Group #16934208 — subgroups

Subgroups — #16934208

Order 4352.

478 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 139 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	#14529762	C₂	1	2	yes	maximal
2	C₄×C₈×Dic₁₇	C₂	1	1	yes	maximal, characteristic
3	#14527543	C₂	1	1	yes	maximal, characteristic
4	#14527239	C₂	1	2	yes	maximal
5	C₁₇×#3170	C₂	1	1	yes	maximal, characteristic
6	#11762833	C₂²	1	2	yes	—
7	C₂×C₄×#3622	C₂²	1	1	yes	characteristic
8	C₂×C₈×Dic₁₇	—	2	2	no	—
9	C₄²×Dic₁₇	C₂²	1	1	yes	characteristic
10	#11762568	—	2	4	no	—
11	#11762562	—	2	2	no	—
12	Q₈⋊#3622	—	2	4	no	—
13	C₁₇×#533	C₂²	1	2	yes	—
14	C₁₇×#500	C₄	1	1	yes	characteristic, complemented
15	C₁₇×#494	C₄	1	1	yes	characteristic, complemented
16	C₁₇×#487	C₄	1	2	yes	complemented
17	C₁₇×#467	—	2	2	no	—
18	C₄×Q₁₆×C₁₇	—	2	2	no	—
19	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
20	C₂×Q₁₆×C₁₇	—	2	2	no	—
21	C₂²×C₈×C₁₇	D₄	1	2	yes	—
22	C₁₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
23	C₁₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
24	C₁₇×#125	—	2	2	no	—
25	C₁₇×C₂²⋊Q₈	—	2	2	no	—
26	C₁₇×C₂²⋊Q₈	—	2	2	no	—
27	C₄×Q₈×C₁₇	—	2	2	no	—
28	C₄×Q₈×C₁₇	—	2	2	no	—
29	C₁₇×#117	—	2	2	no	—
30	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
31	C₂×C₄×Dic₁₇	—	2	1	no	—
32	C₂×C₄×Dic₁₇	—	2	1	no	—
33	C₂×C₄×Dic₁₇	D₄	1	2	yes	—
34	C₂×#63223	—	2	2	no	—
35	C₂²×#3622	—	2	1	no	—
36	C₁₇×#107	—	2	2	no	—
37	C₁₇×#103	—	2	4	no	—
38	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
39	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
40	C₄×C₈×C₁₇	D₄	1	2	yes	—
41	C₈×Dic₁₇	—	2	8	no	—
42	C₄⋊#3622	—	2	2	no	—
43	C₄⋊#3622	—	2	2	no	—
44	C₄×#3622	—	2	1	no	—
45	C₄×#3622	D₄	1	2	yes	—
46	C₂×Q₈×C₁₇	—	2	2	no	—
47	C₂×Q₈×C₁₇	—	2	2	no	—
48	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
51	C₂²×Dic₁₇	—	2	2	no	—
52	Q₁₆×C₁₇	—	4	4	no	—
53	C₂×C₈×C₁₇	—	2	4	no	—
54	C₂×C₈×C₁₇	C₂²⋊C₄	1	2	yes	—
55	C₂×C₈×C₁₇	C₂²⋊C₄	1	2	yes	—
56	C₄⋊C₄×C₁₇	—	2	2	no	—
57	C₄⋊C₄×C₁₇	—	2	2	no	—
58	C₄⋊C₄×C₁₇	—	2	2	no	—
59	C₄⋊C₄×C₁₇	—	2	2	no	—
60	C₄⋊C₄×C₁₇	—	4	2	no	—
61	C₄⋊C₄×C₁₇	—	4	2	no	—
62	C₂²⋊C₄×C₁₇	—	4	2	no	—
63	C₄²×C₁₇	—	4	2	no	—
64	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
65	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
66	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
67	C₄²×C₁₇	#41	1	1	yes	characteristic
68	C₄×Dic₁₇	—	2	4	no	—
