Group #16950516 — subgroups

Subgroups — #16950516

Order 4352.

354 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 111 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×#11763227	C₂	1	1	yes	maximal, characteristic
2	C₂×#11762638	C₂	1	2	yes	maximal, complemented
3	#14528831	C₂	1	2	yes	maximal
4	#14526888	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#1385	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10587587	C₂²	1	1	yes	characteristic
7	#11763227	—	2	4	no	—
8	C₂×#10587469	C₄	1	2	yes	—
9	C₂²×#63214	C₂²	1	1	yes	characteristic
10	C₂×C₁₆×D₁₇	C₄	1	2	yes	—
11	C₂×#10587490	C₂²	1	2	yes	—
12	#11762791	—	2	2	no	—
13	#11762638	—	2	4	no	—
14	#11762567	—	2	2	no	—
15	C₂×C₁₇×M₃₂	C₂²	1	1	yes	characteristic
16	C₂×C₁₇×#108	C₂²	1	2	yes	—
17	C₂×#63252	D₄	1	1	yes	characteristic
18	C₂×M₁₆×C₁₇	—	2	2	no	—
19	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
20	C₂×#63223	—	2	2	no	—
21	C₂×#63223	D₄	1	1	yes	characteristic
22	#10587587	—	2	2	no	—
23	#10587587	—	2	2	no	—
24	C₂×#63218	Q₈	1	2	yes	—
25	C₂×C₈×D₁₇	C₂×C₄	1	2	yes	—
26	C₁₇×M₃₂	—	2	2	no	—
27	C₂×C₁₆×C₁₇	C₂×C₄	1	2	yes	—
28	C₁₇×#108	—	2	2	no	—
29	C₁₇×#108	—	2	2	no	—
30	#10587495	—	4	2	no	—
31	#10587494	—	4	2	no	—
32	#10587490	—	2	2	no	—
33	#10587490	—	2	2	no	—
34	C₂×#63214	C₂×C₄	1	1	yes	characteristic
35	C₂×#63214	C₂×C₄	1	1	yes	characteristic
36	C₂×#63214	D₄	1	4	yes	—
37	#10587469	—	2	4	no	—
38	C₁₆×D₁₇	—	2	4	no	—
39	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
40	C₂×C₂²⋊D₁₇	Q₁₆	1	2	yes	—
41	#63252	—	2	2	no	—
42	#63252	—	2	2	no	—
43	C₂×D₆₈	D₈	1	1	yes	characteristic
44	C₂×C₄×D₁₇	C₄⋊C₄	1	2	yes	—
45	C₂×Dic₃₄	D₈	1	1	yes	characteristic
46	M₁₆×C₁₇	—	4	2	no	—
47	M₁₆×C₁₇	—	4	2	no	—
48	C₂×C₈×C₁₇	—	4	2	no	—
49	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
50	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
51	C₂×C₈×C₁₇	C₂×Q₈	1	1	yes	characteristic
52	C₂×C₈×C₁₇	#41	1	2	yes	—
53	#63223	—	2	2	no	—
54	#63223	—	4	2	no	—
55	#63223	—	4	2	no	—
56	C₂×#3622	—	4	2	no	—
57	C₂×#3622	C₄⋊C₄	1	2	yes	—
58	#63218	—	2	4	no	—
59	C₈×D₁₇	—	2	2	no	—
60	C₈×D₁₇	—	2	2	no	—
61	C₁₆×C₁₇	—	2	2	no	—
62	#63214	C₂²⋊C₄	1	2	yes	—
63	#63214	C₂²⋊C₄	1	2	yes	—
64	#12840	—	17	1	no	maximal, Sylow
65	C₂³×C₁₇	C₂×Q₁₆	1	1	yes	characteristic
66	C₂²×D₁₇	#107	1	2	yes	—
67	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
68	C₂×C₄×C₁₇	#121	1	2	yes	—
69	C₂×C₄×C₁₇	C₂×D₈	1	1	yes	characteristic
70	C₂×C₄×C₁₇	#135	1	2	yes	—
71	C₂²⋊D₁₇	—	2	4	no	—
72	C₂×Dic₁₇	#107	1	2	yes	—
73	D₆₈	—	2	2	no	—
74	C₄×D₁₇	—	2	2	no	—
75	C₄×D₁₇	—	2	2	no	—
76	Dic₃₄	—	2	2	no	—
77	C₈×C₁₇	—	8	2	no	—
78	C₈×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
79	C₈×C₁₇	#117	1	1	yes	characteristic
80	C₈×C₁₇	C₂²⋊Q₈	1	2	yes	—
81	#3622	—	2	2	no	—
82	#3622	—	8	2	no	—
83	C₂×#504	—	17	1	no	—
84	C₂×#368	—	17	2	no	—
85	#1813	—	17	2	no	—
