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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 136 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1344.9508.1.a1.a1 $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_1$ $1$ ✓
1344.9508.2.a1.a1 $C_{84}.D_4$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9508.2.b1.a1 $C_{84}.C_2^3$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9508.2.c1.a1 $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9508.2.d1.a1 $D_{12}.D_{14}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9508.2.e1.a1 $C_{84}.D_4$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9508.2.f1.a1 $C_{84}.C_2^3$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9508.2.g1.a1 $C_{12}.D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9508.2.h1.a1 $D_{12}:D_{14}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9508.2.h1.b1 $D_{12}:D_{14}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9508.2.i1.a1 $D_{12}.D_{14}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9508.2.i1.b1 $D_{12}.D_{14}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9508.2.j1.a1 $D_{28}.D_6$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9508.2.j1.b1 $D_{28}.D_6$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9508.2.k1.a1 $C_{84}.C_2^3$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9508.2.k1.b1 $C_{84}.C_2^3$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9508.4.a1.a1 $D_4\times C_{42}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9508.4.b1.a1 $D_{12}:C_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9508.4.c1.a1 $D_{28}:C_6$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9508.4.d1.a1 $D_{28}:C_6$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9508.4.e1.a1 $C_{42}:Q_8$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9508.4.f1.a1 $C_{12}.C_{28}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9508.4.g1.a1 $C_{42}:C_8$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9508.4.h1.a1 $C_{21}:D_8$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9508.4.h1.b1 $C_{21}:D_8$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9508.4.i1.a1 $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9508.4.i1.b1 $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9508.4.j1.a1 $C_{12}.D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9508.4.j1.b1 $C_{12}.D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9508.4.k1.a1 $C_{21}:\SD_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9508.4.k1.b1 $C_{21}:\SD_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9508.4.l1.a1 $C_{21}:\SD_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9508.4.l1.b1 $C_{21}:\SD_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9508.4.m1.a1 $C_{21}:\SD_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9508.4.m1.b1 $C_{21}:\SD_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9508.4.n1.a1 $D_{12}:D_7$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9508.4.n1.b1 $D_{12}:D_7$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9508.4.o1.a1 $C_{21}:D_8$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9508.4.p1.a1 $C_{21}:\SD_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9508.4.q1.a1 $C_{12}.D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9508.4.q1.b1 $C_{12}.D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9508.4.r1.a1 $C_{12}.D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9508.4.r1.b1 $C_{12}.D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9508.4.s1.a1 $C_{21}:\OD_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9508.4.s1.b1 $C_{21}:\OD_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9508.4.t1.a1 $C_{21}:\SD_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9508.4.u1.a1 $C_{21}:\SD_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9508.4.u1.b1 $C_{21}:\SD_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9508.4.v1.a1 $C_{21}:Q_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9508.4.w1.a1 $C_{21}:Q_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
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