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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 174 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
128.1626.64.c1 $C_2$ $2$ ✓ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1627.64.b1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1642.64.d1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1672.64.d1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1673.64.c1 $C_2$ $2$ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1677.64.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1730.64.b1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^3:\SD_{16}$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1731.64.d1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^3:Q_{16}$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1733.64.b1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1736.64.b1 $C_2$ $2$ ✓ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1739.64.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1762.64.d1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1765.64.d1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1766.64.c1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1769.64.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1771.64.a1 $C_2$ $2$ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1783.64.b1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1785.64.c1 $C_2$ $2$ ✓ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1788.64.c1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $\OD_{16}:D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1802.64.d1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1805.64.d1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1807.64.c1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1810.64.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1811.64.c1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1817.64.b1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^3.D_8$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1818.64.d1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1820.64.d1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1824.64.c1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1827.64.c1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1839.64.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1840.64.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1842.64.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1844.64.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1845.64.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1845.64.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1848.64.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1849.64.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1864.64.d1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1866.64.c1 $C_2$ $2$ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1871.64.a1 $C_2$ $2$ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1873.64.c1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1881.64.c1 $C_2$ $2$ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1884.64.a1 $C_2$ $2$ ✓ ✓ ✓ $\OD_{16}:D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1893.64.c1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1897.64.c1 $C_2$ $2$ ✓ ✓ ✓ ✓ $\OD_{16}:Q_8$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1904.64.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1913.64.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1914.64.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1917.64.a1 $C_2$ $2$ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
128.1922.64.c1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $Q_{16}:C_2^2$ $2^{6}$ ✓
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