Subgroups — #14531031

Order 2176.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763189	C₂	1	1	yes	maximal, characteristic
2	#11762612	C₂	1	4	yes	maximal
3	#11762585	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#499	C₂	1	1	yes	maximal, characteristic
5	C₁₇×#125	—	2	1	no	—
6	C₂×Dic₆₈	—	2	1	no	—
7	C₂×Dic₆₈	C₂²	1	2	yes	—
8	#10587555	—	2	1	no	—
9	C₁₇×#107	C₂²	1	2	yes	—
10	C₁₇×#106	—	2	1	no	—
11	C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
12	C₂×#63214	C₂²	1	2	yes	—
13	C₂×Dic₃₄	—	2	2	no	—
14	C₂×C₈×C₁₇	D₄	1	1	yes	characteristic
15	C₂×C₈×C₁₇	C₂³	1	1	yes	characteristic
16	C₄⋊C₄×C₁₇	—	2	2	no	—
17	C₄⋊C₄×C₁₇	—	4	2	no	—
18	C₄²×C₁₇	D₄	1	1	yes	characteristic
19	C₄⋊Dic₁₇	—	4	2	no	—
20	Dic₆₈	—	2	4	no	—
21	Dic₆₈	—	4	2	no	—
22	#63214	—	2	2	no	—
23	C₂×C₄×C₁₇	—	4	2	no	—
24	C₂×C₄×C₁₇	D₈	1	2	yes	—
25	C₂×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
26	C₂×Dic₁₇	—	4	2	no	—
27	Dic₃₄	—	4	2	no	—
28	Dic₃₄	—	4	2	no	—
29	C₈×C₁₇	SD₁₆	1	2	yes	—
30	C₈×C₁₇	#41	1	2	yes	—
31	#2245	—	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	#124	1	1	yes	characteristic
36	C₄×C₁₇	C₂×SD₁₆	1	1	yes	characteristic
37	Dic₁₇	—	8	2	no	—
38	#499	D₁₇	1	1	yes	characteristic
39	#494	—	17	1	no	—
40	#358	—	17	4	no	—
41	#346	—	17	1	no	—
42	C₂×C₁₇	#486	1	1	yes	characteristic
43	C₂×C₁₇	#510	1	2	yes	—
44	C₂×Q₁₆	—	17	2	no	—
45	C₂×Q₁₆	—	34	1	no	—
46	C₄⋊Q₈	—	34	1	no	—
47	#125	—	2	1	no	—
48	C₂×C₁₆	—	17	2	no	—
49	#107	C₂×D₁₇	1	2	yes	—
50	#106	—	2	1	no	—
51	C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
52	C₁₇	#2245	1	1	yes	characteristic, complemented, Sylow
53	C₂×Q₈	—	34	2	no	—
54	Q₁₆	—	34	4	no	—
55	Q₁₆	—	68	2	no	—
56	C₂×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
57	C₂×C₈	C₂²×D₁₇	1	1	yes	characteristic
58	C₄⋊C₄	—	2	2	no	—
59	C₄⋊C₄	—	4	2	no	—
60	C₄⋊C₄	—	68	2	no	—
61	C₄²	C₂²⋊D₁₇	1	1	yes	characteristic
62	C₁₆	—	34	2	no	—
63	Q₈	—	68	2	no	—
64	Q₈	—	68	2	no	—
65	C₂×C₄	—	4	2	no	—
66	C₂×C₄	—	68	2	no	—
67	C₂×C₄	#63228	1	2	yes	—
68	C₂×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
69	C₈	#63230	1	2	yes	—
70	C₈	#63256	1	2	yes	—
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×#63230	1	1	yes	characteristic
76	C₄	#10587633	1	1	yes	characteristic
77	C₂	#11763157	1	1	yes	characteristic
78	C₂	#11763249	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	#2245
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
52. C₁₇	#2245	semidirect

Maximal subgroups

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

subgroup	index
#11763189	2
#11762612	2
#11762585	2
C₁₇×#499	2
#2245	17