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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 248 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1344.2349.1.a1.a1 $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ ✓ ✓ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $C_1$ $1$ ✓
1344.2349.2.a1.a1 $C_{12}:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.2349.2.b1.a1 $C_{24}\times D_{14}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.2349.2.c1.a1 $C_{12}.D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.2349.2.d1.a1 $C_8:D_{42}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.2349.2.e1.a1 $D_{42}:C_8$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.2349.2.f1.a1 $C_{24}:C_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.2349.2.g1.a1 $C_{12}.D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.2349.3.a1.a1 $C_8:D_{28}$ $2^{6} \cdot 7$ ✓ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $3$ $-$
1344.2349.4.a1.a1 $C_6:D_{28}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $C_4$ $2^{2}$ ✓
1344.2349.4.b1.a1 $C_{12}\times D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.2349.4.c1.a1 $C_6.D_{28}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $C_4$ $2^{2}$ ✓
1344.2349.4.d1.a1 $C_4\times D_{42}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.2349.4.e1.a1 $D_{42}:C_4$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $C_4$ $2^{2}$ ✓
1344.2349.4.f1.a1 $C_{12}:C_{28}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.2349.4.g1.a1 $C_2\times C_{168}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.2349.4.h1.a1 $C_6:C_{56}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.2349.4.i1.a1 $C_{14}:C_{24}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.2349.4.j1.a1 $C_{42}:C_8$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.2349.4.k1.a1 $C_6.D_{28}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $C_4$ $2^{2}$ ✓
1344.2349.4.l1.a1 $D_7\times C_{24}$ $2^{4} \cdot 3 \cdot 7$ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $2^{2}$ $-$
1344.2349.4.l1.b1 $D_7\times C_{24}$ $2^{4} \cdot 3 \cdot 7$ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $2^{2}$ $-$
1344.2349.4.m1.a1 $C_{168}:C_2$ $2^{4} \cdot 3 \cdot 7$ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $2^{2}$ $-$
1344.2349.4.m1.b1 $C_{168}:C_2$ $2^{4} \cdot 3 \cdot 7$ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $2^{2}$ $-$
1344.2349.6.a1.a1 $C_8\times D_{14}$ $2^{5} \cdot 7$ ✓ ✓ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $S_3$ $2 \cdot 3$
1344.2349.6.b1.a1 $C_4\times D_{28}$ $2^{5} \cdot 7$ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
1344.2349.6.c1.a1 $D_{14}:C_8$ $2^{5} \cdot 7$ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
1344.2349.6.d1.a1 $C_8:D_{14}$ $2^{5} \cdot 7$ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
1344.2349.6.e1.a1 $D_{14}:C_8$ $2^{5} \cdot 7$ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
1344.2349.6.f1.a1 $C_8:C_{28}$ $2^{5} \cdot 7$ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
1344.2349.6.g1.a1 $C_{28}:C_8$ $2^{5} \cdot 7$ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
1344.2349.7.a1.a1 $C_{24}:D_4$ $2^{6} \cdot 3$ ✓ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $7$ $-$
1344.2349.8.a1.a1 $C_6\times D_{14}$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $C_2\times C_4$ $2^{3}$ ✓
1344.2349.8.b1.a1 $C_2\times D_{42}$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $C_2\times C_4$ $2^{3}$ ✓
1344.2349.8.c1.a1 $C_2\times C_{84}$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $C_2^3$ $2^{3}$ ✓
1344.2349.8.d1.a1 $C_6:C_{28}$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $C_2\times C_4$ $2^{3}$ ✓
1344.2349.8.e1.a1 $C_6:C_{28}$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $C_2\times C_4$ $2^{3}$ ✓
1344.2349.8.f1.a1 $C_{14}:C_{12}$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $C_2\times C_4$ $2^{3}$ ✓
1344.2349.8.g1.a1 $C_{42}:C_4$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $C_2\times C_4$ $2^{3}$ ✓
1344.2349.8.h1.a1 $C_{168}$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $D_4$ $2^{3}$
1344.2349.8.h1.b1 $C_{168}$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $D_4$ $2^{3}$
1344.2349.8.i1.a1 $C_{12}\times D_7$ $2^{3} \cdot 3 \cdot 7$ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $2^{3}$ $-$
1344.2349.8.j1.a1 $C_{12}\times D_7$ $2^{3} \cdot 3 \cdot 7$ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $2^{3}$ $-$
1344.2349.8.k1.a1 $C_4\times D_{21}$ $2^{3} \cdot 3 \cdot 7$ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $2^{3}$ $-$
1344.2349.8.l1.a1 $C_4\times D_{21}$ $2^{3} \cdot 3 \cdot 7$ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $2^{3}$ $-$
1344.2349.8.m1.a1 $C_7:C_{24}$ $2^{3} \cdot 3 \cdot 7$ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $2^{3}$ $-$
1344.2349.8.n1.a1 $C_{21}:C_8$ $2^{3} \cdot 3 \cdot 7$ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $2^{3}$ $-$
1344.2349.8.o1.a1 $C_3:C_{56}$ $2^{3} \cdot 3 \cdot 7$ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $2^{3}$ $-$
1344.2349.8.p1.a1 $C_3:D_{28}$ $2^{3} \cdot 3 \cdot 7$ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $2^{3}$ $-$
1344.2349.8.p1.b1 $C_3:D_{28}$ $2^{3} \cdot 3 \cdot 7$ $C_{24}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $2^{3}$ $-$
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