Subgroups — C₁₇×(C₃⋊D₃)⋊D₄₉ #44472466

Order 29988.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₃⋊D₃×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₁₇×D₁₄₇	C₂	1	2	yes	maximal, complemented
3	D₃×C₁₇×D₄₉	—	3	2	no	maximal
4	C₃²×C₁₇×C₄₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₇×D₁₄₇	D₃	1	2	yes	complemented
6	D₃×C₁₇×C₄₉	—	3	2	no	—
7	D₃×C₁₇×C₄₉	—	6	1	no	—
8	C₃×C₁₇×D₄₉	—	3	2	no	—
9	C₁₇×(C₃⋊D₃)⋊D₇	—	7	1	no	maximal
10	C₂×C₁₇×D₄₉	—	9	1	no	Hall
11	C₃×C₁₇×C₄₉	—	2	1	no	—
12	C₃×C₁₇×C₄₉	C₂×D₃	1	2	yes	complemented
13	C₇×C₁₇×C₃⋊D₃	D₇	1	1	yes	characteristic
14	C₃×C₁₇×D₂₁	—	7	2	no	—
15	(C₃⋊D₃)⋊D₄₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₁₇×C₄₉	—	9	1	no	—
17	C₁₇×D₄₉	—	3	2	no	—
18	D₃×D₇×C₁₇	—	21	2	no	—
19	C₃²×C₇×C₁₇	C₂×D₇	1	1	yes	characteristic
20	C₃⋊D₃×C₄₉	C₂×C₁₇	1	1	yes	characteristic, complemented
21	C₃×D₁₄₇	C₂×C₁₇	1	2	yes	complemented
22	C₁₇×C₄₉	D₃²	1	1	yes	characteristic, complemented, Hall
23	C₁₇×D₂₁	—	7	2	no	—
24	D₃×C₇×C₁₇	—	3	2	no	—
25	D₃×C₇×C₁₇	—	6	1	no	—
26	C₃×D₇×C₁₇	—	21	2	no	—
27	D₃²×C₁₇	—	49	1	no	Hall
28	D₃×D₄₉	—	3	2	no	—
29	C₂×D₇×C₁₇	—	63	1	no	—
30	C₃²×C₄₉	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
31	C₃×C₇×C₁₇	—	2	1	no	—
32	C₃×C₇×C₁₇	D₃×D₇	1	2	yes	—
33	C₁₇×C₃⋊D₃	D₄₉	1	1	yes	characteristic, complemented
34	C₃×D₃×C₁₇	—	49	2	no	—
35	D₁₄₇	D₃×C₁₇	1	2	yes	complemented
36	C₃×D₄₉	—	3	2	no	—
37	D₃×C₄₉	—	3	2	no	—
38	D₃×C₄₉	—	6	1	no	—
39	(C₃⋊D₃)⋊D₇	—	7	1	no	—
40	C₂×C₇×C₁₇	—	9	1	no	—
41	D₇×C₁₇	—	21	2	no	—
42	C₂×D₃×C₁₇	—	147	2	no	—
43	C₂×D₄₉	—	9	1	no	Hall
44	C₃²×C₁₇	C₂×D₄₉	1	1	yes	characteristic, complemented, Hall
45	C₃×C₄₉	—	2	1	no	—
46	C₃×C₄₉	C₂×D₃×C₁₇	1	2	yes	complemented
47	C₇×C₃⋊D₃	D₇×C₁₇	1	1	yes	characteristic
48	C₃×D₂₁	—	7	2	no	—
49	C₇×C₁₇	(C₃⋊D₃)⋊D₇	1	1	yes	characteristic
50	C₂×C₃×C₁₇	—	147	2	no	—
51	D₃×C₁₇	—	3	2	no	—
52	D₃×C₁₇	—	6	1	no	—
53	D₃×C₁₇	—	49	2	no	—
54	C₂×C₄₉	—	9	1	no	—
55	D₄₉	—	3	2	no	—
56	D₃×D₇	—	21	2	no	—
57	C₂²×C₁₇	—	441	1	no	Hall
58	C₃²×C₇	C₂×D₇×C₁₇	1	1	yes	characteristic
59	C₃×C₁₇	—	2	1	no	—
60	C₃×C₁₇	D₃×D₄₉	1	2	yes	complemented
61	C₄₉	D₃²×C₁₇	1	1	yes	characteristic, complemented, Sylow
62	D₂₁	—	7	2	no	—
63	C₃×D₇	—	21	2	no	—
64	D₃×C₇	—	3	2	no	—
65	D₃×C₇	—	6	1	no	—
66	D₃²	—	49	1	no	Hall
67	C₂×C₁₇	—	9	1	no	—
68	C₂×C₁₇	—	147	2	no	—
69	C₂×D₇	—	63	1	no	—
70	C₃×C₇	—	2	1	no	—
71	C₃×C₇	D₃×D₇×C₁₇	1	2	yes	—
72	C₃⋊D₃	C₁₇×D₄₉	1	1	yes	characteristic, complemented
73	C₃×D₃	—	49	2	no	—
74	C₁₇	(C₃⋊D₃)⋊D₄₉	1	1	yes	characteristic, direct product factor, Sylow
75	C₂×C₇	—	9	1	no	—
76	D₇	—	21	2	no	—
77	C₂×D₃	—	147	2	no	—
78	C₃²	C₂×C₁₇×D₄₉	1	1	yes	characteristic, complemented, Sylow
79	C₇	C₁₇×(C₃⋊D₃)⋊D₇	1	1	yes	characteristic
80	C₂×C₃	—	147	2	no	—
81	D₃	—	3	2	no	—
82	D₃	—	6	1	no	—
83	D₃	—	49	2	no	—
84	C₂²	—	441	1	no	Sylow
85	C₃	—	2	1	no	—
86	C₃	D₃×C₁₇×D₄₉	1	2	yes	complemented
87	C₂	—	9	1	no	—
88	C₂	—	147	2	no	—

