Subgroups — C₂×#26042759 #37551649

Order 23268.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042759	C₂	1	2	yes	maximal, direct product factor
2	C₂×#19154113	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×D₂₇₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	#19154113	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇×C₂₇₇	C₂×C₃	1	1	yes	characteristic, complemented
6	C₇×D₂₇₇	C₂×C₃	1	2	yes	complemented
7	C₂×D₂₇₇⋊C₃	—	7	1	no	maximal, Hall
8	C₇×C₂₇₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₂₇₇⋊C₃	—	7	1	no	—
10	D₂₇₇⋊C₃	—	7	2	no	—
11	C₂×D₂₇₇	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
12	C₂₇₇⋊C₃	—	7	1	no	Hall
13	C₂×C₂₇₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
14	D₂₇₇	C₂×ΓL(1,𝔽₈)	1	2	yes	complemented
15	C₂₇₇	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
16	C₂²×ΓL(1,𝔽₈)	—	277	1	no	maximal, Hall
17	C₂×ΓL(1,𝔽₈)	—	277	2	no	—
18	C₂×ΓL(1,𝔽₈)	—	554	1	no	—
19	C₂²×C₇	—	277	1	no	Hall
20	ΓL(1,𝔽₈)	—	554	1	no	Hall
21	C₂×C₇	—	277	2	no	—
22	C₂×C₇	D₂₇₇⋊C₃	1	1	yes	characteristic, complemented
23	C₂²×C₃	—	1939	1	no	Hall
24	C₇	C₂×D₂₇₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃	—	3878	1	no	—
26	C₂×C₃	—	1939	2	no	—
27	C₂²	—	277	1	no	Sylow
28	C₃	—	3878	1	no	Sylow
29	C₂	—	277	2	no	—
30	C₂	#26042759	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#26042759
commutator, cosocle, hypocenter	C₇×C₂₇₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₂₇₇	C₂×C₃
LCS	G ▷ C₇×C₂₇₇
UCS	C₁ ◁ C₂

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.