Subgroups — C₇×#4935 #13055969

Order 1344.

372 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	C₂×C₇×C₄⋊Dic₃	C₂	1	6	yes	maximal
3	C₇×#384	—	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	C₇×C₄⋊Dic₃	—	2	12	no	—
8	C₂×C₇×C₄⋊C₄	—	3	6	no	—
9	C₂×C₄²×C₇	D₃	1	1	yes	characteristic
10	#4935	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
12	C₂×C₃×C₄×C₇	C₂×C₄	1	6	yes	—
13	C₂×C₃×C₄×C₇	D₄	1	6	yes	—
14	C₂×C₃×C₄×C₇	Q₈	1	6	yes	—
15	C₂×C₇×Dic₃	—	2	12	no	—
16	C₂²×C₄×C₇	—	3	4	no	—
17	C₂²×C₄×C₇	C₂×D₃	1	3	yes	—
18	C₇×C₄⋊C₄	—	6	12	no	—
19	C₄²×C₇	Dic₃	1	4	yes	complemented
20	C₂×C₃×C₄²	C₂×C₇	1	1	yes	characteristic
21	C₂×C₄⋊Dic₃	C₂×C₇	1	6	yes	—
22	C₂²×C₃×C₇	C₂²×C₄	1	1	yes	characteristic
23	C₂²×C₃×C₇	C₂×D₄	1	3	yes	—
24	C₂²×C₃×C₇	C₂×Q₈	1	3	yes	—
25	C₃×C₄×C₇	C₄⋊C₄	1	12	yes	complemented
26	C₇×Dic₃	—	4	4	no	—
27	#384	—	3	1	no	Sylow
28	C₂³×C₇	C₂²×D₃	1	1	yes	characteristic
29	C₂×C₄×C₇	—	6	12	no	—
30	C₂×C₄×C₇	Dic₆	1	6	yes	—
31	C₂×C₄×C₇	D₁₂	1	6	yes	—
32	C₂×C₄×C₇	C₂×Dic₃	1	6	yes	—
33	C₂²×C₃×C₄	C₂²×C₇	1	3	yes	—
34	C₂²×Dic₃	C₂²×C₇	1	4	yes	—
35	C₃×C₄²	C₄×C₇	1	4	yes	complemented
36	C₄⋊Dic₃	—	2	12	no	—
37	C₂×C₃×C₇	C₂×C₄⋊C₄	1	3	yes	—
38	C₂×C₃×C₇	#127	1	1	yes	characteristic
39	C₂×C₃×C₇	C₄⋊Q₈	1	3	yes	—
40	C₂×C₄⋊C₄	—	3	6	no	—
41	C₂×C₄²	D₃×C₇	1	1	yes	characteristic
42	C₂²×C₇	C₂×Dic₆	1	3	yes	—
43	C₂²×C₇	C₂×D₁₂	1	3	yes	—
44	C₂²×C₇	C₂²×Dic₃	1	1	yes	characteristic
45	C₄×C₇	—	12	4	no	—
46	C₄×C₇	C₄⋊Dic₃	1	12	yes	complemented
47	C₂³×C₃	C₂³×C₇	1	1	yes	characteristic
48	C₂×C₃×C₄	C₂×C₄×C₇	1	6	yes	—
49	C₂×C₃×C₄	C₇×D₄	1	6	yes	—
50	C₂×C₃×C₄	C₇×Q₈	1	6	yes	—
51	C₂×Dic₃	—	2	12	no	—
52	C₃×C₇	#384	1	1	yes	characteristic, complemented, Hall
53	C₂²×C₄	—	3	4	no	—
54	C₂²×C₄	C₂×D₃×C₇	1	3	yes	—
55	C₄⋊C₄	—	6	12	no	—
56	C₄²	C₇×Dic₃	1	4	yes	complemented
57	C₂×C₇	#869	1	3	yes	—
58	C₂×C₇	#874	1	1	yes	characteristic
59	C₂×C₇	C₂×C₄⋊Dic₃	1	3	yes	—
60	C₂²×C₃	C₂²×C₄×C₇	1	1	yes	characteristic
61	C₂²×C₃	C₂×C₇×D₄	1	3	yes	—
62	C₂²×C₃	C₂×C₇×Q₈	1	3	yes	—
63	C₃×C₄	C₇×C₄⋊C₄	1	12	yes	complemented
64	Dic₃	—	4	4	no	—
65	C₂³	C₂²×D₃×C₇	1	1	yes	characteristic
66	C₂×C₄	—	6	12	no	—
67	C₂×C₄	C₇×Dic₆	1	6	yes	—
68	C₂×C₄	C₇×D₁₂	1	6	yes	—
69	C₂×C₄	C₂×C₇×Dic₃	1	6	yes	—
70	C₇	#4935	1	1	yes	characteristic, direct product factor, Sylow
71	C₂×C₃	C₂×C₇×C₄⋊C₄	1	3	yes	—
72	C₂×C₃	C₇×#127	1	1	yes	characteristic
73	C₂×C₃	C₇×C₄⋊Q₈	1	3	yes	—
74	C₂²	C₂×C₇×Dic₆	1	3	yes	—
75	C₂²	C₂×C₇×D₁₂	1	3	yes	—
76	C₂²	C₂²×C₇×Dic₃	1	1	yes	characteristic
77	C₄	—	12	4	no	—
78	C₄	C₇×C₄⋊Dic₃	1	12	yes	complemented
79	C₃	C₇×#384	1	1	yes	characteristic, complemented, Sylow
80	C₂	C₇×#869	1	3	yes	—
81	C₂	C₇×#874	1	1	yes	characteristic
82	C₂	C₂×C₇×C₄⋊Dic₃	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×#384
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
10. #4935	C₇	direct (N × H)
19. C₄²×C₇	Dic₃	semidirect
25. C₃×C₄×C₇	C₄⋊C₄	semidirect
35. C₃×C₄²	C₄×C₇	semidirect
46. C₄×C₇	C₄⋊Dic₃	semidirect
52. C₃×C₇	#384	semidirect
56. C₄²	C₇×Dic₃	semidirect
63. C₃×C₄	C₇×C₄⋊C₄	semidirect
70. C₇	#4935	direct (N × H)
78. C₄	C₇×C₄⋊Dic₃	semidirect
79. C₃	C₇×#384	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
C₂×C₇×C₄⋊Dic₃	2
C₇×#384	3
#4935	7

Subgroups — C7×#4935 #13055969

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#4935 #13055969