Subgroups — D₃₃⋊D₂₀₁ #40997705

Order 26532.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₃₃×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₂₂₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×C₃⋊D₂₀₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃₃⋊D₆₇	—	3	1	no	maximal
5	D₁₁×D₂₀₁	—	3	1	no	maximal
6	C₃²×C₁₁×C₆₇	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₂₂₁₁	D₃	1	1	yes	characteristic, complemented
8	D₃₃×C₆₇	D₃	1	1	yes	characteristic, complemented
9	C₁₁×D₂₀₁	—	3	1	no	—
10	C₁₁×D₂₀₁	—	3	1	no	—
11	C₁₁×D₂₀₁	—	6	1	no	—
12	C₃×D₇₃₇	—	3	1	no	—
13	C₃×D₁₁×C₆₇	—	3	1	no	—
14	D₁₁×D₆₇	—	9	1	no	Hall
15	D₃×D₂₀₁	—	11	1	no	maximal, Hall
16	C₃×C₁₁×C₆₇	—	2	1	no	—
17	C₃×C₁₁×C₆₇	C₂×D₃	1	1	yes	characteristic, complemented
18	C₃×C₁₁×C₆₇	C₂×D₃	1	1	yes	characteristic, complemented
19	D₇₃₇	—	3	1	no	—
20	C₁₁×D₆₇	—	9	1	no	—
21	D₁₁×C₆₇	—	3	1	no	—
22	C₃⋊D₂₀₁	D₁₁	1	1	yes	characteristic, complemented
23	C₃×D₂₀₁	—	11	1	no	—
24	C₃×D₃×C₆₇	—	11	1	no	—
25	C₂×D₂₀₁	—	33	1	no	—
26	D₃×D₆₇	—	33	1	no	—
27	C₁₁×C₆₇	D₃²	1	1	yes	characteristic, complemented, Hall
28	C₃²×C₆₇	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
29	C₂×C₃×C₆₇	—	33	1	no	—
30	D₂₀₁	—	3	1	no	—
31	D₂₀₁	—	3	1	no	—
32	D₂₀₁	—	6	1	no	—
33	D₂₀₁	—	11	1	no	—
34	C₃×D₆₇	—	33	1	no	—
35	D₃×C₆₇	—	11	1	no	—
36	(C₃⋊D₃)⋊D₁₁	—	67	1	no	maximal, Hall
37	C₂×D₆₇	—	99	1	no	Hall
38	C₃×C₆₇	—	2	1	no	—
39	C₃×C₆₇	D₃×D₁₁	1	1	yes	characteristic, complemented
40	C₃×C₆₇	D₃×D₁₁	1	1	yes	characteristic, complemented
41	C₁₁×C₃⋊D₃	—	67	1	no	—
42	C₃×D₃₃	—	67	1	no	—
43	C₃×D₃₃	D₆₇	1	1	yes	characteristic, complemented
44	C₂×C₆₇	—	33	1	no	—
45	D₆₇	—	9	1	no	—
46	D₆₇	—	33	1	no	—
47	D₃×D₁₁	—	201	1	no	—
48	D₃×D₁₁	—	201	1	no	—
49	C₃²×C₁₁	C₂×D₆₇	1	1	yes	characteristic, complemented, Hall
50	C₆₇	(C₃⋊D₃)⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
51	D₃₃	—	67	1	no	—
52	D₃₃	D₂₀₁	1	1	yes	characteristic, complemented
53	C₃×D₁₁	—	3	1	no	—
54	C₃×D₁₁	—	201	1	no	—
55	D₃×C₁₁	—	402	1	no	—
56	D₃×C₁₁	—	201	1	no	—
57	D₃×C₁₁	—	201	1	no	—
58	C₂×D₁₁	—	603	1	no	Hall
59	D₃²	—	737	1	no	Hall
60	C₃×C₁₁	—	2	1	no	—
61	C₃×C₁₁	D₃×D₆₇	1	1	yes	characteristic, complemented
62	C₃×C₁₁	C₂×D₂₀₁	1	1	yes	characteristic, complemented
63	C₂×C₁₁	—	603	1	no	—
64	D₁₁	—	3	1	no	—
65	D₁₁	—	201	1	no	—
66	C₃⋊D₃	—	67	1	no	—
67	C₃×D₃	—	11	1	no	—
68	C₃×D₃	—	737	1	no	—
69	C₂×D₃	—	2211	1	no	—
70	C₂×D₃	—	2211	1	no	—
71	C₁₁	D₃×D₂₀₁	1	1	yes	characteristic, complemented, Sylow
72	C₃²	D₁₁×D₆₇	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	33	1	no	—
74	C₂×C₃	—	2211	1	no	—
75	D₃	—	11	1	no	—
76	D₃	—	402	1	no	—
77	D₃	—	201	1	no	—
78	D₃	—	201	1	no	—
79	D₃	—	737	1	no	—
80	C₂²	—	6633	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₁₁×D₂₀₁	1	1	yes	characteristic, complemented
83	C₃	D₃₃⋊D₆₇	1	1	yes	characteristic, complemented
84	C₂	—	33	1	no	—
85	C₂	—	603	1	no	—
86	C₂	—	2211	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₁₁×C₆₇	C₂²
LCS	G ▷ C₃²×C₁₁×C₆₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×D₃₃×C₆₇	C₂	semidirect
2. C₃×D₂₂₁₁	C₂	semidirect
3. C₁₁×C₃⋊D₂₀₁	C₂	semidirect
6. C₃²×C₁₁×C₆₇	C₂²	semidirect
7. D₂₂₁₁	D₃	semidirect
8. D₃₃×C₆₇	D₃	semidirect
17. C₃×C₁₁×C₆₇	C₂×D₃	semidirect
18. C₃×C₁₁×C₆₇	C₂×D₃	semidirect
22. C₃⋊D₂₀₁	D₁₁	semidirect
27. C₁₁×C₆₇	D₃²	semidirect
28. C₃²×C₆₇	C₂×D₁₁	semidirect
39. C₃×C₆₇	D₃×D₁₁	semidirect
40. C₃×C₆₇	D₃×D₁₁	semidirect
43. C₃×D₃₃	D₆₇	semidirect
49. C₃²×C₁₁	C₂×D₆₇	semidirect
50. C₆₇	(C₃⋊D₃)⋊D₁₁	semidirect
52. D₃₃	D₂₀₁	semidirect
61. C₃×C₁₁	D₃×D₆₇	semidirect
62. C₃×C₁₁	C₂×D₂₀₁	semidirect
71. C₁₁	D₃×D₂₀₁	semidirect
72. C₃²	D₁₁×D₆₇	semidirect
82. C₃	D₁₁×D₂₀₁	semidirect
83. C₃	D₃₃⋊D₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₃₃×C₆₇	2
C₃×D₂₂₁₁	2
C₁₁×C₃⋊D₂₀₁	2
D₃₃⋊D₆₇	3
D₁₁×D₂₀₁	3
D₃×D₂₀₁	11
(C₃⋊D₃)⋊D₁₁	67

Subgroups — D33⋊D201 #40997705

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₃⋊D₂₀₁ #40997705