Subgroups — C₇×C₁₇×C₃⋊Dic₂₁ #44472690

Order 29988.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₇²×C₁₇	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₇×Dic₂₁	—	3	4	no	maximal
3	C₃²×C₇²×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇²×C₁₇	D₃	1	4	yes	—
5	C₁₇×C₃⋊Dic₂₁	C₇	1	1	yes	maximal, characteristic, direct product factor
6	C₇×C₁₇×C₃⋊Dic₃	—	7	1	no	maximal
7	C₇×C₁₇×Dic₇	—	9	1	no	Hall
8	C₃×C₇²×C₁₇	Dic₃	1	4	yes	complemented
9	C₂×C₃²×C₇×C₁₇	—	2	3	no	—
10	C₂×C₃²×C₇×C₁₇	D₇	1	1	yes	characteristic
11	C₂×C₃²×C₇×C₁₇	C₂×C₇	1	1	yes	characteristic
12	C₇×C₃⋊Dic₂₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₇²×C₁₇	C₃⋊D₃	1	1	yes	characteristic
14	C₁₇×Dic₂₁	—	3	4	no	—
15	C₇×Dic₃×C₁₇	—	21	4	no	—
16	C₃²×C₇×C₁₇	—	2	3	no	—
17	C₃²×C₇×C₁₇	Dic₇	1	1	yes	characteristic, complemented
18	C₃²×C₇×C₁₇	C₄×C₇	1	1	yes	characteristic, complemented
19	C₂×C₃²×C₇²	C₂×C₁₇	1	1	yes	characteristic
20	C₇²×C₁₇	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₇×C₁₇	—	2	12	no	—
22	C₂×C₃×C₇×C₁₇	D₃×C₇	1	4	yes	—
23	C₂×C₃×C₇×C₁₇	D₂₁	1	4	yes	—
24	C₁₇×C₃⋊Dic₃	—	7	1	no	Hall
25	C₇×Dic₂₁	—	3	4	no	—
26	C₄×C₇×C₁₇	—	63	1	no	—
27	C₁₇×Dic₇	—	9	1	no	—
28	C₃²×C₇²	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
29	C₃×C₇×C₁₇	—	2	12	no	—
30	C₃×C₇×C₁₇	C₇×Dic₃	1	4	yes	complemented
31	C₃×C₇×C₁₇	Dic₂₁	1	4	yes	complemented
32	C₂×C₃²×C₁₇	C₇×D₇	1	1	yes	characteristic
33	C₂×C₃×C₇²	D₃×C₁₇	1	4	yes	—
34	C₃⋊Dic₂₁	C₇×C₁₇	1	1	yes	characteristic, direct product factor
35	C₇×C₃⋊Dic₃	—	7	1	no	—
36	C₂×C₇×C₁₇	—	2	3	no	—
37	C₂×C₇×C₁₇	C₇×C₃⋊D₃	1	1	yes	characteristic
38	C₂×C₇×C₁₇	C₃⋊D₂₁	1	1	yes	characteristic
39	Dic₃×C₁₇	—	21	4	no	—
40	C₇×Dic₇	—	9	1	no	Hall
41	C₃²×C₁₇	C₇×Dic₇	1	1	yes	characteristic, complemented, Hall
42	C₃×C₇²	Dic₃×C₁₇	1	4	yes	complemented
43	C₂×C₃²×C₇	—	2	3	no	—
44	C₂×C₃²×C₇	D₇×C₁₇	1	1	yes	characteristic
45	C₂×C₃²×C₇	C₂×C₇×C₁₇	1	1	yes	characteristic
46	C₇×C₁₇	—	2	3	no	—
47	C₇×C₁₇	C₇×C₃⋊Dic₃	1	1	yes	characteristic, complemented
48	C₇×C₁₇	C₃⋊Dic₂₁	1	1	yes	characteristic, direct product factor
49	C₂×C₃×C₁₇	C₇×D₂₁	1	4	yes	—
50	C₂×C₇²	C₁₇×C₃⋊D₃	1	1	yes	characteristic
51	Dic₂₁	—	3	4	no	—
52	C₇×Dic₃	—	21	4	no	—
53	C₄×C₁₇	—	63	1	no	Hall
54	C₃²×C₇	—	2	3	no	—
55	C₃²×C₇	C₁₇×Dic₇	1	1	yes	characteristic, complemented
56	C₃²×C₇	C₄×C₇×C₁₇	1	1	yes	characteristic, complemented
57	C₃×C₁₇	C₇×Dic₂₁	1	4	yes	complemented
58	C₇²	C₁₇×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₃×C₇	—	2	12	no	—
60	C₂×C₃×C₇	D₃×C₇×C₁₇	1	4	yes	—
61	C₂×C₃×C₇	C₁₇×D₂₁	1	4	yes	—
62	C₃⋊Dic₃	—	7	1	no	Hall
63	C₂×C₁₇	C₇×C₃⋊D₂₁	1	1	yes	characteristic
64	C₄×C₇	—	63	1	no	—
65	Dic₇	—	9	1	no	—
66	C₃×C₇	—	2	12	no	—
67	C₃×C₇	C₇×Dic₃×C₁₇	1	4	yes	complemented
68	C₃×C₇	C₁₇×Dic₂₁	1	4	yes	complemented
69	C₂×C₃²	C₇×D₇×C₁₇	1	1	yes	characteristic
70	C₁₇	C₇×C₃⋊Dic₂₁	1	1	yes	characteristic, direct product factor, Sylow
71	C₂×C₇	—	2	3	no	—
72	C₂×C₇	C₇×C₁₇×C₃⋊D₃	1	1	yes	characteristic
73	C₂×C₇	C₁₇×C₃⋊D₂₁	1	1	yes	characteristic
74	Dic₃	—	21	4	no	—
75	C₃²	C₇×C₁₇×Dic₇	1	1	yes	characteristic, complemented, Sylow
76	C₇	—	2	3	no	—
77	C₇	C₇×C₁₇×C₃⋊Dic₃	1	1	yes	characteristic, complemented
78	C₇	C₁₇×C₃⋊Dic₂₁	1	1	yes	characteristic, direct product factor
79	C₂×C₃	C₇×C₁₇×D₂₁	1	4	yes	—
80	C₄	—	63	1	no	Sylow
81	C₃	C₇×C₁₇×Dic₂₁	1	4	yes	complemented
82	C₂	C₇×C₁₇×C₃⋊D₂₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₇×C₁₇	C₃⋊D₂₁
commutator, hypocenter	C₃²×C₇	C₄×C₇×C₁₇
Frattini	C₂	C₇×C₁₇×C₃⋊D₂₁
Fitting, socle, prime radical	C₂×C₃²×C₇²×C₁₇	C₂
cosocle	C₂×C₃²×C₇	C₂×C₇×C₁₇
LCS	G ▷ C₃²×C₇
UCS	C₁ ◁ C₂×C₇×C₁₇

