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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 309 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
5184.ch.1.a1.a1 $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ ✓ ✓ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $C_1$ $1$ ✓
5184.ch.2.a1.a1 $C_3^4:C_4\wr C_2$ $2^{5} \cdot 3^{4}$ ✓ ✓ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $C_2$ $2$ ✓
5184.ch.2.a1.b1 $C_3^4:C_4\wr C_2$ $2^{5} \cdot 3^{4}$ ✓ ✓ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $C_2$ $2$ ✓
5184.ch.2.b1.a1 $C_3^4:Q_{16}:C_2$ $2^{5} \cdot 3^{4}$ ✓ ✓ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $C_2$ $2$ ✓
5184.ch.2.b1.b1 $C_3^4:Q_{16}:C_2$ $2^{5} \cdot 3^{4}$ ✓ ✓ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $C_2$ $2$ ✓
5184.ch.2.c1.a1 $C_3^4:C_4.C_2^3$ $2^{5} \cdot 3^{4}$ ✓ ✓ ✓ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $C_2$ $2$ ✓
5184.ch.2.d1.a1 $C_3^3:C_{12}:Q_8$ $2^{5} \cdot 3^{4}$ ✓ ✓ ✓ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $C_2$ $2$ ✓
5184.ch.2.e1.a1 $C_3^4:C_4.D_4$ $2^{5} \cdot 3^{4}$ ✓ ✓ ✓ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $C_2$ $2$ ✓
5184.ch.4.a1.a1 $C_3^4:D_4:C_2$ $2^{4} \cdot 3^{4}$ ✓ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
5184.ch.4.a1.b1 $C_3^4:D_4:C_2$ $2^{4} \cdot 3^{4}$ ✓ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
5184.ch.4.b1.a1 $C_3^4:C_4^2$ $2^{4} \cdot 3^{4}$ ✓ ✓ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
5184.ch.4.c1.a1 $C_3^4:(C_2\times Q_8)$ $2^{4} \cdot 3^{4}$ ✓ ✓ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
5184.ch.4.d1.a1 $C_3^4:(C_2\times Q_8)$ $2^{4} \cdot 3^{4}$ ✓ ✓ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
5184.ch.4.e1.a1 $C_3^4:\OD_{16}$ $2^{4} \cdot 3^{4}$ ✓ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
5184.ch.4.e1.b1 $C_3^4:\OD_{16}$ $2^{4} \cdot 3^{4}$ ✓ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
5184.ch.4.f1.a1 $C_3^4:D_4:C_2$ $2^{4} \cdot 3^{4}$ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $2^{2}$ $-$
5184.ch.4.f1.b1 $C_3^4:D_4:C_2$ $2^{4} \cdot 3^{4}$ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $2^{2}$ $-$
5184.ch.4.g1.a1 $C_3^2\wr C_2.Q_8$ $2^{4} \cdot 3^{4}$ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $2^{2}$ $-$
5184.ch.4.g1.b1 $C_3^2\wr C_2.Q_8$ $2^{4} \cdot 3^{4}$ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $2^{2}$ $-$
5184.ch.4.h1.a1 $C_3^4:(C_2\times Q_8)$ $2^{4} \cdot 3^{4}$ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $2^{2}$ $-$
5184.ch.4.h1.b1 $C_3^4:(C_2\times Q_8)$ $2^{4} \cdot 3^{4}$ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $2^{2}$ $-$
5184.ch.4.i1.a1 $C_3^4:\SD_{16}$ $2^{4} \cdot 3^{4}$ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $2^{2}$ $-$
5184.ch.4.i1.b1 $C_3^4:\SD_{16}$ $2^{4} \cdot 3^{4}$ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $2^{2}$ $-$
5184.ch.4.j1.a1 $C_3^4:D_4:C_2$ $2^{4} \cdot 3^{4}$ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $2^{2}$ $-$
5184.ch.4.j1.b1 $C_3^4:D_4:C_2$ $2^{4} \cdot 3^{4}$ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $2^{2}$ $-$