69	C₄×Dic₁₇	—	2	4	no	—
70	C₄×Dic₁₇	—	2	2	no	—
71	C₄×Dic₁₇	Q₁₆	1	4	yes	complemented
72	#63223	—	4	4	no	—
73	C₂×#3622	—	2	4	no	—
74	C₂×#3622	—	2	2	no	—
75	C₂×#3622	—	4	2	no	—
76	#9845	—	17	1	no	maximal, Sylow
77	C₂³×C₁₇	#121	1	1	yes	characteristic
78	Q₈×C₁₇	—	4	4	no	—
79	Q₈×C₁₇	—	4	4	no	—
80	C₂×C₄×C₁₇	—	2	2	no	—
81	C₂×C₄×C₁₇	—	2	2	no	—
82	C₂×C₄×C₁₇	—	4	2	no	—
83	C₂×C₄×C₁₇	—	4	2	no	—
84	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
86	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
87	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
88	C₂×C₄×C₁₇	#124	1	1	yes	characteristic
89	C₂×C₄×C₁₇	#127	1	1	yes	characteristic
90	C₂×C₄×C₁₇	C₂×Q₁₆	1	2	yes	—
91	C₂×C₄×C₁₇	#135	1	2	yes	—
92	C₂×Dic₁₇	—	2	4	no	—
93	C₂×Dic₁₇	—	2	4	no	—
94	C₂×Dic₁₇	—	2	4	no	—
95	C₈×C₁₇	—	2	2	no	—
96	C₈×C₁₇	#104	1	4	yes	—
97	#3622	—	2	4	no	—
98	#3622	—	8	2	no	—
99	#3170	D₁₇	1	1	yes	characteristic
100	#1994	—	17	2	no	—
101	C₄²×C₈	—	17	1	no	—
102	#1567	—	17	1	no	—
103	#1493	—	17	2	no	—
104	C₂²×C₁₇	—	2	1	no	—
105	C₂²×C₁₇	—	2	1	no	—
106	C₂²×C₁₇	#390	1	1	yes	characteristic
107	C₂²×C₁₇	#467	1	2	yes	—
108	C₄×C₁₇	—	2	1	no	—
109	C₄×C₁₇	—	2	1	no	—
110	C₄×C₁₇	—	8	2	no	—
111	C₄×C₁₇	—	8	2	no	—
112	C₄×C₁₇	C₂×#104	1	2	yes	—
113	C₄×C₁₇	C₄×Q₁₆	1	2	yes	—
114	C₄×C₁₇	#443	1	2	yes	—
115	C₄×C₁₇	#494	1	1	yes	characteristic
116	C₄×C₁₇	#495	1	1	yes	characteristic
117	Dic₁₇	—	2	8	no	—
118	#533	C₂×D₁₇	1	2	yes	—
119	#500	Dic₁₇	1	1	yes	characteristic, complemented
120	#494	Dic₁₇	1	1	yes	characteristic, complemented
121	#487	Dic₁₇	1	2	yes	complemented
122	#467	—	2	2	no	—
123	C₄×Q₁₆	—	2	2	no	—
124	#423	—	17	2	no	—
125	C₂×C₄×C₈	—	17	1	no	—
126	C₂×C₄×C₈	—	34	2	no	—
127	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
128	C₄³	—	17	1	no	—
129	#339	—	34	4	no	—
130	#335	—	34	2	no	—
131	Q₈⋊C₈	—	34	4	no	—
132	C₂×C₁₇	—	2	2	no	—
133	C₂×C₁₇	#1962	1	1	yes	characteristic
134	C₂×C₁₇	#1969	1	1	yes	characteristic
135	C₂×C₁₇	#1974	1	1	yes	characteristic
136	C₂×Q₁₆	—	2	2	no	—
137	C₂×M₁₆	—	34	2	no	—
138	C₂²×C₈	—	34	1	no	—
139	C₂²×C₈	C₂²⋊D₁₇	1	2	yes	—
140	C₄⋊Q₈	C₂×Dic₁₇	1	2	yes	—
141	C₄⋊Q₈	C₂×Dic₁₇	1	2	yes	—
142	#125	—	2	2	no	—
143	C₂²⋊Q₈	—	2	2	no	—
144	C₂²⋊Q₈	—	2	2	no	—
145	C₄×Q₈	—	2	2	no	—
146	C₄×Q₈	—	2	2	no	—
147	#117	—	2	2	no	—
148	C₂×C₄²	—	17	2	no	—
149	C₂×C₄²	—	34	1	no	—
150	C₂×C₄²	—	34	1	no	—
151	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
