Group #14540018 — subgroups

Subgroups — #14540018

Order 2176.

362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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	C₄⋊Q₈×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#11763346	C₂	1	1	yes	maximal, characteristic
3	#11763216	C₂	1	2	yes	maximal, complemented
4	#11763170	C₂	1	2	yes	maximal, complemented
5	#11763143	C₂	1	2	yes	maximal, complemented
6	#11763129	C₂	1	2	yes	maximal
7	#11763094	C₂	1	1	yes	maximal, characteristic, complemented
8	#11763090	C₂	1	1	yes	maximal, characteristic, complemented
9	#11763086	C₂	1	1	yes	maximal, characteristic, complemented
10	#11762865	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#475	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₈×D₁₇	—	2	1	no	—
13	C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
15	#10587633	C₂²	1	1	yes	characteristic
16	#10587632	C₂²	1	1	yes	characteristic
17	#10587630	—	2	1	no	—
18	#10587584	—	2	1	no	—
19	#10587581	C₂²	1	1	yes	characteristic
20	#10587580	—	2	1	no	—
21	C₄⋊C₄×D₁₇	—	2	1	no	—
22	C₄⋊C₄×D₁₇	C₂²	1	2	yes	—
23	#10587576	C₂²	1	1	yes	characteristic
24	#10587574	—	2	1	no	—
25	#10587574	C₂²	1	2	yes	—
26	C₄×D₆₈	—	2	1	no	—
27	C₄×D₆₈	C₂²	1	1	yes	characteristic
28	#10587558	—	2	1	no	—
29	C₄²×D₁₇	C₂²	1	1	yes	characteristic
30	#10587555	C₂²	1	1	yes	characteristic
31	C₁₇×#106	C₂²	1	2	yes	—
32	C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₁₇×#103	C₂²	1	2	yes	—
34	#10587506	C₂²	1	2	yes	—
35	#10587492	C₂²	1	2	yes	—
36	#10587491	C₂²	1	2	yes	—
37	#10587489	C₂²	1	2	yes	—
38	#10587486	C₂²	1	2	yes	—
39	#10587480	C₂²	1	2	yes	—
40	#10587479	C₂²	1	2	yes	—
41	#10587478	C₂²	1	2	yes	—
42	C₄⋊#3622	C₂²	1	1	yes	characteristic
43	C₂×Q₈×C₁₇	—	2	1	no	—
44	C₂×Q₈×C₁₇	C₂³	1	1	yes	characteristic
45	Q₈×D₁₇	—	4	4	no	—
46	C₂×D₆₈	—	2	1	no	—
47	C₂×D₆₈	C₂³	1	1	yes	characteristic
48	C₂×C₄×D₁₇	—	2	2	no	—
49	C₂×C₄×D₁₇	—	2	1	no	—
50	C₂×C₄×D₁₇	D₄	1	1	yes	characteristic
