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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 948 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1410554953728.gb.1.a1.a1 $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $C_1$ $1$ ✓
1410554953728.gb.2._.A $C_3^{12}.C_2^8.C_3^4.C_4.C_4^2$ $2^{14} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $C_2$ $2$ ✓
1410554953728.gb.2._.B $C_3^{12}.C_2^8.C_3^4.C_4:C_4.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $C_2$ $2$ ✓
1410554953728.gb.2._.C $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $C_2$ $2$ ✓
1410554953728.gb.2._.D $C_3^{12}.C_2^8.C_3^4.C_4.C_4^2$ $2^{14} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $C_2$ $2$ ✓
1410554953728.gb.2._.E $C_3^{12}.C_2^8.C_3^4.\OD_{16}.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $C_2$ $2$ ✓
1410554953728.gb.2._.F $C_3^{12}.C_2^8.C_3^4.C_4:C_4.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $C_2$ $2$ ✓
1410554953728.gb.2._.G $C_3^{12}.C_2^4.A_4^2.D_6^2.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $C_2$ $2$ ✓
1410554953728.gb.4._.A $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2$ $2^{13} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
1410554953728.gb.4._.B $C_3^{12}.C_2^8.C_3^4.C_4.C_2^3$ $2^{13} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
1410554953728.gb.4._.C $C_3^{12}.C_2^4.A_4^2.C_3^2.C_2^3.C_2^2$ $2^{13} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
1410554953728.gb.4._.D $C_3^{12}.C_2^8.C_3^4.C_4.C_2^3$ $2^{13} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
1410554953728.gb.4._.E $C_3^{12}.C_2^4.C_2^4.C_3^4.C_2^4.C_2$ $2^{13} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
1410554953728.gb.4._.F $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2$ $2^{13} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
1410554953728.gb.4._.G $C_3^{12}.C_2^4.C_2^4.C_3^4.C_2^4.C_2$ $2^{13} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
1410554953728.gb.4._.H $C_3^{12}.C_2^4.A_4^2.C_4:S_3\wr C_2$ $2^{13} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $C_4$ $2^{2}$ ✓
1410554953728.gb.4._.I $C_3^{12}.C_2^4.A_4^2.C_4:S_3\wr C_2$ $2^{13} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $C_4$ $2^{2}$ ✓
1410554953728.gb.4._.J $C_3^{12}.C_2^4.A_4^2.C_4:S_3\wr C_2$ $2^{13} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $C_4$ $2^{2}$ ✓
1410554953728.gb.4._.K $C_3^{12}.C_2^4.C_2^4.C_3^4.C_4:D_4$ $2^{13} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $C_4$ $2^{2}$ ✓
1410554953728.gb.4._.L $C_3^{12}.C_2^4.A_4^2.C_4:S_3\wr C_2$ $2^{13} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $2^{2}$ $-$
1410554953728.gb.4._.M $C_3^{12}.C_2^8.C_3^4.(C_4\times D_4)$ $2^{13} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $2^{2}$ $-$
1410554953728.gb.4._.N $C_3^{12}.C_2^8.C_3^4.(C_4\times D_4)$ $2^{13} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $2^{2}$ $-$
1410554953728.gb.4._.O $C_3^{12}.C_2^4.C_2^4.C_3^4.C_2^4.C_2$ $2^{13} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $2^{2}$ $-$
1410554953728.gb.4._.P $C_3^{12}.C_2^8.C_3^4.\OD_{16}.C_2$ $2^{13} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $2^{2}$ $-$
1410554953728.gb.4._.Q $C_3^{12}.C_2^8.C_3^4.\OD_{16}.C_2$ $2^{13} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $2^{2}$ $-$