Complements

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

N	H ≅ G/N	type
3. C₃²×C₇²×C₁₇	C₄	semidirect
5. C₁₇×C₃⋊Dic₂₁	C₇	direct (N × H)
8. C₃×C₇²×C₁₇	Dic₃	semidirect
12. C₇×C₃⋊Dic₂₁	C₁₇	direct (N × H)
17. C₃²×C₇×C₁₇	Dic₇	semidirect
18. C₃²×C₇×C₁₇	C₄×C₇	semidirect
20. C₇²×C₁₇	C₃⋊Dic₃	semidirect
28. C₃²×C₇²	C₄×C₁₇	semidirect
30. C₃×C₇×C₁₇	C₇×Dic₃	semidirect
31. C₃×C₇×C₁₇	Dic₂₁	semidirect
34. C₃⋊Dic₂₁	C₇×C₁₇	direct (N × H)
41. C₃²×C₁₇	C₇×Dic₇	semidirect
42. C₃×C₇²	Dic₃×C₁₇	semidirect
47. C₇×C₁₇	C₇×C₃⋊Dic₃	semidirect
48. C₇×C₁₇	C₃⋊Dic₂₁	direct (N × H)
55. C₃²×C₇	C₁₇×Dic₇	semidirect
56. C₃²×C₇	C₄×C₇×C₁₇	semidirect
57. C₃×C₁₇	C₇×Dic₂₁	semidirect
58. C₇²	C₁₇×C₃⋊Dic₃	semidirect
67. C₃×C₇	C₇×Dic₃×C₁₇	semidirect
68. C₃×C₇	C₁₇×Dic₂₁	semidirect
70. C₁₇	C₇×C₃⋊Dic₂₁	direct (N × H)
75. C₃²	C₇×C₁₇×Dic₇	semidirect
77. C₇	C₇×C₁₇×C₃⋊Dic₃	semidirect
78. C₇	C₁₇×C₃⋊Dic₂₁	direct (N × H)
81. C₃	C₇×C₁₇×Dic₂₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₇²×C₁₇	2
C₇×C₁₇×Dic₂₁	3
C₁₇×C₃⋊Dic₂₁	7
C₇×C₁₇×C₃⋊Dic₃	7
C₇×C₃⋊Dic₂₁	17

Subgroups — C7×C17×C3⋊Dic21 #44472690

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₁₇×C₃⋊Dic₂₁ #44472690