51	C₂×C₄×D₁₇	D₄	1	1	yes	characteristic
52	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
53	C₂×Dic₃₄	—	2	1	no	—
54	C₂×Dic₃₄	—	2	2	no	—
55	C₂×C₈×C₁₇	C₂³	1	2	yes	—
56	C₄⋊C₄×C₁₇	—	2	1	no	—
57	C₄⋊C₄×C₁₇	—	2	1	no	—
58	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
59	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
60	C₄²×C₁₇	—	2	1	no	—
61	C₄²×C₁₇	C₂³	1	1	yes	characteristic
62	#63227	—	2	1	no	—
63	#63227	—	2	1	no	—
64	#63227	—	2	1	no	—
65	#63227	—	2	1	no	—
66	#63227	—	2	1	no	—
67	C₄⋊Dic₁₇	—	2	1	no	—
68	C₄⋊Dic₁₇	—	2	1	no	—
69	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
70	C₄⋊Dic₁₇	C₂³	1	2	yes	—
71	#63225	—	2	1	no	—
72	#63225	—	2	1	no	—
73	#63225	—	2	2	no	—
74	#63225	—	2	2	no	—
75	C₄×Dic₁₇	D₄	1	1	yes	characteristic
76	C₄×Dic₁₇	D₄	1	1	yes	characteristic
77	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
78	C₂×#3622	C₂³	1	2	yes	—
79	C₂²×D₁₇	—	2	1	no	—
80	C₂²×D₁₇	C₂×D₄	1	1	yes	characteristic
81	Q₈×C₁₇	—	2	1	no	—
82	Q₈×C₁₇	—	2	1	no	—
83	Q₈×C₁₇	—	4	2	no	—
84	C₂×C₄×C₁₇	—	2	1	no	—
85	C₂×C₄×C₁₇	—	2	1	no	—
86	C₂×C₄×C₁₇	—	2	2	no	—
87	C₂×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
88	C₂×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
89	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
90	C₂×Dic₁₇	—	2	2	no	—
91	C₂×Dic₁₇	—	2	1	no	—
92	C₂×Dic₁₇	C₂×D₄	1	1	yes	characteristic
93	C₂×Dic₁₇	C₂×D₄	1	1	yes	characteristic
94	C₂×Dic₁₇	C₂×D₄	1	1	yes	characteristic
95	D₆₈	—	2	1	no	—
96	D₆₈	—	2	1	no	—
97	D₆₈	—	4	2	no	—
98	C₄×D₁₇	—	2	2	no	—
99	C₄×D₁₇	—	2	2	no	—
100	C₄×D₁₇	—	2	1	no	—
101	C₄×D₁₇	—	2	1	no	—
102	C₄×D₁₇	—	4	4	no	—
103	C₄×D₁₇	—	4	2	no	—
104	Dic₃₄	—	4	4	no	—
105	Dic₃₄	—	4	2	no	—
106	C₈×C₁₇	—	2	2	no	—
107	#3622	—	2	2	no	—
108	#3239	—	17	1	no	maximal, Sylow
109	C₂²×C₁₇	C₂²×D₄	1	1	yes	characteristic
110	C₂×D₁₇	—	2	1	no	—
111	C₂×D₁₇	—	2	1	no	—
112	C₂×D₁₇	—	4	1	no	—
113	C₂×D₁₇	—	4	1	no	—
114	C₂×D₁₇	—	4	1	no	—
115	C₂×D₁₇	#137	1	2	yes	—
