Subgroups — D₄₂₇⋊D₂₁ #49089986

Order 35868.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×D₄₂₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₁₂₈₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×C₃⋊(C₇⋊D₇)	C₂	1	1	yes	maximal, characteristic, complemented
4	(C₇⋊D₇)⋊D₆₁	—	3	1	no	maximal, Hall
5	C₃×C₇²×C₆₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₆₁×C₇⋊D₇	—	3	1	no	—
7	C₇×D₄₂₇	—	3	1	no	—
8	C₇×D₄₂₇	D₃	1	1	yes	characteristic, complemented
9	D₂₁⋊D₆₁	—	7	1	no	maximal
10	D₂₁×D₆₁	—	7	1	no	maximal
11	C₇²×C₆₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
12	D₁₂₈₁	D₇	1	1	yes	characteristic, complemented
13	D₂₁×C₆₁	—	7	1	no	—
14	D₂₁×C₆₁	—	7	1	no	—
15	D₂₁×C₆₁	—	14	3	no	—
16	C₇×D₁₈₃	—	7	1	no	—
17	C₃×D₄₂₇	D₇	1	1	yes	characteristic, complemented
18	C₃×C₇×D₆₁	—	7	1	no	—
19	D₇×D₆₁	—	21	1	no	—
20	D₇×D₆₁	—	21	1	no	—
21	C₃×C₇×C₆₁	—	2	3	no	—
22	C₃×C₇×C₆₁	C₂×D₇	1	1	yes	characteristic, complemented
23	C₃×C₇×C₆₁	C₂×D₇	1	1	yes	characteristic, complemented
24	D₄₂₇	—	3	1	no	—
25	D₄₂₇	D₂₁	1	1	yes	characteristic, complemented
26	C₇×D₆₁	—	7	1	no	—
27	C₇×D₆₁	—	21	1	no	—
28	D₇×C₆₁	—	21	1	no	—
29	D₇×C₆₁	—	21	1	no	—
30	D₇×C₆₁	—	42	3	no	—
31	D₃×D₆₁	—	49	1	no	Hall
32	D₇×D₂₁	—	61	1	no	maximal, Hall
33	C₇×C₆₁	—	2	3	no	—
34	C₇×C₆₁	D₃×D₇	1	1	yes	characteristic, complemented
35	C₇×C₆₁	C₂×D₂₁	1	1	yes	characteristic, complemented
36	D₁₈₃	—	7	1	no	—
37	C₃×D₆₁	—	7	1	no	—
38	D₃×C₆₁	—	49	1	no	—
39	C₃⋊(C₇⋊D₇)	D₆₁	1	1	yes	characteristic, complemented
40	C₇×D₂₁	—	61	1	no	—
41	C₃×C₇×D₇	—	61	1	no	—
42	C₂×D₆₁	—	147	1	no	Hall
43	D₇²	—	183	1	no	Hall
44	C₃×C₆₁	D₇²	1	1	yes	characteristic, complemented, Hall
45	C₃×C₇²	C₂×D₆₁	1	1	yes	characteristic, complemented, Hall
46	C₂×C₆₁	—	147	1	no	—
47	D₆₁	—	7	1	no	—
48	D₆₁	—	21	1	no	—
49	C₇⋊D₇	—	3	1	no	—
50	C₇×D₇	—	61	1	no	—
51	C₇×D₇	—	183	1	no	—
52	C₂×D₂₁	—	427	1	no	—
53	D₃×D₇	—	427	1	no	—
54	C₆₁	D₇×D₂₁	1	1	yes	characteristic, complemented, Sylow
55	C₇²	D₃×D₆₁	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₃×C₇	—	427	1	no	—
57	D₂₁	—	7	1	no	—
58	D₂₁	—	7	1	no	—
59	D₂₁	—	14	3	no	—
60	D₂₁	—	61	1	no	—
61	C₃×D₇	—	61	1	no	—
62	D₃×C₇	—	427	1	no	—
63	C₂×D₇	—	1281	1	no	—
64	C₂×D₇	—	1281	1	no	—
65	C₃×C₇	—	2	3	no	—
66	C₃×C₇	D₇×D₆₁	1	1	yes	characteristic, complemented
67	C₃×C₇	D₇×D₆₁	1	1	yes	characteristic, complemented
68	C₂×C₇	—	1281	1	no	—
69	C₂×C₇	—	427	1	no	—
70	D₇	—	21	1	no	—
71	D₇	—	21	1	no	—
72	D₇	—	42	3	no	—
73	D₇	—	61	1	no	—
74	D₇	—	183	1	no	—
75	C₂×D₃	—	2989	1	no	Hall
76	C₇	—	2	3	no	—
77	C₇	D₂₁×D₆₁	1	1	yes	characteristic, complemented
78	C₇	D₂₁⋊D₆₁	1	1	yes	characteristic, complemented
79	C₂×C₃	—	427	1	no	—
80	D₃	—	49	1	no	—
81	D₃	—	427	1	no	—
82	C₂²	—	8967	1	no	Sylow
83	C₃	(C₇⋊D₇)⋊D₆₁	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	1281	1	no	—
85	C₂	—	147	1	no	—
86	C₂	—	427	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇²×C₆₁	C₂²
LCS	G ▷ C₃×C₇²×C₆₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×D₄₂₇	C₂	semidirect
2. C₇×D₁₂₈₁	C₂	semidirect
3. C₆₁×C₃⋊(C₇⋊D₇)	C₂	semidirect
5. C₃×C₇²×C₆₁	C₂²	semidirect
8. C₇×D₄₂₇	D₃	semidirect
11. C₇²×C₆₁	C₂×D₃	semidirect
12. D₁₂₈₁	D₇	semidirect
17. C₃×D₄₂₇	D₇	semidirect
22. C₃×C₇×C₆₁	C₂×D₇	semidirect
23. C₃×C₇×C₆₁	C₂×D₇	semidirect
25. D₄₂₇	D₂₁	semidirect
34. C₇×C₆₁	D₃×D₇	semidirect
35. C₇×C₆₁	C₂×D₂₁	semidirect
39. C₃⋊(C₇⋊D₇)	D₆₁	semidirect
44. C₃×C₆₁	D₇²	semidirect
45. C₃×C₇²	C₂×D₆₁	semidirect
54. C₆₁	D₇×D₂₁	semidirect
55. C₇²	D₃×D₆₁	semidirect
66. C₃×C₇	D₇×D₆₁	semidirect
67. C₃×C₇	D₇×D₆₁	semidirect
77. C₇	D₂₁×D₆₁	semidirect
78. C₇	D₂₁⋊D₆₁	semidirect
83. C₃	(C₇⋊D₇)⋊D₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₇×D₄₂₇	2
C₇×D₁₂₈₁	2
C₆₁×C₃⋊(C₇⋊D₇)	2
(C₇⋊D₇)⋊D₆₁	3
D₂₁⋊D₆₁	7
D₂₁×D₆₁	7
D₇×D₂₁	61

Subgroups — D427⋊D21 #49089986

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₂₇⋊D₂₁ #49089986