Subgroups — C₇×#4626 #13051535

Order 1344.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#127⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₇×#353	—	3	1	no	maximal, Hall
3	C₇×SL(2,ℤ/4)	—	4	1	no	maximal
4	C₇×C₄²⋊C₃	C₄	1	1	yes	characteristic, complemented
5	C₇×#127	D₃	1	1	yes	characteristic
6	C₇×#99	—	3	1	no	—
7	C₇×#99	—	3	1	no	—
8	#4626	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₇×A₄	—	4	1	no	—
10	C₂×C₇×D₄	—	3	1	no	—
11	C₂×C₇×D₄	—	3	1	no	—
12	C₇×C₂²⋊C₄	—	6	1	no	—
13	C₇×C₂²⋊C₄	—	6	1	no	—
14	C₄²×C₇	Dic₃	1	1	yes	characteristic, complemented
15	#127⋊C₃	C₂×C₇	1	1	yes	characteristic
16	C₇×A₄	—	4	1	no	—
17	C₇×Dic₃	—	16	1	no	—
18	#353	—	3	1	no	Sylow
19	C₂³×C₇	—	3	1	no	—
20	C₂³×C₇	S₄	1	1	yes	characteristic
21	C₇×D₄	—	12	1	no	—
22	C₇×D₄	—	12	1	no	—
23	C₂×C₄×C₇	—	3	1	no	—
24	C₂×C₄×C₇	—	12	1	no	—
25	C₂×C₄×C₇	—	12	1	no	—
26	SL(2,ℤ/4)	—	4	1	no	—
27	C₄²⋊C₃	C₄×C₇	1	1	yes	characteristic, complemented
28	C₂×C₃×C₇	—	16	1	no	—
29	#127	D₃×C₇	1	1	yes	characteristic
30	#99	—	3	1	no	—
31	#99	—	3	1	no	—
32	C₂²×C₇	—	6	1	no	—
33	C₂²×C₇	—	6	1	no	—
34	C₂²×C₇	—	12	1	no	—
35	C₂²×C₇	SL(2,ℤ/4)	1	1	yes	characteristic
36	C₄×C₇	—	6	1	no	—
37	C₄×C₇	—	24	1	no	—
38	C₄×C₇	—	24	1	no	—
39	C₂×A₄	—	4	1	no	—
40	C₃×C₇	—	16	1	no	Hall
41	C₂×D₄	—	3	1	no	—
42	C₂×D₄	—	3	1	no	—
43	C₂²⋊C₄	—	6	1	no	—
44	C₂²⋊C₄	—	6	1	no	—
45	C₄²	C₇×Dic₃	1	1	yes	characteristic, complemented
46	C₂×C₇	—	3	1	no	—
47	C₂×C₇	—	4	1	no	—
48	C₂×C₇	—	12	1	no	—
49	A₄	—	4	1	no	—
50	Dic₃	—	16	1	no	—
51	C₂³	—	3	1	no	—
52	C₂³	C₇×S₄	1	1	yes	characteristic
53	D₄	—	12	1	no	—
54	D₄	—	12	1	no	—
55	C₂×C₄	—	3	1	no	—
56	C₂×C₄	—	12	1	no	—
57	C₂×C₄	—	12	1	no	—
58	C₇	#4626	1	1	yes	characteristic, direct product factor, Sylow
59	C₂×C₃	—	16	1	no	—
60	C₂²	—	6	1	no	—
61	C₂²	—	6	1	no	—
62	C₂²	—	12	1	no	—
63	C₂²	C₇×SL(2,ℤ/4)	1	1	yes	characteristic
64	C₄	—	6	1	no	—
65	C₄	—	24	1	no	—
66	C₄	—	24	1	no	—
67	C₃	—	16	1	no	Sylow
68	C₂	—	3	1	no	—
69	C₂	—	4	1	no	—
70	C₂	—	12	1	no	—

	subgroup	G/H
center, hypercenter	C₇	#4626
commutator, hypocenter	C₄²⋊C₃	C₄×C₇
Frattini	C₂³	C₇×S₄
Fitting	C₇×#127	D₃
socle	C₂²×C₇	SL(2,ℤ/4)
prime radical	C₇×#127⋊C₃	C₂
cosocle	#127⋊C₃	C₂×C₇
LCS	G ▷ C₄²⋊C₃
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
4. C₇×C₄²⋊C₃	C₄	semidirect
8. #4626	C₇	direct (N × H)
14. C₄²×C₇	Dic₃	semidirect
27. C₄²⋊C₃	C₄×C₇	semidirect
45. C₄²	C₇×Dic₃	semidirect
58. C₇	#4626	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#127⋊C₃	2
C₇×#353	3
C₇×SL(2,ℤ/4)	4
#4626	7

Subgroups — C7×#4626 #13051535

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#4626 #13051535