116	C₄×C₁₇	—	2	1	no	—
117	C₄×C₁₇	—	4	1	no	—
118	C₄×C₁₇	—	4	2	no	—
119	C₄×C₁₇	—	4	1	no	—
120	C₄×C₁₇	AGL(1,ℤ/8)	1	2	yes	—
121	C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
122	C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
123	Dic₁₇	—	2	1	no	—
124	Dic₁₇	—	2	1	no	—
125	Dic₁₇	—	2	1	no	—
126	Dic₁₇	—	4	2	no	—
127	Dic₁₇	—	4	1	no	—
128	C₂×C₄⋊Q₈	—	17	1	no	—
129	#529	—	17	1	no	—
130	#501	—	17	2	no	—
131	#489	—	17	2	no	—
132	#484	—	17	2	no	—
133	#481	—	17	2	no	—
134	#475	—	17	1	no	—
135	#475	D₁₇	1	1	yes	characteristic, complemented
136	#474	—	17	1	no	—
137	#474	—	17	1	no	—
138	#432	—	17	1	no	—
139	C₂×C₁₇	#536	1	1	yes	characteristic
140	C₂×C₁₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
141	C₂×C₁₇	C₂×#137	1	1	yes	characteristic
142	D₁₇	—	2	2	no	—
143	D₁₇	—	8	1	no	—
144	C₂²×Q₈	—	34	1	no	—
145	C₄⋊Q₈	—	17	2	no	—
146	C₄⋊Q₈	—	17	1	no	—
147	C₄⋊Q₈	—	34	1	no	—
148	C₄⋊Q₈	—	34	1	no	—
149	C₄⋊Q₈	C₂×D₁₇	1	1	yes	characteristic
150	#126	—	34	1	no	—
151	#125	—	17	1	no	—
152	#124	—	17	1	no	—
153	#123	—	34	1	no	—
154	C₂²⋊Q₈	—	17	1	no	—
155	#121	—	17	1	no	—
156	C₄×Q₈	C₂×D₁₇	1	1	yes	characteristic
157	C₄×D₄	—	17	1	no	—
158	C₄×D₄	—	34	1	no	—
159	#117	—	34	1	no	—
160	C₂×C₄⋊C₄	—	17	2	no	—
161	C₂×C₄⋊C₄	—	34	1	no	—
162	C₂×C₄²	—	17	1	no	—
163	#107	—	17	2	no	—
164	#107	—	17	2	no	—
165	#106	—	17	2	no	—
166	#106	C₂×D₁₇	1	2	yes	—
167	C₄⋊C₈	—	17	1	no	—
168	C₄⋊C₈	C₂×D₁₇	1	1	yes	characteristic
169	#103	—	17	2	no	—
170	#103	C₂×D₁₇	1	2	yes	—
171	#102	—	17	2	no	—
172	#102	—	17	2	no	—
173	C₂²⋊C₈	—	17	2	no	—
174	#97	—	17	2	no	—
175	C₁₇	#3239	1	1	yes	characteristic, complemented, Sylow
176	C₂×Q₈	—	2	1	no	—
177	C₂×Q₈	—	34	2	no	—
178	C₂×Q₈	—	34	1	no	—
179	C₂×Q₈	—	68	4	no	—
180	C₂×Q₈	C₂²×D₁₇	1	1	yes	characteristic
181	C₂×D₄	—	17	1	no	—
182	C₂×D₄	—	34	1	no	—
183	C₂²×C₄	—	17	1	no	—
184	C₂²×C₄	—	17	1	no	—
185	C₂²×C₄	—	17	1	no	—
186	C₂²×C₄	—	34	2	no	—
187	C₂²×C₄	—	34	1	no	—
188	C₂×C₈	—	17	2	no	—
