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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 71 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
96.53.48.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $Q_8:C_{12}$ $2^{5} \cdot 3$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
96.57.48.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_8:C_{12}$ $2^{5} \cdot 3$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
96.181.48.a1.a1 $C_2$ $2$ ✓ ✓ ✓ $C_6\times Q_{16}$ $2^{5} \cdot 3$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
96.181.48.a1.b1 $C_2$ $2$ ✓ ✓ ✓ $C_6\times Q_{16}$ $2^{5} \cdot 3$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
144.27.48.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_9\times Q_{16}$ $2^{4} \cdot 3^{2}$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
144.73.48.b1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_3^2:Q_{16}$ $2^{4} \cdot 3^{2}$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
144.83.48.b1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_3^2:Q_{16}$ $2^{4} \cdot 3^{2}$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
144.108.48.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_3^2\times Q_{16}$ $2^{4} \cdot 3^{2}$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
144.108.48.a1.b1 $C_3$ $3$ ✓ ✓ ✓ $C_3^2\times Q_{16}$ $2^{4} \cdot 3^{2}$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
144.108.48.a1.c1 $C_3$ $3$ ✓ ✓ ✓ $C_3^2\times Q_{16}$ $2^{4} \cdot 3^{2}$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
144.108.48.a1.d1 $C_3$ $3$ ✓ ✓ ✓ $C_3^2\times Q_{16}$ $2^{4} \cdot 3^{2}$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
192.1016.48.b1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $A_4\times Q_{16}$ $2^{6} \cdot 3$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
240.37.48.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $C_{15}:Q_{16}$ $2^{4} \cdot 3 \cdot 5$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
240.47.48.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $C_{15}:Q_{16}$ $2^{4} \cdot 3 \cdot 5$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
240.88.48.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ ✓ $C_{15}\times Q_{16}$ $2^{4} \cdot 3 \cdot 5$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
336.11.48.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $C_{56}.C_6$ $2^{4} \cdot 3 \cdot 7$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
336.21.48.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $Q_8.F_7$ $2^{4} \cdot 3 \cdot 7$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
336.55.48.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $C_{56}.C_6$ $2^{4} \cdot 3 \cdot 7$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
336.62.48.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $C_{21}:Q_{16}$ $2^{4} \cdot 3 \cdot 7$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
336.72.48.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $C_{21}:Q_{16}$ $2^{4} \cdot 3 \cdot 7$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
336.113.48.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ ✓ $Q_{16}\times C_{21}$ $2^{4} \cdot 3 \cdot 7$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
432.578.48.a1.a1 $C_3^2$ $3^{2}$ ✓ ✓ ✓ $C_3^3:Q_{16}$ $2^{4} \cdot 3^{3}$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
528.35.48.a1.a1 $C_{11}$ $11$ $11$ ✓ ✓ ✓ $C_{33}:Q_{16}$ $2^{4} \cdot 3 \cdot 11$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
528.45.48.a1.a1 $C_{11}$ $11$ $11$ ✓ ✓ ✓ $C_{33}:Q_{16}$ $2^{4} \cdot 3 \cdot 11$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
528.86.48.a1.a1 $C_{11}$ $11$ $11$ ✓ ✓ ✓ ✓ $Q_{16}\times C_{33}$ $2^{4} \cdot 3 \cdot 11$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
