Subgroups — D₂₁⋊D₄₀₇ #46803292

Order 34188.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₃₇×D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₁₂₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₂₈₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×D₄₀₇	—	3	1	no	maximal, Hall
5	C₃×C₇×C₁₁×C₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₈₄₉	D₃	1	1	yes	characteristic, complemented
7	C₁₁×D₇×C₃₇	—	3	1	no	—
8	C₇×D₄₀₇	—	3	1	no	—
9	D₃×D₄₀₇	—	7	1	no	maximal, Hall
10	D₂₁⋊D₃₇	—	11	1	no	maximal, Hall
11	C₇×C₁₁×C₃₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
12	D₁₂₂₁	D₇	1	1	yes	characteristic, complemented
13	D₃×C₁₁×C₃₇	—	7	1	no	—
14	C₃×D₄₀₇	—	7	1	no	—
15	C₂×D₄₀₇	—	21	1	no	Hall
16	C₃₇×D₂₁	D₁₁	1	1	yes	characteristic, complemented
17	C₇×D₁₁₁	—	11	1	no	—
18	C₃×D₂₅₉	—	11	1	no	—
19	C₃×C₁₁×C₃₇	C₂×D₇	1	1	yes	characteristic, complemented, Hall
20	D₇×D₃₇	—	33	1	no	Hall
21	D₂₁⋊D₁₁	—	37	1	no	maximal, Hall
22	C₂×C₁₁×C₃₇	—	21	1	no	—
23	D₄₀₇	—	3	1	no	—
24	D₄₀₇	—	7	1	no	—
25	C₃×C₇×C₃₇	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
26	D₂₅₉	—	11	1	no	—
27	C₇×D₃₇	—	33	1	no	—
28	D₇×C₃₇	—	3	1	no	—
29	C₁₁×D₂₁	D₃₇	1	1	yes	characteristic, complemented
30	C₇×D₃₃	—	37	1	no	—
31	C₃×D₇₇	—	37	1	no	—
32	D₃×D₃₇	—	77	1	no	Hall
33	C₁₁×C₃₇	D₃×D₇	1	1	yes	characteristic, complemented, Hall
34	D₇×D₁₁	—	111	1	no	Hall
35	C₇×C₃₇	D₃×D₁₁	1	1	yes	characteristic, complemented, Hall
36	C₃×C₇×C₁₁	C₂×D₃₇	1	1	yes	characteristic, complemented, Hall
37	D₁₁₁	—	11	1	no	—
38	C₃×D₃₇	—	77	1	no	—
39	D₃×C₃₇	—	7	1	no	—
40	D₇₇	—	37	1	no	—
41	C₇×D₁₁	—	111	1	no	—
42	C₁₁×D₇	—	3	1	no	—
43	C₂×D₃₇	—	231	1	no	Hall
44	D₃×D₁₁	—	259	1	no	Hall
45	C₃×C₃₇	D₇×D₁₁	1	1	yes	characteristic, complemented, Hall
46	D₃×D₇	—	407	1	no	Hall
47	C₇×C₁₁	D₃×D₃₇	1	1	yes	characteristic, complemented, Hall
48	C₂×C₃₇	—	21	1	no	—
49	D₃₇	—	33	1	no	—
50	D₃₇	—	77	1	no	—
51	D₃₃	—	37	1	no	—
52	C₃×D₁₁	—	259	1	no	—
53	D₃×C₁₁	—	7	1	no	—
54	C₂×D₁₁	—	777	1	no	Hall
55	D₂₁	D₄₀₇	1	1	yes	characteristic, complemented
56	C₃×D₇	—	407	1	no	—
57	D₃×C₇	—	407	1	no	—
58	C₃₇	D₂₁⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
59	C₃×C₁₁	D₇×D₃₇	1	1	yes	characteristic, complemented, Hall
60	C₂×D₇	—	1221	1	no	Hall
61	C₂×C₁₁	—	21	1	no	—
62	D₁₁	—	259	1	no	—
63	D₁₁	—	111	1	no	—
64	C₃×C₇	C₂×D₄₀₇	1	1	yes	characteristic, complemented, Hall
65	C₂×C₇	—	1221	1	no	—
66	D₇	—	3	1	no	—
67	D₇	—	407	1	no	—
68	C₂×D₃	—	2849	1	no	Hall
69	C₁₁	D₂₁⋊D₃₇	1	1	yes	characteristic, complemented, Sylow
70	C₇	D₃×D₄₀₇	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₃	—	2849	1	no	—
72	D₃	—	7	1	no	—
73	D₃	—	407	1	no	—
74	C₂²	—	8547	1	no	Sylow
75	C₃	D₇×D₄₀₇	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	21	1	no	—
77	C₂	—	2849	1	no	—
78	C₂	—	1221	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₁₁×C₃₇	C₂²
LCS	G ▷ C₃×C₇×C₁₁×C₃₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₃₇×D₂₁	C₂	semidirect
2. C₇×D₁₂₂₁	C₂	semidirect
3. C₃×D₂₈₄₉	C₂	semidirect
5. C₃×C₇×C₁₁×C₃₇	C₂²	semidirect
6. D₂₈₄₉	D₃	semidirect
11. C₇×C₁₁×C₃₇	C₂×D₃	semidirect
12. D₁₂₂₁	D₇	semidirect
16. C₃₇×D₂₁	D₁₁	semidirect
19. C₃×C₁₁×C₃₇	C₂×D₇	semidirect
25. C₃×C₇×C₃₇	C₂×D₁₁	semidirect
29. C₁₁×D₂₁	D₃₇	semidirect
33. C₁₁×C₃₇	D₃×D₇	semidirect
35. C₇×C₃₇	D₃×D₁₁	semidirect
36. C₃×C₇×C₁₁	C₂×D₃₇	semidirect
45. C₃×C₃₇	D₇×D₁₁	semidirect
47. C₇×C₁₁	D₃×D₃₇	semidirect
55. D₂₁	D₄₀₇	semidirect
58. C₃₇	D₂₁⋊D₁₁	semidirect
59. C₃×C₁₁	D₇×D₃₇	semidirect
64. C₃×C₇	C₂×D₄₀₇	semidirect
69. C₁₁	D₂₁⋊D₃₇	semidirect
70. C₇	D₃×D₄₀₇	semidirect
75. C₃	D₇×D₄₀₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×C₃₇×D₂₁	2
C₇×D₁₂₂₁	2
C₃×D₂₈₄₉	2
D₇×D₄₀₇	3
D₃×D₄₀₇	7
D₂₁⋊D₃₇	11
D₂₁⋊D₁₁	37

Subgroups — D21⋊D407 #46803292

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₁⋊D₄₀₇ #46803292