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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 (46 matches)

  displayed columns for results
Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
192.1402.96.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^2\times C_4:C_{12}$ $2^{6} \cdot 3$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
192.1405.96.b1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2\times Q_8\times C_{12}$ $2^{6} \cdot 3$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
192.1412.96.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^2:Q_8\times C_6$ $2^{6} \cdot 3$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
192.1416.96.b1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2\times C_{12}.Q_8$ $2^{6} \cdot 3$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
192.1420.96.c1 $C_2$ $2$ ✓ ✓ ✓ $C_2\times C_{12}:Q_8$ $2^{6} \cdot 3$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
192.1422.96.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_2\times C_{12}):Q_8$ $2^{6} \cdot 3$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
192.1432.96.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_3\times C_2^3:Q_8$ $2^{6} \cdot 3$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
192.1433.96.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_2\times C_{12}):Q_8$ $2^{6} \cdot 3$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
192.1438.96.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_3\times D_4\times Q_8$ $2^{6} \cdot 3$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
192.1443.96.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_3\times D_4:Q_8$ $2^{6} \cdot 3$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
192.1446.96.b1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_3\times Q_8:Q_8$ $2^{6} \cdot 3$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
192.1447.96.a1 $C_2$ $2$ ✓ ✓ ✓ $C_3\times Q_8^2$ $2^{6} \cdot 3$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
192.1532.96.a1 $C_2$ $2$ ✓ ✓ ✓ $C_{12}.C_2^4$ $2^{6} \cdot 3$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
288.369.96.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_{36}.C_2^3$ $2^{5} \cdot 3^{2}$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
288.988.96.b1 $C_3$ $3$ ✓ ✓ ✓ $C_6^2:Q_8$ $2^{5} \cdot 3^{2}$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
288.995.96.b1 $C_3$ $3$ ✓ ✓ ✓ $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
288.1020.96.a1 $C_3$ $3$ ✓ ✓ ✓ $Q_8\times C_6^2$ $2^{5} \cdot 3^{2}$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
384.20104.96.d1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^2\times Q_8\times A_4$ $2^{7} \cdot 3$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
480.1135.96.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $C_{60}.C_2^3$ $2^{5} \cdot 3 \cdot 5$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
480.1142.96.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $C_{60}.C_2^3$ $2^{5} \cdot 3 \cdot 5$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
480.1182.96.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ ✓ $C_{60}.C_2^3$ $2^{5} \cdot 3 \cdot 5$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
672.1089.96.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $C_{14}:(C_6\times Q_8)$ $2^{5} \cdot 3 \cdot 7$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
672.1096.96.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $C_2\times Q_8\times F_7$ $2^{5} \cdot 3 \cdot 7$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
672.1181.96.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $C_{14}:C_6\times Q_8$ $2^{5} \cdot 3 \cdot 7$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
672.1203.96.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $C_{84}.C_2^3$ $2^{5} \cdot 3 \cdot 7$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
672.1210.96.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $C_{84}.C_2^3$ $2^{5} \cdot 3 \cdot 7$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
672.1250.96.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ ✓ $C_{84}.C_2^3$ $2^{5} \cdot 3 \cdot 7$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
864.4702.96.a1 $C_3^2$ $3^{2}$ ✓ ✓ ✓ $C_3\times C_6^2:Q_8$ $2^{5} \cdot 3^{3}$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
1056.964.96.a1 $C_{11}$ $11$ $11$ ✓ ✓ ✓ $C_{132}.C_2^3$ $2^{5} \cdot 3 \cdot 11$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
1056.971.96.a1 $C_{11}$ $11$ $11$ ✓ ✓ ✓ $C_{132}.C_2^3$ $2^{5} \cdot 3 \cdot 11$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
1056.1011.96.a1 $C_{11}$ $11$ $11$ ✓ ✓ ✓ ✓ $C_{132}.C_2^3$ $2^{5} \cdot 3 \cdot 11$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
1248.1242.96.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ $C_{26}:(C_6\times Q_8)$ $2^{5} \cdot 3 \cdot 13$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
1248.1249.96.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ $C_{26}:C_6\times Q_8$ $2^{5} \cdot 3 \cdot 13$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
1248.1360.96.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ $C_{26}:C_6\times Q_8$ $2^{5} \cdot 3 \cdot 13$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
1248.1382.96.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ $C_{156}.C_2^3$ $2^{5} \cdot 3 \cdot 13$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
1248.1389.96.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ $C_{156}.C_2^3$ $2^{5} \cdot 3 \cdot 13$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
1248.1429.96.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ ✓ $C_{156}.C_2^3$ $2^{5} \cdot 3 \cdot 13$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
1632.1135.96.a1 $C_{17}$ $17$ $17$ ✓ ✓ ✓ $C_{204}.C_2^3$ $2^{5} \cdot 3 \cdot 17$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
1632.1142.96.a1 $C_{17}$ $17$ $17$ ✓ ✓ ✓ $C_{204}.C_2^3$ $2^{5} \cdot 3 \cdot 17$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
1632.1182.96.a1 $C_{17}$ $17$ $17$ ✓ ✓ ✓ ✓ $C_{204}.C_2^3$ $2^{5} \cdot 3 \cdot 17$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
1824.1080.96.a1 $C_{19}$ $19$ $19$ ✓ ✓ ✓ $C_{38}:(C_6\times Q_8)$ $2^{5} \cdot 3 \cdot 19$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
1824.1087.96.a1 $C_{19}$ $19$ $19$ ✓ ✓ ✓ $C_{38}:C_6\times Q_8$ $2^{5} \cdot 3 \cdot 19$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
1824.1172.96.a1 $C_{19}$ $19$ $19$ ✓ ✓ ✓ $C_{38}:C_6\times Q_8$ $2^{5} \cdot 3 \cdot 19$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
1824.1194.96.a1 $C_{19}$ $19$ $19$ ✓ ✓ ✓ $C_{228}.C_2^3$ $2^{5} \cdot 3 \cdot 19$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
1824.1201.96.a1 $C_{19}$ $19$ $19$ ✓ ✓ ✓ $C_{228}.C_2^3$ $2^{5} \cdot 3 \cdot 19$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
1824.1241.96.a1 $C_{19}$ $19$ $19$ ✓ ✓ ✓ ✓ $C_{228}.C_2^3$ $2^{5} \cdot 3 \cdot 19$ $C_6.C_2^4$ $2^{5} \cdot 3$ ✓
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