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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 65 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
432.520.432.a1.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
864.2194.432.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_2\times \He_3).\SD_{16}$ $2^{5} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$ ✓
864.2195.432.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_2\times \He_3).\SD_{16}$ $2^{5} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$ ✓
864.2196.432.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $\SU(3,2):C_4$ $2^{5} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$ ✓
864.3997.432.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $\SU(3,2):C_2^2$ $2^{5} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$ ✓
1296.2900.432.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $\SU(3,2):C_6$ $2^{4} \cdot 3^{4}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$ ✓
1296.2902.432.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $(C_3\times \He_3):\SD_{16}$ $2^{4} \cdot 3^{4}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$ ✓
1296.2904.432.b1.a1 $C_3$ $3$ ✓ ✓ $\SU(3,2):S_3$ $2^{4} \cdot 3^{4}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$ ✓
1296.2904.432.b1.b1 $C_3$ $3$ ✓ ✓ $\SU(3,2):S_3$ $2^{4} \cdot 3^{4}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$ ✓
1296.2904.432.b1.c1 $C_3$ $3$ ✓ ✓ $\SU(3,2):S_3$ $2^{4} \cdot 3^{4}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$ ✓
1296.2907.432.b1.a1 $C_3$ $3$ ✓ ✓ ✓ $(C_3\times \He_3):\SD_{16}$ $2^{4} \cdot 3^{4}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$ ✓
1728.12230.432.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $(C_4\times \He_3).\SD_{16}$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
1728.12231.432.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $(C_4\times \He_3).\SD_{16}$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
1728.12232.432.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $(C_4\times \He_3).\SD_{16}$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
1728.12233.432.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $(C_4\times \He_3).\SD_{16}$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
1728.12234.432.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $(C_4\times \He_3).\SD_{16}$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
1728.12235.432.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $(C_4\times \He_3).\SD_{16}$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
1728.12236.432.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $(C_4\times \He_3).\SD_{16}$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
1728.12237.432.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $(C_4\times \He_3).\SD_{16}$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
1728.12238.432.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $\SU(3,2):C_8$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
1728.12239.432.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $(C_4\times \He_3).\SD_{16}$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
1728.12240.432.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $(C_4\times \He_3).\SD_{16}$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
1728.12241.432.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $(C_2^2\times \He_3).\SD_{16}$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
1728.12242.432.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $(C_2^2\times \He_3).\SD_{16}$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
1728.12243.432.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $(C_2^2\times \He_3).\SD_{16}$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
1728.12244.432.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $(C_2^2\times \He_3).\SD_{16}$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
1728.12245.432.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $(C_2^2\times \He_3).\SD_{16}$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
1728.12246.432.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $(C_2^2\times \He_3).\SD_{16}$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
1728.12247.432.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $(C_2^2\times \He_3).\SD_{16}$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
1728.30145.432.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $(C_4\times \He_3).\SD_{16}$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
1728.30146.432.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $(C_4\times \He_3).\SD_{16}$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
1728.30147.432.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $(C_4\times \He_3).\SD_{16}$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
1728.30148.432.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $\SU(3,2):Q_8$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
1728.30149.432.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $(C_4\times \He_3).\SD_{16}$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
1728.30150.432.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $C_4\times \He_3:\SD_{16}$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
1728.30151.432.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $\SU(3,2):D_4$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
1728.30152.432.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $(C_4\times \He_3):\SD_{16}$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
1728.30153.432.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $(C_4\times \He_3):\SD_{16}$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
1728.30154.432.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $(C_2^2\times \He_3).\SD_{16}$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
1728.30155.432.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $(C_2^2\times \He_3).\SD_{16}$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
1728.30156.432.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $(C_2^2\times \He_3).\SD_{16}$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
1728.30157.432.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $(C_2^2\times \He_3).\SD_{16}$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
1728.30158.432.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $(C_2^2\times \He_3).\SD_{16}$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
1728.30159.432.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $\SU(3,2):D_4$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
1728.30160.432.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $(C_2^2\times \He_3):\SD_{16}$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
1728.30161.432.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $(C_2^2\times \He_3):\SD_{16}$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
1728.46113.432.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $\SU(3,2):C_2^3$ $2^{6} \cdot 3^{3}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
3888.jk.432.a1.a1 $C_3^2$ $3^{2}$ ✓ ✓ ✓ $(C_3^2\times \He_3):\SD_{16}$ $2^{4} \cdot 3^{5}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$ ✓
11664.ek.432.a1.a1 $C_3^3$ $3^{3}$ ✓ ✓ ✓ $C_3^4.F_9:C_2$ $2^{4} \cdot 3^{6}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
11664.kr.432.a1.a1 $C_3^3$ $3^{3}$ ✓ ✓ ✓ $(C_3^3\times \He_3):\SD_{16}$ $2^{4} \cdot 3^{6}$ $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$
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