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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 62 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1632586752.gj.1.a1.a1 $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ ✓ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $C_1$ $1$ ✓
1632586752.gj.2._.A $C_3^{12}.C_2^6.D_6.C_2$ $2^{9} \cdot 3^{13}$ ✓ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $C_2$ $2$ ✓
1632586752.gj.2._.B $C_3^{12}.C_2^6.C_3.D_4$ $2^{9} \cdot 3^{13}$ ✓ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $C_2$ $2$ ✓
1632586752.gj.2._.C $C_3^{12}.C_2^6.C_6.C_4$ $2^{9} \cdot 3^{13}$ ✓ ✓ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $C_2$ $2$ ✓
1632586752.gj.2._.D $C_3^{12}.C_2^6.D_6.C_2$ $2^{9} \cdot 3^{13}$ ✓ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $C_2$ $2$ ✓
1632586752.gj.2._.E $C_3^{12}.C_2^6.C_3.C_2^3$ $2^{9} \cdot 3^{13}$ ✓ ✓ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $C_2$ $2$ ✓
1632586752.gj.2._.F $C_3^{12}.C_2^6.C_3.D_4$ $2^{9} \cdot 3^{13}$ ✓ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $C_2$ $2$ ✓
1632586752.gj.2._.G $C_3^6.(C_3^6.C_2^6:S_4)$ $2^{9} \cdot 3^{13}$ ✓ ✓ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $C_2$ $2$ ✓
1632586752.gj.4._.A $C_3^{12}.C_2^6.C_6.C_2$ $2^{8} \cdot 3^{13}$ ✓ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $C_2^2$ $2^{2}$ ✓
1632586752.gj.4._.B $C_3^{12}.C_2^6.C_3.C_4$ $2^{8} \cdot 3^{13}$ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $C_2^2$ $2^{2}$ ✓
1632586752.gj.4._.C $C_3^{12}.C_2^6.C_6.C_2$ $2^{8} \cdot 3^{13}$ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $C_2^2$ $2^{2}$ ✓
1632586752.gj.4._.D $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ ✓ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $C_2^2$ $2^{2}$ ✓
1632586752.gj.4._.E $C_3^{12}.C_2^6.C_6.C_2$ $2^{8} \cdot 3^{13}$ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $C_2^2$ $2^{2}$ ✓
1632586752.gj.4._.F $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ ✓ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $C_2^2$ $2^{2}$ ✓
1632586752.gj.4._.G $C_3^{12}.C_2^6.C_3.C_4$ $2^{8} \cdot 3^{13}$ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $C_2^2$ $2^{2}$ ✓
1632586752.gj.6._.A $C_3^{12}.C_2^6.C_2^3$ $2^{9} \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $S_3$ $2 \cdot 3$
1632586752.gj.8._.A $C_3^{12}.C_2^6.C_6$ $2^{7} \cdot 3^{13}$ ✓ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $D_4$ $2^{3}$
1632586752.gj.8._.B $C_3^{12}.C_2^6.C_6$ $2^{7} \cdot 3^{13}$ ✓ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $C_2^3$ $2^{3}$ ✓
1632586752.gj.8._.C $C_3^{12}.C_2^6.C_6$ $2^{7} \cdot 3^{13}$ ✓ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $D_4$ $2^{3}$
1632586752.gj.12._.A $C_3^{12}.C_2^6.C_2^2$ $2^{8} \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $D_6$ $2^{2} \cdot 3$
1632586752.gj.12._.B $C_3^{12}.C_2^6.C_2^2$ $2^{8} \cdot 3^{12}$ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $D_6$ $2^{2} \cdot 3$
1632586752.gj.12._.C $C_3^{12}.C_2^6.C_2^2$ $2^{8} \cdot 3^{12}$ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $D_6$ $2^{2} \cdot 3$
1632586752.gj.16._.A $C_3^{12}.C_2^6.C_3$ $2^{6} \cdot 3^{13}$ ✓ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $C_2\times D_4$ $2^{4}$
1632586752.gj.24._.A $C_3^{12}.C_2^5.C_2^2$ $2^{7} \cdot 3^{12}$ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $S_4$ $2^{3} \cdot 3$
1632586752.gj.24._.B $C_3^{12}.C_2^5.C_2^2$ $2^{7} \cdot 3^{12}$ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $S_4$ $2^{3} \cdot 3$
