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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 64 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
629856.ka.1.a1.a1 $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ ✓ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $C_1$ $1$ ✓
629856.ka.2._.A $C_9^4.C_6.C_2^3$ $2^{4} \cdot 3^{9}$ ✓ ✓ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $C_2$ $2$ ✓
629856.ka.2._.B $C_9^4.C_6:D_4$ $2^{4} \cdot 3^{9}$ ✓ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $C_2$ $2$ ✓
629856.ka.2._.C $C_9^4.C_6.D_4$ $2^{4} \cdot 3^{9}$ ✓ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $C_2$ $2$ ✓
629856.ka.2._.D $C_9^4.C_6.C_2^3$ $2^{4} \cdot 3^{9}$ ✓ ✓ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $C_2$ $2$ ✓
629856.ka.2._.E $C_9^4.C_6.D_4$ $2^{4} \cdot 3^{9}$ ✓ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $C_2$ $2$ ✓
629856.ka.2._.F $C_9^4.C_6.D_4$ $2^{4} \cdot 3^{9}$ ✓ ✓ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $C_2$ $2$ ✓
629856.ka.2._.G $C_9^4.C_6:D_4$ $2^{4} \cdot 3^{9}$ ✓ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $C_2$ $2$ ✓
629856.ka.4._.A $C_9^2\wr C_2.D_6$ $2^{3} \cdot 3^{9}$ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $C_2^2$ $2^{2}$ ✓
629856.ka.4._.B $C_9^4.C_6.C_2^2$ $2^{3} \cdot 3^{9}$ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $C_2^2$ $2^{2}$ ✓
629856.ka.4._.C $C_9^4.C_6:C_4$ $2^{3} \cdot 3^{9}$ ✓ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $C_2^2$ $2^{2}$ ✓
629856.ka.4._.D $C_9^4.C_6.C_2^2$ $2^{3} \cdot 3^{9}$ ✓ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $C_2^2$ $2^{2}$ ✓
629856.ka.4._.E $C_9^2\wr C_2.D_6$ $2^{3} \cdot 3^{9}$ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $C_2^2$ $2^{2}$ ✓
629856.ka.4._.F $C_9^4.C_6.C_2^2$ $2^{3} \cdot 3^{9}$ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $C_2^2$ $2^{2}$ ✓
629856.ka.4._.G $C_9^4:(C_2\times D_6)$ $2^{3} \cdot 3^{9}$ ✓ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $C_2^2$ $2^{2}$ ✓
629856.ka.6._.A $D_9^4$ $2^{4} \cdot 3^{8}$ ✓ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $S_3$ $2 \cdot 3$
629856.ka.8._.A $C_9^4.C_6.C_2$ $2^{2} \cdot 3^{9}$ ✓ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $C_2^3$ $2^{3}$ ✓
629856.ka.8._.B $C_9^2.C_3^3.C_6^2$ $2^{2} \cdot 3^{9}$ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $D_4$ $2^{3}$
629856.ka.8._.C $C_9^4.C_6.C_2$ $2^{2} \cdot 3^{9}$ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $D_4$ $2^{3}$
629856.ka.8._.D $C_9^4.C_6.C_2$ $2^{2} \cdot 3^{9}$ ✓ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $D_4$ $2^{3}$
629856.ka.8._.E $C_9^4.C_6.C_2$ $2^{2} \cdot 3^{9}$ ✓ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $D_4$ $2^{3}$
629856.ka.8._.F $C_9^2.C_3^3.C_6^2$ $2^{2} \cdot 3^{9}$ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $D_4$ $2^{3}$
629856.ka.8._.G $C_9^4.C_6.C_2$ $2^{2} \cdot 3^{9}$ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $D_4$ $2^{3}$
629856.ka.12._.A $D_9^2\times C_9:D_9$ $2^{3} \cdot 3^{8}$ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $D_6$ $2^{2} \cdot 3$
629856.ka.12._.B $D_9^2\times C_9:D_9$ $2^{3} \cdot 3^{8}$ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $D_6$ $2^{2} \cdot 3$
629856.ka.12._.C $C_9:D_9^3$ $2^{3} \cdot 3^{8}$ ✓ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $D_6$ $2^{2} \cdot 3$
