Subgroups — D₁₂₉⋊D₂₁ #24925655

Order 10836.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

Maximal subgroups

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

subgroup	index
C₄₃×C₃⋊D₂₁	2
C₃×D₉₀₃	2
C₃×C₇×D₁₂₉	2
D₂₁⋊D₄₃	3
D₂₁×D₄₃	3
(C₃⋊D₃)⋊D₄₃	7
D₃×D₂₁	43

Subgroups — D129⋊D21 #24925655

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₂₉⋊D₂₁ #24925655