Subgroups — C₂×C₄×D₃×C₄₁ #14520239

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	1	yes	maximal, characteristic
2	C₂×C₃×C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×Dic₃×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₃×C₄₁	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₄×C₄₁	—	3	1	no	maximal, Hall
6	C₂²×C₃×C₄₁	C₂²	1	1	yes	characteristic
7	C₂×D₃×C₄₁	C₄	1	4	yes	direct product factor
8	C₂×D₃×C₄₁	C₂²	1	2	yes	—
9	C₃×C₄×C₄₁	C₂²	1	2	yes	complemented
10	Dic₃×C₄₁	C₂²	1	2	yes	complemented
11	C₂³×C₄₁	—	3	1	no	—
12	C₂×C₄×C₄₁	—	3	1	no	—
13	C₂×C₄×C₄₁	—	3	4	no	—
14	C₂×C₄×C₄₁	D₃	1	1	yes	characteristic, direct product factor
15	C₂×C₃×C₄₁	C₂×C₄	1	2	yes	complemented
16	C₂×C₃×C₄₁	C₂³	1	1	yes	characteristic
17	D₃×C₄₁	C₂×C₄	1	4	yes	direct product factor
18	C₂²×C₄₁	—	3	4	no	—
19	C₂²×C₄₁	—	3	2	no	—
20	C₂²×C₄₁	C₂×D₃	1	1	yes	characteristic
21	C₄×C₄₁	—	3	2	no	—
22	C₄×C₄₁	C₂×D₃	1	2	yes	direct product factor
23	C₃×C₄₁	C₂²×C₄	1	1	yes	characteristic, complemented, Hall
24	C₂×C₄₁	—	3	4	no	—
25	C₂×C₄₁	C₄×D₃	1	2	yes	direct product factor
26	C₂×C₄₁	C₂²×D₃	1	1	yes	characteristic
27	C₂×C₄×D₃	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₄₁	C₂×C₄×D₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₂²×D₃	C₂×C₄₁	1	1	yes	characteristic
30	C₂×C₃×C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
31	C₂×Dic₃	C₂×C₄₁	1	1	yes	characteristic, complemented
32	C₄×D₃	C₂×C₄₁	1	4	yes	direct product factor
33	C₂²×C₄	—	3	1	no	Sylow
34	C₂²×C₃	C₂²×C₄₁	1	1	yes	characteristic
35	C₂×D₃	C₄×C₄₁	1	4	yes	direct product factor
36	C₂×D₃	C₂²×C₄₁	1	2	yes	—
37	C₃×C₄	C₂²×C₄₁	1	2	yes	complemented
38	Dic₃	C₂²×C₄₁	1	2	yes	complemented
39	C₂³	—	3	1	no	—
40	C₂×C₄	—	3	1	no	—
41	C₂×C₄	—	3	4	no	—
42	C₂×C₄	D₃×C₄₁	1	1	yes	characteristic, direct product factor
43	C₂×C₃	C₂×C₄×C₄₁	1	2	yes	complemented
44	C₂×C₃	C₂³×C₄₁	1	1	yes	characteristic
45	D₃	C₂×C₄×C₄₁	1	4	yes	direct product factor
46	C₂²	—	3	4	no	—
47	C₂²	—	3	2	no	—
48	C₂²	C₂×D₃×C₄₁	1	1	yes	characteristic
49	C₄	—	3	2	no	—
50	C₄	C₂×D₃×C₄₁	1	2	yes	direct product factor
51	C₃	C₂²×C₄×C₄₁	1	1	yes	characteristic, complemented, Sylow
52	C₂	—	3	4	no	—
53	C₂	C₄×D₃×C₄₁	1	2	yes	direct product factor
54	C₂	C₂²×D₃×C₄₁	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₄×C₄₁	C₂	semidirect
3. C₂×Dic₃×C₄₁	C₂	semidirect
4. C₄×D₃×C₄₁	C₂	direct (N × H)
7. C₂×D₃×C₄₁	C₄	direct (N × H)
9. C₃×C₄×C₄₁	C₂²	semidirect
10. Dic₃×C₄₁	C₂²	semidirect
14. C₂×C₄×C₄₁	D₃	direct (N × H)
15. C₂×C₃×C₄₁	C₂×C₄	semidirect
17. D₃×C₄₁	C₂×C₄	direct (N × H)
22. C₄×C₄₁	C₂×D₃	direct (N × H)
23. C₃×C₄₁	C₂²×C₄	semidirect
25. C₂×C₄₁	C₄×D₃	direct (N × H)
27. C₂×C₄×D₃	C₄₁	direct (N × H)
28. C₄₁	C₂×C₄×D₃	direct (N × H)
30. C₂×C₃×C₄	C₂×C₄₁	semidirect
31. C₂×Dic₃	C₂×C₄₁	semidirect
32. C₄×D₃	C₂×C₄₁	direct (N × H)
35. C₂×D₃	C₄×C₄₁	direct (N × H)
37. C₃×C₄	C₂²×C₄₁	semidirect
38. Dic₃	C₂²×C₄₁	semidirect
42. C₂×C₄	D₃×C₄₁	direct (N × H)
43. C₂×C₃	C₂×C₄×C₄₁	semidirect
45. D₃	C₂×C₄×C₄₁	direct (N × H)
50. C₄	C₂×D₃×C₄₁	direct (N × H)
51. C₃	C₂²×C₄×C₄₁	semidirect
53. C₂	C₄×D₃×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
C₂×Dic₃×C₄₁	2
C₄×D₃×C₄₁	2
C₂²×C₄×C₄₁	3
C₂×C₄×D₃	41

Subgroups — C2×C4×D3×C41 #14520239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×D₃×C₄₁ #14520239