Group #16952932 — subgroups

Subgroups — #16952932

Order 4352.

374 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 159 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	C₂×#11763211	C₂	1	1	yes	maximal, characteristic
2	C₂×#11762585	C₂	1	1	yes	maximal, characteristic
3	#14526875	C₂	1	4	yes	maximal
4	C₁₇×#1845	C₂	1	1	yes	maximal, characteristic
5	C₂×#10587556	—	2	1	no	—
6	C₂²×#63214	C₂²	1	2	yes	—
7	#11763211	—	2	2	no	—
8	#11763211	C₄	1	4	yes	complemented
9	C₂×#10587489	C₂²	1	2	yes	—
10	C₂×#10587488	—	2	1	no	—
11	#11762585	—	2	2	no	—
12	C₂×C₁₇×#107	—	2	1	no	—
13	C₂×C₁₇×#107	C₂²	1	2	yes	—
14	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
15	C₁₇×#384	—	2	1	no	—
16	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
18	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
19	C₂×C₄⋊C₄×C₁₇	—	4	2	no	—
20	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
21	C₂×C₄⋊Dic₁₇	—	2	2	no	—
22	C₂×#63225	—	4	2	no	—
23	#10587556	—	2	4	no	—
24	#10587556	—	4	2	no	—
25	C₁₇×#107	—	2	4	no	—
26	C₁₇×#107	—	4	2	no	—
27	C₄×C₈×C₁₇	C₂×C₄	1	2	yes	—
28	C₄×C₈×C₁₇	D₄	1	2	yes	—
29	#10587489	—	2	2	no	—
30	#10587489	C₂×C₄	1	4	yes	—
31	#10587488	—	2	4	no	—
32	C₂×#63214	—	2	2	no	—
33	C₂×#63214	—	2	2	no	—
34	C₂×#63214	Q₈	1	4	yes	—
35	C₂²×C₄×C₁₇	—	4	2	no	—
36	C₂²×C₄×C₁₇	D₈	1	2	yes	—
37	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
38	C₂²×Dic₁₇	—	4	2	no	—
39	C₂×C₈×C₁₇	C₂²⋊C₄	1	2	yes	—
40	C₂×C₈×C₁₇	SD₁₆	1	2	yes	—
41	C₂×C₈×C₁₇	Q₁₆	1	2	yes	—
42	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
43	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
44	C₂×C₈×C₁₇	C₂×Q₈	1	2	yes	—
45	C₂×C₈×C₁₇	#41	1	2	yes	—
46	C₄⋊C₄×C₁₇	—	4	2	no	—
47	C₄⋊C₄×C₁₇	—	4	2	no	—
48	C₄⋊C₄×C₁₇	—	8	4	no	—
49	C₄²×C₁₇	C₂²⋊C₄	1	2	yes	—
50	C₄²×C₁₇	SD₁₆	1	2	yes	—
51	C₄⋊Dic₁₇	—	2	4	no	—
52	C₄⋊Dic₁₇	—	4	2	no	—
53	#63225	—	4	8	no	—
54	#63214	—	2	4	no	—
55	#13284	—	17	1	no	maximal, Sylow
56	C₂³×C₁₇	C₂×D₈	1	1	yes	characteristic
57	C₂×C₄×C₁₇	—	2	2	no	—
58	C₂×C₄×C₁₇	—	2	2	no	—
59	C₂×C₄×C₁₇	—	8	2	no	—
60	C₂×C₄×C₁₇	—	8	4	no	—
61	C₂×C₄×C₁₇	#102	1	4	yes	—
62	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
63	C₂×C₄×C₁₇	#124	1	1	yes	characteristic
64	C₂×C₄×C₁₇	C₄⋊Q₈	1	1	yes	characteristic
65	C₂×C₄×C₁₇	C₂×SD₁₆	1	1	yes	characteristic
66	C₂×C₄×C₁₇	C₂×SD₁₆	1	1	yes	characteristic
67	C₂×C₄×C₁₇	C₂×Q₁₆	1	1	yes	characteristic
68	C₂×Dic₁₇	—	4	4	no	—
69	C₂×Dic₁₇	—	8	2	no	—
70	C₂×Dic₁₇	—	8	2	no	—
71	C₈×C₁₇	#103	1	4	yes	—
72	C₈×C₁₇	C₄×Q₈	1	2	yes	—
73	C₈×C₁₇	C₂²⋊Q₈	1	2	yes	—
74	C₂×#499	—	17	1	no	—
75	C₂×#346	—	17	1	no	—
76	#1845	D₁₇	1	1	yes	characteristic
77	#1380	—	17	4	no	—
78	C₂²×C₁₇	C₂×#102	1	1	yes	characteristic
79	C₂²×C₁₇	#486	1	1	yes	characteristic
80	C₂²×C₁₇	#500	1	1	yes	characteristic
81	C₂²×C₁₇	#509	1	2	yes	—
82	C₂²×C₁₇	#510	1	2	yes	—
83	C₄×C₁₇	—	2	4	no	—
84	C₄×C₁₇	—	16	2	no	—
85	C₄×C₁₇	#391	1	1	yes	characteristic
86	C₄×C₁₇	C₂×#103	1	1	yes	characteristic
87	C₄×C₁₇	#487	1	1	yes	characteristic
