Subgroups — #14531060

Order 2176.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763211	C₂	1	1	yes	maximal, characteristic
2	#11762636	C₂	1	2	yes	maximal
3	#11762634	C₂	1	2	yes	maximal
4	C₄×#63214	C₂	1	1	yes	maximal, characteristic
5	C₁₇×#499	C₂	1	1	yes	maximal, characteristic
6	C₁₇×#125	—	2	1	no	—
7	#10587556	—	2	1	no	—
8	C₁₇×#107	C₂²	1	2	yes	—
9	C₁₇×#106	—	2	1	no	—
10	C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
11	#10587489	C₂²	1	2	yes	—
12	#10587488	—	2	1	no	—
13	C₂×#63214	C₂²	1	1	yes	characteristic
14	C₂×#63214	C₂²	1	1	yes	characteristic
15	C₂×C₈×C₁₇	D₄	1	1	yes	characteristic
16	C₂×C₈×C₁₇	C₂³	1	1	yes	characteristic
17	C₄⋊C₄×C₁₇	—	2	2	no	—
18	C₄⋊C₄×C₁₇	—	4	2	no	—
19	C₄²×C₁₇	D₄	1	1	yes	characteristic
20	C₄⋊Dic₁₇	—	2	2	no	—
21	#63225	—	4	2	no	—
22	#63214	Q₈	1	2	yes	—
23	#63214	Q₈	1	2	yes	—
24	C₂×C₄×C₁₇	—	4	2	no	—
25	C₂×C₄×C₁₇	D₈	1	2	yes	—
26	C₂×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
27	C₂×Dic₁₇	—	4	2	no	—
28	C₈×C₁₇	Q₁₆	1	2	yes	—
29	C₈×C₁₇	C₂×Q₈	1	1	yes	characteristic
30	C₈×C₁₇	C₂×Q₈	1	1	yes	characteristic
31	#2253	—	17	1	no	maximal, Sylow
32	C₂²×C₁₇	C₂×D₈	1	1	yes	characteristic
33	C₄×C₁₇	—	2	2	no	—
34	C₄×C₁₇	—	8	2	no	—
35	C₄×C₁₇	C₄⋊Q₈	1	1	yes	characteristic
36	C₄×C₁₇	C₂×Q₁₆	1	1	yes	characteristic
37	Dic₁₇	—	8	2	no	—
38	#499	—	17	1	no	—
39	#499	D₁₇	1	1	yes	characteristic
40	#367	—	17	2	no	—
41	#366	—	17	2	no	—
42	C₄×C₁₆	—	17	1	no	—
43	C₂×C₁₇	#500	1	1	yes	characteristic
44	C₂×C₁₇	#508	1	2	yes	—
45	#125	—	2	1	no	—
46	#125	—	34	1	no	—
47	C₂×C₁₆	—	17	1	no	—
48	C₂×C₁₆	—	17	1	no	—
49	#107	—	17	2	no	—
50	#107	C₂×D₁₇	1	2	yes	—
51	#106	—	2	1	no	—
52	#106	—	34	1	no	—
53	C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
54	C₁₇	#2253	1	1	yes	characteristic, complemented, Sylow
55	C₂×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
56	C₂×C₈	C₂²×D₁₇	1	1	yes	characteristic
57	C₄⋊C₄	—	2	2	no	—
58	C₄⋊C₄	—	4	2	no	—
59	C₄⋊C₄	—	34	2	no	—
60	C₄⋊C₄	—	68	2	no	—
61	C₄²	C₂²⋊D₁₇	1	1	yes	characteristic
62	C₁₆	—	17	2	no	—
63	C₁₆	—	17	2	no	—
64	C₂×C₄	—	4	2	no	—
65	C₂×C₄	—	68	2	no	—
66	C₂×C₄	#63228	1	2	yes	—
67	C₂×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
68	C₈	#63231	1	2	yes	—
69	C₈	Q₈×D₁₇	1	1	yes	characteristic
70	C₈	Q₈×D₁₇	1	1	yes	characteristic
71	C₂²	C₂×#63228	1	1	yes	characteristic
72	C₄	—	2	2	no	—
73	C₄	—	8	2	no	—
74	C₄	—	136	2	no	—
75	C₄	C₂×#63231	1	1	yes	characteristic
76	C₄	#10587630	1	1	yes	characteristic
77	C₂	#11763212	1	1	yes	characteristic
78	C₂	#11763239	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#63228
commutator, cosocle	C₂×C₈×C₁₇	C₂³
Frattini	C₂×C₈	C₂²×D₁₇
Fitting	C₁₇×#499	C₂
socle, prime radical	C₂²×C₁₇	C₂×D₈
hypercenter	#499	D₁₇
hypocenter	C₁₇	#2253
LCS	G ▷ C₂×C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #499

Complements

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

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

Maximal subgroups

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

subgroup	index
#11763211	2
#11762636	2
#11762634	2
C₄×#63214	2
C₁₇×#499	2
#2253	17