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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 59 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
288.78.144.c1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{36}:Q_8$ $2^{5} \cdot 3^{2}$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
288.80.144.b1.a1 $C_2$ $2$ ✓ ✓ ✓ $C_{36}.Q_8$ $2^{5} \cdot 3^{2}$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
288.80.144.b1.b1 $C_2$ $2$ ✓ ✓ ✓ $C_{36}.Q_8$ $2^{5} \cdot 3^{2}$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
288.82.144.b1.a1 $C_2$ $2$ ✓ ✓ ✓ $C_4^2:D_9$ $2^{5} \cdot 3^{2}$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
288.82.144.b1.b1 $C_2$ $2$ ✓ ✓ ✓ $C_4^2:D_9$ $2^{5} \cdot 3^{2}$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
288.83.144.c1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4\times D_{36}$ $2^{5} \cdot 3^{2}$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
288.85.144.b1.a1 $C_2$ $2$ ✓ ✓ ✓ $C_4^2:D_9$ $2^{5} \cdot 3^{2}$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
288.85.144.b1.b1 $C_2$ $2$ ✓ ✓ ✓ $C_4^2:D_9$ $2^{5} \cdot 3^{2}$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
288.86.144.a1.a1 $C_2$ $2$ ✓ ✓ ✓ $C_4^2:D_9$ $2^{5} \cdot 3^{2}$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
288.86.144.a1.b1 $C_2$ $2$ ✓ ✓ ✓ $C_4^2:D_9$ $2^{5} \cdot 3^{2}$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
288.86.144.a1.c1 $C_2$ $2$ ✓ ✓ ✓ $C_4^2:D_9$ $2^{5} \cdot 3^{2}$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
288.89.144.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^3.D_{18}$ $2^{5} \cdot 3^{2}$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
288.93.144.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{18}.D_4$ $2^{5} \cdot 3^{2}$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
288.94.144.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{18}:D_4$ $2^{5} \cdot 3^{2}$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
288.95.144.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^3.D_{18}$ $2^{5} \cdot 3^{2}$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
288.99.144.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_2\times C_4).D_{18}$ $2^{5} \cdot 3^{2}$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
288.104.144.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{18}.D_4$ $2^{5} \cdot 3^{2}$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
288.106.144.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{18}:Q_8$ $2^{5} \cdot 3^{2}$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
288.108.144.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_2\times C_4).D_{18}$ $2^{5} \cdot 3^{2}$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
288.134.144.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{36}.D_4$ $2^{5} \cdot 3^{2}$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
288.136.144.a1.a1 $C_2$ $2$ ✓ ✓ ✓ $C_2^3.D_{18}$ $2^{5} \cdot 3^{2}$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
288.136.144.a1.b1 $C_2$ $2$ ✓ ✓ ✓ $C_2^3.D_{18}$ $2^{5} \cdot 3^{2}$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
288.138.144.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{36}:D_4$ $2^{5} \cdot 3^{2}$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
288.139.144.a1.a1 $C_2$ $2$ ✓ ✓ ✓ $C_2^3.D_{18}$ $2^{5} \cdot 3^{2}$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
288.139.144.a1.b1 $C_2$ $2$ ✓ ✓ ✓ $C_2^3.D_{18}$ $2^{5} \cdot 3^{2}$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
288.140.144.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{36}:D_4$ $2^{5} \cdot 3^{2}$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
288.355.144.a1 $C_2$ $2$ ✓ ✓ ✓ $D_{36}:C_2^2$ $2^{5} \cdot 3^{2}$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
432.46.144.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $D_{108}:C_2$ $2^{4} \cdot 3^{3}$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
432.287.144.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_{12}.D_{18}$ $2^{4} \cdot 3^{3}$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
432.288.144.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $D_{36}:S_3$ $2^{4} \cdot 3^{3}$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
432.289.144.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_{12}.D_{18}$ $2^{4} \cdot 3^{3}$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
432.305.144.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $D_{18}.D_6$ $2^{4} \cdot 3^{3}$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
432.344.144.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $D_{36}:C_6$ $2^{4} \cdot 3^{3}$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
432.383.144.a1 $C_3$ $3$ ✓ ✓ $C_{12}.D_{18}$ $2^{4} \cdot 3^{3}$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
576.4969.144.d1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^4.D_{18}$ $2^{6} \cdot 3^{2}$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
720.132.144.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $C_{20}.D_{18}$ $2^{4} \cdot 3^{2} \cdot 5$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
720.133.144.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $D_{36}:D_5$ $2^{4} \cdot 3^{2} \cdot 5$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
720.134.144.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $D_{180}:C_2$ $2^{4} \cdot 3^{2} \cdot 5$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
720.141.144.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $D_{18}.D_{10}$ $2^{4} \cdot 3^{2} \cdot 5$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
720.168.144.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ ✓ $D_{36}:C_{10}$ $2^{4} \cdot 3^{2} \cdot 5$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
720.178.144.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $D_{180}:C_2$ $2^{4} \cdot 3^{2} \cdot 5$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
1008.153.144.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $C_{28}.D_{18}$ $2^{4} \cdot 3^{2} \cdot 7$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
1008.154.144.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $D_{36}:D_7$ $2^{4} \cdot 3^{2} \cdot 7$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
1008.155.144.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $D_{252}:C_2$ $2^{4} \cdot 3^{2} \cdot 7$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
1008.162.144.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $D_{18}.D_{14}$ $2^{4} \cdot 3^{2} \cdot 7$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
1008.196.144.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ ✓ $D_{36}:C_{14}$ $2^{4} \cdot 3^{2} \cdot 7$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
1008.206.144.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $D_{252}:C_2$ $2^{4} \cdot 3^{2} \cdot 7$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
1584.109.144.a1.a1 $C_{11}$ $11$ $11$ ✓ ✓ ✓ $C_{36}.D_{22}$ $2^{4} \cdot 3^{2} \cdot 11$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
1584.110.144.a1.a1 $C_{11}$ $11$ $11$ ✓ ✓ ✓ $D_{36}:D_{11}$ $2^{4} \cdot 3^{2} \cdot 11$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
1584.111.144.a1.a1 $C_{11}$ $11$ $11$ ✓ ✓ ✓ $D_{396}:C_2$ $2^{4} \cdot 3^{2} \cdot 11$ $D_{36}:C_2$ $2^{4} \cdot 3^{2}$ ✓
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