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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 71 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1344.9827.1.a1 $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_1$ $1$ ✓
1344.9827.2.a1 $C_{12}.D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9827.2.b1 $D_{28}:D_6$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9827.2.c1 $C_{12}.D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9827.2.d1 $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9827.2.e1 $C_{84}.C_2^3$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9827.2.f1 $D_4:D_{42}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9827.2.g1 $C_{84}.C_2^3$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9827.4.a1 $D_{28}:C_6$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9827.4.b1 $D_{84}:C_2$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9827.4.c1 $C_2\times D_{84}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9827.4.d1 $C_{42}:Q_8$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9827.4.e1 $C_6:C_{56}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9827.4.f1 $C_{12}.C_{28}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9827.4.g1 $D_4:C_{42}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9827.4.h1 $C_3:D_{56}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9827.4.i1 $C_{21}:\SD_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9827.4.j1 $C_{21}:\SD_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9827.4.k1 $C_{21}:\SD_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9827.4.l1 $C_{21}:Q_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9827.6.a1 $D_4.D_{14}$ $2^{5} \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $S_3$ $2 \cdot 3$
1344.9827.8.a1 $C_2\times C_{84}$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^3$ $2^{3}$ ✓
1344.9827.8.b1 $D_4\times C_{21}$ $2^{3} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $D_4$ $2^{3}$
1344.9827.8.c1 $C_3\times D_{28}$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^3$ $2^{3}$ ✓
1344.9827.8.d1 $D_{84}$ $2^{3} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^3$ $2^{3}$ ✓
1344.9827.8.e1 $C_{21}:Q_8$ $2^{3} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^3$ $2^{3}$ ✓
1344.9827.8.f1 $C_{21}:Q_8$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^3$ $2^{3}$ ✓
1344.9827.8.g1 $C_3:C_{56}$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^3$ $2^{3}$ ✓
1344.9827.8.h1 $C_3:C_{56}$ $2^{3} \cdot 3 \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^3$ $2^{3}$ ✓
1344.9827.8.i1 $Q_8\times C_{21}$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $D_4$ $2^{3}$
1344.9827.12.a1 $D_{28}:C_2$ $2^{4} \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $D_6$ $2^{2} \cdot 3$
1344.9827.12.b1 $C_{14}:Q_8$ $2^{4} \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $D_6$ $2^{2} \cdot 3$
1344.9827.12.c1 $D_4:C_{14}$ $2^{4} \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $D_6$ $2^{2} \cdot 3$
1344.9827.14.a1 $C_{12}.C_2^3$ $2^{5} \cdot 3$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $D_7$ $2 \cdot 7$
1344.9827.16.a1 $C_2\times C_{42}$ $2^{2} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2\times D_4$ $2^{4}$
1344.9827.16.b1 $C_{84}$ $2^{2} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^4$ $2^{4}$ ✓
1344.9827.16.c1 $C_{84}$ $2^{2} \cdot 3 \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2\times D_4$ $2^{4}$
1344.9827.24.a1 $C_2\times C_{28}$ $2^{3} \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2\times D_6$ $2^{3} \cdot 3$
1344.9827.24.b1 $C_7\times D_4$ $2^{3} \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_3:D_4$ $2^{3} \cdot 3$
1344.9827.24.c1 $D_{28}$ $2^{3} \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2\times D_6$ $2^{3} \cdot 3$
1344.9827.24.d1 $C_7:Q_8$ $2^{3} \cdot 7$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2\times D_6$ $2^{3} \cdot 3$
1344.9827.24.e1 $C_7\times Q_8$ $2^{3} \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_3:D_4$ $2^{3} \cdot 3$
1344.9827.28.a1 $C_6:C_8$ $2^{4} \cdot 3$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $D_{14}$ $2^{2} \cdot 7$
1344.9827.28.b1 $C_3:\OD_{16}$ $2^{4} \cdot 3$ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $D_{14}$ $2^{2} \cdot 7$
1344.9827.28.c1 $D_4:C_6$ $2^{4} \cdot 3$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $D_{14}$ $2^{2} \cdot 7$
1344.9827.32.a1 $C_{42}$ $2 \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2\times D_4$ $2^{5}$
1344.9827.48.a1 $C_2\times C_{14}$ $2^{2} \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_6:D_4$ $2^{4} \cdot 3$
1344.9827.48.b1 $C_{28}$ $2^{2} \cdot 7$ ✓ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2^2\times D_6$ $2^{4} \cdot 3$
1344.9827.48.c1 $C_{28}$ $2^{2} \cdot 7$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_6:D_4$ $2^{4} \cdot 3$
1344.9827.56.a1 $C_2\times C_{12}$ $2^{3} \cdot 3$ ✓ ✓ $C_{84}.C_2^4$ $2^{6} \cdot 3 \cdot 7$ $C_2\times D_{14}$ $2^{3} \cdot 7$
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