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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 (42 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
118206.b.1.a1.a1 $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ ✓ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_1$ $1$ ✓
118206.b.2.a1.a1 $C_{597}:C_{99}$ $3^{3} \cdot 11 \cdot 199$ ✓ ✓ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_2$ $2$ ✓
118206.b.3.a1.a1 $C_{597}:C_{66}$ $2 \cdot 3^{2} \cdot 11 \cdot 199$ ✓ ✓ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_3$ $3$ ✓
118206.b.3.b1.a1 $F_{199}$ $2 \cdot 3^{2} \cdot 11 \cdot 199$ ✓ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_3$ $3$ ✓
118206.b.3.b1.b1 $F_{199}$ $2 \cdot 3^{2} \cdot 11 \cdot 199$ ✓ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_3$ $3$ ✓
118206.b.3.b1.c1 $F_{199}$ $2 \cdot 3^{2} \cdot 11 \cdot 199$ ✓ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_3$ $3$ ✓
118206.b.6.a1.a1 $C_{597}:C_{33}$ $3^{2} \cdot 11 \cdot 199$ ✓ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_6$ $2 \cdot 3$ ✓
118206.b.6.b1.a1 $C_{199}:C_{99}$ $3^{2} \cdot 11 \cdot 199$ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_6$ $2 \cdot 3$ ✓
118206.b.6.b1.b1 $C_{199}:C_{99}$ $3^{2} \cdot 11 \cdot 199$ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_6$ $2 \cdot 3$ ✓
118206.b.6.b1.c1 $C_{199}:C_{99}$ $3^{2} \cdot 11 \cdot 199$ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_6$ $2 \cdot 3$ ✓
118206.b.9.a1.a1 $C_{199}:C_{66}$ $2 \cdot 3 \cdot 11 \cdot 199$ ✓ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_9$ $3^{2}$ ✓
118206.b.9.b1.a1 $C_{199}:C_{66}$ $2 \cdot 3 \cdot 11 \cdot 199$ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_9$ $3^{2}$ ✓
118206.b.9.b1.b1 $C_{199}:C_{66}$ $2 \cdot 3 \cdot 11 \cdot 199$ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_9$ $3^{2}$ ✓
118206.b.9.c1.a1 $C_{199}:C_{66}$ $2 \cdot 3 \cdot 11 \cdot 199$ ✓ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_3^2$ $3^{2}$ ✓
118206.b.11.a1.a1 $C_{597}:C_{18}$ $2 \cdot 3^{3} \cdot 199$ ✓ ✓ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_{11}$ $11$ ✓
118206.b.18.a1.a1 $C_{199}:C_{33}$ $3 \cdot 11 \cdot 199$ ✓ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_{18}$ $2 \cdot 3^{2}$ ✓
118206.b.18.b1.a1 $C_{199}:C_{33}$ $3 \cdot 11 \cdot 199$ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_{18}$ $2 \cdot 3^{2}$ ✓
118206.b.18.b1.b1 $C_{199}:C_{33}$ $3 \cdot 11 \cdot 199$ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_{18}$ $2 \cdot 3^{2}$ ✓
118206.b.18.c1.a1 $C_{199}:C_{33}$ $3 \cdot 11 \cdot 199$ ✓ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_3\times C_6$ $2 \cdot 3^{2}$ ✓
118206.b.22.a1.a1 $C_{597}:C_9$ $3^{3} \cdot 199$ ✓ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_{22}$ $2 \cdot 11$ ✓
118206.b.27.a1.a1 $C_{199}:C_{22}$ $2 \cdot 11 \cdot 199$ ✓ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_3\times C_9$ $3^{3}$ ✓
118206.b.33.a1.a1 $C_{597}:C_6$ $2 \cdot 3^{2} \cdot 199$ ✓ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_{33}$ $3 \cdot 11$ ✓
118206.b.33.b1.a1 $C_{199}:C_{18}$ $2 \cdot 3^{2} \cdot 199$ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_{33}$ $3 \cdot 11$ ✓
118206.b.33.b1.b1 $C_{199}:C_{18}$ $2 \cdot 3^{2} \cdot 199$ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_{33}$ $3 \cdot 11$ ✓
118206.b.33.b1.c1 $C_{199}:C_{18}$ $2 \cdot 3^{2} \cdot 199$ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_{33}$ $3 \cdot 11$ ✓
118206.b.54.a1.a1 $C_{199}:C_{11}$ $11 \cdot 199$ ✓ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_3\times C_{18}$ $2 \cdot 3^{3}$ ✓
118206.b.66.a1.a1 $C_{597}:C_3$ $3^{2} \cdot 199$ ✓ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_{66}$ $2 \cdot 3 \cdot 11$ ✓
118206.b.66.b1.a1 $C_{199}:C_9$ $3^{2} \cdot 199$ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_{66}$ $2 \cdot 3 \cdot 11$ ✓
118206.b.66.b1.b1 $C_{199}:C_9$ $3^{2} \cdot 199$ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_{66}$ $2 \cdot 3 \cdot 11$ ✓
118206.b.66.b1.c1 $C_{199}:C_9$ $3^{2} \cdot 199$ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_{66}$ $2 \cdot 3 \cdot 11$ ✓
118206.b.99.a1.a1 $C_3\times D_{199}$ $2 \cdot 3 \cdot 199$ ✓ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_{99}$ $3^{2} \cdot 11$ ✓
118206.b.99.b1.a1 $C_{199}:C_6$ $2 \cdot 3 \cdot 199$ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_{99}$ $3^{2} \cdot 11$ ✓
118206.b.99.b1.b1 $C_{199}:C_6$ $2 \cdot 3 \cdot 199$ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_{99}$ $3^{2} \cdot 11$ ✓
118206.b.99.c1.a1 $C_{199}:C_6$ $2 \cdot 3 \cdot 199$ ✓ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_3\times C_{33}$ $3^{2} \cdot 11$ ✓
118206.b.198.a1.a1 $C_{597}$ $3 \cdot 199$ ✓ ✓ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_{198}$ $2 \cdot 3^{2} \cdot 11$ ✓
118206.b.198.b1.a1 $C_{199}:C_3$ $3 \cdot 199$ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_{198}$ $2 \cdot 3^{2} \cdot 11$ ✓
118206.b.198.b1.b1 $C_{199}:C_3$ $3 \cdot 199$ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_{198}$ $2 \cdot 3^{2} \cdot 11$ ✓
118206.b.198.c1.a1 $C_{199}:C_3$ $3 \cdot 199$ ✓ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_3\times C_{66}$ $2 \cdot 3^{2} \cdot 11$ ✓
118206.b.297.a1.a1 $D_{199}$ $2 \cdot 199$ ✓ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_3\times C_{99}$ $3^{3} \cdot 11$ ✓
118206.b.594.a1.a1 $C_{199}$ $199$ $199$ ✓ ✓ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_3\times C_{198}$ $2 \cdot 3^{3} \cdot 11$ ✓ ✓
118206.b.39402.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $F_{199}$ $2 \cdot 3^{2} \cdot 11 \cdot 199$ ✓
118206.b.118206.a1.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$ $C_3\times F_{199}$ $2 \cdot 3^{3} \cdot 11 \cdot 199$
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