Subgroups — D₃×Dic₂₁ #92686

Order 504.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₃×C₇	C₂	1	1	yes	maximal, characteristic
2	C₃⋊Dic₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×Dic₂₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Dic₂₁	—	3	1	no	maximal
5	D₃×Dic₇	—	3	1	no	maximal
6	C₂×C₃²×C₇	C₂²	1	1	yes	characteristic
7	C₃×D₃×C₇	C₄	1	2	yes	complemented
8	C₂²×C₃×C₇	—	3	1	no	—
9	C₂×D₃×C₇	D₃	1	1	yes	characteristic
10	Dic₂₁	—	3	1	no	—
11	Dic₂₁	—	3	1	no	—
12	Dic₂₁	—	6	1	no	—
13	Dic₂₁	D₃	1	1	yes	characteristic, direct product factor
14	C₃×Dic₇	—	3	1	no	—
15	D₃×Dic₃	—	7	1	no	maximal, Hall
16	C₃²×C₇	C₂×C₄	1	1	yes	characteristic, complemented, Hall
17	C₂×Dic₇	—	9	1	no	Hall
18	C₂×C₃×C₇	—	2	1	no	—
19	C₂×C₃×C₇	—	3	2	no	—
20	C₂×C₃×C₇	C₂×D₃	1	1	yes	characteristic
21	C₂×C₃×C₇	C₂×D₃	1	1	yes	characteristic
22	D₃×C₇	Dic₃	1	2	yes	complemented
23	C₂×C₃×D₃	D₇	1	1	yes	characteristic
24	C₃⋊Dic₃	—	7	1	no	—
25	C₃×Dic₃	—	7	1	no	—
26	C₂²×C₇	—	3	1	no	—
27	Dic₇	—	3	1	no	—
28	Dic₇	—	9	1	no	—
29	C₂×Dic₃	—	21	1	no	—
30	C₄×D₃	—	21	1	no	—
31	C₃×C₇	—	2	1	no	—
32	C₃×C₇	C₄×D₃	1	1	yes	characteristic, complemented
33	C₃×C₇	C₂×Dic₃	1	1	yes	characteristic, complemented
34	C₂×C₃²	C₂×D₇	1	1	yes	characteristic
35	C₃×D₃	Dic₇	1	2	yes	complemented
36	C₂×C₇	—	3	2	no	—
37	C₂×C₇	D₃²	1	1	yes	characteristic
38	C₂²×C₃	—	3	1	no	—
39	C₂×D₃	D₂₁	1	1	yes	characteristic
40	C₃×C₄	—	21	1	no	—
41	Dic₃	—	7	1	no	—
42	Dic₃	—	21	1	no	—
43	Dic₃	—	21	1	no	—
44	Dic₃	—	42	1	no	—
45	C₃²	C₂×Dic₇	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₄	—	63	1	no	Sylow
47	C₇	D₃×Dic₃	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃	—	2	1	no	—
49	C₂×C₃	—	3	2	no	—
50	C₂×C₃	D₃×D₇	1	1	yes	characteristic
51	C₂×C₃	C₂×D₂₁	1	1	yes	characteristic
52	D₃	Dic₂₁	1	2	yes	direct product factor
53	C₂²	—	3	1	no	—
54	C₄	—	21	1	no	—
55	C₄	—	63	1	no	—
56	C₃	—	2	1	no	—
57	C₃	D₃×Dic₇	1	1	yes	characteristic, complemented
58	C₃	C₂×Dic₂₁	1	1	yes	characteristic, complemented
59	C₂	—	3	2	no	—
60	C₂	D₃×D₂₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×D₂₁
commutator, hypocenter	C₃²×C₇	C₂×C₄
Fitting, socle, cosocle	C₂×C₃²×C₇	C₂²
prime radical	C₂×C₃×D₃×C₇	C₂
LCS	G ▷ C₃²×C₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. C₃⋊Dic₂₁	C₂	semidirect
3. C₃×Dic₂₁	C₂	semidirect
7. C₃×D₃×C₇	C₄	semidirect
13. Dic₂₁	D₃	direct (N × H)
16. C₃²×C₇	C₂×C₄	semidirect
22. D₃×C₇	Dic₃	semidirect
32. C₃×C₇	C₄×D₃	semidirect
33. C₃×C₇	C₂×Dic₃	semidirect
35. C₃×D₃	Dic₇	semidirect
45. C₃²	C₂×Dic₇	semidirect
47. C₇	D₃×Dic₃	semidirect
52. D₃	Dic₂₁	direct (N × H)
57. C₃	D₃×Dic₇	semidirect
58. C₃	C₂×Dic₂₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×D₃×C₇	2
C₃⋊Dic₂₁	2
C₃×Dic₂₁	2
C₂×Dic₂₁	3
D₃×Dic₇	3
D₃×Dic₃	7

Subgroups — D3×Dic21 #92686

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×Dic₂₁ #92686