Group #16927585 — subgroups

Subgroups — #16927585

Order 4352.

414 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 119 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	#14537497	C₂	1	1	yes	maximal, characteristic
2	C₂×#11762560	C₂	1	1	yes	maximal, characteristic, complemented
3	#14527462	C₂	1	2	yes	maximal
4	#14526658	C₂	1	2	yes	maximal, complemented
5	C₁₇×#1837	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10587587	—	2	1	no	—
7	#11763359	C₂²	1	1	yes	characteristic
8	#11762888	—	2	1	no	—
9	#11762888	C₄	1	2	yes	—
10	C₈×D₆₈	—	2	1	no	—
11	C₈×D₆₈	C₄	1	2	yes	—
12	#11762833	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊#3622	C₂²	1	2	yes	—
14	#11762775	—	2	1	no	—
15	#11762560	—	2	1	no	—
16	#11762560	—	2	1	no	—
17	#11762556	—	2	2	no	—
18	#11762552	—	2	2	no	—
19	C₁₇×#423	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
21	C₁₇×#341	—	2	1	no	—
22	C₁₇×#341	—	2	1	no	—
23	C₂×#63252	—	2	1	no	—
24	C₂×M₁₆×C₁₇	—	2	2	no	—
25	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
28	#10587616	—	2	1	no	—
29	#10587616	Q₈	1	2	yes	—
30	C₂×#63223	—	2	1	no	—
31	C₂²×#3622	—	2	2	no	—
32	#10587587	—	4	4	no	—
33	C₂×#63218	—	2	2	no	—
34	C₂×C₈×D₁₇	—	2	2	no	—
35	#10587561	—	2	1	no	—
36	#10587560	D₄	1	1	yes	characteristic
37	C₄×D₆₈	—	2	1	no	—
38	C₄×D₆₈	C₂×C₄	1	2	yes	—
39	#10587555	D₄	1	1	yes	characteristic
40	C₁₇×C₄⋊C₈	—	2	2	no	—
41	C₁₇×C₄⋊C₈	—	2	2	no	—
42	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₁₇	D₄	1	1	yes	characteristic
45	C₄×C₈×C₁₇	D₄	1	1	yes	characteristic
46	#10587491	—	2	2	no	—
47	#10587491	—	2	2	no	—
48	C₄⋊#3622	—	2	1	no	—
49	C₄⋊#3622	—	2	2	no	—
50	C₄⋊#3622	—	2	2	no	—
51	C₄⋊#3622	C₂×C₄	1	2	yes	—
52	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
54	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
55	C₂×C₂²⋊D₁₇	—	2	2	no	—
56	#63252	—	4	2	no	—
57	#63252	—	4	2	no	—
58	C₂×D₆₈	—	2	1	no	—
59	C₂×D₆₈	—	2	1	no	—
60	C₂×D₆₈	C₄⋊C₄	1	2	yes	—
61	C₂×C₄×D₁₇	—	2	2	no	—
62	C₂×Dic₃₄	—	2	1	no	—
63	M₁₆×C₁₇	—	4	2	no	—
64	M₁₆×C₁₇	—	4	2	no	—
65	C₂×C₈×C₁₇	—	2	2	no	—
66	C₂×C₈×C₁₇	—	2	2	no	—
67	C₂×C₈×C₁₇	—	4	2	no	—
68	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
72	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
73	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
75	C₄²×C₁₇	#41	1	1	yes	characteristic
76	#63227	—	2	2	no	—
77	#63227	—	2	2	no	—
78	C₄⋊Dic₁₇	—	2	1	no	—
79	C₄⋊Dic₁₇	C₄⋊C₄	1	2	yes	—
80	#63223	—	4	2	no	—
81	C₂×#3622	—	2	2	no	—
82	C₂×#3622	—	4	2	no	—
83	C₂×#3622	—	8	2	no	—
84	#63218	—	4	4	no	—
85	C₈×D₁₇	—	4	4	no	—
