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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 (38 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._.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.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.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.36._.B $C_3^{12}.C_2^5$ $2^{5} \cdot 3^{12}$ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $C_3^2:C_4$ $2^{2} \cdot 3^{2}$
612220032.fm.36._.H $C_3^8.C_2^4.C_3^4.C_2$ $2^{5} \cdot 3^{12}$ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $C_3^2:C_4$ $2^{2} \cdot 3^{2}$
612220032.fm.72._.A $C_3^{12}.C_2^4$ $2^{4} \cdot 3^{12}$ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $C_2\times C_3^2:C_4$ $2^{3} \cdot 3^{2}$
612220032.fm.72._.I $C_3^8.C_2^4.C_3^4$ $2^{4} \cdot 3^{12}$ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $C_2\times C_3^2:C_4$ $2^{3} \cdot 3^{2}$
612220032.fm.324._.A $C_3^{10}.C_2^5$ $2^{5} \cdot 3^{10}$ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $C_3^4:C_4$ $2^{2} \cdot 3^{4}$
612220032.fm.576._.A $C_3^{12}.C_2$ $2 \cdot 3^{12}$ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $A_4^2:C_4$ $2^{6} \cdot 3^{2}$
612220032.fm.648._.A $C_3^{10}.C_2^4$ $2^{4} \cdot 3^{10}$ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $C_2\times C_3^4:C_4$ $2^{3} \cdot 3^{4}$
612220032.fm.972._.A $C_3^9.C_2^5$ $2^{5} \cdot 3^{9}$ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $C_3^3:C_3^2:C_4$ $2^{2} \cdot 3^{5}$
612220032.fm.972._.B $C_3^9.C_2^5$ $2^{5} \cdot 3^{9}$ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $C_3^3:C_3^2:C_4$ $2^{2} \cdot 3^{5}$
612220032.fm.1152._.A $C_3^{12}$ $3^{12}$ ✓ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $C_2\times A_4^2:C_4$ $2^{7} \cdot 3^{2}$
612220032.fm.1944._.A $C_3^9.C_2^4$ $2^{4} \cdot 3^{9}$ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $C_6.C_3^4:C_4$ $2^{3} \cdot 3^{5}$
612220032.fm.1944._.B $C_3^9.C_2^4$ $2^{4} \cdot 3^{9}$ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $C_6.C_3^4:C_4$ $2^{3} \cdot 3^{5}$
612220032.fm.2916._.A $C_3^8.C_2^5$ $2^{5} \cdot 3^{8}$ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $\He_3^2:C_4$ $2^{2} \cdot 3^{6}$
612220032.fm.5184._.A $C_3^9.C_6$ $2 \cdot 3^{10}$ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $(C_3^2\times A_4^2):C_4$ $2^{6} \cdot 3^{4}$
612220032.fm.5832._.A $C_3^8.C_2^4$ $2^{4} \cdot 3^{8}$ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $C_2\times \He_3^2:C_4$ $2^{3} \cdot 3^{6}$
612220032.fm.10368._.A $C_3^{10}$ $3^{10}$ ✓ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $C_2^5:(C_3^4:C_4)$ $2^{7} \cdot 3^{4}$
612220032.fm.15552._.A $C_3^9.C_2$ $2 \cdot 3^{9}$ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $(C_3\times A_4^2).C_3^2.C_4$ $2^{6} \cdot 3^{5}$
612220032.fm.15552._.B $C_3^9.C_2$ $2 \cdot 3^{9}$ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $(C_2\times C_6^3).C_3^2.C_4$ $2^{6} \cdot 3^{5}$
612220032.fm.26244._.A $C_3^6.C_2^5$ $2^{5} \cdot 3^{6}$ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $(C_3\wr C_3)^2:C_4$ $2^{2} \cdot 3^{8}$
612220032.fm.31104._.A $C_3^9$ $3^{9}$ ✓ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $(C_3\times A_4^2).C_3^2.C_4.C_2$ $2^{7} \cdot 3^{5}$
612220032.fm.31104._.B $C_3^9$ $3^{9}$ ✓ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $(C_3\times A_4^2).C_3:S_3.C_2^2$ $2^{7} \cdot 3^{5}$
612220032.fm.46656._.A $C_3^8.C_2$ $2 \cdot 3^{8}$ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $C_3^4:(A_4^2:C_4)$ $2^{6} \cdot 3^{6}$
612220032.fm.52488._.A $C_3^6.C_2^4$ $2^{4} \cdot 3^{6}$ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $C_2\times (C_3\wr C_3)^2:C_4$ $2^{3} \cdot 3^{8}$
612220032.fm.93312._.A $C_3^8$ $3^{8}$ ✓ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{6}$
612220032.fm.419904._.A $C_3^5:S_3$ $2 \cdot 3^{6}$ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $C_6^4.C_3^4:C_4$ $2^{6} \cdot 3^{8}$
612220032.fm.839808._.A $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $C_3^6.(C_2\times A_4^2:C_4)$ $2^{7} \cdot 3^{8}$
612220032.fm.839808._.B $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $C_2\times C_6^4.C_3^4:C_4$ $2^{7} \cdot 3^{8}$ ✓
612220032.fm.7558272._.A $C_3^4$ $3^{4}$ ✓ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $C_3^8.(C_2\times A_4^2:C_4)$ $2^{7} \cdot 3^{10}$
612220032.fm.22674816._.A $C_3^3$ $3^{3}$ ✓ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $C_3^7.C_2^4.C_3^4.C_2^2.C_2$ $2^{7} \cdot 3^{11}$
612220032.fm.22674816._.B $C_3^3$ $3^{3}$ ✓ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $C_3^7.A_4^2.C_3:S_3.C_2^2$ $2^{7} \cdot 3^{11}$
612220032.fm.68024448._.A $C_3^2$ $3^{2}$ ✓ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $C_3^8.C_2^5:(C_3^4:C_4)$ $2^{7} \cdot 3^{12}$ ✓
612220032.fm.612220032.a1.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$ $C_3^8.C_2^5:(\He_3^2:C_4)$ $2^{7} \cdot 3^{14}$
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