Subgroups — D₃×C₂²⋊D₁₇ #11717876

Order 816.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₃×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₃×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#87992	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₂²⋊D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#87975	C₂	1	1	yes	maximal, characteristic, complemented
6	#87973	C₂	1	1	yes	maximal, characteristic, complemented
7	D₃×Dic₁₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂²⋊D₁₇	—	3	1	no	maximal, Hall
9	C₂²×C₃×C₁₇	C₂²	1	1	yes	characteristic, complemented
10	C₂×D₅₁	C₂²	1	1	yes	characteristic, complemented
11	C₂×D₃×C₁₇	—	2	2	no	—
12	C₂×D₃×C₁₇	C₂²	1	1	yes	characteristic
13	C₂×D₃×C₁₇	C₂²	1	1	yes	characteristic, complemented
14	C₂×C₃×D₁₇	C₂²	1	1	yes	characteristic, complemented
15	D₃×D₁₇	—	2	2	no	—
16	Dic₅₁	C₂²	1	1	yes	characteristic, complemented
17	C₃×Dic₁₇	C₂²	1	1	yes	characteristic, complemented
18	C₂³×C₁₇	—	3	1	no	—
19	C₂²×D₁₇	—	3	1	no	—
20	C₂²⋊D₁₇	—	3	1	no	—
21	C₂²⋊D₁₇	—	3	1	no	—
22	C₂²⋊D₁₇	—	3	1	no	—
23	C₂²⋊D₁₇	D₃	1	1	yes	characteristic, direct product factor
24	C₂×Dic₁₇	—	3	1	no	—
25	C₂×C₃×C₁₇	—	2	1	no	—
26	C₂×C₃×C₁₇	C₂³	1	1	yes	characteristic
27	D₅₁	—	2	1	no	—
28	C₃×D₁₇	—	2	1	no	—
29	D₃×C₁₇	—	2	1	no	—
30	D₃×C₁₇	D₄	1	2	yes	complemented
31	C₂²×C₁₇	—	3	1	no	—
32	C₂²×C₁₇	—	3	1	no	—
33	C₂²×C₁₇	—	6	2	no	—
34	C₂²×C₁₇	C₂×D₃	1	1	yes	characteristic, complemented
35	C₂×D₁₇	—	3	1	no	—
36	C₂×D₁₇	—	6	2	no	—
37	C₂×D₁₇	C₂×D₃	1	1	yes	characteristic, complemented
38	Dic₁₇	—	3	1	no	—
39	Dic₁₇	C₂×D₃	1	1	yes	characteristic, complemented
40	C₃×C₁₇	C₂×D₄	1	1	yes	characteristic, complemented, Hall
41	D₃×D₄	—	17	1	no	maximal, Hall
42	C₂×C₁₇	—	2	1	no	—
43	C₂×C₁₇	—	3	2	no	—
44	C₂×C₁₇	—	6	1	no	—
45	C₂×C₁₇	C₂²×D₃	1	1	yes	characteristic
46	D₁₇	—	2	1	no	—
47	D₁₇	—	6	1	no	—
48	C₂²×D₃	—	17	1	no	—
49	C₂²×D₃	D₁₇	1	1	yes	characteristic, complemented
50	C₃×D₄	—	17	1	no	—
51	#67	—	17	1	no	—
52	#67	—	17	1	no	—
53	D₁₂	—	17	1	no	—
54	C₄×D₃	—	17	1	no	—
55	C₁₇	D₃×D₄	1	1	yes	characteristic, complemented, Sylow
56	C₂×D₄	—	51	1	no	Sylow
57	C₂²×C₃	—	17	1	no	—
