Subgroups — C₂×C₁₇×#11759818 #46828310

Order 34476.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#92789	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×#11759818	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₁₃×C₁₇×D₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₇×#92789	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₃×C₁₇×D₁₃	C₂×C₃	1	2	yes	complemented
6	C₂×C₁₃²×C₁₇	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₃²×C₁₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂²×C₁₇×C₁₃⋊C₃	—	13	1	no	maximal
9	C₂×C₁₇×D₁₃⋊C₃	—	13	1	no	maximal
10	C₂×#11759818	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₁₇×C₁₃⋊C₃	—	13	2	no	—
12	C₂×C₁₇×C₁₃⋊C₃	—	13	1	no	—
13	C₂×C₁₇×C₁₃⋊C₃	—	13	1	no	—
14	C₁₇×D₁₃⋊C₃	—	13	2	no	—
15	C₂×#92789	C₂×C₁₇	1	1	yes	characteristic, complemented
16	#11759818	C₂×C₁₇	1	2	yes	direct product factor
17	C₂²×C₁₃×C₁₇	—	13	1	no	—
18	C₂×C₁₇×D₁₃	C₁₃⋊C₃	1	1	yes	characteristic, complemented
19	C₂×C₁₃×D₁₃	C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
20	C₁₇×C₁₃⋊C₃	—	13	1	no	—
21	C₁₇×C₁₃⋊C₃	—	13	1	no	—
22	#92789	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
23	C₂×C₁₃×C₁₇	—	6	2	no	—
24	C₂×C₁₃×C₁₇	—	13	2	no	—
25	C₂×C₁₃×C₁₇	D₁₃⋊C₃	1	1	yes	characteristic, complemented
26	C₂×C₁₃×C₁₇	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
27	C₁₇×D₁₃	C₂×C₁₃⋊C₃	1	2	yes	complemented
28	C₂×C₁₃²	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented
29	C₁₃×D₁₃	C₂×C₃×C₁₇	1	2	yes	complemented
30	C₁₃×C₁₇	—	6	2	no	—
31	C₁₃×C₁₇	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented
32	C₁₃×C₁₇	C₂²×C₁₃⋊C₃	1	1	yes	characteristic, complemented
33	C₂²×C₃×C₁₇	—	169	1	no	Hall
34	C₁₃²	C₂²×C₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
35	C₂²×C₁₃⋊C₃	—	13	1	no	—
36	C₂×D₁₃⋊C₃	—	13	1	no	—
37	C₂×C₃×C₁₇	—	169	2	no	—
38	C₂×C₃×C₁₇	—	169	1	no	—
39	C₂×C₁₃⋊C₃	—	13	2	no	—
40	C₂×C₁₃⋊C₃	—	13	1	no	—
41	C₂×C₁₃⋊C₃	—	13	1	no	—
42	D₁₃⋊C₃	—	13	2	no	—
43	C₂²×C₁₇	—	13	1	no	Hall
44	C₂²×C₁₃	—	13	1	no	—
45	C₂×D₁₃	C₁₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented
46	C₃×C₁₇	—	169	1	no	Hall
47	C₁₃⋊C₃	—	13	1	no	—
48	C₁₃⋊C₃	—	13	1	no	—
49	C₂×C₁₇	—	13	2	no	—
50	C₂×C₁₇	#11759818	1	1	yes	characteristic, direct product factor
51	C₂×C₁₃	—	6	2	no	—
52	C₂×C₁₃	—	13	2	no	—
53	C₂×C₁₃	C₁₇×D₁₃⋊C₃	1	1	yes	characteristic, complemented
54	C₂×C₁₃	C₂×C₁₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented
55	D₁₃	C₂×C₁₇×C₁₃⋊C₃	1	2	yes	complemented
56	C₁₇	C₂×#11759818	1	1	yes	characteristic, direct product factor, Sylow
57	C₁₃	—	6	2	no	—
58	C₁₃	C₂×C₁₇×D₁₃⋊C₃	1	1	yes	characteristic, complemented
59	C₁₃	C₂²×C₁₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented
60	C₂²×C₃	—	169	1	no	Hall
61	C₂×C₃	—	169	2	no	—
62	C₂×C₃	—	169	1	no	—
63	C₂²	—	13	1	no	Sylow
64	C₃	—	169	1	no	Sylow
65	C₂	—	13	2	no	—
66	C₂	C₁₇×#11759818	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₇	#11759818
commutator, cosocle, hypocenter	C₁₃²	C₂²×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₁₃²×C₁₇	C₂×C₃
LCS	G ▷ C₁₃²
UCS	C₁ ◁ C₂×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₇×#92789	C₂	semidirect
2. C₁₇×#11759818	C₂	direct (N × H)
3. C₂×C₁₃×C₁₇×D₁₃	C₃	semidirect
4. C₁₇×#92789	C₂²	semidirect
5. C₁₃×C₁₇×D₁₃	C₂×C₃	semidirect
6. C₂×C₁₃²×C₁₇	C₂×C₃	semidirect
7. C₁₃²×C₁₇	C₂²×C₃	semidirect
10. C₂×#11759818	C₁₇	direct (N × H)
15. C₂×#92789	C₂×C₁₇	semidirect
16. #11759818	C₂×C₁₇	direct (N × H)
18. C₂×C₁₇×D₁₃	C₁₃⋊C₃	semidirect
19. C₂×C₁₃×D₁₃	C₃×C₁₇	semidirect
22. #92789	C₂²×C₁₇	semidirect
25. C₂×C₁₃×C₁₇	D₁₃⋊C₃	semidirect
26. C₂×C₁₃×C₁₇	C₂×C₁₃⋊C₃	semidirect
27. C₁₇×D₁₃	C₂×C₁₃⋊C₃	semidirect
28. C₂×C₁₃²	C₂×C₃×C₁₇	semidirect
29. C₁₃×D₁₃	C₂×C₃×C₁₇	semidirect
31. C₁₃×C₁₇	C₂×D₁₃⋊C₃	semidirect
32. C₁₃×C₁₇	C₂²×C₁₃⋊C₃	semidirect
34. C₁₃²	C₂²×C₃×C₁₇	semidirect
45. C₂×D₁₃	C₁₇×C₁₃⋊C₃	semidirect
50. C₂×C₁₇	#11759818	direct (N × H)
53. C₂×C₁₃	C₁₇×D₁₃⋊C₃	semidirect
54. C₂×C₁₃	C₂×C₁₇×C₁₃⋊C₃	semidirect
55. D₁₃	C₂×C₁₇×C₁₃⋊C₃	semidirect
56. C₁₇	C₂×#11759818	direct (N × H)
58. C₁₃	C₂×C₁₇×D₁₃⋊C₃	semidirect
59. C₁₃	C₂²×C₁₇×C₁₃⋊C₃	semidirect
66. C₂	C₁₇×#11759818	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₇×#92789	2
C₁₇×#11759818	2
C₂×C₁₃×C₁₇×D₁₃	3
C₂²×C₁₇×C₁₃⋊C₃	13
C₂×C₁₇×D₁₃⋊C₃	13
C₂×#11759818	17

Subgroups — C2×C17×#11759818 #46828310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×#11759818 #46828310