Subgroups — C₂×C₃×C₄×D₄₁ #14520229

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	1	yes	maximal, characteristic
2	C₂×C₃×C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×Dic₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄×D₄₁	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₄×D₄₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂²×C₃×C₄₁	C₂²	1	1	yes	characteristic
7	C₂×C₃×D₄₁	C₄	1	4	yes	direct product factor
8	C₂×C₃×D₄₁	C₂²	1	2	yes	—
9	C₃×C₄×C₄₁	C₂²	1	2	yes	complemented
10	C₃×Dic₄₁	C₂²	1	2	yes	complemented
11	C₂²×D₄₁	C₂×C₃	1	1	yes	characteristic
12	C₂×C₄×C₄₁	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂×Dic₄₁	C₂×C₃	1	1	yes	characteristic, complemented
14	C₄×D₄₁	C₂×C₃	1	4	yes	direct product factor
15	C₂×C₃×C₄₁	C₂×C₄	1	2	yes	complemented
16	C₂×C₃×C₄₁	C₂³	1	1	yes	characteristic
17	C₃×D₄₁	C₂×C₄	1	4	yes	direct product factor
18	C₂²×C₄₁	C₂²×C₃	1	1	yes	characteristic
19	C₂×D₄₁	C₃×C₄	1	4	yes	direct product factor
20	C₂×D₄₁	C₂²×C₃	1	2	yes	—
21	C₄×C₄₁	C₂²×C₃	1	2	yes	complemented
22	Dic₄₁	C₂²×C₃	1	2	yes	complemented
23	C₃×C₄₁	C₂²×C₄	1	1	yes	characteristic, complemented, Hall
24	C₂×C₄₁	C₂×C₃×C₄	1	2	yes	complemented
25	C₂×C₄₁	C₂³×C₃	1	1	yes	characteristic
26	D₄₁	C₂×C₃×C₄	1	4	yes	direct product factor
27	C₂²×C₃×C₄	—	41	1	no	maximal, Hall
28	C₄₁	C₂²×C₃×C₄	1	1	yes	characteristic, complemented, Sylow
29	C₂³×C₃	—	41	1	no	—
30	C₂×C₃×C₄	—	41	1	no	—
31	C₂×C₃×C₄	—	41	4	no	—
32	C₂×C₃×C₄	D₄₁	1	1	yes	characteristic, direct product factor
33	C₂²×C₄	—	41	1	no	Sylow
34	C₂²×C₃	—	41	4	no	—
35	C₂²×C₃	—	41	2	no	—
36	C₂²×C₃	C₂×D₄₁	1	1	yes	characteristic
37	C₃×C₄	—	41	2	no	—
38	C₃×C₄	C₂×D₄₁	1	2	yes	direct product factor
39	C₂³	—	41	1	no	—
40	C₂×C₄	—	41	1	no	—
41	C₂×C₄	—	41	4	no	—
42	C₂×C₄	C₃×D₄₁	1	1	yes	characteristic, direct product factor
43	C₂×C₃	—	41	4	no	—
44	C₂×C₃	C₄×D₄₁	1	2	yes	direct product factor
45	C₂×C₃	C₂²×D₄₁	1	1	yes	characteristic
46	C₂²	—	41	4	no	—
47	C₂²	—	41	2	no	—
48	C₂²	C₂×C₃×D₄₁	1	1	yes	characteristic
49	C₄	—	41	2	no	—
50	C₄	C₂×C₃×D₄₁	1	2	yes	direct product factor
51	C₃	C₂×C₄×D₄₁	1	1	yes	characteristic, direct product factor, Sylow
52	C₂	—	41	4	no	—
53	C₂	C₃×C₄×D₄₁	1	2	yes	direct product factor
54	C₂	C₂²×C₃×D₄₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₄	D₄₁
commutator, hypocenter	C₄₁	C₂²×C₃×C₄
Frattini	C₂	C₂²×C₃×D₄₁
Fitting	C₂×C₃×C₄×C₄₁	C₂
socle	C₂²×C₃×C₄₁	C₂²
prime radical	C₂²×C₃×D₄₁	C₂
cosocle	C₂×C₄₁	C₂³×C₃
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₂×C₃×C₄

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×C₃×Dic₄₁	C₂	semidirect
4. C₃×C₄×D₄₁	C₂	direct (N × H)
5. C₂×C₄×D₄₁	C₃	direct (N × H)
7. C₂×C₃×D₄₁	C₄	direct (N × H)
9. C₃×C₄×C₄₁	C₂²	semidirect
10. C₃×Dic₄₁	C₂²	semidirect
12. C₂×C₄×C₄₁	C₂×C₃	semidirect
13. C₂×Dic₄₁	C₂×C₃	semidirect
14. C₄×D₄₁	C₂×C₃	direct (N × H)
15. C₂×C₃×C₄₁	C₂×C₄	semidirect
17. C₃×D₄₁	C₂×C₄	direct (N × H)
19. C₂×D₄₁	C₃×C₄	direct (N × H)
21. C₄×C₄₁	C₂²×C₃	semidirect
22. Dic₄₁	C₂²×C₃	semidirect
23. C₃×C₄₁	C₂²×C₄	semidirect
24. C₂×C₄₁	C₂×C₃×C₄	semidirect
26. D₄₁	C₂×C₃×C₄	direct (N × H)
28. C₄₁	C₂²×C₃×C₄	semidirect
32. C₂×C₃×C₄	D₄₁	direct (N × H)
38. C₃×C₄	C₂×D₄₁	direct (N × H)
42. C₂×C₄	C₃×D₄₁	direct (N × H)
44. C₂×C₃	C₄×D₄₁	direct (N × H)
50. C₄	C₂×C₃×D₄₁	direct (N × H)
51. C₃	C₂×C₄×D₄₁	direct (N × H)
53. C₂	C₃×C₄×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
C₂×C₃×C₄×C₄₁	2
C₂×C₃×Dic₄₁	2
C₃×C₄×D₄₁	2
C₂×C₄×D₄₁	3
C₂²×C₃×C₄	41

Subgroups — C2×C3×C4×D41 #14520229

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₄×D₄₁ #14520229