Subgroups — C₂×A₄×D₄₁ #14520271

Order 1968.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×A₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	A₄×D₄₁	C₂	1	2	yes	maximal, direct product factor
3	C₂³×D₄₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₃×D₄₁	—	4	1	no	maximal
5	A₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
6	C₂³×C₄₁	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂²×D₄₁	—	3	1	no	—
8	C₂²×D₄₁	—	3	1	no	—
9	C₂²×D₄₁	—	3	2	no	—
10	C₂²×D₄₁	C₂×C₃	1	2	yes	complemented
11	C₂×C₃×C₄₁	—	4	1	no	—
12	C₃×D₄₁	—	4	2	no	—
13	C₂²×C₄₁	—	3	1	no	—
14	C₂²×C₄₁	—	3	1	no	—
15	C₂²×C₄₁	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₂×D₄₁	—	3	2	no	—
17	C₂×D₄₁	—	3	1	no	—
18	C₂×D₄₁	—	3	2	no	—
19	C₂×D₄₁	—	3	2	no	—
20	C₂×D₄₁	—	3	2	no	—
21	C₂×D₄₁	A₄	1	1	yes	characteristic, direct product factor
22	C₃×C₄₁	—	4	1	no	Hall
23	C₂×C₄₁	—	3	1	no	—
24	C₂×C₄₁	—	3	1	no	—
25	C₂×C₄₁	C₂×A₄	1	1	yes	characteristic, complemented
26	D₄₁	—	3	2	no	—
27	D₄₁	C₂×A₄	1	2	yes	direct product factor
28	C₂²×A₄	—	41	1	no	maximal, Hall
29	C₄₁	C₂²×A₄	1	1	yes	characteristic, complemented, Sylow
30	C₂×A₄	—	41	2	no	—
31	C₂×A₄	D₄₁	1	1	yes	characteristic, direct product factor
32	C₂⁴	—	41	1	no	Sylow
33	C₂²×C₃	—	164	1	no	—
34	A₄	C₂×D₄₁	1	1	yes	characteristic, direct product factor
35	C₂³	—	41	2	no	—
36	C₂³	—	123	1	no	—
37	C₂³	—	123	2	no	—
38	C₂³	—	123	1	no	—
39	C₂³	C₃×D₄₁	1	1	yes	characteristic, complemented
40	C₂×C₃	—	4	1	no	—
41	C₂×C₃	—	164	2	no	—
42	C₂²	—	3	1	no	—
43	C₂²	—	3	1	no	—
44	C₂²	—	41	1	no	—
45	C₂²	—	123	2	no	—
46	C₂²	—	123	2	no	—
47	C₂²	—	123	2	no	—
48	C₂²	—	123	2	no	—
49	C₂²	—	123	1	no	—
50	C₂²	C₂×C₃×D₄₁	1	1	yes	characteristic, complemented
51	C₃	—	4	1	no	Sylow
52	C₂	—	3	1	no	—
53	C₂	—	3	1	no	—
54	C₂	—	41	2	no	—
55	C₂	—	123	2	no	—
56	C₂	A₄×D₄₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	A₄×D₄₁
commutator, cosocle, hypocenter	C₂²×C₄₁	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂³×C₄₁	C₂×C₃
LCS	G ▷ C₂²×C₄₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×A₄×C₄₁	C₂	semidirect
2. A₄×D₄₁	C₂	direct (N × H)
3. C₂³×D₄₁	C₃	semidirect
5. A₄×C₄₁	C₂²	semidirect
6. C₂³×C₄₁	C₂×C₃	semidirect
10. C₂²×D₄₁	C₂×C₃	semidirect
15. C₂²×C₄₁	C₂²×C₃	semidirect
21. C₂×D₄₁	A₄	direct (N × H)
25. C₂×C₄₁	C₂×A₄	semidirect
27. D₄₁	C₂×A₄	direct (N × H)
29. C₄₁	C₂²×A₄	semidirect
31. C₂×A₄	D₄₁	direct (N × H)
34. A₄	C₂×D₄₁	direct (N × H)
39. C₂³	C₃×D₄₁	semidirect
50. C₂²	C₂×C₃×D₄₁	semidirect
56. C₂	A₄×D₄₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×A₄×C₄₁	2
A₄×D₄₁	2
C₂³×D₄₁	3
C₂×C₃×D₄₁	4
C₂²×A₄	41

Subgroups — C2×A4×D41 #14520271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×A₄×D₄₁ #14520271