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Note: Search results may be incomplete due to uncomputed quantities: Subgroup label (103813812 objects)

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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 196 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
16.1.2.a1.a1 $C_8$ $2^{3}$ ✓ ✓ ✓ ✓ ✓ $C_{16}$ $2^{4}$ $C_2$ $2$ ✓
16.5.2.b1.a1 $C_8$ $2^{3}$ ✓ ✓ ✓ ✓ $C_2\times C_8$ $2^{4}$ $C_2$ $2$ ✓
16.5.2.b1.b1 $C_8$ $2^{3}$ ✓ ✓ ✓ ✓ $C_2\times C_8$ $2^{4}$ $C_2$ $2$ ✓
16.6.2.b1.a1 $C_8$ $2^{3}$ ✓ ✓ ✓ $\OD_{16}$ $2^{4}$ $C_2$ $2$ ✓
16.6.2.b1.b1 $C_8$ $2^{3}$ ✓ ✓ ✓ $\OD_{16}$ $2^{4}$ $C_2$ $2$ ✓
16.7.2.b1.a1 $C_8$ $2^{3}$ ✓ ✓ ✓ ✓ $D_8$ $2^{4}$ $C_2$ $2$ ✓
16.8.2.c1.a1 $C_8$ $2^{3}$ ✓ ✓ ✓ ✓ $\SD_{16}$ $2^{4}$ $C_2$ $2$ ✓
16.9.2.b1.a1 $C_8$ $2^{3}$ ✓ ✓ ✓ ✓ $Q_{16}$ $2^{4}$ $C_2$ $2$ ✓
24.1.3.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ $C_3:C_8$ $2^{3} \cdot 3$ $3$ $-$
24.2.3.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ ✓ ✓ ✓ $C_{24}$ $2^{3} \cdot 3$ $C_3$ $3$ ✓
40.1.5.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ $C_5:C_8$ $2^{3} \cdot 5$ $5$ $-$
40.2.5.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ ✓ ✓ ✓ $C_{40}$ $2^{3} \cdot 5$ $C_5$ $5$ ✓
40.3.5.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ $C_5:C_8$ $2^{3} \cdot 5$ $5$ $-$
56.1.7.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ $C_7:C_8$ $2^{3} \cdot 7$ $7$ $-$
56.2.7.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ ✓ ✓ ✓ $C_{56}$ $2^{3} \cdot 7$ $C_7$ $7$ ✓
72.19.9.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ $C_3^2:C_8$ $2^{3} \cdot 3^{2}$ $3^{2}$ $-$
72.39.9.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ $F_9$ $2^{3} \cdot 3^{2}$ $3^{2}$ $-$
88.1.11.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ $C_{11}:C_8$ $2^{3} \cdot 11$ $11$ $-$
88.2.11.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ ✓ ✓ ✓ $C_{88}$ $2^{3} \cdot 11$ $C_{11}$ $11$ ✓
104.1.13.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ $C_{13}:C_8$ $2^{3} \cdot 13$ $13$ $-$
104.2.13.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ ✓ ✓ ✓ $C_{104}$ $2^{3} \cdot 13$ $C_{13}$ $13$ ✓
104.3.13.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ $C_{13}:C_8$ $2^{3} \cdot 13$ $13$ $-$
136.1.17.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ $C_{17}:C_8$ $2^{3} \cdot 17$ $17$ $-$
136.2.17.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ ✓ ✓ ✓ $C_{136}$ $2^{3} \cdot 17$ $C_{17}$ $17$ ✓
136.3.17.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ $C_{17}:C_8$ $2^{3} \cdot 17$ $17$ $-$
136.12.17.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ $C_{17}:C_8$ $2^{3} \cdot 17$ $17$ $-$
152.1.19.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ $C_{19}:C_8$ $2^{3} \cdot 19$ $19$ $-$
152.2.19.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ ✓ ✓ ✓ $C_{152}$ $2^{3} \cdot 19$ $C_{19}$ $19$ ✓
184.1.23.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ $C_{23}:C_8$ $2^{3} \cdot 23$ $23$ $-$
184.2.23.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ ✓ ✓ ✓ $C_{184}$ $2^{3} \cdot 23$ $C_{23}$ $23$ ✓
200.40.25.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ $C_5^2:C_8$ $2^{3} \cdot 5^{2}$ $5^{2}$ $-$
232.1.29.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ $C_{29}:C_8$ $2^{3} \cdot 29$ $29$ $-$
232.2.29.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ ✓ ✓ ✓ $C_{232}$ $2^{3} \cdot 29$ $C_{29}$ $29$ ✓
232.3.29.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ $C_{29}:C_8$ $2^{3} \cdot 29$ $29$ $-$
248.1.31.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ $C_{31}:C_8$ $2^{3} \cdot 31$ $31$ $-$
248.2.31.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ ✓ ✓ ✓ $C_{248}$ $2^{3} \cdot 31$ $C_{31}$ $31$ ✓
296.1.37.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ $C_{37}:C_8$ $2^{3} \cdot 37$ $37$ $-$
296.2.37.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ ✓ ✓ ✓ $C_{296}$ $2^{3} \cdot 37$ $C_{37}$ $37$ ✓
296.3.37.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ $C_{37}:C_8$ $2^{3} \cdot 37$ $37$ $-$
328.1.41.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ $C_{41}:C_8$ $2^{3} \cdot 41$ $41$ $-$
328.2.41.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ ✓ ✓ ✓ $C_{328}$ $2^{3} \cdot 41$ $C_{41}$ $41$ ✓
328.3.41.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ $C_{41}:C_8$ $2^{3} \cdot 41$ $41$ $-$
328.12.41.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ $C_{41}:C_8$ $2^{3} \cdot 41$ $41$ $-$
344.1.43.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ $C_{43}:C_8$ $2^{3} \cdot 43$ $43$ $-$
344.2.43.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ ✓ ✓ ✓ $C_{344}$ $2^{3} \cdot 43$ $C_{43}$ $43$ ✓
376.1.47.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ $C_{47}:C_8$ $2^{3} \cdot 47$ $47$ $-$
376.2.47.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ ✓ ✓ ✓ $C_{376}$ $2^{3} \cdot 47$ $C_{47}$ $47$ ✓
392.17.49.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ $C_7^2:C_8$ $2^{3} \cdot 7^{2}$ $7^{2}$ $-$
392.36.49.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ $C_7^2:C_8$ $2^{3} \cdot 7^{2}$ $7^{2}$ $-$
424.1.53.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ $C_{53}:C_8$ $2^{3} \cdot 53$ $53$ $-$
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