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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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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
408146688.wu.1.a1.a1 $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_1$ $1$ ✓
408146688.wu.2._.A $C_3^{12}.C_2^6.C_6$ $2^{7} \cdot 3^{13}$ ✓ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_2$ $2$ ✓
408146688.wu.2._.B $C_3^{12}.C_2^6.S_3$ $2^{7} \cdot 3^{13}$ ✓ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_2$ $2$ ✓
408146688.wu.2._.C $C_3^{12}.C_2^6.S_3$ $2^{7} \cdot 3^{13}$ ✓ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_2$ $2$ ✓
408146688.wu.3.a1.a1 $C_3^{12}.C_2^6.C_2^2$ $2^{8} \cdot 3^{12}$ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $3$ $-$
408146688.wu.4._.A $C_3^{12}.C_2^6.C_3$ $2^{6} \cdot 3^{13}$ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_2^2$ $2^{2}$ ✓
408146688.wu.4._.B $C_3^{12}.C_2^4.D_6$ $2^{6} \cdot 3^{13}$ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2^{2}$ $-$
408146688.wu.4._.C $C_3^8.C_6^4:D_6$ $2^{6} \cdot 3^{13}$ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2^{2}$ $-$
408146688.wu.4._.D $C_3^{12}.C_2^4.D_6$ $2^{6} \cdot 3^{13}$ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2^{2}$ $-$
408146688.wu.6._.A $C_3^{12}.C_2^6.C_2$ $2^{7} \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $S_3$ $2 \cdot 3$
408146688.wu.6._.B $C_3^9.C_6^3.C_2^4$ $2^{7} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2 \cdot 3$ $-$
408146688.wu.6._.C $C_3^{12}.C_2^6.C_2$ $2^{7} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2 \cdot 3$ $-$
408146688.wu.6._.D $C_3^{12}.C_2^5.C_2^2$ $2^{7} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2 \cdot 3$ $-$
408146688.wu.6._.E $C_3^{12}.D_4^2.C_2$ $2^{7} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2 \cdot 3$ $-$
408146688.wu.6._.F $C_3^{12}.C_2^5.C_2^2$ $2^{7} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2 \cdot 3$ $-$
408146688.wu.6._.G $C_3^{12}.C_2^5.C_2^2$ $2^{7} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2 \cdot 3$ $-$
408146688.wu.6._.H $C_3^9.C_6^3.C_2.C_2^3$ $2^{7} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2 \cdot 3$ $-$
408146688.wu.6._.I $C_3^{12}.C_2^5.C_2^2$ $2^{7} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2 \cdot 3$ $-$
408146688.wu.6._.J $C_3^9.C_6^3.C_2^4$ $2^{7} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2 \cdot 3$ $-$
408146688.wu.6._.K $C_3^{11}.C_2^4.C_6.C_2^2$ $2^{7} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2 \cdot 3$ $-$
408146688.wu.6._.L $C_3^{12}.C_2^5.C_2^2$ $2^{7} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2 \cdot 3$ $-$
408146688.wu.6._.M $C_3^{12}.C_2^5.C_2^2$ $2^{7} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2 \cdot 3$ $-$
408146688.wu.6._.N $C_3^{12}.C_2^5.C_2^2$ $2^{7} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2 \cdot 3$ $-$
408146688.wu.6._.O $C_3^{12}.C_2^5.C_2^2$ $2^{7} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2 \cdot 3$ $-$
408146688.wu.8._.A $C_3^{12}.C_2^4.S_3$ $2^{5} \cdot 3^{13}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2^{3}$ $-$
408146688.wu.8._.B $C_3^{12}.C_2^4.S_3$ $2^{5} \cdot 3^{13}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2^{3}$ $-$
408146688.wu.8._.C $C_3^8.C_6^2.C_6^2.S_3$ $2^{5} \cdot 3^{13}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2^{3}$ $-$
408146688.wu.8._.D $C_3^{12}.C_2^4.C_6$ $2^{5} \cdot 3^{13}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2^{3}$ $-$
408146688.wu.8._.E $C_3^8.C_6^4:C_6$ $2^{5} \cdot 3^{13}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2^{3}$ $-$
408146688.wu.8._.F $C_3^{12}.C_2^4.C_6$ $2^{5} \cdot 3^{13}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2^{3}$ $-$
408146688.wu.8._.G $C_3^{12}.C_2^4.S_3$ $2^{5} \cdot 3^{13}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2^{3}$ $-$
408146688.wu.8._.H $C_3^{12}.C_2^4.S_3$ $2^{5} \cdot 3^{13}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2^{3}$ $-$
408146688.wu.8._.I $C_3^8.C_6^4:S_3$ $2^{5} \cdot 3^{13}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2^{3}$ $-$
408146688.wu.8._.J $C_3^9.C_6^2.C_3:S_4$ $2^{5} \cdot 3^{13}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2^{3}$ $-$
408146688.wu.8._.K $C_3^{12}.C_2^4.S_3$ $2^{5} \cdot 3^{13}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2^{3}$ $-$
408146688.wu.8._.L $C_3^{12}.C_2^4.C_6$ $2^{5} \cdot 3^{13}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2^{3}$ $-$
408146688.wu.8._.M $C_3^{12}.C_2^4.S_3$ $2^{5} \cdot 3^{13}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2^{3}$ $-$
408146688.wu.8._.N $C_3^{12}.C_2^4.S_3$ $2^{5} \cdot 3^{13}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2^{3}$ $-$
408146688.wu.9._.A $C_3^{11}.C_2^6.C_2^2$ $2^{8} \cdot 3^{11}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $3^{2}$ $-$
408146688.wu.9._.B $C_3^{11}.C_2^6.C_2^2$ $2^{8} \cdot 3^{11}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $3^{2}$ $-$
408146688.wu.12._.A $C_3^{12}.C_2^6$ $2^{6} \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $D_6$ $2^{2} \cdot 3$
408146688.wu.12._.B $C_3^{10}.C_6^2.C_2.C_2^3$ $2^{6} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2^{2} \cdot 3$ $-$
408146688.wu.12._.C $C_3^{12}.C_2^4.C_2^2$ $2^{6} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2^{2} \cdot 3$ $-$
408146688.wu.12._.D $C_3^{10}.C_6^2.C_2.C_2^3$ $2^{6} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2^{2} \cdot 3$ $-$
408146688.wu.12._.E $C_3^{12}.C_2^4.C_2^2$ $2^{6} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2^{2} \cdot 3$ $-$
408146688.wu.12._.F $C_3^9.C_6^3.C_2^3$ $2^{6} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2^{2} \cdot 3$ $-$
408146688.wu.12._.G $C_3^9.C_6^3.C_2^3$ $2^{6} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2^{2} \cdot 3$ $-$
408146688.wu.12._.H $C_3^{10}.C_6^2.C_2^4$ $2^{6} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2^{2} \cdot 3$ $-$
408146688.wu.12._.I $C_3^{10}.C_6^2.C_2^4$ $2^{6} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2^{2} \cdot 3$ $-$
408146688.wu.12._.J $C_3^{12}.C_2^5.C_2$ $2^{6} \cdot 3^{12}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $2^{2} \cdot 3$ $-$
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