Subgroups — C₂×Dic₇⋊Dic₃ #10621103

Order 672.

184 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₂₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₇×Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃×Dic₇	C₂	1	1	yes	maximal, characteristic
4	Dic₇⋊Dic₃	C₂	1	4	yes	maximal, direct product factor
5	C₂×Dic₇⋊C₄	—	3	1	no	maximal, Hall
6	C₂³×C₃×C₇	C₂²	1	1	yes	characteristic
7	C₂×Dic₂₁	—	2	2	no	—
8	C₂×Dic₂₁	C₂²	1	2	yes	—
9	C₂×C₇×Dic₃	—	2	2	no	—
10	C₂×C₇×Dic₃	C₂²	1	2	yes	—
11	C₂×C₃×Dic₇	C₄	1	4	yes	complemented
12	C₂×C₃×Dic₇	C₂²	1	2	yes	—
13	C₂²×C₄×C₇	—	3	1	no	—
14	C₂²×Dic₇	—	3	1	no	—
15	C₂²×Dic₇	D₃	1	1	yes	characteristic
16	Dic₇⋊C₄	—	3	4	no	—
17	C₂×C₄⋊Dic₃	—	7	1	no	maximal, Hall
18	C₂²×C₃×C₇	C₂×C₄	1	2	yes	—
19	C₂²×C₃×C₇	D₄	1	2	yes	—
20	C₂²×C₃×C₇	Q₈	1	2	yes	—
21	C₂²×C₃×C₇	C₂³	1	1	yes	characteristic
22	Dic₂₁	—	2	2	no	—
23	C₃×Dic₇	C₂×C₄	1	4	yes	complemented
24	C₇×Dic₃	—	2	2	no	—
25	C₂³×C₇	C₂×D₃	1	1	yes	characteristic
26	C₂×C₄×C₇	—	3	2	no	—
27	C₂×C₄×C₇	—	6	2	no	—
28	C₂×Dic₇	—	3	2	no	—
29	C₂×Dic₇	—	6	2	no	—
30	C₂×Dic₇	Dic₃	1	4	yes	complemented
31	C₂×Dic₇	C₂×D₃	1	2	yes	—
32	C₂²×C₃×C₄	—	7	1	no	—
33	C₂²×Dic₃	—	7	1	no	—
34	C₂²×Dic₃	D₇	1	1	yes	characteristic
35	C₄⋊Dic₃	—	7	4	no	—
36	C₂×C₃×C₇	C₄⋊C₄	1	4	yes	complemented
37	C₂×C₃×C₇	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₃×C₇	C₂×D₄	1	1	yes	characteristic
39	C₂×C₃×C₇	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₄⋊C₄	—	21	1	no	Sylow
41	C₂²×C₇	Dic₆	1	2	yes	—
42	C₂²×C₇	D₁₂	1	2	yes	—
43	C₂²×C₇	C₂×Dic₃	1	2	yes	—
44	C₂²×C₇	C₂²×D₃	1	1	yes	characteristic
45	C₄×C₇	—	6	2	no	—
46	Dic₇	—	6	2	no	—
47	Dic₇	C₂×Dic₃	1	4	yes	complemented
48	C₂³×C₃	C₂×D₇	1	1	yes	characteristic
49	C₂×C₃×C₄	—	7	4	no	—
50	C₂×C₃×C₄	—	7	2	no	—
51	C₂×Dic₃	—	2	2	no	—
52	C₂×Dic₃	—	7	2	no	—
53	C₂×Dic₃	—	14	2	no	—
54	C₂×Dic₃	C₂×D₇	1	2	yes	—
55	C₃×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
56	C₂²×C₄	—	3	1	no	—
57	C₂²×C₄	—	7	1	no	—
58	C₂²×C₄	—	21	1	no	—
59	C₄⋊C₄	—	21	4	no	—
60	C₂×C₇	C₄⋊Dic₃	1	4	yes	complemented
