Subgroups — C₇×#4513 #13051295

Order 1344.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₇×#819	C₂	1	1	yes	maximal, characteristic
3	C₇×#817	C₂	1	1	yes	maximal, characteristic
4	C₇×#365	—	3	1	no	maximal, Hall
5	C₂×C₃×C₇×C₈	C₂²	1	1	yes	characteristic
6	C₇×C₄⋊Dic₃	—	2	1	no	—
7	C₇×#208	—	2	1	no	—
8	C₃×C₇×C₁₆	C₄	1	2	yes	complemented
9	C₇×M₃₂	D₃	1	1	yes	characteristic
10	C₇×#108	—	3	1	no	—
11	C₇×#106	—	3	1	no	—
12	#4513	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₄×C₇	D₄	1	1	yes	characteristic
14	C₂×C₇×Dic₃	—	4	1	no	—
15	C₃×C₇×C₈	C₂×C₄	1	1	yes	characteristic
16	C₃×C₇×C₈	Q₈	1	1	yes	characteristic
17	C₇×C₃⋊C₈	—	4	1	no	—
18	C₇×M₁₆	—	6	1	no	—
19	C₂×C₇×C₈	C₂×D₃	1	1	yes	characteristic
20	C₇×C₄⋊C₄	—	6	1	no	—
21	C₇×C₁₆	Dic₃	1	2	yes	complemented
22	C₃×M₃₂	C₂×C₇	1	1	yes	characteristic
23	#819	C₂×C₇	1	1	yes	characteristic
24	#817	C₂×C₇	1	1	yes	characteristic
25	C₂²×C₃×C₇	SD₁₆	1	1	yes	characteristic
26	C₃×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
27	C₃×C₄×C₇	SD₁₆	1	1	yes	characteristic
28	C₇×Dic₃	—	8	1	no	—
29	#365	—	3	1	no	Sylow
30	C₂×C₄×C₇	—	12	1	no	—
31	C₂×C₄×C₇	D₁₂	1	1	yes	characteristic
32	C₇×C₈	—	12	1	no	—
33	C₇×C₈	Dic₆	1	1	yes	characteristic
34	C₇×C₈	C₂×Dic₃	1	1	yes	characteristic
35	C₂×C₃×C₈	C₂²×C₇	1	1	yes	characteristic
36	C₄⋊Dic₃	—	2	1	no	—
37	#208	—	2	1	no	—
38	C₃×C₁₆	C₄×C₇	1	2	yes	complemented
39	C₂×C₃×C₇	—	2	1	no	—
40	C₂×C₃×C₇	#106	1	1	yes	characteristic
41	M₃₂	D₃×C₇	1	1	yes	characteristic
42	#108	—	3	1	no	—
43	#106	—	3	1	no	—
44	C₂²×C₇	#204	1	1	yes	characteristic
45	C₄×C₇	—	24	1	no	—
46	C₄×C₇	#204	1	1	yes	characteristic
47	C₄×C₇	C₄⋊Dic₃	1	1	yes	characteristic
48	C₂×C₃×C₄	C₇×D₄	1	1	yes	characteristic
49	C₂×Dic₃	—	4	1	no	—
50	C₃×C₈	C₂×C₄×C₇	1	1	yes	characteristic
51	C₃×C₈	C₇×Q₈	1	1	yes	characteristic
52	C₃⋊C₈	—	4	1	no	—
53	C₃×C₇	#365	1	1	yes	characteristic, complemented, Hall
54	M₁₆	—	6	1	no	—
55	C₂×C₈	C₂×D₃×C₇	1	1	yes	characteristic
56	C₄⋊C₄	—	6	1	no	—
57	C₁₆	C₇×Dic₃	1	2	yes	complemented
58	C₂×C₇	—	2	1	no	—
59	C₂×C₇	#817	1	1	yes	characteristic
60	C₂²×C₃	C₇×SD₁₆	1	1	yes	characteristic
61	C₃×C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
62	C₃×C₄	C₇×SD₁₆	1	1	yes	characteristic
63	Dic₃	—	8	1	no	—
64	C₂×C₄	—	12	1	no	—
65	C₂×C₄	C₇×D₁₂	1	1	yes	characteristic
66	C₈	—	12	1	no	—
67	C₈	C₇×Dic₆	1	1	yes	characteristic
68	C₈	C₂×C₇×Dic₃	1	1	yes	characteristic
69	C₇	#4513	1	1	yes	characteristic, direct product factor, Sylow
70	C₂×C₃	—	2	1	no	—
71	C₂×C₃	C₇×#106	1	1	yes	characteristic
72	C₂²	C₇×#204	1	1	yes	characteristic
73	C₄	—	24	1	no	—
74	C₄	C₇×#204	1	1	yes	characteristic
75	C₄	C₇×C₄⋊Dic₃	1	1	yes	characteristic
76	C₃	C₇×#365	1	1	yes	characteristic, complemented, Sylow
77	C₂	—	2	1	no	—
78	C₂	C₇×#817	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₇	#817
commutator	C₃×C₈	C₂×C₄×C₇
Frattini	C₂×C₈	C₂×D₃×C₇
Fitting	C₃×C₇×M₃₂	C₂
socle	C₂×C₃×C₇	#106
prime radical	C₂²×C₃×C₇	SD₁₆
cosocle	C₂×C₃×C₈	C₂²×C₇
hypercenter	C₇×M₃₂	D₃
hypocenter	C₃	C₇×#365
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₇ ◁ C₂×C₄×C₇ ◁ C₂×C₇×C₈ ◁ C₇×M₃₂

Complements

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

N	H ≅ G/N	type
8. C₃×C₇×C₁₆	C₄	semidirect
12. #4513	C₇	direct (N × H)
21. C₇×C₁₆	Dic₃	semidirect
38. C₃×C₁₆	C₄×C₇	semidirect
53. C₃×C₇	#365	semidirect
57. C₁₆	C₇×Dic₃	semidirect
69. C₇	#4513	direct (N × H)
76. C₃	C₇×#365	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₇×M₃₂	2
C₇×#819	2
C₇×#817	2
C₇×#365	3
#4513	7

Subgroups — C7×#4513 #13051295

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#4513 #13051295