Group #14545201 — subgroups

Subgroups — #14545201

Order 2176.

126 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763730	C₂	1	1	yes	maximal, characteristic
2	#11763730	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#63216	C₂	1	1	yes	maximal, characteristic
4	#11763698	C₂	1	1	yes	maximal, characteristic
5	#11763697	C₂	1	1	yes	maximal, characteristic
6	#11763695	C₂	1	1	yes	maximal, characteristic
7	#11762933	C₂	1	1	yes	maximal, characteristic
8	C₄×Dic₃₄	C₄	1	1	yes	characteristic
9	C₂×#63216	C₂²	1	1	yes	characteristic
10	C₂×#63216	C₂²	1	1	yes	characteristic
11	C₂×#63216	C₂²	1	1	yes	characteristic
12	C₂×#63216	C₂²	1	1	yes	characteristic
13	C₁₇×C₄⋊C₈	C₄	1	1	yes	characteristic
14	#10587485	C₄	1	1	yes	characteristic
15	#10587485	C₄	1	1	yes	characteristic
16	C₈×Dic₁₇	C₂²	1	1	yes	characteristic
17	C₈×Dic₁₇	C₂²	1	1	yes	characteristic
18	C₄×#3622	C₂²	1	1	yes	characteristic
19	C₂×Dic₃₄	C₈	1	1	yes	characteristic
20	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
22	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
23	C₄⋊Dic₁₇	C₈	1	1	yes	characteristic
24	#63225	C₈	1	1	yes	characteristic
25	#63225	C₈	1	1	yes	characteristic
26	C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
27	C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
28	C₂×#3622	C₂×C₄	1	1	yes	characteristic
29	C₂×#3622	C₂³	1	1	yes	characteristic
30	#63216	—	2	1	no	—
31	#63216	—	2	1	no	—
32	#63216	—	2	1	no	—
33	#63216	Q₈	1	2	yes	complemented
34	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
35	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
36	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
37	C₂×Dic₁₇	C₂×C₈	1	1	yes	characteristic
38	C₂×Dic₁₇	C₂×C₈	1	1	yes	characteristic
39	C₂×Dic₁₇	C₂×C₈	1	1	yes	characteristic
40	C₂×Dic₁₇	C₂×C₈	1	1	yes	characteristic
41	Dic₃₄	—	2	2	no	—
42	C₈×C₁₇	—	2	1	no	—
43	C₈×C₁₇	—	2	1	no	—
44	#3622	—	2	1	no	—
45	#3622	C₂×Q₈	1	1	yes	characteristic
46	#3622	#41	1	1	yes	characteristic
47	#2183	—	17	1	no	maximal, Sylow
48	C₂²×C₁₇	C₂²×C₈	1	1	yes	characteristic
49	C₄×C₁₇	—	2	1	no	—
50	C₄×C₁₇	—	2	1	no	—
51	C₄×C₁₇	C₄×Q₈	1	1	yes	characteristic
52	C₄×C₁₇	#131	1	1	yes	characteristic
53	Dic₁₇	—	2	1	no	—
54	Dic₁₇	—	2	1	no	—
55	Dic₁₇	—	2	1	no	—
56	Dic₁₇	M₃₂	1	2	yes	—
57	C₈×Q₈	—	17	1	no	—
58	C₄⋊C₁₆	—	17	1	no	—
59	C₄⋊C₁₆	—	17	1	no	—
60	C₄⋊C₁₆	—	17	1	no	—
61	#346	—	17	1	no	—
62	#346	—	17	1	no	—
63	C₄×C₁₆	—	17	1	no	—
64	C₂×C₁₇	C₈×Q₈	1	1	yes	characteristic
65	C₂×C₁₇	C₂×M₃₂	1	1	yes	characteristic
66	C₂×C₁₇	#504	1	1	yes	characteristic
67	C₄×Q₈	—	17	1	no	—
68	C₂×C₁₆	—	17	1	no	—
69	C₂×C₁₆	—	17	1	no	—
70	C₂×C₁₆	—	17	1	no	—
71	C₂×C₁₆	—	17	1	no	—
72	C₄⋊C₈	—	17	1	no	—
73	C₄⋊C₈	—	17	1	no	—
74	C₄⋊C₈	#595	1	1	yes	characteristic
75	C₄×C₈	—	17	1	no	—
76	C₄×C₈	—	17	1	no	—
77	C₄×C₈	—	17	1	no	—
78	C₁₇	#2183	1	1	yes	characteristic, complemented, Sylow
79	C₂×Q₈	—	17	1	no	—
80	C₂×C₈	—	17	1	no	—
81	C₂×C₈	—	17	1	no	—
82	C₂×C₈	C₂×#595	1	1	yes	characteristic
83	C₂×C₈	C₂×#595	1	1	yes	characteristic
84	C₄⋊C₄	—	17	1	no	—
85	C₄⋊C₄	—	17	1	no	—
86	C₄⋊C₄	—	17	1	no	—
87	C₄²	—	17	1	no	—
88	C₄²	—	17	1	no	—
89	C₄²	C₂×#595	1	1	yes	characteristic
90	C₁₆	—	17	2	no	—
91	C₁₆	—	34	1	no	—
92	C₁₆	—	34	1	no	—
93	C₁₆	—	34	1	no	—
94	Q₈	—	34	2	no	—
95	C₂×C₄	—	17	1	no	—
96	C₂×C₄	—	17	1	no	—
97	C₂×C₄	—	17	1	no	—
98	C₂×C₄	—	17	1	no	—
99	C₂×C₄	#63242	1	1	yes	characteristic
100	C₂×C₄	#63242	1	1	yes	characteristic
101	C₂×C₄	C₂²×#595	1	1	yes	characteristic
102	C₈	—	2	1	no	—
103	C₈	—	2	1	no	—
104	C₈	—	17	1	no	—
105	C₈	—	17	1	no	—
106	C₈	—	34	1	no	—
107	C₂²	C₂×#63242	1	1	yes	characteristic
108	C₄	—	2	1	no	—
109	C₄	—	2	1	no	—
110	C₄	—	17	2	no	—
111	C₄	—	34	1	no	—
112	C₄	—	34	1	no	—
113	C₄	—	34	1	no	—
114	C₄	#10587678	1	1	yes	characteristic
115	C₄	Q₈×#595	1	1	yes	characteristic
116	C₂	#11763858	1	1	yes	characteristic
117	C₂	#11763865	1	1	yes	characteristic
118	C₂	#11763868	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11763730