189	C₂×C₈	C₂²×D₁₇	1	2	yes	—
190	C₄⋊C₄	—	2	1	no	—
191	C₄⋊C₄	—	2	1	no	—
192	C₄⋊C₄	—	17	2	no	—
193	C₄⋊C₄	—	17	1	no	—
194	C₄⋊C₄	—	34	2	no	—
195	C₄⋊C₄	—	34	2	no	—
196	C₄⋊C₄	—	34	1	no	—
197	C₄⋊C₄	—	34	1	no	—
198	C₄⋊C₄	—	34	1	no	—
199	C₄⋊C₄	—	34	1	no	—
200	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
201	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
202	C₂²⋊C₄	—	34	1	no	—
203	C₂²⋊C₄	—	34	1	no	—
204	C₂²⋊C₄	—	34	1	no	—
205	C₂²⋊C₄	—	34	1	no	—
206	C₂²⋊C₄	—	34	1	no	—
207	C₄²	—	2	1	no	—
208	C₄²	—	17	1	no	—
209	C₄²	—	17	1	no	—
210	C₄²	—	17	1	no	—
211	C₄²	C₂²×D₁₇	1	1	yes	characteristic
212	C₂³	—	17	1	no	—
213	C₂³	—	34	1	no	—
214	Q₈	—	2	1	no	—
215	Q₈	—	2	1	no	—
216	Q₈	—	4	2	no	—
217	Q₈	—	68	4	no	—
218	Q₈	—	68	2	no	—
219	D₄	—	34	1	no	—
220	D₄	—	34	1	no	—
221	D₄	—	68	2	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	1	no	—
224	C₂×C₄	—	2	2	no	—
225	C₂×C₄	—	17	1	no	—
226	C₂×C₄	—	17	1	no	—
227	C₂×C₄	—	17	1	no	—
228	C₂×C₄	—	34	2	no	—
229	C₂×C₄	—	34	1	no	—
230	C₂×C₄	—	34	1	no	—
231	C₂×C₄	—	34	2	no	—
232	C₂×C₄	—	34	1	no	—
233	C₂×C₄	—	34	2	no	—
234	C₂×C₄	—	68	4	no	—
235	C₂×C₄	—	68	2	no	—
236	C₂×C₄	D₄×D₁₇	1	1	yes	characteristic
237	C₂×C₄	D₄×D₁₇	1	1	yes	characteristic
238	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
239	C₈	—	2	2	no	—
240	C₈	—	34	2	no	—
241	C₂²	—	17	2	no	—
242	C₂²	—	34	1	no	—
243	C₂²	—	34	1	no	—
244	C₂²	—	68	1	no	—
245	C₂²	—	68	1	no	—
246	C₂²	—	68	1	no	—
247	C₂²	C₂×D₄×D₁₇	1	1	yes	characteristic
248	C₄	—	2	1	no	—
249	C₄	—	4	2	no	—
250	C₄	—	4	1	no	—
251	C₄	—	4	1	no	—
252	C₄	—	34	1	no	—
253	C₄	—	34	1	no	—
254	C₄	—	34	1	no	—
255	C₄	—	68	2	no	—
256	C₄	—	68	1	no	—
257	C₄	#10587600	1	2	yes	—
258	C₄	#10587694	1	1	yes	characteristic
259	C₄	#10587697	1	1	yes	characteristic
260	C₂	—	34	2	no	—
261	C₂	—	136	1	no	—
262	C₂	#11763382	1	1	yes	characteristic
263	C₂	C₂×#10587600	1	1	yes	characteristic
264	C₂	#137×D₁₇	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄⋊Q₈×D₁₇

