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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 902 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
612220032.fm.1.a1.a1 $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $C_1$ $1$ ✓
612220032.fm.2._.A $C_3^6.C_3^6:(A_4^2:C_4)$ $2^{6} \cdot 3^{14}$ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $C_2$ $2$ ✓
612220032.fm.2._.B $C_3^{10}.C_2^4.C_3^3.D_6$ $2^{6} \cdot 3^{14}$ ✓ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $C_2$ $2$ ✓
612220032.fm.2._.C $C_3^6.C_3^6:(A_4^2:C_4)$ $2^{6} \cdot 3^{14}$ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $C_2$ $2$ ✓
612220032.fm.4._.A $C_3^{10}.C_2^4.C_3^4.C_2$ $2^{5} \cdot 3^{14}$ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $C_2^2$ $2^{2}$ ✓
612220032.fm.4._.B $C_3^{10}.C_2^4.C_3^4.C_2$ $2^{5} \cdot 3^{14}$ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $C_4$ $2^{2}$ ✓
612220032.fm.4._.C $C_3^{10}.C_2^4.C_3^4.C_2$ $2^{5} \cdot 3^{14}$ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $C_4$ $2^{2}$ ✓
612220032.fm.6._.A $C_3^8.C_6^2.C_6^2.D_6$ $2^{6} \cdot 3^{13}$ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $2 \cdot 3$ $-$
612220032.fm.6._.B $C_3^8.C_6^2.C_6^2.D_6$ $2^{6} \cdot 3^{13}$ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $2 \cdot 3$ $-$
612220032.fm.6._.C $C_3^8.C_6^2.C_6^2.D_6$ $2^{6} \cdot 3^{13}$ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $2 \cdot 3$ $-$
612220032.fm.6._.D $C_3^8.C_6^2.C_6^2.D_6$ $2^{6} \cdot 3^{13}$ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $2 \cdot 3$ $-$
612220032.fm.6._.E $C_3^8.C_6^2.C_6^2.D_6$ $2^{6} \cdot 3^{13}$ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $2 \cdot 3$ $-$
612220032.fm.6._.F $C_3^8.C_6^2.C_6^2.D_6$ $2^{6} \cdot 3^{13}$ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $2 \cdot 3$ $-$
612220032.fm.6._.G $C_3^8.C_6^2.C_6^2.D_6$ $2^{6} \cdot 3^{13}$ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $2 \cdot 3$ $-$
612220032.fm.6._.H $C_3^8.C_6^2.C_6^2.D_6$ $2^{6} \cdot 3^{13}$ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $2 \cdot 3$ $-$
612220032.fm.6._.I $C_3^8.C_6^2.C_6^2.D_6$ $2^{6} \cdot 3^{13}$ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $2 \cdot 3$ $-$
612220032.fm.6._.J $C_3^8.C_2^4.C_3.C_3^4.C_2^2$ $2^{6} \cdot 3^{13}$ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $2 \cdot 3$ $-$
612220032.fm.6._.K $C_3^8.C_6^2.C_6^2.D_6$ $2^{6} \cdot 3^{13}$ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $2 \cdot 3$ $-$
612220032.fm.6._.L $C_3^8.C_2^4.C_3.C_3^4.C_2^2$ $2^{6} \cdot 3^{13}$ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $2 \cdot 3$ $-$
612220032.fm.6._.M $C_3^8.C_6^2.C_6^2.D_6$ $2^{6} \cdot 3^{13}$ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $2 \cdot 3$ $-$
612220032.fm.6._.N $C_3^7.C_6^2.C_3^3.C_6.C_2^3$ $2^{6} \cdot 3^{13}$ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $2 \cdot 3$ $-$
612220032.fm.6._.O $C_3^8.C_6^2.C_6^2.D_6$ $2^{6} \cdot 3^{13}$ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $2 \cdot 3$ $-$
612220032.fm.6._.P $C_3^8.C_6^2.C_6^2.D_6$ $2^{6} \cdot 3^{13}$ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $2 \cdot 3$ $-$
612220032.fm.6._.Q $C_3^8.C_6^2.C_6^2.D_6$ $2^{6} \cdot 3^{13}$ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $2 \cdot 3$ $-$
612220032.fm.6._.R $C_3^8.C_2^4.C_3^4.C_6.C_2$ $2^{6} \cdot 3^{13}$ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $2 \cdot 3$ $-$
