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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 59 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1296.2039.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2040.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2041.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2042.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2043.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2044.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2045.648.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2046.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2047.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2048.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2049.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2050.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2051.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2052.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2053.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2054.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2055.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2056.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2057.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2058.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2059.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2060.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2061.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2062.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2063.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2064.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2065.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2066.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2067.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2068.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2069.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2070.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2071.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2072.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2073.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2074.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2075.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2076.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2077.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.S_3^3$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1296.2985.648.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_3^2:D_6^2$ $2^{4} \cdot 3^{4}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1944.2340.648.c1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1944.2341.648.b1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1944.2342.648.a1.a1 $C_3$ $3$ ✓ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1944.2342.648.a1.b1 $C_3$ $3$ ✓ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1944.2344.648.b1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1944.2345.648.b1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1944.2346.648.b1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1944.3565.648.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1944.3569.648.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_3^2:S_3^3$ $2^{3} \cdot 3^{5}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
1944.3570.648.a1 $C_3$ $3$ ✓ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $C_3.S_3^3$ $2^{3} \cdot 3^{4}$ ✓
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