Subgroups — #11763678

Order 1088.

86 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×#63218	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×D₁₇	C₂²	1	1	yes	characteristic
4	#63247	—	2	2	no	—
5	#63243	—	2	2	no	—
6	#63242	C₄	1	4	yes	—
7	C₂×C₈×C₁₇	C₄	1	1	yes	characteristic
8	C₂×#3622	C₄	1	1	yes	characteristic
9	#63218	—	2	2	no	—
10	C₂²×D₁₇	Q₈	1	1	yes	characteristic
11	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
12	C₂×Dic₁₇	D₄	1	1	yes	characteristic
13	C₄×D₁₇	C₂×C₄	1	2	yes	—
14	C₄×D₁₇	D₄	1	2	yes	—
15	#3624	—	2	4	no	—
16	C₈×C₁₇	—	2	1	no	—
17	#3622	—	2	1	no	—
18	C₂²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
19	C₂×D₁₇	—	4	1	no	—
20	C₂×D₁₇	C₄⋊C₄	1	2	yes	—
21	C₄×C₁₇	C₄²	1	1	yes	characteristic
22	C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
23	Dic₁₇	C₂²⋊C₄	1	2	yes	—
24	#338	—	17	1	no	maximal, Sylow
25	C₂×C₁₇	—	2	1	no	—
26	C₂×C₁₇	#95	1	1	yes	characteristic
27	D₁₇	—	2	2	no	—
28	C₂×M₁₆	—	17	2	no	—
29	C₂×M₁₆	—	17	1	no	—
30	C₁₇	#338	1	1	yes	characteristic, complemented, Sylow
31	C₂²×C₄	—	17	1	no	—
32	M₁₆	—	34	2	no	—
33	M₁₆	—	34	2	no	—
34	M₁₆	—	34	2	no	—
35	C₂×C₈	—	17	4	no	—
36	C₂×C₈	—	17	1	no	—
37	C₂×C₈	#595	1	1	yes	characteristic
38	C₂³	—	17	1	no	—
39	C₂×C₄	—	17	1	no	—
40	C₂×C₄	—	17	2	no	—
41	C₂×C₄	—	17	2	no	—
42	C₂×C₄	C₂×#595	1	1	yes	characteristic
43	C₈	—	2	1	no	—
44	C₈	—	34	4	no	—
45	C₈	—	34	1	no	—
46	C₂²	—	17	2	no	—
47	C₂²	—	68	1	no	—
48	C₂²	C₄⋊#595	1	1	yes	characteristic
49	C₄	—	17	2	no	—
50	C₄	C₄×#595	1	1	yes	characteristic
51	C₄	C₂²⋊#595	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	34	2	no	—
54	C₂	(C₂×#595)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄×#595
commutator	C₄×C₁₇	C₄²
Frattini	C₂×C₄	C₂×#595
Fitting	C₂×C₈×C₁₇	C₄
socle	C₂×C₁₇	#95
prime radical	C₂²×D₁₇	Q₈
cosocle	C₂×C₄×D₁₇	C₂²
hypercenter	C₂×C₈	#595
hypocenter	C₁₇	#338
LCS	G ▷ C₄×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
30. C₁₇	#338	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×#63218	2
#338	17