Subgroups — C₃×D₄×D₄₁ #14520232

Order 1968.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₄₁	C₂	1	2	yes	maximal, complemented
2	C₃×D₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₂²⋊D₄₁	C₂	1	2	yes	maximal, complemented
4	C₃×D₁₆₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×D₄₁	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄×D₄₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₄₁	C₂²	1	2	yes	complemented
8	C₂×C₃×D₄₁	—	2	4	no	—
9	C₂×C₃×D₄₁	C₂²	1	1	yes	characteristic
10	C₂×C₃×D₄₁	C₂²	1	2	yes	complemented
11	C₃×C₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
12	C₃×Dic₄₁	C₂²	1	1	yes	characteristic, complemented
13	C₂²×D₄₁	C₂×C₃	1	2	yes	complemented
14	D₄×C₄₁	C₂×C₃	1	1	yes	characteristic, complemented
15	C₂²⋊D₄₁	C₂×C₃	1	2	yes	complemented
16	D₁₆₄	C₂×C₃	1	1	yes	characteristic, complemented
17	C₄×D₄₁	C₂×C₃	1	1	yes	characteristic, complemented
18	C₂×C₃×C₄₁	—	2	2	no	—
19	C₂×C₃×C₄₁	C₂³	1	1	yes	characteristic
20	C₃×D₄₁	—	2	2	no	—
21	C₃×D₄₁	D₄	1	2	yes	direct product factor
22	C₂²×C₄₁	C₂²×C₃	1	2	yes	complemented
23	C₂×D₄₁	—	2	4	no	—
24	C₂×D₄₁	C₂²×C₃	1	1	yes	characteristic
25	C₂×D₄₁	C₂²×C₃	1	2	yes	complemented
26	C₄×C₄₁	C₂²×C₃	1	1	yes	characteristic, complemented
27	Dic₄₁	C₂²×C₃	1	1	yes	characteristic, complemented
28	C₃×C₄₁	C₂×D₄	1	1	yes	characteristic, complemented, Hall
29	C₂×C₄₁	—	2	2	no	—
30	C₂×C₄₁	C₂³×C₃	1	1	yes	characteristic
31	D₄₁	—	2	2	no	—
32	D₄₁	C₃×D₄	1	2	yes	direct product factor
33	C₂×C₃×D₄	—	41	1	no	maximal, Hall
34	C₄₁	C₂×C₃×D₄	1	1	yes	characteristic, complemented, Sylow
35	C₂³×C₃	—	41	2	no	—
36	C₃×D₄	—	41	2	no	—
37	C₃×D₄	—	41	1	no	—
38	C₃×D₄	D₄₁	1	1	yes	characteristic, direct product factor
39	C₂×C₃×C₄	—	41	1	no	—
40	C₂×D₄	—	41	1	no	Sylow
41	C₂²×C₃	—	41	1	no	—
42	C₂²×C₃	—	41	2	no	—
43	C₂²×C₃	—	82	4	no	—
44	C₂²×C₃	C₂×D₄₁	1	2	yes	complemented
45	C₃×C₄	—	41	1	no	—
46	C₃×C₄	C₂×D₄₁	1	1	yes	characteristic, complemented
47	C₂³	—	41	2	no	—
48	D₄	—	41	2	no	—
49	D₄	—	41	1	no	—
50	D₄	C₃×D₄₁	1	1	yes	characteristic, direct product factor
51	C₂×C₄	—	41	1	no	—
52	C₂×C₃	—	2	2	no	—
53	C₂×C₃	—	41	2	no	—
54	C₂×C₃	—	82	2	no	—
55	C₂×C₃	C₂²×D₄₁	1	1	yes	characteristic
56	C₂²	—	41	1	no	—
57	C₂²	—	41	2	no	—
58	C₂²	—	82	4	no	—
59	C₂²	C₂×C₃×D₄₁	1	2	yes	complemented
60	C₄	—	41	1	no	—
61	C₄	C₂×C₃×D₄₁	1	1	yes	characteristic, complemented
62	C₃	D₄×D₄₁	1	1	yes	characteristic, direct product factor, Sylow
63	C₂	—	2	2	no	—
64	C₂	—	41	2	no	—
65	C₂	—	82	2	no	—
66	C₂	C₂²×C₃×D₄₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂²×D₄₁
commutator, cosocle	C₂×C₄₁	C₂³×C₃
Frattini	C₂	C₂²×C₃×D₄₁
Fitting	C₃×D₄×C₄₁	C₂
socle	C₂×C₃×C₄₁	C₂³
hypercenter	C₃×D₄	D₄₁
hypocenter	C₄₁	C₂×C₃×D₄
LCS	G ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂×C₃ ◁ C₃×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×D₄₁	C₂	semidirect
2. C₃×D₄×C₄₁	C₂	semidirect
3. C₃×C₂²⋊D₄₁	C₂	semidirect
4. C₃×D₁₆₄	C₂	semidirect
5. C₃×C₄×D₄₁	C₂	semidirect
6. D₄×D₄₁	C₃	direct (N × H)
7. C₂²×C₃×C₄₁	C₂²	semidirect
10. C₂×C₃×D₄₁	C₂²	semidirect
11. C₃×C₄×C₄₁	C₂²	semidirect
12. C₃×Dic₄₁	C₂²	semidirect
13. C₂²×D₄₁	C₂×C₃	semidirect
14. D₄×C₄₁	C₂×C₃	semidirect
15. C₂²⋊D₄₁	C₂×C₃	semidirect
16. D₁₆₄	C₂×C₃	semidirect
17. C₄×D₄₁	C₂×C₃	semidirect
21. C₃×D₄₁	D₄	direct (N × H)
22. C₂²×C₄₁	C₂²×C₃	semidirect
25. C₂×D₄₁	C₂²×C₃	semidirect
26. C₄×C₄₁	C₂²×C₃	semidirect
27. Dic₄₁	C₂²×C₃	semidirect
28. C₃×C₄₁	C₂×D₄	semidirect
32. D₄₁	C₃×D₄	direct (N × H)
34. C₄₁	C₂×C₃×D₄	semidirect
38. C₃×D₄	D₄₁	direct (N × H)
44. C₂²×C₃	C₂×D₄₁	semidirect
46. C₃×C₄	C₂×D₄₁	semidirect
50. D₄	C₃×D₄₁	direct (N × H)
59. C₂²	C₂×C₃×D₄₁	semidirect
61. C₄	C₂×C₃×D₄₁	semidirect
62. C₃	D₄×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×C₃×D₄₁	2
C₃×D₄×C₄₁	2
C₃×C₂²⋊D₄₁	2
C₃×D₁₆₄	2
C₃×C₄×D₄₁	2
D₄×D₄₁	3
C₂×C₃×D₄	41

Subgroups — C3×D4×D41 #14520232

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₄×D₄₁ #14520232