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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 141 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
64.98.32.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^3.D_4$ $2^{6}$ $Q_{16}:C_2$ $2^{5}$ ✓
64.100.32.b1.a1 $C_2$ $2$ ✓ ✓ ✓ $C_2^3.D_4$ $2^{6}$ $Q_{16}:C_2$ $2^{5}$ ✓
64.100.32.b1.b1 $C_2$ $2$ ✓ ✓ ✓ $C_2^3.D_4$ $2^{6}$ $Q_{16}:C_2$ $2^{5}$ ✓
64.109.32.c1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $\OD_{16}:C_4$ $2^{6}$ $Q_{16}:C_2$ $2^{5}$ ✓
64.121.32.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $\SD_{16}:C_4$ $2^{6}$ $Q_{16}:C_2$ $2^{5}$ ✓
64.122.32.a1.a1 $C_2$ $2$ ✓ ✓ ✓ $Q_{16}:C_4$ $2^{6}$ $Q_{16}:C_2$ $2^{5}$ ✓
64.122.32.a1.b1 $C_2$ $2$ ✓ ✓ ✓ $Q_{16}:C_4$ $2^{6}$ $Q_{16}:C_2$ $2^{5}$ ✓
64.129.32.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $Q_8:D_4$ $2^{6}$ $Q_{16}:C_2$ $2^{5}$ ✓
64.132.32.c1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^2:Q_{16}$ $2^{6}$ $Q_{16}:C_2$ $2^{5}$ ✓
64.133.32.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_4.D_4$ $2^{6}$ $Q_{16}:C_2$ $2^{5}$ ✓
64.142.32.c1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4:\SD_{16}$ $2^{6}$ $Q_{16}:C_2$ $2^{5}$ ✓
64.143.32.c1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4:Q_{16}$ $2^{6}$ $Q_{16}:C_2$ $2^{5}$ ✓
64.145.32.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $Q_8.D_4$ $2^{6}$ $Q_{16}:C_2$ $2^{5}$ ✓
64.149.32.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_8:D_4$ $2^{6}$ $Q_{16}:C_2$ $2^{5}$ ✓
64.151.32.b1.a1 $C_2$ $2$ ✓ ✓ ✓ $C_8.D_4$ $2^{6}$ $Q_{16}:C_2$ $2^{5}$ ✓
64.151.32.b1.b1 $C_2$ $2$ ✓ ✓ ✓ $C_8.D_4$ $2^{6}$ $Q_{16}:C_2$ $2^{5}$ ✓
64.155.32.c1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_4:Q_8$ $2^{6}$ $Q_{16}:C_2$ $2^{5}$ ✓
64.156.32.c1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $Q_8:Q_8$ $2^{6}$ $Q_{16}:C_2$ $2^{5}$ ✓
64.160.32.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $Q_8.Q_8$ $2^{6}$ $Q_{16}:C_2$ $2^{5}$ ✓
64.161.32.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^2.D_8$ $2^{6}$ $Q_{16}:C_2$ $2^{5}$ ✓
64.164.32.c1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^3.D_4$ $2^{6}$ $Q_{16}:C_2$ $2^{5}$ ✓
64.166.32.c1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^3.D_4$ $2^{6}$ $Q_{16}:C_2$ $2^{5}$ ✓
64.170.32.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.C_2^2$ $2^{6}$ $Q_{16}:C_2$ $2^{5}$ ✓
64.172.32.a1.a1 $C_2$ $2$ ✓ ✓ ✓ $C_4^2.C_2^2$ $2^{6}$ $Q_{16}:C_2$ $2^{5}$ ✓
64.172.32.a1.b1 $C_2$ $2$ ✓ ✓ ✓ $C_4^2.C_2^2$ $2^{6}$ $Q_{16}:C_2$ $2^{5}$ ✓
64.178.32.a1.a1 $C_2$ $2$ ✓ ✓ ✓ $C_8.D_4$ $2^{6}$ $Q_{16}:C_2$ $2^{5}$ ✓
64.178.32.a1.b1 $C_2$ $2$ ✓ ✓ ✓ $C_8.D_4$ $2^{6}$ $Q_{16}:C_2$ $2^{5}$ ✓