152	#107	—	2	2	no	—
153	C₄⋊C₈	—	34	2	no	—
154	C₄⋊C₈	—	34	2	no	—
155	#103	—	2	4	no	—
156	C₄×C₈	—	17	2	no	—
157	C₄×C₈	—	34	8	no	—
158	C₄×C₈	—	34	1	no	—
159	C₄×C₈	C₂×Dic₁₇	1	1	yes	characteristic
160	C₄×C₈	C₂×Dic₁₇	1	1	yes	characteristic
161	C₄×C₈	C₂²⋊D₁₇	1	2	yes	—
162	C₁₇	#9845	1	1	yes	characteristic, complemented, Sylow
163	C₂×Q₈	—	2	2	no	—
164	C₂×Q₈	—	2	2	no	—
165	C₂²×C₄	—	34	2	no	—
166	C₂²×C₄	D₄×D₁₇	1	1	yes	characteristic
167	C₂²×C₄	#63254	1	1	yes	characteristic
168	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
169	Q₁₆	—	4	4	no	—
170	M₁₆	—	68	4	no	—
171	C₂×C₈	—	2	4	no	—
172	C₂×C₈	—	34	4	no	—
173	C₂×C₈	—	34	2	no	—
174	C₂×C₈	—	68	2	no	—
175	C₂×C₈	C₂²⋊Dic₁₇	1	2	yes	—
176	C₂×C₈	C₂²⋊Dic₁₇	1	2	yes	—
177	C₄⋊C₄	—	2	2	no	—
178	C₄⋊C₄	—	2	2	no	—
179	C₄⋊C₄	—	2	2	no	—
180	C₄⋊C₄	—	2	2	no	—
181	C₄⋊C₄	—	4	2	no	—
182	C₄⋊C₄	—	4	2	no	—
183	C₂²⋊C₄	—	4	2	no	—
184	C₄²	—	4	2	no	—
185	C₄²	—	17	4	no	—
186	C₄²	—	34	4	no	—
187	C₄²	—	34	4	no	—
188	C₄²	—	34	2	no	—
189	C₄²	D₄×D₁₇	1	1	yes	characteristic
190	C₄²	#63254	1	1	yes	characteristic
191	C₄²	C₂²×Dic₁₇	1	1	yes	characteristic
192	C₄²	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
193	C₂³	#10587624	1	1	yes	characteristic
194	Q₈	—	4	4	no	—
195	Q₈	—	4	4	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	—	4	2	no	—
200	C₂×C₄	—	34	4	no	—
201	C₂×C₄	—	34	4	no	—
202	C₂×C₄	—	34	4	no	—
203	C₂×C₄	Q₁₆×D₁₇	1	2	yes	—
204	C₂×C₄	#10587605	1	2	yes	—
205	C₂×C₄	D₄×Dic₁₇	1	1	yes	characteristic
206	C₂×C₄	D₄×Dic₁₇	1	1	yes	characteristic
207	C₂×C₄	#10587622	1	1	yes	characteristic
208	C₂×C₄	#10587624	1	1	yes	characteristic
209	C₂×C₄	#10587626	1	1	yes	characteristic
210	C₂×C₄	C₂×C₂²⋊Dic₁₇	1	1	yes	characteristic
211	C₈	—	2	2	no	—
212	C₈	—	34	4	no	—
213	C₈	—	136	2	no	—
214	C₈	#10587508	1	4	yes	—
215	C₂²	—	2	1	no	—
216	C₂²	—	2	1	no	—
217	C₂²	#11762712	1	1	yes	characteristic
218	C₂²	#11763047	1	2	yes	—
219	C₄	—	2	1	no	—
220	C₄	—	2	1	no	—
221	C₄	—	8	2	no	—
222	C₄	—	8	2	no	—
223	C₄	—	34	8	no	—
224	C₄	C₂×#10587508	1	2	yes	—
225	C₄	Q₁₆×Dic₁₇	1	2	yes	—
226	C₄	#11762926	1	2	yes	—
227	C₄	#11763187	1	1	yes	characteristic
228	C₄	#11763194	1	1	yes	characteristic
229	C₂	—	2	2	no	—
230	C₂	#14529613	1	1	yes	characteristic
231	C₂	#14529646	1	1	yes	characteristic
232	C₂	#14529673	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14529762