86	#8686	—	17	1	no	maximal, Sylow
87	C₂³×C₁₇	C₂²⋊Q₈	1	1	yes	characteristic
88	C₂²×D₁₇	—	2	2	no	—
89	C₂×C₄×C₁₇	—	2	2	no	—
90	C₂×C₄×C₁₇	—	4	1	no	—
91	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
93	C₂×C₄×C₁₇	#117	1	1	yes	characteristic
94	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
95	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
96	C₂×C₄×C₁₇	C₂²⋊Q₈	1	1	yes	characteristic
97	C₂×C₄×C₁₇	#135	1	2	yes	—
98	C₂×C₄×C₁₇	AGL(1,ℤ/8)	1	2	yes	—
99	C₂²⋊D₁₇	—	4	4	no	—
100	C₂×Dic₁₇	—	2	2	no	—
101	D₆₈	—	4	2	no	—
102	D₆₈	—	4	2	no	—
103	D₆₈	—	4	2	no	—
104	C₄×D₁₇	—	4	2	no	—
105	C₄×D₁₇	—	4	2	no	—
106	Dic₃₄	—	4	2	no	—
107	C₈×C₁₇	—	2	1	no	—
108	C₈×C₁₇	—	2	1	no	—
109	C₈×C₁₇	—	2	1	no	—
110	C₈×C₁₇	—	2	1	no	—
111	C₈×C₁₇	—	8	2	no	—
112	#3622	—	4	2	no	—
113	#3622	—	8	2	no	—
114	#2931	—	17	1	no	—
115	#1837	D₁₇	1	1	yes	characteristic, complemented
116	C₂×#334	—	17	1	no	—
117	#1547	—	17	2	no	—
118	#1292	—	17	2	no	—
119	C₂²×C₁₇	—	2	1	no	—
120	C₂²×C₁₇	—	2	1	no	—
121	C₂²×C₁₇	#380	1	1	yes	characteristic
122	C₂²×C₁₇	#478	1	2	yes	—
123	C₂×D₁₇	—	4	2	no	—
124	C₂×D₁₇	—	4	2	no	—
125	C₂×D₁₇	—	4	2	no	—
126	C₄×C₁₇	—	2	1	no	—
127	C₄×C₁₇	—	2	1	no	—
128	C₄×C₁₇	—	2	1	no	—
129	C₄×C₁₇	#416	1	1	yes	characteristic
130	C₄×C₁₇	#418	1	1	yes	characteristic
131	C₄×C₁₇	#463	1	2	yes	—
132	C₄×C₁₇	#471	1	2	yes	—
133	Dic₁₇	—	4	2	no	—
134	C₂×#131	—	34	1	no	—
135	#532	—	17	1	no	—
136	#436	—	17	2	no	—
137	#436	—	34	1	no	—
138	C₈×D₄	—	17	2	no	—
139	C₈×D₄	—	34	1	no	—
140	#423	—	17	1	no	—
141	#423	C₂×D₁₇	1	2	yes	—
142	C₂×C₄⋊C₈	—	17	2	no	—
143	#408	—	34	1	no	—
144	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
145	#341	—	2	1	no	—
146	#341	—	2	1	no	—
147	#334	—	34	1	no	—
148	#334	—	34	1	no	—
149	#332	—	34	2	no	—
150	#331	—	34	2	no	—
151	C₂×C₁₇	—	2	2	no	—
152	C₂×C₁₇	#1804	1	1	yes	characteristic
153	C₂×C₁₇	#1813	1	1	yes	characteristic
154	C₂×C₁₇	#1815	1	1	yes	characteristic
155	D₁₇	—	8	2	no	—
156	C₂×#41	—	34	1	no	—
157	#131	—	68	4	no	—
158	C₂×M₁₆	—	2	2	no	—
159	C₂×M₁₆	—	34	1	no	—
160	C₂×M₁₆	—	34	2	no	—
161	C₂²×C₈	—	34	2	no	—
162	C₂²×C₈	—	34	2	no	—
163	C₂²×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
164	C₂²×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
165	C₄⋊Q₈	—	17	1	no	—
166	#127	—	17	1	no	—
167	#124	—	34	1	no	—
168	#121	—	17	2	no	—
169	#121	—	34	1	no	—
170	C₄×D₄	—	17	2	no	—
171	C₄×D₄	—	34	1	no	—
172	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
173	C₄⋊C₈	—	2	2	no	—
174	C₄⋊C₈	—	2	2	no	—
175	C₄⋊C₈	—	17	2	no	—
176	C₄⋊C₈	—	34	1	no	—
177	C₄⋊C₈	—	34	2	no	—
178	C₄⋊C₈	—	34	2	no	—
179	C₂²⋊C₈	—	34	2	no	—
