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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 155 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
288.491.1.a1.a1 $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ ✓ ✓ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $C_1$ $1$ ✓
288.491.2.a1.a1 $C_{12}.D_6$ $2^{4} \cdot 3^{2}$ ✓ ✓ ✓ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $C_2$ $2$ ✓
288.491.2.b1.a1 $C_{12}:C_{12}$ $2^{4} \cdot 3^{2}$ ✓ ✓ ✓ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $C_2$ $2$ ✓
288.491.2.c1.a1 $C_3^2:C_4^2$ $2^{4} \cdot 3^{2}$ ✓ ✓ ✓ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $C_2$ $2$ ✓
288.491.2.d1.a1 $C_3^2:C_4^2$ $2^{4} \cdot 3^{2}$ ✓ ✓ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $C_2$ $2$ ✓
288.491.2.d1.b1 $C_3^2:C_4^2$ $2^{4} \cdot 3^{2}$ ✓ ✓ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $C_2$ $2$ ✓
288.491.2.e1.a1 $C_6.D_{12}$ $2^{4} \cdot 3^{2}$ ✓ ✓ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $C_2$ $2$ ✓
288.491.2.e1.b1 $C_6.D_{12}$ $2^{4} \cdot 3^{2}$ ✓ ✓ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $C_2$ $2$ ✓
288.491.3.a1.a1 $C_3:(C_4\times Q_8)$ $2^{5} \cdot 3$ ✓ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $3$ $-$
288.491.3.b1.a1 $C_3:C_4\times Q_8$ $2^{5} \cdot 3$ ✓ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $3$ $-$
288.491.4.a1.a1 $C_6\times C_{12}$ $2^{3} \cdot 3^{2}$ ✓ ✓ ✓ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
288.491.4.b1.a1 $C_6:C_{12}$ $2^{3} \cdot 3^{2}$ ✓ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
288.491.4.b1.b1 $C_6:C_{12}$ $2^{3} \cdot 3^{2}$ ✓ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
288.491.4.c1.a1 $C_6:C_{12}$ $2^{3} \cdot 3^{2}$ ✓ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
288.491.4.c1.b1 $C_6:C_{12}$ $2^{3} \cdot 3^{2}$ ✓ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
288.491.4.d1.a1 $C_6.D_6$ $2^{3} \cdot 3^{2}$ ✓ ✓ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
288.491.4.e1.a1 $C_6.D_6$ $2^{3} \cdot 3^{2}$ ✓ ✓ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
288.491.4.f1.a1 $C_3^2:Q_8$ $2^{3} \cdot 3^{2}$ ✓ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $C_4$ $2^{2}$ ✓
288.491.4.f1.b1 $C_3^2:Q_8$ $2^{3} \cdot 3^{2}$ ✓ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $C_4$ $2^{2}$ ✓
288.491.4.f1.c1 $C_3^2:Q_8$ $2^{3} \cdot 3^{2}$ ✓ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $C_4$ $2^{2}$ ✓
288.491.4.f1.d1 $C_3^2:Q_8$ $2^{3} \cdot 3^{2}$ ✓ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $C_4$ $2^{2}$ ✓
288.491.6.a1.a1 $C_6:Q_8$ $2^{4} \cdot 3$ ✓ ✓ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $S_3$ $2 \cdot 3$
288.491.6.b1.a1 $C_{12}:C_4$ $2^{4} \cdot 3$ ✓ ✓ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $S_3$ $2 \cdot 3$
288.491.6.c1.a1 $C_4:C_{12}$ $2^{4} \cdot 3$ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $2 \cdot 3$ $-$
288.491.6.d1.a1 $C_{12}:C_4$ $2^{4} \cdot 3$ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $2 \cdot 3$ $-$
288.491.6.e1.a1 $C_{12}:C_4$ $2^{4} \cdot 3$ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $2 \cdot 3$ $-$
288.491.6.e1.b1 $C_{12}:C_4$ $2^{4} \cdot 3$ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $2 \cdot 3$ $-$
288.491.6.f1.a1 $C_6.D_4$ $2^{4} \cdot 3$ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $2 \cdot 3$ $-$
288.491.6.f1.b1 $C_6.D_4$ $2^{4} \cdot 3$ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $2 \cdot 3$ $-$
288.491.6.g1.a1 $C_6\times Q_8$ $2^{4} \cdot 3$ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $2 \cdot 3$ $-$
288.491.6.h1.a1 $C_{12}:C_4$ $2^{4} \cdot 3$ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $2 \cdot 3$ $-$
288.491.6.i1.a1 $C_{12}:C_4$ $2^{4} \cdot 3$ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $2 \cdot 3$ $-$
288.491.6.i1.b1 $C_{12}:C_4$ $2^{4} \cdot 3$ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $2 \cdot 3$ $-$
288.491.6.j1.a1 $C_{12}:C_4$ $2^{4} \cdot 3$ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $2 \cdot 3$ $-$
288.491.6.j1.b1 $C_{12}:C_4$ $2^{4} \cdot 3$ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $2 \cdot 3$ $-$
288.491.6.k1.a1 $C_{12}:C_4$ $2^{4} \cdot 3$ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $2 \cdot 3$ $-$
288.491.8.a1.a1 $C_6^2$ $2^{2} \cdot 3^{2}$ ✓ ✓ ✓ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $C_2^3$ $2^{3}$ ✓
288.491.8.b1.a1 $C_3^2:C_4$ $2^{2} \cdot 3^{2}$ ✓ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $Q_8$ $2^{3}$
288.491.8.b1.b1 $C_3^2:C_4$ $2^{2} \cdot 3^{2}$ ✓ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $Q_8$ $2^{3}$
288.491.8.c1.a1 $C_3\times C_{12}$ $2^{2} \cdot 3^{2}$ ✓ ✓ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $C_2\times C_4$ $2^{3}$ ✓
288.491.8.c1.b1 $C_3\times C_{12}$ $2^{2} \cdot 3^{2}$ ✓ ✓ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $C_2\times C_4$ $2^{3}$ ✓
288.491.8.d1.a1 $C_3:C_{12}$ $2^{2} \cdot 3^{2}$ ✓ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $C_2\times C_4$ $2^{3}$ ✓
288.491.8.d1.b1 $C_3:C_{12}$ $2^{2} \cdot 3^{2}$ ✓ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $C_2\times C_4$ $2^{3}$ ✓
288.491.8.d1.c1 $C_3:C_{12}$ $2^{2} \cdot 3^{2}$ ✓ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $C_2\times C_4$ $2^{3}$ ✓
288.491.8.d1.d1 $C_3:C_{12}$ $2^{2} \cdot 3^{2}$ ✓ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $C_2\times C_4$ $2^{3}$ ✓
288.491.8.e1.a1 $C_3:C_{12}$ $2^{2} \cdot 3^{2}$ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $2^{3}$ $-$
288.491.8.e1.b1 $C_3:C_{12}$ $2^{2} \cdot 3^{2}$ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $2^{3}$ $-$
288.491.8.f1.a1 $C_3^2:C_4$ $2^{2} \cdot 3^{2}$ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $2^{3}$ $-$
288.491.9.a1.a1 $C_4\times Q_8$ $2^{5}$ $2$ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $3^{2}$ $-$
288.491.12.a1.a1 $C_2\times C_{12}$ $2^{3} \cdot 3$ ✓ ✓ ✓ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $D_6$ $2^{2} \cdot 3$
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