C₂

yes

maximal

C₄×C₈×Dic₁₇

C₂

yes

maximal, characteristic

#14527543

C₂

yes

maximal, characteristic

#14527239

C₂

yes

maximal

C₁₇×#3170

C₂

yes

maximal, characteristic

#11762833

C₂²

yes

—

C₂×C₄×#3622

C₂²

yes

characteristic

C₂×C₈×Dic₁₇

—

C₄²×Dic₁₇

C₂²

yes

—

—

—

C₁₇×#533

C₂²

yes

—

C₁₇×#500

C₄

yes

characteristic, complemented

C₁₇×#494

C₄

yes

characteristic, complemented

C₁₇×#487

C₄

yes

complemented

C₁₇×#467

—

C₄×Q₁₆×C₁₇

—

C₂×C₄×C₈×C₁₇

C₂²

yes

characteristic

C₂×Q₁₆×C₁₇

—

C₂²×C₈×C₁₇

D₄

yes

—

C₁₇×C₄⋊Q₈

C₂×C₄

yes

—

C₁₇×C₄⋊Q₈

C₂×C₄

yes

—

C₁₇×#125

—

C₁₇×C₂²⋊Q₈

—

C₁₇×C₂²⋊Q₈

—

C₄×Q₈×C₁₇

—

C₄×Q₈×C₁₇

—

C₁₇×#117

—

C₂×C₄²×C₁₇

C₂³

yes

characteristic

C₂×C₄×Dic₁₇

—

C₂×C₄×Dic₁₇

—

C₂×C₄×Dic₁₇

D₄

yes

—

C₂×#63223

—

C₂²×#3622

—

C₁₇×#107

—

C₁₇×#103

—

C₄×C₈×C₁₇

C₂×C₄

yes

characteristic

C₄×C₈×C₁₇

C₂×C₄

yes

characteristic

C₄×C₈×C₁₇

D₄

yes

—

C₈×Dic₁₇

—

—

—

—

D₄

yes

—

C₂×Q₈×C₁₇

—

C₂×Q₈×C₁₇

—

C₂²×C₄×C₁₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₇

#41

yes

characteristic

C₂²×Dic₁₇

—

Q₁₆×C₁₇

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

C₂²⋊C₄

yes

—

C₂×C₈×C₁₇

C₂²⋊C₄

yes

—

C₄⋊C₄×C₁₇

—

C₄⋊C₄×C₁₇

—

C₄⋊C₄×C₁₇

—

C₄⋊C₄×C₁₇

—

C₄⋊C₄×C₁₇

—

C₄⋊C₄×C₁₇

—

C₂²⋊C₄×C₁₇

—

C₄²×C₁₇

—

C₄²×C₁₇

C₂²×C₄

yes

characteristic

C₄²×C₁₇

C₂×D₄

yes

characteristic

C₄²×C₁₇

C₂×D₄

yes

characteristic

C₄²×C₁₇

#41

yes

characteristic

C₄×Dic₁₇

—

C₄×Dic₁₇

—

C₄×Dic₁₇

—

C₄×Dic₁₇

Q₁₆

yes

—

—

—

—

—

C₂³×C₁₇

yes

Q₈×C₁₇

—

Q₈×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₇

C₄×D₄

yes

characteristic

C₂×C₄×C₁₇

C₄×D₄

yes

C₂×C₄×C₁₇

yes

C₂×C₄×C₁₇

yes

C₂×C₄×C₁₇

yes

C₂×C₄×C₁₇

C₂×Q₁₆

yes

—

C₂×C₄×C₁₇

#135

yes

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₈×C₁₇

—

C₈×C₁₇

#104

yes

—

#3622

—

#3622

—

#3170

D₁₇

yes

characteristic

100

#1994

—

101

C₄²×C₈

—

102

#1567

—

103

#1493

—

104

C₂²×C₁₇

—

105

C₂²×C₁₇

—

106

C₂²×C₁₇

#390

yes

characteristic

107

C₂²×C₁₇

#467

yes

—

108

C₄×C₁₇

—

109

C₄×C₁₇

