↑

Learn more

Note: Search results may be incomplete due to uncomputed quantities: Characteristic (9102698 objects)

Refine search

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
Sort order Select

Results (1-50 of 279 matches)

Next   displayed columns for results
Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
98304.m.1.a1 $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_1$ $1$ ✓
98304.m.2.A $(C_4^3\times C_8).\GL(2,\mathbb{Z}/4)$ $2^{14} \cdot 3$ ✓ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_2$ $2$ ✓
98304.m.2.B $C_2\times C_4^4.\GL(2,\mathbb{Z}/4)$ $2^{14} \cdot 3$ ✓ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_2$ $2$ ✓
98304.m.2.C $(C_4^3\times C_8).\GL(2,\mathbb{Z}/4)$ $2^{14} \cdot 3$ ✓ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_2$ $2$ ✓
98304.m.2.D $(C_2\times C_4^4).\GL(2,\mathbb{Z}/4)$ $2^{14} \cdot 3$ ✓ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_2$ $2$ ✓
98304.m.2.E $(C_4^3\times C_8).\GL(2,\mathbb{Z}/4)$ $2^{14} \cdot 3$ ✓ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_2$ $2$ ✓
98304.m.2.F $C_4^3.(A_4\times C_8^2)$ $2^{14} \cdot 3$ ✓ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_2$ $2$ ✓
98304.m.2.G $(C_4^3\times C_8).\GL(2,\mathbb{Z}/4)$ $2^{14} \cdot 3$ ✓ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_2$ $2$ ✓
98304.m.4.A $C_4^4.(C_2^2\times S_4)$ $2^{13} \cdot 3$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_2^2$ $2^{2}$ ✓
98304.m.4.B $C_2^5.C_4^2:D_{24}$ $2^{13} \cdot 3$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_4$ $2^{2}$ ✓
98304.m.4.C $C_4^3.C_2^3:D_{24}$ $2^{13} \cdot 3$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_4$ $2^{2}$ ✓
98304.m.4.D $C_4^3.C_4^2:S_4$ $2^{13} \cdot 3$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_2^2$ $2^{2}$ ✓
98304.m.4.E $C_4^4.(C_2^3\times A_4)$ $2^{13} \cdot 3$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_2^2$ $2^{2}$ ✓
98304.m.4.F $C_4^4.(C_8\times A_4)$ $2^{13} \cdot 3$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_2^2$ $2^{2}$ ✓
98304.m.4.G $C_4^4.(C_8\times A_4)$ $2^{13} \cdot 3$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_2^2$ $2^{2}$ ✓
98304.m.4.H $C_2^3.C_4^4.D_6$ $2^{13} \cdot 3$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_2^2$ $2^{2}$ ✓
98304.m.4.I $C_2^3.C_4^4.D_6$ $2^{13} \cdot 3$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_2^2$ $2^{2}$ ✓
98304.m.4.J $C_4^2.Q_8.C_{12}:C_4:C_4$ $2^{13} \cdot 3$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_4$ $2^{2}$ ✓
98304.m.4.K $C_4^3.C_4^2.D_{12}$ $2^{13} \cdot 3$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_4$ $2^{2}$ ✓
98304.m.6.A $(C_4^3\times C_8).C_2^5$ $2^{14}$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $S_3$ $2 \cdot 3$
98304.m.8.A $C_4^3.(C_2^3\times S_4)$ $2^{12} \cdot 3$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_2\times C_4$ $2^{3}$ ✓
98304.m.8.B $C_4^4.(C_4\times A_4)$ $2^{12} \cdot 3$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_2^3$ $2^{3}$ ✓
98304.m.8.C $C_4^2.Q_8.C_6.C_2^3.C_2$ $2^{12} \cdot 3$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_2\times C_4$ $2^{3}$ ✓
98304.m.8.D $C_4^3.C_2^3:C_{24}$ $2^{12} \cdot 3$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $D_4$ $2^{3}$
