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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 235 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
84934656.br.1.a1.a1 $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $C_1$ $1$ ✓
84934656.br.2._.A $C_2^{16}.C_3^4.D_4$ $2^{19} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $C_2$ $2$ ✓
84934656.br.2._.B $C_2^{10}.A_4^2\wr C_2$ $2^{19} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $C_2$ $2$ ✓
84934656.br.2._.C $C_2^{16}.C_3^4.C_2^3$ $2^{19} \cdot 3^{4}$ ✓ ✓ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $C_2$ $2$ ✓
84934656.br.2._.D $C_2^{16}.C_3^4.C_2^3$ $2^{19} \cdot 3^{4}$ ✓ ✓ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $C_2$ $2$ ✓
84934656.br.2._.E $C_2^{16}.C_3^4.D_4$ $2^{19} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $C_2$ $2$ ✓
84934656.br.2._.F $C_2^{10}.A_4^2\wr C_2$ $2^{19} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $C_2$ $2$ ✓
84934656.br.2._.G $C_2^9.A_4^2:\POPlus(4,3)$ $2^{19} \cdot 3^{4}$ ✓ ✓ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $C_2$ $2$ ✓
84934656.br.4._.A $C_2^{16}.C_3^4.C_2^2$ $2^{18} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
84934656.br.4._.B $C_2^{16}.C_3^3.D_6$ $2^{18} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
84934656.br.4._.C $C_2^9.A_4^2\wr C_2$ $2^{18} \cdot 3^{4}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
84934656.br.4._.D $C_2^9.A_4^2\wr C_2$ $2^{18} \cdot 3^{4}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
84934656.br.4._.E $C_2^{16}.C_3^3.D_6$ $2^{18} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
84934656.br.4._.F $C_2^9.A_4^2\wr C_2$ $2^{18} \cdot 3^{4}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
84934656.br.4._.G $C_2^9.A_4^2\wr C_2$ $2^{18} \cdot 3^{4}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
84934656.br.6._.A $C_2^{12}.A_4^2:S_4$ $2^{19} \cdot 3^{3}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $S_3$ $2 \cdot 3$
84934656.br.6._.B $C_2^{12}.A_4^2:S_4$ $2^{19} \cdot 3^{3}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $S_3$ $2 \cdot 3$
84934656.br.6._.C $C_2^{12}.A_4^2:S_4$ $2^{19} \cdot 3^{3}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $S_3$ $2 \cdot 3$
84934656.br.6._.D $C_2^{12}.A_4^2:S_4$ $2^{19} \cdot 3^{3}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $S_3$ $2 \cdot 3$
84934656.br.6._.E $C_2^{12}.A_4^2:S_4$ $2^{19} \cdot 3^{3}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $S_3$ $2 \cdot 3$
84934656.br.6._.F $C_2^{12}.A_4^2:S_4$ $2^{19} \cdot 3^{3}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $S_3$ $2 \cdot 3$
84934656.br.6._.G $C_2^{12}.A_4^2:S_4$ $2^{19} \cdot 3^{3}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $S_3$ $2 \cdot 3$
84934656.br.6._.H $C_2^{12}.A_4^2:S_4$ $2^{19} \cdot 3^{3}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $S_3$ $2 \cdot 3$
84934656.br.8._.A $C_2^{16}.C_3^4.C_2$ $2^{17} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $C_2^3$ $2^{3}$ ✓
84934656.br.8._.B $C_2^{16}.C_3^4.C_2$ $2^{17} \cdot 3^{4}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $D_4$ $2^{3}$
84934656.br.8._.C $C_2^{16}.C_3^4.C_2$ $2^{17} \cdot 3^{4}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $D_4$ $2^{3}$
84934656.br.12._.A $C_2^{16}.C_3.C_6^2$ $2^{18} \cdot 3^{3}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
84934656.br.12._.B $C_2^{16}.C_3.C_6^2$ $2^{18} \cdot 3^{3}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
84934656.br.12._.C $C_2^{16}.C_3.C_6^2$ $2^{18} \cdot 3^{3}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
84934656.br.12._.D $C_2^{16}.C_3.C_6^2$ $2^{18} \cdot 3^{3}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
84934656.br.12._.E $C_2^{16}.C_3.C_6^2$ $2^{18} \cdot 3^{3}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
84934656.br.12._.F $C_2^{16}.C_3.C_6^2$ $2^{18} \cdot 3^{3}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
84934656.br.12._.G $C_2^{16}.C_3.C_6^2$ $2^{18} \cdot 3^{3}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
84934656.br.12._.H $C_2^{16}.C_3.C_6^2$ $2^{18} \cdot 3^{3}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
84934656.br.12._.I $C_2^{10}.A_4^3:C_2^2$ $2^{18} \cdot 3^{3}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
84934656.br.12._.J $C_2^{10}.A_4^3:C_2^2$ $2^{18} \cdot 3^{3}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
84934656.br.12._.K $C_2^{10}.A_4^3:C_2^2$ $2^{18} \cdot 3^{3}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
84934656.br.12._.L $C_2^{10}.A_4^3:C_2^2$ $2^{18} \cdot 3^{3}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
84934656.br.12._.M $C_2^{10}.A_4^3:C_2^2$ $2^{18} \cdot 3^{3}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
84934656.br.12._.N $C_2^{10}.A_4^3:C_2^2$ $2^{18} \cdot 3^{3}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
84934656.br.12._.O $C_2^{10}.A_4^3:C_2^2$ $2^{18} \cdot 3^{3}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
84934656.br.12._.P $C_2^{10}.A_4^3:C_2^2$ $2^{18} \cdot 3^{3}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
84934656.br.12._.Q $C_2^{10}.A_4^3:C_4$ $2^{18} \cdot 3^{3}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
84934656.br.12._.R $C_2^{10}.A_4^3:C_4$ $2^{18} \cdot 3^{3}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
84934656.br.12._.S $C_2^{10}.A_4^3:C_4$ $2^{18} \cdot 3^{3}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
84934656.br.12._.T $C_2^{10}.A_4^3:C_4$ $2^{18} \cdot 3^{3}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
84934656.br.12._.U $C_2^{10}.A_4^3:C_4$ $2^{18} \cdot 3^{3}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
84934656.br.12._.V $C_2^{10}.A_4^3:C_4$ $2^{18} \cdot 3^{3}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
84934656.br.12._.W $C_2^{10}.A_4^3:C_4$ $2^{18} \cdot 3^{3}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
84934656.br.12._.X $C_2^{10}.A_4^3:C_4$ $2^{18} \cdot 3^{3}$ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
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