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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 226 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
57344.v.1.a1 $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ $C_1$ $1$ ✓
114688.a.2.a1 $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ ✓ $C_2^{12}.C_{28}$ $2^{14} \cdot 7$ $C_2$ $2$ ✓
114688.b.2.A $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ ✓ $C_2\times C_2^{12}.C_{14}$ $2^{14} \cdot 7$ $C_2$ $2$ ✓
114688.c.2.a1 $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ ✓ $C_2^{12}.C_7:C_4$ $2^{14} \cdot 7$ $C_2$ $2$ ✓
114688.d.2.A $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ ✓ $C_2^{12}.D_{14}$ $2^{14} \cdot 7$ $C_2$ $2$ ✓
114688.bl.2._.A $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ $C_2^7.C_2\wr C_7$ $2^{14} \cdot 7$ $C_2$ $2$ ✓
114688.bl.2._.B $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ $C_2^7.C_2\wr C_7$ $2^{14} \cdot 7$ $C_2$ $2$ ✓
114688.bl.2._.C $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ $C_2^7.C_2\wr C_7$ $2^{14} \cdot 7$ $C_2$ $2$ ✓
172032.x.3.a1.a1 $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ ✓ $C_2^9.F_8:C_6$ $2^{13} \cdot 3 \cdot 7$ $C_3$ $3$ ✓
172032.be.3.a1 $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ ✓ $C_2^{12}.C_{42}$ $2^{13} \cdot 3 \cdot 7$ $C_3$ $3$ ✓
229376.a.4.A $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ $\ASigmaL(1,16384)$ $2^{15} \cdot 7$ $C_2^2$ $2^{2}$ ✓
229376.b.4.A $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ $C_2^7.C_2\wr D_7$ $2^{15} \cdot 7$ $C_2^2$ $2^{2}$ ✓
229376.c.4.A $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ $C_2^7.C_2\wr D_7$ $2^{15} \cdot 7$ $C_2^2$ $2^{2}$ ✓
229376.d.4.A $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ $C_2\times C_2^{12}.D_{14}$ $2^{15} \cdot 7$ $C_2^2$ $2^{2}$ ✓
229376.e.4.A $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ $C_2^{12}.D_{28}$ $2^{15} \cdot 7$ $C_2^2$ $2^{2}$ ✓
229376.f.4.A $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ $C_2^7.C_2\wr D_7$ $2^{15} \cdot 7$ $C_2^2$ $2^{2}$ ✓
229376.z.4.A $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ $C_2\times C_2^{12}.D_{14}$ $2^{15} \cdot 7$ $C_2^2$ $2^{2}$ ✓
344064.b.6.A $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ $C_2\times C_2^{12}.F_7$ $2^{14} \cdot 3 \cdot 7$ $C_6$ $2 \cdot 3$ ✓
344064.c.6.a1 $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ $C_2^{12}.C_7:C_{12}$ $2^{14} \cdot 3 \cdot 7$ $C_6$ $2 \cdot 3$ ✓
344064.d.6.a1 $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ $C_2^{12}.C_7:C_{12}$ $2^{14} \cdot 3 \cdot 7$ $C_6$ $2 \cdot 3$ ✓
344064.e.6.A $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ $C_2^{12}.C_{14}:C_6$ $2^{14} \cdot 3 \cdot 7$ $C_6$ $2 \cdot 3$ ✓
344064.bi.6.a1 $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ $C_2^{12}.C_{14}:C_6$ $2^{14} \cdot 3 \cdot 7$ $C_6$ $2 \cdot 3$ ✓
344064.bn.6.a1 $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ $C_2^{12}.C_7:A_4$ $2^{14} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
344064.bq.6.a1.a1 $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ $C_2^{14}.C_{21}$ $2^{14} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
344064.bu.6.A $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ $C_2^{12}.(C_3\times D_{14})$ $2^{14} \cdot 3 \cdot 7$ $C_6$ $2 \cdot 3$ ✓
344064.bv.6.A $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ $C_2^{12}.D_{42}$ $2^{14} \cdot 3 \cdot 7$ $S_3$ $2 \cdot 3$