98304.m.8.E $C_4^3.C_2^3:C_{24}$ $2^{12} \cdot 3$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $D_4$ $2^{3}$
98304.m.8.F $C_4^3.C_2^3:D_{12}$ $2^{12} \cdot 3$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_2\times C_4$ $2^{3}$ ✓
98304.m.8.G $C_4^3.C_2^3:D_{12}$ $2^{12} \cdot 3$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_2\times C_4$ $2^{3}$ ✓
98304.m.8.H $C_4^3.C_2^3:C_{24}$ $2^{12} \cdot 3$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_2\times C_4$ $2^{3}$ ✓
98304.m.8.I $C_4^3.C_2^3:C_{24}$ $2^{12} \cdot 3$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_2\times C_4$ $2^{3}$ ✓
98304.m.12.A $C_2\times C_4^4.C_2^4$ $2^{13}$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $D_6$ $2^{2} \cdot 3$
98304.m.12.B $(C_4^2\times C_8^2).D_4$ $2^{13}$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $D_6$ $2^{2} \cdot 3$
98304.m.12.C $(C_4^2\times C_8^2).D_4$ $2^{13}$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $D_6$ $2^{2} \cdot 3$
98304.m.16.A $C_2\times C_4^4.A_4$ $2^{11} \cdot 3$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $D_4:C_2$ $2^{4}$
98304.m.16.B $C_2^3.C_4^2.C_6.C_2^3$ $2^{11} \cdot 3$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_2\times D_4$ $2^{4}$
98304.m.16.C $C_2^3.C_4^2.C_6.C_2^3$ $2^{11} \cdot 3$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_2^2\times C_4$ $2^{4}$ ✓
98304.m.16.D $C_4^3.(C_2^2\times S_4)$ $2^{11} \cdot 3$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_2\times C_8$ $2^{4}$ ✓
98304.m.16.F $C_4^3.(C_2^2\times S_4)$ $2^{11} \cdot 3$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_2\times C_8$ $2^{4}$ ✓
98304.m.16.K $C_2^3.C_4^2.(C_4\times C_{12})$ $2^{11} \cdot 3$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $D_4:C_2$ $2^{4}$
98304.m.16.L $C_2^3.C_4^2.(C_4\times C_{12})$ $2^{11} \cdot 3$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_2\times D_4$ $2^{4}$
98304.m.16.M $C_2^3.C_4^2.(C_4\times C_{12})$ $2^{11} \cdot 3$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $D_4:C_2$ $2^{4}$
98304.m.16.N $C_2^3.C_4^2.(C_4\times C_{12})$ $2^{11} \cdot 3$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $D_4:C_2$ $2^{4}$
98304.m.24.A $C_4^3.C_8^2$ $2^{12}$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $S_4$ $2^{3} \cdot 3$
98304.m.24.B $C_2^4.C_4^4$ $2^{12}$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_2\times D_6$ $2^{3} \cdot 3$
98304.m.24.C $C_2^2\times C_8^2.D_8$ $2^{12}$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $D_{12}$ $2^{3} \cdot 3$
98304.m.24.D $C_2^2\times C_8^2.D_8$ $2^{12}$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $D_{12}$ $2^{3} \cdot 3$
98304.m.24.E $C_2^2\times C_8^2.\SD_{16}$ $2^{12}$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_4\times S_3$ $2^{3} \cdot 3$
98304.m.24.F $C_2^2\times C_8^2.\SD_{16}$ $2^{12}$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_4\times S_3$ $2^{3} \cdot 3$
98304.m.32.A $C_2^2\times C_4^3.A_4$ $2^{10} \cdot 3$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_4\times D_4$ $2^{5}$
98304.m.32.B $C_4^3.(C_4\times A_4)$ $2^{10} \cdot 3$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $C_2\times D_8$ $2^{5}$
98304.m.32.C $C_4^3.(C_4\times A_4)$ $2^{10} \cdot 3$ ✓ ✓ $C_4^4.C_4^2:S_4$ $2^{15} \cdot 3$ $D_8:C_2$ $2^{5}$
Next   displayed columns for results