Subgroups — (C₃⋊D₃)⋊D₁₁₉ #16862822

Order 4284.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₇×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₃₅₇	C₂	1	2	yes	maximal, complemented
3	D₃×D₁₁₉	—	3	2	no	maximal
4	C₃²×C₇×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₃₅₇	D₃	1	2	yes	complemented
6	D₃×C₇×C₁₇	—	3	2	no	—
7	D₃×C₇×C₁₇	—	6	1	no	—
8	C₃×D₁₁₉	—	3	2	no	—
9	(C₃⋊D₃)⋊D₁₇	—	7	1	no	maximal, Hall
10	C₂×D₁₁₉	—	9	1	no	Hall
11	C₃×C₇×C₁₇	—	2	1	no	—
12	C₃×C₇×C₁₇	C₂×D₃	1	2	yes	complemented
13	C₁₇×C₃⋊D₃	D₇	1	1	yes	characteristic, complemented
14	C₃×D₅₁	—	7	2	no	—
15	(C₃⋊D₃)⋊D₇	—	17	1	no	maximal, Hall
16	C₂×C₇×C₁₇	—	9	1	no	—
17	D₁₁₉	—	3	2	no	—
18	D₃×D₁₇	—	21	2	no	—
19	C₃²×C₁₇	C₂×D₇	1	1	yes	characteristic, complemented, Hall
20	C₇×C₃⋊D₃	D₁₇	1	1	yes	characteristic, complemented
21	C₃×D₂₁	—	17	2	no	—
22	C₇×C₁₇	D₃²	1	1	yes	characteristic, complemented, Hall
23	D₅₁	—	7	2	no	—
24	C₃×D₁₇	—	21	2	no	—
25	D₃×C₁₇	—	3	2	no	—
26	D₃×C₁₇	—	6	1	no	—
27	D₃×D₇	—	51	2	no	—
28	C₂×D₁₇	—	63	1	no	Hall
29	C₃²×C₇	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
30	C₃×C₁₇	—	2	1	no	—
31	C₃×C₁₇	D₃×D₇	1	2	yes	complemented
32	D₂₁	—	17	2	no	—
33	C₃×D₇	—	51	2	no	—
34	D₃×C₇	—	3	2	no	—
35	D₃×C₇	—	6	1	no	—
36	D₃²	—	119	1	no	Hall
37	C₂×C₁₇	—	9	1	no	—
38	D₁₇	—	21	2	no	—
39	C₂×D₇	—	153	1	no	Hall
40	C₃×C₇	—	2	1	no	—
41	C₃×C₇	D₃×D₁₇	1	2	yes	complemented
42	C₃⋊D₃	D₁₁₉	1	1	yes	characteristic, complemented
43	C₃×D₃	—	119	2	no	—
44	C₁₇	(C₃⋊D₃)⋊D₇	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₇	—	9	1	no	—
46	D₇	—	51	2	no	—
47	C₂×D₃	—	357	2	no	—
48	C₃²	C₂×D₁₁₉	1	1	yes	characteristic, complemented, Sylow
49	C₇	(C₃⋊D₃)⋊D₁₇	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	357	2	no	—
51	D₃	—	3	2	no	—
52	D₃	—	6	1	no	—
53	D₃	—	119	2	no	—
54	C₂²	—	1071	1	no	Sylow
55	C₃	—	2	1	no	—
56	C₃	D₃×D₁₁₉	1	2	yes	complemented
57	C₂	—	9	1	no	—
58	C₂	—	357	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₇×C₁₇	C₂²
LCS	G ▷ C₃²×C₇×C₁₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₇×C₃⋊D₃	C₂	semidirect
2. C₃×D₃₅₇	C₂	semidirect
4. C₃²×C₇×C₁₇	C₂²	semidirect
5. D₃₅₇	D₃	semidirect
12. C₃×C₇×C₁₇	C₂×D₃	semidirect
13. C₁₇×C₃⋊D₃	D₇	semidirect
19. C₃²×C₁₇	C₂×D₇	semidirect
20. C₇×C₃⋊D₃	D₁₇	semidirect
22. C₇×C₁₇	D₃²	semidirect
29. C₃²×C₇	C₂×D₁₇	semidirect
31. C₃×C₁₇	D₃×D₇	semidirect
41. C₃×C₇	D₃×D₁₇	semidirect
42. C₃⋊D₃	D₁₁₉	semidirect
44. C₁₇	(C₃⋊D₃)⋊D₇	semidirect
48. C₃²	C₂×D₁₁₉	semidirect
49. C₇	(C₃⋊D₃)⋊D₁₇	semidirect
56. C₃	D₃×D₁₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₁₇×C₃⋊D₃	2
C₃×D₃₅₇	2
D₃×D₁₁₉	3
(C₃⋊D₃)⋊D₁₇	7
(C₃⋊D₃)⋊D₇	17

Subgroups — (C3⋊D3)⋊D119 #16862822

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₃⋊D₃)⋊D₁₁₉ #16862822