Subgroups — D₃×D₂₈ #66680

Order 336.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×D₇	C₂	1	2	yes	maximal, complemented
2	D₈₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₃×C₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₂₈	C₂	1	1	yes	maximal, characteristic, complemented
5	#4246	C₂	1	2	yes	maximal, complemented
6	C₂×D₂₈	—	3	1	no	maximal, Hall
7	C₂×D₂₁	C₂²	1	2	yes	complemented
8	C₂×D₃×C₇	C₂²	1	1	yes	characteristic
9	C₂×C₃×D₇	C₂²	1	2	yes	complemented
10	D₃×D₇	—	2	4	no	—
11	C₃×C₄×C₇	C₂²	1	1	yes	characteristic, complemented
12	C₇×Dic₃	C₂²	1	1	yes	characteristic, complemented
13	C₂²×D₇	—	3	2	no	—
14	C₂×C₄×C₇	—	3	1	no	—
15	D₂₈	—	3	2	no	—
16	D₂₈	—	3	1	no	—
17	D₂₈	D₃	1	1	yes	characteristic, direct product factor
18	D₃×D₄	—	7	1	no	maximal, Hall
19	C₂×C₃×C₇	C₂³	1	1	yes	characteristic
20	D₂₁	—	2	2	no	—
21	C₃×D₇	—	2	2	no	—
22	D₃×C₇	D₄	1	2	yes	complemented
23	C₂²×C₇	—	3	1	no	—
24	C₂×D₇	—	3	2	no	—
25	C₂×D₇	—	6	4	no	—
26	C₂×D₇	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	—	7	2	no	—
30	C₃×D₄	—	7	1	no	—
31	#67	—	7	2	no	—
32	D₁₂	—	7	1	no	—
33	C₄×D₃	D₇	1	1	yes	characteristic, complemented
34	C₃×C₇	C₂×D₄	1	1	yes	characteristic, complemented, Hall
35	C₂×D₄	—	21	1	no	Sylow
36	C₂×C₇	—	3	2	no	—
37	C₂×C₇	C₂²×D₃	1	1	yes	characteristic
38	D₇	—	2	2	no	—
39	D₇	—	6	2	no	—
40	C₂²×C₃	—	7	2	no	—
41	C₂×D₃	—	7	2	no	—
42	C₂×D₃	—	14	4	no	—
43	C₂×D₃	C₂×D₇	1	1	yes	characteristic
44	C₃×C₄	C₂×D₇	1	1	yes	characteristic, complemented
45	Dic₃	C₂×D₇	1	1	yes	characteristic, complemented
46	C₂³	—	21	2	no	—
47	D₄	—	7	1	no	—
48	D₄	—	21	2	no	—
49	D₄	—	21	1	no	—
50	C₂×C₄	—	3	1	no	—
51	C₇	D₃×D₄	1	1	yes	characteristic, complemented, Sylow
52	C₂×C₃	—	14	2	no	—
53	C₂×C₃	C₂²×D₇	1	1	yes	characteristic
54	D₃	—	14	2	no	—
55	D₃	D₂₈	1	2	yes	direct product factor
56	C₂²	—	3	1	no	—
57	C₂²	—	7	2	no	—
58	C₂²	—	21	2	no	—
59	C₂²	—	42	4	no	—
60	C₄	—	3	1	no	—
61	C₄	D₃×D₇	1	1	yes	characteristic, complemented
62	C₃	C₂×D₂₈	1	1	yes	characteristic, complemented, Sylow
63	C₂	—	3	2	no	—
64	C₂	—	14	2	no	—
65	C₂	—	42	2	no	—
66	C₂	C₂×D₃×D₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×D₃×D₇
commutator, socle, cosocle	C₂×C₃×C₇	C₂³
Fitting	C₃×C₄×C₇	C₂²
hypercenter	C₄	D₃×D₇
hypocenter	C₃×C₇	C₂×D₄
LCS	G ▷ C₂×C₃×C₇ ▷ C₃×C₇
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
1. C₂×D₃×D₇	C₂	semidirect
2. D₈₄	C₂	semidirect
3. C₄×D₃×C₇	C₂	semidirect
4. C₃×D₂₈	C₂	semidirect
5. #4246	C₂	semidirect
7. C₂×D₂₁	C₂²	semidirect
9. C₂×C₃×D₇	C₂²	semidirect
11. C₃×C₄×C₇	C₂²	semidirect
12. C₇×Dic₃	C₂²	semidirect
17. D₂₈	D₃	direct (N × H)
22. D₃×C₇	D₄	semidirect
26. C₂×D₇	C₂×D₃	semidirect
28. C₄×C₇	C₂×D₃	semidirect
33. C₄×D₃	D₇	semidirect
34. C₃×C₇	C₂×D₄	semidirect
44. C₃×C₄	C₂×D₇	semidirect
45. Dic₃	C₂×D₇	semidirect
51. C₇	D₃×D₄	semidirect
55. D₃	D₂₈	direct (N × H)
61. C₄	D₃×D₇	semidirect
62. C₃	C₂×D₂₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×D₇	2
D₈₄	2
C₄×D₃×C₇	2
C₃×D₂₈	2
#4246	2
C₂×D₂₈	3
D₃×D₄	7

Subgroups — D3×D28 #66680

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₂₈ #66680