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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 143 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
7114752.a.1.a1 $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_1$ $1$ ✓
7114752.a.2.A $C_{192}\times C_{193}:C_{96}$ $2^{11} \cdot 3^{2} \cdot 193$ ✓ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_2$ $2$ ✓
7114752.a.3.A $C_{192}\times C_{193}:C_{64}$ $2^{12} \cdot 3 \cdot 193$ ✓ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_3$ $3$ ✓
7114752.a.4.A $C_{18528}:C_{96}$ $2^{10} \cdot 3^{2} \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_2^2$ $2^{2}$ ✓
7114752.a.4.B $C_{37056}.C_{48}$ $2^{10} \cdot 3^{2} \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_4$ $2^{2}$ ✓
7114752.a.4.C $C_3\times C_{386}.C_2.C_8^2.C_6.C_2$ $2^{10} \cdot 3^{2} \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_4$ $2^{2}$ ✓
7114752.a.6.A $C_{12352}.C_{96}$ $2^{11} \cdot 3 \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_6$ $2 \cdot 3$ ✓
7114752.a.8.A $C_{18528}:C_{48}$ $2^{9} \cdot 3^{2} \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_2\times C_4$ $2^{3}$ ✓
7114752.a.8.C $C_{37056}.C_{24}$ $2^{9} \cdot 3^{2} \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_8$ $2^{3}$ ✓
7114752.a.8.D $C_{18528}.C_{48}$ $2^{9} \cdot 3^{2} \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_8$ $2^{3}$ ✓
7114752.a.9.a1 $C_{12352}:C_{64}$ $2^{12} \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_3^2$ $3^{2}$ ✓
7114752.a.12.A $C_{18528}:C_{32}$ $2^{10} \cdot 3 \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_2\times C_6$ $2^{2} \cdot 3$ ✓
7114752.a.12.B $C_{12352}.C_{48}$ $2^{10} \cdot 3 \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_{12}$ $2^{2} \cdot 3$ ✓
7114752.a.12.C $C_{18528}.C_{32}$ $2^{10} \cdot 3 \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_{12}$ $2^{2} \cdot 3$ ✓
7114752.a.16.A $C_{9264}:C_{48}$ $2^{8} \cdot 3^{2} \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_4^2$ $2^{4}$ ✓
7114752.a.16.B $C_{18528}:C_{24}$ $2^{8} \cdot 3^{2} \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_2\times C_8$ $2^{4}$ ✓
7114752.a.16.C $C_{9264}.C_{48}$ $2^{8} \cdot 3^{2} \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_2\times C_8$ $2^{4}$ ✓
7114752.a.16.E $C_{37056}.C_{12}$ $2^{8} \cdot 3^{2} \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_{16}$ $2^{4}$ ✓
7114752.a.16.F $C_{18528}.C_{24}$ $2^{8} \cdot 3^{2} \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_{16}$ $2^{4}$ ✓
7114752.a.18.A $C_{12352}:C_{32}$ $2^{11} \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_3\times C_6$ $2 \cdot 3^{2}$ ✓
7114752.a.24.A $C_{18528}:C_{16}$ $2^{9} \cdot 3 \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_2\times C_{12}$ $2^{3} \cdot 3$ ✓
7114752.a.24.C $C_{12352}.C_{24}$ $2^{9} \cdot 3 \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_{24}$ $2^{3} \cdot 3$ ✓
7114752.a.24.D $C_{18528}.C_{16}$ $2^{9} \cdot 3 \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_{24}$ $2^{3} \cdot 3$ ✓
7114752.a.32.A $C_{9264}:C_{24}$ $2^{7} \cdot 3^{2} \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_4\times C_8$ $2^{5}$ ✓
7114752.a.32.C $C_{18528}:C_{12}$ $2^{7} \cdot 3^{2} \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_2\times C_{16}$ $2^{5}$ ✓
