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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 404 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1344.11566.1.a1 $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_1$ $1$ ✓
1344.11566.2.a1 $D_{28}:D_6$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.11566.2.b1 $D_{84}:C_2^2$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.11566.2.c1 $D_{12}:D_{14}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.11566.2.d1 $D_{12}.D_{14}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.11566.2.e1 $D_{12}:D_{14}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.11566.2.f1 $D_{84}:C_2^2$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.11566.2.g1 $C_{84}.C_2^3$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.11566.2.h1 $C_{84}.C_2^3$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.11566.2.i1 $D_4:D_{42}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.11566.2.j1 $C_{84}.C_2^3$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.11566.2.k1 $D_{12}:D_{14}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.11566.3.a1 $C_{14}.C_2^5$ $2^{6} \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $3$ $-$
1344.11566.4.a1 $D_6:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.11566.4.b1 $C_{14}:D_{12}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.11566.4.c1 $D_6\times C_{28}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.11566.4.d1 $D_6:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.11566.4.e1 $D_6.D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.11566.4.f1 $D_{12}:C_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.11566.4.g1 $D_{14}.D_6$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.11566.4.h1 $D_{28}:C_6$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.11566.4.i1 $D_{84}:C_2$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.11566.4.j1 $D_{42}:C_4$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.11566.4.k1 $C_2\times D_{84}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.11566.4.l1 $C_{42}:Q_8$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.11566.4.m1 $C_{28}:D_6$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.11566.4.n1 $C_{28}.D_6$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.11566.4.o1 $C_{12}.D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.11566.4.p1 $D_4\times D_{21}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.11566.4.q1 $D_4:C_{42}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.11566.4.r1 $C_{12}.D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.11566.4.s1 $D_{28}:S_3$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.11566.4.t1 $D_{84}:C_2$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.11566.4.u1 $D_{84}:C_2$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.11566.4.v1 $C_{28}.D_6$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.11566.4.w1 $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.11566.4.x1 $S_3\times D_{28}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.11566.4.y1 $D_{84}:C_2$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.11566.4.z1 $D_{84}:C_2$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.11566.4.ba1 $C_{12}.D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.11566.4.bb1 $D_7\times D_{12}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.11566.4.bc1 $D_{12}:D_7$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.11566.4.bd1 $D_{12}:C_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.11566.4.be1 $D_{84}:C_2$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.11566.4.bf1 $C_{12}.D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.11566.4.bg1 $D_{21}:Q_8$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.11566.4.bh1 $D_{84}:C_2$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.11566.6.a1 $D_4.D_{14}$ $2^{5} \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $S_3$ $2 \cdot 3$
1344.11566.6.b1 $D_{28}:C_2^2$ $2^{5} \cdot 7$ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
1344.11566.6.c1 $D_{28}:C_2^2$ $2^{5} \cdot 7$ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
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