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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 66 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
3072.fw.3072.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $C_2^7:S_4$ $2^{10} \cdot 3$ $C_2^7:S_4$ $2^{10} \cdot 3$
12288.dq.3072.B $C_2^2$ $2^{2}$ ✓ ✓ $C_2^9.S_4$ $2^{12} \cdot 3$ $C_2^7:S_4$ $2^{10} \cdot 3$ ✓
24576.bbb.3072._.A $C_2^3$ $2^{3}$ ✓ ✓ $C_2^8.\GL(2,\mathbb{Z}/4)$ $2^{13} \cdot 3$ $C_2^7:S_4$ $2^{10} \cdot 3$
24576.bbb.3072._.D $C_2^3$ $2^{3}$ ✓ ✓ $C_2^8.\GL(2,\mathbb{Z}/4)$ $2^{13} \cdot 3$ $C_2^7:S_4$ $2^{10} \cdot 3$
24576.bbc.3072.E $C_2^3$ $2^{3}$ ✓ ✓ $C_2^8.\GL(2,\mathbb{Z}/4)$ $2^{13} \cdot 3$ $C_2^7:S_4$ $2^{10} \cdot 3$
196608.x.3072.E $C_2^6$ $2^{6}$ ✓ ✓ $C_2^{10}.(C_2\times \GL(2,\mathbb{Z}/4))$ $2^{16} \cdot 3$ $C_2^7:S_4$ $2^{10} \cdot 3$
196608.hr.3072.D $C_2^6$ $2^{6}$ ✓ ✓ $C_2^7.C_2\wr S_4$ $2^{16} \cdot 3$ $C_2^7:S_4$ $2^{10} \cdot 3$
196608.ja.3072.E $C_4^3$ $2^{6}$ ✓ ✓ $C_4^3.C_2^7:S_4$ $2^{16} \cdot 3$ $C_2^7:S_4$ $2^{10} \cdot 3$
196608.ji.3072.E $C_4^3$ $2^{6}$ ✓ ✓ $C_4^3.C_2^7:S_4$ $2^{16} \cdot 3$ $C_2^7:S_4$ $2^{10} \cdot 3$
196608.mw.3072.B $C_2^2\times C_4^2$ $2^{6}$ ✓ ✓ ✓ $C_2^7.C_2\wr S_4$ $2^{16} \cdot 3$ $C_2^7:S_4$ $2^{10} \cdot 3$
196608.mw.3072.E $C_2^4\times C_4$ $2^{6}$ ✓ ✓ ✓ $C_2^7.C_2\wr S_4$ $2^{16} \cdot 3$ $C_2^7:S_4$ $2^{10} \cdot 3$
196608.mx.3072.B $C_2^2\times C_4^2$ $2^{6}$ ✓ ✓ ✓ $C_2^7.C_2\wr S_4$ $2^{16} \cdot 3$ $C_2^7:S_4$ $2^{10} \cdot 3$
196608.mx.3072.D $C_2^4\times C_4$ $2^{6}$ ✓ ✓ ✓ $C_2^7.C_2\wr S_4$ $2^{16} \cdot 3$ $C_2^7:S_4$ $2^{10} \cdot 3$
1572864.m.3072.G $C_2^8.C_2$ $2^{9}$ ✓ ✓ $C_2^{10}.C_2\wr S_4$ $2^{19} \cdot 3$ $C_2^7:S_4$ $2^{10} \cdot 3$
1572864.m.3072.H $C_4^2.C_2^5$ $2^{9}$ ✓ ✓ $C_2^{10}.C_2\wr S_4$ $2^{19} \cdot 3$ $C_2^7:S_4$ $2^{10} \cdot 3$
1572864.p.3072.D $C_2^8.C_2$ $2^{9}$ ✓ ✓ $C_2^{10}.C_2\wr S_4$ $2^{19} \cdot 3$ $C_2^7:S_4$ $2^{10} \cdot 3$
1572864.p.3072.H $C_4^2.C_2^5$ $2^{9}$ ✓ ✓ $C_2^{10}.C_2\wr S_4$ $2^{19} \cdot 3$ $C_2^7:S_4$ $2^{10} \cdot 3$
1572864.ck.3072.B $C_2^6:D_4$ $2^{9}$ ✓ $C_2^{10}.C_2\wr S_4$ $2^{19} \cdot 3$ $C_2^7:S_4$ $2^{10} \cdot 3$
1572864.cl.3072.B $C_2^6:D_4$ $2^{9}$ ✓ $C_2^{10}.C_2\wr S_4$ $2^{19} \cdot 3$ $C_2^7:S_4$ $2^{10} \cdot 3$
17915904.x.3072._.C $(C_3:S_3)^3$ $2^{3} \cdot 3^{6}$ ✓ $C_3^6.(C_2^8.\GL(2,\mathbb{Z}/4))$ $2^{13} \cdot 3^{7}$ $C_2^7:S_4$ $2^{10} \cdot 3$
