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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 287 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1728.18214.1.a1.a1 $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ ✓ ✓ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $C_1$ $1$ ✓
1728.18214.2.a1.a1 $C_9\times \SL(2,3):C_2^2$ $2^{5} \cdot 3^{3}$ ✓ ✓ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.18214.2.a1.b1 $C_9\times \SL(2,3):C_2^2$ $2^{5} \cdot 3^{3}$ ✓ ✓ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.18214.2.b1.a1 $C_{72}.A_4$ $2^{5} \cdot 3^{3}$ ✓ ✓ ✓ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.18214.3.a1.a1 $C_3\times Q_{16}.A_4$ $2^{6} \cdot 3^{2}$ ✓ ✓ ✓ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $C_3$ $3$ ✓
1728.18214.3.b1.a1 $C_{72}.C_2^3$ $2^{6} \cdot 3^{2}$ ✓ ✓ ✓ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $C_3$ $3$ ✓
1728.18214.3.c1.a1 $C_{24}.(C_2\times A_4)$ $2^{6} \cdot 3^{2}$ ✓ ✓ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $C_3$ $3$ ✓
1728.18214.3.c1.b1 $C_{24}.(C_2\times A_4)$ $2^{6} \cdot 3^{2}$ ✓ ✓ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $C_3$ $3$ ✓
1728.18214.4.a1.a1 $\SL(2,3):C_{18}$ $2^{4} \cdot 3^{3}$ ✓ ✓ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.18214.4.b1.a1 $\SL(2,3):C_{18}$ $2^{4} \cdot 3^{3}$ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $2^{2}$ $-$
1728.18214.4.b1.b1 $\SL(2,3):C_{18}$ $2^{4} \cdot 3^{3}$ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $2^{2}$ $-$
1728.18214.4.c1.a1 $C_{24}.C_{18}$ $2^{4} \cdot 3^{3}$ ✓ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $2^{2}$ $-$
1728.18214.6.a1.a1 $Q_8.C_6^2$ $2^{5} \cdot 3^{2}$ ✓ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $C_6$ $2 \cdot 3$ ✓
1728.18214.6.a1.b1 $Q_8.C_6^2$ $2^{5} \cdot 3^{2}$ ✓ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $C_6$ $2 \cdot 3$ ✓
1728.18214.6.b1.a1 $C_{36}.C_2^3$ $2^{5} \cdot 3^{2}$ ✓ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $C_6$ $2 \cdot 3$ ✓
1728.18214.6.b1.b1 $C_{36}.C_2^3$ $2^{5} \cdot 3^{2}$ ✓ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $C_6$ $2 \cdot 3$ ✓
1728.18214.6.c1.a1 $C_{12}.(C_2\times A_4)$ $2^{5} \cdot 3^{2}$ ✓ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $C_6$ $2 \cdot 3$ ✓
1728.18214.6.c1.b1 $C_{12}.(C_2\times A_4)$ $2^{5} \cdot 3^{2}$ ✓ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $C_6$ $2 \cdot 3$ ✓
1728.18214.6.c1.c1 $C_{12}.(C_2\times A_4)$ $2^{5} \cdot 3^{2}$ ✓ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $C_6$ $2 \cdot 3$ ✓
1728.18214.6.c1.d1 $C_{12}.(C_2\times A_4)$ $2^{5} \cdot 3^{2}$ ✓ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $C_6$ $2 \cdot 3$ ✓
1728.18214.6.d1.a1 $C_{24}.A_4$ $2^{5} \cdot 3^{2}$ ✓ ✓ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $C_6$ $2 \cdot 3$ ✓
1728.18214.6.e1.a1 $\OD_{16}:C_{18}$ $2^{5} \cdot 3^{2}$ ✓ ✓ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $C_6$ $2 \cdot 3$ ✓
1728.18214.6.f1.a1 $C_{24}.A_4$ $2^{5} \cdot 3^{2}$ ✓ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $C_6$ $2 \cdot 3$ ✓
1728.18214.6.f1.b1 $C_{24}.A_4$ $2^{5} \cdot 3^{2}$ ✓ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $C_6$ $2 \cdot 3$ ✓
