Subgroups — D₂₁⋊D₁₂₉ #24925658

Order 10836.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

Subgroups — D21⋊D129 #24925658

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₁⋊D₁₂₉ #24925658