Subgroups — D₁₄₁⋊D₅₇ #44565337

Order 32148.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×D₁₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₂₆₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×C₃⋊D₅₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅₇⋊D₄₇	—	3	1	no	maximal
5	D₄₇×D₅₇	—	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	—	3	1	no	—
9	C₄₇×D₅₇	—	3	1	no	—
10	C₄₇×D₅₇	—	6	1	no	—
11	C₁₉×D₁₄₁	D₃	1	1	yes	characteristic, complemented
12	C₃×D₈₉₃	—	3	1	no	—
13	C₃×C₁₉×D₄₇	—	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	—	3	1	no	—
20	D₁₉×C₄₇	—	9	1	no	—
21	(C₃⋊D₃)⋊D₄₇	—	19	1	no	maximal, Hall
22	C₁₉×C₄₇	D₃²	1	1	yes	characteristic, complemented, Hall
23	C₃⋊D₃×C₄₇	—	19	1	no	—
24	C₃×D₁₄₁	—	19	1	no	—
25	C₃×D₁₄₁	D₁₉	1	1	yes	characteristic, complemented
26	D₃×D₅₇	—	47	1	no	maximal, Hall
27	D₃×D₄₇	—	57	1	no	—
28	D₃×D₄₇	—	57	1	no	—
29	C₃²×C₄₇	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
30	C₃⋊D₅₇	D₄₇	1	1	yes	characteristic, complemented
31	C₃×D₅₇	—	47	1	no	—
32	C₃×D₃×C₁₉	—	47	1	no	—
33	D₁₄₁	—	19	1	no	—
34	D₁₄₁	D₅₇	1	1	yes	characteristic, complemented
35	C₃×D₄₇	—	3	1	no	—
36	C₃×D₄₇	—	57	1	no	—
37	D₃×C₄₇	—	57	1	no	—
38	D₃×C₄₇	—	57	1	no	—
39	D₃×C₄₇	—	114	1	no	—
40	C₂×D₅₇	—	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	C₂×D₅₇	1	1	yes	characteristic, complemented
47	C₂×C₃×C₁₉	—	141	1	no	—
48	D₅₇	—	3	1	no	—
49	D₅₇	—	3	1	no	—
50	D₅₇	—	6	1	no	—
51	D₅₇	—	47	1	no	—
52	C₃×D₁₉	—	141	1	no	—
53	D₃×C₁₉	—	47	1	no	—
54	C₂×C₄₇	—	171	1	no	—
55	D₄₇	—	3	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	D₃×D₄₇	1	1	yes	characteristic, complemented
61	C₄₇	D₃×D₅₇	1	1	yes	characteristic, complemented, Sylow
62	C₂×C₁₉	—	141	1	no	—
63	D₁₉	—	9	1	no	—
64	D₁₉	—	141	1	no	—
65	D₃²	—	893	1	no	Hall
66	C₁₉	(C₃⋊D₃)⋊D₄₇	1	1	yes	characteristic, complemented, Sylow
67	C₃⋊D₃	—	19	1	no	—
68	C₃×D₃	—	47	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	—	2679	1	no	—
74	C₂×C₃	—	141	1	no	—
75	D₃	—	47	1	no	—
76	D₃	—	57	1	no	—
77	D₃	—	57	1	no	—
78	D₃	—	114	1	no	—
79	D₃	—	893	1	no	—
80	C₂²	—	8037	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₄₇×D₅₇	1	1	yes	characteristic, complemented
83	C₃	D₅₇⋊D₄₇	1	1	yes	characteristic, complemented
84	C₂	—	2679	1	no	—
85	C₂	—	141	1	no	—
86	C₂	—	171	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×C₁₉×D₁₄₁	C₂	semidirect
2. C₃×D₂₆₇₉	C₂	semidirect
3. C₄₇×C₃⋊D₅₇	C₂	semidirect
6. C₃²×C₁₉×C₄₇	C₂²	semidirect
7. D₂₆₇₉	D₃	semidirect
11. C₁₉×D₁₄₁	D₃	semidirect
16. C₃×C₁₉×C₄₇	C₂×D₃	semidirect
17. C₃×C₁₉×C₄₇	C₂×D₃	semidirect
22. C₁₉×C₄₇	D₃²	semidirect
25. C₃×D₁₄₁	D₁₉	semidirect
29. C₃²×C₄₇	C₂×D₁₉	semidirect
30. C₃⋊D₅₇	D₄₇	semidirect
34. D₁₄₁	D₅₇	semidirect
43. C₃²×C₁₉	C₂×D₄₇	semidirect
45. C₃×C₄₇	D₃×D₁₉	semidirect
46. C₃×C₄₇	C₂×D₅₇	semidirect
59. C₃×C₁₉	D₃×D₄₇	semidirect
60. C₃×C₁₉	D₃×D₄₇	semidirect
61. C₄₇	D₃×D₅₇	semidirect
66. C₁₉	(C₃⋊D₃)⋊D₄₇	semidirect
72. C₃²	D₁₉×D₄₇	semidirect
82. C₃	D₄₇×D₅₇	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×C₁₉×D₁₄₁	2
C₃×D₂₆₇₉	2
C₄₇×C₃⋊D₅₇	2
D₅₇⋊D₄₇	3
D₄₇×D₅₇	3
(C₃⋊D₃)⋊D₄₇	19
D₃×D₅₇	47

Subgroups — D141⋊D57 #44565337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₄₁⋊D₅₇ #44565337