Subgroups — D₃×D₉₀₃ #24925654

Order 10836.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₉₀₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₉₀₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₃×C₇×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₉₀₃	—	3	1	no	maximal
5	D₃×D₃₀₁	—	3	1	no	maximal
6	C₃²×C₇×C₄₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₇×C₄₃	—	3	1	no	—
8	D₉₀₃	—	3	1	no	—
9	D₉₀₃	—	3	1	no	—
10	D₉₀₃	—	6	1	no	—
11	D₉₀₃	D₃	1	1	yes	characteristic, direct product factor
12	D₃×C₇×C₄₃	D₃	1	1	yes	characteristic, complemented
13	C₃×D₃₀₁	—	3	1	no	—
14	D₃×D₁₂₉	—	7	1	no	maximal, Hall
15	C₂×D₃₀₁	—	9	1	no	Hall
16	C₃×C₇×C₄₃	—	2	1	no	—
17	C₃×C₇×C₄₃	C₂×D₃	1	1	yes	characteristic, complemented
18	C₃×C₇×C₄₃	C₂×D₃	1	1	yes	characteristic, complemented
19	C₃⋊D₁₂₉	—	7	1	no	—
20	C₃×D₁₂₉	—	7	1	no	—
21	C₃×D₃×C₄₃	D₇	1	1	yes	characteristic, complemented
22	C₂×C₇×C₄₃	—	3	1	no	—
23	D₃₀₁	—	3	1	no	—
24	D₃₀₁	—	9	1	no	—
25	C₂×D₁₂₉	—	21	1	no	—
26	D₃×D₄₃	—	21	1	no	—
27	C₃²×C₄₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
28	C₇×C₄₃	D₃²	1	1	yes	characteristic, complemented, Hall
29	C₂×C₃×C₄₃	—	3	1	no	—
30	D₁₂₉	—	7	1	no	—
31	D₁₂₉	—	21	1	no	—
32	D₁₂₉	—	21	1	no	—
33	D₁₂₉	—	42	1	no	—
34	C₃×D₄₃	—	21	1	no	—
35	D₃×C₄₃	D₂₁	1	1	yes	characteristic, complemented
36	D₃×D₂₁	—	43	1	no	maximal, Hall
37	C₂×D₄₃	—	63	1	no	Hall
38	C₃×C₄₃	—	2	1	no	—
39	C₃×C₄₃	D₃×D₇	1	1	yes	characteristic, complemented
40	C₃×C₄₃	C₂×D₂₁	1	1	yes	characteristic, complemented
41	C₃⋊D₂₁	—	43	1	no	—
42	C₃×D₂₁	—	43	1	no	—
43	C₃×D₃×C₇	D₄₃	1	1	yes	characteristic, complemented
44	C₂×C₄₃	—	3	1	no	—
45	D₄₃	—	21	1	no	—
46	D₄₃	—	63	1	no	—
47	C₂×D₂₁	—	129	1	no	—
48	D₃×D₇	—	129	1	no	—
49	C₃²×C₇	C₂×D₄₃	1	1	yes	characteristic, complemented, Hall
50	C₄₃	D₃×D₂₁	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃×C₇	—	3	1	no	—
52	D₂₁	—	258	1	no	—
53	D₂₁	—	43	1	no	—
54	D₂₁	—	129	1	no	—
55	D₂₁	—	129	1	no	—
56	C₃×D₇	—	129	1	no	—
57	D₃×C₇	D₁₂₉	1	1	yes	characteristic, complemented
58	D₃²	—	301	1	no	Hall
59	C₂×D₇	—	387	1	no	Hall
60	C₃×C₇	—	2	1	no	—
61	C₃×C₇	D₃×D₄₃	1	1	yes	characteristic, complemented
62	C₃×C₇	C₂×D₁₂₉	1	1	yes	characteristic, complemented
63	C₃⋊D₃	—	301	1	no	—
64	C₃×D₃	—	301	1	no	—
65	C₃×D₃	D₃₀₁	1	1	yes	characteristic, complemented
66	C₂×C₇	—	3	1	no	—
67	D₇	—	129	1	no	—
68	D₇	—	387	1	no	—
69	C₂×D₃	—	903	1	no	—
70	C₂×D₃	—	903	1	no	—
71	C₃²	C₂×D₃₀₁	1	1	yes	characteristic, complemented, Sylow
72	C₇	D₃×D₁₂₉	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	3	1	no	—
74	C₂×C₃	—	903	1	no	—
75	D₃	—	1806	1	no	—
76	D₃	—	301	1	no	—
77	D₃	—	903	1	no	—
78	D₃	—	903	1	no	—
79	D₃	D₉₀₃	1	1	yes	characteristic, direct product factor
80	C₂²	—	2709	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₃×D₃₀₁	1	1	yes	characteristic, complemented
83	C₃	C₂×D₉₀₃	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	903	1	no	—
86	C₂	—	2709	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₇×C₄₃	C₂²
LCS	G ▷ C₃²×C₇×C₄₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₉₀₃	C₂	semidirect
2. C₃×D₉₀₃	C₂	semidirect
3. C₃×D₃×C₇×C₄₃	C₂	semidirect
6. C₃²×C₇×C₄₃	C₂²	semidirect
11. D₉₀₃	D₃	direct (N × H)
12. D₃×C₇×C₄₃	D₃	semidirect
17. C₃×C₇×C₄₃	C₂×D₃	semidirect
18. C₃×C₇×C₄₃	C₂×D₃	semidirect
21. C₃×D₃×C₄₃	D₇	semidirect
27. C₃²×C₄₃	C₂×D₇	semidirect
28. C₇×C₄₃	D₃²	semidirect
35. D₃×C₄₃	D₂₁	semidirect
39. C₃×C₄₃	D₃×D₇	semidirect
40. C₃×C₄₃	C₂×D₂₁	semidirect
43. C₃×D₃×C₇	D₄₃	semidirect
49. C₃²×C₇	C₂×D₄₃	semidirect
50. C₄₃	D₃×D₂₁	semidirect
57. D₃×C₇	D₁₂₉	semidirect
61. C₃×C₇	D₃×D₄₃	semidirect
62. C₃×C₇	C₂×D₁₂₉	semidirect
65. C₃×D₃	D₃₀₁	semidirect
71. C₃²	C₂×D₃₀₁	semidirect
72. C₇	D₃×D₁₂₉	semidirect
79. D₃	D₉₀₃	direct (N × H)
82. C₃	D₃×D₃₀₁	semidirect
83. C₃	C₂×D₉₀₃	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊D₉₀₃	2
C₃×D₉₀₃	2
C₃×D₃×C₇×C₄₃	2
C₂×D₉₀₃	3
D₃×D₃₀₁	3
D₃×D₁₂₉	7
D₃×D₂₁	43

Subgroups — D3×D903 #24925654

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₉₀₃ #24925654