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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 82 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
432.131.432.a1.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
864.331.432.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{12}:C_{72}$ $2^{5} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$ ✓
864.332.432.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{12}^2.C_6$ $2^{5} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$ ✓
864.375.432.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{24}:C_{36}$ $2^{5} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$ ✓
864.377.432.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{24}:C_{36}$ $2^{5} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$ ✓
864.443.432.d1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_2\times C_{12}):C_{36}$ $2^{5} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$ ✓
864.1545.432.b1 $C_2$ $2$ ✓ ✓ ✓ $C_2\times C_{12}:C_{36}$ $2^{5} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$ ✓
1296.305.432.b1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_{36}:C_{36}$ $2^{4} \cdot 3^{4}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$ ✓
1296.313.432.b1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_4\times C_3^2:C_{36}$ $2^{4} \cdot 3^{4}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$ ✓
1296.323.432.b1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_{36}:C_{36}$ $2^{4} \cdot 3^{4}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$ ✓
1296.334.432.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_{12}:C_{108}$ $2^{4} \cdot 3^{4}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$ ✓
1296.1325.432.b1.a1 $C_3$ $3$ ✓ ✓ $C_9\times C_3^2:C_4^2$ $2^{4} \cdot 3^{4}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$ ✓
1296.1325.432.b1.b1 $C_3$ $3$ ✓ ✓ $C_9\times C_3^2:C_4^2$ $2^{4} \cdot 3^{4}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$ ✓
1296.1544.432.a1 $C_3$ $3$ ✓ ✓ ✓ $C_3^2.C_{12}^2$ $2^{4} \cdot 3^{4}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$ ✓
1296.1645.432.b1 $C_3$ $3$ ✓ ✓ $C_4\times C_3^2:C_{36}$ $2^{4} \cdot 3^{4}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$ ✓
1728.1332.432.b1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{24}:C_{72}$ $2^{6} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
1728.1333.432.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_6.(C_4\times C_{72})$ $2^{6} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
1728.1334.432.b1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{24}:C_{72}$ $2^{6} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
1728.1337.432.c1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{12}:C_{144}$ $2^{6} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
1728.1338.432.c1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{24}.C_{72}$ $2^{6} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
1728.1368.432.b1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{12}^2.C_{12}$ $2^{6} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
1728.1513.432.c1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{48}:C_{36}$ $2^{6} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
1728.1515.432.c1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{48}:C_{36}$ $2^{6} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
1728.1559.432.b1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{48}:C_{36}$ $2^{6} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
1728.1605.432.f1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{12}^2.C_{12}$ $2^{6} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
1728.1606.432.d1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $(C_2\times C_{12}):C_{72}$ $2^{6} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
1728.1615.432.d1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_9\times C_2^3.D_{12}$ $2^{6} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
1728.1616.432.b1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $(C_2^2\times C_{12}):C_{36}$ $2^{6} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
1728.1627.432.i1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_9\times C_{12}.C_4^2$ $2^{6} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
1728.1628.432.b1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $(C_2\times C_{36}).D_{12}$ $2^{6} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
1728.1638.432.g1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_9\times C_{12}.C_4^2$ $2^{6} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
1728.1639.432.d1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{12}^2.C_{12}$ $2^{6} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
1728.1640.432.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $(C_2\times C_{36}).D_{12}$ $2^{6} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
1728.1712.432.d1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $(C_2\times C_{24}):C_{36}$ $2^{6} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
1728.1713.432.g1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $(C_2\times C_{24}):C_{36}$ $2^{6} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
1728.1714.432.d1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_9\times C_{12}.C_4^2$ $2^{6} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
1728.1732.432.b1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $(C_3\times \OD_{16}):C_{36}$ $2^{6} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
1728.1733.432.f1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_9\times C_{12}.C_4^2$ $2^{6} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
1728.1734.432.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $(C_2\times C_{24}):C_{36}$ $2^{6} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
1728.1735.432.c1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $(C_2\times C_{24}):C_{36}$ $2^{6} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
1728.1736.432.g1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_9\times C_{12}.C_4^2$ $2^{6} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
1728.1737.432.c1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $C_9\times C_{12}.C_4^2$ $2^{6} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
1728.1738.432.b1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $(C_3\times \OD_{16}):C_{36}$ $2^{6} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
1728.8434.432.b1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_{12}^2.C_{12}$ $2^{6} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
1728.8434.432.f1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{12}^2.C_{12}$ $2^{6} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
1728.8435.432.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_{12}^2.C_{12}$ $2^{6} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
1728.8435.432.e1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{12}^2.C_{12}$ $2^{6} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
1728.8436.432.c1 $C_2^2$ $2^{2}$ ✓ ✓ $C_{12}^2.C_{12}$ $2^{6} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
1728.8436.432.e1 $C_4$ $2^{2}$ ✓ ✓ $C_{12}^2.C_{12}$ $2^{6} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
1728.8453.432.b1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{12}^2.C_{12}$ $2^{6} \cdot 3^{3}$ $C_{12}:C_{36}$ $2^{4} \cdot 3^{3}$
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