58	C₂²×C₃	C₂×D₁₇	1	1	yes	characteristic, complemented
59	C₂×D₃	—	2	2	no	—
60	C₂×D₃	—	17	1	no	—
61	C₂×D₃	—	34	2	no	—
62	C₂×D₃	C₂×D₁₇	1	1	yes	characteristic
63	C₂×D₃	C₂×D₁₇	1	1	yes	characteristic, complemented
64	C₃×C₄	—	17	1	no	—
65	Dic₃	—	17	1	no	—
66	C₂³	—	3	1	no	—
67	C₂³	—	51	1	no	—
68	D₄	—	17	1	no	—
69	D₄	—	51	1	no	—
70	D₄	—	51	1	no	—
71	D₄	—	51	1	no	—
72	C₂×C₄	—	51	1	no	—
73	C₂×C₃	—	2	1	no	—
74	C₂×C₃	—	34	1	no	—
75	C₂×C₃	C₂²×D₁₇	1	1	yes	characteristic
76	D₃	—	2	1	no	—
77	D₃	—	34	1	no	—
78	D₃	C₂²⋊D₁₇	1	2	yes	direct product factor
79	C₂²	—	3	1	no	—
80	C₂²	—	3	1	no	—
81	C₂²	—	6	2	no	—
82	C₂²	—	17	1	no	—
83	C₂²	—	51	1	no	—
84	C₂²	—	102	2	no	—
85	C₂²	D₃×D₁₇	1	1	yes	characteristic, complemented
86	C₄	—	17	1	no	—
87	C₄	—	51	1	no	—
88	C₃	C₂×C₂²⋊D₁₇	1	1	yes	characteristic, complemented, Sylow
89	C₂	—	2	1	no	—
90	C₂	—	3	2	no	—
91	C₂	—	6	1	no	—
92	C₂	—	34	1	no	—
93	C₂	—	102	1	no	—
94	C₂	C₂×D₃×D₁₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×D₃×D₁₇
commutator, socle, cosocle	C₂×C₃×C₁₇	C₂³
Fitting	C₂²×C₃×C₁₇	C₂²
hypercenter	C₂²	D₃×D₁₇
hypocenter	C₃×C₁₇	C₂×D₄
LCS	G ▷ C₂×C₃×C₁₇ ▷ C₃×C₁₇
UCS	C₁ ◁ C₂ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂²×D₃×C₁₇	C₂	semidirect
2. C₂×D₃×D₁₇	C₂	semidirect
3. #87992	C₂	semidirect
4. C₃×C₂²⋊D₁₇	C₂	semidirect
5. #87975	C₂	semidirect
6. #87973	C₂	semidirect
7. D₃×Dic₁₇	C₂	semidirect
9. C₂²×C₃×C₁₇	C₂²	semidirect
10. C₂×D₅₁	C₂²	semidirect
13. C₂×D₃×C₁₇	C₂²	semidirect
14. C₂×C₃×D₁₇	C₂²	semidirect
16. Dic₅₁	C₂²	semidirect
17. C₃×Dic₁₇	C₂²	semidirect
23. C₂²⋊D₁₇	D₃	direct (N × H)
30. D₃×C₁₇	D₄	semidirect
34. C₂²×C₁₇	C₂×D₃	semidirect
37. C₂×D₁₇	C₂×D₃	semidirect
39. Dic₁₇	C₂×D₃	semidirect
40. C₃×C₁₇	C₂×D₄	semidirect
49. C₂²×D₃	D₁₇	semidirect
55. C₁₇	D₃×D₄	semidirect
58. C₂²×C₃	C₂×D₁₇	semidirect
63. C₂×D₃	C₂×D₁₇	semidirect
78. D₃	C₂²⋊D₁₇	direct (N × H)
85. C₂²	D₃×D₁₇	semidirect
88. C₃	C₂×C₂²⋊D₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×D₃×C₁₇	2
C₂×D₃×D₁₇	2
#87992	2
C₃×C₂²⋊D₁₇	2
#87975	2
#87973	2
D₃×Dic₁₇	2
C₂×C₂²⋊D₁₇	3
D₃×D₄	17

Subgroups — D3×C22⋊D17 #11717876

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₂²⋊D₁₇ #11717876