Subgroups — #14543761

Order 2176.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763706	C₂	1	1	yes	maximal, characteristic
2	#11763678	C₂	1	1	yes	maximal, characteristic
3	#11763068	C₂	1	1	yes	maximal, characteristic
4	D₁₇⋊M₁₆	—	2	1	no	—
5	C₂×Dic₆₈	C₄	1	1	yes	characteristic
6	C₂×#63218	C₂²	1	1	yes	characteristic
7	#10587583	—	2	1	no	—
8	#10587538	—	2	1	no	—
9	C₁₇×#106	C₄	1	1	yes	characteristic
10	#10587481	—	2	1	no	—
11	C₂×C₄×D₁₇	D₄	1	1	yes	characteristic
12	C₂×Dic₃₄	—	2	1	no	—
13	#63247	—	4	1	no	—
14	#63243	—	4	1	no	—
15	#63242	—	2	2	no	—
16	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
17	C₄⋊C₄×C₁₇	—	2	1	no	—
18	#63227	—	4	1	no	—
19	C₄⋊Dic₁₇	—	4	1	no	—
20	C₂×#3622	D₄	1	1	yes	characteristic
21	Dic₆₈	—	4	1	no	—
22	#63218	—	4	1	no	—
23	#63216	—	4	1	no	—
24	C₂²×D₁₇	SD₁₆	1	1	yes	characteristic
25	C₂×C₄×C₁₇	—	4	1	no	—
26	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×Dic₁₇	—	4	1	no	—
28	C₂×Dic₁₇	D₈	1	1	yes	characteristic
29	C₄×D₁₇	—	2	1	no	—
30	C₄×D₁₇	—	2	1	no	—
31	Dic₃₄	—	4	1	no	—
32	Dic₃₄	—	4	1	no	—
33	#3624	—	4	2	no	—
34	C₈×C₁₇	—	2	1	no	—
35	#3622	—	2	1	no	—
36	#1342	—	17	1	no	maximal, Sylow
37	C₂²×C₁₇	#102	1	1	yes	characteristic
38	C₂×D₁₇	—	2	1	no	—
39	C₂×D₁₇	—	4	1	no	—
40	C₄×C₁₇	—	8	1	no	—
41	C₄×C₁₇	#99	1	1	yes	characteristic
42	C₄×C₁₇	#104	1	1	yes	characteristic
43	Dic₁₇	—	2	1	no	—
44	Dic₁₇	—	8	1	no	—
45	#470	—	17	1	no	—
46	#349	—	17	1	no	—
47	#338	—	17	1	no	—
48	C₂×C₁₇	—	2	1	no	—
49	C₂×C₁₇	#327	1	1	yes	characteristic
50	D₁₇	—	4	1	no	—
51	C₂×Q₁₆	—	17	1	no	—
52	C₂×M₁₆	—	17	1	no	—
53	C₂×M₁₆	—	34	1	no	—
54	C₂²⋊Q₈	—	34	1	no	—
55	M₃₂	—	34	1	no	—
56	#106	#595	1	1	yes	characteristic
57	#103	—	34	1	no	—
58	C₁₇	#1342	1	1	yes	characteristic, complemented, Sylow
59	C₂×Q₈	—	34	1	no	—
60	C₂²×C₄	—	17	1	no	—
61	Q₁₆	—	68	1	no	—
62	M₁₆	—	68	1	no	—
63	M₁₆	—	68	1	no	—
64	M₁₆	—	68	1	no	—
65	C₂×C₈	—	17	1	no	—
66	C₂×C₈	—	34	2	no	—
67	C₂×C₈	C₂×#595	1	1	yes	characteristic
68	C₄⋊C₄	—	2	1	no	—
69	C₄⋊C₄	—	68	1	no	—
70	C₂²⋊C₄	—	68	1	no	—
71	C₁₆	—	68	1	no	—
72	C₂³	—	17	1	no	—
73	Q₈	—	68	1	no	—
74	Q₈	—	68	1	no	—
75	C₂×C₄	—	4	1	no	—
76	C₂×C₄	—	17	1	no	—
77	C₂×C₄	—	34	1	no	—
78	C₂×C₄	—	34	1	no	—
79	C₂×C₄	—	68	1	no	—
80	C₂×C₄	C₂²⋊#595	1	1	yes	characteristic
81	C₈	—	2	1	no	—
82	C₈	—	34	1	no	—
83	C₈	—	68	2	no	—
84	C₂²	—	34	1	no	—
85	C₂²	—	68	1	no	—
86	C₂²	#10587547	1	1	yes	characteristic
87	C₄	—	8	1	no	—
88	C₄	—	34	1	no	—
89	C₄	—	136	1	no	—
90	C₄	#10587539	1	1	yes	characteristic
91	C₄	#10587550	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	68	1	no	—
94	C₂	#11763661	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11763661
commutator	C₂×C₈×C₁₇	C₂×C₄
Frattini	C₂×C₈	C₂×#595
Fitting	C₁₇×#106	C₄
socle	C₂×C₁₇	#327
prime radical	C₂²×D₁₇	SD₁₆
cosocle	C₂×#63218	C₂²
hypercenter	#106	#595
hypocenter	C₁₇	#1342
LCS	G ▷ C₂×C₈×C₁₇ ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #106

Complements

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

N	H ≅ G/N	type
58. C₁₇	#1342	semidirect

Maximal subgroups

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

subgroup	index
#11763706	2
#11763678	2
#11763068	2
#1342	17