	subgroup	G/H
center, hypercenter	C₁₇	(C₃⋊D₃)⋊D₄₉
commutator, cosocle, hypocenter	C₃²×C₄₉	C₂²×C₁₇
Frattini	C₇	C₁₇×(C₃⋊D₃)⋊D₇
Fitting	C₃²×C₁₇×C₄₉	C₂²
socle	C₃²×C₇×C₁₇	C₂×D₇
LCS	G ▷ C₃²×C₄₉
UCS	C₁ ◁ C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₇×C₃⋊D₃×C₄₉	C₂	semidirect
2. C₃×C₁₇×D₁₄₇	C₂	semidirect
4. C₃²×C₁₇×C₄₉	C₂²	semidirect
5. C₁₇×D₁₄₇	D₃	semidirect
12. C₃×C₁₇×C₄₉	C₂×D₃	semidirect
15. (C₃⋊D₃)⋊D₄₉	C₁₇	direct (N × H)
20. C₃⋊D₃×C₄₉	C₂×C₁₇	semidirect
21. C₃×D₁₄₇	C₂×C₁₇	semidirect
22. C₁₇×C₄₉	D₃²	semidirect
30. C₃²×C₄₉	C₂²×C₁₇	semidirect
33. C₁₇×C₃⋊D₃	D₄₉	semidirect
35. D₁₄₇	D₃×C₁₇	semidirect
44. C₃²×C₁₇	C₂×D₄₉	semidirect
46. C₃×C₄₉	C₂×D₃×C₁₇	semidirect
60. C₃×C₁₇	D₃×D₄₉	semidirect
61. C₄₉	D₃²×C₁₇	semidirect
72. C₃⋊D₃	C₁₇×D₄₉	semidirect
74. C₁₇	(C₃⋊D₃)⋊D₄₉	direct (N × H)
78. C₃²	C₂×C₁₇×D₄₉	semidirect
86. C₃	D₃×C₁₇×D₄₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×C₃⋊D₃×C₄₉	2
C₃×C₁₇×D₁₄₇	2
D₃×C₁₇×D₄₉	3
C₁₇×(C₃⋊D₃)⋊D₇	7
(C₃⋊D₃)⋊D₄₉	17

Subgroups — C17×(C3⋊D3)⋊D49 #44472466

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×(C₃⋊D₃)⋊D₄₉ #44472466