Subgroups — C₂²×#13046197 #19104016

Order 5124.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13046197	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₇×C₆₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#13046197	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₇×C₆₁	C₂×C₃	1	3	yes	complemented
5	C₂²×C₆₁⋊C₃	—	7	1	no	maximal, Hall
6	C₇×C₆₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
7	C₂×C₆₁⋊C₃	—	7	3	no	—
8	C₂²×C₆₁	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
9	C₆₁⋊C₃	—	7	1	no	Hall
10	C₂×C₆₁	C₂×ΓL(1,𝔽₈)	1	3	yes	complemented
11	C₂²×ΓL(1,𝔽₈)	—	61	1	no	maximal, Hall
12	C₆₁	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
13	C₂×ΓL(1,𝔽₈)	—	61	3	no	—
14	C₂²×C₇	C₆₁⋊C₃	1	1	yes	characteristic, complemented, Hall
15	ΓL(1,𝔽₈)	—	61	1	no	Hall
16	C₂×C₇	C₂×C₆₁⋊C₃	1	3	yes	complemented
17	C₂²×C₃	—	427	1	no	Hall
18	C₇	C₂²×C₆₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃	—	427	3	no	—
20	C₂²	#13046197	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	—	427	1	no	Sylow
22	C₂	C₂×#13046197	1	3	yes	direct product factor

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