Subgroups — C₂²×D₃×D₄₁ #14520274

Order 1968.

268 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₁₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₃×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×D₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₃×D₄₁	C₂	1	12	yes	maximal, direct product factor
5	C₂³×D₄₁	—	3	1	no	maximal, Hall
6	C₂²×C₃×C₄₁	C₂²	1	1	yes	characteristic, complemented
7	C₂×D₁₂₃	C₂²	1	6	yes	complemented
8	C₂×D₃×C₄₁	C₂²	1	6	yes	complemented
9	C₂×C₃×D₄₁	C₂²	1	6	yes	complemented
10	D₃×D₄₁	C₂²	1	16	yes	direct product factor
11	C₂³×C₄₁	—	3	1	no	—
12	C₂²×D₄₁	—	3	1	no	—
13	C₂²×D₄₁	—	3	12	no	—
14	C₂²×D₄₁	D₃	1	1	yes	characteristic, direct product factor
15	C₂×C₃×C₄₁	C₂³	1	3	yes	complemented
16	D₁₂₃	C₂³	1	4	yes	complemented
17	C₃×D₄₁	C₂³	1	4	yes	complemented
18	D₃×C₄₁	C₂³	1	4	yes	complemented
19	C₂²×C₄₁	—	3	6	no	—
20	C₂²×C₄₁	C₂×D₃	1	1	yes	characteristic, complemented
21	C₂×D₄₁	—	3	6	no	—
22	C₂×D₄₁	—	3	16	no	—
23	C₂×D₄₁	C₂×D₃	1	6	yes	direct product factor
24	C₃×C₄₁	C₂⁴	1	1	yes	characteristic, complemented, Hall
25	C₂×C₄₁	—	3	4	no	—
26	C₂×C₄₁	C₂²×D₃	1	3	yes	complemented
27	D₄₁	—	3	4	no	—
28	D₄₁	C₂²×D₃	1	4	yes	direct product factor
29	C₂³×D₃	—	41	1	no	maximal, Hall
30	C₄₁	C₂³×D₃	1	1	yes	characteristic, complemented, Sylow
31	C₂³×C₃	—	41	1	no	—
32	C₂²×D₃	—	41	1	no	—
33	C₂²×D₃	—	41	12	no	—
34	C₂²×D₃	D₄₁	1	1	yes	characteristic, direct product factor
35	C₂⁴	—	123	1	no	Sylow
36	C₂²×C₃	—	41	6	no	—
37	C₂²×C₃	C₂×D₄₁	1	1	yes	characteristic, complemented
38	C₂×D₃	—	41	6	no	—
39	C₂×D₃	—	41	16	no	—
40	C₂×D₃	C₂×D₄₁	1	6	yes	direct product factor
41	C₂³	—	3	1	no	—
42	C₂³	—	41	1	no	—
43	C₂³	—	123	12	no	—
44	C₂³	—	123	1	no	—
45	C₂×C₃	—	41	4	no	—
46	C₂×C₃	C₂²×D₄₁	1	3	yes	complemented
47	D₃	—	41	4	no	—
48	D₃	C₂²×D₄₁	1	4	yes	direct product factor
49	C₂²	—	3	6	no	—
50	C₂²	—	41	6	no	—
51	C₂²	—	123	16	no	—
52	C₂²	—	123	6	no	—
53	C₂²	D₃×D₄₁	1	1	yes	characteristic, direct product factor
54	C₃	C₂³×D₄₁	1	1	yes	characteristic, complemented, Sylow
55	C₂	—	3	4	no	—
56	C₂	—	41	4	no	—
57	C₂	—	123	4	no	—
58	C₂	C₂×D₃×D₄₁	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²	D₃×D₄₁
commutator, cosocle, hypocenter	C₃×C₄₁	C₂⁴
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₄₁	C₂²
LCS	G ▷ C₃×C₄₁
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂²×D₁₂₃	C₂	semidirect
2. C₂²×D₃×C₄₁	C₂	semidirect
3. C₂²×C₃×D₄₁	C₂	semidirect
4. C₂×D₃×D₄₁	C₂	direct (N × H)
6. C₂²×C₃×C₄₁	C₂²	semidirect
7. C₂×D₁₂₃	C₂²	semidirect
8. C₂×D₃×C₄₁	C₂²	semidirect
9. C₂×C₃×D₄₁	C₂²	semidirect
10. D₃×D₄₁	C₂²	direct (N × H)
14. C₂²×D₄₁	D₃	direct (N × H)
15. C₂×C₃×C₄₁	C₂³	semidirect
16. D₁₂₃	C₂³	semidirect
17. C₃×D₄₁	C₂³	semidirect
18. D₃×C₄₁	C₂³	semidirect
20. C₂²×C₄₁	C₂×D₃	semidirect
23. C₂×D₄₁	C₂×D₃	direct (N × H)
24. C₃×C₄₁	C₂⁴	semidirect
26. C₂×C₄₁	C₂²×D₃	semidirect
28. D₄₁	C₂²×D₃	direct (N × H)
30. C₄₁	C₂³×D₃	semidirect
34. C₂²×D₃	D₄₁	direct (N × H)
37. C₂²×C₃	C₂×D₄₁	semidirect
40. C₂×D₃	C₂×D₄₁	direct (N × H)
46. C₂×C₃	C₂²×D₄₁	semidirect
48. D₃	C₂²×D₄₁	direct (N × H)
53. C₂²	D₃×D₄₁	direct (N × H)
54. C₃	C₂³×D₄₁	semidirect
58. C₂	C₂×D₃×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
C₂²×D₁₂₃	2
C₂²×D₃×C₄₁	2
C₂²×C₃×D₄₁	2
C₂×D₃×D₄₁	2
C₂³×D₄₁	3
C₂³×D₃	41

Subgroups — C22×D3×D41 #14520274

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₃×D₄₁ #14520274