17915904.x.3072._.E $(C_3:S_3)^3$ $2^{3} \cdot 3^{6}$ ✓ $C_3^6.(C_2^8.\GL(2,\mathbb{Z}/4))$ $2^{13} \cdot 3^{7}$ $C_2^7:S_4$ $2^{10} \cdot 3$
17915904.bb.3072.D $(C_3:S_3)^3$ $2^{3} \cdot 3^{6}$ ✓ $C_3^6.(C_2^8.\GL(2,\mathbb{Z}/4))$ $2^{13} \cdot 3^{7}$ $C_2^7:S_4$ $2^{10} \cdot 3$
17915904.ci.3072.C $C_3^6.C_2^3$ $2^{3} \cdot 3^{6}$ ✓ ✓ $C_3^6.(C_2^8.\GL(2,\mathbb{Z}/4))$ $2^{13} \cdot 3^{7}$ $C_2^7:S_4$ $2^{10} \cdot 3$
17915904.ci.3072.D $C_3^6.C_2^3$ $2^{3} \cdot 3^{6}$ ✓ ✓ $C_3^6.(C_2^8.\GL(2,\mathbb{Z}/4))$ $2^{13} \cdot 3^{7}$ $C_2^7:S_4$ $2^{10} \cdot 3$
17915904.cj.3072.C $C_3^6.C_2^3$ $2^{3} \cdot 3^{6}$ ✓ ✓ $C_3^6.(C_2^8.\GL(2,\mathbb{Z}/4))$ $2^{13} \cdot 3^{7}$ $C_2^7:S_4$ $2^{10} \cdot 3$
17915904.cj.3072.D $C_3^6.C_2^3$ $2^{3} \cdot 3^{6}$ ✓ ✓ $C_3^6.(C_2^8.\GL(2,\mathbb{Z}/4))$ $2^{13} \cdot 3^{7}$ $C_2^7:S_4$ $2^{10} \cdot 3$
1632586752.eq.3072._.A $C_3^{12}$ $3^{12}$ ✓ ✓ ✓ $C_3^{12}.C_2^5.S_4.C_2^2$ $2^{10} \cdot 3^{13}$ $C_2^7:S_4$ $2^{10} \cdot 3$ ✓
1632586752.es.3072._.A $C_3^{12}$ $3^{12}$ ✓ ✓ ✓ $C_3^{12}.C_2^5.S_4.C_2^2$ $2^{10} \cdot 3^{13}$ $C_2^7:S_4$ $2^{10} \cdot 3$ ✓
6530347008.cl.3072._.C $C_3^{11}.D_6$ $2^{2} \cdot 3^{12}$ ✓ $C_3^{12}.C_2.C_2^6.S_4.C_2^2$ $2^{12} \cdot 3^{13}$ $C_2^7:S_4$ $2^{10} \cdot 3$
6530347008.cl.3072._.D $C_3^{11}.D_6$ $2^{2} \cdot 3^{12}$ ✓ $C_3^{12}.C_2.C_2^6.S_4.C_2^2$ $2^{12} \cdot 3^{13}$ $C_2^7:S_4$ $2^{10} \cdot 3$
13060694016.ve.3072._.E $C_3^{12}.C_2^3$ $2^{3} \cdot 3^{12}$ ✓ $C_3^6.(C_3^6.(C_2^8.\GL(2,\mathbb{Z}/4)))$ $2^{13} \cdot 3^{13}$ $C_2^7:S_4$ $2^{10} \cdot 3$
13060694016.ve.3072._.H $C_3^{12}.C_2^3$ $2^{3} \cdot 3^{12}$ ✓ $C_3^6.(C_3^6.(C_2^8.\GL(2,\mathbb{Z}/4)))$ $2^{13} \cdot 3^{13}$ $C_2^7:S_4$ $2^{10} \cdot 3$
13060694016.vx.3072._.C $C_3^{12}.C_2^3$ $2^{3} \cdot 3^{12}$ ✓ $C_3^6.(C_3^6.(C_2^8.\GL(2,\mathbb{Z}/4)))$ $2^{13} \cdot 3^{13}$ $C_2^7:S_4$ $2^{10} \cdot 3$
13060694016.vx.3072._.D $C_3^{12}.C_2^3$ $2^{3} \cdot 3^{12}$ ✓ $C_3^6.(C_3^6.(C_2^8.\GL(2,\mathbb{Z}/4)))$ $2^{13} \cdot 3^{13}$ $C_2^7:S_4$ $2^{10} \cdot 3$
13060694016.bbf.3072._.C $C_3^{12}.C_2^3$ $2^{3} \cdot 3^{12}$ ✓ ✓ $C_3^6.(C_3^6.(C_2^8.\GL(2,\mathbb{Z}/4)))$ $2^{13} \cdot 3^{13}$ $C_2^7:S_4$ $2^{10} \cdot 3$
13060694016.bbf.3072._.D $C_3^9.S_3^3$ $2^{3} \cdot 3^{12}$ ✓ ✓ $C_3^6.(C_3^6.(C_2^8.\GL(2,\mathbb{Z}/4)))$ $2^{13} \cdot 3^{13}$ $C_2^7:S_4$ $2^{10} \cdot 3$
