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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 112 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
192.937.192.a1.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $\OD_{32}:C_6$ $2^{6} \cdot 3$ $\OD_{32}:C_6$ $2^{6} \cdot 3$
384.5399.192.b1.a1 $C_2$ $2$ ✓ ✓ ✓ $\OD_{32}:C_{12}$ $2^{7} \cdot 3$ $\OD_{32}:C_6$ $2^{6} \cdot 3$ ✓
384.5399.192.b1.b1 $C_2$ $2$ ✓ ✓ ✓ $\OD_{32}:C_{12}$ $2^{7} \cdot 3$ $\OD_{32}:C_6$ $2^{6} \cdot 3$ ✓
384.5404.192.a1.a1 $C_2$ $2$ ✓ ✓ ✓ $(C_2^2\times C_{16}):C_6$ $2^{7} \cdot 3$ $\OD_{32}:C_6$ $2^{6} \cdot 3$ ✓
384.5404.192.a1.b1 $C_2$ $2$ ✓ ✓ ✓ $(C_2^2\times C_{16}):C_6$ $2^{7} \cdot 3$ $\OD_{32}:C_6$ $2^{6} \cdot 3$ ✓
384.5442.192.b1.a1 $C_2$ $2$ ✓ ✓ ✓ $C_8.(C_6\times D_4)$ $2^{7} \cdot 3$ $\OD_{32}:C_6$ $2^{6} \cdot 3$ ✓
384.5442.192.b1.b1 $C_2$ $2$ ✓ ✓ ✓ $C_8.(C_6\times D_4)$ $2^{7} \cdot 3$ $\OD_{32}:C_6$ $2^{6} \cdot 3$ ✓
384.5455.192.a1.a1 $C_2$ $2$ ✓ ✓ ✓ $C_{24}.\OD_{16}$ $2^{7} \cdot 3$ $\OD_{32}:C_6$ $2^{6} \cdot 3$ ✓
384.5455.192.a1.b1 $C_2$ $2$ ✓ ✓ ✓ $C_{24}.\OD_{16}$ $2^{7} \cdot 3$ $\OD_{32}:C_6$ $2^{6} \cdot 3$ ✓
384.5458.192.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_4\times C_{48}$ $2^{7} \cdot 3$ $\OD_{32}:C_6$ $2^{6} \cdot 3$ ✓
384.5459.192.c1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{48}:D_4$ $2^{7} \cdot 3$ $\OD_{32}:C_6$ $2^{6} \cdot 3$ ✓
384.5460.192.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{48}:D_4$ $2^{7} \cdot 3$ $\OD_{32}:C_6$ $2^{6} \cdot 3$ ✓
384.5473.192.b1 $C_2$ $2$ ✓ ✓ ✓ ✓ $Q_8\times C_{48}$ $2^{7} \cdot 3$ $\OD_{32}:C_6$ $2^{6} \cdot 3$ ✓
384.5474.192.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{48}:Q_8$ $2^{7} \cdot 3$ $\OD_{32}:C_6$ $2^{6} \cdot 3$ ✓
384.17846.192.a1 $C_2$ $2$ ✓ ✓ ✓ $C_{48}.C_2^3$ $2^{7} \cdot 3$ $\OD_{32}:C_6$ $2^{6} \cdot 3$ ✓
576.940.192.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $\OD_{32}:C_{18}$ $2^{6} \cdot 3^{2}$ $\OD_{32}:C_6$ $2^{6} \cdot 3$ ✓
576.3880.192.b1.a1 $C_3$ $3$ ✓ ✓ ✓ $D_{12}.C_{24}$ $2^{6} \cdot 3^{2}$ $\OD_{32}:C_6$ $2^{6} \cdot 3$ ✓
576.3886.192.b1.a1 $C_3$ $3$ ✓ ✓ ✓ $D_{12}.C_{24}$ $2^{6} \cdot 3^{2}$ $\OD_{32}:C_6$ $2^{6} \cdot 3$ ✓
576.4119.192.b1 $C_3$ $3$ ✓ ✓ ✓ $C_3\times C_{24}.C_2^3$ $2^{6} \cdot 3^{2}$ $\OD_{32}:C_6$ $2^{6} \cdot 3$ ✓
576.4959.192.a1 $C_3$ $3$ ✓ ✓ ✓ $C_{16}.C_6^2$ $2^{6} \cdot 3^{2}$ $\OD_{32}:C_6$ $2^{6} \cdot 3$ ✓
768.5036.192.c1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $\SD_{16}\times C_{48}$ $2^{8} \cdot 3$ $\OD_{32}:C_6$ $2^{6} \cdot 3$
768.6635.192.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $D_8.C_{48}$ $2^{8} \cdot 3$ $\OD_{32}:C_6$ $2^{6} \cdot 3$
960.3993.192.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $C_{48}.D_{10}$ $2^{6} \cdot 3 \cdot 5$ $\OD_{32}:C_6$ $2^{6} \cdot 3$ ✓
960.3999.192.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $C_{48}.D_{10}$ $2^{6} \cdot 3 \cdot 5$ $\OD_{32}:C_6$ $2^{6} \cdot 3$ ✓
960.4232.192.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $C_{120}.C_2^3$ $2^{6} \cdot 3 \cdot 5$ $\OD_{32}:C_6$ $2^{6} \cdot 3$ ✓
