Subgroups — #14543801

Order 2176.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763730	C₂	1	1	yes	maximal, characteristic
2	#11763671	C₂	1	1	yes	maximal, characteristic
3	#11763210	C₂	1	1	yes	maximal, characteristic
4	#10587576	—	2	1	no	—
5	C₄⋊#3624	—	2	1	no	—
6	C₂×#63216	—	2	1	no	—
7	C₁₇×#107	C₄	1	1	yes	characteristic
8	#10587489	C₄	1	1	yes	characteristic
9	C₈×Dic₁₇	C₂²	1	1	yes	characteristic
10	#10587479	—	2	1	no	—
11	C₂×#3624	—	4	1	no	—
12	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
13	C₄⋊C₄×C₁₇	—	2	1	no	—
14	C₄⋊Dic₁₇	—	2	1	no	—
15	C₄⋊Dic₁₇	—	4	1	no	—
16	#63225	—	4	1	no	—
17	C₄×Dic₁₇	D₄	1	1	yes	characteristic
18	C₂×#3622	D₄	1	1	yes	characteristic
19	#63216	—	4	1	no	—
20	C₂×C₄×C₁₇	—	4	1	no	—
21	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×Dic₁₇	—	4	1	no	—
23	C₂×Dic₁₇	D₈	1	1	yes	characteristic
24	C₂×Dic₁₇	SD₁₆	1	1	yes	characteristic
25	#3624	—	8	1	no	—
26	C₈×C₁₇	—	2	1	no	—
27	#3622	SD₁₆	1	1	yes	characteristic
28	#3622	Q₁₆	1	1	yes	characteristic
29	#1363	—	17	1	no	maximal, Sylow
30	C₂²×C₁₇	#102	1	1	yes	characteristic
31	C₄×C₁₇	—	8	1	no	—
32	C₄×C₁₇	#101	1	1	yes	characteristic
33	C₄×C₁₇	#103	1	1	yes	characteristic
34	Dic₁₇	—	2	1	no	—
35	Dic₁₇	—	2	1	no	—
36	Dic₁₇	—	8	1	no	—
37	#499	—	17	1	no	—
38	C₄⋊C₁₆	—	17	1	no	—
39	#334	—	17	1	no	—
40	C₂×C₁₇	#332	1	1	yes	characteristic
41	C₂×C₁₇	#359	1	1	yes	characteristic
42	C₂×C₁₇	#360	1	1	yes	characteristic
43	#125	—	34	1	no	—
44	C₂×C₁₆	—	34	1	no	—
45	#107	—	17	1	no	—
46	#107	#595	1	1	yes	characteristic
47	#106	—	34	1	no	—
48	C₄⋊C₈	—	34	1	no	—
49	C₄×C₈	—	17	1	no	—
50	C₁₇	#1363	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₈	—	17	1	no	—
52	C₂×C₈	—	68	1	no	—
53	C₂×C₈	C₂×#595	1	1	yes	characteristic
54	C₄⋊C₄	—	2	1	no	—
55	C₄⋊C₄	—	34	1	no	—
56	C₄⋊C₄	—	68	1	no	—
57	C₄⋊C₄	—	68	1	no	—
58	C₄²	—	17	1	no	—
59	C₁₆	—	68	1	no	—
60	C₂×C₄	—	4	1	no	—
61	C₂×C₄	—	17	1	no	—
62	C₂×C₄	—	17	1	no	—
63	C₂×C₄	—	68	1	no	—
64	C₂×C₄	C₂²⋊#595	1	1	yes	characteristic
65	C₈	—	2	1	no	—
66	C₈	—	17	1	no	—
67	C₈	—	17	1	no	—
68	C₈	—	136	1	no	—
69	C₂²	#10587547	1	1	yes	characteristic
70	C₄	—	8	1	no	—
71	C₄	—	34	1	no	—
72	C₄	—	34	1	no	—
73	C₄	—	136	1	no	—
74	C₄	#10587545	1	1	yes	characteristic
75	C₄	#10587549	1	1	yes	characteristic
76	C₂	#11763668	1	1	yes	characteristic
77	C₂	#11763724	1	1	yes	characteristic
78	C₂	#11763725	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10587547
commutator	C₂×C₈×C₁₇	C₂×C₄
Frattini	C₂×C₈	C₂×#595
Fitting	C₁₇×#107	C₄
socle, prime radical	C₂²×C₁₇	#102
cosocle	C₈×Dic₁₇	C₂²
hypercenter	#107	#595
hypocenter	C₁₇	#1363
LCS	G ▷ C₂×C₈×C₁₇ ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

Complements

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

N	H ≅ G/N	type
50. C₁₇	#1363	semidirect

Maximal subgroups

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

subgroup	index
#11763730	2
#11763671	2
#11763210	2
#1363	17