Subgroups — #14543649

Order 2176.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763830	C₂	1	2	yes	maximal
2	C₂×#10587485	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈×C₁₇	C₄	1	1	yes	characteristic
4	C₂×C₄×Dic₁₇	C₂²	1	1	yes	characteristic
5	C₂²×#3622	C₄	1	1	yes	characteristic
6	C₂²⋊#3624	—	2	2	no	—
7	#10587542	C₄	1	4	yes	—
8	C₄⋊#3624	—	2	2	no	—
9	#10587485	—	2	2	no	—
10	C₂²×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
11	C₂²×Dic₁₇	D₄	1	1	yes	characteristic
12	C₂²×Dic₁₇	Q₈	1	1	yes	characteristic
13	C₂×#3624	—	2	4	no	—
14	C₂×C₈×C₁₇	—	2	1	no	—
15	C₂×C₈×C₁₇	—	4	1	no	—
16	C₄×Dic₁₇	C₂×C₄	1	2	yes	—
17	C₄×Dic₁₇	D₄	1	2	yes	—
18	C₂×#3622	—	2	1	no	—
19	C₂×#3622	—	4	1	no	—
20	C₂³×C₁₇	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₁₇	—	2	1	no	—
22	C₂×C₄×C₁₇	—	2	1	no	—
23	C₂×C₄×C₁₇	C₄²	1	1	yes	characteristic
24	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×Dic₁₇	—	2	1	no	—
26	C₂×Dic₁₇	—	2	1	no	—
27	C₂×Dic₁₇	—	4	1	no	—
28	C₂×Dic₁₇	C₂²⋊C₄	1	2	yes	—
29	C₂×Dic₁₇	C₄⋊C₄	1	2	yes	—
30	#3624	—	4	4	no	—
31	C₈×C₁₇	—	4	1	no	—
32	#3622	—	4	1	no	—
33	#1290	—	17	1	no	maximal, Sylow
34	C₂²×C₁₇	—	2	1	no	—
35	C₂²×C₁₇	—	2	1	no	—
36	C₂²×C₁₇	#95	1	1	yes	characteristic
37	C₂²×C₁₇	#108	1	1	yes	characteristic
38	C₂²×C₁₇	#108	1	1	yes	characteristic
39	C₄×C₁₇	—	2	1	no	—
40	C₄×C₁₇	#100	1	1	yes	characteristic
41	C₄×C₁₇	#101	1	1	yes	characteristic
42	Dic₁₇	—	2	2	no	—
43	Dic₁₇	—	2	2	no	—
44	#432	—	17	2	no	—
45	C₂×C₄⋊C₈	—	17	1	no	—
46	C₂×C₁₇	—	2	1	no	—
47	C₂×C₁₇	—	2	1	no	—
48	C₂×C₁₇	H(3,ℤ/4)	1	1	yes	characteristic
49	C₂×C₁₇	#341	1	1	yes	characteristic
50	C₂×C₁₇	#343	1	1	yes	characteristic
51	C₂²×C₈	—	17	1	no	—
52	C₂²×C₈	#595	1	1	yes	characteristic
53	C₂×C₄²	—	17	1	no	—
54	C₄⋊C₈	—	34	2	no	—
55	C₄⋊C₈	—	34	2	no	—
56	C₂²⋊C₈	—	34	2	no	—
57	#97	—	17	4	no	—
58	C₁₇	#1290	1	1	yes	characteristic, complemented, Sylow
59	C₂²×C₄	—	17	1	no	—
60	C₂²×C₄	—	17	1	no	—
61	C₂²×C₄	C₂×#595	1	1	yes	characteristic
62	C₂×C₈	—	2	1	no	—
63	C₂×C₈	—	4	1	no	—
64	C₂×C₈	—	34	4	no	—
65	C₂×C₈	—	34	1	no	—
66	C₂×C₈	—	68	1	no	—
67	C₄²	—	17	2	no	—
68	C₄²	—	17	2	no	—
69	C₂³	C₄⋊#595	1	1	yes	characteristic
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	17	2	no	—
73	C₂×C₄	—	17	2	no	—
74	C₂×C₄	—	34	1	no	—
75	C₂×C₄	—	34	1	no	—
76	C₂×C₄	—	68	1	no	—
77	C₂×C₄	C₄×#595	1	1	yes	characteristic
78	C₂×C₄	C₂²⋊#595	1	1	yes	characteristic
79	C₈	—	4	1	no	—
80	C₈	—	68	4	no	—
81	C₈	—	68	1	no	—
82	C₂²	—	2	1	no	—
83	C₂²	—	2	1	no	—
84	C₂²	#10587535	1	1	yes	characteristic
85	C₂²	#10587536	1	1	yes	characteristic
86	C₂²	(C₂×#595)⋊C₄	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	—	34	2	no	—
89	C₄	—	34	2	no	—
90	C₄	#10587545	1	1	yes	characteristic
91	C₄	#10587553	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	2	1	no	—
94	C₂	#11763677	1	1	yes	characteristic
95	C₂	#11763685	1	1	yes	characteristic
96	C₂	#11763689	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	(C₂×#595)⋊C₄
commutator	C₂×C₄×C₁₇	C₄²
Frattini	C₂²×C₄	C₂×#595
Fitting	C₂²×C₈×C₁₇	C₄
socle	C₂²×C₁₇	#95
prime radical	C₂³×C₁₇	C₄⋊C₄
cosocle	C₂×C₄×Dic₁₇	C₂²
hypercenter	C₂²×C₈	#595
hypocenter	C₁₇	#1290
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
58. C₁₇	#1290	semidirect

Maximal subgroups

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

subgroup	index
#11763830	2
C₂×#10587485	2
#1290	17