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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 378 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
3888.dk.1.a1 $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ ✓ ✓ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $C_1$ $1$ ✓
3888.dk.2.a1 $C_3^2:S_3^3$ $2^{3} \cdot 3^{5}$ ✓ ✓ ✓ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $C_2$ $2$ ✓
3888.dk.2.b1 $C_3^4:(C_4\times S_3)$ $2^{3} \cdot 3^{5}$ ✓ ✓ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $C_2$ $2$ ✓
3888.dk.3.a1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ ✓ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $3$ $-$
3888.dk.4.a1 $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ ✓ ✓ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $C_2^2$ $2^{2}$ ✓
3888.dk.4.b1 $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ ✓ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $C_4$ $2^{2}$ ✓
3888.dk.4.c1 $C_3^3:C_6^2$ $2^{2} \cdot 3^{5}$ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $2^{2}$ $-$
3888.dk.4.d1 $C_3^4:C_{12}$ $2^{2} \cdot 3^{5}$ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $2^{2}$ $-$
3888.dk.6.a1 $C_3:S_3^3$ $2^{3} \cdot 3^{4}$ ✓ ✓ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $S_3$ $2 \cdot 3$
3888.dk.6.b1 $C_3\times S_3^3$ $2^{3} \cdot 3^{4}$ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $2 \cdot 3$ $-$
3888.dk.6.c1 $C_3^3:C_4\times S_3$ $2^{3} \cdot 3^{4}$ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $2 \cdot 3$ $-$
3888.dk.6.d1 $C_3^3:(C_4\times S_3)$ $2^{3} \cdot 3^{4}$ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $2 \cdot 3$ $-$
3888.dk.8.a1 $C_3^4:C_6$ $2 \cdot 3^{5}$ ✓ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $D_4$ $2^{3}$
3888.dk.8.b1 $C_3^4:C_6$ $2 \cdot 3^{5}$ ✓ ✓ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $C_2\times C_4$ $2^{3}$ ✓
3888.dk.8.c1 $C_3^4:C_6$ $2 \cdot 3^{5}$ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $2^{3}$ $-$
3888.dk.9.a1 $(C_3\times S_3^2):C_4$ $2^{4} \cdot 3^{3}$ ✓ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $3^{2}$ $-$
3888.dk.12.a1 $C_3^2:S_3^2$ $2^{2} \cdot 3^{4}$ ✓ ✓ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $D_6$ $2^{2} \cdot 3$
3888.dk.12.b1 $C_3^2:S_3^2$ $2^{2} \cdot 3^{4}$ ✓ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $C_3:C_4$ $2^{2} \cdot 3$
3888.dk.12.c1 $C_3^2\times S_3^2$ $2^{2} \cdot 3^{4}$ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
3888.dk.12.d1 $C_3^2\times S_3^2$ $2^{2} \cdot 3^{4}$ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
3888.dk.12.e1 $C_3\wr C_2^2$ $2^{2} \cdot 3^{4}$ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
3888.dk.12.f1 $C_3\wr C_2^2$ $2^{2} \cdot 3^{4}$ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
3888.dk.12.g1 $C_3\wr C_2^2$ $2^{2} \cdot 3^{4}$ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
3888.dk.12.h1 $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
3888.dk.12.i1 $C_3^4:C_4$ $2^{2} \cdot 3^{4}$ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
3888.dk.12.j1 $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
3888.dk.12.k1 $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
3888.dk.12.l1 $C_3^2:S_3^2$ $2^{2} \cdot 3^{4}$ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
3888.dk.12.m1 $C_3^2:S_3^2$ $2^{2} \cdot 3^{4}$ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
3888.dk.12.n1 $C_3^2:S_3^2$ $2^{2} \cdot 3^{4}$ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
3888.dk.12.o1 $C_3^2:S_3^2$ $2^{2} \cdot 3^{4}$ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
3888.dk.16.a1 $C_3^5$ $3^{5}$ $3$ ✓ ✓ ✓ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $C_2^2:C_4$ $2^{4}$
3888.dk.18.a1 $C_6\times S_3^2$ $2^{3} \cdot 3^{3}$ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $2 \cdot 3^{2}$ $-$
3888.dk.18.b1 $C_6\times S_3^2$ $2^{3} \cdot 3^{3}$ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $2 \cdot 3^{2}$ $-$
3888.dk.18.c1 $C_6.S_3^2$ $2^{3} \cdot 3^{3}$ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $2 \cdot 3^{2}$ $-$
3888.dk.18.d1 $C_2\times C_3^3:C_4$ $2^{3} \cdot 3^{3}$ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $2 \cdot 3^{2}$ $-$
3888.dk.18.e1 $S_3^3$ $2^{3} \cdot 3^{3}$ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $2 \cdot 3^{2}$ $-$
3888.dk.18.f1 $C_3^2:C_4\times S_3$ $2^{3} \cdot 3^{3}$ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $2 \cdot 3^{2}$ $-$
3888.dk.24.a1 $C_3^2\wr C_2$ $2 \cdot 3^{4}$ ✓ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $C_3:D_4$ $2^{3} \cdot 3$
3888.dk.24.b1 $C_3^3:S_3$ $2 \cdot 3^{4}$ ✓ ✓ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $C_6:C_4$ $2^{3} \cdot 3$
3888.dk.24.c1 $S_3\times C_3^3$ $2 \cdot 3^{4}$ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $2^{3} \cdot 3$ $-$
3888.dk.24.d1 $S_3\times C_3^3$ $2 \cdot 3^{4}$ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $2^{3} \cdot 3$ $-$
3888.dk.24.e1 $C_3^2\wr C_2$ $2 \cdot 3^{4}$ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $2^{3} \cdot 3$ $-$
3888.dk.24.f1 $C_3^2\wr C_2$ $2 \cdot 3^{4}$ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $2^{3} \cdot 3$ $-$
3888.dk.24.g1 $C_3^2\wr C_2$ $2 \cdot 3^{4}$ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $2^{3} \cdot 3$ $-$
3888.dk.24.h1 $C_3^2\wr C_2$ $2 \cdot 3^{4}$ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $2^{3} \cdot 3$ $-$
3888.dk.24.i1 $S_3\times C_3^3$ $2 \cdot 3^{4}$ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $2^{3} \cdot 3$ $-$
3888.dk.24.j1 $S_3\times C_3^3$ $2 \cdot 3^{4}$ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $2^{3} \cdot 3$ $-$
3888.dk.24.k1 $C_3^2\wr C_2$ $2 \cdot 3^{4}$ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $2^{3} \cdot 3$ $-$
3888.dk.24.l1 $C_3^2\wr C_2$ $2 \cdot 3^{4}$ $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ $2^{3} \cdot 3$ $-$
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