Subgroups — AGL(1,𝔽₇)×C₁₂₁ #19099604

Order 5082.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	ΓL(1,𝔽₈)×C₁₂₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₇×C₁₂₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₂₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₂₁	—	7	1	no	maximal, Hall
5	C₁₁×AGL(1,𝔽₇)	C₁₁	1	1	yes	maximal, characteristic
6	C₃×C₁₂₁	—	7	1	no	Hall
7	C₂×C₁₂₁	—	7	1	no	Hall
8	C₁₁×ΓL(1,𝔽₈)	C₂×C₁₁	1	1	yes	characteristic
9	C₁₁×D₇	C₃×C₁₁	1	1	yes	characteristic
10	C₁₂₁	AGL(1,𝔽₇)	1	1	yes	characteristic, direct product factor, Sylow
11	C₇×C₁₁	C₂×C₃×C₁₁	1	1	yes	characteristic
12	C₂×C₃×C₁₁	—	7	1	no	—
13	AGL(1,𝔽₇)	C₁₂₁	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₁₁	—	7	1	no	—
15	C₂×C₁₁	—	7	1	no	—
16	ΓL(1,𝔽₈)	C₂×C₁₂₁	1	1	yes	characteristic, complemented, Hall
17	D₇	C₃×C₁₂₁	1	1	yes	characteristic, complemented, Hall
18	C₁₁	C₁₁×AGL(1,𝔽₇)	1	1	yes	characteristic
19	C₇	C₂×C₃×C₁₂₁	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃	—	7	1	no	Hall
21	C₃	—	7	1	no	Sylow
22	C₂	—	7	1	no	Sylow

Splittings G = N ⋊ H with N normal; H ≅ G/N.