Subgroups — C₂²×D₃×Dic₇ #10621586

Order 672.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₃×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₃×Dic₇	C₂	1	12	yes	maximal, direct product factor
5	C₂³×Dic₇	—	3	1	no	maximal, Hall
6	C₂³×C₃×C₇	C₂²	1	1	yes	characteristic
7	C₂²×D₃×C₇	C₄	1	8	yes	complemented
8	C₂²×D₃×C₇	C₂²	1	6	yes	—
9	C₂×Dic₂₁	C₂²	1	6	yes	complemented
10	C₂×C₃×Dic₇	C₂²	1	6	yes	complemented
11	D₃×Dic₇	C₂²	1	16	yes	direct product factor
12	C₂⁴×C₇	—	3	1	no	—
13	C₂²×Dic₇	—	3	1	no	—
14	C₂²×Dic₇	—	3	12	no	—
15	C₂²×Dic₇	D₃	1	1	yes	characteristic, direct product factor
16	C₂²×C₄×D₃	—	7	1	no	maximal, Hall
17	C₂²×C₃×C₇	C₂×C₄	1	4	yes	complemented
18	C₂²×C₃×C₇	C₂³	1	3	yes	—
19	C₂×D₃×C₇	C₂×C₄	1	24	yes	complemented
20	C₂×D₃×C₇	C₂³	1	4	yes	—
21	Dic₂₁	C₂³	1	4	yes	complemented
22	C₃×Dic₇	C₂³	1	4	yes	complemented
23	C₂³×C₇	—	3	8	no	—
24	C₂³×C₇	—	3	6	no	—
25	C₂³×C₇	C₂×D₃	1	1	yes	characteristic
26	C₂×Dic₇	—	3	6	no	—
27	C₂×Dic₇	—	3	16	no	—
28	C₂×Dic₇	C₂×D₃	1	6	yes	direct product factor
29	C₂³×D₃	D₇	1	1	yes	characteristic
30	C₂²×C₃×C₄	—	7	1	no	—
31	C₂²×Dic₃	—	7	1	no	—
32	C₂×C₄×D₃	—	7	12	no	—
33	C₂×C₃×C₇	C₂²×C₄	1	6	yes	complemented
34	C₂×C₃×C₇	C₂⁴	1	1	yes	characteristic
35	D₃×C₇	C₂²×C₄	1	8	yes	complemented
36	C₂³×C₄	—	21	1	no	Sylow
37	C₂²×C₇	—	3	24	no	—
38	C₂²×C₇	—	3	4	no	—
39	C₂²×C₇	C₄×D₃	1	4	yes	complemented
40	C₂²×C₇	C₂²×D₃	1	3	yes	—
41	Dic₇	—	3	4	no	—
42	Dic₇	C₂²×D₃	1	4	yes	direct product factor
43	C₂³×C₃	C₂×D₇	1	1	yes	characteristic
44	C₂²×D₃	Dic₇	1	8	yes	direct product factor
45	C₂²×D₃	C₂×D₇	1	6	yes	—
46	C₂×C₃×C₄	—	7	6	no	—
47	C₂×Dic₃	—	7	6	no	—
48	C₄×D₃	—	7	16	no	—
49	C₃×C₇	C₂³×C₄	1	1	yes	characteristic, complemented, Hall
50	C₂⁴	—	3	1	no	—
51	C₂²×C₄	—	7	1	no	—
52	C₂²×C₄	—	21	12	no	—
53	C₂²×C₄	—	21	1	no	—
54	C₂×C₇	—	3	8	no	—
55	C₂×C₇	C₂×C₄×D₃	1	6	yes	complemented
56	C₂×C₇	C₂³×D₃	1	1	yes	characteristic
57	C₂²×C₃	C₂×Dic₇	1	4	yes	complemented
58	C₂²×C₃	C₂²×D₇	1	3	yes	—
59	C₂×D₃	C₂×Dic₇	1	24	yes	direct product factor
60	C₂×D₃	C₂²×D₇	1	4	yes	—
61	C₃×C₄	—	7	4	no	—
62	Dic₃	—	7	4	no	—
63	C₂³	—	3	8	no	—
64	C₂³	—	3	6	no	—
65	C₂³	D₃×D₇	1	1	yes	characteristic
66	C₂×C₄	—	7	6	no	—
67	C₂×C₄	—	21	16	no	—
68	C₂×C₄	—	21	6	no	—
69	C₇	C₂²×C₄×D₃	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₃	C₂²×Dic₇	1	6	yes	complemented
71	C₂×C₃	C₂³×D₇	1	1	yes	characteristic
72	D₃	C₂²×Dic₇	1	8	yes	direct product factor
73	C₂²	—	3	24	no	—
74	C₂²	—	3	4	no	—
75	C₂²	D₃×Dic₇	1	4	yes	direct product factor
76	C₂²	C₂×D₃×D₇	1	3	yes	—
77	C₄	—	7	4	no	—
78	C₄	—	21	4	no	—
79	C₃	C₂³×Dic₇	1	1	yes	characteristic, complemented, Sylow
80	C₂	—	3	8	no	—
81	C₂	C₂×D₃×Dic₇	1	6	yes	direct product factor
82	C₂	C₂²×D₃×D₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³	D₃×D₇
commutator, hypocenter	C₃×C₇	C₂³×C₄
Frattini	C₂	C₂²×D₃×D₇
Fitting, socle	C₂³×C₃×C₇	C₂²
prime radical	C₂³×D₃×C₇	C₂
cosocle	C₂×C₃×C₇	C₂⁴
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₂³

Complements

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

N	H ≅ G/N	type
2. C₂²×Dic₂₁	C₂	semidirect
3. C₂²×C₃×Dic₇	C₂	semidirect
4. C₂×D₃×Dic₇	C₂	direct (N × H)
7. C₂²×D₃×C₇	C₄	semidirect
9. C₂×Dic₂₁	C₂²	semidirect
10. C₂×C₃×Dic₇	C₂²	semidirect
11. D₃×Dic₇	C₂²	direct (N × H)
15. C₂²×Dic₇	D₃	direct (N × H)
17. C₂²×C₃×C₇	C₂×C₄	semidirect
19. C₂×D₃×C₇	C₂×C₄	semidirect
21. Dic₂₁	C₂³	semidirect
22. C₃×Dic₇	C₂³	semidirect
28. C₂×Dic₇	C₂×D₃	direct (N × H)
33. C₂×C₃×C₇	C₂²×C₄	semidirect
35. D₃×C₇	C₂²×C₄	semidirect
39. C₂²×C₇	C₄×D₃	semidirect
42. Dic₇	C₂²×D₃	direct (N × H)
44. C₂²×D₃	Dic₇	direct (N × H)
49. C₃×C₇	C₂³×C₄	semidirect
55. C₂×C₇	C₂×C₄×D₃	semidirect
57. C₂²×C₃	C₂×Dic₇	semidirect
59. C₂×D₃	C₂×Dic₇	direct (N × H)
69. C₇	C₂²×C₄×D₃	semidirect
70. C₂×C₃	C₂²×Dic₇	semidirect
72. D₃	C₂²×Dic₇	direct (N × H)
75. C₂²	D₃×Dic₇	direct (N × H)
79. C₃	C₂³×Dic₇	semidirect
81. C₂	C₂×D₃×Dic₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₃×C₇	2
C₂²×Dic₂₁	2
C₂²×C₃×Dic₇	2
C₂×D₃×Dic₇	2
C₂³×Dic₇	3
C₂²×C₄×D₃	7

Subgroups — C22×D3×Dic7 #10621586

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₃×Dic₇ #10621586