 3^{3} \cdot 13$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
1404.99.108.a1.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ $(C_3\times C_{78}):C_6$ $2^{2} \cdot 3^{3} \cdot 13$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
1404.114.108.a1.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ $\He_3:D_{26}$ $2^{2} \cdot 3^{3} \cdot 13$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
1404.147.108.a1.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ ✓ $C_2\times C_3^2:C_{78}$ $2^{2} \cdot 3^{3} \cdot 13$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
1404.151.108.a1.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ $C_3^2:D_{78}$ $2^{2} \cdot 3^{3} \cdot 13$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
1728.46108.108.a1.a1 $C_2^4$ $2^{4}$ ✓ ✓ ✓ $C_6.A_4\wr C_2$ $2^{6} \cdot 3^{3}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
1836.45.108.a1.a1 $C_{17}$ $17$ $17$ ✓ ✓ ✓ $\He_3:D_{34}$ $2^{2} \cdot 3^{3} \cdot 17$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
1836.66.108.a1.a1 $C_{17}$ $17$ $17$ ✓ ✓ ✓ ✓ $C_2\times C_3^2:C_{102}$ $2^{2} \cdot 3^{3} \cdot 17$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
1836.70.108.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.l.108.a1.a1 $C_5^2$ $5^{2}$ $5$ ✓ ✓ ✓ $C_{15}^2:(C_2\times C_6)$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
2700.s.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.cl.108.a1.a1 $A_5$ $2^{2} \cdot 3 \cdot 5$ ✓ ✓ $C_3^2:C_6\times S_5$ $2^{4} \cdot 3^{4} \cdot 5$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
6912.bk.108.a1 $C_2^6$ $2^{6}$ ✓ ✓ ✓ $C_2^3:A_4^2:C_6$ $2^{8} \cdot 3^{3}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
38880.bg.108.a1 $A_6$ $2^{3} \cdot 3^{2} \cdot 5$ ✓ ✓ $C_3^2:C_6\times S_6$ $2^{5} \cdot 3^{5} \cdot 5$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
1687500.g.108.a1 $C_5^6$ $5^{6}$ $5$ ✓ ✓ ✓ $C_5^6:\He_3:C_2^2$ $2^{2} \cdot 3^{3} \cdot 5^{6}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
12706092.j.108.a1.a1 $C_7^6$ $7^{6}$ $7$ ✓ ✓ ✓ $C_7^6.\He_3.C_2^2$ $2^{2} \cdot 3^{3} \cdot 7^{6}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓
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