Subgroups — C₃×D₁₇×D₁₁₉ #37566263

Order 24276.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₇×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₁₇×D₁₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇⋊(C₁₇⋊D₁₇)	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₇×D₁₁₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₇×C₁₇²	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₇⋊(C₁₇⋊D₁₇)	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₇×D₁₁₉	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇×C₁₇×D₁₇	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃×D₁₇²	—	7	1	no	maximal, Hall
10	C₇×C₁₇²	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₃×C₁₇×D₁₇	—	7	1	no	—
12	C₃×C₁₇×D₁₇	D₇	1	1	yes	characteristic, complemented
13	C₃×C₁₇⋊D₁₇	—	7	1	no	—
14	C₂×C₃×D₁₁₉	—	17	1	no	maximal
15	C₃×D₇×D₁₇	—	17	1	no	maximal
16	D₁₇²	—	7	1	no	Hall
17	C₃×C₁₇²	C₂×D₇	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₇×C₁₇	—	17	1	no	—
19	C₃×D₁₁₉	—	17	1	no	—
20	C₃×D₁₁₉	—	17	1	no	—
21	C₃×D₁₁₉	—	34	8	no	—
22	C₃×D₁₁₉	D₁₇	1	1	yes	characteristic, direct product factor
23	C₃×D₇×C₁₇	—	17	1	no	—
24	C₃×C₇×D₁₇	D₁₇	1	1	yes	characteristic, complemented
25	C₁₇⋊D₁₇	—	7	1	no	—
26	C₁₇×D₁₇	—	7	1	no	—
27	C₁₇×D₁₇	C₃×D₇	1	1	yes	characteristic, complemented
28	C₂×D₁₁₉	—	17	1	no	—
29	D₇×D₁₇	—	17	1	no	—
30	C₃×C₇×C₁₇	—	2	8	no	—
31	C₃×C₇×C₁₇	C₂×D₁₇	1	1	yes	characteristic, complemented
32	C₃×C₇×C₁₇	C₂×D₁₇	1	1	yes	characteristic, complemented
33	C₁₇²	C₂×C₃×D₇	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₇×C₁₇	—	17	1	no	—
35	D₁₁₉	—	17	1	no	—
36	D₁₁₉	—	17	1	no	—
37	D₁₁₉	—	34	8	no	—
38	D₁₁₉	C₃×D₁₇	1	1	yes	characteristic, direct product factor
39	C₇×D₁₇	C₃×D₁₇	1	1	yes	characteristic, complemented
40	D₇×C₁₇	—	17	1	no	—
41	C₂×C₃×D₁₇	—	119	1	no	—
42	C₂×C₃×D₁₇	—	119	1	no	—
43	C₇×C₁₇	—	2	8	no	—
44	C₇×C₁₇	C₂×C₃×D₁₇	1	1	yes	characteristic, complemented
45	C₇×C₁₇	C₂×C₃×D₁₇	1	1	yes	characteristic, complemented
46	C₂×C₃×C₁₇	—	17	1	no	—
47	C₂×C₃×C₁₇	—	119	1	no	—
48	C₃×D₁₇	—	7	1	no	—
49	C₃×D₁₇	—	119	1	no	—
50	C₃×D₁₇	—	119	1	no	—
51	C₃×D₁₇	—	238	8	no	—
52	C₃×D₁₇	D₁₁₉	1	1	yes	characteristic, direct product factor
53	C₂×C₃×D₇	—	289	1	no	Hall
54	C₂×D₁₇	—	119	1	no	—
55	C₂×D₁₇	—	119	1	no	—
56	C₃×C₁₇	—	2	8	no	—
57	C₃×C₁₇	D₇×D₁₇	1	1	yes	characteristic, complemented
