Subgroups — #16922221

Order 4352.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14526995	C₂	1	1	yes	maximal, characteristic
2	C₃₂×Dic₁₇	C₂	1	1	yes	maximal, characteristic
3	C₁₇×M₁₂₈	C₂	1	1	yes	maximal, characteristic
4	C₂×#10587465	C₄	1	1	yes	characteristic
5	C₁₆×Dic₁₇	C₄	1	1	yes	characteristic
6	#11762528	—	2	1	no	—
7	C₂×C₁₇×C₃₂	C₂²	1	1	yes	characteristic
8	C₁₇×C₆₄	—	2	1	no	—
9	C₂×C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
10	C₈×Dic₁₇	C₈	1	1	yes	characteristic
11	C₂×#63214	C₈	1	1	yes	characteristic
12	C₁₇×C₃₂	D₄	1	1	yes	characteristic
13	C₁₇×C₃₂	Q₈	1	1	yes	characteristic
14	#10587465	—	2	1	no	—
15	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
16	C₄×Dic₁₇	C₁₆	1	1	yes	characteristic
17	C₂×#3622	C₁₆	1	1	yes	characteristic
18	C₁₆×C₁₇	C₄⋊C₄	1	1	yes	characteristic
19	C₁₆×C₁₇	M₁₆	1	1	yes	characteristic
20	#63214	—	2	1	no	—
21	#7544	—	17	1	no	maximal, Sylow
22	C₂×C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
23	C₂×Dic₁₇	—	2	1	no	—
24	C₈×C₁₇	C₄⋊C₈	1	1	yes	characteristic
25	C₈×C₁₇	M₃₂	1	1	yes	characteristic
26	#3622	C₃₂	1	2	yes	—
27	M₁₂₈	—	17	1	no	—
28	M₁₂₈	D₁₇	1	1	yes	characteristic
29	C₄×C₃₂	—	17	1	no	—
30	C₂²×C₁₇	M₆₄	1	1	yes	characteristic
31	C₄×C₁₇	C₄⋊C₁₆	1	1	yes	characteristic
32	C₄×C₁₇	C₂×C₃₂	1	1	yes	characteristic
33	Dic₁₇	—	2	2	no	—
34	C₂×C₃₂	—	17	1	no	—
35	C₂×C₃₂	C₂×D₁₇	1	1	yes	characteristic
36	C₄×C₁₆	—	17	1	no	—
37	C₆₄	—	2	1	no	—
38	C₆₄	—	34	1	no	—
39	C₂×C₁₇	—	2	1	no	—
40	C₂×C₁₇	C₄⋊C₃₂	1	1	yes	characteristic
41	C₂×C₁₆	—	17	1	no	—
42	C₂×C₁₆	C₄×D₁₇	1	1	yes	characteristic
43	C₄×C₈	—	17	1	no	—
44	C₃₂	—	34	1	no	—
45	C₃₂	Dic₃₄	1	1	yes	characteristic
46	C₃₂	C₂²⋊D₁₇	1	1	yes	characteristic
47	C₁₇	#7544	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₈	—	17	1	no	—
49	C₂×C₈	C₈×D₁₇	1	1	yes	characteristic
50	C₄²	—	17	1	no	—
51	C₁₆	—	34	1	no	—
52	C₁₆	#63218	1	1	yes	characteristic
53	C₁₆	#63225	1	1	yes	characteristic
54	C₂×C₄	—	34	1	no	—
55	C₂×C₄	C₁₆×D₁₇	1	1	yes	characteristic
56	C₈	—	17	2	no	—
57	C₈	#10587469	1	1	yes	characteristic
58	C₈	#10587485	1	1	yes	characteristic
59	C₂²	#11762642	1	1	yes	characteristic
60	C₄	—	34	2	no	—
61	C₄	#11762627	1	1	yes	characteristic
62	C₄	C₃₂×D₁₇	1	1	yes	characteristic
63	C₂	—	2	1	no	—
64	C₂	#14526979	1	1	yes	characteristic

	subgroup	G/H
center	C₃₂	C₂²⋊D₁₇
commutator	C₄×C₁₇	C₂×C₃₂
Frattini	C₂×C₃₂	C₂×D₁₇
Fitting	C₁₇×M₁₂₈	C₂
socle	C₂×C₁₇	C₄⋊C₃₂
prime radical	C₂²×C₁₇	M₆₄
cosocle	C₂×C₁₇×C₃₂	C₂²
hypercenter	M₁₂₈	D₁₇
hypocenter	C₁₇	#7544
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₃₂ ◁ C₂×C₃₂ ◁ M₁₂₈

Complements

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

N	H ≅ G/N	type
47. C₁₇	#7544	semidirect

Maximal subgroups

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

subgroup	index
#14526995	2
C₃₂×Dic₁₇	2
C₁₇×M₁₂₈	2
#7544	17