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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 (37 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
896.5502.896.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $C_2^4:F_8$ $2^{7} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$
1792.1083476.896.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^6:C_{28}$ $2^{8} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$ ✓
1792.1083486.896.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^5:F_8$ $2^{8} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$ ✓
3584.bd.896._.A $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^8.C_{14}$ $2^{9} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$
7168.w.896._.B $C_2^3$ $2^{3}$ ✓ ✓ ✓ $C_2^9.C_{14}$ $2^{10} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$ ✓
14336.l.896.A $C_2^4$ $2^{4}$ ✓ ✓ ✓ $C_2^8.F_8$ $2^{11} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$
14336.m.896._.B $C_2^4$ $2^{4}$ ✓ ✓ ✓ $C_2^{10}.C_{14}$ $2^{11} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$
14336.n.896._.A $C_2^4$ $2^{4}$ ✓ ✓ ✓ $C_2^9.C_{28}$ $2^{11} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$
28672.f.896._.C $C_2^5$ $2^{5}$ ✓ ✓ ✓ $C_2^6.(D_4\times F_8)$ $2^{12} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$
57344.c.896.B $C_2^6$ $2^{6}$ ✓ ✓ $C_2^{12}.C_{14}$ $2^{13} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$
114688.a.896.B $C_2^7$ $2^{7}$ ✓ ✓ $C_2^{12}.C_{28}$ $2^{14} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$
114688.b.896.A $C_2^7$ $2^{7}$ ✓ ✓ $C_2\times C_2^{12}.C_{14}$ $2^{14} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$
229376.a.896.B $C_2^8$ $2^{8}$ ✓ ✓ $\ASigmaL(1,16384)$ $2^{15} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$
94058496.a.896._.A $C_3^8:C_2^4$ $2^{4} \cdot 3^{8}$ ✓ ✓ $C_3^8:(C_2^8.F_8)$ $2^{11} \cdot 3^{8} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$
4285540224.a.896.a1.a1 $C_3^{14}$ $3^{14}$ $3$ ✓ ✓ ✓ $C_3^{14}.C_2^6.C_{14}$ $2^{7} \cdot 3^{14} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$ ✓
5600000000.a.896._.A $C_5^4.D_5^4$ $2^{4} \cdot 5^{8}$ ✓ ✓ $C_5^4.D_5^4.C_2^4:F_8$ $2^{11} \cdot 5^{8} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$
5600000000.b.896._.A $C_5^4.D_5^4$ $2^{4} \cdot 5^{8}$ ✓ ✓ $C_5^4.D_5^4.C_2^4:F_8$ $2^{11} \cdot 5^{8} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$
8571080448.a.896._.A $C_3^{14}.C_2$ $2 \cdot 3^{14}$ ✓ ✓ $C_3^{14}.C_2^6.C_{28}$ $2^{8} \cdot 3^{14} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$
8571080448.b.896._.A $C_3^{14}.C_2$ $2 \cdot 3^{14}$ ✓ ✓ $C_3^{14}.C_2^6.C_{14}.C_2$ $2^{8} \cdot 3^{14} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$
11200000000.a.896._.A $C_5^7.(C_2^3\times F_5)$ $2^{5} \cdot 5^{8}$ ✓ ✓ $C_5^4.D_5^4.C_2^5:F_8$ $2^{12} \cdot 5^{8} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$
