Subgroups — C₂²×#20296697 #43246789

Order 28308.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20296697	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₇×C₃₃₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#20296697	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₇×C₃₃₇	C₂×C₃	1	3	yes	complemented
5	C₂²×C₃₃₇⋊C₃	—	7	1	no	maximal, Hall
6	C₇×C₃₃₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃₃₇⋊C₃	—	7	3	no	—
8	C₂²×C₃₃₇	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
9	C₃₃₇⋊C₃	—	7	1	no	Hall
10	C₂×C₃₃₇	C₂×ΓL(1,𝔽₈)	1	3	yes	complemented
11	C₃₃₇	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
12	C₂²×ΓL(1,𝔽₈)	—	337	1	no	maximal, Hall
13	C₂×ΓL(1,𝔽₈)	—	337	3	no	—
14	C₂²×C₇	C₃₃₇⋊C₃	1	1	yes	characteristic, complemented, Hall
15	ΓL(1,𝔽₈)	—	337	1	no	Hall
16	C₂×C₇	C₂×C₃₃₇⋊C₃	1	3	yes	complemented
17	C₂²×C₃	—	2359	1	no	Hall
18	C₇	C₂²×C₃₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃	—	2359	3	no	—
20	C₂²	#20296697	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	—	2359	1	no	Sylow
22	C₂	C₂×#20296697	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²	#20296697
commutator, cosocle, hypocenter	C₇×C₃₃₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂²×C₇×C₃₃₇	C₃
LCS	G ▷ C₇×C₃₃₇
UCS	C₁ ◁ C₂²

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

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.