Group #14545100 — subgroups

Subgroups — #14545100

Order 2176.

220 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 62 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	#11763865	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₇⋊#108	C₂	1	1	yes	maximal, characteristic, complemented
3	#11763724	C₂	1	4	yes	maximal, complemented
4	C₂×#10587605	C₂	1	1	yes	maximal, characteristic
5	C₂×#63256	—	2	1	no	—
6	D₁₇⋊M₁₆	—	2	1	no	—
7	C₂×Q₁₆×C₁₇	C₄	1	1	yes	characteristic
8	C₂×#63230	—	2	1	no	—
9	#10587605	—	2	1	no	—
10	#10587605	—	2	1	no	—
11	#10587605	C₄	1	2	yes	—
12	#10587605	C₂²	1	2	yes	—
13	C₂×D₁₃₆	C₄	1	1	yes	characteristic
14	C₂×C₈×D₁₇	C₂²	1	1	yes	characteristic
15	#10587538	—	2	1	no	—
16	#10587536	C₂²	1	2	yes	complemented
17	#10587535	—	2	1	no	—
18	#10587530	—	2	1	no	—
19	#10587529	C₂²	1	2	yes	complemented
20	C₂×Q₈×C₁₇	—	2	1	no	—
21	#63256	—	2	2	no	—
22	#63256	—	2	2	no	—
23	#63256	—	4	1	no	—
24	#63256	—	4	1	no	—
25	C₂×D₆₈	—	2	1	no	—
26	C₂×D₆₈	—	4	1	no	—
27	C₂×C₄×D₁₇	—	4	1	no	—
28	C₂×C₄×D₁₇	D₄	1	1	yes	characteristic
29	#63247	—	4	1	no	—
30	#63243	—	2	2	no	—
31	#63242	—	4	1	no	—
32	Q₁₆×C₁₇	—	2	1	no	—
33	Q₁₆×C₁₇	C₂×C₄	1	2	yes	—
34	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
35	#63230	—	2	2	no	—
36	#63230	—	2	2	no	—
37	C₂×#3622	D₄	1	1	yes	characteristic
38	D₁₃₆	—	2	1	no	—
39	D₁₃₆	C₂×C₄	1	2	yes	—
40	C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
41	C₈×D₁₇	D₄	1	1	yes	characteristic
42	C₈×D₁₇	D₄	1	1	yes	characteristic
43	C₈×D₁₇	C₂³	1	1	yes	characteristic
44	#63216	—	2	2	no	—
45	C₂²×D₁₇	—	4	1	no	—
46	C₂²×D₁₇	SD₁₆	1	1	yes	characteristic
47	Q₈×C₁₇	—	2	2	no	—
48	Q₈×C₁₇	—	4	1	no	—
49	C₂×C₄×C₁₇	—	4	1	no	—
50	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
51	C₂×Dic₁₇	D₈	1	1	yes	characteristic
52	D₆₈	—	2	2	no	—
53	D₆₈	—	4	2	no	—
54	D₆₈	—	4	2	no	—
55	D₆₈	—	4	1	no	—
56	C₄×D₁₇	—	4	2	no	—
57	C₄×D₁₇	—	4	2	no	—
58	C₄×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
59	C₄×D₁₇	D₈	1	1	yes	characteristic
60	C₄×D₁₇	SD₁₆	1	1	yes	characteristic
61	C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
62	#3624	—	4	2	no	—
63	C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
64	C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
65	#3622	C₂²⋊C₄	1	1	yes	characteristic
66	#3622	C₂×D₄	1	1	yes	characteristic
67	#2143	—	17	1	no	maximal, Sylow
68	C₂²×C₁₇	#102	1	1	yes	characteristic
69	C₂×D₁₇	—	4	1	no	—
70	C₂×D₁₇	—	4	2	no	—
