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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 (39 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
2654208.kw.1.a1 $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $C_1$ $1$ ✓
2654208.kw.2.A $A_4^3.C_2^6:A_4$ $2^{14} \cdot 3^{4}$ ✓ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $C_2$ $2$ ✓
2654208.kw.2.B $C_2^5.A_4^3:S_4$ $2^{14} \cdot 3^{4}$ ✓ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $C_2$ $2$ ✓
2654208.kw.2.C $C_2^5.A_4^3:S_4$ $2^{14} \cdot 3^{4}$ ✓ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $C_2$ $2$ ✓
2654208.kw.4.A $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
2654208.kw.6.A $C_2\times C_2^6.C_3^3.C_2^5.C_2^2$ $2^{14} \cdot 3^{3}$ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $S_3$ $2 \cdot 3$
2654208.kw.8.A $C_2^4.A_4^3:A_4$ $2^{12} \cdot 3^{4}$ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $D_4$ $2^{3}$
2654208.kw.12.A $C_2\times C_2^6.C_3^3.C_2^6$ $2^{13} \cdot 3^{3}$ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
2654208.kw.24.A $C_2^8.C_6^3.C_2$ $2^{12} \cdot 3^{3}$ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $S_4$ $2^{3} \cdot 3$
2654208.kw.24.B $C_2^2\times C_2^6.C_3^3.C_2^4$ $2^{12} \cdot 3^{3}$ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $S_4$ $2^{3} \cdot 3$
2654208.kw.24.C $C_2^6.C_6^3.C_2^3$ $2^{12} \cdot 3^{3}$ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $S_4$ $2^{3} \cdot 3$
2654208.kw.24.D $C_2^6.C_3^3.C_2^6$ $2^{12} \cdot 3^{3}$ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $C_3:D_4$ $2^{3} \cdot 3$
2654208.kw.48.A $C_2^2\times C_2^6.C_6^3$ $2^{11} \cdot 3^{3}$ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $C_2\times S_4$ $2^{4} \cdot 3$
2654208.kw.48.B $C_2\times C_2^6.C_3^3.C_2^4$ $2^{11} \cdot 3^{3}$ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $C_2\times S_4$ $2^{4} \cdot 3$
2654208.kw.48.C $C_2^2\times C_2^6.C_3^3.C_2^3$ $2^{11} \cdot 3^{3}$ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $C_2\times S_4$ $2^{4} \cdot 3$
2654208.kw.96.A $C_2^3\times C_2^6.C_3^3.C_2$ $2^{10} \cdot 3^{3}$ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $C_2^2:S_4$ $2^{5} \cdot 3$
2654208.kw.96.B $C_2\times C_2^6.C_6^3$ $2^{10} \cdot 3^{3}$ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $\GL(2,\mathbb{Z}/4)$ $2^{5} \cdot 3$
2654208.kw.96.C $C_2^6.C_3^3.C_2^4$ $2^{10} \cdot 3^{3}$ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $\GL(2,\mathbb{Z}/4)$ $2^{5} \cdot 3$
2654208.kw.96.D $C_2\times C_2^6.C_3^3.C_2^3$ $2^{10} \cdot 3^{3}$ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $\GL(2,\mathbb{Z}/4)$ $2^{5} \cdot 3$
2654208.kw.192.A $C_2^2\times C_2^6.C_3^3.C_2$ $2^{9} \cdot 3^{3}$ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $C_2^3:S_4$ $2^{6} \cdot 3$
2654208.kw.384.A $C_2\times C_2^6.C_3^3.C_2$ $2^{8} \cdot 3^{3}$ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $C_2\wr S_3$ $2^{7} \cdot 3$
2654208.kw.648.A $C_2^6.C_2^6$ $2^{12}$ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $C_3^3:S_4$ $2^{3} \cdot 3^{4}$
2654208.kw.768.A $C_2\times A_4^3$ $2^{7} \cdot 3^{3}$ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $C_2^5:S_4$ $2^{8} \cdot 3$
2654208.kw.1296.A $C_2^{11}$ $2^{11}$ ✓ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $C_2\times C_3^3:S_4$ $2^{4} \cdot 3^{4}$
2654208.kw.1536.A $A_4^3$ $2^{6} \cdot 3^{3}$ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{9} \cdot 3$
2654208.kw.2592.A $C_2^{10}$ $2^{10}$ ✓ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $(C_3\times C_6^2):S_4$ $2^{5} \cdot 3^{4}$
2654208.kw.2592.B $C_2^{10}$ $2^{10}$ ✓ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $C_3^3:\GL(2,\mathbb{Z}/4)$ $2^{5} \cdot 3^{4}$
2654208.kw.5184.A $C_2^9$ $2^{9}$ ✓ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $C_6^3:S_4$ $2^{6} \cdot 3^{4}$
2654208.kw.10368.A $C_2^8$ $2^{8}$ ✓ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $(C_2\times C_6^3):S_4$ $2^{7} \cdot 3^{4}$
2654208.kw.20736.A $C_2^7$ $2^{7}$ ✓ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
2654208.kw.41472.A $C_2^3:D_4$ $2^{6}$ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $A_4^3:S_4$ $2^{9} \cdot 3^{4}$
2654208.kw.41472.B $C_2^6$ $2^{6}$ ✓ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $(C_2\times C_6^3).\GL(2,\mathbb{Z}/4)$ $2^{9} \cdot 3^{4}$ ✓
2654208.kw.82944.A $C_2^5$ $2^{5}$ ✓ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $C_2\times A_4^3:S_4$ $2^{10} \cdot 3^{4}$
2654208.kw.165888.A $C_2^4$ $2^{4}$ ✓ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $A_4:S_4^2.S_4$ $2^{11} \cdot 3^{4}$
2654208.kw.165888.B $C_2^4$ $2^{4}$ ✓ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $A_4^3.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3^{4}$
2654208.kw.331776.A $C_2^3$ $2^{3}$ ✓ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $A_4^3.C_2^3:S_4$ $2^{12} \cdot 3^{4}$
2654208.kw.663552.A $C_2^2$ $2^{2}$ ✓ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $A_4^3.C_2\wr S_3$ $2^{13} \cdot 3^{4}$ ✓
2654208.kw.1327104.A $C_2$ $2$ ✓ ✓ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $A_4^3.C_2^5:S_4$ $2^{14} \cdot 3^{4}$ ✓
2654208.kw.2654208.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$
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