Subgroups — D₃×C₇×D₄ #66719

Order 336.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₃×C₇	C₂	1	2	yes	maximal, complemented
2	C₃×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#67	C₂	1	2	yes	maximal, complemented
4	C₇×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×D₃×C₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×D₄	—	3	1	no	maximal, Hall
7	C₂²×C₃×C₇	C₂²	1	2	yes	complemented
8	C₂×D₃×C₇	—	2	4	no	—
9	C₂×D₃×C₇	C₂²	1	1	yes	characteristic
10	C₂×D₃×C₇	C₂²	1	2	yes	complemented
11	C₃×C₄×C₇	C₂²	1	1	yes	characteristic, complemented
12	C₇×Dic₃	C₂²	1	1	yes	characteristic, complemented
13	C₂³×C₇	—	3	2	no	—
14	C₇×D₄	—	3	2	no	—
15	C₇×D₄	—	3	1	no	—
16	C₇×D₄	D₃	1	1	yes	characteristic, direct product factor
17	C₂×C₄×C₇	—	3	1	no	—
18	D₃×D₄	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₃×C₇	—	2	2	no	—
20	C₂×C₃×C₇	C₂³	1	1	yes	characteristic
21	D₃×C₇	—	2	2	no	—
22	D₃×C₇	D₄	1	2	yes	direct product factor
23	C₂²×C₇	—	3	1	no	—
24	C₂²×C₇	—	3	2	no	—
25	C₂²×C₇	—	6	4	no	—
26	C₂²×C₇	C₂×D₃	1	2	yes	complemented
27	C₄×C₇	—	3	1	no	—
28	C₄×C₇	C₂×D₃	1	1	yes	characteristic, complemented
29	C₂²×D₃	C₂×C₇	1	2	yes	complemented
30	C₃×D₄	C₂×C₇	1	1	yes	characteristic, complemented
31	#67	C₂×C₇	1	2	yes	complemented
32	D₁₂	C₂×C₇	1	1	yes	characteristic, complemented
33	C₄×D₃	C₂×C₇	1	1	yes	characteristic, complemented
34	C₃×C₇	C₂×D₄	1	1	yes	characteristic, complemented, Hall
35	C₂×D₄	—	3	1	no	Sylow
36	C₂×C₇	—	2	2	no	—
37	C₂×C₇	—	3	2	no	—
38	C₂×C₇	—	6	2	no	—
39	C₂×C₇	C₂²×D₃	1	1	yes	characteristic
40	C₂²×C₃	C₂²×C₇	1	2	yes	complemented
41	C₂×D₃	—	2	4	no	—
42	C₂×D₃	C₂²×C₇	1	1	yes	characteristic
43	C₂×D₃	C₂²×C₇	1	2	yes	complemented
44	C₃×C₄	C₂²×C₇	1	1	yes	characteristic, complemented
45	Dic₃	C₂²×C₇	1	1	yes	characteristic, complemented
46	C₂³	—	3	2	no	—
47	D₄	—	3	2	no	—
48	D₄	—	3	1	no	—
49	D₄	D₃×C₇	1	1	yes	characteristic, direct product factor
50	C₂×C₄	—	3	1	no	—
51	C₇	D₃×D₄	1	1	yes	characteristic, direct product factor, Sylow
52	C₂×C₃	—	2	2	no	—
53	C₂×C₃	C₂³×C₇	1	1	yes	characteristic
54	D₃	—	2	2	no	—
55	D₃	C₇×D₄	1	2	yes	direct product factor
56	C₂²	—	3	1	no	—
57	C₂²	—	3	2	no	—
58	C₂²	—	6	4	no	—
59	C₂²	C₂×D₃×C₇	1	2	yes	complemented
60	C₄	—	3	1	no	—
61	C₄	C₂×D₃×C₇	1	1	yes	characteristic, complemented
62	C₃	C₂×C₇×D₄	1	1	yes	characteristic, complemented, Sylow
63	C₂	—	2	2	no	—
64	C₂	—	3	2	no	—
65	C₂	—	6	2	no	—
66	C₂	C₂²×D₃×C₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₇	C₂²×D₃
commutator, cosocle	C₂×C₃	C₂³×C₇
Frattini	C₂	C₂²×D₃×C₇
Fitting	C₃×C₇×D₄	C₂
socle	C₂×C₃×C₇	C₂³
hypercenter	C₇×D₄	D₃
hypocenter	C₃	C₂×C₇×D₄
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₇ ◁ C₇×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×D₃×C₇	C₂	semidirect
2. C₃×C₇×D₄	C₂	semidirect
3. C₇×#67	C₂	semidirect
4. C₇×D₁₂	C₂	semidirect
5. C₄×D₃×C₇	C₂	semidirect
7. C₂²×C₃×C₇	C₂²	semidirect
10. C₂×D₃×C₇	C₂²	semidirect
11. C₃×C₄×C₇	C₂²	semidirect
12. C₇×Dic₃	C₂²	semidirect
16. C₇×D₄	D₃	direct (N × H)
18. D₃×D₄	C₇	direct (N × H)
22. D₃×C₇	D₄	direct (N × H)
26. C₂²×C₇	C₂×D₃	semidirect
28. C₄×C₇	C₂×D₃	semidirect
29. C₂²×D₃	C₂×C₇	semidirect
30. C₃×D₄	C₂×C₇	semidirect
31. #67	C₂×C₇	semidirect
32. D₁₂	C₂×C₇	semidirect
33. C₄×D₃	C₂×C₇	semidirect
34. C₃×C₇	C₂×D₄	semidirect
40. C₂²×C₃	C₂²×C₇	semidirect
43. C₂×D₃	C₂²×C₇	semidirect
44. C₃×C₄	C₂²×C₇	semidirect
45. Dic₃	C₂²×C₇	semidirect
49. D₄	D₃×C₇	direct (N × H)
51. C₇	D₃×D₄	direct (N × H)
55. D₃	C₇×D₄	direct (N × H)
59. C₂²	C₂×D₃×C₇	semidirect
61. C₄	C₂×D₃×C₇	semidirect
62. C₃	C₂×C₇×D₄	semidirect

Maximal subgroups

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

subgroup	index
C₂²×D₃×C₇	2
C₃×C₇×D₄	2
C₇×#67	2
C₇×D₁₂	2
C₄×D₃×C₇	2
C₂×C₇×D₄	3
D₃×D₄	7

Subgroups — D3×C7×D4 #66719

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₇×D₄ #66719