Subgroups — D₁₇×Q₆₄ #14531087

Order 2176.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₃₂×D₁₇	C₂	1	2	yes	maximal
2	Dic₂₇₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#11762649	C₂	1	2	yes	maximal, complemented
4	C₃₂×D₁₇	C₂	1	1	yes	maximal, characteristic
5	C₁₇×Q₆₄	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₁₆×D₁₇	—	2	2	no	—
7	C₁₇×Q₃₂	C₂²	1	2	yes	—
8	#10587500	—	2	2	no	—
9	Dic₁₃₆	C₂²	1	2	yes	—
10	C₁₆×D₁₇	C₂²	1	1	yes	characteristic
11	C₁₇×C₃₂	C₂²	1	1	yes	characteristic
12	#10587465	C₂²	1	1	yes	characteristic
13	Q₈×D₁₇	—	4	2	no	—
14	Q₁₆×C₁₇	—	2	2	no	—
15	#63231	—	4	2	no	—
16	Dic₆₈	—	2	2	no	—
17	C₈×D₁₇	D₄	1	1	yes	characteristic
18	C₁₆×C₁₇	C₂³	1	1	yes	characteristic
19	#63214	D₄	1	1	yes	characteristic
20	Q₈×C₁₇	—	4	2	no	—
21	C₄×D₁₇	—	8	2	no	—
22	C₄×D₁₇	D₈	1	1	yes	characteristic
23	Dic₃₄	—	4	2	no	—
24	Dic₃₄	—	8	2	no	—
25	C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
26	#3622	D₈	1	1	yes	characteristic
27	C₂×Q₆₄	—	17	1	no	maximal, Sylow
28	C₂×D₁₇	D₁₆	1	1	yes	characteristic
29	C₄×C₁₇	—	8	2	no	—
30	C₄×C₁₇	C₂×D₈	1	1	yes	characteristic
31	Dic₁₇	—	8	2	no	—
32	Dic₁₇	D₁₆	1	1	yes	characteristic
33	C₂×Q₃₂	—	17	2	no	—
34	Q₆₄	—	17	2	no	—
35	Q₆₄	—	17	1	no	—
36	Q₆₄	D₁₇	1	1	yes	characteristic, direct product factor
37	C₂×C₃₂	—	17	1	no	—
38	C₂×C₁₇	C₂×D₁₆	1	1	yes	characteristic
39	D₁₇	Q₆₄	1	2	yes	direct product factor
40	C₂×Q₁₆	—	34	2	no	—
41	Q₃₂	—	17	2	no	—
42	Q₃₂	—	34	2	no	—
43	Q₃₂	C₂×D₁₇	1	2	yes	—
44	C₂×C₁₆	—	17	1	no	—
45	C₃₂	—	17	1	no	—
46	C₃₂	C₂×D₁₇	1	1	yes	characteristic
47	C₁₇	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
48	C₂×Q₈	—	68	2	no	—
49	Q₁₆	—	2	2	no	—
50	Q₁₆	—	34	2	no	—
51	Q₁₆	—	68	2	no	—
52	C₂×C₈	—	17	1	no	—
53	C₁₆	—	17	1	no	—
54	C₁₆	C₂²×D₁₇	1	1	yes	characteristic
55	Q₈	—	4	2	no	—
56	Q₈	—	68	2	no	—
57	Q₈	—	136	2	no	—
58	C₂×C₄	—	17	1	no	—
59	C₂×C₄	—	136	2	no	—
60	C₈	—	17	1	no	—
61	C₈	D₄×D₁₇	1	1	yes	characteristic
62	C₂²	—	17	1	no	—
63	C₄	—	8	2	no	—
64	C₄	—	17	1	no	—
65	C₄	—	136	2	no	—
66	C₄	D₈×D₁₇	1	1	yes	characteristic
67	C₂	—	17	2	no	—
68	C₂	D₁₆×D₁₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₆×D₁₇
commutator, cosocle	C₁₆×C₁₇	C₂³
Frattini	C₁₆	C₂²×D₁₇
Fitting	C₁₇×Q₆₄	C₂
socle	C₂×C₁₇	C₂×D₁₆
prime radical	C₂×D₁₇	D₁₆
hypercenter	Q₆₄	D₁₇
hypocenter	C₁₇	C₂×Q₆₄
LCS	G ▷ C₁₆×C₁₇ ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₆₄

Complements

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

N	H ≅ G/N	type
2. Dic₂₇₂	C₂	semidirect
3. #11762649	C₂	semidirect
5. C₁₇×Q₆₄	C₂	semidirect
36. Q₆₄	D₁₇	direct (N × H)
39. D₁₇	Q₆₄	direct (N × H)
47. C₁₇	C₂×Q₆₄	semidirect

Maximal subgroups

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

subgroup	index
Q₃₂×D₁₇	2
Dic₂₇₂	2
#11762649	2
C₃₂×D₁₇	2
C₁₇×Q₆₄	2
C₂×Q₆₄	17

Subgroups — D17×Q64 #14531087

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₇×Q₆₄ #14531087