Subgroups — D₅₇⋊D₁₄₁ #44565340

Order 32148.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₇×D₅₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₂₆₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×C₃⋊D₁₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅₇⋊D₄₇	—	3	1	no	maximal
5	D₁₉×D₁₄₁	—	3	1	no	maximal
6	C₃²×C₁₉×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₂₆₇₉	D₃	1	1	yes	characteristic, complemented
8	C₄₇×D₅₇	D₃	1	1	yes	characteristic, complemented
9	C₁₉×D₁₄₁	—	3	1	no	—
10	C₁₉×D₁₄₁	—	3	1	no	—
11	C₁₉×D₁₄₁	—	6	1	no	—
12	C₃×D₈₉₃	—	3	1	no	—
13	C₃×D₁₉×C₄₇	—	3	1	no	—
14	D₁₉×D₄₇	—	9	1	no	Hall
15	C₃×C₁₉×C₄₇	—	2	1	no	—
16	C₃×C₁₉×C₄₇	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₁₉×C₄₇	C₂×D₃	1	1	yes	characteristic, complemented
18	D₈₉₃	—	3	1	no	—
19	C₁₉×D₄₇	—	9	1	no	—
20	D₁₉×C₄₇	—	3	1	no	—
21	D₃×D₁₄₁	—	19	1	no	maximal, Hall
22	C₁₉×C₄₇	D₃²	1	1	yes	characteristic, complemented, Hall
23	C₃⋊D₁₄₁	D₁₉	1	1	yes	characteristic, complemented
24	C₃×D₁₄₁	—	19	1	no	—
25	C₃×D₃×C₄₇	—	19	1	no	—
26	(C₃⋊D₃)⋊D₁₉	—	47	1	no	maximal, Hall
27	C₂×D₁₄₁	—	57	1	no	—
28	D₃×D₄₇	—	57	1	no	—
29	C₃²×C₄₇	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
30	C₃⋊D₃×C₁₉	—	47	1	no	—
31	C₃×D₅₇	—	47	1	no	—
32	C₃×D₅₇	D₄₇	1	1	yes	characteristic, complemented
33	C₂×C₃×C₄₇	—	57	1	no	—
34	D₁₄₁	—	3	1	no	—
35	D₁₄₁	—	3	1	no	—
36	D₁₄₁	—	6	1	no	—
37	D₁₄₁	—	19	1	no	—
38	C₃×D₄₇	—	57	1	no	—
39	D₃×C₄₇	—	19	1	no	—
40	D₃×D₁₉	—	141	1	no	—
41	D₃×D₁₉	—	141	1	no	—
42	C₂×D₄₇	—	171	1	no	Hall
43	C₃²×C₁₉	C₂×D₄₇	1	1	yes	characteristic, complemented, Hall
44	C₃×C₄₇	—	2	1	no	—
45	C₃×C₄₇	D₃×D₁₉	1	1	yes	characteristic, complemented
46	C₃×C₄₇	D₃×D₁₉	1	1	yes	characteristic, complemented
47	D₅₇	—	47	1	no	—
48	D₅₇	D₁₄₁	1	1	yes	characteristic, complemented
49	C₃×D₁₉	—	3	1	no	—
50	C₃×D₁₉	—	141	1	no	—
51	D₃×C₁₉	—	282	1	no	—
52	D₃×C₁₉	—	141	1	no	—
53	D₃×C₁₉	—	141	1	no	—
54	C₂×C₄₇	—	57	1	no	—
55	D₄₇	—	9	1	no	—
56	D₄₇	—	57	1	no	—
57	C₂×D₁₉	—	423	1	no	Hall
58	C₃×C₁₉	—	2	1	no	—
59	C₃×C₁₉	D₃×D₄₇	1	1	yes	characteristic, complemented
60	C₃×C₁₉	C₂×D₁₄₁	1	1	yes	characteristic, complemented
61	C₄₇	(C₃⋊D₃)⋊D₁₉	1	1	yes	characteristic, complemented, Sylow
62	C₂×C₁₉	—	423	1	no	—
63	D₁₉	—	3	1	no	—
64	D₁₉	—	141	1	no	—
65	D₃²	—	893	1	no	Hall
66	C₁₉	D₃×D₁₄₁	1	1	yes	characteristic, complemented, Sylow
67	C₃⋊D₃	—	47	1	no	—
68	C₃×D₃	—	19	1	no	—
69	C₃×D₃	—	893	1	no	—
70	C₂×D₃	—	2679	1	no	—
71	C₂×D₃	—	2679	1	no	—
72	C₃²	D₁₉×D₄₇	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	57	1	no	—
74	C₂×C₃	—	2679	1	no	—
75	D₃	—	19	1	no	—
76	D₃	—	282	1	no	—
77	D₃	—	893	1	no	—
78	D₃	—	141	1	no	—
79	D₃	—	141	1	no	—
80	C₂²	—	8037	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₁₉×D₁₄₁	1	1	yes	characteristic, complemented
83	C₃	D₅₇⋊D₄₇	1	1	yes	characteristic, complemented
84	C₂	—	57	1	no	—
85	C₂	—	2679	1	no	—
86	C₂	—	423	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₁₉×C₄₇	C₂²
LCS	G ▷ C₃²×C₁₉×C₄₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₄₇×D₅₇	C₂	semidirect
2. C₃×D₂₆₇₉	C₂	semidirect
3. C₁₉×C₃⋊D₁₄₁	C₂	semidirect
6. C₃²×C₁₉×C₄₇	C₂²	semidirect
7. D₂₆₇₉	D₃	semidirect
8. C₄₇×D₅₇	D₃	semidirect
16. C₃×C₁₉×C₄₇	C₂×D₃	semidirect
17. C₃×C₁₉×C₄₇	C₂×D₃	semidirect
22. C₁₉×C₄₇	D₃²	semidirect
23. C₃⋊D₁₄₁	D₁₉	semidirect
29. C₃²×C₄₇	C₂×D₁₉	semidirect
32. C₃×D₅₇	D₄₇	semidirect
43. C₃²×C₁₉	C₂×D₄₇	semidirect
45. C₃×C₄₇	D₃×D₁₉	semidirect
46. C₃×C₄₇	D₃×D₁₉	semidirect
48. D₅₇	D₁₄₁	semidirect
59. C₃×C₁₉	D₃×D₄₇	semidirect
60. C₃×C₁₉	C₂×D₁₄₁	semidirect
61. C₄₇	(C₃⋊D₃)⋊D₁₉	semidirect
66. C₁₉	D₃×D₁₄₁	semidirect
72. C₃²	D₁₉×D₄₇	semidirect
82. C₃	D₁₉×D₁₄₁	semidirect
83. C₃	D₅₇⋊D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄₇×D₅₇	2
C₃×D₂₆₇₉	2
C₁₉×C₃⋊D₁₄₁	2
D₅₇⋊D₄₇	3
D₁₉×D₁₄₁	3
D₃×D₁₄₁	19
(C₃⋊D₃)⋊D₁₉	47

Subgroups — D57⋊D141 #44565340

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₇⋊D₁₄₁ #44565340