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Note: Search results may be incomplete due to uncomputed quantities: Subgroup label (103780224 objects)

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Subgroup label Subgroup order Cyclic Abelian Solvable
Normal Characteristic Perfect Maximal Central Non-trivial proper
Ambient label Ambient order Direct product Semidirect product
Quotient label Subgroup index Cyclic quotient Abelian quotient Solvable quotient Maximal quotient
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Results (49 matches)

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Label Subgroup Ambient Quotient
Name Order norm char cyc ab solv max perf cent Name Order Name Size cyc ab solv max
192.1468.2.c1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $C_2^4.D_6$ $2^{6} \cdot 3$ $C_2$ $2$ ✓ ✓ ✓
192.1471.2.e1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ ✓ $\GL(2,\mathbb{Z}/4):C_2$ $2^{6} \cdot 3$ $C_2$ $2$ ✓ ✓ ✓
192.1473.2.e1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ ✓ $D_4:S_4$ $2^{6} \cdot 3$ $C_2$ $2$ ✓ ✓ ✓
192.1477.2.b1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $Q_8\times S_4$ $2^{6} \cdot 3$ $C_2$ $2$ ✓ ✓ ✓
192.957.2.a1.b1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $A_4:Q_{16}$ $2^{6} \cdot 3$ $C_2$ $2$ ✓ ✓ ✓
192.957.2.a1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $A_4:Q_{16}$ $2^{6} \cdot 3$ $C_2$ $2$ ✓ ✓ ✓
192.960.2.b1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ ✓ $C_8:S_4$ $2^{6} \cdot 3$ $C_2$ $2$ ✓ ✓ ✓
192.973.2.b1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ ✓ $A_4:\SD_{16}$ $2^{6} \cdot 3$ $C_2$ $2$ ✓ ✓ ✓
192.975.2.b1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ ✓ $A_4:Q_{16}$ $2^{6} \cdot 3$ $C_2$ $2$ ✓ ✓ ✓
288.852.3.b1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ $C_2^3.S_3^2$ $2^{5} \cdot 3^{2}$ $3$ $-$ $-$ $-$
288.896.3.a1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ ✓ $C_{12}.S_4$ $2^{5} \cdot 3^{2}$ $C_3$ $3$ ✓ ✓ ✓
288.907.3.b1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ $C_{12}.S_4$ $2^{5} \cdot 3^{2}$ $3$ $-$ $-$ $-$
288.907.3.b1.c1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ $C_{12}.S_4$ $2^{5} \cdot 3^{2}$ $3$ $-$ $-$ $-$
288.907.3.b1.b1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ $C_{12}.S_4$ $2^{5} \cdot 3^{2}$ $3$ $-$ $-$ $-$
384.20078.4.b1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ $C_2^5.D_6$ $2^{7} \cdot 3$ $2^{2}$ $-$ $-$ $-$
384.20084.4.b1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ $Q_8.(C_2\times S_4)$ $2^{7} \cdot 3$ $2^{2}$ $-$ $-$ $-$
384.20093.4.b1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ $(C_2^2\times C_4).S_4$ $2^{7} \cdot 3$ $2^{2}$ $-$ $-$ $-$
384.20094.4.c1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ $Q_8.(C_2\times S_4)$ $2^{7} \cdot 3$ $2^{2}$ $-$ $-$ $-$
384.5556.4.b1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ $C_4^3.S_3$ $2^{7} \cdot 3$ $2^{2}$ $-$ $-$ $-$
384.5562.4.b1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ $(C_2^2\times C_4).S_4$ $2^{7} \cdot 3$ $2^{2}$ $-$ $-$ $-$
384.5565.4.b1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ $C_2^5.D_6$ $2^{7} \cdot 3$ $2^{2}$ $-$ $-$ $-$
384.5568.4.b1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ $(C_2^2\times C_4).S_4$ $2^{7} \cdot 3$ $2^{2}$ $-$ $-$ $-$
384.5571.4.b1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ $(C_2^2\times C_4).S_4$ $2^{7} \cdot 3$ $2^{2}$ $-$ $-$ $-$
