Subgroups — C₂×Q₁₆×D₁₇ #11763584

Order 1088.

258 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×D₁₇	C₂	1	2	yes	maximal
2	C₂×Q₁₆×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#63231	C₂	1	2	yes	maximal, complemented
4	Q₁₆×D₁₇	C₂	1	8	yes	maximal, direct product factor
5	C₂×Dic₆₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₁₇	C₂	1	1	yes	maximal, characteristic
7	C₂×Q₈×C₁₇	C₂²	1	2	yes	—
8	Q₈×D₁₇	—	2	4	no	—
9	Q₈×D₁₇	C₂²	1	8	yes	—
10	C₂×C₄×D₁₇	—	2	2	no	—
11	C₂×C₄×D₁₇	C₂²	1	1	yes	characteristic
12	C₂×Dic₃₄	—	2	2	no	—
13	C₂×Dic₃₄	C₂²	1	2	yes	—
14	Q₁₆×C₁₇	C₂²	1	4	yes	complemented
15	C₂×C₈×C₁₇	C₂²	1	1	yes	characteristic
16	#63231	C₂²	1	8	yes	complemented
17	C₂×#3622	C₂²	1	1	yes	characteristic
18	Dic₆₈	C₂²	1	4	yes	complemented
19	C₈×D₁₇	C₂²	1	4	yes	—
20	C₂²×D₁₇	D₄	1	1	yes	characteristic
21	Q₈×C₁₇	—	2	2	no	—
22	Q₈×C₁₇	C₂³	1	4	yes	—
23	C₂×C₄×C₁₇	—	2	2	no	—
24	C₂×C₄×C₁₇	C₂³	1	1	yes	characteristic
25	C₂×Dic₁₇	—	2	2	no	—
26	C₂×Dic₁₇	D₄	1	1	yes	characteristic
27	C₄×D₁₇	—	2	8	no	—
28	C₄×D₁₇	D₄	1	2	yes	—
29	C₄×D₁₇	C₂³	1	2	yes	—
30	Dic₃₄	—	2	2	no	—
31	Dic₃₄	—	2	8	no	—
32	Dic₃₄	C₂³	1	4	yes	—
33	C₈×C₁₇	C₂³	1	2	yes	—
34	#3622	C₂³	1	2	yes	—
35	C₂²×C₁₇	C₂×D₄	1	1	yes	characteristic
36	C₂×D₁₇	Q₁₆	1	4	yes	direct product factor
37	C₂×D₁₇	C₂×D₄	1	2	yes	—
38	C₄×C₁₇	—	2	4	no	—
39	C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
40	C₄×C₁₇	C₂⁴	1	1	yes	characteristic
41	Dic₁₇	—	2	4	no	—
42	Dic₁₇	C₂×D₄	1	2	yes	—
43	C₂²×Q₁₆	—	17	1	no	maximal, Sylow
44	C₂×C₁₇	C₂×Q₁₆	1	2	yes	complemented
45	C₂×C₁₇	C₂²×D₄	1	1	yes	characteristic
46	D₁₇	C₂×Q₁₆	1	4	yes	direct product factor
47	C₂²×Q₈	—	17	2	no	—
48	C₂×Q₁₆	—	17	2	no	—
49	C₂×Q₁₆	—	17	8	no	—
50	C₂×Q₁₆	—	17	1	no	—
51	C₂×Q₁₆	D₁₇	1	1	yes	characteristic, direct product factor
52	C₂²×C₈	—	17	1	no	—
53	C₁₇	C₂²×Q₁₆	1	1	yes	characteristic, complemented, Sylow
54	C₂×Q₈	—	17	8	no	—
55	C₂×Q₈	—	17	2	no	—
56	C₂×Q₈	—	34	2	no	—
57	C₂×Q₈	—	34	4	no	—
58	C₂×Q₈	C₂×D₁₇	1	2	yes	—
59	C₂²×C₄	—	17	1	no	—
60	C₂²×C₄	—	34	2	no	—
61	Q₁₆	—	17	8	no	—
62	Q₁₆	—	17	4	no	—
63	Q₁₆	C₂×D₁₇	1	4	yes	direct product factor
64	C₂×C₈	—	17	1	no	—
65	C₂×C₈	—	17	4	no	—
66	C₂×C₈	C₂×D₁₇	1	1	yes	characteristic
67	C₂³	—	17	1	no	—
68	Q₈	—	2	2	no	—
69	Q₈	—	17	4	no	—
70	Q₈	—	34	8	no	—
71	Q₈	—	34	2	no	—
72	Q₈	C₂²×D₁₇	1	4	yes	—
73	C₂×C₄	—	2	2	no	—
74	C₂×C₄	—	17	1	no	—
75	C₂×C₄	—	17	2	no	—
76	C₂×C₄	—	17	2	no	—
77	C₂×C₄	—	34	8	no	—
78	C₂×C₄	—	34	2	no	—
79	C₂×C₄	C₂²×D₁₇	1	1	yes	characteristic
80	C₈	—	17	2	no	—
81	C₈	C₂²×D₁₇	1	2	yes	—
82	C₂²	—	17	2	no	—
83	C₂²	—	17	4	no	—
84	C₂²	D₄×D₁₇	1	1	yes	characteristic
85	C₄	—	2	4	no	—
86	C₄	—	17	2	no	—
87	C₄	—	34	4	no	—
88	C₄	D₄×D₁₇	1	1	yes	characteristic
89	C₄	C₂³×D₁₇	1	1	yes	characteristic
90	C₂	—	17	4	no	—
91	C₂	Q₁₆×D₁₇	1	2	yes	direct product factor
92	C₂	C₂×D₄×D₁₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₇
commutator, cosocle	C₄×C₁₇	C₂⁴
Frattini	C₄	C₂³×D₁₇
Fitting	C₂×Q₁₆×C₁₇	C₂
socle	C₂²×C₁₇	C₂×D₄
prime radical	C₂²×D₁₇	D₄
hypercenter	C₂×Q₁₆	D₁₇
hypocenter	C₁₇	C₂²×Q₁₆
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×Q₁₆×C₁₇	C₂	semidirect
3. C₂×#63231	C₂	semidirect
4. Q₁₆×D₁₇	C₂	direct (N × H)
5. C₂×Dic₆₈	C₂	semidirect
14. Q₁₆×C₁₇	C₂²	semidirect
16. #63231	C₂²	semidirect
18. Dic₆₈	C₂²	semidirect
36. C₂×D₁₇	Q₁₆	direct (N × H)
44. C₂×C₁₇	C₂×Q₁₆	semidirect
46. D₁₇	C₂×Q₁₆	direct (N × H)
51. C₂×Q₁₆	D₁₇	direct (N × H)
53. C₁₇	C₂²×Q₁₆	semidirect
63. Q₁₆	C₂×D₁₇	direct (N × H)
91. C₂	Q₁₆×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
C₂×Q₈×D₁₇	2
C₂×Q₁₆×C₁₇	2
C₂×#63231	2
Q₁₆×D₁₇	2
C₂×Dic₆₈	2
C₂×C₈×D₁₇	2
C₂²×Q₁₆	17

Subgroups — C2×Q16×D17 #11763584

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Q₁₆×D₁₇ #11763584