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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 51 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1536.408545323.2.A $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ ✓ ✓ $C_2^4.\GL(2,\mathbb{Z}/4)$ $2^{9} \cdot 3$ $C_2$ $2$ ✓
1536.408548193.2.B $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ ✓ ✓ $C_2^6:D_{12}$ $2^{9} \cdot 3$ $C_2$ $2$ ✓
1536.408560345.2.B $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ ✓ $C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{9} \cdot 3$ $C_2$ $2$ ✓
1536.408610984.2.C $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ ✓ ✓ $C_2^7:D_6$ $2^{9} \cdot 3$ $C_2$ $2$ ✓
1536.408610986.2.B $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ ✓ $C_2^7:D_6$ $2^{9} \cdot 3$ $C_2$ $2$ ✓
1536.408626277.2.B $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ ✓ $C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{9} \cdot 3$ $C_2$ $2$ ✓
1536.408633186.2.a1 $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ ✓ ✓ $C_2^4.\GL(2,\mathbb{Z}/4)$ $2^{9} \cdot 3$ $C_2$ $2$ ✓
1536.408639737.2.b1 $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ ✓ ✓ $C_2^6:D_{12}$ $2^{9} \cdot 3$ $C_2$ $2$ ✓
1536.408640713.2.A $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ ✓ ✓ $C_2^7.D_6$ $2^{9} \cdot 3$ $C_2$ $2$ ✓
1536.408640724.2.D $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ ✓ $C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{9} \cdot 3$ $C_2$ $2$ ✓
1536.408640849.2.A $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ ✓ $C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{9} \cdot 3$ $C_2$ $2$ ✓
1536.408640971.2.B $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ ✓ $C_2^7:D_6$ $2^{9} \cdot 3$ $C_2$ $2$ ✓
1536.408640973.2.a1 $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ ✓ $C_2^7:D_6$ $2^{9} \cdot 3$ $C_2$ $2$ ✓
2304.fg.3.a1 $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ $C_2^3:\PSOPlus(4,3)$ $2^{8} \cdot 3^{2}$ $3$ $-$
2304.hw.3.a1 $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ ✓ ✓ $C_2\times A_4^2:D_4$ $2^{8} \cdot 3^{2}$ $C_3$ $3$ ✓
2304.iq.3.b1 $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ $(C_2^3\times A_4):S_4$ $2^{8} \cdot 3^{2}$ $3$ $-$
2304.jf.3.A $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ $C_2^6:S_3^2$ $2^{8} \cdot 3^{2}$ $3$ $-$
2304.nb.3.b1 $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ $C_2\times A_4:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3^{2}$ $3$ $-$
2304.bet.3.A $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ ✓ ✓ $C_2\wr S_3\times C_6$ $2^{8} \cdot 3^{2}$ $C_3$ $3$ ✓
3072.eb.4.B $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ $C_2^7:S_4$ $2^{10} \cdot 3$ $2^{2}$ $-$
3072.ft.4._.F $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ $C_2^5.\GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3$ $2^{2}$ $-$
3072.fu.4.B $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ $C_2^5.\GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3$ $2^{2}$ $-$
3072.fw.4.f1 $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ $C_2^7:S_4$ $2^{10} \cdot 3$ $2^{2}$ $-$
3072.fx.4.F $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ $C_2^7.S_4$ $2^{10} \cdot 3$ $2^{2}$ $-$
3072.ig.4.E $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ $C_2^5.\GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3$ $2^{2}$ $-$
3072.ij.4.E $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ $C_2^7:S_4$ $2^{10} \cdot 3$ $2^{2}$ $-$
3072.im.4.B $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ $C_2^5.\GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3$ $2^{2}$ $-$
3072.jd.4.B $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ $C_2^5.\GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3$ $2^{2}$ $-$
3072.je.4.E $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ $C_2^7.S_4$ $2^{10} \cdot 3$ $2^{2}$ $-$
3072.jf.4.E $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ $C_2^5:\GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3$ $2^{2}$ $-$
3072.jg.4.B $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ $C_2^6:\GL(2,3)$ $2^{10} \cdot 3$ $2^{2}$ $-$
3072.jv.4.B $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ $C_2^5.\GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3$ $2^{2}$ $-$
3072.jw.4.B $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ $C_2^5:\GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3$ $2^{2}$ $-$
3072.jx.4.B $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ $C_2^5.\GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3$ $2^{2}$ $-$
3072.kl.4.B $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ $C_2^5.\GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3$ $2^{2}$ $-$
3072.ll.4.B $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ $C_2^5.\GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3$ $2^{2}$ $-$
3072.lm.4.B $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ $C_2^5.\GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3$ $2^{2}$ $-$
3072.ln.4.B $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ $C_2^7:S_4$ $2^{10} \cdot 3$ $2^{2}$ $-$
3072.lo.4.B $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ $C_2^5.\GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3$ $2^{2}$ $-$
3072.zy.4.E $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ $C_2^5:\GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3$ $2^{2}$ $-$
3072.bdv.4.G $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ $C_2^5.\GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3$ $2^{2}$ $-$
3072.bgp.4.b1 $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ $C_2^5:\GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3$ $2^{2}$ $-$
3072.bgq.4.E $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ $C_2^7:S_4$ $2^{10} \cdot 3$ $2^{2}$ $-$
3072.bjj.4.B $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ $C_2^7:S_4$ $2^{10} \cdot 3$ $2^{2}$ $-$
6912.et.9.a1 $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ $C_2\times C_6^2:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3^{3}$ $3^{2}$ $-$
7680.be.10.a1 $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ $C_2^7.A_5$ $2^{9} \cdot 3 \cdot 5$ $2 \cdot 5$ $-$
7680.bf.10.a1 $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ $C_2^7:A_5$ $2^{9} \cdot 3 \cdot 5$ $2 \cdot 5$ $-$
20736.im.27.A $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ $S_3^3.\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3^{4}$ $3^{3}$ $-$
37632.j.49.a1 $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ $C_2^6:(C_7^2:D_6)$ $2^{8} \cdot 3 \cdot 7^{2}$ $7^{2}$ $-$
559872.mp.729.A $C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ ✓ $(C_3:S_3)^3.\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3^{7}$ $3^{6}$ $-$
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