88	C₄×C₁₇	#498	1	1	yes	characteristic
89	Dic₁₇	—	8	4	no	—
90	C₂×#125	—	34	1	no	—
91	C₂²×C₁₆	—	17	2	no	—
92	#499	—	17	4	no	—
93	#499	—	34	2	no	—
94	C₂×#107	—	2	1	no	—
95	C₂×#107	—	17	2	no	—
96	C₂×#107	C₂×D₁₇	1	2	yes	—
97	C₂×#106	—	34	1	no	—
98	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
99	#384	—	2	1	no	—
100	#346	—	34	2	no	—
101	C₂×C₁₇	#1990	1	1	yes	characteristic
102	C₂×C₁₇	#2139	1	2	yes	—
103	C₂×C₁₇	#2244	1	1	yes	characteristic
104	C₂×C₁₇	#2245	1	1	yes	characteristic
105	C₂×C₁₇	#2255	1	2	yes	—
106	C₂²×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
107	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
108	#125	—	34	4	no	—
109	#125	—	68	2	no	—
110	C₂×C₄⋊C₄	—	2	2	no	—
111	C₂×C₄⋊C₄	—	4	2	no	—
112	C₂×C₄⋊C₄	—	34	2	no	—
113	C₂×C₄⋊C₄	—	68	2	no	—
114	C₂×C₄²	C₂²⋊D₁₇	1	1	yes	characteristic
115	C₂×C₁₆	—	17	4	no	—
116	C₂×C₁₆	—	34	2	no	—
117	C₂×C₁₆	—	34	2	no	—
118	#107	—	2	4	no	—
119	#107	—	4	2	no	—
120	#107	—	17	4	no	—
121	#107	—	34	2	no	—
122	#106	—	34	4	no	—
123	C₄×C₈	C₄×D₁₇	1	2	yes	—
124	C₄×C₈	D₆₈	1	2	yes	—
125	C₁₇	#13284	1	1	yes	characteristic, complemented, Sylow
126	C₂²×C₄	—	4	2	no	—
127	C₂²×C₄	—	68	2	no	—
128	C₂²×C₄	#63228	1	2	yes	—
129	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
130	C₂×C₈	#63227	1	2	yes	—
131	C₂×C₈	#63229	1	2	yes	—
132	C₂×C₈	#63231	1	2	yes	—
133	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
134	C₂×C₈	C₂×D₆₈	1	1	yes	characteristic
135	C₂×C₈	#63254	1	2	yes	—
136	C₂×C₈	Q₈×D₁₇	1	2	yes	—
137	C₄⋊C₄	—	4	2	no	—
138	C₄⋊C₄	—	4	2	no	—
139	C₄⋊C₄	—	8	4	no	—
140	C₄⋊C₄	—	34	4	no	—
141	C₄⋊C₄	—	68	8	no	—
142	C₄⋊C₄	—	68	2	no	—
143	C₄²	#63227	1	2	yes	—
144	C₄²	#63230	1	2	yes	—
145	C₁₆	—	34	4	no	—
146	C₂³	C₂×#63228	1	1	yes	characteristic
147	C₂×C₄	—	2	2	no	—
148	C₂×C₄	—	2	2	no	—
149	C₂×C₄	—	8	4	no	—
150	C₂×C₄	—	8	2	no	—
151	C₂×C₄	—	68	4	no	—
152	C₂×C₄	—	136	2	no	—
153	C₂×C₄	—	136	2	no	—
154	C₂×C₄	#10587480	1	4	yes	—
155	C₂×C₄	C₂×#63227	1	1	yes	characteristic
156	C₂×C₄	C₂×#63229	1	1	yes	characteristic
157	C₂×C₄	#10587622	1	1	yes	characteristic
158	C₂×C₄	C₂×#63230	1	1	yes	characteristic
159	C₂×C₄	C₂×#63231	1	1	yes	characteristic
160	C₂×C₄	#10587630	1	1	yes	characteristic
161	C₈	#10587481	1	4	yes	—
162	C₈	#10587573	1	2	yes	—
163	C₈	#10587583	1	2	yes	—
164	C₂²	C₂×#10587480	1	1	yes	characteristic
165	C₂²	#11763155	1	1	yes	characteristic
166	C₂²	#11763212	1	1	yes	characteristic
167	C₂²	#11763245	1	2	yes	—
168	C₂²	#11763250	1	2	yes	—
169	C₄	—	2	4	no	—
170	C₄	—	16	2	no	—
171	C₄	—	136	4	no	—
172	C₄	#11762714	1	1	yes	characteristic
173	C₄	C₂×#10587481	1	1	yes	characteristic
174	C₄	#11763159	1	1	yes	characteristic
175	C₄	#11763205	1	1	yes	characteristic
176	C₂	#14529744	1	1	yes	characteristic
177	C₂	#14530494	1	2	yes	—
178	C₂	#14531025	1	1	yes	characteristic
179	C₂	#14531029	1	1	yes	characteristic
180	C₂	#14531067	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11763211

