Subgroups — #14543898

Order 2176.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10587467	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₆×D₁₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×D₁₇	C₄	1	1	yes	characteristic
4	C₂×C₁₆×C₁₇	C₄	1	1	yes	characteristic
5	C₂×#63214	C₂²	1	1	yes	characteristic
6	C₁₆×D₁₇	—	2	2	no	—
7	#10587467	—	2	2	no	—
8	C₂×C₄×D₁₇	C₈	1	1	yes	characteristic
9	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
10	C₂×#3622	C₈	1	1	yes	characteristic
11	C₈×D₁₇	—	2	1	no	—
12	C₈×D₁₇	—	2	1	no	—
13	C₁₆×C₁₇	—	2	1	no	—
14	#63214	D₄	1	2	yes	—
15	C₂²×D₁₇	C₁₆	1	1	yes	characteristic
16	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
17	C₂×Dic₁₇	C₁₆	1	1	yes	characteristic
18	C₄×D₁₇	—	2	1	no	—
19	C₄×D₁₇	—	2	1	no	—
20	C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
21	C₈×C₁₇	M₁₆	1	1	yes	characteristic
22	#3622	—	2	1	no	—
23	C₂²⋊C₃₂	—	17	1	no	maximal, Sylow
24	C₂²×C₁₇	C₂×C₁₆	1	1	yes	characteristic
25	C₂×D₁₇	—	2	1	no	—
26	C₂×D₁₇	—	2	1	no	—
27	C₂×D₁₇	C₃₂	1	2	yes	complemented
28	C₄×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
29	C₄×C₁₇	M₃₂	1	1	yes	characteristic
30	Dic₁₇	—	2	1	no	—
31	C₂²×C₁₆	—	17	1	no	—
32	C₂×C₃₂	—	17	2	no	—
33	C₂×C₁₇	C₂²⋊C₁₆	1	1	yes	characteristic
34	C₂×C₁₇	C₂×C₃₂	1	1	yes	characteristic
35	C₂×C₁₇	M₆₄	1	1	yes	characteristic
36	D₁₇	—	2	2	no	—
37	C₂²×C₈	—	17	1	no	—
38	C₂×C₁₆	—	17	1	no	—
39	C₂×C₁₆	—	34	2	no	—
40	C₂×C₁₆	#595	1	1	yes	characteristic
41	C₃₂	—	34	2	no	—
42	C₁₇	C₂²⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
43	C₂²×C₄	—	17	1	no	—
44	C₂×C₈	—	17	1	no	—
45	C₂×C₈	—	34	1	no	—
46	C₂×C₈	—	34	1	no	—
47	C₂×C₈	C₂×#595	1	1	yes	characteristic
48	C₁₆	—	2	1	no	—
49	C₁₆	—	17	2	no	—
50	C₂³	—	17	1	no	—
51	C₂×C₄	—	17	1	no	—
52	C₂×C₄	—	34	1	no	—
53	C₂×C₄	—	34	1	no	—
54	C₂×C₄	#63242	1	1	yes	characteristic
55	C₈	—	34	1	no	—
56	C₈	#63243	1	1	yes	characteristic
57	C₈	C₂²⋊#595	1	1	yes	characteristic
58	C₂²	—	17	2	no	—
59	C₂²	—	34	1	no	—
60	C₂²	—	34	1	no	—
61	C₂²	#10587529	1	1	yes	characteristic
62	C₄	—	34	1	no	—
63	C₄	#10587530	1	1	yes	characteristic
64	C₄	#10587543	1	1	yes	characteristic
65	C₂	—	34	2	no	—
66	C₂	#11763704	1	1	yes	characteristic
67	C₂	#11763740	1	1	yes	characteristic
68	C₂	#11763742	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×#595
commutator	C₂×C₁₇	C₂×C₃₂
Fitting	C₂×C₁₆×C₁₇	C₄
socle	C₂²×C₁₇	C₂×C₁₆
prime radical	C₂²×D₁₇	C₁₆
cosocle	C₂×#63214	C₂²
hypercenter	C₂×C₁₆	#595
hypocenter	C₁₇	C₂²⋊C₃₂
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#10587467	C₂	semidirect
27. C₂×D₁₇	C₃₂	semidirect
42. C₁₇	C₂²⋊C₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10587467	2
C₂×C₁₆×D₁₇	2
C₂²⋊C₃₂	17