58	C₃×C₁₇	C₂×D₁₁₉	1	1	yes	characteristic, complemented
59	C₂×C₃×C₇	—	17	1	no	—
60	C₃×D₇	—	17	1	no	—
61	C₃×D₇	—	289	1	no	—
62	C₂×C₁₇	—	17	1	no	—
63	C₂×C₁₇	—	119	1	no	—
64	D₁₇	—	7	1	no	—
65	D₁₇	—	119	1	no	—
66	D₁₇	—	119	1	no	—
67	D₁₇	—	238	8	no	—
68	D₁₇	C₃×D₁₁₉	1	1	yes	characteristic, direct product factor
69	C₂×D₇	—	289	1	no	Hall
70	C₃×C₇	D₁₇²	1	1	yes	characteristic, complemented, Hall
71	C₁₇	—	2	8	no	—
72	C₁₇	C₃×D₇×D₁₇	1	1	yes	characteristic, complemented
73	C₁₇	C₂×C₃×D₁₁₉	1	1	yes	characteristic, complemented
74	C₂×C₇	—	17	1	no	—
75	D₇	—	17	1	no	—
76	D₇	—	289	1	no	—
77	C₂²×C₃	—	2023	1	no	Hall
78	C₇	C₃×D₁₇²	1	1	yes	characteristic, complemented, Sylow
79	C₂×C₃	—	17	1	no	—
80	C₂×C₃	—	119	1	no	—
81	C₂×C₃	—	2023	1	no	—
82	C₂²	—	2023	1	no	Sylow
83	C₃	D₁₇×D₁₁₉	1	1	yes	characteristic, direct product factor, Sylow
84	C₂	—	17	1	no	—
85	C₂	—	119	1	no	—
86	C₂	—	2023	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₁₇×D₁₁₉
commutator, cosocle, hypocenter	C₇×C₁₇²	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₇²	C₂²
LCS	G ▷ C₇×C₁₇²
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₇×D₁₇	C₂	semidirect
2. C₃×C₁₇×D₁₁₉	C₂	semidirect
3. C₃×C₇⋊(C₁₇⋊D₁₇)	C₂	semidirect
4. D₁₇×D₁₁₉	C₃	direct (N × H)
5. C₃×C₇×C₁₇²	C₂²	semidirect
6. C₇⋊(C₁₇⋊D₁₇)	C₂×C₃	semidirect
7. C₁₇×D₁₁₉	C₂×C₃	semidirect
8. C₇×C₁₇×D₁₇	C₂×C₃	semidirect
10. C₇×C₁₇²	C₂²×C₃	semidirect
12. C₃×C₁₇×D₁₇	D₇	semidirect
17. C₃×C₁₇²	C₂×D₇	semidirect
22. C₃×D₁₁₉	D₁₇	direct (N × H)
24. C₃×C₇×D₁₇	D₁₇	semidirect
27. C₁₇×D₁₇	C₃×D₇	semidirect
31. C₃×C₇×C₁₇	C₂×D₁₇	semidirect
32. C₃×C₇×C₁₇	C₂×D₁₇	semidirect
33. C₁₇²	C₂×C₃×D₇	semidirect
38. D₁₁₉	C₃×D₁₇	direct (N × H)
39. C₇×D₁₇	C₃×D₁₇	semidirect
44. C₇×C₁₇	C₂×C₃×D₁₇	semidirect
45. C₇×C₁₇	C₂×C₃×D₁₇	semidirect
52. C₃×D₁₇	D₁₁₉	direct (N × H)
57. C₃×C₁₇	D₇×D₁₇	semidirect
58. C₃×C₁₇	C₂×D₁₁₉	semidirect
68. D₁₇	C₃×D₁₁₉	direct (N × H)
70. C₃×C₇	D₁₇²	semidirect
72. C₁₇	C₃×D₇×D₁₇	semidirect
73. C₁₇	C₂×C₃×D₁₁₉	semidirect
78. C₇	C₃×D₁₇²	semidirect
83. C₃	D₁₇×D₁₁₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₇×C₁₇×D₁₇	2
C₃×C₁₇×D₁₁₉	2
C₃×C₇⋊(C₁₇⋊D₁₇)	2
D₁₇×D₁₁₉	3
C₃×D₁₇²	7
C₂×C₃×D₁₁₉	17
C₃×D₇×D₁₇	17

Subgroups — C3×D17×D119 #37566263

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₁₇×D₁₁₉ #37566263