71	C₂×D₁₇	—	8	2	no	—
72	C₂×D₁₇	#102	1	1	yes	characteristic
73	C₂×D₁₇	C₂×SD₁₆	1	1	yes	characteristic
74	C₄×C₁₇	—	4	2	no	—
75	C₄×C₁₇	#102	1	1	yes	characteristic
76	C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
77	Dic₁₇	#102	1	1	yes	characteristic
78	Dic₁₇	C₂×D₈	1	1	yes	characteristic
79	C₂×#135	—	17	1	no	—
80	C₂×M₃₂	—	17	1	no	—
81	C₂×#108	—	17	1	no	—
82	#359	—	17	4	no	—
83	C₂×C₁₇	—	2	1	no	—
84	C₂×C₁₇	C₂×#102	1	1	yes	characteristic
85	D₁₇	—	2	1	no	—
86	D₁₇	—	2	1	no	—
87	D₁₇	—	8	2	no	—
88	C₂×#41	—	34	1	no	—
89	#135	—	17	2	no	—
90	#135	—	17	2	no	—
91	#135	—	34	1	no	—
92	#135	—	34	1	no	—
93	C₂×Q₁₆	#595	1	1	yes	characteristic
94	C₂×SD₁₆	—	34	1	no	—
95	C₂×D₈	—	17	1	no	—
96	C₂×M₁₆	—	34	1	no	—
97	C₂²×C₈	—	17	1	no	—
98	M₃₂	—	34	1	no	—
99	M₃₂	—	34	1	no	—
100	C₂×C₁₆	—	17	2	no	—
101	#108	—	17	2	no	—
102	#108	—	34	1	no	—
103	C₁₇	#2143	1	1	yes	characteristic, complemented, Sylow
104	#41	—	34	2	no	—
105	#41	—	34	2	no	—
106	#41	—	68	1	no	—
107	#41	—	68	1	no	—
108	C₂×Q₈	—	2	1	no	—
109	C₂×D₄	—	34	1	no	—
110	C₂×D₄	—	68	1	no	—
111	C₂²×C₄	—	17	1	no	—
112	C₂²×C₄	—	68	1	no	—
113	Q₁₆	—	2	1	no	—
114	Q₁₆	C₂×#595	1	2	yes	—
115	SD₁₆	—	34	2	no	—
116	SD₁₆	—	34	2	no	—
117	D₈	—	17	2	no	—
118	D₈	—	34	1	no	—
119	M₁₆	—	34	2	no	—
120	M₁₆	—	68	1	no	—
121	C₂×C₈	—	17	1	no	—
122	C₂×C₈	—	17	1	no	—
123	C₂×C₈	—	17	1	no	—
124	C₂×C₈	—	17	1	no	—
125	C₂×C₈	—	17	1	no	—
126	C₂×C₈	—	68	1	no	—
127	C₂×C₈	C₂×#595	1	1	yes	characteristic
128	C₁₆	—	34	2	no	—
129	C₂³	—	17	1	no	—
130	C₂³	—	68	1	no	—
131	Q₈	—	2	2	no	—
132	Q₈	—	4	1	no	—
133	D₄	—	34	2	no	—
134	D₄	—	68	2	no	—
135	D₄	—	68	2	no	—
136	D₄	—	68	1	no	—
137	C₂×C₄	—	4	1	no	—
138	C₂×C₄	—	17	1	no	—
139	C₂×C₄	—	17	1	no	—
140	C₂×C₄	—	17	1	no	—
141	C₂×C₄	—	17	1	no	—
142	C₂×C₄	—	17	1	no	—
143	C₂×C₄	—	68	2	no	—
144	C₂×C₄	—	68	2	no	—
145	C₂×C₄	C₂²⋊#595	1	1	yes	characteristic
146	C₈	—	17	1	no	—
147	C₈	—	17	1	no	—
148	C₈	—	68	2	no	—
149	C₈	C₂²⋊#595	1	1	yes	characteristic
150	C₈	C₂²×#595	1	1	yes	characteristic
151	C₂²	—	17	1	no	—
152	C₂²	—	17	1	no	—
153	C₂²	—	68	1	no	—
154	C₂²	—	68	2	no	—
155	C₂²	—	136	2	no	—
156	C₂²	#10587547	1	1	yes	characteristic
157	C₄	—	4	2	no	—
158	C₄	—	17	1	no	—
159	C₄	—	17	1	no	—
160	C₄	#10587547	1	1	yes	characteristic
161	C₄	C₂×C₂²⋊#595	1	1	yes	characteristic
162	C₂	—	2	1	no	—
163	C₂	—	34	1	no	—
164	C₂	—	34	1	no	—
165	C₂	—	136	2	no	—
166	C₂	C₂×#10587547	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11763865