1632586752.gj.24._.C $C_3^{12}.C_2^6.C_2$ $2^{7} \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $C_3:D_4$ $2^{3} \cdot 3$
1632586752.gj.24._.D $C_3^{12}.C_2^6.C_2$ $2^{7} \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $C_2\times D_6$ $2^{3} \cdot 3$
1632586752.gj.24._.E $C_3^{12}.C_2^6.C_2$ $2^{7} \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $C_3:D_4$ $2^{3} \cdot 3$
1632586752.gj.24._.F $C_3^{12}.C_2^5.C_2^2$ $2^{7} \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $S_4$ $2^{3} \cdot 3$
1632586752.gj.48._.A $C_3^{10}.D_6\wr C_2.C_2$ $2^{6} \cdot 3^{12}$ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $C_2\times S_4$ $2^{4} \cdot 3$
1632586752.gj.48._.B $C_3^{12}.C_2^4.C_2^2$ $2^{6} \cdot 3^{12}$ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $C_2\times S_4$ $2^{4} \cdot 3$
1632586752.gj.48._.C $C_3^{12}.C_2^4.C_2^2$ $2^{6} \cdot 3^{12}$ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $C_2\times S_4$ $2^{4} \cdot 3$
1632586752.gj.48._.D $C_3^{12}.C_2^5.C_2$ $2^{6} \cdot 3^{12}$ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $C_2\times S_4$ $2^{4} \cdot 3$
1632586752.gj.48._.E $C_3^{10}.D_6\wr C_2.C_2$ $2^{6} \cdot 3^{12}$ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $C_2\times S_4$ $2^{4} \cdot 3$
1632586752.gj.48._.F $C_3^{12}.C_2^4.C_2^2$ $2^{6} \cdot 3^{12}$ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $C_2\times S_4$ $2^{4} \cdot 3$
1632586752.gj.48._.G $C_3^{12}.C_2^4.C_2^2$ $2^{6} \cdot 3^{12}$ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $C_2\times S_4$ $2^{4} \cdot 3$
1632586752.gj.48._.H $C_3^{12}.C_2^5.C_2$ $2^{6} \cdot 3^{12}$ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $C_2\times S_4$ $2^{4} \cdot 3$
1632586752.gj.48._.I $C_3^{12}.C_2^6$ $2^{6} \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $C_6:D_4$ $2^{4} \cdot 3$
1632586752.gj.48._.J $C_3^{12}.C_2^6$ $2^{6} \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $C_2\times S_4$ $2^{4} \cdot 3$
1632586752.gj.96._.A $C_3^{12}.C_2^5$ $2^{5} \cdot 3^{12}$ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $\GL(2,\mathbb{Z}/4)$ $2^{5} \cdot 3$
1632586752.gj.96._.B $C_3^{12}.C_2^5$ $2^{5} \cdot 3^{12}$ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $\GL(2,\mathbb{Z}/4)$ $2^{5} \cdot 3$
1632586752.gj.96._.C $C_3^{10}.D_6\wr C_2$ $2^{5} \cdot 3^{12}$ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $C_2^2\times S_4$ $2^{5} \cdot 3$
1632586752.gj.96._.D $C_3^{10}.D_6\wr C_2$ $2^{5} \cdot 3^{12}$ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $C_2^2\times S_4$ $2^{5} \cdot 3$
1632586752.gj.96._.E $C_3^{12}.C_2^5$ $2^{5} \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $\GL(2,\mathbb{Z}/4)$ $2^{5} \cdot 3$
1632586752.gj.96._.F $C_3^{10}.D_6\wr C_2$ $2^{5} \cdot 3^{12}$ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $\GL(2,\mathbb{Z}/4)$ $2^{5} \cdot 3$
1632586752.gj.96._.G $C_3^{10}.D_6\wr C_2$ $2^{5} \cdot 3^{12}$ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $\GL(2,\mathbb{Z}/4)$ $2^{5} \cdot 3$
1632586752.gj.96._.H $C_3^{12}.C_2^5$ $2^{5} \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $C_2^2\times S_4$ $2^{5} \cdot 3$
1632586752.gj.96._.I $C_3^{12}.C_2^5$ $2^{5} \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $\GL(2,\mathbb{Z}/4)$ $2^{5} \cdot 3$
1632586752.gj.96._.J $C_3^{12}.C_2^5$ $2^{5} \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $C_2^2:S_4$ $2^{5} \cdot 3$
1632586752.gj.192._.A $C_3^{12}.C_2^4$ $2^{4} \cdot 3^{12}$ ✓ $C_3^{12}.C_2^6.C_6.D_4$ $2^{10} \cdot 3^{13}$ $C_2^3:S_4$ $2^{6} \cdot 3$
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