Subgroups — C₂×C₃×D₂₇₁₇ #45656830

Order 32604.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₂₇₁₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₁×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₇₁₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₁₁×C₁₃×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₂₇₁₇	C₂×C₃	1	2	yes	direct product factor
6	C₂×C₁₁×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×C₃×D₂₄₇	—	11	1	no	maximal, Hall
8	C₁₁×C₁₃×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×D₂₀₉	—	13	1	no	maximal, Hall
10	C₂×C₃×D₁₄₃	—	19	1	no	maximal, Hall
11	C₂×C₃×C₁₃×C₁₉	D₁₁	1	1	yes	characteristic, complemented
12	C₃×D₂₄₇	—	11	2	no	—
13	C₂×C₃×C₁₁×C₁₉	D₁₃	1	1	yes	characteristic, complemented
14	C₃×D₂₀₉	—	13	2	no	—
15	C₂×D₂₄₇	—	11	1	no	Hall
16	C₂×C₃×C₁₁×C₁₃	D₁₉	1	1	yes	characteristic, complemented
17	C₃×D₁₄₃	—	19	2	no	—
18	C₂×D₂₀₉	—	13	1	no	Hall
19	C₃×C₁₃×C₁₉	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
20	C₃×C₁₁×C₁₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
21	C₂×D₁₄₃	—	19	1	no	Hall
22	C₂×C₁₃×C₁₉	C₃×D₁₁	1	1	yes	characteristic, complemented
23	D₂₄₇	—	11	2	no	—
24	C₃×C₁₁×C₁₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
25	C₂×C₁₁×C₁₉	C₃×D₁₃	1	1	yes	characteristic, complemented
26	D₂₀₉	—	13	2	no	—
27	C₂×C₁₁×C₁₃	C₃×D₁₉	1	1	yes	characteristic, complemented
28	D₁₄₃	—	19	2	no	—
29	C₁₃×C₁₉	C₂×C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×D₁₉	—	143	1	no	Hall
31	C₁₁×C₁₉	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented, Hall
32	C₂×C₃×D₁₃	—	209	1	no	Hall
33	C₁₁×C₁₃	C₂×C₃×D₁₉	1	1	yes	characteristic, complemented, Hall
34	C₂×C₃×D₁₁	—	247	1	no	Hall
35	C₂×C₃×C₁₉	D₁₄₃	1	1	yes	characteristic, complemented
36	C₃×D₁₉	—	143	2	no	—
37	C₂×C₃×C₁₃	D₂₀₉	1	1	yes	characteristic, complemented
38	C₃×D₁₃	—	209	2	no	—
39	C₂×D₁₉	—	143	1	no	Hall
40	C₂×C₃×C₁₁	D₂₄₇	1	1	yes	characteristic, complemented
41	C₃×D₁₁	—	247	2	no	—
42	C₃×C₁₉	C₂×D₁₄₃	1	1	yes	characteristic, complemented, Hall
43	C₂×D₁₃	—	209	1	no	Hall
44	C₂×D₁₁	—	247	1	no	Hall
45	C₃×C₁₃	C₂×D₂₀₉	1	1	yes	characteristic, complemented, Hall
46	C₂×C₁₉	C₃×D₁₄₃	1	1	yes	characteristic, complemented
47	D₁₉	—	143	2	no	—
48	C₃×C₁₁	C₂×D₂₄₇	1	1	yes	characteristic, complemented, Hall
49	C₂×C₁₃	C₃×D₂₀₉	1	1	yes	characteristic, complemented
50	D₁₃	—	209	2	no	—
51	C₂×C₁₁	C₃×D₂₄₇	1	1	yes	characteristic, complemented
52	D₁₁	—	247	2	no	—
53	C₁₉	C₂×C₃×D₁₄₃	1	1	yes	characteristic, complemented, Sylow
54	C₁₃	C₂×C₃×D₂₀₉	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₃	—	2717	1	no	Hall
56	C₁₁	C₂×C₃×D₂₄₇	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₃	—	2717	2	no	—
58	C₂×C₃	D₂₇₁₇	1	1	yes	characteristic, direct product factor
59	C₂²	—	2717	1	no	Sylow
60	C₃	C₂×D₂₇₁₇	1	1	yes	characteristic, direct product factor, Sylow
61	C₂	—	2717	2	no	—
62	C₂	C₃×D₂₇₁₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	D₂₇₁₇
commutator, cosocle, hypocenter	C₁₁×C₁₃×C₁₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₁×C₁₃×C₁₉	C₂
LCS	G ▷ C₁₁×C₁₃×C₁₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₂₇₁₇	C₂	direct (N × H)
2. C₂×C₃×C₁₁×C₁₃×C₁₉	C₂	semidirect
3. C₂×D₂₇₁₇	C₃	direct (N × H)
4. C₃×C₁₁×C₁₃×C₁₉	C₂²	semidirect
5. D₂₇₁₇	C₂×C₃	direct (N × H)
6. C₂×C₁₁×C₁₃×C₁₉	C₂×C₃	semidirect
8. C₁₁×C₁₃×C₁₉	C₂²×C₃	semidirect
11. C₂×C₃×C₁₃×C₁₉	D₁₁	semidirect
13. C₂×C₃×C₁₁×C₁₉	D₁₃	semidirect
16. C₂×C₃×C₁₁×C₁₃	D₁₉	semidirect
19. C₃×C₁₃×C₁₉	C₂×D₁₁	semidirect
20. C₃×C₁₁×C₁₉	C₂×D₁₃	semidirect
22. C₂×C₁₃×C₁₉	C₃×D₁₁	semidirect
24. C₃×C₁₁×C₁₃	C₂×D₁₉	semidirect
25. C₂×C₁₁×C₁₉	C₃×D₁₃	semidirect
27. C₂×C₁₁×C₁₃	C₃×D₁₉	semidirect
29. C₁₃×C₁₉	C₂×C₃×D₁₁	semidirect
31. C₁₁×C₁₉	C₂×C₃×D₁₃	semidirect
33. C₁₁×C₁₃	C₂×C₃×D₁₉	semidirect
35. C₂×C₃×C₁₉	D₁₄₃	semidirect
37. C₂×C₃×C₁₃	D₂₀₉	semidirect
40. C₂×C₃×C₁₁	D₂₄₇	semidirect
42. C₃×C₁₉	C₂×D₁₄₃	semidirect
45. C₃×C₁₃	C₂×D₂₀₉	semidirect
46. C₂×C₁₉	C₃×D₁₄₃	semidirect
48. C₃×C₁₁	C₂×D₂₄₇	semidirect
49. C₂×C₁₃	C₃×D₂₀₉	semidirect
51. C₂×C₁₁	C₃×D₂₄₇	semidirect
53. C₁₉	C₂×C₃×D₁₄₃	semidirect
54. C₁₃	C₂×C₃×D₂₀₉	semidirect
56. C₁₁	C₂×C₃×D₂₄₇	semidirect
58. C₂×C₃	D₂₇₁₇	direct (N × H)
60. C₃	C₂×D₂₇₁₇	direct (N × H)
62. C₂	C₃×D₂₇₁₇	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×D₂₇₁₇	2
C₂×C₃×C₁₁×C₁₃×C₁₉	2
C₂×D₂₇₁₇	3
C₂×C₃×D₂₄₇	11
C₂×C₃×D₂₀₉	13
C₂×C₃×D₁₄₃	19

Subgroups — C2×C3×D2717 #45656830

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₂₇₁₇ #45656830