344064.bw.6.A $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ $C_2^{12}.(S_3\times C_{14})$ $2^{14} \cdot 3 \cdot 7$ $S_3$ $2 \cdot 3$
458752.a.8.A $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ $C_2^8.C_2\wr D_7$ $2^{16} \cdot 7$ $C_2^3$ $2^{3}$ ✓
458752.b.8.A $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ $C_2^{13}.F_8$ $2^{16} \cdot 7$ $2^{3}$ $-$
516096.h.9.a1 $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ $C_2^{12}.C_{21}:C_6$ $2^{13} \cdot 3^{2} \cdot 7$ $C_3^2$ $3^{2}$ ✓
688128.a.12.A $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ $C_2^7.C_2\wr F_7$ $2^{15} \cdot 3 \cdot 7$ $C_2\times C_6$ $2^{2} \cdot 3$ ✓
688128.a.12.B $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ $C_2^7.C_2\wr F_7$ $2^{15} \cdot 3 \cdot 7$ $2^{2} \cdot 3$ $-$
688128.b.12.A $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ $C_2^{12}.C_{28}:C_6$ $2^{15} \cdot 3 \cdot 7$ $C_2\times C_6$ $2^{2} \cdot 3$ ✓
688128.b.12.B $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ $C_2^{12}.C_{28}:C_6$ $2^{15} \cdot 3 \cdot 7$ $2^{2} \cdot 3$ $-$
688128.c.12.A $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ $C_2^7.C_2\wr F_7$ $2^{15} \cdot 3 \cdot 7$ $C_2\times C_6$ $2^{2} \cdot 3$ ✓
688128.d.12.A $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ $C_2^7.C_2\wr F_7$ $2^{15} \cdot 3 \cdot 7$ $C_2\times C_6$ $2^{2} \cdot 3$ ✓
688128.e.12.A $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ $C_2^7.C_2\wr F_7$ $2^{15} \cdot 3 \cdot 7$ $C_2\times C_6$ $2^{2} \cdot 3$ ✓
688128.f.12.A $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ $C_2^7.C_2\wr F_7$ $2^{15} \cdot 3 \cdot 7$ $C_2\times C_6$ $2^{2} \cdot 3$ ✓
688128.v.12.A $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ $C_2^2\times C_2^{12}.F_7$ $2^{15} \cdot 3 \cdot 7$ $C_2\times C_6$ $2^{2} \cdot 3$ ✓
688128.ba.12.B $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ $C_2^{12}.D_7:A_4$ $2^{15} \cdot 3 \cdot 7$ $2^{2} \cdot 3$ $-$
688128.bb.12.A $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ $C_2^{14}.D_{21}$ $2^{15} \cdot 3 \cdot 7$ $2^{2} \cdot 3$ $-$
688128.bd.12.A $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ $C_2^{12}.(C_7\times S_4)$ $2^{15} \cdot 3 \cdot 7$ $2^{2} \cdot 3$ $-$
688128.bg.12.A $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ $C_2^{14}.C_{42}$ $2^{15} \cdot 3 \cdot 7$ $A_4$ $2^{2} \cdot 3$
688128.bj.12.A $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ $C_2^{12}.C_{14}:A_4$ $2^{15} \cdot 3 \cdot 7$ $A_4$ $2^{2} \cdot 3$
688128.bm.12.A $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ $C_2^{12}.(S_3\times D_{14})$ $2^{15} \cdot 3 \cdot 7$ $D_6$ $2^{2} \cdot 3$
802816.a.14.A $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ $C_2^7.F_8\wr C_2$ $2^{14} \cdot 7^{2}$ $D_7$ $2 \cdot 7$
802816.a.14.B $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ $C_2^7.F_8\wr C_2$ $2^{14} \cdot 7^{2}$ $C_{14}$ $2 \cdot 7$ ✓
802816.a.14.D $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ $C_2^7.F_8\wr C_2$ $2^{14} \cdot 7^{2}$ $2 \cdot 7$ $-$
802816.a.14.E $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ $C_2^7.F_8\wr C_2$ $2^{14} \cdot 7^{2}$ $2 \cdot 7$ $-$
802816.b.14.A $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ ✓ ✓ $C_2^{12}.(C_7\times D_{14})$ $2^{14} \cdot 7^{2}$ $D_7$ $2 \cdot 7$
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