Subgroups — D₂₁×D₁₄₁ #26044943

Order 11844.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₉₈₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₂₁×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×D₁₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×D₁₄₁	—	3	1	no	maximal
5	D₂₁×D₄₇	—	3	1	no	maximal
6	C₃²×C₇×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₉₈₇	—	3	1	no	—
8	D₉₈₇	—	3	1	no	—
9	D₉₈₇	—	6	1	no	—
10	D₂₁×C₄₇	D₃	1	1	yes	characteristic, complemented
11	C₇×D₁₄₁	D₃	1	1	yes	characteristic, complemented
12	C₃×D₇×C₄₇	—	3	1	no	—
13	C₃×C₇×D₄₇	—	3	1	no	—
14	D₃×D₁₄₁	—	7	1	no	maximal, Hall
15	D₇×D₄₇	—	9	1	no	Hall
16	C₃×C₇×C₄₇	—	2	1	no	—
17	C₃×C₇×C₄₇	C₂×D₃	1	1	yes	characteristic, complemented
18	C₃×C₇×C₄₇	C₂×D₃	1	1	yes	characteristic, complemented
19	C₃⋊D₁₄₁	—	7	1	no	—
20	C₃×D₁₄₁	D₇	1	1	yes	characteristic, complemented
21	C₃×D₃×C₄₇	—	7	1	no	—
22	D₃₂₉	—	9	1	no	—
23	C₇×D₄₇	—	3	1	no	—
24	D₇×C₄₇	—	3	1	no	—
25	C₂×D₁₄₁	—	21	1	no	—
26	D₃×D₄₇	—	21	1	no	—
27	C₃²×C₄₇	C₂×D₇	1	1	yes	characteristic, complemented, Hall
28	C₇×C₄₇	D₃²	1	1	yes	characteristic, complemented, Hall
29	C₂×C₃×C₄₇	—	21	1	no	—
30	D₁₄₁	—	21	1	no	—
31	D₁₄₁	—	21	1	no	—
32	D₁₄₁	—	42	1	no	—
33	D₁₄₁	D₂₁	1	1	yes	characteristic, direct product factor
34	C₃×D₄₇	—	3	1	no	—
35	D₃×C₄₇	—	7	1	no	—
36	D₃×D₂₁	—	47	1	no	maximal, Hall
37	C₂×D₄₇	—	63	1	no	Hall
38	C₃×C₄₇	—	2	1	no	—
39	C₃×C₄₇	D₃×D₇	1	1	yes	characteristic, complemented
40	C₃×C₄₇	C₂×D₂₁	1	1	yes	characteristic, complemented
41	C₃⋊D₂₁	—	47	1	no	—
42	C₃×D₂₁	D₄₇	1	1	yes	characteristic, complemented
43	C₃×D₃×C₇	—	47	1	no	—
44	C₂×C₄₇	—	21	1	no	—
45	D₄₇	—	3	1	no	—
46	D₄₇	—	63	1	no	—
47	C₂×D₂₁	—	141	1	no	—
48	D₃×D₇	—	141	1	no	—
49	C₃²×C₇	C₂×D₄₇	1	1	yes	characteristic, complemented, Hall
50	C₄₇	D₃×D₂₁	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃×C₇	—	141	1	no	—
52	D₂₁	—	282	1	no	—
53	D₂₁	—	141	1	no	—
54	D₂₁	—	141	1	no	—
55	D₂₁	D₁₄₁	1	1	yes	characteristic, direct product factor
56	C₃×D₇	—	3	1	no	—
57	D₃×C₇	—	47	1	no	—
58	D₃²	—	329	1	no	Hall
59	C₂×D₇	—	423	1	no	Hall
60	C₃×C₇	—	2	1	no	—
61	C₃×C₇	D₃×D₄₇	1	1	yes	characteristic, complemented
62	C₃×C₇	C₂×D₁₄₁	1	1	yes	characteristic, complemented
63	C₃⋊D₃	—	329	1	no	—
64	C₃×D₃	—	7	1	no	—
65	C₃×D₃	—	47	1	no	—
66	C₂×C₇	—	141	1	no	—
67	D₇	—	3	1	no	—
68	D₇	—	423	1	no	—
69	C₂×D₃	—	987	1	no	—
70	C₂×D₃	—	987	1	no	—
71	C₃²	D₇×D₄₇	1	1	yes	characteristic, complemented, Sylow
72	C₇	D₃×D₁₄₁	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	21	1	no	—
74	C₂×C₃	—	141	1	no	—
75	D₃	—	7	1	no	—
76	D₃	—	47	1	no	—
77	D₃	—	1974	1	no	—
78	D₃	—	987	1	no	—
79	D₃	—	987	1	no	—
80	C₂²	—	2961	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₂₁×D₄₇	1	1	yes	characteristic, complemented
83	C₃	D₇×D₁₄₁	1	1	yes	characteristic, complemented
84	C₂	—	21	1	no	—
85	C₂	—	141	1	no	—
86	C₂	—	2961	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₇×C₄₇	C₂²
LCS	G ▷ C₃²×C₇×C₄₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₉₈₇	C₂	semidirect
2. C₃×D₂₁×C₄₇	C₂	semidirect
3. C₃×C₇×D₁₄₁	C₂	semidirect
6. C₃²×C₇×C₄₇	C₂²	semidirect
10. D₂₁×C₄₇	D₃	semidirect
11. C₇×D₁₄₁	D₃	semidirect
17. C₃×C₇×C₄₇	C₂×D₃	semidirect
18. C₃×C₇×C₄₇	C₂×D₃	semidirect
20. C₃×D₁₄₁	D₇	semidirect
27. C₃²×C₄₇	C₂×D₇	semidirect
28. C₇×C₄₇	D₃²	semidirect
33. D₁₄₁	D₂₁	direct (N × H)
39. C₃×C₄₇	D₃×D₇	semidirect
40. C₃×C₄₇	C₂×D₂₁	semidirect
42. C₃×D₂₁	D₄₇	semidirect
49. C₃²×C₇	C₂×D₄₇	semidirect
50. C₄₇	D₃×D₂₁	semidirect
55. D₂₁	D₁₄₁	direct (N × H)
61. C₃×C₇	D₃×D₄₇	semidirect
62. C₃×C₇	C₂×D₁₄₁	semidirect
71. C₃²	D₇×D₄₇	semidirect
72. C₇	D₃×D₁₄₁	semidirect
82. C₃	D₂₁×D₄₇	semidirect
83. C₃	D₇×D₁₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊D₉₈₇	2
C₃×D₂₁×C₄₇	2
C₃×C₇×D₁₄₁	2
D₇×D₁₄₁	3
D₂₁×D₄₇	3
D₃×D₁₄₁	7
D₃×D₂₁	47

Subgroups — D21×D141 #26044943

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₁×D₁₄₁ #26044943