Subgroups — D₂₈₇⋊D₂₁ #37563151

Order 24108.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×D₂₈₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₈₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×C₃⋊(C₇⋊D₇)	C₂	1	1	yes	maximal, characteristic, complemented
4	(C₇⋊D₇)⋊D₄₁	—	3	1	no	maximal, Hall
5	C₃×C₇²×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₄₁×C₇⋊D₇	—	3	1	no	—
7	C₇×D₂₈₇	—	3	1	no	—
8	C₇×D₂₈₇	D₃	1	1	yes	characteristic, complemented
9	D₂₁⋊D₄₁	—	7	1	no	maximal
10	D₂₁×D₄₁	—	7	1	no	maximal
11	C₇²×C₄₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
12	D₈₆₁	D₇	1	1	yes	characteristic, complemented
13	C₄₁×D₂₁	—	7	1	no	—
14	C₄₁×D₂₁	—	7	1	no	—
15	C₄₁×D₂₁	—	14	3	no	—
16	C₇×D₁₂₃	—	7	1	no	—
17	C₃×D₂₈₇	D₇	1	1	yes	characteristic, complemented
18	C₃×C₇×D₄₁	—	7	1	no	—
19	D₇×D₄₁	—	21	1	no	—
20	D₇×D₄₁	—	21	1	no	—
21	C₃×C₇×C₄₁	—	2	3	no	—
22	C₃×C₇×C₄₁	C₂×D₇	1	1	yes	characteristic, complemented
23	C₃×C₇×C₄₁	C₂×D₇	1	1	yes	characteristic, complemented
24	D₇×D₂₁	—	41	1	no	maximal, Hall
25	D₂₈₇	—	3	1	no	—
26	D₂₈₇	D₂₁	1	1	yes	characteristic, complemented
27	C₇×D₄₁	—	7	1	no	—
28	C₇×D₄₁	—	21	1	no	—
29	D₇×C₄₁	—	21	1	no	—
30	D₇×C₄₁	—	21	1	no	—
31	D₇×C₄₁	—	42	3	no	—
32	D₃×D₄₁	—	49	1	no	Hall
33	C₃⋊(C₇⋊D₇)	D₄₁	1	1	yes	characteristic, complemented
34	C₇×D₂₁	—	41	1	no	—
35	C₃×C₇×D₇	—	41	1	no	—
36	C₇×C₄₁	—	2	3	no	—
37	C₇×C₄₁	D₃×D₇	1	1	yes	characteristic, complemented
38	C₇×C₄₁	C₂×D₂₁	1	1	yes	characteristic, complemented
39	D₁₂₃	—	7	1	no	—
40	C₃×D₄₁	—	7	1	no	—
41	D₃×C₄₁	—	49	1	no	—
42	D₇²	—	123	1	no	Hall
43	C₂×D₄₁	—	147	1	no	Hall
44	C₃×C₇²	C₂×D₄₁	1	1	yes	characteristic, complemented, Hall
45	C₃×C₄₁	D₇²	1	1	yes	characteristic, complemented, Hall
46	C₇⋊D₇	—	3	1	no	—
47	C₇×D₇	—	41	1	no	—
48	C₇×D₇	—	123	1	no	—
49	C₂×D₂₁	—	287	1	no	—
50	D₃×D₇	—	287	1	no	—
51	C₂×C₄₁	—	147	1	no	—
52	D₄₁	—	7	1	no	—
53	D₄₁	—	21	1	no	—
54	C₇²	D₃×D₄₁	1	1	yes	characteristic, complemented, Sylow
55	C₂×C₃×C₇	—	287	1	no	—
56	D₂₁	—	7	1	no	—
57	D₂₁	—	7	1	no	—
58	D₂₁	—	14	3	no	—
59	D₂₁	—	41	1	no	—
60	C₃×D₇	—	41	1	no	—
61	D₃×C₇	—	287	1	no	—
62	C₄₁	D₇×D₂₁	1	1	yes	characteristic, complemented, Sylow
63	C₂×D₇	—	861	1	no	—
64	C₂×D₇	—	861	1	no	—
65	C₃×C₇	—	2	3	no	—
66	C₃×C₇	D₇×D₄₁	1	1	yes	characteristic, complemented
67	C₃×C₇	D₇×D₄₁	1	1	yes	characteristic, complemented
68	C₂×C₇	—	287	1	no	—
69	C₂×C₇	—	861	1	no	—
70	D₇	—	21	1	no	—
71	D₇	—	21	1	no	—
72	D₇	—	41	1	no	—
73	D₇	—	42	3	no	—
74	D₇	—	123	1	no	—
75	C₂×D₃	—	2009	1	no	Hall
76	C₇	—	2	3	no	—
77	C₇	D₂₁×D₄₁	1	1	yes	characteristic, complemented
78	C₇	D₂₁⋊D₄₁	1	1	yes	characteristic, complemented
79	C₂×C₃	—	287	1	no	—
80	D₃	—	287	1	no	—
81	D₃	—	49	1	no	—
82	C₂²	—	6027	1	no	Sylow
83	C₃	(C₇⋊D₇)⋊D₄₁	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	287	1	no	—
85	C₂	—	861	1	no	—
86	C₂	—	147	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇²×C₄₁	C₂²
LCS	G ▷ C₃×C₇²×C₄₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×D₂₈₇	C₂	semidirect
2. C₇×D₈₆₁	C₂	semidirect
3. C₄₁×C₃⋊(C₇⋊D₇)	C₂	semidirect
5. C₃×C₇²×C₄₁	C₂²	semidirect
8. C₇×D₂₈₇	D₃	semidirect
11. C₇²×C₄₁	C₂×D₃	semidirect
12. D₈₆₁	D₇	semidirect
17. C₃×D₂₈₇	D₇	semidirect
22. C₃×C₇×C₄₁	C₂×D₇	semidirect
23. C₃×C₇×C₄₁	C₂×D₇	semidirect
26. D₂₈₇	D₂₁	semidirect
33. C₃⋊(C₇⋊D₇)	D₄₁	semidirect
37. C₇×C₄₁	D₃×D₇	semidirect
38. C₇×C₄₁	C₂×D₂₁	semidirect
44. C₃×C₇²	C₂×D₄₁	semidirect
45. C₃×C₄₁	D₇²	semidirect
54. C₇²	D₃×D₄₁	semidirect
62. C₄₁	D₇×D₂₁	semidirect
66. C₃×C₇	D₇×D₄₁	semidirect
67. C₃×C₇	D₇×D₄₁	semidirect
77. C₇	D₂₁×D₄₁	semidirect
78. C₇	D₂₁⋊D₄₁	semidirect
83. C₃	(C₇⋊D₇)⋊D₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₇×D₂₈₇	2
C₇×D₈₆₁	2
C₄₁×C₃⋊(C₇⋊D₇)	2
(C₇⋊D₇)⋊D₄₁	3
D₂₁⋊D₄₁	7
D₂₁×D₄₁	7
D₇×D₂₁	41

Subgroups — D287⋊D21 #37563151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₈₇⋊D₂₁ #37563151