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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 131 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
384.18063.1.a1.a1 $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ ✓ ✓ $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $C_1$ $1$ ✓
768.1087538.2.c1.a1 $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ ✓ ✓ ✓ $Q_8:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ $C_2$ $2$ ✓
768.1087705.2.c1.a1 $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ ✓ ✓ ✓ $D_4.\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ $C_2$ $2$ ✓
768.1088025.2.c1.a1 $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ ✓ ✓ ✓ $C_8:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ $C_2$ $2$ ✓
768.1088320.2.d1 $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ ✓ ✓ $D_4.\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ $C_2$ $2$ ✓
768.1089054.2.e1 $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ ✓ ✓ $C_2^3.\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ $C_2$ $2$ ✓
768.1089249.2.e1 $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ ✓ ✓ ✓ $C_2\times D_8:S_4$ $2^{8} \cdot 3$ $C_2$ $2$ ✓
768.1089272.2.c1 $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ ✓ ✓ ✓ $C_2\times \SD_{16}\times S_4$ $2^{8} \cdot 3$ $C_2$ $2$ ✓
1152.156064.3.a1.a1 $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ ✓ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $3$ $-$
1536.408626847.4.q1 $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $C_2^4.\GL(2,\mathbb{Z}/4)$ $2^{9} \cdot 3$ $2^{2}$ $-$
1536.408631920.4.m1 $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ ✓ ✓ $\SD_{16}\times \GL(2,\mathbb{Z}/4)$ $2^{9} \cdot 3$ $C_2^2$ $2^{2}$ ✓
1536.408631920.4.s1 $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ ✓ ✓ $\SD_{16}\times \GL(2,\mathbb{Z}/4)$ $2^{9} \cdot 3$ $C_2^2$ $2^{2}$ ✓
1536.408632022.4.x1 $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $C_2\times D_4:\GL(2,\mathbb{Z}/4)$ $2^{9} \cdot 3$ $2^{2}$ $-$
1536.408639471.4.P $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ ✓ $C_8:C_2^3\times S_4$ $2^{9} \cdot 3$ $C_2^2$ $2^{2}$ ✓
1920.240562.5.a1.a1 $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ ✓ $C_2\times A_5:\SD_{16}$ $2^{7} \cdot 3 \cdot 5$ $5$ $-$
2304.c.6.j1.a1 $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $\SL(2,3):\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3^{2}$ $2 \cdot 3$ $-$
2304.d.6.j1 $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $C_2^2.S_4^2$ $2^{8} \cdot 3^{2}$ $2 \cdot 3$ $-$
2304.ou.6.U $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $S_3\times \SD_{16}\times S_4$ $2^{8} \cdot 3^{2}$ $2 \cdot 3$ $-$
2304.tg.6.BC $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $S_3\times C_4.\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3^{2}$ $2 \cdot 3$ $-$
2304.beb.6.U $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $S_3\times D_8:S_4$ $2^{8} \cdot 3^{2}$ $2 \cdot 3$ $-$
3072.bhd.8.BK $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $(C_2^4\times S_4):D_4$ $2^{10} \cdot 3$ $2^{3}$ $-$
3072.bhe.8.BK $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $C_2^5:\GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3$ $2^{3}$ $-$
3072.bhi.8._.IN $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $C_2^4.(D_4\times S_4)$ $2^{10} \cdot 3$ $2^{3}$ $-$
3072.bhi.8._.JB $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $C_2^4.(D_4\times S_4)$ $2^{10} \cdot 3$ $2^{3}$ $-$
3456.nz.9.a1.a1 $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ ✓ $A_4:F_9:C_2^2$ $2^{7} \cdot 3^{3}$ $3^{2}$ $-$
3840.ga.10.F $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $(C_2^2\times D_4):S_5$ $2^{8} \cdot 3 \cdot 5$ $2 \cdot 5$ $-$
3840.gg.10.D $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $C_2\times \SD_{16}\times S_5$ $2^{8} \cdot 3 \cdot 5$ $2 \cdot 5$ $-$
3840.go.10.D $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $C_2\times D_8:S_5$ $2^{8} \cdot 3 \cdot 5$ $2 \cdot 5$ $-$
4608.a.12.CB $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $\GL(2,3)\times \GL(2,\mathbb{Z}/4)$ $2^{9} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
4608.a.12.CL $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $\GL(2,3)\times \GL(2,\mathbb{Z}/4)$ $2^{9} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
4608.ix.12.J $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $(A_4\times C_2^4).S_4$ $2^{9} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
4608.jd.12.I $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $(C_2^2\times A_4).\GL(2,\mathbb{Z}/4)$ $2^{9} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
4608.lv.12._.IZ $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $C_4^2.(D_6\times S_4)$ $2^{9} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
4608.lv.12._.KH $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $C_4^2.(D_6\times S_4)$ $2^{9} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
4608.tx.12._.IZ $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $C_4.(D_6\times \GL(2,\mathbb{Z}/4))$ $2^{9} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
6144.bjd.16.HH $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $D_4^2.(C_2^2\times S_4)$ $2^{11} \cdot 3$ $2^{4}$ $-$
6912.ia.18.bc1 $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $D_6.S_4^2$ $2^{8} \cdot 3^{3}$ $2 \cdot 3^{2}$ $-$
6912.ka.18.e1 $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $F_9:C_2^2\times S_4$ $2^{8} \cdot 3^{3}$ $2 \cdot 3^{2}$ $-$
7680.er.20.V $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $C_4^2:(C_2^2\times S_5)$ $2^{9} \cdot 3 \cdot 5$ $2^{2} \cdot 5$ $-$
7680.ey.20.BU $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $C_8:C_2^3\times S_5$ $2^{9} \cdot 3 \cdot 5$ $2^{2} \cdot 5$ $-$
9216.iq.24.CQ $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $C_2^4.S_4^2$ $2^{10} \cdot 3^{2}$ $2^{3} \cdot 3$ $-$
9216.it.24.CE $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $C_4^3:C_6:S_4$ $2^{10} \cdot 3^{2}$ $2^{3} \cdot 3$ $-$
9216.it.24.CF $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $C_4^3:C_6:S_4$ $2^{10} \cdot 3^{2}$ $2^{3} \cdot 3$ $-$
9216.it.24.CG $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $C_4^3:C_6:S_4$ $2^{10} \cdot 3^{2}$ $2^{3} \cdot 3$ $-$
9216.iw.24.DJ $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $C_2^4.S_4^2$ $2^{10} \cdot 3^{2}$ $2^{3} \cdot 3$ $-$
9216.iw.24.DL $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $C_2^4.S_4^2$ $2^{10} \cdot 3^{2}$ $2^{3} \cdot 3$ $-$
9216.iz.24.CY $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $C_2^4.S_4^2$ $2^{10} \cdot 3^{2}$ $2^{3} \cdot 3$ $-$
9216.kb.24.CS $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $C_2^4.S_4^2$ $2^{10} \cdot 3^{2}$ $2^{3} \cdot 3$ $-$
9216.mo.24.cr1 $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $C_2^4.S_4^2$ $2^{10} \cdot 3^{2}$ $2^{3} \cdot 3$ $-$
11520.de.30.b1 $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $\SD_{16}\times S_6$ $2^{8} \cdot 3^{2} \cdot 5$ $2 \cdot 3 \cdot 5$ $-$
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