Subgroups — C₂×C₄⋊Dic₂₁ #10621408

Order 672.

184 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₂₁	C₂	1	2	yes	maximal
3	C₄⋊Dic₂₁	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄⋊Dic₇	—	3	1	no	maximal, Hall
5	C₂³×C₃×C₇	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₄×C₇	C₄	1	4	yes	complemented
7	C₂×C₃×C₄×C₇	C₂²	1	2	yes	—
8	C₂×Dic₂₁	—	2	4	no	—
9	C₂×Dic₂₁	C₂²	1	4	yes	—
10	C₂²×C₄×C₇	D₃	1	1	yes	characteristic
11	C₂²×Dic₇	—	3	2	no	—
12	C₄⋊Dic₇	—	3	4	no	—
13	C₂×C₄⋊Dic₃	—	7	1	no	maximal, Hall
14	C₂²×C₃×C₇	C₂×C₄	1	2	yes	—
15	C₂²×C₃×C₇	D₄	1	2	yes	—
16	C₂²×C₃×C₇	Q₈	1	2	yes	—
17	C₂²×C₃×C₇	C₂³	1	1	yes	characteristic
18	C₃×C₄×C₇	C₂×C₄	1	4	yes	complemented
19	Dic₂₁	—	2	4	no	—
20	C₂³×C₇	C₂×D₃	1	1	yes	characteristic
21	C₂×C₄×C₇	Dic₃	1	4	yes	complemented
22	C₂×C₄×C₇	C₂×D₃	1	2	yes	—
23	C₂×Dic₇	—	3	4	no	—
24	C₂×Dic₇	—	6	4	no	—
25	C₂²×C₃×C₄	D₇	1	1	yes	characteristic
26	C₂²×Dic₃	—	7	2	no	—
27	C₄⋊Dic₃	—	7	4	no	—
28	C₂×C₃×C₇	C₄⋊C₄	1	4	yes	complemented
29	C₂×C₃×C₇	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₃×C₇	C₂×D₄	1	1	yes	characteristic
31	C₂×C₃×C₇	C₂×Q₈	1	1	yes	characteristic
32	C₂×C₄⋊C₄	—	21	1	no	Sylow
33	C₂²×C₇	Dic₆	1	2	yes	—
34	C₂²×C₇	D₁₂	1	2	yes	—
35	C₂²×C₇	C₂×Dic₃	1	2	yes	—
36	C₂²×C₇	C₂²×D₃	1	1	yes	characteristic
37	C₄×C₇	C₂×Dic₃	1	4	yes	complemented
38	Dic₇	—	6	4	no	—
39	C₂³×C₃	C₂×D₇	1	1	yes	characteristic
40	C₂×C₃×C₄	Dic₇	1	4	yes	complemented
41	C₂×C₃×C₄	C₂×D₇	1	2	yes	—
42	C₂×Dic₃	—	7	4	no	—
43	C₂×Dic₃	—	14	4	no	—
44	C₃×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
45	C₂²×C₄	—	21	2	no	—
46	C₂²×C₄	D₂₁	1	1	yes	characteristic
47	C₄⋊C₄	—	21	4	no	—
48	C₂×C₇	C₄⋊Dic₃	1	4	yes	complemented
49	C₂×C₇	C₂×Dic₆	1	1	yes	characteristic
50	C₂×C₇	C₂×D₁₂	1	1	yes	characteristic
51	C₂×C₇	C₂²×Dic₃	1	1	yes	characteristic
52	C₂²×C₃	Dic₁₄	1	2	yes	—
53	C₂²×C₃	D₂₈	1	2	yes	—
54	C₂²×C₃	C₂×Dic₇	1	2	yes	—
55	C₂²×C₃	C₂²×D₇	1	1	yes	characteristic
56	C₃×C₄	C₂×Dic₇	1	4	yes	complemented
57	Dic₃	—	14	4	no	—
58	C₂³	C₂×D₂₁	1	1	yes	characteristic
59	C₂×C₄	—	21	4	no	—
60	C₂×C₄	—	42	4	no	—
61	C₂×C₄	Dic₂₁	1	4	yes	complemented
62	C₂×C₄	C₂×D₂₁	1	2	yes	—
63	C₇	C₂×C₄⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₃	C₄⋊Dic₇	1	4	yes	complemented
65	C₂×C₃	C₂×Dic₁₄	1	1	yes	characteristic
66	C₂×C₃	C₂×D₂₈	1	1	yes	characteristic
67	C₂×C₃	C₂²×Dic₇	1	1	yes	characteristic
68	C₂²	Dic₄₂	1	2	yes	—
69	C₂²	D₈₄	1	2	yes	—
70	C₂²	C₂×Dic₂₁	1	2	yes	—
71	C₂²	C₂²×D₂₁	1	1	yes	characteristic
72	C₄	—	42	4	no	—
73	C₄	C₂×Dic₂₁	1	4	yes	complemented
74	C₃	C₂×C₄⋊Dic₇	1	1	yes	characteristic, complemented, Sylow
75	C₂	C₄⋊Dic₂₁	1	4	yes	direct product factor
76	C₂	C₂×Dic₄₂	1	1	yes	characteristic
77	C₂	C₂×D₈₄	1	1	yes	characteristic
78	C₂	C₂²×Dic₂₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₂₁
commutator	C₂×C₃×C₇	C₂²×C₄
Frattini	C₂²	C₂²×D₂₁
Fitting	C₂²×C₃×C₄×C₇	C₂
socle, prime radical	C₂³×C₃×C₇	C₂²
cosocle	C₂²×C₃×C₇	C₂³
hypercenter	C₂²×C₄	D₂₁
hypocenter	C₃×C₇	C₂×C₄⋊C₄
LCS	G ▷ C₂×C₃×C₇ ▷ C₃×C₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
3. C₄⋊Dic₂₁	C₂	direct (N × H)
6. C₂×C₃×C₄×C₇	C₄	semidirect
18. C₃×C₄×C₇	C₂×C₄	semidirect
21. C₂×C₄×C₇	Dic₃	semidirect
28. C₂×C₃×C₇	C₄⋊C₄	semidirect
37. C₄×C₇	C₂×Dic₃	semidirect
40. C₂×C₃×C₄	Dic₇	semidirect
44. C₃×C₇	C₂×C₄⋊C₄	semidirect
48. C₂×C₇	C₄⋊Dic₃	semidirect
56. C₃×C₄	C₂×Dic₇	semidirect
61. C₂×C₄	Dic₂₁	semidirect
63. C₇	C₂×C₄⋊Dic₃	semidirect
64. C₂×C₃	C₄⋊Dic₇	semidirect
73. C₄	C₂×Dic₂₁	semidirect
74. C₃	C₂×C₄⋊Dic₇	semidirect
75. C₂	C₄⋊Dic₂₁	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×C₃×C₄×C₇	2
C₂²×Dic₂₁	2
C₄⋊Dic₂₁	2
C₂×C₄⋊Dic₇	3
C₂×C₄⋊Dic₃	7

Subgroups — C2×C4⋊Dic21 #10621408

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄⋊Dic₂₁ #10621408