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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 55 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
288.376.288.a1.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$
576.1910.288.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_6\times C_{12}).D_4$ $2^{6} \cdot 3^{2}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$ ✓
576.1918.288.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_6\times C_{12}).D_4$ $2^{6} \cdot 3^{2}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$ ✓
576.1920.288.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_3\times C_{12}).D_8$ $2^{6} \cdot 3^{2}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$ ✓
576.1921.288.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_6\times C_{12}).D_4$ $2^{6} \cdot 3^{2}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$ ✓
576.1934.288.c1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_6\times C_{12}).D_4$ $2^{6} \cdot 3^{2}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$ ✓
576.5196.288.b1.a1 $C_2$ $2$ ✓ ✓ ✓ $(C_6\times C_{12}).D_4$ $2^{6} \cdot 3^{2}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$ ✓
576.5196.288.b1.b1 $C_2$ $2$ ✓ ✓ ✓ $(C_6\times C_{12}).D_4$ $2^{6} \cdot 3^{2}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$ ✓
864.667.288.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_{12}.\SOPlus(4,2)$ $2^{5} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$ ✓
864.2702.288.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_{12}.\SOPlus(4,2)$ $2^{5} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$ ✓
864.2722.288.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_{12}.\SOPlus(4,2)$ $2^{5} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$ ✓
864.2723.288.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_{12}.\SOPlus(4,2)$ $2^{5} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$ ✓
864.2749.288.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_{12}.\SOPlus(4,2)$ $2^{5} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$ ✓
1440.1873.288.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ ✓ $C_{20}.\SOPlus(4,2)$ $2^{5} \cdot 3^{2} \cdot 5$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$ ✓
1440.1893.288.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $C_{20}.\SOPlus(4,2)$ $2^{5} \cdot 3^{2} \cdot 5$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$ ✓
1440.1894.288.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $C_{20}.\SOPlus(4,2)$ $2^{5} \cdot 3^{2} \cdot 5$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$ ✓
1440.1920.288.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $C_{20}.\SOPlus(4,2)$ $2^{5} \cdot 3^{2} \cdot 5$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$ ✓
1440.4670.288.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $C_{15}:C_{12}.D_4$ $2^{5} \cdot 3^{2} \cdot 5$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$ ✓
1728.2737.288.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_6.C_6^2.D_4$ $2^{6} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$
1728.2739.288.b1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_6.S_3^2:C_8$ $2^{6} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$
1728.2745.288.b1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $(C_4\times \He_3).Q_{16}$ $2^{6} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$
1728.2749.288.b1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $(C_4\times \He_3).D_8$ $2^{6} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$
1728.2769.288.b1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_{12}.S_3^2:C_4$ $2^{6} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$
1728.12622.288.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ $C_{12}.S_3^2:C_4$ $2^{6} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$
1728.12622.288.a1.b1 $C_6$ $2 \cdot 3$ ✓ ✓ $C_{12}.S_3^2:C_4$ $2^{6} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$
1728.20941.288.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $C_2.S_3^2:C_{24}$ $2^{6} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$
1728.20949.288.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $C_6^2.C_2^2:C_{12}$ $2^{6} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$
1728.20951.288.b1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $(C_3^2\times C_{12}).D_8$ $2^{6} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$
1728.20952.288.b1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $(C_3^2\times C_{12}).Q_{16}$ $2^{6} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$
1728.20965.288.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $C_3^2:\OD_{16}:C_{12}$ $2^{6} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$
1728.21023.288.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_{12}:D_6.D_6$ $2^{6} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$
1728.21024.288.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_{12}:D_6.D_6$ $2^{6} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$
1728.21039.288.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_6^2.D_6:C_4$ $2^{6} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$
1728.21040.288.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_3^2:C_4^2.D_6$ $2^{6} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$
1728.21043.288.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $(C_3^2\times C_{12}).D_8$ $2^{6} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$
1728.21044.288.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $(C_3^2\times C_{12}).D_8$ $2^{6} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$
1728.21045.288.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $(C_3^2\times C_{12}).Q_{16}$ $2^{6} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$
1728.21046.288.b1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $(C_3^2\times C_{12}).Q_{16}$ $2^{6} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$
1728.21066.288.b1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_{12}:D_6.D_6$ $2^{6} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$
1728.21067.288.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_{12}:D_6.D_6$ $2^{6} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$
1728.21135.288.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $(C_6\times C_{12}).D_{12}$ $2^{6} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$
1728.21143.288.b1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $(C_6\times C_{12}).D_{12}$ $2^{6} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$
1728.21145.288.b1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $(C_3\times C_{12}).D_{24}$ $2^{6} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$
1728.21146.288.b1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $(C_6\times C_{12}).D_{12}$ $2^{6} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$
1728.21159.288.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $(C_6\times C_{12}).D_{12}$ $2^{6} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$
1728.31211.288.b1.a1 $S_3$ $2 \cdot 3$ ✓ $C_2.S_3^3:C_4$ $2^{6} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$
1728.31211.288.b1.b1 $S_3$ $2 \cdot 3$ ✓ $C_2.S_3^3:C_4$ $2^{6} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$
1728.32752.288.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_4.S_3^2:C_{12}$ $2^{6} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$
1728.32752.288.a1.b1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_4.S_3^2:C_{12}$ $2^{6} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$
1728.33041.288.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ $C_{12}:D_6.D_6$ $2^{6} \cdot 3^{3}$ $C_4.\SOPlus(4,2)$ $2^{5} \cdot 3^{2}$
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