C₂

yes

maximal, characteristic

C₂×#11762585

C₂

yes

maximal, characteristic

#14526875

C₂

yes

maximal

C₁₇×#1845

C₂

yes

maximal, characteristic

C₂×#10587556

—

C₂²×#63214

C₂²

yes

—

#11763211

—

#11763211

C₄

yes

complemented

C₂×#10587489

C₂²

yes

—

C₂×#10587488

—

#11762585

—

C₂×C₁₇×#107

—

C₂×C₁₇×#107

C₂²

yes

—

C₂×C₄×C₈×C₁₇

C₂²

yes

characteristic

C₁₇×#384

—

C₂²×C₈×C₁₇

D₄

yes

characteristic

C₂²×C₈×C₁₇

C₂³

yes

characteristic

C₂×C₄⋊C₄×C₁₇

—

C₂×C₄⋊C₄×C₁₇

—

C₂×C₄²×C₁₇

D₄

yes

characteristic

C₂×C₄⋊Dic₁₇

—

C₂×#63225

—

#10587556

—

#10587556

—

C₁₇×#107

—

C₁₇×#107

—

C₄×C₈×C₁₇

C₂×C₄

yes

—

C₄×C₈×C₁₇

D₄

yes

—

#10587489

—

#10587489

C₂×C₄

yes

—

—

—

—

Q₈

yes

—

C₂²×C₄×C₁₇

—

C₂²×C₄×C₁₇

D₈

yes

—

C₂²×C₄×C₁₇

C₂×D₄

yes

characteristic

C₂²×Dic₁₇

—

C₂×C₈×C₁₇

C₂²⋊C₄

yes

—

C₂×C₈×C₁₇

SD₁₆

yes

—

C₂×C₈×C₁₇

Q₁₆

yes

—

C₂×C₈×C₁₇

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₇

C₂×D₄

yes

characteristic

C₂×C₈×C₁₇

C₂×Q₈

yes

—

C₂×C₈×C₁₇

#41

yes

—

C₄⋊C₄×C₁₇

—

C₄⋊C₄×C₁₇

—

C₄⋊C₄×C₁₇

—

C₄²×C₁₇

C₂²⋊C₄

yes

—

C₄²×C₁₇

SD₁₆

yes

—

C₄⋊Dic₁₇

—

C₄⋊Dic₁₇

—

—

—

—

C₂³×C₁₇

C₂×D₈

yes

characteristic

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

#102

yes

—

C₂×C₄×C₁₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₇

#124

yes

characteristic

C₂×C₄×C₁₇

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₇

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₁₇

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₁₇

C₂×Q₁₆

yes

characteristic

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₈×C₁₇

#103

yes

—

C₈×C₁₇

C₄×Q₈

yes

—

C₈×C₁₇

C₂²⋊Q₈

yes

—

C₂×#499

—

C₂×#346

—

#1845

D₁₇

yes

characteristic

#1380

—

C₂²×C₁₇

yes

C₂²×C₁₇

yes

C₂²×C₁₇

yes

C₂²×C₁₇

yes

—

C₂²×C₁₇

#510

yes

—

C₄×C₁₇

—

C₄×C₁₇

—

C₄×C₁₇

yes

C₄×C₁₇

yes

C₄×C₁₇

yes

C₄×C₁₇

yes

Dic₁₇

—

C₂×#125

—

C₂²×C₁₆

—

—

—

—

—

C₂×D₁₇

yes

—

C₂×#106

—

C₂×C₄×C₈

C₂×D₁₇

yes

characteristic

#384

—

100

#346

—

101

C₂×C₁₇

#1990

yes

characteristic

102

C₂×C₁₇

#2139

yes

—

103

C₂×C₁₇

#2244

yes

characteristic

104

C₂×C₁₇

#2245

yes

characteristic

105

C₂×C₁₇

#2255

yes

—

106

C₂²×C₈

C₂²⋊D₁₇

yes

characteristic

107

C₂²×C₈

C₂²×D₁₇

yes

characteristic

108

#125

—

109

#125

—

110

C₂×C₄⋊C₄

—

111

C₂×C₄⋊C₄

—

112

C₂×C₄⋊C₄

—

113

C₂×C₄⋊C₄

—

114

C₂×C₄²

C₂²⋊D₁₇

yes

characteristic

115

C₂×C₁₆

—

116

C₂×C₁₆

—

117

C₂×C₁₆

—

118

#107

—

119

#107

—

120

#107

—

121

#107

—

122

#106

—

123

C₄×C₈

C₄×D₁₇

yes

—

124

C₄×C₈