—

110

C₄×C₁₇

—

111

C₄×C₁₇

—

112

C₄×C₁₇

C₂×#104

yes

—

113

C₄×C₁₇

C₄×Q₁₆

yes

—

114

C₄×C₁₇

#443

yes

—

115

C₄×C₁₇

#494

yes

characteristic

116

C₄×C₁₇

#495

yes

characteristic

117

Dic₁₇

—

118

#533

C₂×D₁₇

yes

—

119

#500

Dic₁₇

yes

characteristic, complemented

120

#494

Dic₁₇

yes

characteristic, complemented

121

#487

Dic₁₇

yes

complemented

122

#467

—

123

C₄×Q₁₆

—

124

#423

—

125

C₂×C₄×C₈

—

126

C₂×C₄×C₈

—

127

C₂×C₄×C₈

C₂×D₁₇

yes

characteristic

128

C₄³

—

129

#339

—

130

#335

—

131

Q₈⋊C₈

—

132

C₂×C₁₇

—

133

C₂×C₁₇

#1962

yes

characteristic

134

C₂×C₁₇

#1969

yes

characteristic

135

C₂×C₁₇

#1974

yes

characteristic

136

C₂×Q₁₆

—

137

C₂×M₁₆

—

138

C₂²×C₈

—

139

C₂²×C₈

C₂²⋊D₁₇

yes

—

140

C₄⋊Q₈

C₂×Dic₁₇

yes

—

141

C₄⋊Q₈

C₂×Dic₁₇

yes

—

142

#125

—

143

C₂²⋊Q₈

—

144

C₂²⋊Q₈

—

145

C₄×Q₈

—

146

C₄×Q₈

—

147

#117

—

148

C₂×C₄²

—

149

C₂×C₄²

—

150

C₂×C₄²

—

151

C₂×C₄²

C₂²×D₁₇

yes

characteristic

152

#107

—

153

C₄⋊C₈

—

154

C₄⋊C₈

—

155

#103

—

156

C₄×C₈

—

157

C₄×C₈

—

158

C₄×C₈

—

159

C₄×C₈

C₂×Dic₁₇

yes

characteristic

160

C₄×C₈

C₂×Dic₁₇

yes

characteristic

161

C₄×C₈

C₂²⋊D₁₇

yes

—

162

C₁₇

#9845

yes

characteristic, complemented, Sylow

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂²×C₄

—

166

C₂²×C₄

D₄×D₁₇

yes

characteristic

167

C₂²×C₄

#63254

yes

characteristic

168

C₂²×C₄

C₂×C₂²⋊D₁₇

yes

characteristic

169

Q₁₆

—

170

M₁₆

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

C₂²⋊Dic₁₇

yes

—

176

C₂×C₈

C₂²⋊Dic₁₇

yes

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₂²⋊C₄

—

184

C₄²

—

185

C₄²

—

186

C₄²

—

187

C₄²

—

188

C₄²

—

189

C₄²

D₄×D₁₇

yes

characteristic

190

C₄²

#63254

yes

characteristic

191

C₄²

C₂²×Dic₁₇

yes

characteristic

192

C₄²

C₂×C₂²⋊D₁₇

yes

characteristic

193

C₂³

#10587624

yes

characteristic

194

Q₈

—

195

Q₈

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

Q₁₆×D₁₇

yes

—

204

C₂×C₄

#10587605

yes

—

205

C₂×C₄

D₄×Dic₁₇

yes