17142160896.a.896._.A $C_3^{13}.D_6$ $2^{2} \cdot 3^{14}$ ✓ ✓ $C_3^{14}.C_2^6.C_{28}.C_2$ $2^{9} \cdot 3^{14} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$
34284321792.a.896._.B $C_3^{14}.C_2^3$ $2^{3} \cdot 3^{14}$ ✓ ✓ $C_3^{14}.C_2^6.F_8.C_2$ $2^{10} \cdot 3^{14} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$
68568643584.a.896._.A $C_3^{14}.C_2^4$ $2^{4} \cdot 3^{14}$ ✓ ✓ $C_3^{14}.C_2^6.F_8.C_4$ $2^{11} \cdot 3^{14} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$
68568643584.b.896._.C $C_3^{14}.C_2^4$ $2^{4} \cdot 3^{14}$ ✓ ✓ $C_3^{14}.C_2^6.F_8.C_2^2$ $2^{11} \cdot 3^{14} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$
89600000000.a.896._.C $C_5^8.C_2^4.C_2^4$ $2^{8} \cdot 5^{8}$ ✓ ✓ $D_5^4.D_5\wr C_2^2.C_2^2.F_8$ $2^{15} \cdot 5^{8} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$
137137287168.a.896._.C $C_3^{14}.C_2^5$ $2^{5} \cdot 3^{14}$ ✓ ✓ $C_3^{14}.C_2^6.F_8.D_4$ $2^{12} \cdot 3^{14} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$
274274574336.a.896._.A $C_3^{14}.C_2^6$ $2^{6} \cdot 3^{14}$ ✓ $C_3^{14}.C_2^6.C_2^6.C_{14}$ $2^{13} \cdot 3^{14} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$
274274574336.a.896._.B $C_3^{14}.C_2^6$ $2^{6} \cdot 3^{14}$ ✓ $C_3^{14}.C_2^6.C_2^6.C_{14}$ $2^{13} \cdot 3^{14} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$
548549148672.a.896._.A $C_3^{14}.C_2^6.C_2$ $2^{7} \cdot 3^{14}$ ✓ $C_3^{14}.C_2^6.C_2^6.C_{28}$ $2^{14} \cdot 3^{14} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$
548549148672.a.896._.B $C_3^{14}.C_2^6.C_2$ $2^{7} \cdot 3^{14}$ ✓ $C_3^{14}.C_2^6.C_2^6.C_{28}$ $2^{14} \cdot 3^{14} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$
548549148672.b.896._.C $C_3^{14}.C_2^6.C_2$ $2^{7} \cdot 3^{14}$ ✓ $C_3^{14}.C_2^6.C_2^6.C_{14}.C_2$ $2^{14} \cdot 3^{14} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$
548549148672.b.896._.D $C_3^{14}.C_2^6.C_2$ $2^{7} \cdot 3^{14}$ ✓ $C_3^{14}.C_2^6.C_2^6.C_{14}.C_2$ $2^{14} \cdot 3^{14} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$
1097098297344.a.896._.C $C_3^{13}.D_6.C_2^6$ $2^{8} \cdot 3^{14}$ ✓ $C_3^{14}.C_2^4.C_2^6.F_8.C_2^2$ $2^{15} \cdot 3^{14} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$
1097098297344.a.896._.D $C_3^{14}.C_2^6.C_2^2$ $2^{8} \cdot 3^{14}$ ✓ $C_3^{14}.C_2^4.C_2^6.F_8.C_2^2$ $2^{15} \cdot 3^{14} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$
1433600000000.a.896._.A $C_5^8.C_2^6.C_2^6$ $2^{12} \cdot 5^{8}$ ✓ ✓ $C_5^8.C_2^6.C_2^5.C_2^6.C_{28}$ $2^{19} \cdot 5^{8} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$
6164217593856.a.896._.A $C_2^{16}.C_3^5.S_3^3.C_2$ $2^{20} \cdot 3^{8}$ ✓ ✓ $C_2^{16}.C_3^8.C_2.C_2^6.F_8.C_2$ $2^{27} \cdot 3^{8} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$
2407897497600000000.a.896._.A $A_5.A_5.A_5.A_5.A_5.A_5.A_5.A_5.C_2^4$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_2.C_2^6.F_8.C_2$ $2^{27} \cdot 3^{8} \cdot 5^{8} \cdot 7$ $C_2^4:F_8$ $2^{7} \cdot 7$
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