5184.ch.4.k1.a1 $C_3^4:Q_{16}$ $2^{4} \cdot 3^{4}$ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $2^{2}$ $-$
5184.ch.4.k1.b1 $C_3^4:Q_{16}$ $2^{4} \cdot 3^{4}$ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $2^{2}$ $-$
5184.ch.8.a1.a1 $C_3^4:(C_2\times C_4)$ $2^{3} \cdot 3^{4}$ ✓ ✓ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $C_2^3$ $2^{3}$ ✓
5184.ch.8.b1.a1 $C_3^4:(C_2\times C_4)$ $2^{3} \cdot 3^{4}$ ✓ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $D_4$ $2^{3}$
5184.ch.8.b1.b1 $C_3^4:(C_2\times C_4)$ $2^{3} \cdot 3^{4}$ ✓ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $D_4$ $2^{3}$
5184.ch.8.c1.a1 $C_3^4:D_4$ $2^{3} \cdot 3^{4}$ ✓ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $D_4$ $2^{3}$
5184.ch.8.c1.b1 $C_3^4:D_4$ $2^{3} \cdot 3^{4}$ ✓ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $D_4$ $2^{3}$
5184.ch.8.d1.a1 $C_3^4:Q_8$ $2^{3} \cdot 3^{4}$ ✓ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $D_4$ $2^{3}$
5184.ch.8.d1.b1 $C_3^4:Q_8$ $2^{3} \cdot 3^{4}$ ✓ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $D_4$ $2^{3}$
5184.ch.8.e1.a1 $C_3^4:D_4$ $2^{3} \cdot 3^{4}$ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $2^{3}$ $-$
5184.ch.8.e1.b1 $C_3^4:D_4$ $2^{3} \cdot 3^{4}$ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $2^{3}$ $-$
5184.ch.8.f1.a1 $C_3^3:(C_4\times S_3)$ $2^{3} \cdot 3^{4}$ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $2^{3}$ $-$
5184.ch.8.g1.a1 $C_3^4:(C_2\times C_4)$ $2^{3} \cdot 3^{4}$ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $2^{3}$ $-$
5184.ch.8.h1.a1 $C_3^4:(C_2\times C_4)$ $2^{3} \cdot 3^{4}$ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $2^{3}$ $-$
5184.ch.8.h1.b1 $C_3^4:(C_2\times C_4)$ $2^{3} \cdot 3^{4}$ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $2^{3}$ $-$
5184.ch.8.i1.a1 $C_3^4:(C_2\times C_4)$ $2^{3} \cdot 3^{4}$ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $2^{3}$ $-$
5184.ch.8.i1.b1 $C_3^4:(C_2\times C_4)$ $2^{3} \cdot 3^{4}$ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $2^{3}$ $-$
5184.ch.8.i1.c1 $C_3^4:(C_2\times C_4)$ $2^{3} \cdot 3^{4}$ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $2^{3}$ $-$
5184.ch.8.i1.d1 $C_3^4:(C_2\times C_4)$ $2^{3} \cdot 3^{4}$ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $2^{3}$ $-$
5184.ch.8.j1.a1 $C_3^4:D_4$ $2^{3} \cdot 3^{4}$ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $2^{3}$ $-$
5184.ch.8.j1.b1 $C_3^4:D_4$ $2^{3} \cdot 3^{4}$ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $2^{3}$ $-$
5184.ch.8.k1.a1 $C_3^4:Q_8$ $2^{3} \cdot 3^{4}$ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $2^{3}$ $-$
5184.ch.8.k1.b1 $C_3^4:Q_8$ $2^{3} \cdot 3^{4}$ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $2^{3}$ $-$
5184.ch.8.l1.a1 $C_3^4:Q_8$ $2^{3} \cdot 3^{4}$ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $2^{3}$ $-$
5184.ch.8.l1.b1 $C_3^4:Q_8$ $2^{3} \cdot 3^{4}$ $C_3^4:D_4.D_4$ $2^{6} \cdot 3^{4}$ $2^{3}$ $-$
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