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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 171 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
17496.qe.1.a1 $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ ✓ ✓ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $C_1$ $1$ ✓
17496.qe.2.a1 $C_3^5.C_3^2.C_4$ $2^{2} \cdot 3^{7}$ ✓ ✓ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $C_2$ $2$ ✓
17496.qe.4.a1 $C_3^5.C_3.S_3$ $2 \cdot 3^{7}$ ✓ ✓ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $C_2^2$ $2^{2}$ ✓
17496.qe.8.a1 $C_3^4.C_3^3$ $3^{7}$ $3$ ✓ ✓ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $Q_8$ $2^{3}$
17496.qe.9.a1 $C_3^5:Q_8$ $2^{3} \cdot 3^{5}$ ✓ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $3^{2}$ $-$
17496.qe.12.a1 $(C_3^2\times \He_3):S_3$ $2 \cdot 3^{6}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3$ $-$
17496.qe.12.b1 $C_3^5:S_3$ $2 \cdot 3^{6}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3$ $-$
17496.qe.18.a1 $C_3^4:C_{12}$ $2^{2} \cdot 3^{5}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2 \cdot 3^{2}$ $-$
17496.qe.18.b1 $(C_3^2\times \He_3):C_4$ $2^{2} \cdot 3^{5}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2 \cdot 3^{2}$ $-$
17496.qe.24.a1 $C_3^3:\He_3$ $3^{6}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2^{3} \cdot 3$ $-$
17496.qe.24.b1 $C_3^5:C_3$ $3^{6}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2^{3} \cdot 3$ $-$
17496.qe.27.a1 $C_3^4:Q_8$ $2^{3} \cdot 3^{4}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $3^{3}$ $-$
17496.qe.36.a1 $C_3^4:S_3$ $2 \cdot 3^{5}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
17496.qe.36.b1 $C_3^4:S_3$ $2 \cdot 3^{5}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
17496.qe.36.c1 $C_3^4:S_3$ $2 \cdot 3^{5}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
17496.qe.36.c2 $C_3^4:C_6$ $2 \cdot 3^{5}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
17496.qe.36.d1 $C_3^4:S_3$ $2 \cdot 3^{5}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
17496.qe.36.e1 $C_3^4:S_3$ $2 \cdot 3^{5}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
17496.qe.54.a1 $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2 \cdot 3^{3}$ $-$
17496.qe.54.b1 $(C_3\times \He_3):C_4$ $2^{2} \cdot 3^{4}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2 \cdot 3^{3}$ $-$
17496.qe.54.c1 $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2 \cdot 3^{3}$ $-$
17496.qe.54.d1 $C_3^4:C_4$ $2^{2} \cdot 3^{4}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2 \cdot 3^{3}$ $-$
17496.qe.54.e1 $(C_3\times \He_3):C_4$ $2^{2} \cdot 3^{4}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2 \cdot 3^{3}$ $-$
17496.qe.72.a1 $C_3^5$ $3^{5}$ ✓ ✓ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $\PSU(3,2)$ $2^{3} \cdot 3^{2}$
17496.qe.72.b1 $C_3^2\times \He_3$ $3^{5}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2^{3} \cdot 3^{2}$ $-$
17496.qe.72.c1 $C_3^2\times \He_3$ $3^{5}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2^{3} \cdot 3^{2}$ $-$
17496.qe.72.d1 $C_3^2\times \He_3$ $3^{5}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2^{3} \cdot 3^{2}$ $-$
17496.qe.72.e1 $C_3^2\times \He_3$ $3^{5}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2^{3} \cdot 3^{2}$ $-$
17496.qe.72.f1 $C_3^4:C_3$ $3^{5}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2^{3} \cdot 3^{2}$ $-$
17496.qe.72.f2 $C_3^4:C_3$ $3^{5}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2^{3} \cdot 3^{2}$ $-$
17496.qe.72.g1 $C_3^4:C_3$ $3^{5}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2^{3} \cdot 3^{2}$ $-$
17496.qe.81.a1 $C_3^3:Q_8$ $2^{3} \cdot 3^{3}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $3^{4}$ $-$
17496.qe.81.b1 $C_3^3:Q_8$ $2^{3} \cdot 3^{3}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $3^{4}$ $-$
17496.qe.108.a1 $S_3\times C_3^3$ $2 \cdot 3^{4}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{3}$ $-$
17496.qe.108.b1 $S_3\times C_3^3$ $2 \cdot 3^{4}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{3}$ $-$
17496.qe.108.c1 $C_3^3:S_3$ $2 \cdot 3^{4}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{3}$ $-$
17496.qe.108.d1 $C_3^3:S_3$ $2 \cdot 3^{4}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{3}$ $-$
17496.qe.108.e1 $C_3^3:S_3$ $2 \cdot 3^{4}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{3}$ $-$
17496.qe.108.e2 $C_3^2\wr C_2$ $2 \cdot 3^{4}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{3}$ $-$
17496.qe.108.f1 $C_3^3:S_3$ $2 \cdot 3^{4}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{3}$ $-$
17496.qe.108.g1 $C_3^3:S_3$ $2 \cdot 3^{4}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{3}$ $-$
17496.qe.108.h1 $C_3^2\wr C_2$ $2 \cdot 3^{4}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{3}$ $-$
17496.qe.108.i1 $C_3^3:S_3$ $2 \cdot 3^{4}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{3}$ $-$
17496.qe.108.j1 $C_3^3:S_3$ $2 \cdot 3^{4}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{3}$ $-$
17496.qe.108.k1 $C_3^3:S_3$ $2 \cdot 3^{4}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{3}$ $-$
17496.qe.108.l1 $C_3^2\wr C_2$ $2 \cdot 3^{4}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{3}$ $-$
17496.qe.108.m1 $C_3^3:S_3$ $2 \cdot 3^{4}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{3}$ $-$
17496.qe.162.a1 $C_3^2:C_{12}$ $2^{2} \cdot 3^{3}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2 \cdot 3^{4}$ $-$
17496.qe.162.b1 $C_3^2:C_{12}$ $2^{2} \cdot 3^{3}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2 \cdot 3^{4}$ $-$
17496.qe.162.c1 $C_3^3:C_4$ $2^{2} \cdot 3^{3}$ $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $2 \cdot 3^{4}$ $-$
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