Subgroups — C₇×#4179 #11765670

Order 1134.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#732	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₃⋊D₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₇×(C₃⋊D₃)⋊C₃	—	3	1	no	maximal
4	C₇×H(3,𝔽₃)	—	2	1	no	—
5	C₇×H(3,𝔽₃)	D₃	1	1	yes	characteristic
6	C₃×C₇×C₉	C₂×C₃	1	1	yes	characteristic, complemented
7	#4179	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₇×C₃⋊D₃	—	3	1	no	—
9	C₃×D₃×C₇	—	9	1	no	—
10	C₇×D₉	—	9	1	no	—
11	#732	C₂×C₇	1	1	yes	characteristic, complemented, Sylow
12	C₃²×C₇	—	3	1	no	—
13	C₃²×C₇	—	6	1	no	—
14	C₃²×C₇	C₃×D₃	1	1	yes	characteristic
15	C₇×C₉	—	3	1	no	—
16	C₃⋊D₉	C₃×C₇	1	1	yes	characteristic, complemented
17	(C₃⋊D₃)⋊C₃	—	3	1	no	—
18	C₂×C₃×C₇	—	27	1	no	—
19	D₃×C₇	—	9	1	no	—
20	D₃×C₇	—	27	1	no	—
21	H(3,𝔽₃)	—	2	1	no	—
22	H(3,𝔽₃)	D₃×C₇	1	1	yes	characteristic
23	C₃×C₉	C₂×C₃×C₇	1	1	yes	characteristic, complemented
24	C₃×C₇	—	3	1	no	—
25	C₃×C₇	—	9	1	no	—
26	C₃×C₇	—	18	1	no	—
27	C₃×C₇	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
28	C₃⋊D₃	—	3	1	no	—
29	C₃×D₃	—	9	1	no	—
30	D₉	—	9	1	no	—
31	C₂×C₇	—	27	1	no	Hall
32	C₃²	—	3	1	no	—
33	C₃²	—	6	1	no	—
34	C₃²	C₃×D₃×C₇	1	1	yes	characteristic
35	C₉	—	3	1	no	—
36	C₇	#4179	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×C₃	—	27	1	no	—
38	D₃	—	9	1	no	—
39	D₃	—	27	1	no	—
40	C₃	—	3	1	no	—
41	C₃	—	9	1	no	—
42	C₃	—	18	1	no	—
43	C₃	C₇×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
44	C₂	—	27	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	#4179
commutator, cosocle, hypocenter	C₃×C₉	C₂×C₃×C₇
Frattini	C₃²	C₃×D₃×C₇
Fitting	C₇×#732	C₂
socle	C₃×C₇	(C₃⋊D₃)⋊C₃
LCS	G ▷ C₃×C₉
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.