Subgroups — C₄²×Dic₂₁ #13056565

Order 1344.

516 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄²×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₂₁	C₂	1	6	yes	maximal
3	C₄²×Dic₇	—	3	1	no	maximal, Hall
4	C₂²×C₃×C₄×C₇	C₂²	1	3	yes	—
5	C₂²×Dic₂₁	C₂²	1	4	yes	—
6	C₃×C₄²×C₇	C₄	1	4	yes	complemented
7	C₄×Dic₂₁	C₄	1	24	yes	direct product factor
8	C₂×C₄²×C₇	D₃	1	1	yes	characteristic
9	C₂×C₄×Dic₇	—	3	6	no	—
10	C₄²×Dic₃	—	7	1	no	maximal, Hall
11	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
12	C₂×C₃×C₄×C₇	C₂×C₄	1	12	yes	—
13	C₂×C₃×C₄×C₇	C₂×C₄	1	6	yes	—
14	C₂×Dic₂₁	C₂×C₄	1	24	yes	—
15	C₂²×C₄×C₇	C₂×D₃	1	3	yes	—
16	C₂²×Dic₇	—	3	4	no	—
17	C₄²×C₇	Dic₃	1	4	yes	complemented
18	C₄×Dic₇	—	3	24	no	—
19	C₂×C₃×C₄²	D₇	1	1	yes	characteristic
20	C₂×C₄×Dic₃	—	7	6	no	—
21	C₂²×C₃×C₇	C₂²×C₄	1	6	yes	—
22	C₂²×C₃×C₇	C₂²×C₄	1	1	yes	characteristic
23	C₃×C₄×C₇	C₄²	1	12	yes	complemented
24	Dic₂₁	C₄²	1	16	yes	direct product factor
25	C₄³	—	21	1	no	Sylow
26	C₂³×C₇	C₂²×D₃	1	1	yes	characteristic
27	C₂×C₄×C₇	C₄×D₃	1	12	yes	—
28	C₂×C₄×C₇	C₂×Dic₃	1	6	yes	—
29	C₂×Dic₇	—	3	24	no	—
30	C₂²×C₃×C₄	C₂×D₇	1	3	yes	—
31	C₂²×Dic₃	—	7	4	no	—
32	C₃×C₄²	Dic₇	1	4	yes	complemented
33	C₄×Dic₃	—	7	24	no	—
34	C₂×C₃×C₇	C₂×C₄²	1	4	yes	—
35	C₂×C₃×C₇	C₂×C₄²	1	3	yes	—
36	C₂×C₄²	—	21	6	no	—
37	C₂×C₄²	D₂₁	1	1	yes	characteristic
38	C₂²×C₇	C₂×C₄×D₃	1	6	yes	—
39	C₂²×C₇	C₂²×Dic₃	1	1	yes	characteristic
40	C₄×C₇	C₄×Dic₃	1	12	yes	complemented
41	Dic₇	—	3	16	no	—
42	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
43	C₂×C₃×C₄	C₄×D₇	1	12	yes	—
44	C₂×C₃×C₄	C₂×Dic₇	1	6	yes	—
45	C₂×Dic₃	—	7	24	no	—
46	C₃×C₇	C₄³	1	1	yes	characteristic, complemented, Hall
47	C₂²×C₄	—	21	4	no	—
48	C₂²×C₄	C₂×D₂₁	1	3	yes	—
49	C₄²	—	21	24	no	—
50	C₄²	Dic₂₁	1	4	yes	direct product factor
51	C₂×C₇	C₄²×D₃	1	4	yes	—
52	C₂×C₇	C₂×C₄×Dic₃	1	3	yes	—
53	C₂²×C₃	C₂×C₄×D₇	1	6	yes	—
54	C₂²×C₃	C₂²×Dic₇	1	1	yes	characteristic
55	C₃×C₄	C₄×Dic₇	1	12	yes	complemented
56	Dic₃	—	7	16	no	—
57	C₂³	C₂²×D₂₁	1	1	yes	characteristic
58	C₂×C₄	—	21	24	no	—
59	C₂×C₄	C₄×D₂₁	1	12	yes	—
60	C₂×C₄	C₂×Dic₂₁	1	6	yes	—
61	C₇	C₄²×Dic₃	1	1	yes	characteristic, complemented, Sylow
62	C₂×C₃	C₄²×D₇	1	4	yes	—
63	C₂×C₃	C₂×C₄×Dic₇	1	3	yes	—
64	C₂²	C₂×C₄×D₂₁	1	6	yes	—
65	C₂²	C₂²×Dic₂₁	1	1	yes	characteristic
66	C₄	—	21	16	no	—
67	C₄	C₄×Dic₂₁	1	12	yes	direct product factor
68	C₃	C₄²×Dic₇	1	1	yes	characteristic, complemented, Sylow
69	C₂	C₄²×D₂₁	1	4	yes	—
70	C₂	C₂×C₄×Dic₂₁	1	3	yes	—

	subgroup	G/H
center, hypercenter	C₂×C₄²	D₂₁
commutator, hypocenter	C₃×C₇	C₄³
Frattini	C₂³	C₂²×D₂₁
Fitting	C₂×C₃×C₄²×C₇	C₂
socle, prime radical, cosocle	C₂³×C₃×C₇	C₂³
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
6. C₃×C₄²×C₇	C₄	semidirect
7. C₄×Dic₂₁	C₄	direct (N × H)
17. C₄²×C₇	Dic₃	semidirect
23. C₃×C₄×C₇	C₄²	semidirect
24. Dic₂₁	C₄²	direct (N × H)
32. C₃×C₄²	Dic₇	semidirect
40. C₄×C₇	C₄×Dic₃	semidirect
46. C₃×C₇	C₄³	semidirect
50. C₄²	Dic₂₁	direct (N × H)
55. C₃×C₄	C₄×Dic₇	semidirect
61. C₇	C₄²×Dic₃	semidirect
67. C₄	C₄×Dic₂₁	direct (N × H)
68. C₃	C₄²×Dic₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄²×C₇	2
C₂×C₄×Dic₂₁	2
C₄²×Dic₇	3
C₄²×Dic₃	7

Subgroups — C42×Dic21 #13056565

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×Dic₂₁ #13056565