Subgroups — D₃₃⋊D₁₄₁ #32915949

Order 18612.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₃⋊D₁₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₁₅₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄₇×D₃₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃₃⋊D₄₇	—	3	1	no	maximal
5	D₁₁×D₁₄₁	—	3	1	no	maximal
6	C₃²×C₁₁×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₁₅₅₁	D₃	1	1	yes	characteristic, complemented
8	C₄₇×D₃₃	D₃	1	1	yes	characteristic, complemented
9	C₁₁×D₁₄₁	—	3	1	no	—
10	C₁₁×D₁₄₁	—	3	1	no	—
11	C₁₁×D₁₄₁	—	6	1	no	—
12	C₃×D₅₁₇	—	3	1	no	—
13	C₃×D₁₁×C₄₇	—	3	1	no	—
14	D₁₁×D₄₇	—	9	1	no	Hall
15	D₃×D₁₄₁	—	11	1	no	maximal, Hall
16	C₃×C₁₁×C₄₇	—	2	1	no	—
17	C₃×C₁₁×C₄₇	C₂×D₃	1	1	yes	characteristic, complemented
18	C₃×C₁₁×C₄₇	C₂×D₃	1	1	yes	characteristic, complemented
19	D₅₁₇	—	3	1	no	—
20	C₁₁×D₄₇	—	9	1	no	—
21	D₁₁×C₄₇	—	3	1	no	—
22	C₃⋊D₁₄₁	D₁₁	1	1	yes	characteristic, complemented
23	C₃×D₁₄₁	—	11	1	no	—
24	C₃×D₃×C₄₇	—	11	1	no	—
25	C₂×D₁₄₁	—	33	1	no	—
26	D₃×D₄₇	—	33	1	no	—
27	C₁₁×C₄₇	D₃²	1	1	yes	characteristic, complemented, Hall
28	C₃²×C₄₇	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
29	(C₃⋊D₃)⋊D₁₁	—	47	1	no	maximal, Hall
30	C₂×C₃×C₄₇	—	33	1	no	—
31	D₁₄₁	—	3	1	no	—
32	D₁₄₁	—	3	1	no	—
33	D₁₄₁	—	6	1	no	—
34	D₁₄₁	—	11	1	no	—
35	C₃×D₄₇	—	33	1	no	—
36	D₃×C₄₇	—	11	1	no	—
37	C₁₁×C₃⋊D₃	—	47	1	no	—
38	C₃×D₃₃	—	47	1	no	—
39	C₃×D₃₃	D₄₇	1	1	yes	characteristic, complemented
40	C₂×D₄₇	—	99	1	no	Hall
41	C₃×C₄₇	—	2	1	no	—
42	C₃×C₄₇	D₃×D₁₁	1	1	yes	characteristic, complemented
43	C₃×C₄₇	D₃×D₁₁	1	1	yes	characteristic, complemented
44	D₃×D₁₁	—	141	1	no	—
45	D₃×D₁₁	—	141	1	no	—
46	C₃²×C₁₁	C₂×D₄₇	1	1	yes	characteristic, complemented, Hall
47	C₂×C₄₇	—	33	1	no	—
48	D₄₇	—	9	1	no	—
49	D₄₇	—	33	1	no	—
50	D₃₃	—	47	1	no	—
51	D₃₃	D₁₄₁	1	1	yes	characteristic, complemented
52	C₃×D₁₁	—	3	1	no	—
53	C₃×D₁₁	—	141	1	no	—
54	D₃×C₁₁	—	282	1	no	—
55	D₃×C₁₁	—	141	1	no	—
56	D₃×C₁₁	—	141	1	no	—
57	C₄₇	(C₃⋊D₃)⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
58	C₂×D₁₁	—	423	1	no	Hall
59	D₃²	—	517	1	no	Hall
60	C₃×C₁₁	—	2	1	no	—
61	C₃×C₁₁	D₃×D₄₇	1	1	yes	characteristic, complemented
62	C₃×C₁₁	C₂×D₁₄₁	1	1	yes	characteristic, complemented
63	C₂×C₁₁	—	423	1	no	—
64	D₁₁	—	3	1	no	—
65	D₁₁	—	141	1	no	—
66	C₃⋊D₃	—	47	1	no	—
67	C₃×D₃	—	517	1	no	—
68	C₃×D₃	—	11	1	no	—
69	C₂×D₃	—	1551	1	no	—
70	C₂×D₃	—	1551	1	no	—
71	C₁₁	D₃×D₁₄₁	1	1	yes	characteristic, complemented, Sylow
72	C₃²	D₁₁×D₄₇	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	1551	1	no	—
74	C₂×C₃	—	33	1	no	—
75	D₃	—	517	1	no	—
76	D₃	—	11	1	no	—
77	D₃	—	282	1	no	—
78	D₃	—	141	1	no	—
79	D₃	—	141	1	no	—
80	C₂²	—	4653	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₁₁×D₁₄₁	1	1	yes	characteristic, complemented
83	C₃	D₃₃⋊D₄₇	1	1	yes	characteristic, complemented
84	C₂	—	1551	1	no	—
85	C₂	—	33	1	no	—
86	C₂	—	423	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₁₁×C₄₇	C₂²
LCS	G ▷ C₃²×C₁₁×C₄₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₃⋊D₁₄₁	C₂	semidirect
2. C₃×D₁₅₅₁	C₂	semidirect
3. C₃×C₄₇×D₃₃	C₂	semidirect
6. C₃²×C₁₁×C₄₇	C₂²	semidirect
7. D₁₅₅₁	D₃	semidirect
8. C₄₇×D₃₃	D₃	semidirect
17. C₃×C₁₁×C₄₇	C₂×D₃	semidirect
18. C₃×C₁₁×C₄₇	C₂×D₃	semidirect
22. C₃⋊D₁₄₁	D₁₁	semidirect
27. C₁₁×C₄₇	D₃²	semidirect
28. C₃²×C₄₇	C₂×D₁₁	semidirect
39. C₃×D₃₃	D₄₇	semidirect
42. C₃×C₄₇	D₃×D₁₁	semidirect
43. C₃×C₄₇	D₃×D₁₁	semidirect
46. C₃²×C₁₁	C₂×D₄₇	semidirect
51. D₃₃	D₁₄₁	semidirect
57. C₄₇	(C₃⋊D₃)⋊D₁₁	semidirect
61. C₃×C₁₁	D₃×D₄₇	semidirect
62. C₃×C₁₁	C₂×D₁₄₁	semidirect
71. C₁₁	D₃×D₁₄₁	semidirect
72. C₃²	D₁₁×D₄₇	semidirect
82. C₃	D₁₁×D₁₄₁	semidirect
83. C₃	D₃₃⋊D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×C₃⋊D₁₄₁	2
C₃×D₁₅₅₁	2
C₃×C₄₇×D₃₃	2
D₃₃⋊D₄₇	3
D₁₁×D₁₄₁	3
D₃×D₁₄₁	11
(C₃⋊D₃)⋊D₁₁	47

Subgroups — D33⋊D141 #32915949

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₃⋊D₁₄₁ #32915949