D₆₈

yes

—

125

C₁₇

#13284

yes

characteristic, complemented, Sylow

126

C₂²×C₄

—

127

C₂²×C₄

—

128

C₂²×C₄

#63228

yes

—

129

C₂²×C₄

C₂×C₂²⋊D₁₇

yes

characteristic

130

C₂×C₈

#63227

yes

—

131

C₂×C₈

#63229

yes

—

132

C₂×C₈

#63231

yes

—

133

C₂×C₈

C₂×C₄×D₁₇

yes

characteristic

134

C₂×C₈

C₂×D₆₈

yes

characteristic

135

C₂×C₈

#63254

yes

—

136

C₂×C₈

Q₈×D₁₇

yes

—

137

C₄⋊C₄

—

138

C₄⋊C₄

—

139

C₄⋊C₄

—

140

C₄⋊C₄

—

141

C₄⋊C₄

—

142

C₄⋊C₄

—

143

C₄²

#63227

yes

—

144

C₄²

#63230

yes

—

145

C₁₆

—

146

C₂³

C₂×#63228

yes

characteristic

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

136

—

153

C₂×C₄

—

136

—

154

C₂×C₄

#10587480

yes

—

155

C₂×C₄

C₂×#63227

yes

characteristic

156

C₂×C₄

C₂×#63229

yes

characteristic

157

C₂×C₄

#10587622

yes

characteristic

158

C₂×C₄

C₂×#63230

yes

characteristic

159

C₂×C₄

C₂×#63231

yes

characteristic

160

C₂×C₄

#10587630

yes

characteristic

161

C₈

#10587481

yes

—

162

C₈

#10587573

yes

—

163

C₈

#10587583

yes

—

164

C₂²

C₂×#10587480

yes

characteristic

165

C₂²

#11763155

yes

characteristic

166

C₂²

#11763212

yes

characteristic

167

C₂²

#11763245

yes

—

168

C₂²

#11763250

yes

—

169

C₄

—

170

C₄

—

171

C₄

—

136

—

172

C₄

#11762714

yes

characteristic

173

C₄

C₂×#10587481

yes

characteristic

174

C₄

#11763159

yes

characteristic

175

C₄

#11763205

yes

characteristic

176

C₂

#14529744

yes

characteristic

177

C₂

#14530494

yes

—

178

C₂

#14531025

yes

characteristic

179

C₂

#14531029

yes

characteristic

180

C₂

#14531067

yes

—

	subgroup	G/H
center	C₂³	C₂×#63228
commutator	C₂×C₈×C₁₇	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₇
Fitting	C₁₇×#1845	C₂
socle, prime radical	C₂³×C₁₇	C₂×D₈
cosocle	C₂²×C₈×C₁₇	C₂³
hypercenter	#1845	D₁₇
hypocenter	C₁₇	#13284
LCS	G ▷ C₂×C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1845

subgroup

G/H

center

C₂³

C₂×#63228

commutator

C₂×C₈×C₁₇

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₁₇

Fitting

C₁₇×#1845

C₂

socle, prime radical

C₂³×C₁₇

C₂×D₈

cosocle

C₂²×C₈×C₁₇

C₂³

D₁₇

C₁₇

G ▷ C₂×C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1845

N	H ≅ G/N	type
8. #11763211	C₄	semidirect
125. C₁₇	#13284	semidirect

H ≅ G/N

type

8. #11763211

C₄

semidirect

125. C₁₇

#13284

semidirect

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

subgroup	index
C₂×#11763211	2
C₂×#11762585	2
#14526875	2
C₁₇×#1845	2
#13284	17

subgroup

index

C₁₇×#1845

Subgroups — #16952932

Conjugacy classes of subgroups

Complements

Maximal subgroups