Subgroups — C₇×#13095536 #24925939

Order 10878.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#11715912	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₇×C₃₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇²×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₃₇⋊C₃	—	7	1	no	maximal
5	#13095536	C₇	1	1	yes	maximal, characteristic, direct product factor
6	#11715912	C₂×C₇	1	1	yes	characteristic, complemented
7	C₇×C₃₇⋊C₃	—	7	1	no	—
8	C₂×C₇×C₃₇	—	7	1	no	—
9	D₇×C₃₇	C₃×C₇	1	1	yes	characteristic, complemented
10	C₇×AGL(1,𝔽₇)	—	37	1	no	maximal, Hall
11	C₇×C₃₇	—	6	1	no	—
12	C₇×C₃₇	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
13	C₇×C₃₇	C₂×C₃×C₇	1	1	yes	characteristic, complemented
14	C₂×C₃₇⋊C₃	—	7	1	no	Hall
15	C₇×ΓL(1,𝔽₈)	—	37	1	no	Hall
16	C₃₇⋊C₃	—	7	1	no	Hall
17	C₇×D₇	C₃₇⋊C₃	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃₇	—	7	1	no	Hall
19	C₇²	C₂×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃×C₇	—	259	1	no	—
21	AGL(1,𝔽₇)	—	37	1	no	—
22	C₃₇	C₇×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
23	C₃×C₇	—	259	1	no	—
24	ΓL(1,𝔽₈)	—	37	1	no	—
25	C₂×C₇	—	7	1	no	—
26	D₇	C₇×C₃₇⋊C₃	1	1	yes	characteristic, complemented
27	C₇	—	6	1	no	—
28	C₇	#13095536	1	1	yes	characteristic, direct product factor
29	C₇	C₂×C₇×C₃₇⋊C₃	1	1	yes	characteristic, complemented
30	C₂×C₃	—	259	1	no	Hall
31	C₃	—	259	1	no	Sylow
32	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	#13095536
commutator, cosocle, hypocenter	C₇×C₃₇	C₂×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₇²×C₃₇	C₂×C₃
LCS	G ▷ C₇×C₃₇
UCS	C₁ ◁ C₇

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.