64.182.32.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_8:Q_8$ $2^{6}$ $Q_{16}:C_2$ $2^{5}$ ✓
64.255.32.a1 $C_2$ $2$ ✓ ✓ ✓ $Q_{16}:C_2^2$ $2^{6}$ $Q_{16}:C_2$ $2^{5}$ ✓
96.116.32.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ $C_4.D_{12}$ $2^{5} \cdot 3$ $Q_{16}:C_2$ $2^{5}$ ✓
96.122.32.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ $C_8.D_6$ $2^{5} \cdot 3$ $Q_{16}:C_2$ $2^{5}$ ✓
96.125.32.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ $Q_{16}:S_3$ $2^{5} \cdot 3$ $Q_{16}:C_2$ $2^{5}$ ✓
96.149.32.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ $C_{12}.D_4$ $2^{5} \cdot 3$ $Q_{16}:C_2$ $2^{5}$ ✓
96.158.32.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ $C_{12}.D_4$ $2^{5} \cdot 3$ $Q_{16}:C_2$ $2^{5}$ ✓
96.184.32.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ ✓ $Q_{16}:C_6$ $2^{5} \cdot 3$ $Q_{16}:C_2$ $2^{5}$ ✓
160.130.32.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $C_4.D_{20}$ $2^{5} \cdot 5$ $Q_{16}:C_2$ $2^{5}$ ✓
160.136.32.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $C_8.D_{10}$ $2^{5} \cdot 5$ $Q_{16}:C_2$ $2^{5}$ ✓
160.139.32.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $Q_{16}:D_5$ $2^{5} \cdot 5$ $Q_{16}:C_2$ $2^{5}$ ✓
160.163.32.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $C_{20}.D_4$ $2^{5} \cdot 5$ $Q_{16}:C_2$ $2^{5}$ ✓
160.172.32.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $C_{20}.D_4$ $2^{5} \cdot 5$ $Q_{16}:C_2$ $2^{5}$ ✓
160.198.32.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ ✓ $Q_{16}:C_{10}$ $2^{5} \cdot 5$ $Q_{16}:C_2$ $2^{5}$ ✓
224.104.32.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $C_4.D_{28}$ $2^{5} \cdot 7$ $Q_{16}:C_2$ $2^{5}$ ✓
224.110.32.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $C_8.D_{14}$ $2^{5} \cdot 7$ $Q_{16}:C_2$ $2^{5}$ ✓
224.113.32.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $Q_{16}:D_7$ $2^{5} \cdot 7$ $Q_{16}:C_2$ $2^{5}$ ✓
224.137.32.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $C_{28}.D_4$ $2^{5} \cdot 7$ $Q_{16}:C_2$ $2^{5}$ ✓
224.146.32.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $C_{28}.D_4$ $2^{5} \cdot 7$ $Q_{16}:C_2$ $2^{5}$ ✓
224.172.32.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ ✓ $Q_{16}:C_{14}$ $2^{5} \cdot 7$ $Q_{16}:C_2$ $2^{5}$ ✓
288.874.32.a1.a1 $C_3^2$ $3^{2}$ $3$ ✓ ✓ ✓ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$ $Q_{16}:C_2$ $2^{5}$ ✓
288.887.32.a1.a1 $C_3^2$ $3^{2}$ $3$ ✓ ✓ ✓ $C_6^2.D_4$ $2^{5} \cdot 3^{2}$ $Q_{16}:C_2$ $2^{5}$ ✓
352.104.32.a1.a1 $C_{11}$ $11$ $11$ ✓ ✓ ✓ $C_4.D_{44}$ $2^{5} \cdot 11$ $Q_{16}:C_2$ $2^{5}$ ✓
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