629856.ka.16._.A $C_9^2.C_3^3.C_3.C_6$ $2 \cdot 3^{9}$ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $C_2\times D_4$ $2^{4}$
629856.ka.16._.B $C_9^2.C_3^3.C_3.C_6$ $2 \cdot 3^{9}$ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $C_2\times D_4$ $2^{4}$
629856.ka.16._.C $C_9^4.C_6$ $2 \cdot 3^{9}$ ✓ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $C_2\times D_4$ $2^{4}$
629856.ka.24._.A $(C_9:D_9)^2$ $2^{2} \cdot 3^{8}$ ✓ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $C_2\times D_6$ $2^{3} \cdot 3$
629856.ka.24._.B $C_9^2\times D_9^2$ $2^{2} \cdot 3^{8}$ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $C_3:D_4$ $2^{3} \cdot 3$
629856.ka.24._.C $C_9^4.C_2^2$ $2^{2} \cdot 3^{8}$ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $C_3:D_4$ $2^{3} \cdot 3$
629856.ka.24._.D $C_9^4.C_2^2$ $2^{2} \cdot 3^{8}$ ✓ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $C_3:D_4$ $2^{3} \cdot 3$
629856.ka.24._.E $C_9^4.C_2^2$ $2^{2} \cdot 3^{8}$ ✓ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $C_3:D_4$ $2^{3} \cdot 3$
629856.ka.24._.F $C_9^2\times D_9^2$ $2^{2} \cdot 3^{8}$ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $C_3:D_4$ $2^{3} \cdot 3$
629856.ka.24._.G $C_9^4.C_2^2$ $2^{2} \cdot 3^{8}$ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $C_3:D_4$ $2^{3} \cdot 3$
629856.ka.32.a1.a1 $C_9^4.C_3$ $3^{9}$ $3$ ✓ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $C_2^2\wr C_2$ $2^{5}$
629856.ka.48._.A $C_9^2\wr C_2$ $2 \cdot 3^{8}$ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $C_6:D_4$ $2^{4} \cdot 3$
629856.ka.48._.B $C_9^2\wr C_2$ $2 \cdot 3^{8}$ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $C_6:D_4$ $2^{4} \cdot 3$
629856.ka.48._.C $C_9^4.C_2$ $2 \cdot 3^{8}$ ✓ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $C_6:D_4$ $2^{4} \cdot 3$
629856.ka.72._.A $C_3^2\times (C_3.(C_3.C_3^3)):C_2^2$ $2^{2} \cdot 3^{7}$ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $\SOPlus(4,2)$ $2^{3} \cdot 3^{2}$
629856.ka.72._.B $C_3^2\times (C_3.(C_3.C_3^3)):C_2^2$ $2^{2} \cdot 3^{7}$ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $\SOPlus(4,2)$ $2^{3} \cdot 3^{2}$
629856.ka.96._.A $C_9^4$ $3^{8}$ ✓ ✓ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $C_2^4:S_3$ $2^{5} \cdot 3$
629856.ka.144._.A $C_3^2\times C_9:(D_9:C_3)$ $2 \cdot 3^{7}$ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $S_3^2:C_2^2$ $2^{4} \cdot 3^{2}$
629856.ka.144._.B $C_3^2\times C_9:(D_9:C_3)$ $2 \cdot 3^{7}$ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $S_3^2:C_2^2$ $2^{4} \cdot 3^{2}$
629856.ka.216._.A $C_3^2\times D_9^2$ $2^{2} \cdot 3^{6}$ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $S_3^2:S_3$ $2^{3} \cdot 3^{3}$
629856.ka.216._.B $C_3^2\times D_9^2$ $2^{2} \cdot 3^{6}$ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $S_3^2:S_3$ $2^{3} \cdot 3^{3}$
629856.ka.288._.A $C_3^2\times C_3.(C_3.C_3^3)$ $3^{7}$ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $D_6\wr C_2$ $2^{5} \cdot 3^{2}$
629856.ka.288._.B $C_3^2\times C_3.(C_3.C_3^3)$ $3^{7}$ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $D_6\wr C_2$ $2^{5} \cdot 3^{2}$
629856.ka.432._.A $C_3\times C_9^2:C_6$ $2 \cdot 3^{6}$ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $S_3^2:D_6$ $2^{4} \cdot 3^{3}$
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