Subgroups — #14526821

Order 2176.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11762630	C₂	1	2	yes	maximal, complemented
2	C₁₇×#493	C₂	1	1	yes	maximal, characteristic
3	C₂×D₈×C₁₇	—	2	2	no	—
4	C₁₇×#127	C₄	1	2	yes	—
5	C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
6	#10587483	—	2	2	no	—
7	C₂×D₄×C₁₇	—	2	2	no	—
8	C₂×D₄×C₁₇	—	4	2	no	—
9	D₈×C₁₇	—	4	2	no	—
10	D₈×C₁₇	—	4	2	no	—
11	C₂×C₈×C₁₇	D₄	1	2	yes	—
12	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
13	#63214	—	4	2	no	—
14	C₂³×C₁₇	—	4	2	no	—
15	D₄×C₁₇	—	4	4	no	—
16	D₄×C₁₇	—	8	4	no	—
17	C₂×C₄×C₁₇	—	2	1	no	—
18	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
19	C₈×C₁₇	D₈	1	2	yes	—
20	C₈×C₁₇	SD₁₆	1	2	yes	—
21	#1357	—	17	1	no	maximal, Sylow
22	C₂²×C₁₇	—	8	4	no	—
23	C₂²×C₁₇	—	8	2	no	—
24	C₂²×C₁₇	#100	1	1	yes	characteristic
25	C₄×C₁₇	—	2	2	no	—
26	C₄×C₁₇	#102	1	2	yes	—
27	#493	D₁₇	1	1	yes	characteristic
28	#364	—	17	2	no	—
29	C₂×C₁₇	—	2	1	no	—
30	C₂×C₁₇	—	16	2	no	—
31	C₂×C₁₇	#331	1	1	yes	characteristic
32	C₂×D₈	—	2	2	no	—
33	#127	Dic₁₇	1	2	yes	—
34	M₃₂	—	34	2	no	—
35	C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
36	C₁₇	#1357	1	1	yes	characteristic, complemented, Sylow
37	C₂×D₄	—	2	2	no	—
38	C₂×D₄	—	4	2	no	—
39	D₈	—	4	2	no	—
40	D₈	—	4	2	no	—
41	C₂×C₈	C₂²⋊D₁₇	1	2	yes	—
42	C₄²	C₂×Dic₁₇	1	1	yes	characteristic
43	C₁₆	—	68	2	no	—
44	C₂³	—	4	2	no	—
45	D₄	—	4	4	no	—
46	D₄	—	8	4	no	—
47	C₂×C₄	—	2	1	no	—
48	C₂×C₄	C₂²⋊Dic₁₇	1	1	yes	characteristic
49	C₈	#63228	1	2	yes	—
50	C₈	#63229	1	2	yes	—
51	C₂²	—	8	4	no	—
52	C₂²	—	8	2	no	—
53	C₂²	#10587504	1	1	yes	characteristic
54	C₄	—	2	2	no	—
55	C₄	#10587503	1	2	yes	—
56	C₂	—	2	1	no	—
57	C₂	—	16	2	no	—
58	C₂	#11762553	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11762553
commutator	C₄²×C₁₇	C₂×C₄
Frattini	C₄×C₈	C₂×D₁₇
Fitting, prime radical	C₁₇×#493	C₂
socle	C₂×C₁₇	#331
cosocle	C₄×C₈×C₁₇	C₂²
hypercenter	#493	D₁₇
hypocenter	C₁₇	#1357
LCS	G ▷ C₄²×C₁₇ ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #493

Complements

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

N	H ≅ G/N	type
1. #11762630	C₂	semidirect
36. C₁₇	#1357	semidirect

Maximal subgroups

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

subgroup	index
#11762630	2
C₁₇×#493	2
#1357	17