Subgroups — C₂×D₁₂×C₄₁ #14520240

Order 1968.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₃×C₄₁	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₂×C₄₁	C₂	1	4	yes	maximal, direct product factor
4	C₂×D₄×C₄₁	—	3	1	no	maximal, Hall
5	C₂²×C₃×C₄₁	C₂²	1	1	yes	characteristic
6	C₂×D₃×C₄₁	—	2	4	no	—
7	C₂×D₃×C₄₁	C₂²	1	4	yes	complemented
8	C₃×C₄×C₄₁	C₂²	1	2	yes	complemented
9	C₂³×C₄₁	—	3	2	no	—
10	D₄×C₄₁	—	3	4	no	—
11	C₂×C₄×C₄₁	D₃	1	1	yes	characteristic, complemented
12	C₂×C₃×C₄₁	D₄	1	2	yes	complemented
13	C₂×C₃×C₄₁	C₂³	1	1	yes	characteristic
14	D₃×C₄₁	—	2	4	no	—
15	C₂²×C₄₁	—	3	4	no	—
16	C₂²×C₄₁	—	6	4	no	—
17	C₂²×C₄₁	C₂×D₃	1	1	yes	characteristic
18	C₄×C₄₁	C₂×D₃	1	2	yes	complemented
19	C₃×C₄₁	C₂×D₄	1	1	yes	characteristic, complemented, Hall
20	C₂×C₄₁	—	6	4	no	—
21	C₂×C₄₁	D₁₂	1	2	yes	direct product factor
22	C₂×C₄₁	C₂²×D₃	1	1	yes	characteristic
23	C₂×D₁₂	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₄₁	C₂×D₁₂	1	1	yes	characteristic, direct product factor, Sylow
25	C₂²×D₃	C₂×C₄₁	1	2	yes	complemented
26	C₂×C₃×C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
27	D₁₂	C₂×C₄₁	1	4	yes	direct product factor
28	C₂×D₄	—	3	1	no	Sylow
29	C₂²×C₃	C₂²×C₄₁	1	1	yes	characteristic
30	C₂×D₃	—	2	4	no	—
31	C₂×D₃	C₂²×C₄₁	1	4	yes	complemented
32	C₃×C₄	C₂²×C₄₁	1	2	yes	complemented
33	C₂³	—	3	2	no	—
34	D₄	—	3	4	no	—
35	C₂×C₄	D₃×C₄₁	1	1	yes	characteristic, complemented
36	C₂×C₃	D₄×C₄₁	1	2	yes	complemented
37	C₂×C₃	C₂³×C₄₁	1	1	yes	characteristic
38	D₃	—	2	4	no	—
39	C₂²	—	3	4	no	—
40	C₂²	—	6	4	no	—
41	C₂²	C₂×D₃×C₄₁	1	1	yes	characteristic
42	C₄	C₂×D₃×C₄₁	1	2	yes	complemented
43	C₃	C₂×D₄×C₄₁	1	1	yes	characteristic, complemented, Sylow
44	C₂	—	6	4	no	—
45	C₂	D₁₂×C₄₁	1	2	yes	direct product factor
46	C₂	C₂²×D₃×C₄₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄₁	C₂×D₃
commutator, cosocle	C₂×C₃	C₂³×C₄₁
Frattini	C₂	C₂²×D₃×C₄₁
Fitting	C₂×C₃×C₄×C₄₁	C₂
socle	C₂²×C₃×C₄₁	C₂²
hypercenter	C₂×C₄×C₄₁	D₃
hypocenter	C₃	C₂×D₄×C₄₁
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂×C₄×C₄₁

Complements

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

N	H ≅ G/N	type
1. C₂²×D₃×C₄₁	C₂	semidirect
2. C₂×C₃×C₄×C₄₁	C₂	semidirect
3. D₁₂×C₄₁	C₂	direct (N × H)
7. C₂×D₃×C₄₁	C₂²	semidirect
8. C₃×C₄×C₄₁	C₂²	semidirect
11. C₂×C₄×C₄₁	D₃	semidirect
12. C₂×C₃×C₄₁	D₄	semidirect
18. C₄×C₄₁	C₂×D₃	semidirect
19. C₃×C₄₁	C₂×D₄	semidirect
21. C₂×C₄₁	D₁₂	direct (N × H)
23. C₂×D₁₂	C₄₁	direct (N × H)
24. C₄₁	C₂×D₁₂	direct (N × H)
25. C₂²×D₃	C₂×C₄₁	semidirect
26. C₂×C₃×C₄	C₂×C₄₁	semidirect
27. D₁₂	C₂×C₄₁	direct (N × H)
31. C₂×D₃	C₂²×C₄₁	semidirect
32. C₃×C₄	C₂²×C₄₁	semidirect
35. C₂×C₄	D₃×C₄₁	semidirect
36. C₂×C₃	D₄×C₄₁	semidirect
42. C₄	C₂×D₃×C₄₁	semidirect
43. C₃	C₂×D₄×C₄₁	semidirect
45. C₂	D₁₂×C₄₁	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×D₃×C₄₁	2
C₂×C₃×C₄×C₄₁	2
D₁₂×C₄₁	2
C₂×D₄×C₄₁	3
C₂×D₁₂	41

Subgroups — C2×D12×C41 #14520240

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₂×C₄₁ #14520240