Subgroups — #11759405

Order 1008.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#92696	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#625	C₂	1	1	yes	maximal, characteristic
3	C₇⋊#622	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×D₃×C₇	—	2	1	no	—
5	C₇×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
6	C₃×Dic₂₁	—	2	1	no	—
7	C₇×#67	—	6	1	no	—
8	#4248	—	6	1	no	—
9	#3775	—	7	1	no	maximal, Hall
10	C₂×C₃²×C₇	D₄	1	1	yes	characteristic
11	C₃×D₃×C₇	—	4	1	no	—
12	#1142	—	9	1	no	maximal, Hall
13	C₂²×C₃×C₇	—	6	1	no	—
14	C₂×D₃×C₇	—	2	1	no	—
15	Dic₂₁	—	2	1	no	—
16	C₃×Dic₇	—	6	1	no	—
17	C₇×Dic₃	—	6	1	no	—
18	C₇×Dic₃	—	6	1	no	—
19	#627	—	7	1	no	—
20	#625	D₇	1	1	yes	characteristic
21	#622	—	7	1	no	—
22	C₃²×C₇	SD₁₆	1	1	yes	characteristic, complemented, Hall
23	C₇×D₄	—	9	1	no	—
24	Dic₁₄	—	9	1	no	—
25	C₇⋊C₈	—	9	1	no	—
26	C₂×C₃×C₇	—	2	1	no	—
27	C₂×C₃×C₇	—	2	1	no	—
28	C₂×C₃×C₇	—	12	1	no	—
29	D₃×C₇	—	4	1	no	—
30	C₂×C₃×D₃	—	2	1	no	—
31	C₃⋊Dic₃	C₂×D₇	1	1	yes	characteristic
32	C₃×Dic₃	—	14	1	no	—
33	C₂²×C₇	—	6	1	no	—
34	C₄×C₇	—	9	1	no	—
35	Dic₇	—	6	1	no	—
36	#67	—	6	1	no	—
37	Dic₆	—	42	1	no	—
38	C₃×C₇	—	2	1	no	—
39	C₃×C₇	—	2	1	no	—
40	C₂×C₃²	C₂²⋊D₇	1	1	yes	characteristic
41	C₃×D₃	—	4	1	no	—
42	SD₁₆	—	63	1	no	Sylow
43	C₂×C₇	—	12	1	no	—
44	C₂×C₇	GO⁺(4,𝔽₂)	1	1	yes	characteristic
45	C₂²×C₃	—	6	1	no	—
46	C₂×D₃	—	2	1	no	—
47	C₃×C₄	—	42	1	no	—
48	Dic₃	—	6	1	no	—
49	Dic₃	—	6	1	no	—
50	Dic₃	—	14	1	no	—
51	C₃²	#1142	1	1	yes	characteristic, complemented, Sylow
52	Q₈	—	63	1	no	—
53	D₄	—	9	1	no	—
54	C₈	—	63	1	no	—
55	C₇	#3775	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₃	—	2	1	no	—
57	C₂×C₃	—	2	1	no	—
58	C₂×C₃	—	12	1	no	—
59	D₃	—	4	1	no	—
60	C₂²	—	6	1	no	—
61	C₄	—	9	1	no	—
62	C₄	—	42	1	no	—
63	C₃	—	2	1	no	—
64	C₃	—	2	1	no	—
65	C₂	—	12	1	no	—
66	C₂	D₃²⋊D₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃²⋊D₇
commutator, cosocle	C₇×C₃⋊Dic₃	C₂²
Fitting, socle	C₂×C₃²×C₇	D₄
prime radical	C₇×#625	C₂
hypocenter	C₃²×C₇	SD₁₆
LCS	G ▷ C₇×C₃⋊Dic₃ ▷ C₂×C₃²×C₇ ▷ C₃²×C₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. #92696	C₂	semidirect
3. C₇⋊#622	C₂	semidirect
22. C₃²×C₇	SD₁₆	semidirect
51. C₃²	#1142	semidirect
55. C₇	#3775	semidirect

Maximal subgroups

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

subgroup	index
#92696	2
C₇×#625	2
C₇⋊#622	2
#3775	7
#1142	9