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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 101 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
14.2.7.a1.a1 $C_2$ $2$ $2$ ✓ ✓ ✓ ✓ ✓ $C_{14}$ $2 \cdot 7$ $C_7$ $7$ ✓ ✓
21.2.7.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ ✓ ✓ $C_{21}$ $3 \cdot 7$ $C_7$ $7$ ✓ ✓
35.1.7.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ ✓ ✓ $C_{35}$ $5 \cdot 7$ $C_7$ $7$ ✓ ✓
49.1.7.a1.a1 $C_7$ $7$ ✓ ✓ ✓ ✓ ✓ $C_{49}$ $7^{2}$ $C_7$ $7$ ✓ ✓
49.2.7.a1.a1 $C_7$ $7$ ✓ ✓ ✓ ✓ $C_7^2$ $7^{2}$ $C_7$ $7$ ✓ ✓
49.2.7.a1.b1 $C_7$ $7$ ✓ ✓ ✓ ✓ $C_7^2$ $7^{2}$ $C_7$ $7$ ✓ ✓
49.2.7.a1.c1 $C_7$ $7$ ✓ ✓ ✓ ✓ $C_7^2$ $7^{2}$ $C_7$ $7$ ✓ ✓
49.2.7.a1.d1 $C_7$ $7$ ✓ ✓ ✓ ✓ $C_7^2$ $7^{2}$ $C_7$ $7$ ✓ ✓
49.2.7.a1.e1 $C_7$ $7$ ✓ ✓ ✓ ✓ $C_7^2$ $7^{2}$ $C_7$ $7$ ✓ ✓
49.2.7.a1.f1 $C_7$ $7$ ✓ ✓ ✓ ✓ $C_7^2$ $7^{2}$ $C_7$ $7$ ✓ ✓
49.2.7.a1.g1 $C_7$ $7$ ✓ ✓ ✓ ✓ $C_7^2$ $7^{2}$ $C_7$ $7$ ✓ ✓
49.2.7.a1.h1 $C_7$ $7$ ✓ ✓ ✓ ✓ $C_7^2$ $7^{2}$ $C_7$ $7$ ✓ ✓
56.11.7.a1.a1 $C_2^3$ $2^{3}$ $2$ ✓ ✓ ✓ ✓ $F_8$ $2^{3} \cdot 7$ $C_7$ $7$ ✓ ✓
77.1.7.a1.a1 $C_{11}$ $11$ $11$ ✓ ✓ ✓ ✓ ✓ $C_{77}$ $7 \cdot 11$ $C_7$ $7$ ✓ ✓
91.1.7.a1.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ ✓ ✓ $C_{91}$ $7 \cdot 13$ $C_7$ $7$ ✓ ✓
119.1.7.a1.a1 $C_{17}$ $17$ $17$ ✓ ✓ ✓ ✓ ✓ $C_{119}$ $7 \cdot 17$ $C_7$ $7$ ✓ ✓
133.1.7.a1.a1 $C_{19}$ $19$ $19$ ✓ ✓ ✓ ✓ ✓ $C_{133}$ $7 \cdot 19$ $C_7$ $7$ ✓ ✓
161.1.7.a1.a1 $C_{23}$ $23$ $23$ ✓ ✓ ✓ ✓ ✓ $C_{161}$ $7 \cdot 23$ $C_7$ $7$ ✓ ✓
203.1.7.a1.a1 $C_{29}$ $29$ $29$ ✓ ✓ ✓ ✓ $C_{29}:C_7$ $7 \cdot 29$ $C_7$ $7$ ✓ ✓
203.2.7.a1.a1 $C_{29}$ $29$ $29$ ✓ ✓ ✓ ✓ ✓ $C_{203}$ $7 \cdot 29$ $C_7$ $7$ ✓ ✓
217.1.7.a1.a1 $C_{31}$ $31$ $31$ ✓ ✓ ✓ ✓ ✓ $C_{217}$ $7 \cdot 31$ $C_7$ $7$ ✓ ✓
259.1.7.a1.a1 $C_{37}$ $37$ $37$ ✓ ✓ ✓ ✓ ✓ $C_{259}$ $7 \cdot 37$ $C_7$ $7$ ✓ ✓
287.1.7.a1.a1 $C_{41}$ $41$ $41$ ✓ ✓ ✓ ✓ ✓ $C_{287}$ $7 \cdot 41$ $C_7$ $7$ ✓ ✓
301.1.7.a1.a1 $C_{43}$ $43$ $43$ ✓ ✓ ✓ ✓ $C_{43}:C_7$ $7 \cdot 43$ $C_7$ $7$ ✓ ✓
301.2.7.a1.a1 $C_{43}$ $43$ $43$ ✓ ✓ ✓ ✓ ✓ $C_{301}$ $7 \cdot 43$ $C_7$ $7$ ✓ ✓
329.1.7.a1.a1 $C_{47}$ $47$ $47$ ✓ ✓ ✓ ✓ ✓ $C_{329}$ $7 \cdot 47$ $C_7$ $7$ ✓ ✓