1410554953728.gb.4._.R $C_3^{12}.C_2^8.C_3^4.D_4:C_4$ $2^{13} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $2^{2}$ $-$
1410554953728.gb.4._.S $C_3^{12}.C_2^8.C_3^4.D_4:C_4$ $2^{13} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $2^{2}$ $-$
1410554953728.gb.4._.T $C_3^{12}.C_2^8.C_3^4.(C_4\times D_4)$ $2^{13} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $2^{2}$ $-$
1410554953728.gb.4._.U $C_3^{12}.C_2^8.C_3^4.D_4:C_4$ $2^{13} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $2^{2}$ $-$
1410554953728.gb.4._.V $C_3^{12}.C_2^8.C_3^4.(C_4\times D_4)$ $2^{13} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $2^{2}$ $-$
1410554953728.gb.4._.W $C_3^{12}.C_2^8.C_3^4.D_4:C_4$ $2^{13} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $2^{2}$ $-$
1410554953728.gb.4._.X $C_3^{12}.A_4^2.A_4^2.C_2^4.C_2$ $2^{13} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $2^{2}$ $-$
1410554953728.gb.4._.Y $C_3^{12}.C_2^4.A_4^2.C_4:S_3\wr C_2$ $2^{13} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $2^{2}$ $-$
1410554953728.gb.4._.Z $C_3^{12}.A_4^2.A_4^2.C_2.C_2^4$ $2^{13} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $2^{2}$ $-$
1410554953728.gb.4._.BA $C_3^{12}.C_2^8.C_3^4.C_2^3.C_2^2$ $2^{13} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $2^{2}$ $-$
1410554953728.gb.8._.A $C_3^{12}.C_2^8.C_3^4.C_4:C_4$ $2^{12} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $D_4$ $2^{3}$
1410554953728.gb.8._.B $C_3^{12}.C_2^4.C_2^4.C_3^4.C_4^2$ $2^{12} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $C_2\times C_4$ $2^{3}$ ✓
1410554953728.gb.8._.C $C_3^{12}.C_2^4.A_4^2.C_3:S_3.C_2^3$ $2^{12} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $C_2\times C_4$ $2^{3}$ ✓
1410554953728.gb.8._.D $C_3^{12}.C_2^4.C_2^4.C_3^4.C_2^3.C_2$ $2^{12} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $C_2\times C_4$ $2^{3}$ ✓
1410554953728.gb.8._.E $C_3^{12}.C_2^4.C_2^4.C_3^4.C_2^3.C_2$ $2^{12} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $C_2\times C_4$ $2^{3}$ ✓
1410554953728.gb.8._.F $C_3^{12}.C_2^4.C_2^4.C_3^4.C_4^2$ $2^{12} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $C_2\times C_4$ $2^{3}$ ✓
1410554953728.gb.8._.G $C_3^{12}.C_2^4.C_2^4.C_3^4.C_2^3.C_2$ $2^{12} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $C_2\times C_4$ $2^{3}$ ✓
1410554953728.gb.8._.H $C_3^{12}.C_2^4.A_4^2.C_3:S_3.C_2^3$ $2^{12} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $C_2^3$ $2^{3}$ ✓
1410554953728.gb.8._.I $C_3^{12}.C_2^4.A_4^2.S_3^2.C_2^2$ $2^{12} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $D_4$ $2^{3}$
1410554953728.gb.8._.J $C_3^{12}.C_2^4.C_2^4.C_3^4.C_2^4$ $2^{12} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $D_4$ $2^{3}$
1410554953728.gb.8._.K $C_3^{12}.C_2^4.A_4^2.S_3^2.C_2^2$ $2^{12} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $D_4$ $2^{3}$
1410554953728.gb.8._.L $C_3^{12}.C_2^4.A_4^2.D_6^2$ $2^{12} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $D_4$ $2^{3}$
1410554953728.gb.8._.M $C_3^{12}.C_2^8.C_3^4.C_4:C_4$ $2^{12} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $D_4$ $2^{3}$
1410554953728.gb.8._.N $C_3^{12}.C_2^8.C_3^4.C_4:C_4$ $2^{12} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $D_4$ $2^{3}$
1410554953728.gb.8._.O $C_3^{12}.C_2^8.C_3^4.C_4:C_4$ $2^{12} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $D_4$ $2^{3}$
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