13060694016.bbg.3072._.E $C_3^9.S_3^3$ $2^{3} \cdot 3^{12}$ ✓ ✓ $C_3^6.(C_3^6.(C_2^8.\GL(2,\mathbb{Z}/4)))$ $2^{13} \cdot 3^{13}$ $C_2^7:S_4$ $2^{10} \cdot 3$
13060694016.bbg.3072._.F $C_3^9.S_3^3$ $2^{3} \cdot 3^{12}$ ✓ ✓ $C_3^6.(C_3^6.(C_2^8.\GL(2,\mathbb{Z}/4)))$ $2^{13} \cdot 3^{13}$ $C_2^7:S_4$ $2^{10} \cdot 3$
73383542784.q.3072._.E $C_2^{12}.C_3^5.D_6.C_2$ $2^{15} \cdot 3^{6}$ ✓ $C_2^{12}.(C_3^6.(C_2^8.\GL(2,\mathbb{Z}/4)))$ $2^{25} \cdot 3^{7}$ $C_2^7:S_4$ $2^{10} \cdot 3$
73383542784.q.3072._.G $C_2^{12}.C_3^5.D_6.C_2$ $2^{15} \cdot 3^{6}$ ✓ $C_2^{12}.(C_3^6.(C_2^8.\GL(2,\mathbb{Z}/4)))$ $2^{25} \cdot 3^{7}$ $C_2^7:S_4$ $2^{10} \cdot 3$
73383542784.u.3072._.E $C_2^{12}.C_3^3.S_3^3$ $2^{15} \cdot 3^{6}$ ✓ $C_2^{12}.(C_3^6.(C_2^8.\GL(2,\mathbb{Z}/4)))$ $2^{25} \cdot 3^{7}$ $C_2^7:S_4$ $2^{10} \cdot 3$
73383542784.u.3072._.F $C_2^{12}.C_3^4.C_6^2.C_2$ $2^{15} \cdot 3^{6}$ ✓ $C_2^{12}.(C_3^6.(C_2^8.\GL(2,\mathbb{Z}/4)))$ $2^{25} \cdot 3^{7}$ $C_2^7:S_4$ $2^{10} \cdot 3$
73383542784.cb.3072._.C $C_2^{12}.C_3^4.C_6^2.C_2$ $2^{15} \cdot 3^{6}$ ✓ ✓ $C_2^{12}.(C_3^6.(C_2^8.\GL(2,\mathbb{Z}/4)))$ $2^{25} \cdot 3^{7}$ $C_2^7:S_4$ $2^{10} \cdot 3$
73383542784.cb.3072._.D $C_2^{12}.C_3^5.D_6.C_2$ $2^{15} \cdot 3^{6}$ ✓ ✓ $C_2^{12}.(C_3^6.(C_2^8.\GL(2,\mathbb{Z}/4)))$ $2^{25} \cdot 3^{7}$ $C_2^7:S_4$ $2^{10} \cdot 3$
73383542784.cc.3072._.C $C_2^{12}.C_3^5.D_6.C_2$ $2^{15} \cdot 3^{6}$ ✓ ✓ $C_2^{12}.(C_3^6.(C_2^8.\GL(2,\mathbb{Z}/4)))$ $2^{25} \cdot 3^{7}$ $C_2^7:S_4$ $2^{10} \cdot 3$
73383542784.cc.3072._.E $C_2^{12}.C_3^4.C_6^2.C_2$ $2^{15} \cdot 3^{6}$ ✓ ✓ $C_2^{12}.(C_3^6.(C_2^8.\GL(2,\mathbb{Z}/4)))$ $2^{25} \cdot 3^{7}$ $C_2^7:S_4$ $2^{10} \cdot 3$
104485552128.q.3072._.B $C_3^{12}.C_2^6$ $2^{6} \cdot 3^{12}$ ✓ $C_3^{12}.C_2^6.C_2^6.C_6.C_2^3$ $2^{16} \cdot 3^{13}$ $C_2^7:S_4$ $2^{10} \cdot 3$
104485552128.q.3072._.C $C_3^{12}.C_2^6$ $2^{6} \cdot 3^{12}$ ✓ $C_3^{12}.C_2^6.C_2^6.C_6.C_2^3$ $2^{16} \cdot 3^{13}$ $C_2^7:S_4$ $2^{10} \cdot 3$
104485552128.hw.3072._.B $C_3^{12}.C_2^6$ $2^{6} \cdot 3^{12}$ ✓ $C_3^{12}.C_2^6.C_4^2.A_4.(C_2\times D_4)$ $2^{16} \cdot 3^{13}$ $C_2^7:S_4$ $2^{10} \cdot 3$
104485552128.hw.3072._.C $C_3^{12}.C_2^6$ $2^{6} \cdot 3^{12}$ ✓ $C_3^{12}.C_2^6.C_4^2.A_4.(C_2\times D_4)$ $2^{16} \cdot 3^{13}$ $C_2^7:S_4$ $2^{10} \cdot 3$
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