characteristic

206

C₂×C₄

D₄×Dic₁₇

yes

characteristic

207

C₂×C₄

#10587622

yes

characteristic

208

C₂×C₄

#10587624

yes

characteristic

209

C₂×C₄

#10587626

yes

characteristic

210

C₂×C₄

C₂×C₂²⋊Dic₁₇

yes

characteristic

211

C₈

—

212

C₈

—

213

C₈

—

136

—

214

C₈

#10587508

yes

—

215

C₂²

—

216

C₂²

—

217

C₂²

#11762712

yes

characteristic

218

C₂²

#11763047

yes

—

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

—

223

C₄

—

224

C₄

C₂×#10587508

yes

—

225

C₄

Q₁₆×Dic₁₇

yes

—

226

C₄

#11762926

yes

—

227

C₄

#11763187

yes

characteristic

228

C₄

#11763194

yes

characteristic

229

C₂

—

230

C₂

#14529613

yes

characteristic

231

C₂

#14529646

yes

characteristic

232

C₂

#14529673

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10587626
commutator	C₄²×C₁₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₇
Fitting	C₁₇×#3170	C₂
socle	C₂²×C₁₇	#390
prime radical	C₂³×C₁₇	#121
cosocle	C₂×C₄²×C₁₇	C₂³
hypercenter	#3170	D₁₇
hypocenter	C₁₇	#9845
LCS	G ▷ C₄²×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3170

subgroup

G/H

center

C₂×C₄

#10587626

commutator

C₄²×C₁₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₇

Fitting

C₁₇×#3170

C₂

C₂²×C₁₇

C₂³×C₁₇

C₂×C₄²×C₁₇

C₂³

D₁₇

C₁₇

G ▷ C₄²×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3170

N	H ≅ G/N	type
14. C₁₇×#500	C₄	semidirect
15. C₁₇×#494	C₄	semidirect
16. C₁₇×#487	C₄	semidirect
71. C₄×Dic₁₇	Q₁₆	semidirect
119. #500	Dic₁₇	semidirect
120. #494	Dic₁₇	semidirect
121. #487	Dic₁₇	semidirect
162. C₁₇	#9845	semidirect

H ≅ G/N

type

14. C₁₇×#500

C₄

semidirect

15. C₁₇×#494

C₄

semidirect

16. C₁₇×#487

C₄

semidirect

71. C₄×Dic₁₇

Q₁₆

semidirect

119. #500

Dic₁₇

semidirect

120. #494

Dic₁₇

semidirect

121. #487

Dic₁₇

semidirect

162. C₁₇

#9845

semidirect

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

subgroup	index
#14529762	2
C₄×C₈×Dic₁₇	2
#14527543	2
#14527239	2
C₁₇×#3170	2
#9845	17

subgroup

index

C₄×C₈×Dic₁₇

C₁₇×#3170

Subgroups — #16934208

Conjugacy classes of subgroups

Complements

Maximal subgroups