C₂

yes

maximal, characteristic, complemented

#11763346

C₂

yes

maximal, characteristic

#11763216

C₂

yes

maximal, complemented

#11763170

C₂

yes

maximal, complemented

#11763143

C₂

yes

maximal, complemented

#11763129

C₂

yes

maximal

#11763094

C₂

yes

maximal, characteristic, complemented

#11763090

C₂

yes

maximal, characteristic, complemented

#11763086

C₂

yes

maximal, characteristic, complemented

#11762865

C₂

yes

maximal, characteristic, complemented

C₁₇×#475

C₂

yes

maximal, characteristic, complemented

C₂×Q₈×D₁₇

—

C₁₇×C₄⋊Q₈

C₂²

yes

characteristic

C₄×Q₈×C₁₇

C₂²

yes

characteristic

#10587633

C₂²

yes

characteristic

#10587632

C₂²

yes

—

—

C₂²

yes

characteristic

#10587580

—

C₄⋊C₄×D₁₇

—

C₄⋊C₄×D₁₇

C₂²

yes

—

#10587576

C₂²

yes

characteristic

#10587574

—

#10587574

C₂²

yes

—

C₄×D₆₈

—

C₄×D₆₈

C₂²

yes

characteristic

#10587558

—

C₄²×D₁₇

C₂²

yes

characteristic

#10587555

C₂²

yes

characteristic

C₁₇×#106

C₂²

yes

—

C₁₇×C₄⋊C₈

C₂²

yes

characteristic

C₁₇×#103

C₂²

yes

—

#10587506

C₂²

yes

—

#10587492

C₂²

yes

—

#10587491

C₂²

yes

—

#10587489

C₂²

yes

—

#10587486

C₂²

yes

—

#10587480

C₂²

yes

—

#10587479

C₂²

yes

—

#10587478

C₂²

yes

—

C₄⋊#3622

C₂²

yes

characteristic

C₂×Q₈×C₁₇

—

C₂×Q₈×C₁₇

C₂³

yes

characteristic

Q₈×D₁₇

—

C₂×D₆₈

—

C₂×D₆₈

C₂³

yes

characteristic

C₂×C₄×D₁₇

—

C₂×C₄×D₁₇

—

C₂×C₄×D₁₇

D₄

yes

characteristic

C₂×C₄×D₁₇

D₄

yes

characteristic

C₂×C₄×D₁₇

C₂³

yes

characteristic

C₂×Dic₃₄

—

C₂×Dic₃₄

—

C₂×C₈×C₁₇

C₂³

yes

—

C₄⋊C₄×C₁₇

—

C₄⋊C₄×C₁₇

—

C₄⋊C₄×C₁₇

C₂³

yes

—

C₄⋊C₄×C₁₇

C₂³

yes

characteristic

C₄²×C₁₇

—

C₄²×C₁₇

C₂³

yes

—

—

—

—

—

C₄⋊Dic₁₇

—

C₄⋊Dic₁₇

—

C₄⋊Dic₁₇

C₂³

yes

characteristic

C₄⋊Dic₁₇

C₂³

yes

—

—

—

—

—

C₄×Dic₁₇

D₄

yes

characteristic

C₄×Dic₁₇

D₄

yes

characteristic

C₄×Dic₁₇

C₂³

yes

characteristic

C₂×#3622

C₂³

yes

—

C₂²×D₁₇

—

C₂²×D₁₇

C₂×D₄

yes

characteristic

Q₈×C₁₇

—

Q₈×C₁₇

—

Q₈×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₂×D₄

yes

characteristic

C₂×C₄×C₁₇

C₂×D₄

yes

characteristic

C₂×C₄×C₁₇

C₂⁴

yes

characteristic

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

C₂×D₄

yes

characteristic

C₂×Dic₁₇

C₂×D₄

yes

characteristic

C₂×Dic₁₇

C₂×D₄

yes

characteristic

D₆₈

—

D₆₈

—

D₆₈

—

C₄×D₁₇

—

C₄×D₁₇

—

100

C₄×D₁₇

—

101

C₄×D₁₇

—

102

C₄×D₁₇

—

103

C₄×D₁₇

—

104

Dic₃₄

—

105

Dic₃₄

—

106

C₈×C₁₇

—

107

#3622

—

108

#3239

—

maximal, Sylow

109

C₂²×C₁₇

C₂²×D₄

yes

characteristic

110

C₂×D₁₇

—

111

C₂×D₁₇

—

112

C₂×D₁₇

—

113

C₂×D₁₇

—

114

C₂×D₁₇

—

115

C₂×D₁₇

#137

yes

—

116

C₄×C₁₇

—

117

C₄×C₁₇

—

118

C₄×C₁₇

—

119

C₄×C₁₇

—

120

C₄×C₁₇

AGL(1,ℤ/8)

yes

—

121

C₄×C₁₇

2₋¹⁺⁴

yes

characteristic

122

C₄×C₁₇

2₋¹⁺⁴

yes

characteristic

123

Dic₁₇

—

124

Dic₁₇

—

125

Dic₁₇

—

126

Dic₁₇

—

127

Dic₁₇

—

128

C₂×C₄⋊Q₈

—

129

#529

—

130

#501

—

131

#489

—

132

#484

—

133

#481

—

134

#475

—

135

#475

D₁₇

yes

characteristic, complemented

136

#474

—

137

#474

—

138

#432

—

139

C₂×C₁₇

#536

yes

characteristic

140

C₂×C₁₇

C₂×AGL(1,ℤ/8)