1728.18214.6.g1.a1 $D_8:C_{18}$ $2^{5} \cdot 3^{2}$ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.18214.6.h1.a1 $D_8:C_{18}$ $2^{5} \cdot 3^{2}$ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.18214.6.h1.b1 $D_8:C_{18}$ $2^{5} \cdot 3^{2}$ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.18214.6.i1.a1 $D_8\times C_{18}$ $2^{5} \cdot 3^{2}$ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.18214.8.a1.a1 $C_9\times \SL(2,3)$ $2^{3} \cdot 3^{3}$ ✓ ✓ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $D_4$ $2^{3}$
1728.18214.8.b1.a1 $C_{12}.C_{18}$ $2^{3} \cdot 3^{3}$ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $2^{3}$ $-$
1728.18214.8.b1.b1 $C_{12}.C_{18}$ $2^{3} \cdot 3^{3}$ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $2^{3}$ $-$
1728.18214.8.c1.a1 $C_3\times C_{72}$ $2^{3} \cdot 3^{3}$ ✓ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $2^{3}$ $-$
1728.18214.9.a1.a1 $C_{12}.C_2^4$ $2^{6} \cdot 3$ ✓ ✓ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $C_3^2$ $3^{2}$ ✓
1728.18214.9.b1.a1 $Q_{16}.A_4$ $2^{6} \cdot 3$ ✓ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $C_9$ $3^{2}$ ✓
1728.18214.9.b1.b1 $Q_{16}.A_4$ $2^{6} \cdot 3$ ✓ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $C_9$ $3^{2}$ ✓
1728.18214.9.b1.c1 $Q_{16}.A_4$ $2^{6} \cdot 3$ ✓ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $C_9$ $3^{2}$ ✓
1728.18214.12.a1.a1 $\SL(2,3):C_6$ $2^{4} \cdot 3^{2}$ ✓ ✓ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $C_2\times C_6$ $2^{2} \cdot 3$ ✓
1728.18214.12.b1.a1 $D_4:C_{18}$ $2^{4} \cdot 3^{2}$ ✓ ✓ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $C_2\times C_6$ $2^{2} \cdot 3$ ✓
1728.18214.12.c1.a1 $C_{12}.A_4$ $2^{4} \cdot 3^{2}$ ✓ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $C_2\times C_6$ $2^{2} \cdot 3$ ✓
1728.18214.12.c1.b1 $C_{12}.A_4$ $2^{4} \cdot 3^{2}$ ✓ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $C_2\times C_6$ $2^{2} \cdot 3$ ✓
1728.18214.12.d1.a1 $C_9\times Q_{16}$ $2^{4} \cdot 3^{2}$ ✓ ✓ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $A_4$ $2^{2} \cdot 3$
1728.18214.12.e1.a1 $D_4:C_{18}$ $2^{4} \cdot 3^{2}$ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
1728.18214.12.e1.b1 $D_4:C_{18}$ $2^{4} \cdot 3^{2}$ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
1728.18214.12.f1.a1 $D_4\times C_{18}$ $2^{4} \cdot 3^{2}$ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
1728.18214.12.f1.b1 $D_4\times C_{18}$ $2^{4} \cdot 3^{2}$ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
1728.18214.12.g1.a1 $C_2\times C_{72}$ $2^{4} \cdot 3^{2}$ ✓ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
1728.18214.12.h1.a1 $C_9\times \OD_{16}$ $2^{4} \cdot 3^{2}$ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
1728.18214.12.i1.a1 $D_4\times C_{18}$ $2^{4} \cdot 3^{2}$ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
1728.18214.12.i1.b1 $D_4\times C_{18}$ $2^{4} \cdot 3^{2}$ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
1728.18214.12.j1.a1 $C_9\times \SD_{16}$ $2^{4} \cdot 3^{2}$ $C_9\times Q_{16}.A_4$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
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