86	#1385	—	17	1	no	—
87	#1385	D₁₇	1	1	yes	characteristic, complemented
88	C₂²×C₁₇	—	4	1	no	—
89	C₂²×C₁₇	C₂×#107	1	1	yes	characteristic
90	C₂²×C₁₇	#467	1	2	yes	—
91	C₂×D₁₇	—	2	2	no	—
92	C₂×D₁₇	—	4	2	no	—
93	C₄×C₁₇	#380	1	1	yes	characteristic
94	C₄×C₁₇	#427	1	1	yes	characteristic
95	C₄×C₁₇	#466	1	2	yes	—
96	Dic₁₇	—	2	2	no	—
97	C₂×#131	—	17	1	no	—
98	#504	—	34	4	no	—
99	C₂×M₃₂	—	17	2	no	—
100	C₂×M₃₂	C₂×D₁₇	1	1	yes	characteristic
101	C₂²×C₁₆	—	17	1	no	—
102	C₂²×C₁₆	—	17	2	no	—
103	C₂×#108	—	17	2	no	—
104	C₂×#108	C₂×D₁₇	1	2	yes	—
105	#413	—	34	2	no	—
106	#368	—	34	4	no	—
107	#338	—	34	2	no	—
108	C₂×C₁₇	—	2	1	no	—
109	C₂×C₁₇	—	2	2	no	—
110	C₂×C₁₇	#1808	1	1	yes	characteristic
111	D₁₇	—	4	2	no	—
112	C₂×#41	—	17	1	no	—
113	#131	—	34	2	no	—
114	#131	—	34	2	no	—
115	C₂×M₁₆	—	2	2	no	—
116	C₂×M₁₆	—	17	1	no	—
117	C₂×M₁₆	—	17	2	no	—
118	C₂×M₁₆	—	34	2	no	—
119	C₂²×C₈	—	17	2	no	—
120	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
121	M₃₂	—	2	2	no	—
122	M₃₂	—	34	4	no	—
123	C₂×C₁₆	—	17	1	no	—
124	C₂×C₁₆	—	17	1	no	—
125	C₂×C₁₆	—	17	4	no	—
126	C₂×C₁₆	—	34	4	no	—
127	C₂×C₁₆	C₄×D₁₇	1	2	yes	—
128	#108	—	2	2	no	—
129	#108	—	2	2	no	—
130	#108	—	34	2	no	—
131	#108	—	34	2	no	—
132	#101	—	68	2	no	—
133	#100	—	68	2	no	—
134	C₁₇	#12840	1	1	yes	characteristic, complemented, Sylow
135	#41	—	34	2	no	—
136	#41	—	34	2	no	—
137	C₂×Q₈	—	17	1	no	—
138	C₂×D₄	—	17	2	no	—
139	C₂×D₄	—	17	1	no	—
140	C₂²×C₄	—	17	2	no	—
141	C₂²×C₄	D₄×D₁₇	1	1	yes	characteristic
142	M₁₆	—	4	2	no	—
143	M₁₆	—	4	2	no	—
144	M₁₆	—	34	2	no	—
145	M₁₆	—	34	4	no	—
146	M₁₆	—	68	2	no	—
147	M₁₆	—	68	2	no	—
148	C₂×C₈	—	4	2	no	—
149	C₂×C₈	—	17	2	no	—
150	C₂×C₈	—	34	2	no	—
151	C₂×C₈	—	34	2	no	—
152	C₂×C₈	—	68	2	no	—
153	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
154	C₂×C₈	#63252	1	2	yes	—
155	C₂×C₈	D₄×D₁₇	1	2	yes	—
156	C₂×C₈	Q₈×D₁₇	1	1	yes	characteristic
157	C₁₆	—	2	2	no	—
158	C₁₆	—	17	2	no	—
159	C₁₆	—	17	2	no	—
160	C₂³	—	17	2	no	—
161	C₂³	Q₁₆×D₁₇	1	1	yes	characteristic
162	Q₈	—	34	2	no	—
163	D₄	—	34	4	no	—
164	D₄	—	34	2	no	—
165	C₂×C₄	—	17	2	no	—
166	C₂×C₄	—	34	2	no	—
167	C₂×C₄	—	34	2	no	—
168	C₂×C₄	#10587570	1	2	yes	—
169	C₂×C₄	C₄⋊C₄×D₁₇	1	1	yes	characteristic
170	C₂×C₄	D₈×D₁₇	1	1	yes	characteristic
171	C₂×C₄	#10587602	1	2	yes	—
172	C₈	—	8	2	no	—
173	C₈	—	34	2	no	—
174	C₈	—	136	2	no	—
175	C₈	#10587558	1	1	yes	characteristic
176	C₈	C₂²⋊C₄×D₁₇	1	1	yes	characteristic
177	C₈	#10587582	1	2	yes	—
178	C₂²	—	4	1	no	—
179	C₂²	—	34	2	no	—
180	C₂²	—	68	2	no	—
181	C₂²	#107×D₁₇	1	1	yes	characteristic
182	C₂²	#11763049	1	2	yes	—
183	C₄	—	34	2	no	—
184	C₄	#11762668	1	1	yes	characteristic
185	C₄	#11762844	1	1	yes	characteristic
186	C₄	#11763044	1	2	yes	—
187	C₂	—	2	1	no	—
188	C₂	—	2	2	no	—
189	C₂	—	68	2	no	—
190	C₂	#14528812	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11763227

