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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 856 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1344.9365.1.a1.a1 $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_1$ $1$ ✓
1344.9365.2.a1.a1 $(C_2\times C_{42}):D_4$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9365.2.b1.a1 $C_{84}:C_2^3$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9365.2.c1.a1 $D_{42}:D_4$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9365.2.d1.a1 $(C_2\times C_{42}):D_4$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9365.2.e1.a1 $D_{42}:D_4$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9365.2.f1.a1 $D_{42}:C_2^3$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9365.2.g1.a1 $C_{21}:(C_4\times D_4)$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9365.2.h1.a1 $D_{42}:C_2^3$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9365.2.i1.a1 $C_{14}.(S_3\times D_4)$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9365.2.j1.a1 $(C_2\times C_6):D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9365.2.k1.a1 $D_{42}:D_4$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9365.2.l1.a1 $D_{14}:D_{12}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9365.2.m1.a1 $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9365.2.n1.a1 $C_{21}:(C_4\times D_4)$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9365.2.o1.a1 $(C_6\times D_{28}):C_2$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.9365.3.a1.a1 $D_{28}:D_4$ $2^{6} \cdot 7$ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $3$ $-$
1344.9365.4.a1.a1 $D_4\times C_{42}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9365.4.b1.a1 $C_{42}:D_4$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9365.4.c1.a1 $C_{42}:C_2^3$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9365.4.d1.a1 $C_{42}:D_4$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9365.4.e1.a1 $C_2^2\times D_{42}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9365.4.f1.a1 $C_{42}.C_2^3$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9365.4.g1.a1 $C_{42}.D_4$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9365.4.h1.a1 $C_{42}:D_4$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9365.4.i1.a1 $C_{42}:C_2^3$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9365.4.j1.a1 $C_{42}:D_4$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9365.4.k1.a1 $C_{42}:D_4$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9365.4.l1.a1 $C_{42}:D_4$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9365.4.m1.a1 $C_{42}.D_4$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9365.4.n1.a1 $C_{42}:D_4$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9365.4.o1.a1 $D_6\times D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9365.4.p1.a1 $C_{42}:D_4$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9365.4.q1.a1 $C_{14}:D_{12}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9365.4.r1.a1 $D_6:C_{28}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9365.4.s1.a1 $C_6:D_{28}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9365.4.t1.a1 $C_6:D_{28}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9365.4.u1.a1 $C_{12}\times D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9365.4.v1.a1 $C_6.D_{28}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9365.4.w1.a1 $C_6\times D_{28}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9365.4.x1.a1 $C_6:D_{28}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9365.4.y1.a1 $D_{14}.D_6$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9365.4.z1.a1 $C_6.D_{28}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9365.4.ba1.a1 $C_6:D_{28}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9365.4.bb1.a1 $C_6:D_{28}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9365.4.bc1.a1 $C_6.D_{28}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9365.4.bd1.a1 $D_{42}:C_4$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9365.4.be1.a1 $D_{42}:C_4$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9365.4.bf1.a1 $D_{42}:C_4$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.9365.4.bg1.a1 $C_{42}.D_4$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{21}:D_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
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