384.5577.4.b1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ $(C_2^2\times C_4).S_4$ $2^{7} \cdot 3$ $2^{2}$ $-$ $-$ $-$
384.5605.4.b1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ $(C_2^2\times C_4).S_4$ $2^{7} \cdot 3$ $2^{2}$ $-$ $-$ $-$
384.569.4.a1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ $C_2^3.\GL(2,3)$ $2^{7} \cdot 3$ $2^{2}$ $-$ $-$ $-$
480.1013.5.a1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ ✓ $C_{20}.S_4$ $2^{5} \cdot 3 \cdot 5$ $C_5$ $5$ ✓ ✓ ✓
480.1024.5.a1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ $C_{20}.S_4$ $2^{5} \cdot 3 \cdot 5$ $5$ $-$ $-$ $-$
480.945.5.a1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ $A_5:Q_8$ $2^{5} \cdot 3 \cdot 5$ $5$ $-$ $-$ $-$
480.975.5.a1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ $(C_5\times A_4):Q_8$ $2^{5} \cdot 3 \cdot 5$ $5$ $-$ $-$ $-$
672.1059.7.a1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ $(C_7\times A_4):Q_8$ $2^{5} \cdot 3 \cdot 7$ $7$ $-$ $-$ $-$
672.1067.7.a1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ ✓ $C_{28}.S_4$ $2^{5} \cdot 3 \cdot 7$ $C_7$ $7$ ✓ ✓ ✓
672.1078.7.a1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ $C_{28}.S_4$ $2^{5} \cdot 3 \cdot 7$ $7$ $-$ $-$ $-$
864.4667.9.a1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ $A_4:\PSU(3,2)$ $2^{5} \cdot 3^{3}$ $3^{2}$ $-$ $-$ $-$
1056.862.11.a1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ $(C_{11}\times A_4):Q_8$ $2^{5} \cdot 3 \cdot 11$ $11$ $-$ $-$ $-$
1056.869.11.a1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ ✓ $C_{44}.S_4$ $2^{5} \cdot 3 \cdot 11$ $C_{11}$ $11$ ✓ ✓ ✓
1056.880.11.a1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ $C_{44}.S_4$ $2^{5} \cdot 3 \cdot 11$ $11$ $-$ $-$ $-$
1248.1182.13.a1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ $(A_4\times C_{13}):Q_8$ $2^{5} \cdot 3 \cdot 13$ $13$ $-$ $-$ $-$
1248.1220.13.a1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ ✓ $C_{52}.S_4$ $2^{5} \cdot 3 \cdot 13$ $C_{13}$ $13$ ✓ ✓ ✓
1248.1231.13.a1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ $C_{52}.S_4$ $2^{5} \cdot 3 \cdot 13$ $13$ $-$ $-$ $-$
1632.1014.17.a1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ ✓ $C_{68}.S_4$ $2^{5} \cdot 3 \cdot 17$ $C_{17}$ $17$ ✓ ✓ ✓
1632.1025.17.a1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ $C_{68}.S_4$ $2^{5} \cdot 3 \cdot 17$ $17$ $-$ $-$ $-$
1632.962.17.a1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ $(A_4\times C_{17}):Q_8$ $2^{5} \cdot 3 \cdot 17$ $17$ $-$ $-$ $-$
1824.1051.19.a1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ $(A_4\times C_{19}):Q_8$ $2^{5} \cdot 3 \cdot 19$ $19$ $-$ $-$ $-$
1824.1058.19.a1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ ✓ $C_{76}.S_4$ $2^{5} \cdot 3 \cdot 19$ $C_{19}$ $19$ ✓ ✓ ✓
1824.1069.19.a1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ $C_{76}.S_4$ $2^{5} \cdot 3 \cdot 19$ $19$ $-$ $-$ $-$
2400.eb.25.a1.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ $(A_4\times C_5^2):Q_8$ $2^{5} \cdot 3 \cdot 5^{2}$ $5^{2}$ $-$ $-$ $-$
69984.ck.729.a1 $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ $(C_3:S_3)^3.D_6$ $2^{5} \cdot 3^{7}$ $3^{6}$ $-$ $-$ $-$
1500000.t.15625.a1.M $A_4:Q_8$ $2^{5} \cdot 3$ ✓ ✓ $C_5^6:(A_4:Q_8)$ $2^{5} \cdot 3 \cdot 5^{6}$ $5^{6}$ $-$ $-$ $-$
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