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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 66 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1344.9757.1.a1.a1 $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_1$ $1$ ✓
1344.9757.2.a1.a1 $D_{12}.D_{14}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9757.2.b1.a1 $C_{84}.D_4$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9757.2.c1.a1 $C_{84}.D_4$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9757.2.d1.a1 $C_{84}.C_2^3$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9757.2.e1.a1 $C_{84}.C_2^3$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9757.2.f1.a1 $C_{12}.D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9757.2.g1.a1 $C_{42}:Q_{16}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9757.4.a1.a1 $D_{12}:C_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9757.4.b1.a1 $D_{28}:C_6$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9757.4.c1.a1 $D_{28}:C_6$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9757.4.d1.a1 $Q_8\times C_{42}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9757.4.e1.a1 $C_{42}:Q_8$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9757.4.f1.a1 $C_{12}.C_{28}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9757.4.g1.a1 $C_{42}:C_8$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9757.4.i1.a1 $C_{21}:D_8$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9757.4.k1.a1 $C_{21}:\SD_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9757.4.q1.a1 $C_{21}:\SD_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9757.4.v1.a1 $C_{21}:Q_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9757.6.a1.a1 $Q_8.D_{14}$ $2^{5} \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $S_3$ $2 \cdot 3$
1344.9757.8.b1.a1 $C_2\times C_{84}$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^3$ $2^{3}$ ✓
1344.9757.8.c1.a1 $C_7\times D_{12}$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^3$ $2^{3}$ ✓
1344.9757.8.e1.a1 $C_3\times D_{28}$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $D_4$ $2^{3}$
1344.9757.8.f1.a1 $C_3\times D_{28}$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^3$ $2^{3}$ ✓
1344.9757.8.h1.a1 $C_{21}:Q_8$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^3$ $2^{3}$ ✓
1344.9757.8.i1.a1 $C_{21}:Q_8$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^3$ $2^{3}$ ✓
1344.9757.8.l1.a1 $C_{21}:C_8$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^3$ $2^{3}$ ✓
1344.9757.8.m1.a1 $C_{21}:C_8$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^3$ $2^{3}$ ✓
1344.9757.8.n1.a1 $C_{21}:Q_8$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $D_4$ $2^{3}$
1344.9757.12.a1.a1 $D_{28}:C_2$ $2^{4} \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $D_6$ $2^{2} \cdot 3$
1344.9757.12.b1.a1 $D_{28}:C_2$ $2^{4} \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $D_6$ $2^{2} \cdot 3$
1344.9757.12.c1.a1 $Q_8\times C_{14}$ $2^{4} \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $D_6$ $2^{2} \cdot 3$
1344.9757.14.a1.a1 $C_{12}.D_4$ $2^{5} \cdot 3$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $D_7$ $2 \cdot 7$
1344.9757.16.a1.a1 $C_2\times C_{42}$ $2^{2} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2\times D_4$ $2^{4}$
1344.9757.16.c1.a1 $C_{84}$ $2^{2} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^4$ $2^{4}$ ✓
1344.9757.16.d1.a1 $C_{84}$ $2^{2} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2\times D_4$ $2^{4}$
1344.9757.24.b1.a1 $C_2\times C_{28}$ $2^{3} \cdot 7$ ✓ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2\times D_6$ $2^{3} \cdot 3$
1344.9757.24.d1.a1 $D_{28}$ $2^{3} \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_3:D_4$ $2^{3} \cdot 3$
1344.9757.24.e1.a1 $D_{28}$ $2^{3} \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2\times D_6$ $2^{3} \cdot 3$
1344.9757.24.g1.a1 $C_7:Q_8$ $2^{3} \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2\times D_6$ $2^{3} \cdot 3$
1344.9757.24.h1.a1 $C_7:Q_8$ $2^{3} \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_3:D_4$ $2^{3} \cdot 3$
1344.9757.28.a1.a1 $D_{12}:C_2$ $2^{4} \cdot 3$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $D_{14}$ $2^{2} \cdot 7$
1344.9757.28.b1.a1 $C_6\times Q_8$ $2^{4} \cdot 3$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $D_{14}$ $2^{2} \cdot 7$
1344.9757.28.c1.a1 $C_3:\OD_{16}$ $2^{4} \cdot 3$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $D_{14}$ $2^{2} \cdot 7$
1344.9757.32.a1.a1 $C_{42}$ $2 \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2\times D_4$ $2^{5}$
1344.9757.48.a1.a1 $C_2\times C_{14}$ $2^{2} \cdot 7$ ✓ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_6:D_4$ $2^{4} \cdot 3$
1344.9757.48.c1.a1 $C_{28}$ $2^{2} \cdot 7$ ✓ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2\times D_6$ $2^{4} \cdot 3$
1344.9757.48.d1.a1 $C_{28}$ $2^{2} \cdot 7$ ✓ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_6:D_4$ $2^{4} \cdot 3$
1344.9757.56.a1.a1 $C_2\times C_{12}$ $2^{3} \cdot 3$ ✓ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2\times D_{14}$ $2^{3} \cdot 7$
1344.9757.56.b1.a1 $D_{12}$ $2^{3} \cdot 3$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2\times D_{14}$ $2^{3} \cdot 7$
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