C₂

yes

maximal, characteristic

#11763730

C₂

yes

maximal, characteristic

C₄⋊#63216

C₂

yes

maximal, characteristic

#11763698

C₂

yes

maximal, characteristic

#11763697

C₂

yes

maximal, characteristic

#11763695

C₂

yes

maximal, characteristic

#11762933

C₂

yes

maximal, characteristic

C₄×Dic₃₄

C₄

yes

characteristic

C₂×#63216

C₂²

yes

characteristic

C₂×#63216

C₂²

yes

characteristic

C₂×#63216

C₂²

yes

characteristic

C₂×#63216

C₂²

yes

characteristic

C₁₇×C₄⋊C₈

C₄

yes

characteristic

#10587485

C₄

yes

characteristic

#10587485

C₄

yes

characteristic

C₈×Dic₁₇

C₂²

yes

characteristic

C₈×Dic₁₇

C₂²

yes

characteristic

C₄×#3622

C₂²

yes

characteristic

C₂×Dic₃₄

C₈

yes

characteristic

C₂×C₈×C₁₇

C₂×C₄

yes

characteristic

C₂×C₈×C₁₇

C₂×C₄

yes

characteristic

C₄²×C₁₇

C₂×C₄

yes

characteristic

C₄⋊Dic₁₇

C₈

yes

characteristic

#63225

C₈

yes

characteristic

#63225

C₈

yes

characteristic

C₄×Dic₁₇

C₂×C₄

yes

characteristic

C₄×Dic₁₇

C₂×C₄

yes

characteristic

C₂×#3622

C₂×C₄

yes

characteristic

C₂×#3622

C₂³

yes

—

—

—

Q₈

yes

complemented

C₂×C₄×C₁₇

C₂×C₈

yes

characteristic

C₂×C₄×C₁₇

C₂×C₈

yes

characteristic

C₂×C₄×C₁₇

C₂²×C₄

yes

characteristic

C₂×Dic₁₇

C₂×C₈

yes

characteristic

C₂×Dic₁₇

C₂×C₈

yes

characteristic

C₂×Dic₁₇

C₂×C₈

yes

characteristic

C₂×Dic₁₇

C₂×C₈

yes

characteristic

Dic₃₄

—

C₈×C₁₇

—

C₈×C₁₇

—

#3622

—

#3622

C₂×Q₈

yes

yes

—

C₂²×C₁₇

C₂²×C₈

yes

characteristic

C₄×C₁₇

—

C₄×C₁₇

—

C₄×C₁₇

C₄×Q₈

yes

characteristic

C₄×C₁₇

#131

yes

characteristic

Dic₁₇

—

Dic₁₇

—

Dic₁₇

—

Dic₁₇

M₃₂

yes

—

C₈×Q₈

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

#346

—

#346

—

C₄×C₁₆

—

C₂×C₁₇

C₈×Q₈

yes

characteristic

C₂×C₁₇

C₂×M₃₂

yes

characteristic

C₂×C₁₇

#504

yes

characteristic

C₄×Q₈

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

#595

yes

characteristic

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₁₇

#2183

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

C₂×#595

yes

characteristic

C₁₆

—

C₁₆

—

C₁₆

—

C₁₆

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#63242

yes

characteristic

100

C₂×C₄

#63242

yes

characteristic

101

C₂×C₄

C₂²×#595

yes

characteristic

102

C₈

—

103

C₈

—

104

C₈

—

105

C₈

—

106

C₈

—

107

C₂²

C₂×#63242

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

—

114

C₄

#10587678

yes

characteristic

115

C₄

Q₈×#595

yes

characteristic

116

C₂

#11763858

yes

characteristic

117

C₂

#11763865

yes

characteristic

118

C₂

#11763868

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#595
commutator, socle, prime radical	C₂²×C₁₇	C₂²×C₈
Fitting	C₁₇×C₄⋊C₈	C₄
cosocle	C₂×#3622	C₂³
hypercenter	C₄⋊C₈	#595
hypocenter	C₁₇	#2183
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#595

commutator, socle, prime radical

C₂²×C₁₇

C₂²×C₈

Fitting

C₁₇×C₄⋊C₈

C₄

C₂³

C₄⋊C₈

C₁₇

G ▷ C₂²×C₁₇ ▷ C₁₇

C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

N	H ≅ G/N	type
33. #63216	Q₈	semidirect
78. C₁₇	#2183	semidirect

H ≅ G/N

type

33. #63216

Q₈

semidirect

78. C₁₇

#2183

semidirect

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

subgroup	index
#11763730	2
C₄⋊#63216	2
#11763698	2
#11763697	2
#11763695	2
#11762933	2
#2183	17

subgroup

index

Subgroups — #14545201

Conjugacy classes of subgroups

Complements

Maximal subgroups