yes

characteristic

141

C₂×C₁₇

C₂×#137

yes

characteristic

142

D₁₇

—

143

D₁₇

—

144

C₂²×Q₈

—

145

C₄⋊Q₈

—

146

C₄⋊Q₈

—

147

C₄⋊Q₈

—

148

C₄⋊Q₈

—

149

C₄⋊Q₈

C₂×D₁₇

yes

characteristic

150

#126

—

151

#125

—

152

#124

—

153

#123

—

154

C₂²⋊Q₈

—

155

#121

—

156

C₄×Q₈

C₂×D₁₇

yes

characteristic

157

C₄×D₄

—

158

C₄×D₄

—

159

#117

—

160

C₂×C₄⋊C₄

—

161

C₂×C₄⋊C₄

—

162

C₂×C₄²

—

163

#107

—

164

#107

—

165

#106

—

166

#106

C₂×D₁₇

yes

—

167

C₄⋊C₈

—

168

C₄⋊C₈

C₂×D₁₇

yes

characteristic

169

#103

—

170

#103

C₂×D₁₇

yes

—

171

#102

—

172

#102

—

173

C₂²⋊C₈

—

174

#97

—

175

C₁₇

#3239

yes

characteristic, complemented, Sylow

176

C₂×Q₈

—

177

C₂×Q₈

—

178

C₂×Q₈

—

179

C₂×Q₈

—

180

C₂×Q₈

C₂²×D₁₇

yes

characteristic

181

C₂×D₄

—

182

C₂×D₄

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

—

188

C₂×C₈

—

189

C₂×C₈

C₂²×D₁₇

yes

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₄⋊C₄

C₂²×D₁₇

yes

—

201

C₄⋊C₄

C₂²×D₁₇

yes

characteristic

202

C₂²⋊C₄

—

203

C₂²⋊C₄

—

204

C₂²⋊C₄

—

205

C₂²⋊C₄

—

206

C₂²⋊C₄

—

207

C₄²

—

208

C₄²

—

209

C₄²

—

210

C₄²

—

211

C₄²

C₂²×D₁₇

yes

characteristic

212

C₂³

—

213

C₂³

—

214

Q₈

—

215

Q₈

—

216

Q₈

—

217

Q₈

—

218

Q₈

—

219

D₄

—

220

D₄

—

221

D₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

D₄×D₁₇

yes

characteristic

237

C₂×C₄

D₄×D₁₇

yes

characteristic

238

C₂×C₄

C₂³×D₁₇

yes

characteristic

239

C₈

—

240

C₈

—

241

C₂²

—

242

C₂²

—

243

C₂²

—

244

C₂²

—

245

C₂²

—

246

C₂²

—

247

C₂²

C₂×D₄×D₁₇

yes

characteristic

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

—

252

C₄

—

253

C₄

—

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

#10587600

yes

—

258

C₄

#10587694

yes

characteristic

259

C₄

#10587697

yes

characteristic

260

C₂

—

261

C₂

—

136

—

262

C₂

#11763382

yes

characteristic

263

C₂

C₂×#10587600

yes

characteristic

264

C₂

#137×D₁₇

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₇
commutator, cosocle	C₂×C₄×C₁₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₇
Fitting	C₁₇×#475	C₂
socle	C₂²×C₁₇	C₂²×D₄
prime radical	#10587581	C₂²
hypercenter	#475	D₁₇
hypocenter	C₁₇	#3239
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #475

subgroup

G/H

center

C₂²

C₂×D₄×D₁₇

commutator, cosocle

C₂×C₄×C₁₇

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₇

Fitting

C₁₇×#475

C₂

socle

C₂²×C₁₇

C₂²×D₄

C₂²

D₁₇

C₁₇

G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #475

N	H ≅ G/N	type
1. C₄⋊Q₈×D₁₇	C₂	semidirect
3. #11763216	C₂	semidirect
4. #11763170	C₂	semidirect
5. #11763143	C₂	semidirect
7. #11763094	C₂	semidirect
8. #11763090	C₂	semidirect
9. #11763086	C₂	semidirect
10. #11762865	C₂	semidirect
11. C₁₇×#475	C₂	semidirect
135. #475	D₁₇	semidirect
175. C₁₇	#3239	semidirect

H ≅ G/N

type

1. C₄⋊Q₈×D₁₇

C₂

semidirect

3. #11763216

C₂

semidirect

4. #11763170

C₂

semidirect

5. #11763143

C₂

semidirect

7. #11763094

C₂

semidirect

8. #11763090

C₂

semidirect

9. #11763086

C₂

semidirect

10. #11762865

C₂

semidirect

11. C₁₇×#475

C₂

semidirect

135. #475

D₁₇

semidirect

175. C₁₇

#3239

semidirect

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

subgroup	index
C₄⋊Q₈×D₁₇	2
#11763346	2
#11763216	2
#11763170	2
#11763143	2
#11763129	2
#11763094	2
#11763090	2
#11763086	2
#11762865	2
C₁₇×#475	2
#3239	17

subgroup

index

C₄⋊Q₈×D₁₇

C₁₇×#475

Subgroups — #14540018

Conjugacy classes of subgroups

Complements

Maximal subgroups