Subgroups — #14543802

Order 2176.

86 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	#11763673	C₂	1	1	yes	maximal, characteristic
3	#11763213	C₂	1	1	yes	maximal, characteristic
4	#10587574	—	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	#10587478	—	2	1	no	—
11	C₂×Dic₃₄	—	4	1	no	—
12	C₂×#3624	—	4	1	no	—
13	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
14	C₄⋊C₄×C₁₇	—	2	1	no	—
15	C₄⋊Dic₁₇	—	2	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	Dic₃₄	—	8	1	no	—
26	Dic₃₄	—	8	1	no	—
27	#3624	—	8	1	no	—
28	C₈×C₁₇	—	2	1	no	—
29	#3622	SD₁₆	1	1	yes	characteristic
30	#3622	Q₁₆	1	1	yes	characteristic
31	#1364	—	17	1	no	maximal, Sylow
32	C₂²×C₁₇	#102	1	1	yes	characteristic
33	C₄×C₁₇	—	8	1	no	—
34	C₄×C₁₇	#101	1	1	yes	characteristic
35	C₄×C₁₇	#103	1	1	yes	characteristic
36	Dic₁₇	—	2	1	no	—
37	Dic₁₇	—	8	1	no	—
38	Dic₁₇	D₁₆	1	1	yes	characteristic
39	Dic₁₇	SD₃₂	1	1	yes	characteristic
40	#500	—	17	1	no	—
41	C₄⋊C₁₆	—	17	1	no	—
42	#335	—	17	1	no	—
43	C₂×C₁₇	#332	1	1	yes	characteristic
44	C₂×C₁₇	#357	1	1	yes	characteristic
45	C₂×C₁₇	#362	1	1	yes	characteristic
46	C₄⋊Q₈	—	34	1	no	—
47	C₂×C₁₆	—	34	1	no	—
48	#107	—	17	1	no	—
49	#107	—	34	1	no	—
50	#107	#595	1	1	yes	characteristic
51	C₄⋊C₈	—	34	1	no	—
52	C₄×C₈	—	17	1	no	—
53	C₁₇	#1364	1	1	yes	characteristic, complemented, Sylow
54	C₂×Q₈	—	68	1	no	—
55	C₂×C₈	—	17	1	no	—
56	C₂×C₈	—	68	1	no	—
57	C₂×C₈	C₂×#595	1	1	yes	characteristic
58	C₄⋊C₄	—	2	1	no	—
59	C₄⋊C₄	—	34	1	no	—
60	C₄⋊C₄	—	68	1	no	—
61	C₄²	—	17	1	no	—
62	C₁₆	—	68	1	no	—
63	Q₈	—	136	1	no	—
64	Q₈	—	136	1	no	—
65	C₂×C₄	—	4	1	no	—
66	C₂×C₄	—	17	1	no	—
67	C₂×C₄	—	17	1	no	—
68	C₂×C₄	—	68	1	no	—
69	C₂×C₄	C₂²⋊#595	1	1	yes	characteristic
70	C₈	—	2	1	no	—
71	C₈	—	17	1	no	—
72	C₈	—	17	1	no	—
73	C₈	—	136	1	no	—
74	C₂²	#10587547	1	1	yes	characteristic
75	C₄	—	8	1	no	—
76	C₄	—	17	1	no	—
77	C₄	—	17	1	no	—
78	C₄	—	34	1	no	—
79	C₄	—	136	1	no	—
80	C₄	#10587545	1	1	yes	characteristic
81	C₄	#10587549	1	1	yes	characteristic
82	C₂	#11763668	1	1	yes	characteristic
83	C₂	#11763721	1	1	yes	characteristic
84	C₂	#11763728	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	#1364
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
53. C₁₇	#1364	semidirect

Maximal subgroups

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

subgroup	index
#11763730	2
#11763673	2
#11763213	2
#1364	17