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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 218 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
11019960576.bb.1.a1.a1 $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ ✓ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_1$ $1$ ✓
11019960576.bb.2._.A $C_3^8.C_3^8:(C_2^4.D_4)$ $2^{7} \cdot 3^{16}$ ✓ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2$ $2$ ✓
11019960576.bb.2._.B $C_3^8.C_3^8:(C_2^5:C_4)$ $2^{7} \cdot 3^{16}$ ✓ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2$ $2$ ✓
11019960576.bb.2._.C $C_3^8.C_3^8:(C_2^4.D_4)$ $2^{7} \cdot 3^{16}$ ✓ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2$ $2$ ✓
11019960576.bb.2._.D $C_3^8.C_3^4.C_3^4.C_2^6.C_2$ $2^{7} \cdot 3^{16}$ ✓ ✓ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2$ $2$ ✓
11019960576.bb.2._.E $C_3^8.C_3^8:(C_2^4.D_4)$ $2^{7} \cdot 3^{16}$ ✓ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2$ $2$ ✓
11019960576.bb.2._.F $C_3^8.C_3^8:(C_2^4.D_4)$ $2^{7} \cdot 3^{16}$ ✓ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2$ $2$ ✓
11019960576.bb.2._.G $C_3^8.C_3^8:(C_2^4.D_4)$ $2^{7} \cdot 3^{16}$ ✓ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2$ $2$ ✓
11019960576.bb.2._.H $C_3^{12}.C_3^4.C_2^6.C_2$ $2^{7} \cdot 3^{16}$ ✓ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2$ $2$ ✓
11019960576.bb.2._.I $C_3^8.C_3^8:(C_2^4.D_4)$ $2^{7} \cdot 3^{16}$ ✓ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2$ $2$ ✓
11019960576.bb.2._.J $C_3^8.C_3^8:(C_2^4.D_4)$ $2^{7} \cdot 3^{16}$ ✓ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2$ $2$ ✓
11019960576.bb.2._.K $C_3^8.C_3^8:(C_2^4.D_4)$ $2^{7} \cdot 3^{16}$ ✓ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2$ $2$ ✓
11019960576.bb.2._.L $C_3^8.C_3^4.C_3^4.C_2^6.C_2$ $2^{7} \cdot 3^{16}$ ✓ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2$ $2$ ✓
11019960576.bb.2._.M $C_3^8.C_3^8:(C_2^4.D_4)$ $2^{7} \cdot 3^{16}$ ✓ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2$ $2$ ✓
11019960576.bb.2._.N $C_3^8.C_3^8:(C_2^5:C_4)$ $2^{7} \cdot 3^{16}$ ✓ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2$ $2$ ✓
11019960576.bb.2._.O $C_3^8.C_3^8:(C_2^4.D_4)$ $2^{7} \cdot 3^{16}$ ✓ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2$ $2$ ✓
11019960576.bb.4._.A $C_3^{10}.C_3^5.C_6.C_2^5$ $2^{6} \cdot 3^{16}$ ✓ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
11019960576.bb.4._.B $C_3^8.C_3^5.C_3^3.C_2^5.C_2$ $2^{6} \cdot 3^{16}$ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
11019960576.bb.4._.C $C_3^8.C_3^4.C_3^4.C_2^5.C_2$ $2^{6} \cdot 3^{16}$ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
11019960576.bb.4._.D $C_3^8.C_3^4.C_3^4.C_2^5.C_2$ $2^{6} \cdot 3^{16}$ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
11019960576.bb.4._.E $C_3^{10}.C_3^4.D_6^2.C_2^2$ $2^{6} \cdot 3^{16}$ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
11019960576.bb.4._.F $C_3^8.C_3^4.C_3^4.C_2^5.C_2$ $2^{6} \cdot 3^{16}$ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
11019960576.bb.4._.G $C_3^8.C_3^8:(C_2^2.C_4^2)$ $2^{6} \cdot 3^{16}$ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
11019960576.bb.4._.H $C_3^8.C_3^8:(C_2^4:C_4)$ $2^{6} \cdot 3^{16}$ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
