Subgroups — C₄₁×#237 #14520243

Order 1968.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	#67×C₄₁	C₂	1	2	yes	maximal, complemented
3	C₂×Dic₃×C₄₁	C₂	1	2	yes	maximal, complemented
4	C₄×D₃×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₆×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#41×C₄₁	—	3	1	no	maximal, Hall
7	C₂²×C₃×C₄₁	C₂²	1	2	yes	—
8	C₂×D₃×C₄₁	C₂²	1	1	yes	characteristic
9	C₃×C₄×C₄₁	C₂²	1	1	yes	characteristic
10	Dic₃×C₄₁	C₂²	1	2	yes	—
11	Dic₃×C₄₁	C₂²	1	1	yes	characteristic
12	Q₈×C₄₁	—	3	1	no	—
13	D₄×C₄₁	—	3	2	no	—
14	D₄×C₄₁	D₃	1	1	yes	characteristic, complemented
15	C₂×C₄×C₄₁	—	3	2	no	—
16	C₂×C₄×C₄₁	—	3	1	no	—
17	C₂×C₃×C₄₁	—	2	2	no	—
18	C₂×C₃×C₄₁	C₂³	1	1	yes	characteristic
19	D₃×C₄₁	—	2	1	no	—
20	C₂²×C₄₁	—	3	1	no	—
21	C₂²×C₄₁	C₂×D₃	1	2	yes	—
22	C₄×C₄₁	—	3	1	no	—
23	C₄×C₄₁	—	3	2	no	—
24	C₄×C₄₁	C₂×D₃	1	1	yes	characteristic
25	C₃×C₄₁	#41	1	1	yes	characteristic, complemented, Hall
26	C₂×C₄₁	—	2	2	no	—
27	C₂×C₄₁	—	6	1	no	—
28	C₂×C₄₁	C₂²×D₃	1	1	yes	characteristic
29	#237	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
30	C₄₁	#237	1	1	yes	characteristic, direct product factor, Sylow
31	C₃×D₄	C₂×C₄₁	1	1	yes	characteristic, complemented
32	#67	C₂×C₄₁	1	2	yes	complemented
33	C₂×Dic₃	C₂×C₄₁	1	2	yes	complemented
34	C₄×D₃	C₂×C₄₁	1	1	yes	characteristic, complemented
35	Dic₆	C₂×C₄₁	1	1	yes	characteristic, complemented
36	#41	—	3	1	no	Sylow
37	C₂²×C₃	C₂²×C₄₁	1	2	yes	—
38	C₂×D₃	C₂²×C₄₁	1	1	yes	characteristic
39	C₃×C₄	C₂²×C₄₁	1	1	yes	characteristic
40	Dic₃	C₂²×C₄₁	1	2	yes	—
41	Dic₃	C₂²×C₄₁	1	1	yes	characteristic
42	Q₈	—	3	1	no	—
43	D₄	—	3	2	no	—
44	D₄	D₃×C₄₁	1	1	yes	characteristic, complemented
45	C₂×C₄	—	3	2	no	—
46	C₂×C₄	—	3	1	no	—
47	C₂×C₃	—	2	2	no	—
48	C₂×C₃	C₂³×C₄₁	1	1	yes	characteristic
49	D₃	—	2	1	no	—
50	C₂²	—	3	1	no	—
51	C₂²	C₂×D₃×C₄₁	1	2	yes	—
52	C₄	—	3	1	no	—
53	C₄	—	3	2	no	—
54	C₄	C₂×D₃×C₄₁	1	1	yes	characteristic
55	C₃	#41×C₄₁	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	2	2	no	—
57	C₂	—	6	1	no	—
58	C₂	C₂²×D₃×C₄₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄₁	C₂²×D₃
commutator, cosocle	C₂×C₃	C₂³×C₄₁
Frattini	C₂	C₂²×D₃×C₄₁
Fitting	C₃×D₄×C₄₁	C₂
socle	C₂×C₃×C₄₁	C₂³
hypercenter	D₄×C₄₁	D₃
hypocenter	C₃	#41×C₄₁
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄₁ ◁ D₄×C₄₁

Complements

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

N	H ≅ G/N	type
1. C₃×D₄×C₄₁	C₂	semidirect
2. #67×C₄₁	C₂	semidirect
3. C₂×Dic₃×C₄₁	C₂	semidirect
4. C₄×D₃×C₄₁	C₂	semidirect
5. Dic₆×C₄₁	C₂	semidirect
14. D₄×C₄₁	D₃	semidirect
25. C₃×C₄₁	#41	semidirect
29. #237	C₄₁	direct (N × H)
30. C₄₁	#237	direct (N × H)
31. C₃×D₄	C₂×C₄₁	semidirect
32. #67	C₂×C₄₁	semidirect
33. C₂×Dic₃	C₂×C₄₁	semidirect
34. C₄×D₃	C₂×C₄₁	semidirect
35. Dic₆	C₂×C₄₁	semidirect
44. D₄	D₃×C₄₁	semidirect
55. C₃	#41×C₄₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×D₄×C₄₁	2
#67×C₄₁	2
C₂×Dic₃×C₄₁	2
C₄×D₃×C₄₁	2
Dic₆×C₄₁	2
#41×C₄₁	3
#237	41

Subgroups — C41×#237 #14520243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#237 #14520243