C₂

yes

maximal, characteristic, complemented

D₁₇⋊#108

C₂

yes

maximal, characteristic, complemented

#11763724

C₂

yes

maximal, complemented

C₂×#10587605

C₂

yes

maximal, characteristic

C₂×#63256

—

D₁₇⋊M₁₆

—

C₂×Q₁₆×C₁₇

C₄

yes

—

—

—

C₄

yes

—

#10587605

C₂²

yes

—

C₂×D₁₃₆

C₄

yes

characteristic

C₂×C₈×D₁₇

C₂²

yes

characteristic

#10587538

—

#10587536

C₂²

yes

—

—

C₂²

yes

complemented

C₂×Q₈×C₁₇

—

—

—

—

—

C₂×D₆₈

—

C₂×D₆₈

—

C₂×C₄×D₁₇

—

C₂×C₄×D₁₇

D₄

yes

—

—

—

Q₁₆×C₁₇

—

Q₁₆×C₁₇

C₂×C₄

yes

—

C₂×C₈×C₁₇

C₂×C₄

yes

—

—

D₄

yes

characteristic

D₁₃₆

—

D₁₃₆

C₂×C₄

yes

—

C₈×D₁₇

C₂×C₄

yes

characteristic

C₈×D₁₇

D₄

yes

characteristic

C₈×D₁₇

D₄

yes

characteristic

C₈×D₁₇

C₂³

yes

characteristic

#63216

—

C₂²×D₁₇

—

C₂²×D₁₇

SD₁₆

yes

characteristic

Q₈×C₁₇

—

Q₈×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₂²⋊C₄

yes

characteristic

C₂×Dic₁₇

D₈

yes

characteristic

D₆₈

—

D₆₈

—

D₆₈

—

D₆₈

—

C₄×D₁₇

—

C₄×D₁₇

—

C₄×D₁₇

C₂²⋊C₄

yes

characteristic

C₄×D₁₇

D₈

yes

characteristic

C₄×D₁₇

SD₁₆

yes

characteristic

C₄×D₁₇

C₂×D₄

yes

characteristic

#3624

—

C₈×C₁₇

C₂²⋊C₄

yes

characteristic

C₈×C₁₇

C₂²×C₄

yes

characteristic

#3622

C₂²⋊C₄

yes

characteristic

#3622

C₂×D₄

yes

—

C₂²×C₁₇

yes

C₂×D₁₇

—

C₂×D₁₇

—

C₂×D₁₇

—

C₂×D₁₇

#102

yes

characteristic

C₂×D₁₇

C₂×SD₁₆

yes

characteristic

C₄×C₁₇

—

C₄×C₁₇

#102

yes

characteristic

C₄×C₁₇

C₂×C₂²⋊C₄

yes

characteristic

Dic₁₇

#102

yes

characteristic

Dic₁₇

C₂×D₈

yes

characteristic

C₂×#135

—

C₂×M₃₂

—

C₂×#108

—

#359

—

C₂×C₁₇

—

C₂×C₁₇

C₂×#102

yes

characteristic

D₁₇

—

D₁₇

—

D₁₇

—

C₂×#41

—

—

—

—

—

C₂×Q₁₆

#595

yes

characteristic

C₂×SD₁₆

—

C₂×D₈

—

C₂×M₁₆

—

C₂²×C₈

—

M₃₂

—

M₃₂

—

100

C₂×C₁₆

—

101

#108

—

102

#108

—

103

C₁₇

#2143

yes

characteristic, complemented, Sylow

104

#41

—

105

#41

—

106

#41

—

107

#41

—

108

C₂×Q₈

—

109

C₂×D₄

—

110

C₂×D₄

—

111

C₂²×C₄

—

112

C₂²×C₄

—

113

Q₁₆

—

114

Q₁₆

C₂×#595

yes

—

115

SD₁₆

—

116

SD₁₆

—

117

D₈

—

118

D₈

—

119

M₁₆

—

120

M₁₆

—

121

C₂×C₈

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

—

125

C₂×C₈

—

126

C₂×C₈

—

127

C₂×C₈

C₂×#595

yes

characteristic

128

C₁₆

—

129

C₂³

—

130

C₂³

—

131

Q₈

—

132

Q₈

—

133

D₄

—

134

D₄

—

135

D₄

—

136

D₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

C₂²⋊#595

yes

characteristic

146

C₈

—

147

C₈

—

148

C₈

—

149

C₈

C₂²⋊#595

yes

characteristic

150

C₈

C₂²×#595

yes

characteristic

151

C₂²

—

152

C₂²

—

153

C₂²

—

154

C₂²

—

155

C₂²

—

136

—

156

C₂²

#10587547

yes

characteristic

157

C₄

—

158

C₄

—

159

C₄

—

160

C₄

#10587547

yes

characteristic

161

C₄

C₂×C₂²⋊#595

yes

characteristic

162

C₂

—

163

C₂

—

164

C₂

—

165

C₂

—

136

—

166

C₂

C₂×#10587547

yes

characteristic

	subgroup	G/H
center	C₂	C₂×#10587547
commutator	C₈×C₁₇	C₂²×C₄
Frattini	C₈	C₂²×#595
Fitting	C₂×Q₁₆×C₁₇	C₄
socle	C₂×C₁₇	C₂×#102
prime radical	C₂×#10587605	C₂
cosocle	C₈×D₁₇	C₂³
hypercenter	C₂×Q₁₆	#595
hypocenter	C₁₇	#2143
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

subgroup

G/H

center

C₂

C₂×#10587547

commutator

C₈×C₁₇

C₂²×C₄

Frattini

C₈

C₂²×#595

Fitting

C₂×Q₁₆×C₁₇

C₄

C₂×C₁₇

C₂

C₈×D₁₇

C₂³

C₂×Q₁₆

C₁₇

G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

N	H ≅ G/N	type
1. #11763865	C₂	semidirect
2. D₁₇⋊#108	C₂	semidirect
3. #11763724	C₂	semidirect
16. #10587536	C₂²	semidirect
19. #10587529	C₂²	semidirect
103. C₁₇	#2143	semidirect

H ≅ G/N

type

1. #11763865

C₂

semidirect

2. D₁₇⋊#108

C₂

semidirect

3. #11763724

C₂

semidirect

16. #10587536

C₂²

semidirect

19. #10587529

C₂²

semidirect

103. C₁₇

#2143

semidirect

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

subgroup	index
#11763865	2
D₁₇⋊#108	2
#11763724	2
C₂×#10587605	2
#2143	17

subgroup

index

D₁₇⋊#108

Subgroups — #14545100

Conjugacy classes of subgroups

Complements

Maximal subgroups