180	C₂²⋊C₈	—	34	2	no	—
181	C₄×C₈	C₄×D₁₇	1	1	yes	characteristic
182	C₄×C₈	C₄×D₁₇	1	1	yes	characteristic
183	C₄×C₈	D₆₈	1	1	yes	characteristic
184	C₄×C₈	D₆₈	1	1	yes	characteristic
185	C₁₇	#8686	1	1	yes	characteristic, complemented, Sylow
186	#41	—	68	2	no	—
187	#41	—	68	2	no	—
188	C₂×Q₈	—	34	1	no	—
189	C₂×D₄	—	17	2	no	—
190	C₂×D₄	—	34	2	no	—
191	C₂×D₄	—	34	1	no	—
192	C₂×D₄	—	34	1	no	—
193	C₂²×C₄	—	34	2	no	—
194	C₂²×C₄	Q₈×D₁₇	1	1	yes	characteristic
195	C₂²×C₄	#63256	1	1	yes	characteristic
196	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
197	M₁₆	—	4	2	no	—
198	M₁₆	—	4	2	no	—
199	M₁₆	—	68	4	no	—
200	M₁₆	—	68	2	no	—
201	C₂×C₈	—	2	2	no	—
202	C₂×C₈	—	2	2	no	—
203	C₂×C₈	—	4	2	no	—
204	C₂×C₈	—	34	2	no	—
205	C₂×C₈	—	68	4	no	—
206	C₂×C₈	—	68	2	no	—
207	C₂×C₈	—	136	2	no	—
208	C₂×C₈	#63227	1	1	yes	characteristic
209	C₂×C₈	#63227	1	1	yes	characteristic
210	C₂×C₈	#63227	1	1	yes	characteristic
211	C₂×C₈	#63227	1	1	yes	characteristic
212	C₄⋊C₄	—	17	2	no	—
213	C₄⋊C₄	—	34	1	no	—
214	C₂²⋊C₄	—	34	2	no	—
215	C₂²⋊C₄	—	34	2	no	—
216	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
217	C₄²	C₂×D₆₈	1	1	yes	characteristic
218	C₄²	D₄×D₁₇	1	1	yes	characteristic
219	C₄²	#63254	1	1	yes	characteristic
220	C₂³	—	34	2	no	—
221	C₂³	#10587632	1	1	yes	characteristic
222	Q₈	—	68	2	no	—
223	D₄	—	68	2	no	—
224	D₄	—	68	4	no	—
225	D₄	—	68	2	no	—
226	D₄	—	68	2	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	4	1	no	—
229	C₂×C₄	—	34	2	no	—
230	C₂×C₄	—	68	2	no	—
231	C₂×C₄	—	68	2	no	—
232	C₂×C₄	C₄⋊C₄×D₁₇	1	1	yes	characteristic
233	C₂×C₄	#10587578	1	1	yes	characteristic
234	C₂×C₄	#10587581	1	1	yes	characteristic
235	C₂×C₄	#10587583	1	1	yes	characteristic
236	C₂×C₄	C₂×#63227	1	1	yes	characteristic
237	C₂×C₄	#10587624	1	1	yes	characteristic
238	C₂×C₄	#10587635	1	2	yes	—
239	C₂×C₄	#10587636	1	2	yes	—
240	C₈	—	2	1	no	—
241	C₈	—	2	1	no	—
242	C₈	—	2	1	no	—
243	C₈	—	2	1	no	—
244	C₈	—	8	2	no	—
245	C₈	—	68	2	no	—
246	C₈	—	136	2	no	—
247	C₂²	—	2	1	no	—
248	C₂²	—	2	1	no	—
249	C₂²	—	68	2	no	—
250	C₂²	—	68	2	no	—
251	C₂²	—	68	2	no	—
252	C₂²	#11762666	1	1	yes	characteristic
253	C₂²	#11763106	1	2	yes	—
254	C₄	—	2	1	no	—
255	C₄	—	2	1	no	—
256	C₄	—	2	1	no	—
257	C₄	—	68	2	no	—
258	C₄	#11762803	1	1	yes	characteristic
259	C₄	#11762813	1	1	yes	characteristic
260	C₄	#11763021	1	2	yes	—
261	C₄	#11763073	1	2	yes	—
262	C₂	—	2	2	no	—
263	C₂	—	136	2	no	—
264	C₂	#14528791	1	1	yes	characteristic
265	C₂	#14528831	1	1	yes	characteristic
266	C₂	#14528840	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14537497

