Subgroups — D₃×D₂₇₁₇ #45656809

Order 32604.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₁₁×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₂₇₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₇₁₇	—	3	1	no	maximal, Hall
5	C₃×C₁₁×C₁₃×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₇₁₇	—	3	1	no	—
7	D₂₇₁₇	D₃	1	1	yes	characteristic, direct product factor
8	C₂×C₁₁×C₁₃×C₁₉	—	3	1	no	—
9	D₃×D₂₄₇	—	11	1	no	maximal, Hall
10	C₁₁×C₁₃×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	D₃×D₂₀₉	—	13	1	no	maximal, Hall
12	D₃×D₁₄₃	—	19	1	no	maximal, Hall
13	D₇₄₁	—	11	1	no	—
14	D₃×C₁₃×C₁₉	D₁₁	1	1	yes	characteristic, complemented
15	C₃×D₂₄₇	—	11	1	no	—
16	D₆₂₇	—	13	1	no	—
17	D₃×C₁₁×C₁₉	D₁₃	1	1	yes	characteristic, complemented
18	C₃×D₂₀₉	—	13	1	no	—
19	C₂×D₂₄₇	—	33	1	no	Hall
20	D₄₂₉	—	19	1	no	—
21	D₃×C₁₁×C₁₃	D₁₉	1	1	yes	characteristic, complemented
22	C₃×D₁₄₃	—	19	1	no	—
23	C₂×D₂₀₉	—	39	1	no	Hall
24	C₃×C₁₃×C₁₉	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
25	C₃×C₁₁×C₁₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
26	C₂×D₁₄₃	—	57	1	no	Hall
27	C₂×C₁₃×C₁₉	—	3	1	no	—
28	D₂₄₇	—	11	1	no	—
29	D₂₄₇	—	33	1	no	—
30	C₃×C₁₁×C₁₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
31	C₂×C₁₁×C₁₉	—	3	1	no	—
32	D₂₀₉	—	13	1	no	—
33	D₂₀₉	—	39	1	no	—
34	C₂×C₁₁×C₁₃	—	3	1	no	—
35	D₁₄₃	—	19	1	no	—
36	D₁₄₃	—	57	1	no	—
37	C₁₃×C₁₉	D₃×D₁₁	1	1	yes	characteristic, complemented, Hall
38	D₃×D₁₉	—	143	1	no	Hall
39	C₁₁×C₁₉	D₃×D₁₃	1	1	yes	characteristic, complemented, Hall
40	D₃×D₁₃	—	209	1	no	Hall
41	C₁₁×C₁₃	D₃×D₁₉	1	1	yes	characteristic, complemented, Hall
42	D₃×D₁₁	—	247	1	no	Hall
43	D₅₇	—	143	1	no	—
44	C₃×D₁₉	—	143	1	no	—
45	D₃×C₁₉	D₁₄₃	1	1	yes	characteristic, complemented
46	D₃₉	—	209	1	no	—
47	C₃×D₁₃	—	209	1	no	—
48	D₃×C₁₃	D₂₀₉	1	1	yes	characteristic, complemented
49	C₂×D₁₉	—	429	1	no	Hall
50	D₃₃	—	247	1	no	—
51	C₃×D₁₁	—	247	1	no	—
52	D₃×C₁₁	D₂₄₇	1	1	yes	characteristic, complemented
53	C₃×C₁₉	C₂×D₁₄₃	1	1	yes	characteristic, complemented, Hall
54	C₂×D₁₃	—	627	1	no	Hall
55	C₂×D₁₁	—	741	1	no	Hall
56	C₃×C₁₃	C₂×D₂₀₉	1	1	yes	characteristic, complemented, Hall
57	C₂×C₁₉	—	3	1	no	—
58	D₁₉	—	143	1	no	—
59	D₁₉	—	429	1	no	—
60	C₃×C₁₁	C₂×D₂₄₇	1	1	yes	characteristic, complemented, Hall
61	C₂×C₁₃	—	3	1	no	—
62	D₁₃	—	627	1	no	—
63	D₁₃	—	209	1	no	—
64	C₂×C₁₁	—	3	1	no	—
65	D₁₁	—	741	1	no	—
66	D₁₁	—	247	1	no	—
67	C₁₉	D₃×D₁₄₃	1	1	yes	characteristic, complemented, Sylow
68	C₁₃	D₃×D₂₀₉	1	1	yes	characteristic, complemented, Sylow
69	C₂×D₃	—	2717	1	no	Hall
70	C₁₁	D₃×D₂₄₇	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₃	—	2717	1	no	—
72	D₃	—	2717	1	no	—
73	D₃	D₂₇₁₇	1	1	yes	characteristic, direct product factor
74	C₂²	—	8151	1	no	Sylow
75	C₃	C₂×D₂₇₁₇	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	3	1	no	—
77	C₂	—	2717	1	no	—
78	C₂	—	8151	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. D₈₁₅₁	C₂	semidirect
2. D₃×C₁₁×C₁₃×C₁₉	C₂	semidirect
3. C₃×D₂₇₁₇	C₂	semidirect
5. C₃×C₁₁×C₁₃×C₁₉	C₂²	semidirect
7. D₂₇₁₇	D₃	direct (N × H)
10. C₁₁×C₁₃×C₁₉	C₂×D₃	semidirect
14. D₃×C₁₃×C₁₉	D₁₁	semidirect
17. D₃×C₁₁×C₁₉	D₁₃	semidirect
21. D₃×C₁₁×C₁₃	D₁₉	semidirect
24. C₃×C₁₃×C₁₉	C₂×D₁₁	semidirect
25. C₃×C₁₁×C₁₉	C₂×D₁₃	semidirect
30. C₃×C₁₁×C₁₃	C₂×D₁₉	semidirect
37. C₁₃×C₁₉	D₃×D₁₁	semidirect
39. C₁₁×C₁₉	D₃×D₁₃	semidirect
41. C₁₁×C₁₃	D₃×D₁₉	semidirect
45. D₃×C₁₉	D₁₄₃	semidirect
48. D₃×C₁₃	D₂₀₉	semidirect
52. D₃×C₁₁	D₂₄₇	semidirect
53. C₃×C₁₉	C₂×D₁₄₃	semidirect
56. C₃×C₁₃	C₂×D₂₀₉	semidirect
60. C₃×C₁₁	C₂×D₂₄₇	semidirect
67. C₁₉	D₃×D₁₄₃	semidirect
68. C₁₃	D₃×D₂₀₉	semidirect
70. C₁₁	D₃×D₂₄₇	semidirect
73. D₃	D₂₇₁₇	direct (N × H)
75. C₃	C₂×D₂₇₁₇	semidirect

Maximal subgroups

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

subgroup	index
D₈₁₅₁	2
D₃×C₁₁×C₁₃×C₁₉	2
C₃×D₂₇₁₇	2
C₂×D₂₇₁₇	3
D₃×D₂₄₇	11
D₃×D₂₀₉	13
D₃×D₁₄₃	19

Subgroups — D3×D2717 #45656809

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₂₇₁₇ #45656809