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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 713 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
816293376.sr.1.a1.a1 $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ ✓ ✓ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $C_1$ $1$ ✓
816293376.sr.2._.A $C_3^{12}.C_2^6.C_{12}$ $2^{8} \cdot 3^{13}$ ✓ ✓ ✓ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $C_2$ $2$ ✓
816293376.sr.2._.B $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ ✓ ✓ ✓ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $C_2$ $2$ ✓
816293376.sr.2._.C $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ ✓ ✓ ✓ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $C_2$ $2$ ✓
816293376.sr.3.a1.a1 $C_3^{12}.C_2^6.C_2^3$ $2^{9} \cdot 3^{12}$ ✓ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $3$ $-$
816293376.sr.4._.A $C_3^{12}.C_2^6.C_6$ $2^{7} \cdot 3^{13}$ ✓ ✓ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $C_2^2$ $2^{2}$ ✓
816293376.sr.4._.B $C_3^{12}.C_2^6.S_3$ $2^{7} \cdot 3^{13}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2^{2}$ $-$
816293376.sr.4._.C $C_3^{12}.C_2^6.S_3$ $2^{7} \cdot 3^{13}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2^{2}$ $-$
816293376.sr.4._.D $C_3^{12}.C_2^4.D_{12}$ $2^{7} \cdot 3^{13}$ ✓ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2^{2}$ $-$
816293376.sr.4._.E $C_3^{12}.C_2^4.D_{12}$ $2^{7} \cdot 3^{13}$ ✓ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2^{2}$ $-$
816293376.sr.4._.F $C_3^{12}.C_2^4.D_{12}$ $2^{7} \cdot 3^{13}$ ✓ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2^{2}$ $-$
816293376.sr.6._.A $C_3^{12}.C_2^6.C_2^2$ $2^{8} \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $S_3$ $2 \cdot 3$
816293376.sr.6._.B $C_3^9.C_6^3.C_2^5$ $2^{8} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2 \cdot 3$ $-$
816293376.sr.6._.C $C_3^{12}.C_2^6.C_2^2$ $2^{8} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2 \cdot 3$ $-$
816293376.sr.6._.D $C_3^{12}.C_2^6.C_2^2$ $2^{8} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2 \cdot 3$ $-$
816293376.sr.6._.E $C_3^{12}.C_2^6.C_2^2$ $2^{8} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2 \cdot 3$ $-$
816293376.sr.6._.F $C_3^{12}.C_2^6.C_2^2$ $2^{8} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2 \cdot 3$ $-$
816293376.sr.6._.G $C_3^{12}.C_2^6.C_2^2$ $2^{8} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2 \cdot 3$ $-$
816293376.sr.6._.H $C_3^{12}.C_2^6.C_2^2$ $2^{8} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2 \cdot 3$ $-$
816293376.sr.6._.I $C_3^{12}.C_2^6.C_2^2$ $2^{8} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2 \cdot 3$ $-$
816293376.sr.6._.J $C_3^{12}.C_2^6.C_2^2$ $2^{8} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2 \cdot 3$ $-$
816293376.sr.6._.K $C_3^{12}.C_2^6.C_2^2$ $2^{8} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2 \cdot 3$ $-$
816293376.sr.6._.L $C_3^{12}.C_2^6.C_2^2$ $2^{8} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2 \cdot 3$ $-$
816293376.sr.6._.M $C_3^{12}.C_2^6.C_2^2$ $2^{8} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2 \cdot 3$ $-$
816293376.sr.6._.N $C_3^{12}.C_2^6.C_2^2$ $2^{8} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2 \cdot 3$ $-$
816293376.sr.6._.O $C_3^{12}.C_2^6.C_2^2$ $2^{8} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2 \cdot 3$ $-$
816293376.sr.8._.A $C_3^{12}.C_2^6.C_3$ $2^{6} \cdot 3^{13}$ ✓ ✓ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $D_4$ $2^{3}$
816293376.sr.8._.B $C_3^{12}.C_2^4.C_{12}$ $2^{6} \cdot 3^{13}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2^{3}$ $-$
816293376.sr.8._.C $C_3^{12}.C_2^4.D_6$ $2^{6} \cdot 3^{13}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2^{3}$ $-$
816293376.sr.8._.D $C_3^{12}.C_2^4.D_6$ $2^{6} \cdot 3^{13}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2^{3}$ $-$
816293376.sr.8._.E $C_3^{12}.C_2^4.C_{12}$ $2^{6} \cdot 3^{13}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2^{3}$ $-$
816293376.sr.8._.F $C_3^{12}.C_2^4.D_6$ $2^{6} \cdot 3^{13}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2^{3}$ $-$
816293376.sr.8._.G $C_3^{12}.C_2^4.C_{12}$ $2^{6} \cdot 3^{13}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2^{3}$ $-$
816293376.sr.8._.H $C_3^{12}.C_2^4.D_6$ $2^{6} \cdot 3^{13}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2^{3}$ $-$
816293376.sr.8._.I $C_3^{12}.C_2^4.D_6$ $2^{6} \cdot 3^{13}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2^{3}$ $-$
816293376.sr.8._.J $C_3^{12}.C_2^4.D_6$ $2^{6} \cdot 3^{13}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2^{3}$ $-$
816293376.sr.8._.K $C_3^{11}.C_2^4.S_3^2$ $2^{6} \cdot 3^{13}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2^{3}$ $-$
816293376.sr.8._.L $C_3^{11}.C_2^4.C_3.D_6$ $2^{6} \cdot 3^{13}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2^{3}$ $-$
816293376.sr.8._.M $C_3^{12}.C_2^4.C_{12}$ $2^{6} \cdot 3^{13}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2^{3}$ $-$
816293376.sr.8._.N $C_3^{12}.C_2^4.D_6$ $2^{6} \cdot 3^{13}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2^{3}$ $-$
816293376.sr.8._.O $C_3^{12}.C_2^4.D_6$ $2^{6} \cdot 3^{13}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2^{3}$ $-$
816293376.sr.12._.A $C_3^{12}.C_2^6.C_2$ $2^{7} \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $D_6$ $2^{2} \cdot 3$
816293376.sr.12._.B $C_3^{12}.C_2^5.C_2^2$ $2^{7} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2^{2} \cdot 3$ $-$
816293376.sr.12._.C $C_3^{12}.C_2^5.C_2^2$ $2^{7} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2^{2} \cdot 3$ $-$
816293376.sr.12._.D $C_3^{12}.C_2^5.C_2^2$ $2^{7} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2^{2} \cdot 3$ $-$
816293376.sr.12._.E $C_3^9.C_6^3.C_2^4$ $2^{7} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2^{2} \cdot 3$ $-$
816293376.sr.12._.F $C_3^{12}.C_2^5.C_2^2$ $2^{7} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2^{2} \cdot 3$ $-$
816293376.sr.12._.G $C_3^9.C_6^3.C_2^4$ $2^{7} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2^{2} \cdot 3$ $-$
816293376.sr.12._.H $C_3^{12}.C_2^6.C_2$ $2^{7} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2^{2} \cdot 3$ $-$
816293376.sr.12._.I $C_3^{12}.C_2^6.C_2$ $2^{7} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $2^{2} \cdot 3$ $-$
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