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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 80 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1344.262.1.a1.a1 $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ ✓ ✓ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $C_1$ $1$ ✓
1344.262.2.a1.a1 $C_{24}.C_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.262.2.b1.a1 $C_{168}.C_4$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.262.2.c1.a1 $C_{14}:C_{48}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.262.3.a1.a1 $C_{28}.D_8$ $2^{6} \cdot 7$ ✓ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $3$ $-$
1344.262.4.a1.a1 $C_2\times C_{168}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.262.4.b1.a1 $C_7:C_{48}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $C_4$ $2^{2}$ ✓
1344.262.4.c1.a1 $C_7:C_{48}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $C_4$ $2^{2}$ ✓
1344.262.4.d1.a1 $C_{12}.C_{28}$ $2^{4} \cdot 3 \cdot 7$ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $2^{2}$ $-$
1344.262.4.e1.a1 $C_{21}:\OD_{16}$ $2^{4} \cdot 3 \cdot 7$ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $2^{2}$ $-$
1344.262.6.a1.a1 $C_{14}:C_{16}$ $2^{5} \cdot 7$ ✓ ✓ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $S_3$ $2 \cdot 3$
1344.262.6.b1.a1 $C_8.C_{28}$ $2^{5} \cdot 7$ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
1344.262.6.c1.a1 $C_{56}.C_4$ $2^{5} \cdot 7$ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
1344.262.7.a1.a1 $C_{48}.C_4$ $2^{6} \cdot 3$ ✓ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $7$ $-$
1344.262.8.a1.a1 $C_2\times C_{84}$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $D_4$ $2^{3}$
1344.262.8.b1.a1 $C_{168}$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $C_2\times C_4$ $2^{3}$ ✓
1344.262.8.c1.a1 $C_{168}$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $Q_8$ $2^{3}$
1344.262.8.d1.a1 $C_3:C_{56}$ $2^{3} \cdot 3 \cdot 7$ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $2^{3}$ $-$
1344.262.8.e1.a1 $C_{21}:C_8$ $2^{3} \cdot 3 \cdot 7$ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $2^{3}$ $-$
1344.262.12.a1.a1 $C_2\times C_{56}$ $2^{4} \cdot 7$ ✓ ✓ ✓ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $D_6$ $2^{2} \cdot 3$
1344.262.12.b1.a1 $C_7:C_{16}$ $2^{4} \cdot 7$ ✓ ✓ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $C_3:C_4$ $2^{2} \cdot 3$
1344.262.12.c1.a1 $C_7:C_{16}$ $2^{4} \cdot 7$ ✓ ✓ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $C_3:C_4$ $2^{2} \cdot 3$
1344.262.12.d1.a1 $C_7\times \OD_{16}$ $2^{4} \cdot 7$ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $2^{2} \cdot 3$ $-$
1344.262.12.e1.a1 $C_7:\OD_{16}$ $2^{4} \cdot 7$ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $2^{2} \cdot 3$ $-$
1344.262.14.a1.a1 $C_{24}.C_4$ $2^{5} \cdot 3$ ✓ ✓ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $D_7$ $2 \cdot 7$
1344.262.14.b1.a1 $C_{24}.C_4$ $2^{5} \cdot 3$ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $2 \cdot 7$ $-$
1344.262.14.c1.a1 $C_2\times C_{48}$ $2^{5} \cdot 3$ ✓ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $2 \cdot 7$ $-$
1344.262.16.a1.a1 $C_2\times C_{42}$ $2^{2} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $Q_{16}$ $2^{4}$
1344.262.16.b1.a1 $C_{84}$ $2^{2} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $D_8$ $2^{4}$
1344.262.16.c1.a1 $C_{84}$ $2^{2} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $C_4:C_4$ $2^{4}$
1344.262.21.a1.a1 $C_{16}.C_4$ $2^{6}$ $2$ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $3 \cdot 7$ $-$
1344.262.24.a1.a1 $C_2\times C_{28}$ $2^{3} \cdot 7$ ✓ ✓ ✓ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $D_{12}$ $2^{3} \cdot 3$
1344.262.24.b1.a1 $C_{56}$ $2^{3} \cdot 7$ ✓ ✓ ✓ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $C_6:C_4$ $2^{3} \cdot 3$
1344.262.24.c1.a1 $C_{56}$ $2^{3} \cdot 7$ ✓ ✓ ✓ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $C_3:Q_8$ $2^{3} \cdot 3$
1344.262.24.d1.a1 $C_{56}$ $2^{3} \cdot 7$ ✓ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $2^{3} \cdot 3$ $-$
1344.262.24.e1.a1 $C_7:C_8$ $2^{3} \cdot 7$ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $2^{3} \cdot 3$ $-$
1344.262.28.a1.a1 $C_2\times C_{24}$ $2^{4} \cdot 3$ ✓ ✓ ✓ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $D_{14}$ $2^{2} \cdot 7$
1344.262.28.b1.a1 $C_3:\OD_{16}$ $2^{4} \cdot 3$ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $2^{2} \cdot 7$ $-$
1344.262.28.c1.a1 $C_3:\OD_{16}$ $2^{4} \cdot 3$ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $2^{2} \cdot 7$ $-$
1344.262.28.d1.a1 $C_{48}$ $2^{4} \cdot 3$ ✓ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $2^{2} \cdot 7$ $-$
1344.262.28.e1.a1 $C_{48}$ $2^{4} \cdot 3$ ✓ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $2^{2} \cdot 7$ $-$
1344.262.32.a1.a1 $C_{42}$ $2 \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $C_8:C_4$ $2^{5}$
1344.262.32.b1.a1 $C_{42}$ $2 \cdot 3 \cdot 7$ ✓ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $2^{5}$ $-$
1344.262.42.a1.a1 $C_8.C_4$ $2^{5}$ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $2 \cdot 3 \cdot 7$ $-$
1344.262.42.b1.a1 $C_8.C_4$ $2^{5}$ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $2 \cdot 3 \cdot 7$ $-$
1344.262.42.c1.a1 $C_2\times C_{16}$ $2^{5}$ ✓ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $2 \cdot 3 \cdot 7$ $-$
1344.262.48.a1.a1 $C_2\times C_{14}$ $2^{2} \cdot 7$ ✓ ✓ ✓ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $C_3:Q_{16}$ $2^{4} \cdot 3$
1344.262.48.b1.a1 $C_{28}$ $2^{2} \cdot 7$ ✓ ✓ ✓ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $D_{24}$ $2^{4} \cdot 3$
1344.262.48.c1.a1 $C_{28}$ $2^{2} \cdot 7$ ✓ ✓ ✓ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $C_{12}:C_4$ $2^{4} \cdot 3$
1344.262.56.a1.a1 $C_2\times C_{12}$ $2^{3} \cdot 3$ ✓ ✓ ✓ $C_{28}.D_{24}$ $2^{6} \cdot 3 \cdot 7$ $C_7:D_4$ $2^{3} \cdot 7$
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