C₂

yes

maximal, characteristic

C₂×#11762560

C₂

yes

maximal, characteristic, complemented

#14527462

C₂

yes

maximal

#14526658

C₂

yes

maximal, complemented

C₁₇×#1837

C₂

yes

maximal, characteristic, complemented

C₂×#10587587

—

#11763359

C₂²

yes

characteristic

#11762888

—

#11762888

C₄

yes

—

C₈×D₆₈

—

C₈×D₆₈

C₄

yes

—

#11762833

C₂²

yes

characteristic

C₂×C₄⋊#3622

C₂²

yes

—

—

—

—

—

—

C₁₇×#423

C₂²

yes

—

C₂×C₄×C₈×C₁₇

C₂²

yes

characteristic

C₁₇×#341

—

C₁₇×#341

—

C₂×#63252

—

C₂×M₁₆×C₁₇

—

C₂²×C₈×C₁₇

D₄

yes

characteristic

C₂²×C₈×C₁₇

D₄

yes

characteristic

C₂×C₄²×C₁₇

C₂³

yes

characteristic

#10587616

—

#10587616

Q₈

yes

—

C₂×#63223

—

C₂²×#3622

—

#10587587

—

C₂×#63218

—

C₂×C₈×D₁₇

—

#10587561

—

#10587560

D₄

yes

characteristic

C₄×D₆₈

—

C₄×D₆₈

C₂×C₄

yes

—

#10587555

D₄

yes

characteristic

C₁₇×C₄⋊C₈

—

C₁₇×C₄⋊C₈

—

C₄×C₈×C₁₇

C₂×C₄

yes

characteristic

C₄×C₈×C₁₇

C₂×C₄

yes

characteristic

C₄×C₈×C₁₇

D₄

yes

characteristic

C₄×C₈×C₁₇

D₄

yes

—

—

—

—

—

C₂×C₄

yes

—

C₂²×C₄×C₁₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₇

C₂×Q₈

yes

characteristic

C₂²×C₄×C₁₇

#41

yes

characteristic

C₂×C₂²⋊D₁₇

—

#63252

—

#63252

—

C₂×D₆₈

—

C₂×D₆₈

—

C₂×D₆₈

C₄⋊C₄

yes

—

C₂×C₄×D₁₇

—

C₂×Dic₃₄

—

M₁₆×C₁₇

—

M₁₆×C₁₇

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₇

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₇

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₇

C₂²⋊C₄

yes

characteristic

C₄²×C₁₇

C₂²×C₄

yes

characteristic

C₄²×C₁₇

C₂×D₄

yes

characteristic

C₄²×C₁₇

C₂×D₄

yes

C₄²×C₁₇

yes

—

—

C₄⋊Dic₁₇

—

C₄⋊Dic₁₇

C₄⋊C₄

yes

—

—

—

—

—

—

C₈×D₁₇

—

#8686

—

maximal, Sylow

C₂³×C₁₇

C₂²⋊Q₈

yes

characteristic

C₂²×D₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₇

C₂×C₄⋊C₄

yes

C₂×C₄×C₁₇

yes

C₂×C₄×C₁₇

yes

C₂×C₄×C₁₇

yes

C₂×C₄×C₁₇

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₇

#135

yes

—

C₂×C₄×C₁₇

AGL(1,ℤ/8)

