Subgroups — D₃×D₁₈₃₃ #36347261

Order 21996.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₃×C₁₃×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₁₈₃₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊D₁₈₃₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₈₃₃	—	3	1	no	maximal
5	D₃×D₆₁₁	—	3	1	no	maximal
6	C₃²×C₁₃×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₁₈₃₃	—	3	1	no	—
8	D₁₈₃₃	—	3	1	no	—
9	D₁₈₃₃	—	6	1	no	—
10	D₁₈₃₃	D₃	1	1	yes	characteristic, direct product factor
11	D₃×C₁₃×C₄₇	D₃	1	1	yes	characteristic, complemented
12	C₃×D₆₁₁	—	3	1	no	—
13	C₂×C₃×C₁₃×C₄₇	—	3	1	no	—
14	C₂×D₆₁₁	—	9	1	no	Hall
15	C₃×C₁₃×C₄₇	—	2	1	no	—
16	C₃×C₁₃×C₄₇	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₁₃×C₄₇	C₂×D₃	1	1	yes	characteristic, complemented
18	D₃×D₁₄₁	—	13	1	no	maximal, Hall
19	C₂×C₁₃×C₄₇	—	3	1	no	—
20	D₆₁₁	—	3	1	no	—
21	D₆₁₁	—	9	1	no	—
22	C₃⋊D₁₄₁	—	13	1	no	—
23	C₃×D₁₄₁	—	13	1	no	—
24	C₃×D₃×C₄₇	D₁₃	1	1	yes	characteristic, complemented
25	C₁₃×C₄₇	D₃²	1	1	yes	characteristic, complemented, Hall
26	C₂×D₁₄₁	—	39	1	no	—
27	D₃×D₄₇	—	39	1	no	—
28	D₃×D₃₉	—	47	1	no	maximal, Hall
29	C₃²×C₄₇	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₄₇	—	3	1	no	—
31	D₁₄₁	—	13	1	no	—
32	D₁₄₁	—	39	1	no	—
33	D₁₄₁	—	39	1	no	—
34	D₁₄₁	—	78	1	no	—
35	C₃×D₄₇	—	39	1	no	—
36	D₃×C₄₇	D₃₉	1	1	yes	characteristic, complemented
37	C₃⋊D₃₉	—	47	1	no	—
38	C₃×D₃₉	—	47	1	no	—
39	C₃×D₃×C₁₃	D₄₇	1	1	yes	characteristic, complemented
40	C₂×D₄₇	—	117	1	no	Hall
41	C₂×D₃₉	—	141	1	no	—
42	D₃×D₁₃	—	141	1	no	—
43	C₃×C₄₇	—	2	1	no	—
44	C₃×C₄₇	D₃×D₁₃	1	1	yes	characteristic, complemented
45	C₃×C₄₇	C₂×D₃₉	1	1	yes	characteristic, complemented
46	C₃²×C₁₃	C₂×D₄₇	1	1	yes	characteristic, complemented, Hall
47	C₂×C₄₇	—	3	1	no	—
48	D₄₇	—	39	1	no	—
49	D₄₇	—	117	1	no	—
50	C₂×C₃×C₁₃	—	3	1	no	—
51	D₃₉	—	282	1	no	—
52	D₃₉	—	47	1	no	—
53	D₃₉	—	141	1	no	—
54	D₃₉	—	141	1	no	—
55	C₃×D₁₃	—	141	1	no	—
56	D₃×C₁₃	D₁₄₁	1	1	yes	characteristic, complemented
57	C₂×D₁₃	—	423	1	no	Hall
58	C₄₇	D₃×D₃₉	1	1	yes	characteristic, complemented, Sylow
59	C₃×C₁₃	—	2	1	no	—
60	C₃×C₁₃	D₃×D₄₇	1	1	yes	characteristic, complemented
61	C₃×C₁₃	C₂×D₁₄₁	1	1	yes	characteristic, complemented
62	D₃²	—	611	1	no	Hall
63	C₂×C₁₃	—	3	1	no	—
64	D₁₃	—	141	1	no	—
65	D₁₃	—	423	1	no	—
66	C₃⋊D₃	—	611	1	no	—
67	C₃×D₃	—	611	1	no	—
68	C₃×D₃	D₆₁₁	1	1	yes	characteristic, complemented
69	C₁₃	D₃×D₁₄₁	1	1	yes	characteristic, complemented, Sylow
70	C₂×D₃	—	1833	1	no	—
71	C₂×D₃	—	1833	1	no	—
72	C₃²	C₂×D₆₁₁	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	3	1	no	—
74	C₂×C₃	—	1833	1	no	—
75	D₃	—	1833	1	no	—
76	D₃	—	1833	1	no	—
77	D₃	—	3666	1	no	—
78	D₃	—	611	1	no	—
79	D₃	D₁₈₃₃	1	1	yes	characteristic, direct product factor
80	C₂²	—	5499	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₃×D₆₁₁	1	1	yes	characteristic, complemented
83	C₃	C₂×D₁₈₃₃	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	1833	1	no	—
86	C₂	—	5499	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₁₃×C₄₇	C₂²
LCS	G ▷ C₃²×C₁₃×C₄₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×D₃×C₁₃×C₄₇	C₂	semidirect
2. C₃×D₁₈₃₃	C₂	semidirect
3. C₃⋊D₁₈₃₃	C₂	semidirect
6. C₃²×C₁₃×C₄₇	C₂²	semidirect
10. D₁₈₃₃	D₃	direct (N × H)
11. D₃×C₁₃×C₄₇	D₃	semidirect
16. C₃×C₁₃×C₄₇	C₂×D₃	semidirect
17. C₃×C₁₃×C₄₇	C₂×D₃	semidirect
24. C₃×D₃×C₄₇	D₁₃	semidirect
25. C₁₃×C₄₇	D₃²	semidirect
29. C₃²×C₄₇	C₂×D₁₃	semidirect
36. D₃×C₄₇	D₃₉	semidirect
39. C₃×D₃×C₁₃	D₄₇	semidirect
44. C₃×C₄₇	D₃×D₁₃	semidirect
45. C₃×C₄₇	C₂×D₃₉	semidirect
46. C₃²×C₁₃	C₂×D₄₇	semidirect
56. D₃×C₁₃	D₁₄₁	semidirect
58. C₄₇	D₃×D₃₉	semidirect
60. C₃×C₁₃	D₃×D₄₇	semidirect
61. C₃×C₁₃	C₂×D₁₄₁	semidirect
68. C₃×D₃	D₆₁₁	semidirect
69. C₁₃	D₃×D₁₄₁	semidirect
72. C₃²	C₂×D₆₁₁	semidirect
79. D₃	D₁₈₃₃	direct (N × H)
82. C₃	D₃×D₆₁₁	semidirect
83. C₃	C₂×D₁₈₃₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₃×C₁₃×C₄₇	2
C₃×D₁₈₃₃	2
C₃⋊D₁₈₃₃	2
C₂×D₁₈₃₃	3
D₃×D₆₁₁	3
D₃×D₁₄₁	13
D₃×D₃₉	47

Subgroups — D3×D1833 #36347261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₁₈₃₃ #36347261