Subgroups — #14531062

Order 2176.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763210	C₂	1	2	yes	maximal
2	#11762637	C₂	1	1	yes	maximal, characteristic
3	#11762634	C₂	1	2	yes	maximal
4	C₁₆×Dic₁₇	C₂	1	1	yes	maximal, characteristic
5	C₁₇×#367	C₂	1	1	yes	maximal, characteristic
6	#10587576	—	2	2	no	—
7	C₂×C₁₆×C₁₇	C₂²	1	1	yes	characteristic
8	C₁₇×#107	C₂²	1	2	yes	—
9	#10587489	C₂²	1	2	yes	—
10	C₈×Dic₁₇	C₂²	1	1	yes	characteristic
11	C₂×#63214	C₂²	1	1	yes	characteristic
12	#10587479	—	2	2	no	—
13	C₂×C₈×C₁₇	C₂³	1	1	yes	characteristic
14	C₄⋊C₄×C₁₇	—	2	2	no	—
15	C₄⋊Dic₁₇	—	2	2	no	—
16	C₄⋊Dic₁₇	—	4	2	no	—
17	#63225	—	4	2	no	—
18	C₄×Dic₁₇	D₄	1	1	yes	characteristic
19	C₂×#3622	D₄	1	1	yes	characteristic
20	C₁₆×C₁₇	Q₈	1	2	yes	—
21	#63214	Q₈	1	2	yes	—
22	C₂×C₄×C₁₇	—	4	2	no	—
23	C₂×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
24	C₂×Dic₁₇	—	4	2	no	—
25	C₂×Dic₁₇	D₈	1	2	yes	—
26	C₈×C₁₇	C₂×Q₈	1	1	yes	characteristic
27	C₈×C₁₇	C₂×Q₈	1	1	yes	characteristic
28	#3622	Q₁₆	1	2	yes	—
29	#2253	—	17	1	no	maximal, Sylow
30	C₂²×C₁₇	C₂×D₈	1	1	yes	characteristic
31	C₄×C₁₇	—	8	2	no	—
32	C₄×C₁₇	C₄⋊Q₈	1	1	yes	characteristic
33	C₄×C₁₇	C₂×Q₁₆	1	1	yes	characteristic
34	Dic₁₇	—	2	2	no	—
35	Dic₁₇	—	8	2	no	—
36	#499	—	17	2	no	—
37	#367	—	17	1	no	—
38	#367	D₁₇	1	1	yes	characteristic
39	#366	—	17	2	no	—
40	C₄×C₁₆	—	17	1	no	—
41	C₂×C₁₇	#500	1	1	yes	characteristic
42	C₂×C₁₇	#508	1	2	yes	—
43	#125	—	34	2	no	—
44	C₂×C₁₆	—	17	1	no	—
45	C₂×C₁₆	C₂×D₁₇	1	1	yes	characteristic
46	#107	—	17	2	no	—
47	#107	C₂×D₁₇	1	2	yes	—
48	#106	—	34	2	no	—
49	C₄×C₈	—	17	1	no	—
50	C₁₇	#2253	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₈	—	17	1	no	—
52	C₂×C₈	C₂²×D₁₇	1	1	yes	characteristic
53	C₄⋊C₄	—	2	2	no	—
54	C₄⋊C₄	—	34	2	no	—
55	C₄⋊C₄	—	68	2	no	—
56	C₄⋊C₄	—	68	2	no	—
57	C₄²	—	17	1	no	—
58	C₁₆	—	17	2	no	—
59	C₁₆	Dic₃₄	1	2	yes	—
60	C₂×C₄	—	4	2	no	—
61	C₂×C₄	—	17	2	no	—
62	C₂×C₄	—	68	2	no	—
63	C₂×C₄	D₄×D₁₇	1	1	yes	characteristic
64	C₈	—	17	2	no	—
65	C₈	C₂×Dic₃₄	1	1	yes	characteristic
66	C₈	Q₈×D₁₇	1	1	yes	characteristic
67	C₂²	D₈×D₁₇	1	1	yes	characteristic
68	C₄	—	8	2	no	—
69	C₄	—	34	2	no	—
70	C₄	—	136	2	no	—
71	C₄	#10587574	1	1	yes	characteristic
72	C₄	Q₁₆×D₁₇	1	1	yes	characteristic
73	C₂	#11763213	1	1	yes	characteristic
74	C₂	#11763240	1	2	yes	—

	subgroup	G/H
center	C₂²	D₈×D₁₇
commutator, cosocle	C₂×C₈×C₁₇	C₂³
Frattini	C₂×C₈	C₂²×D₁₇
Fitting	C₁₇×#367	C₂
socle, prime radical	C₂²×C₁₇	C₂×D₈
hypercenter	#367	D₁₇
hypocenter	C₁₇	#2253
LCS	G ▷ C₂×C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #367

Complements

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

N	H ≅ G/N	type
50. C₁₇	#2253	semidirect

Maximal subgroups

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

subgroup	index
#11763210	2
#11762637	2
#11762634	2
C₁₆×Dic₁₇	2
C₁₇×#367	2
#2253	17