C₂

yes

maximal, characteristic

C₂×#11762638

C₂

yes

maximal, complemented

#14528831

C₂

yes

maximal

#14526888

C₂

yes

maximal, characteristic, complemented

C₁₇×#1385

C₂

yes

maximal, characteristic, complemented

C₂×#10587587

C₂²

yes

characteristic

#11763227

—

C₂×#10587469

C₄

yes

—

C₂²×#63214

C₂²

yes

characteristic

C₂×C₁₆×D₁₇

C₄

yes

—

C₂×#10587490

C₂²

yes

—

#11762791

—

#11762638

—

#11762567

—

C₂×C₁₇×M₃₂

C₂²

yes

characteristic

C₂×C₁₇×#108

C₂²

yes

—

C₂×#63252

D₄

yes

characteristic

C₂×M₁₆×C₁₇

—

C₂²×C₈×C₁₇

C₂³

yes

characteristic

C₂×#63223

—

C₂×#63223

D₄

yes

—

—

Q₈

yes

—

C₂×C₈×D₁₇

C₂×C₄

yes

—

C₁₇×M₃₂

—

C₂×C₁₆×C₁₇

C₂×C₄

yes

—

C₁₇×#108

—

C₁₇×#108

—

—

—

—

—

C₂×C₄

yes

characteristic

C₂×#63214

C₂×C₄

yes

characteristic

C₂×#63214

D₄

yes

—

#10587469

—

C₁₆×D₁₇

—

C₂²×C₄×C₁₇

C₂×D₄

yes

characteristic

C₂×C₂²⋊D₁₇

Q₁₆

yes

—

#63252

—

#63252

—

C₂×D₆₈

D₈

yes

characteristic

C₂×C₄×D₁₇

C₄⋊C₄

yes

—

C₂×Dic₃₄

D₈

yes

characteristic

M₁₆×C₁₇

—

M₁₆×C₁₇

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₇

C₂×D₄

yes

—

C₂×C₈×C₁₇

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₇

#41

yes

—

—

—

—

—

C₄⋊C₄

yes

—

#63218

—

C₈×D₁₇

—

C₈×D₁₇

—

C₁₆×C₁₇

—

#63214

C₂²⋊C₄

yes

—

#63214

C₂²⋊C₄

yes

—

#12840

—

maximal, Sylow

C₂³×C₁₇

C₂×Q₁₆

yes

characteristic

C₂²×D₁₇

#107

yes

—

C₂×C₄×C₁₇

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₇

#121

yes

—

C₂×C₄×C₁₇

C₂×D₈

yes

characteristic

C₂×C₄×C₁₇

#135

yes

—

C₂²⋊D₁₇

—

C₂×Dic₁₇

#107

yes

—

D₆₈

—

C₄×D₁₇

—

C₄×D₁₇

—

Dic₃₄

—

C₈×C₁₇

—

C₈×C₁₇

C₂×C₂²⋊C₄

yes

characteristic

C₈×C₁₇

#117

yes

characteristic

C₈×C₁₇

C₂²⋊Q₈

yes

—

—

—

—

—

—

—

D₁₇

yes

characteristic, complemented

C₂²×C₁₇

—

C₂²×C₁₇

C₂×#107

yes

characteristic

C₂²×C₁₇

#467

yes

—

C₂×D₁₇

—

C₂×D₁₇

—

C₄×C₁₇

yes

C₄×C₁₇

yes

C₄×C₁₇

yes

—

Dic₁₇

—

C₂×#131

—

#504

—

C₂×M₃₂

—

100

C₂×M₃₂

C₂×D₁₇

yes

characteristic

101

C₂²×C₁₆

—

102

C₂²×C₁₆

—

103

C₂×#108

—

104

C₂×#108

C₂×D₁₇

yes

—

105

#413

—

106

#368

—

107

#338

—

108

C₂×C₁₇

—

109

C₂×C₁₇

—

110

C₂×C₁₇

#1808

yes

characteristic

111

D₁₇

—

112

C₂×#41

—

113

#131

—

114

#131

—

115

C₂×M₁₆

—

116

C₂×M₁₆

—

117

C₂×M₁₆

—

118

C₂×M₁₆

—

119

C₂²×C₈

—

120

C₂²×C₈

C₂²×D₁₇

yes

characteristic

121

M₃₂

—

122

M₃₂

—

123

C₂×C₁₆

—

124

C₂×C₁₆

—

125

C₂×C₁₆

—

126

C₂×C₁₆

—

127

C₂×C₁₆