11019960576.bb.4._.I $C_3^{10}.C_3^4.D_6^2.C_2^2$ $2^{6} \cdot 3^{16}$ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
11019960576.bb.4._.J $C_3^8.C_3^8:(C_2^2.C_4^2)$ $2^{6} \cdot 3^{16}$ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
11019960576.bb.4._.K $C_3^8.C_3^5.C_3^3.C_2^5.C_2$ $2^{6} \cdot 3^{16}$ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
11019960576.bb.4._.L $C_3^8.(C_3^2:S_3^3.S_3^3)$ $2^{6} \cdot 3^{16}$ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
11019960576.bb.4._.M $C_3^8.C_3^4.C_3^4.C_2^5.C_2$ $2^{6} \cdot 3^{16}$ ✓ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
11019960576.bb.4._.N $C_3^8.C_3^8:(C_2^2.C_4^2)$ $2^{6} \cdot 3^{16}$ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
11019960576.bb.4._.O $C_3^8.C_3^8:(C_2^2.C_4^2)$ $2^{6} \cdot 3^{16}$ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
11019960576.bb.4._.P $C_3^8.C_3^4.C_3^4.C_2^5.C_2$ $2^{6} \cdot 3^{16}$ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
11019960576.bb.4._.Q $C_3^8.C_3^4.C_3^4.C_2^5.C_2$ $2^{6} \cdot 3^{16}$ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
11019960576.bb.4._.R $C_3^{10}.C_3^4.D_6^2.C_2^2$ $2^{6} \cdot 3^{16}$ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
11019960576.bb.4._.S $C_3^8.(C_3^6.D_6^2:C_4)$ $2^{6} \cdot 3^{16}$ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
11019960576.bb.4._.T $C_3^8.C_3^8:(C_2^2.C_4^2)$ $2^{6} \cdot 3^{16}$ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
11019960576.bb.4._.U $C_3^6.C_3^4.C_3^5.C_6.C_2^5$ $2^{6} \cdot 3^{16}$ ✓ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
11019960576.bb.4._.V $C_3^8.C_3^4.C_3^4.C_2^5.C_2$ $2^{6} \cdot 3^{16}$ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
11019960576.bb.4._.W $C_3^8.(C_3^2:S_3^3.S_3^3)$ $2^{6} \cdot 3^{16}$ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
11019960576.bb.4._.X $C_3^8.(C_3^6.D_6^2:C_4)$ $2^{6} \cdot 3^{16}$ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
11019960576.bb.4._.Y $C_3^8.C_3^4.C_3^4.C_2^5.C_2$ $2^{6} \cdot 3^{16}$ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
11019960576.bb.4._.Z $C_3^8.C_3^4.C_3^4.C_2^5.C_2$ $2^{6} \cdot 3^{16}$ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
11019960576.bb.4._.BA $C_3^8.(C_3^6.D_6^2:C_4)$ $2^{6} \cdot 3^{16}$ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
11019960576.bb.4._.BB $C_3^8.C_3^8:(C_2^2.C_4^2)$ $2^{6} \cdot 3^{16}$ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
11019960576.bb.4._.BC $C_3^6.C_3^4.C_3^4.C_3^2.C_2^5.C_2$ $2^{6} \cdot 3^{16}$ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
11019960576.bb.4._.BD $C_3^8.C_3^8:(C_2^2.C_4^2)$ $2^{6} \cdot 3^{16}$ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
11019960576.bb.4._.BE $C_3^{10}.C_3^4.D_6^2.C_2^2$ $2^{6} \cdot 3^{16}$ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
11019960576.bb.4._.BF $C_3^8.(C_3^6.D_6^2:C_4)$ $2^{6} \cdot 3^{16}$ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
11019960576.bb.4._.BG $C_3^8.C_3^4.C_3^4.C_2^5.C_2$ $2^{6} \cdot 3^{16}$ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
11019960576.bb.4._.BH $C_3^8.C_3^8:(C_2^2.C_4^2)$ $2^{6} \cdot 3^{16}$ ✓ $C_3^8.C_3^8:(C_2^5.D_4)$ $2^{8} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
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