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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 439 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
34992.mr.1.a1 $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ ✓ ✓ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $C_1$ $1$ ✓
34992.mr.2.a1 $C_3^5.S_3\wr C_2$ $2^{3} \cdot 3^{7}$ ✓ ✓ ✓ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $C_2$ $2$ ✓
34992.mr.2.b1 $C_3^5:\PSU(3,2)$ $2^{3} \cdot 3^{7}$ ✓ ✓ ✓ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $C_2$ $2$ ✓
34992.mr.2.c1 $C_3^5:F_9$ $2^{3} \cdot 3^{7}$ ✓ ✓ ✓ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $C_2$ $2$ ✓
34992.mr.4.a1 $C_3^5.C_3^2.C_4$ $2^{2} \cdot 3^{7}$ ✓ ✓ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $C_2^2$ $2^{2}$ ✓
34992.mr.4.b1 $C_3^4.C_3^2.D_6$ $2^{2} \cdot 3^{7}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2^{2}$ $-$
34992.mr.4.c1 $C_3^5.C_3^2.C_4$ $2^{2} \cdot 3^{7}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2^{2}$ $-$
34992.mr.8.a1 $C_3^5.C_3.S_3$ $2 \cdot 3^{7}$ ✓ ✓ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $D_4$ $2^{3}$
34992.mr.8.b1 $C_3^4.C_3^3.C_2$ $2 \cdot 3^{7}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2^{3}$ $-$
34992.mr.9.a1 $C_3^5:\SD_{16}$ $2^{4} \cdot 3^{5}$ ✓ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $3^{2}$ $-$
34992.mr.12.a1 $C_3^4:C_3.C_6.C_2$ $2^{2} \cdot 3^{6}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2^{2} \cdot 3$ $-$
34992.mr.16.a1 $C_3^4.C_3^3$ $3^{7}$ $3$ ✓ ✓ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $\SD_{16}$ $2^{4}$
34992.mr.18.a1 $C_3^5:D_4$ $2^{3} \cdot 3^{5}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2 \cdot 3^{2}$ $-$
34992.mr.18.b1 $C_3^5:Q_8$ $2^{3} \cdot 3^{5}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2 \cdot 3^{2}$ $-$
34992.mr.18.c1 $C_3^3:F_9$ $2^{3} \cdot 3^{5}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2 \cdot 3^{2}$ $-$
34992.mr.18.d1 $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2 \cdot 3^{2}$ $-$
34992.mr.24.a1 $(C_3^2\times \He_3):S_3$ $2 \cdot 3^{6}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2^{3} \cdot 3$ $-$
34992.mr.24.b1 $C_3^5:S_3$ $2 \cdot 3^{6}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2^{3} \cdot 3$ $-$
34992.mr.24.c1 $C_3^5:C_6$ $2 \cdot 3^{6}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2^{3} \cdot 3$ $-$
34992.mr.24.d1 $C_3^5:S_3$ $2 \cdot 3^{6}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2^{3} \cdot 3$ $-$
34992.mr.27.a1 $C_3^4:\SD_{16}$ $2^{4} \cdot 3^{4}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $3^{3}$ $-$
34992.mr.36.a1 $C_3^4:D_6$ $2^{2} \cdot 3^{5}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
34992.mr.36.b1 $C_3^3:C_6^2$ $2^{2} \cdot 3^{5}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
34992.mr.36.c1 $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
34992.mr.36.d1 $C_3^4:C_{12}$ $2^{2} \cdot 3^{5}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
34992.mr.36.e1 $C_3^4:C_{12}$ $2^{2} \cdot 3^{5}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
34992.mr.36.f1 $(C_3^2\times \He_3):C_4$ $2^{2} \cdot 3^{5}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
34992.mr.36.g1 $(C_3^2\times \He_3):C_4$ $2^{2} \cdot 3^{5}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
34992.mr.36.h1 $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
34992.mr.48.a1 $C_3^3:\He_3$ $3^{6}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2^{4} \cdot 3$ $-$
34992.mr.48.b1 $C_3^5:C_3$ $3^{6}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2^{4} \cdot 3$ $-$
34992.mr.54.a1 $C_3\wr D_4$ $2^{3} \cdot 3^{4}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2 \cdot 3^{3}$ $-$
34992.mr.54.b1 $C_3^4:D_4$ $2^{3} \cdot 3^{4}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2 \cdot 3^{3}$ $-$
34992.mr.54.c1 $C_3^4:Q_8$ $2^{3} \cdot 3^{4}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2 \cdot 3^{3}$ $-$
34992.mr.54.d1 $C_3^4:Q_8$ $2^{3} \cdot 3^{4}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2 \cdot 3^{3}$ $-$
34992.mr.54.e1 $C_3^2:F_9$ $2^{3} \cdot 3^{4}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2 \cdot 3^{3}$ $-$
34992.mr.72.a1 $C_3^4:S_3$ $2 \cdot 3^{5}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2^{3} \cdot 3^{2}$ $-$
34992.mr.72.b1 $C_3^4:S_3$ $2 \cdot 3^{5}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2^{3} \cdot 3^{2}$ $-$
34992.mr.72.b2 $C_3^4:S_3$ $2 \cdot 3^{5}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2^{3} \cdot 3^{2}$ $-$
34992.mr.72.c1 $C_3^4:C_6$ $2 \cdot 3^{5}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2^{3} \cdot 3^{2}$ $-$
34992.mr.72.c2 $C_3^4:S_3$ $2 \cdot 3^{5}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2^{3} \cdot 3^{2}$ $-$
34992.mr.72.d1 $C_3^4:S_3$ $2 \cdot 3^{5}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2^{3} \cdot 3^{2}$ $-$
34992.mr.72.d2 $C_3^4:S_3$ $2 \cdot 3^{5}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2^{3} \cdot 3^{2}$ $-$
34992.mr.72.e1 $C_3^4:S_3$ $2 \cdot 3^{5}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2^{3} \cdot 3^{2}$ $-$
34992.mr.72.f1 $C_3^4:C_6$ $2 \cdot 3^{5}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2^{3} \cdot 3^{2}$ $-$
34992.mr.72.g1 $C_3^4:C_6$ $2 \cdot 3^{5}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2^{3} \cdot 3^{2}$ $-$
34992.mr.72.h1 $C_3^4:C_6$ $2 \cdot 3^{5}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2^{3} \cdot 3^{2}$ $-$
34992.mr.72.i1 $C_3^4:C_6$ $2 \cdot 3^{5}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2^{3} \cdot 3^{2}$ $-$
34992.mr.72.i2 $C_3^4:C_6$ $2 \cdot 3^{5}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2^{3} \cdot 3^{2}$ $-$
34992.mr.72.j1 $C_3^4:C_6$ $2 \cdot 3^{5}$ $C_3^5:F_9:C_2$ $2^{4} \cdot 3^{7}$ $2^{3} \cdot 3^{2}$ $-$
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