C₄×D₁₇

yes

—

128

#108

—

129

#108

—

130

#108

—

131

#108

—

132

#101

—

133

#100

—

134

C₁₇

#12840

yes

characteristic, complemented, Sylow

135

#41

—

136

#41

—

137

C₂×Q₈

—

138

C₂×D₄

—

139

C₂×D₄

—

140

C₂²×C₄

—

141

C₂²×C₄

D₄×D₁₇

yes

characteristic

142

M₁₆

—

143

M₁₆

—

144

M₁₆

—

145

M₁₆

—

146

M₁₆

—

147

M₁₆

—

148

C₂×C₈

—

149

C₂×C₈

—

150

C₂×C₈

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₂×C₈

C₂×C₄×D₁₇

yes

characteristic

154

C₂×C₈

#63252

yes

—

155

C₂×C₈

D₄×D₁₇

yes

—

156

C₂×C₈

Q₈×D₁₇

yes

characteristic

157

C₁₆

—

158

C₁₆

—

159

C₁₆

—

160

C₂³

—

161

C₂³

Q₁₆×D₁₇

yes

characteristic

162

Q₈

—

163

D₄

—

164

D₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

#10587570

yes

—

169

C₂×C₄

C₄⋊C₄×D₁₇

yes

characteristic

170

C₂×C₄

D₈×D₁₇

yes

characteristic

171

C₂×C₄

#10587602

yes

—

172

C₈

—

173

C₈

—

174

C₈

—

136

—

175

C₈

#10587558

yes

characteristic

176

C₈

C₂²⋊C₄×D₁₇

yes

characteristic

177

C₈

#10587582

yes

—

178

C₂²

—

179

C₂²

—

180

C₂²

—

181

C₂²

#107×D₁₇

yes

characteristic

182

C₂²

#11763049

yes

—

183

C₄

—

184

C₄

#11762668

yes

characteristic

185

C₄

#11762844

yes

characteristic

186

C₄

#11763044

yes

—

187

C₂

—

188

C₂

—

189

C₂

—

190

C₂

#14528812

yes

characteristic

	subgroup	G/H
center	C₄	#11762844
commutator	C₂×C₈×C₁₇	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₇
Fitting	C₁₇×#1385	C₂
socle	C₂×C₁₇	#1808
prime radical	C₂×#63252	D₄
cosocle	C₂²×C₈×C₁₇	C₂³
hypercenter	#1385	D₁₇
hypocenter	C₁₇	#12840
LCS	G ▷ C₂×C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1385

subgroup

G/H

center

C₄

#11762844

commutator

C₂×C₈×C₁₇

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₁₇

Fitting

C₁₇×#1385

C₂

C₂×C₁₇

D₄

C₂²×C₈×C₁₇

C₂³

D₁₇

C₁₇

G ▷ C₂×C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1385

N	H ≅ G/N	type
2. C₂×#11762638	C₂	semidirect
4. #14526888	C₂	semidirect
5. C₁₇×#1385	C₂	semidirect
87. #1385	D₁₇	semidirect
134. C₁₇	#12840	semidirect

H ≅ G/N

type

2. C₂×#11762638

C₂

semidirect

4. #14526888

C₂

semidirect

5. C₁₇×#1385

C₂

semidirect

87. #1385

D₁₇

semidirect

134. C₁₇

#12840

semidirect

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

subgroup	index
C₂×#11763227	2
C₂×#11762638	2
#14528831	2
#14526888	2
C₁₇×#1385	2
#12840	17

subgroup

index

C₁₇×#1385

Subgroups — #16950516

Conjugacy classes of subgroups

Complements

Maximal subgroups