371.1.7.a1.a1 $C_{53}$ $53$ $53$ ✓ ✓ ✓ ✓ ✓ $C_{371}$ $7 \cdot 53$ $C_7$ $7$ ✓ ✓
413.1.7.a1.a1 $C_{59}$ $59$ $59$ ✓ ✓ ✓ ✓ ✓ $C_{413}$ $7 \cdot 59$ $C_7$ $7$ ✓ ✓
420.13.7.a1.a1 $A_5$ $2^{2} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_7\times A_5$ $2^{2} \cdot 3 \cdot 5 \cdot 7$ $C_7$ $7$ ✓ ✓
427.1.7.a1.a1 $C_{61}$ $61$ $61$ ✓ ✓ ✓ ✓ ✓ $C_{427}$ $7 \cdot 61$ $C_7$ $7$ ✓ ✓
469.1.7.a1.a1 $C_{67}$ $67$ $67$ ✓ ✓ ✓ ✓ ✓ $C_{469}$ $7 \cdot 67$ $C_7$ $7$ ✓ ✓
497.1.7.a1.a1 $C_{71}$ $71$ $71$ ✓ ✓ ✓ ✓ $C_{71}:C_7$ $7 \cdot 71$ $C_7$ $7$ ✓ ✓
497.2.7.a1.a1 $C_{71}$ $71$ $71$ ✓ ✓ ✓ ✓ ✓ $C_{497}$ $7 \cdot 71$ $C_7$ $7$ ✓ ✓
511.1.7.a1.a1 $C_{73}$ $73$ $73$ ✓ ✓ ✓ ✓ ✓ $C_{511}$ $7 \cdot 73$ $C_7$ $7$ ✓ ✓
553.1.7.a1.a1 $C_{79}$ $79$ $79$ ✓ ✓ ✓ ✓ ✓ $C_{553}$ $7 \cdot 79$ $C_7$ $7$ ✓ ✓
581.1.7.a1.a1 $C_{83}$ $83$ $83$ ✓ ✓ ✓ ✓ ✓ $C_{581}$ $7 \cdot 83$ $C_7$ $7$ ✓ ✓
623.1.7.a1.a1 $C_{89}$ $89$ $89$ ✓ ✓ ✓ ✓ ✓ $C_{623}$ $7 \cdot 89$ $C_7$ $7$ ✓ ✓
679.1.7.a1.a1 $C_{97}$ $97$ $97$ ✓ ✓ ✓ ✓ ✓ $C_{679}$ $7 \cdot 97$ $C_7$ $7$ ✓ ✓
707.1.7.a1.a1 $C_{101}$ $101$ $101$ ✓ ✓ ✓ ✓ ✓ $C_{707}$ $7 \cdot 101$ $C_7$ $7$ ✓ ✓
721.1.7.a1.a1 $C_{103}$ $103$ $103$ ✓ ✓ ✓ ✓ ✓ $C_{721}$ $7 \cdot 103$ $C_7$ $7$ ✓ ✓
749.1.7.a1.a1 $C_{107}$ $107$ $107$ ✓ ✓ ✓ ✓ ✓ $C_{749}$ $7 \cdot 107$ $C_7$ $7$ ✓ ✓
763.1.7.a1.a1 $C_{109}$ $109$ $109$ ✓ ✓ ✓ ✓ ✓ $C_{763}$ $7 \cdot 109$ $C_7$ $7$ ✓ ✓
791.1.7.a1.a1 $C_{113}$ $113$ $113$ ✓ ✓ ✓ ✓ $C_{113}:C_7$ $7 \cdot 113$ $C_7$ $7$ ✓ ✓
791.2.7.a1.a1 $C_{113}$ $113$ $113$ ✓ ✓ ✓ ✓ ✓ $C_{791}$ $7 \cdot 113$ $C_7$ $7$ ✓ ✓
889.1.7.a1.a1 $C_{127}$ $127$ $127$ ✓ ✓ ✓ ✓ $C_{127}:C_7$ $7 \cdot 127$ $C_7$ $7$ ✓ ✓
889.2.7.a1.a1 $C_{127}$ $127$ $127$ ✓ ✓ ✓ ✓ ✓ $C_{889}$ $7 \cdot 127$ $C_7$ $7$ ✓ ✓
917.1.7.a1.a1 $C_{131}$ $131$ $131$ ✓ ✓ ✓ ✓ ✓ $C_{917}$ $7 \cdot 131$ $C_7$ $7$ ✓ ✓
959.1.7.a1.a1 $C_{137}$ $137$ $137$ ✓ ✓ ✓ ✓ ✓ $C_{959}$ $7 \cdot 137$ $C_7$ $7$ ✓ ✓
973.1.7.a1.a1 $C_{139}$ $139$ $139$ ✓ ✓ ✓ ✓ ✓ $C_{973}$ $7 \cdot 139$ $C_7$ $7$ ✓ ✓
1043.1.7.a1.a1 $C_{149}$ $149$ $149$ ✓ ✓ ✓ ✓ ✓ $C_{1043}$ $7 \cdot 149$ $C_7$ $7$ ✓ ✓
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