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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 562 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
17496.ha.1.a1 $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ ✓ ✓ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $C_1$ $1$ ✓
17496.ha.3.a1 $C_3^6.Q_8$ $2^{3} \cdot 3^{6}$ ✓ ✓ ✓ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $C_3$ $3$ ✓
17496.ha.4.a1 $C_3^6.C_6$ $2 \cdot 3^{7}$ ✓ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2^{2}$ $-$
17496.ha.6.a1 $C_3^6.C_4$ $2^{2} \cdot 3^{6}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2 \cdot 3$ $-$
17496.ha.8.a1 $C_3^6.C_3$ $3^{7}$ $3$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2^{3}$ $-$
17496.ha.9.a1 $C_3^4:\SL(2,3)$ $2^{3} \cdot 3^{5}$ ✓ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $3^{2}$ $-$
17496.ha.9.b1 $C_3^4:\SL(2,3)$ $2^{3} \cdot 3^{5}$ ✓ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $3^{2}$ $-$
17496.ha.12.a1 $C_3^5:S_3$ $2 \cdot 3^{6}$ ✓ ✓ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $A_4$ $2^{2} \cdot 3$
17496.ha.12.b1 $C_3^5:C_6$ $2 \cdot 3^{6}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3$ $-$
17496.ha.12.c1 $C_3^5:C_6$ $2 \cdot 3^{6}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3$ $-$
17496.ha.12.d1 $C_3^5:C_6$ $2 \cdot 3^{6}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3$ $-$
17496.ha.24.a1 $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $\SL(2,3)$ $2^{3} \cdot 3$
17496.ha.24.b1 $C_3^5:C_3$ $3^{6}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2^{3} \cdot 3$ $-$
17496.ha.24.c1 $C_3^5:C_3$ $3^{6}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2^{3} \cdot 3$ $-$
17496.ha.24.d1 $C_3^5:C_3$ $3^{6}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2^{3} \cdot 3$ $-$
17496.ha.24.e1 $C_3^5:C_3$ $3^{6}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2^{3} \cdot 3$ $-$
17496.ha.24.f1 $C_3^5:C_3$ $3^{6}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2^{3} \cdot 3$ $-$
17496.ha.24.g1 $C_3^5.C_3$ $3^{6}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2^{3} \cdot 3$ $-$
17496.ha.27.a1 $C_3^4:Q_8$ $2^{3} \cdot 3^{4}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $3^{3}$ $-$
17496.ha.27.b1 $C_3^4:Q_8$ $2^{3} \cdot 3^{4}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $3^{3}$ $-$
17496.ha.27.c1 $C_3^4:Q_8$ $2^{3} \cdot 3^{4}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $3^{3}$ $-$
17496.ha.36.a1 $C_3^4:C_6$ $2 \cdot 3^{5}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
17496.ha.36.b1 $C_3^4:C_6$ $2 \cdot 3^{5}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
17496.ha.36.c1 $C_3^4:C_6$ $2 \cdot 3^{5}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
17496.ha.36.d1 $C_3^4:C_6$ $2 \cdot 3^{5}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
17496.ha.36.e1 $C_3^4:C_6$ $2 \cdot 3^{5}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
17496.ha.36.f1 $C_3^4:C_6$ $2 \cdot 3^{5}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
17496.ha.36.g1 $C_3^4:C_6$ $2 \cdot 3^{5}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
17496.ha.36.h1 $C_3^4:C_6$ $2 \cdot 3^{5}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
17496.ha.36.i1 $C_3^4:C_6$ $2 \cdot 3^{5}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
17496.ha.36.j1 $C_3^4:C_6$ $2 \cdot 3^{5}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
17496.ha.36.k1 $C_3^4:S_3$ $2 \cdot 3^{5}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
17496.ha.36.l1 $C_3^4:S_3$ $2 \cdot 3^{5}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
17496.ha.36.m1 $C_3^4:S_3$ $2 \cdot 3^{5}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
17496.ha.36.n1 $C_3^4:S_3$ $2 \cdot 3^{5}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
17496.ha.36.o1 $C_3^4:S_3$ $2 \cdot 3^{5}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
17496.ha.36.p1 $C_3^4:S_3$ $2 \cdot 3^{5}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
17496.ha.36.q1 $C_3^4:S_3$ $2 \cdot 3^{5}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
17496.ha.54.a1 $C_3^4:C_4$ $2^{2} \cdot 3^{4}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2 \cdot 3^{3}$ $-$
17496.ha.54.b1 $C_3^4:C_4$ $2^{2} \cdot 3^{4}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2 \cdot 3^{3}$ $-$
17496.ha.54.c1 $C_3^4:C_4$ $2^{2} \cdot 3^{4}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2 \cdot 3^{3}$ $-$
17496.ha.54.d1 $C_3^4:C_4$ $2^{2} \cdot 3^{4}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2 \cdot 3^{3}$ $-$
17496.ha.54.e1 $C_3^4:C_4$ $2^{2} \cdot 3^{4}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2 \cdot 3^{3}$ $-$
17496.ha.54.f1 $C_3^4:C_4$ $2^{2} \cdot 3^{4}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2 \cdot 3^{3}$ $-$
17496.ha.72.a1 $C_3^4:C_3$ $3^{5}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2^{3} \cdot 3^{2}$ $-$
17496.ha.72.b1 $C_3^4:C_3$ $3^{5}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2^{3} \cdot 3^{2}$ $-$
17496.ha.72.c1 $C_3^4:C_3$ $3^{5}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2^{3} \cdot 3^{2}$ $-$
17496.ha.72.d1 $C_3^5$ $3^{5}$ ✓ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2^{3} \cdot 3^{2}$ $-$
17496.ha.72.e1 $C_3^2\times \He_3$ $3^{5}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2^{3} \cdot 3^{2}$ $-$
17496.ha.72.f1 $C_3^2\times \He_3$ $3^{5}$ $C_3^6.\SL(2,3)$ $2^{3} \cdot 3^{7}$ $2^{3} \cdot 3^{2}$ $-$
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