Subgroups — C₃×D₁₁₉⋊D₁₇ #37566264

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	2	yes	maximal, complemented
3	D₁₁₉⋊D₁₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₇×C₁₇²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₇×D₁₁₉	C₂×C₃	1	2	yes	complemented
6	C₇×C₁₇⋊D₁₇	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃×D₁₇²	—	7	1	no	maximal, Hall
8	C₇×C₁₇²	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₃×C₁₇×D₁₇	—	7	2	no	—
10	C₃×C₁₇⋊D₁₇	D₇	1	1	yes	characteristic, complemented
11	C₃×D₇×D₁₇	—	17	2	no	maximal
12	D₁₇²	—	7	1	no	Hall
13	C₃×C₁₇²	C₂×D₇	1	1	yes	characteristic, complemented, Hall
14	C₃×D₁₁₉	D₁₇	1	2	yes	complemented
15	C₃×D₇×C₁₇	—	17	2	no	—
16	C₃×C₇×D₁₇	—	17	2	no	—
17	C₃×C₇×D₁₇	—	34	8	no	—
18	C₁₇⋊D₁₇	C₃×D₇	1	1	yes	characteristic, complemented
19	C₁₇×D₁₇	—	7	2	no	—
20	D₇×D₁₇	—	17	2	no	—
21	C₃×C₇×C₁₇	—	2	8	no	—
22	C₃×C₇×C₁₇	C₂×D₁₇	1	2	yes	complemented
23	C₁₇²	C₂×C₃×D₇	1	1	yes	characteristic, complemented, Sylow
24	D₁₁₉	C₃×D₁₇	1	2	yes	complemented
25	C₇×D₁₇	—	17	2	no	—
26	C₇×D₁₇	—	34	8	no	—
27	D₇×C₁₇	—	17	2	no	—
28	C₂×C₃×D₁₇	—	119	2	no	—
29	C₇×C₁₇	—	2	8	no	—
30	C₇×C₁₇	C₂×C₃×D₁₇	1	2	yes	complemented
31	C₂×C₃×C₁₇	—	119	2	no	—
32	C₃×D₁₇	—	7	2	no	—
33	C₃×D₁₇	—	17	2	no	—
34	C₃×D₁₇	—	34	8	no	—
35	C₂×C₃×D₇	—	289	1	no	Hall
36	C₂×D₁₇	—	119	2	no	—
37	C₃×C₁₇	—	2	8	no	—
38	C₃×C₁₇	D₇×D₁₇	1	2	yes	complemented
39	C₂×C₃×C₇	—	289	1	no	—
40	C₃×D₇	—	17	2	no	—
41	C₂×C₁₇	—	119	2	no	—
42	D₁₇	—	7	2	no	—
43	D₁₇	—	17	2	no	—
44	D₁₇	—	34	8	no	—
45	C₂×D₇	—	289	1	no	Hall
46	C₃×C₇	D₁₇²	1	1	yes	characteristic, complemented, Hall
47	C₁₇	—	2	8	no	—
48	C₁₇	C₃×D₇×D₁₇	1	2	yes	complemented
49	C₂×C₇	—	289	1	no	—
50	D₇	—	17	2	no	—
51	C₂²×C₃	—	2023	1	no	Hall
52	C₇	C₃×D₁₇²	1	1	yes	characteristic, complemented, Sylow
53	C₂×C₃	—	289	1	no	—
54	C₂×C₃	—	119	2	no	—
55	C₂²	—	2023	1	no	Sylow
56	C₃	D₁₁₉⋊D₁₇	1	1	yes	characteristic, direct product factor, Sylow
57	C₂	—	289	1	no	—
58	C₂	—	119	2	no	—

	subgroup	G/H
center, hypercenter	C₃	D₁₁₉⋊D₁₇
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. D₁₁₉⋊D₁₇	C₃	direct (N × H)
4. C₃×C₇×C₁₇²	C₂²	semidirect
5. C₁₇×D₁₁₉	C₂×C₃	semidirect
6. C₇×C₁₇⋊D₁₇	C₂×C₃	semidirect
8. C₇×C₁₇²	C₂²×C₃	semidirect
10. C₃×C₁₇⋊D₁₇	D₇	semidirect
13. C₃×C₁₇²	C₂×D₇	semidirect
14. C₃×D₁₁₉	D₁₇	semidirect
18. C₁₇⋊D₁₇	C₃×D₇	semidirect
22. C₃×C₇×C₁₇	C₂×D₁₇	semidirect
23. C₁₇²	C₂×C₃×D₇	semidirect
24. D₁₁₉	C₃×D₁₇	semidirect
30. C₇×C₁₇	C₂×C₃×D₁₇	semidirect
38. C₃×C₁₇	D₇×D₁₇	semidirect
46. C₃×C₇	D₁₇²	semidirect
48. C₁₇	C₃×D₇×D₁₇	semidirect
52. C₇	C₃×D₁₇²	semidirect
56. C₃	D₁₁₉⋊D₁₇	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
D₁₁₉⋊D₁₇	3
C₃×D₁₇²	7
C₃×D₇×D₁₇	17

Subgroups — C3×D119⋊D17 #37566264

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₁₁₉⋊D₁₇ #37566264