624.12.48.a1.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ $C_{104}.C_6$ $2^{4} \cdot 3 \cdot 13$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
624.22.48.a1.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ $C_{13}:(C_3\times Q_{16})$ $2^{4} \cdot 3 \cdot 13$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
624.58.48.a1.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ $C_{104}.C_6$ $2^{4} \cdot 3 \cdot 13$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
624.65.48.a1.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ $C_{39}:Q_{16}$ $2^{4} \cdot 3 \cdot 13$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
624.75.48.a1.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ $C_{39}:Q_{16}$ $2^{4} \cdot 3 \cdot 13$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
624.116.48.a1.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ ✓ $Q_{16}\times C_{39}$ $2^{4} \cdot 3 \cdot 13$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
816.37.48.a1.a1 $C_{17}$ $17$ $17$ ✓ ✓ ✓ $C_{51}:Q_{16}$ $2^{4} \cdot 3 \cdot 17$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
816.47.48.a1.a1 $C_{17}$ $17$ $17$ ✓ ✓ ✓ $C_{51}:Q_{16}$ $2^{4} \cdot 3 \cdot 17$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
816.88.48.a1.a1 $C_{17}$ $17$ $17$ ✓ ✓ ✓ ✓ $Q_{16}\times C_{51}$ $2^{4} \cdot 3 \cdot 17$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
912.11.48.a1.a1 $C_{19}$ $19$ $19$ ✓ ✓ ✓ $C_{152}.C_6$ $2^{4} \cdot 3 \cdot 19$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
912.21.48.a1.a1 $C_{19}$ $19$ $19$ ✓ ✓ ✓ $C_{19}:(C_3\times Q_{16})$ $2^{4} \cdot 3 \cdot 19$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
912.55.48.a1.a1 $C_{19}$ $19$ $19$ ✓ ✓ ✓ $C_{152}.C_6$ $2^{4} \cdot 3 \cdot 19$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
912.62.48.a1.a1 $C_{19}$ $19$ $19$ ✓ ✓ ✓ $C_{57}:Q_{16}$ $2^{4} \cdot 3 \cdot 19$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
912.72.48.a1.a1 $C_{19}$ $19$ $19$ ✓ ✓ ✓ $C_{57}:Q_{16}$ $2^{4} \cdot 3 \cdot 19$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
912.113.48.a1.a1 $C_{19}$ $19$ $19$ ✓ ✓ ✓ ✓ $Q_{16}\times C_{57}$ $2^{4} \cdot 3 \cdot 19$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
1104.35.48.a1.a1 $C_{23}$ $23$ $23$ ✓ ✓ ✓ $C_{69}:Q_{16}$ $2^{4} \cdot 3 \cdot 23$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
1104.45.48.a1.a1 $C_{23}$ $23$ $23$ ✓ ✓ ✓ $C_{69}:Q_{16}$ $2^{4} \cdot 3 \cdot 23$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
1104.86.48.a1.a1 $C_{23}$ $23$ $23$ ✓ ✓ ✓ ✓ $Q_{16}\times C_{69}$ $2^{4} \cdot 3 \cdot 23$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
1200.248.48.a1.a1 $C_5^2$ $5^{2}$ $5$ ✓ ✓ ✓ $C_5^2:(C_3\times Q_{16})$ $2^{4} \cdot 3 \cdot 5^{2}$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
1200.258.48.a1.a1 $C_5^2$ $5^{2}$ $5$ ✓ ✓ ✓ $C_5^2:(C_3\times Q_{16})$ $2^{4} \cdot 3 \cdot 5^{2}$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
1200.382.48.a1.a1 $C_5^2$ $5^{2}$ $5$ ✓ ✓ ✓ $C_5^2:C_3\times Q_{16}$ $2^{4} \cdot 3 \cdot 5^{2}$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
1200.606.48.a1.a1 $C_5^2$ $5^{2}$ $5$ ✓ ✓ ✓ $C_3\times C_5^2:Q_{16}$ $2^{4} \cdot 3 \cdot 5^{2}$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
1392.37.48.a1.a1 $C_{29}$ $29$ $29$ ✓ ✓ ✓ $C_{87}:Q_{16}$ $2^{4} \cdot 3 \cdot 29$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
1392.47.48.a1.a1 $C_{29}$ $29$ $29$ ✓ ✓ ✓ $C_{87}:Q_{16}$ $2^{4} \cdot 3 \cdot 29$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
1392.88.48.a1.a1 $C_{29}$ $29$ $29$ ✓ ✓ ✓ ✓ $Q_{16}\times C_{87}$ $2^{4} \cdot 3 \cdot 29$ $C_3\times Q_{16}$ $2^{4} \cdot 3$ ✓
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