61	C₂×C₇	C₂×Dic₆	1	1	yes	characteristic
62	C₂×C₇	C₂×D₁₂	1	1	yes	characteristic
63	C₂×C₇	C₂²×Dic₃	1	1	yes	characteristic
64	C₂²×C₃	Dic₁₄	1	2	yes	—
65	C₂²×C₃	C₄×D₇	1	2	yes	—
66	C₂²×C₃	C₂²⋊D₇	1	2	yes	—
67	C₂²×C₃	C₂²×D₇	1	1	yes	characteristic
68	C₃×C₄	—	7	4	no	—
69	Dic₃	—	2	2	no	—
70	Dic₃	—	14	2	no	—
71	C₂³	D₃×D₇	1	1	yes	characteristic
72	C₂×C₄	—	3	2	no	—
73	C₂×C₄	—	6	2	no	—
74	C₂×C₄	—	7	4	no	—
75	C₂×C₄	—	7	2	no	—
76	C₂×C₄	—	21	2	no	—
77	C₂×C₄	—	42	2	no	—
78	C₇	C₂×C₄⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
79	C₂×C₃	Dic₇⋊C₄	1	4	yes	complemented
80	C₂×C₃	C₂×Dic₁₄	1	1	yes	characteristic
81	C₂×C₃	C₂×C₄×D₇	1	1	yes	characteristic
82	C₂×C₃	C₂×C₂²⋊D₇	1	1	yes	characteristic
83	C₂²	Dic₃×D₇	1	2	yes	—
84	C₂²	#4247	1	2	yes	—
85	C₂²	#4248	1	2	yes	—
86	C₂²	C₂×D₃×D₇	1	1	yes	characteristic
87	C₄	—	6	2	no	—
88	C₄	—	7	4	no	—
89	C₄	—	42	2	no	—
90	C₃	C₂×Dic₇⋊C₄	1	1	yes	characteristic, complemented, Sylow
91	C₂	Dic₇⋊Dic₃	1	4	yes	direct product factor
92	C₂	C₂×Dic₃×D₇	1	1	yes	characteristic
93	C₂	C₂×#4247	1	1	yes	characteristic
94	C₂	C₂×#4248	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³	D₃×D₇
commutator	C₂×C₃×C₇	C₂²×C₄
Frattini	C₂²	C₂×D₃×D₇
Fitting, socle, prime radical	C₂³×C₃×C₇	C₂²
cosocle	C₂²×C₃×C₇	C₂³
hypocenter	C₃×C₇	C₂×C₄⋊C₄
LCS	G ▷ C₂×C₃×C₇ ▷ C₃×C₇
UCS	C₁ ◁ C₂³

Complements

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

N	H ≅ G/N	type
4. Dic₇⋊Dic₃	C₂	direct (N × H)
11. C₂×C₃×Dic₇	C₄	semidirect
23. C₃×Dic₇	C₂×C₄	semidirect
30. C₂×Dic₇	Dic₃	semidirect
36. C₂×C₃×C₇	C₄⋊C₄	semidirect
47. Dic₇	C₂×Dic₃	semidirect
55. C₃×C₇	C₂×C₄⋊C₄	semidirect
60. C₂×C₇	C₄⋊Dic₃	semidirect
78. C₇	C₂×C₄⋊Dic₃	semidirect
79. C₂×C₃	Dic₇⋊C₄	semidirect
90. C₃	C₂×Dic₇⋊C₄	semidirect
91. C₂	Dic₇⋊Dic₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×Dic₂₁	2
C₂²×C₇×Dic₃	2
C₂²×C₃×Dic₇	2
Dic₇⋊Dic₃	2
C₂×Dic₇⋊C₄	3
C₂×C₄⋊Dic₃	7

Subgroups — C2×Dic7⋊Dic3 #10621103

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₇⋊Dic₃ #10621103