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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 55 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
672.618.672.a1.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$
1344.1782.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{12}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.1783.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{12}.D_{28}$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.1788.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{12}.D_{28}$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.1789.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{12}.D_{28}$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.1800.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_2\times D_6):D_{28}$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.1801.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_2\times D_6).D_{28}$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.2148.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{12}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.2153.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{12}.D_{28}$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.2160.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{12}.(C_2\times D_{28})$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.2165.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_3\times D_{14}):Q_{16}$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.2178.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{12}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.2179.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{12}.D_{28}$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.2180.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{84}:D_4$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.2181.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{84}.D_4$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.2767.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{84}.D_4$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.2768.672.c1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{42}:\SD_{16}$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.2769.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_6:D_{56}$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.2770.672.c1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{12}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.2785.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(S_3\times C_{14}):\SD_{16}$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.2786.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(S_3\times C_{14}):Q_{16}$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.2787.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{42}:\SD_{16}$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.2788.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{42}:Q_{16}$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.2813.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{28}.(S_3\times D_4)$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.2814.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{12}.(C_2\times D_{28})$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.2815.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_6\times D_{56}):C_2$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.2816.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_6\times D_{56}):C_2$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.2817.672.c1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{12}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.2818.672.c1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{12}.D_{28}$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.2819.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{84}:D_4$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.2820.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{84}.D_4$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.2908.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{12}.D_{28}$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.2909.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{84}.D_4$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.2910.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{12}:D_{28}$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.2911.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{84}:D_4$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.2920.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{12}.D_{28}$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.2921.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{84}.D_4$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.2922.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{12}.D_{28}$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.2923.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{84}.D_4$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.3293.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.(C_4\times D_{28})$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.3550.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_6\times D_{28}):C_4$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.3551.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{42}.(C_4\times D_4)$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.3552.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.(C_4\times D_{28})$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.3566.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{42}.(C_4\times D_4)$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.3574.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.(C_4\times D_{28})$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.3580.672.c1 $C_2$ $2$ ✓ ✓ ✓ $(C_2\times C_{84}):D_4$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.3581.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_2\times D_6).D_{28}$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.3582.672.a1 $C_2$ $2$ ✓ ✓ ✓ $(C_2\times C_{12}):D_{28}$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.3583.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_2\times D_{42}).D_4$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
1344.3584.672.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_2\times C_{28}):D_{12}$ $2^{6} \cdot 3 \cdot 7$ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓
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