960.5674.192.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ ✓ $\OD_{32}:C_{30}$ $2^{6} \cdot 3 \cdot 5$ $\OD_{32}:C_6$ $2^{6} \cdot 3$ ✓
960.6453.192.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $D_{20}.C_{24}$ $2^{6} \cdot 3 \cdot 5$ $\OD_{32}:C_6$ $2^{6} \cdot 3$ ✓
960.6519.192.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $C_{20}.(C_2\times C_{24})$ $2^{6} \cdot 3 \cdot 5$ $\OD_{32}:C_6$ $2^{6} \cdot 3$ ✓
1344.1090.192.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $D_{28}.C_{24}$ $2^{6} \cdot 3 \cdot 7$ $\OD_{32}:C_6$ $2^{6} \cdot 3$ ✓
1344.1096.192.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $D_{28}.C_{24}$ $2^{6} \cdot 3 \cdot 7$ $\OD_{32}:C_6$ $2^{6} \cdot 3$ ✓
1344.1329.192.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $C_{28}.(C_2\times C_{24})$ $2^{6} \cdot 3 \cdot 7$ $\OD_{32}:C_6$ $2^{6} \cdot 3$ ✓
1344.4324.192.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $(C_2\times C_{112}):C_6$ $2^{6} \cdot 3 \cdot 7$ $\OD_{32}:C_6$ $2^{6} \cdot 3$ ✓
1344.4623.192.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $C_{48}.D_{14}$ $2^{6} \cdot 3 \cdot 7$ $\OD_{32}:C_6$ $2^{6} \cdot 3$ ✓
1344.4629.192.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $C_{48}.D_{14}$ $2^{6} \cdot 3 \cdot 7$ $\OD_{32}:C_6$ $2^{6} \cdot 3$ ✓
1344.4862.192.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $C_{168}.C_2^3$ $2^{6} \cdot 3 \cdot 7$ $\OD_{32}:C_6$ $2^{6} \cdot 3$ ✓
1344.6304.192.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ ✓ $\OD_{32}:C_{42}$ $2^{6} \cdot 3 \cdot 7$ $\OD_{32}:C_6$ $2^{6} \cdot 3$ ✓
1536.58268.192.e1.a1 $C_8$ $2^{3}$ ✓ ✓ ✓ $D_{16}.C_{48}$ $2^{9} \cdot 3$ $\OD_{32}:C_6$ $2^{6} \cdot 3$
1536.60782.192.d1.a1 $C_8$ $2^{3}$ ✓ ✓ ✓ $D_8.C_{96}$ $2^{9} \cdot 3$ $\OD_{32}:C_6$ $2^{6} \cdot 3$
1728.946.192.a1 $C_9$ $3^{2}$ ✓ ✓ ✓ ✓ $\OD_{32}:C_{54}$ $2^{6} \cdot 3^{3}$ $\OD_{32}:C_6$ $2^{6} \cdot 3$
1728.8345.192.b1.a1 $C_9$ $3^{2}$ ✓ ✓ ✓ $C_{48}.D_{18}$ $2^{6} \cdot 3^{3}$ $\OD_{32}:C_6$ $2^{6} \cdot 3$
1728.8352.192.a1.a1 $C_3^2$ $3^{2}$ ✓ ✓ ✓ $D_{12}.C_{72}$ $2^{6} \cdot 3^{3}$ $\OD_{32}:C_6$ $2^{6} \cdot 3$
1728.8359.192.b1.a1 $C_3^2$ $3^{2}$ ✓ ✓ ✓ $(C_6\times C_{48}):C_6$ $2^{6} \cdot 3^{3}$ $\OD_{32}:C_6$ $2^{6} \cdot 3$
1728.8366.192.b1.a1 $C_9$ $3^{2}$ ✓ ✓ ✓ $D_{36}.C_{24}$ $2^{6} \cdot 3^{3}$ $\OD_{32}:C_6$ $2^{6} \cdot 3$
1728.8372.192.b1.a1 $C_9$ $3^{2}$ ✓ ✓ ✓ $C_{48}.D_{18}$ $2^{6} \cdot 3^{3}$ $\OD_{32}:C_6$ $2^{6} \cdot 3$
1728.8376.192.a1.a1 $C_3^2$ $3^{2}$ ✓ ✓ ✓ $D_{12}.C_{72}$ $2^{6} \cdot 3^{3}$ $\OD_{32}:C_6$ $2^{6} \cdot 3$
1728.8380.192.b1.a1 $C_3^2$ $3^{2}$ ✓ ✓ ✓ $C_{12}.(S_3\times C_{24})$ $2^{6} \cdot 3^{3}$ $\OD_{32}:C_6$ $2^{6} \cdot 3$
1728.8384.192.b1.a1 $C_9$ $3^{2}$ ✓ ✓ ✓ $D_{36}.C_{24}$ $2^{6} \cdot 3^{3}$ $\OD_{32}:C_6$ $2^{6} \cdot 3$
1728.9307.192.b1 $C_9$ $3^{2}$ ✓ ✓ ✓ $C_3\times C_{72}.C_2^3$ $2^{6} \cdot 3^{3}$ $\OD_{32}:C_6$ $2^{6} \cdot 3$
1728.9308.192.a1 $C_3^2$ $3^{2}$ ✓ ✓ ✓ $C_9\times C_{24}.C_2^3$ $2^{6} \cdot 3^{3}$ $\OD_{32}:C_6$ $2^{6} \cdot 3$
1728.9319.192.b1 $C_3^2$ $3^{2}$ ✓ ✓ ✓ $C_{24}.(C_6\times D_6)$ $2^{6} \cdot 3^{3}$ $\OD_{32}:C_6$ $2^{6} \cdot 3$
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