Subgroups — C₇×#4937 #13055971

Order 1344.

276 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄²×C₇	C₂	1	1	yes	maximal, characteristic
2	C₇×C₃⋊#95	C₂	1	6	yes	maximal
3	C₇×#383	—	3	1	no	maximal, Hall
4	C₂²×C₃×C₄×C₇	C₂²	1	3	yes	—
5	C₂²×C₇×Dic₃	C₂²	1	4	yes	—
6	C₃×C₄²×C₇	C₄	1	4	yes	complemented
7	C₂×C₄²×C₇	D₃	1	1	yes	characteristic
8	C₇×#95	—	3	6	no	—
9	#4937	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
11	C₂×C₃×C₄×C₇	—	2	6	no	—
12	C₂×C₃×C₄×C₇	C₂×C₄	1	6	yes	—
13	C₂×C₇×Dic₃	—	2	12	no	—
14	C₂²×C₄×C₇	—	3	4	no	—
15	C₂²×C₄×C₇	C₂×D₃	1	3	yes	—
16	C₄²×C₇	Dic₃	1	4	yes	complemented
17	C₂×C₃×C₄²	C₂×C₇	1	1	yes	characteristic
18	C₃⋊#95	C₂×C₇	1	6	yes	—
19	C₂²×C₃×C₇	C₂²×C₄	1	1	yes	characteristic
20	C₂²×C₃×C₇	#41	1	6	yes	—
21	C₃×C₄×C₇	—	2	6	no	—
22	C₇×Dic₃	—	4	4	no	—
23	#383	—	3	1	no	Sylow
24	C₂³×C₇	C₂²×D₃	1	1	yes	characteristic
25	C₂×C₄×C₇	—	2	6	no	—
26	C₂×C₄×C₇	—	6	12	no	—
27	C₂×C₄×C₇	C₂×Dic₃	1	6	yes	—
28	C₂²×C₃×C₄	C₂²×C₇	1	3	yes	—
29	C₂²×Dic₃	C₂²×C₇	1	4	yes	—
30	C₃×C₄²	C₄×C₇	1	4	yes	complemented
31	C₂×C₃×C₇	#117	1	3	yes	—
32	C₂×C₃×C₇	#126	1	4	yes	—
33	C₂×C₄²	D₃×C₇	1	1	yes	characteristic
34	#95	—	3	6	no	—
35	C₂²×C₇	#235	1	6	yes	—
36	C₂²×C₇	C₂²×Dic₃	1	1	yes	characteristic
37	C₄×C₇	—	2	6	no	—
38	C₄×C₇	—	12	4	no	—
39	C₂³×C₃	C₂³×C₇	1	1	yes	characteristic
40	C₂×C₃×C₄	—	2	6	no	—
41	C₂×C₃×C₄	C₂×C₄×C₇	1	6	yes	—
42	C₂×Dic₃	—	2	12	no	—
43	C₃×C₇	#383	1	1	yes	characteristic, complemented, Hall
44	C₂²×C₄	—	3	4	no	—
45	C₂²×C₄	C₂×D₃×C₇	1	3	yes	—
46	C₄²	C₇×Dic₃	1	4	yes	complemented
47	C₂×C₇	#876	1	4	yes	—
48	C₂×C₇	#926	1	3	yes	—
49	C₂²×C₃	C₂²×C₄×C₇	1	1	yes	characteristic
50	C₂²×C₃	C₇×#41	1	6	yes	—
51	C₃×C₄	—	2	6	no	—
52	Dic₃	—	4	4	no	—
53	C₂³	C₂²×D₃×C₇	1	1	yes	characteristic
54	C₂×C₄	—	2	6	no	—
55	C₂×C₄	—	6	12	no	—
56	C₂×C₄	C₂×C₇×Dic₃	1	6	yes	—
57	C₇	#4937	1	1	yes	characteristic, direct product factor, Sylow
58	C₂×C₃	C₇×#117	1	3	yes	—
59	C₂×C₃	C₇×#126	1	4	yes	—
60	C₂²	C₇×#235	1	6	yes	—
61	C₂²	C₂²×C₇×Dic₃	1	1	yes	characteristic
62	C₄	—	2	6	no	—
63	C₄	—	12	4	no	—
64	C₃	C₇×#383	1	1	yes	characteristic, complemented, Sylow
65	C₂	C₇×#876	1	4	yes	—
66	C₂	C₇×#926	1	3	yes	—

	subgroup	G/H
center	C₂³×C₇	C₂²×D₃
commutator	C₂²×C₃	C₂²×C₄×C₇
Frattini	C₂³	C₂²×D₃×C₇
Fitting	C₂×C₃×C₄²×C₇	C₂
socle, prime radical	C₂³×C₃×C₇	C₂³
cosocle	C₂³×C₃	C₂³×C₇
hypercenter	C₂×C₄²×C₇	D₃
hypocenter	C₃	C₇×#383
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₄²×C₇

Complements

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

N	H ≅ G/N	type
6. C₃×C₄²×C₇	C₄	semidirect
9. #4937	C₇	direct (N × H)
16. C₄²×C₇	Dic₃	semidirect
30. C₃×C₄²	C₄×C₇	semidirect
43. C₃×C₇	#383	semidirect
46. C₄²	C₇×Dic₃	semidirect
57. C₇	#4937	direct (N × H)
64. C₃	C₇×#383	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄²×C₇	2
C₇×C₃⋊#95	2
C₇×#383	3
#4937	7

Subgroups — C7×#4937 #13055971

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#4937 #13055971