Subgroups — D₁₇⋊#108 #11763822

Order 1088.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₇⋊M₁₆	C₂	1	2	yes	maximal
2	C₂×C₈×D₁₇	C₂	1	1	yes	maximal, characteristic
3	#10587536	C₂	1	2	yes	maximal, complemented
4	#10587535	C₂	1	2	yes	maximal, complemented
5	C₂×C₄×D₁₇	C₂²	1	1	yes	characteristic
6	#63247	—	2	2	no	—
7	#63243	C₂²	1	4	yes	—
8	#63242	—	2	2	no	—
9	C₂×C₈×C₁₇	C₄	1	1	yes	characteristic
10	C₂×#3622	C₄	1	1	yes	characteristic
11	C₈×D₁₇	C₄	1	1	yes	characteristic
12	C₈×D₁₇	C₄	1	1	yes	characteristic
13	C₈×D₁₇	C₂²	1	1	yes	characteristic
14	C₈×D₁₇	C₂²	1	1	yes	characteristic
15	C₂²×D₁₇	Q₈	1	1	yes	characteristic
16	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
17	C₂×Dic₁₇	D₄	1	1	yes	characteristic
18	C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
19	C₄×D₁₇	D₄	1	1	yes	characteristic
20	C₄×D₁₇	Q₈	1	1	yes	characteristic
21	C₄×D₁₇	C₂³	1	1	yes	characteristic
22	#3624	—	2	4	no	—
23	C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
24	C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
25	#3622	C₂×C₄	1	1	yes	characteristic
26	#3622	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
28	C₂×D₁₇	—	2	2	no	—
29	C₂×D₁₇	C₄⋊C₄	1	1	yes	characteristic
30	C₂×D₁₇	C₂×Q₈	1	1	yes	characteristic
31	C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
32	C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
33	Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
34	Dic₁₇	C₂×D₄	1	1	yes	characteristic
35	C₂×#108	—	17	1	no	maximal, Sylow
36	C₂×C₁₇	—	2	1	no	—
37	C₂×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
38	D₁₇	—	2	1	no	—
39	D₁₇	#108	1	2	yes	complemented
40	C₂×M₁₆	—	17	2	no	—
41	C₂²×C₈	—	17	1	no	—
42	#108	—	17	2	no	—
43	#108	—	17	2	no	—
44	C₁₇	C₂×#108	1	1	yes	characteristic, complemented, Sylow
45	C₂²×C₄	—	17	1	no	—
46	M₁₆	—	17	4	no	—
47	M₁₆	—	34	2	no	—
48	C₂×C₈	—	17	1	no	—
49	C₂×C₈	—	17	1	no	—
50	C₂×C₈	—	17	1	no	—
51	C₂×C₈	—	17	1	no	—
52	C₂×C₈	—	17	1	no	—
53	C₂×C₈	—	34	2	no	—
54	C₂×C₈	#595	1	1	yes	characteristic
55	C₂³	—	17	1	no	—
56	C₂×C₄	—	17	1	no	—
57	C₂×C₄	—	17	1	no	—
58	C₂×C₄	—	17	1	no	—
59	C₂×C₄	—	17	1	no	—
60	C₂×C₄	—	17	1	no	—
61	C₂×C₄	C₂×#595	1	1	yes	characteristic
62	C₈	—	17	1	no	—
63	C₈	—	17	1	no	—
64	C₈	—	34	4	no	—
65	C₈	C₂×#595	1	1	yes	characteristic
66	C₈	C₂×#595	1	1	yes	characteristic
67	C₂²	—	17	1	no	—
68	C₂²	—	17	1	no	—
69	C₂²	—	34	2	no	—
70	C₂²	C₄⋊#595	1	1	yes	characteristic
71	C₄	—	17	1	no	—
72	C₄	—	17	1	no	—
73	C₄	C₄⋊#595	1	1	yes	characteristic
74	C₄	C₂²×#595	1	1	yes	characteristic
75	C₂	—	2	1	no	—
76	C₂	—	17	2	no	—
77	C₂	—	34	1	no	—
78	C₂	C₂×C₄⋊#595	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄⋊#595
commutator	C₄×C₁₇	C₂²×C₄
Frattini	C₄	C₂²×#595
Fitting	C₂×C₈×C₁₇	C₄
socle	C₂×C₁₇	C₂×C₄⋊C₄
prime radical	C₂²×D₁₇	Q₈
cosocle	C₄×D₁₇	C₂³
hypercenter	C₂×C₈	#595
hypocenter	C₁₇	C₂×#108
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
3. #10587536	C₂	semidirect
4. #10587535	C₂	semidirect
39. D₁₇	#108	semidirect
44. C₁₇	C₂×#108	semidirect

Maximal subgroups

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

subgroup	index
D₁₇⋊M₁₆	2
C₂×C₈×D₁₇	2
#10587536	2
#10587535	2
C₂×#108	17

Subgroups — D17⋊#108 #11763822

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₇⋊#108 #11763822