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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 149 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
128.10.2.b1.a1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ ✓ $\OD_{16}:C_8$ $2^{7}$ $C_2$ $2$ ✓
128.15.2.a1.a1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ ✓ $\OD_{16}:C_8$ $2^{7}$ $C_2$ $2$ ✓
128.20.2.b1.a1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.23.2.a1.a1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.31.2.a1.a1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.32.2.b1.a1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.181.2.b1.a1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ ✓ $C_8\times \OD_{16}$ $2^{7}$ $C_2$ $2$ ✓
128.183.2.b1.a1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ ✓ $C_8:\OD_{16}$ $2^{7}$ $C_2$ $2$ ✓
128.185.2.a1.a1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ ✓ $C_8^2:C_2$ $2^{7}$ $C_2$ $2$ ✓
128.187.2.a1.a1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ $C_8^2:C_2$ $2^{7}$ $C_2$ $2$ ✓
128.187.2.a1.b1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ $C_8^2:C_2$ $2^{7}$ $C_2$ $2$ ✓
128.187.2.a1.c1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ $C_8^2:C_2$ $2^{7}$ $C_2$ $2$ ✓
128.215.2.b1.a1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.216.2.b1.a1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.217.2.b1.a1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.221.2.c1.a1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ ✓ $D_4:\OD_{16}$ $2^{7}$ $C_2$ $2$ ✓
128.222.2.b1.a1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ ✓ $D_4:\OD_{16}$ $2^{7}$ $C_2$ $2$ ✓
128.223.2.b1.a1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ ✓ $Q_8:\OD_{16}$ $2^{7}$ $C_2$ $2$ ✓
128.256.2.c1.a1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.257.2.b1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.258.2.b1.a1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.258.2.b1.b1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.259.2.b1.a1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.260.2.b1.a1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.261.2.b1.a1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.297.2.a1.a1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ ✓ $\OD_{16}:C_8$ $2^{7}$ $C_2$ $2$ ✓
128.301.2.a1.a1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ ✓ $C_8:\OD_{16}$ $2^{7}$ $C_2$ $2$ ✓
128.487.2.c1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.488.2.b1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.490.2.d1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ ✓ $D_4:C_4^2$ $2^{7}$ $C_2$ $2$ ✓
128.491.2.d1.a1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ ✓ $D_4.C_4^2$ $2^{7}$ $C_2$ $2$ ✓
128.509.2.b1.a1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ $C_8.C_4^2$ $2^{7}$ $C_2$ $2$ ✓
128.509.2.b1.b1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ $C_8.C_4^2$ $2^{7}$ $C_2$ $2$ ✓
128.510.2.b1.a1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ $C_8.C_4^2$ $2^{7}$ $C_2$ $2$ ✓
128.510.2.b1.b1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ $C_8.C_4^2$ $2^{7}$ $C_2$ $2$ ✓
128.573.2.b1.a1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ ✓ $(C_4\times C_8):C_4$ $2^{7}$ $C_2$ $2$ ✓
128.664.2.e1.a1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.682.2.b1.a1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.697.2.c1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ ✓ $\OD_{16}:D_4$ $2^{7}$ $C_2$ $2$ ✓
128.698.2.b1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.699.2.c1.a1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.712.2.d1.a1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ ✓ $\OD_{16}:D_4$ $2^{7}$ $C_2$ $2$ ✓
128.718.2.c1.a1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ ✓ $\OD_{16}:Q_8$ $2^{7}$ $C_2$ $2$ ✓
128.729.2.b1.a1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ ✓ $\OD_{16}:Q_8$ $2^{7}$ $C_2$ $2$ ✓
128.730.2.b1.a1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ ✓ $C_4^2.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.897.2.a1.a1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ ✓ $C_8.\OD_{16}$ $2^{7}$ $C_2$ $2$ ✓
128.1603.2.e1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ $C_2^3.C_4^2$ $2^{7}$ $C_2$ $2$ ✓
128.1605.2.d1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ $C_2^3.C_4^2$ $2^{7}$ $C_2$ $2$ ✓
128.1606.2.b1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ $D_4.C_4^2$ $2^{7}$ $C_2$ $2$ ✓
128.1607.2.b1 $C_4\times \OD_{16}$ $2^{6}$ ✓ ✓ $D_4.C_4^2$ $2^{7}$ $C_2$ $2$ ✓
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