7114752.a.32.D $C_{9264}.C_{24}$ $2^{7} \cdot 3^{2} \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_2\times C_{16}$ $2^{5}$ ✓
7114752.a.32.G $C_{37056}.C_6$ $2^{7} \cdot 3^{2} \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_{32}$ $2^{5}$ ✓
7114752.a.32.H $C_{18528}.C_{12}$ $2^{7} \cdot 3^{2} \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_{32}$ $2^{5}$ ✓
7114752.a.36.A $C_{6176}:C_{32}$ $2^{10} \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_6^2$ $2^{2} \cdot 3^{2}$ ✓
7114752.a.36.B $C_{12352}:C_{16}$ $2^{10} \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_3\times C_{12}$ $2^{2} \cdot 3^{2}$ ✓
7114752.a.36.C $C_{6176}.C_{32}$ $2^{10} \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_3\times C_{12}$ $2^{2} \cdot 3^{2}$ ✓
7114752.a.48.A $C_{3088}:C_{48}$ $2^{8} \cdot 3 \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_4\times C_{12}$ $2^{4} \cdot 3$ ✓
7114752.a.48.B $C_{18528}:C_8$ $2^{8} \cdot 3 \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_2\times C_{24}$ $2^{4} \cdot 3$ ✓
7114752.a.48.C $C_{3088}.C_{48}$ $2^{8} \cdot 3 \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_2\times C_{24}$ $2^{4} \cdot 3$ ✓
7114752.a.48.E $C_{12352}.C_{12}$ $2^{8} \cdot 3 \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_{48}$ $2^{4} \cdot 3$ ✓
7114752.a.48.F $C_{18528}.C_8$ $2^{8} \cdot 3 \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_{48}$ $2^{4} \cdot 3$ ✓
7114752.a.64.A $C_{4632}:C_{24}$ $2^{6} \cdot 3^{2} \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_8^2$ $2^{6}$ ✓
7114752.a.64.B $C_{9264}:C_{12}$ $2^{6} \cdot 3^{2} \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_4\times C_{16}$ $2^{6}$ ✓
7114752.a.64.C $C_{4632}.C_{24}$ $2^{6} \cdot 3^{2} \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_4\times C_{16}$ $2^{6}$ ✓
7114752.a.64.E $C_{18528}.C_6$ $2^{6} \cdot 3^{2} \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_2\times C_{32}$ $2^{6}$ ✓
7114752.a.64.F $C_{9264}.C_{12}$ $2^{6} \cdot 3^{2} \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_2\times C_{32}$ $2^{6}$ ✓
7114752.a.64.J $C_{12352}:C_3^2$ $2^{6} \cdot 3^{2} \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_{64}$ $2^{6}$ ✓
7114752.a.64.K $C_{1158}.C_{96}$ $2^{6} \cdot 3^{2} \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_{64}$ $2^{6}$ ✓
7114752.a.72.A $C_{6176}:C_{16}$ $2^{9} \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_6\times C_{12}$ $2^{3} \cdot 3^{2}$ ✓
7114752.a.72.C $C_{12352}:C_8$ $2^{9} \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_3\times C_{24}$ $2^{3} \cdot 3^{2}$ ✓
7114752.a.72.D $C_{6176}.C_{16}$ $2^{9} \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_3\times C_{24}$ $2^{3} \cdot 3^{2}$ ✓
7114752.a.96.A $C_{3088}:C_{24}$ $2^{7} \cdot 3 \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_4\times C_{24}$ $2^{5} \cdot 3$ ✓
7114752.a.96.C $C_{18528}.C_4$ $2^{7} \cdot 3 \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_2\times C_{48}$ $2^{5} \cdot 3$ ✓
7114752.a.96.D $C_3\times C_{193}:(C_4\times C_{32})$ $2^{7} \cdot 3 \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_2\times C_{48}$ $2^{5} \cdot 3$ ✓
7114752.a.96.G $C_{12352}.C_6$ $2^{7} \cdot 3 \cdot 193$ ✓ ✓ $C_{193}:C_{192}^2$ $2^{12} \cdot 3^{2} \cdot 193$ $C_{96}$ $2^{5} \cdot 3$ ✓
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