612220032.fm.6._.S $C_3^8.C_6^2.C_6^2.D_6$ $2^{6} \cdot 3^{13}$ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $2 \cdot 3$ $-$
612220032.fm.6._.T $C_3^8.C_6^2.C_6^2.D_6$ $2^{6} \cdot 3^{13}$ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $2 \cdot 3$ $-$
612220032.fm.8._.A $C_3^{10}.C_2^4.C_3^4$ $2^{4} \cdot 3^{14}$ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $C_2\times C_4$ $2^{3}$ ✓
612220032.fm.8._.B $C_3^9.C_6^2.C_3^2.D_6$ $2^{4} \cdot 3^{14}$ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $2^{3}$ $-$
612220032.fm.9._.A $C_3^9.C_6^3.C_2^3.C_2$ $2^{7} \cdot 3^{12}$ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $3^{2}$ $-$
612220032.fm.9._.B $C_3^8.(C_6\times A_4^2):C_{12}$ $2^{7} \cdot 3^{12}$ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $3^{2}$ $-$
612220032.fm.9._.C $C_3^9.A_4^2.C_6.C_2^2$ $2^{7} \cdot 3^{12}$ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $3^{2}$ $-$
612220032.fm.9._.D $C_3^9.A_4^2.C_6.C_2^2$ $2^{7} \cdot 3^{12}$ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $3^{2}$ $-$
612220032.fm.9._.E $C_3^9.A_4^2.C_6.C_2^2$ $2^{7} \cdot 3^{12}$ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $3^{2}$ $-$
612220032.fm.9._.F $C_3^9.A_4^2.C_6.C_2^2$ $2^{7} \cdot 3^{12}$ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $3^{2}$ $-$
612220032.fm.9._.G $C_3^8.(C_6\times A_4^2):C_{12}$ $2^{7} \cdot 3^{12}$ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $3^{2}$ $-$
612220032.fm.9._.H $C_3^9.A_4^2.C_6.C_2^2$ $2^{7} \cdot 3^{12}$ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $3^{2}$ $-$
612220032.fm.9._.I $C_3^9.A_4^2.C_6.C_2^2$ $2^{7} \cdot 3^{12}$ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $3^{2}$ $-$
612220032.fm.9._.J $C_3^8.(C_6\times A_4^2):C_{12}$ $2^{7} \cdot 3^{12}$ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $3^{2}$ $-$
612220032.fm.12._.A $C_3^8.C_6^2.C_6^2.C_6$ $2^{5} \cdot 3^{13}$ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $2^{2} \cdot 3$ $-$
612220032.fm.12._.B $C_3^8.C_6^2.C_6^3$ $2^{5} \cdot 3^{13}$ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $2^{2} \cdot 3$ $-$
612220032.fm.12._.C $C_3^9.C_2^4.C_3^4.C_2$ $2^{5} \cdot 3^{13}$ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $2^{2} \cdot 3$ $-$
612220032.fm.12._.D $C_3^9.C_2^4.C_3^4.C_2$ $2^{5} \cdot 3^{13}$ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $2^{2} \cdot 3$ $-$
612220032.fm.12._.E $C_3^9.(C_6^2\times A_4).C_6$ $2^{5} \cdot 3^{13}$ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $2^{2} \cdot 3$ $-$
612220032.fm.12._.F $C_3^{10}.C_2^4.C_3^3.C_2$ $2^{5} \cdot 3^{13}$ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $2^{2} \cdot 3$ $-$
612220032.fm.12._.G $C_3^8.C_6^2.C_6^2.C_6$ $2^{5} \cdot 3^{13}$ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $2^{2} \cdot 3$ $-$
612220032.fm.12._.H $C_3^9.(C_6^2\times A_4).C_6$ $2^{5} \cdot 3^{13}$ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $2^{2} \cdot 3$ $-$
612220032.fm.12._.I $C_3^{10}.C_2^4.C_3^3.C_2$ $2^{5} \cdot 3^{13}$ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $2^{2} \cdot 3$ $-$
612220032.fm.12._.J $C_3^{10}.C_2^4.C_3^3.C_2$ $2^{5} \cdot 3^{13}$ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $2^{2} \cdot 3$ $-$
612220032.fm.12._.K $C_3^8.C_6^2.C_6^2.C_6$ $2^{5} \cdot 3^{13}$ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $2^{2} \cdot 3$ $-$
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