yes

—

C₂²⋊D₁₇

—

100

C₂×Dic₁₇

—

101

D₆₈

—

102

D₆₈

—

103

D₆₈

—

104

C₄×D₁₇

—

105

C₄×D₁₇

—

106

Dic₃₄

—

107

C₈×C₁₇

—

108

C₈×C₁₇

—

109

C₈×C₁₇

—

110

C₈×C₁₇

—

111

C₈×C₁₇

—

112

#3622

—

113

#3622

—

114

#2931

—

115

#1837

D₁₇

yes

characteristic, complemented

116

C₂×#334

—

117

#1547

—

118

#1292

—

119

C₂²×C₁₇

—

120

C₂²×C₁₇

—

121

C₂²×C₁₇

#380

yes

characteristic

122

C₂²×C₁₇

#478

yes

—

123

C₂×D₁₇

—

124

C₂×D₁₇

—

125

C₂×D₁₇

—

126

C₄×C₁₇

—

127

C₄×C₁₇

—

128

C₄×C₁₇

—

129

C₄×C₁₇

#416

yes

characteristic

130

C₄×C₁₇

#418

yes

characteristic

131

C₄×C₁₇

#463

yes

—

132

C₄×C₁₇

#471

yes

—

133

Dic₁₇

—

134

C₂×#131

—

135

#532

—

136

#436

—

137

#436

—

138

C₈×D₄

—

139

C₈×D₄

—

140

#423

—

141

#423

C₂×D₁₇

yes

—

142

C₂×C₄⋊C₈

—

143

#408

—

144

C₂×C₄×C₈

C₂×D₁₇

yes

characteristic

145

#341

—

146

#341

—

147

#334

—

148

#334

—

149

#332

—

150

#331

—

151

C₂×C₁₇

—

152

C₂×C₁₇

#1804

yes

characteristic

153

C₂×C₁₇

#1813

yes

characteristic

154

C₂×C₁₇

#1815

yes

characteristic

155

D₁₇

—

156

C₂×#41

—

157

#131

—

158

C₂×M₁₆

—

159

C₂×M₁₆

—

160

C₂×M₁₆

—

161

C₂²×C₈

—

162

C₂²×C₈

—

163

C₂²×C₈

C₂²⋊D₁₇

yes

characteristic

164

C₂²×C₈

C₂²⋊D₁₇

yes

characteristic

165

C₄⋊Q₈

—

166

#127

—

167

#124

—

168

#121

—

169

#121

—

170

C₄×D₄

—

171

C₄×D₄

—

172

C₂×C₄²

C₂²×D₁₇

yes

characteristic

173

C₄⋊C₈

—

174

C₄⋊C₈

—

175

C₄⋊C₈

—

176

C₄⋊C₈

—

177

C₄⋊C₈

—

178

C₄⋊C₈

—

179

C₂²⋊C₈

—

180

C₂²⋊C₈

—

181

C₄×C₈

C₄×D₁₇

yes

characteristic

182

C₄×C₈

C₄×D₁₇

yes

characteristic

183

C₄×C₈

D₆₈

yes

characteristic

184

C₄×C₈

D₆₈

yes

characteristic

185

C₁₇

#8686

yes

characteristic, complemented, Sylow

186

#41

—

187

#41

—

188

C₂×Q₈

—

189

C₂×D₄

—

190

C₂×D₄

—

191

C₂×D₄

—

192

C₂×D₄

—

193

C₂²×C₄

—

194

C₂²×C₄

Q₈×D₁₇

yes

characteristic

195

C₂²×C₄

#63256

yes

characteristic

196

C₂²×C₄

C₂×C₂²⋊D₁₇

yes

characteristic

197

M₁₆

—

198

M₁₆

—

199

M₁₆

—

200

M₁₆

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₂×C₈

—

136

—

208

C₂×C₈

#63227

yes

characteristic

209

C₂×C₈

#63227

yes

characteristic

210

C₂×C₈

#63227

yes

characteristic

211

C₂×C₈

#63227

yes

characteristic

212

C₄⋊C₄

—

213

C₄⋊C₄

—

214

C₂²⋊C₄

—

215

C₂²⋊C₄

—

216

C₄²

C₂×C₄×D₁₇

yes

characteristic

217

C₄²

C₂×D₆₈

yes

characteristic

218

C₄²

D₄×D₁₇

yes

characteristic

219

C₄²

#63254

yes

characteristic

220

C₂³

—

221

C₂³

#10587632

yes

characteristic

222

Q₈

—

223

D₄

—

224

D₄

—

225

D₄

—

226

D₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

C₄⋊C₄×D₁₇

yes

characteristic

233

C₂×C₄

#10587578

yes

characteristic

234

C₂×C₄

#10587581

yes

characteristic

235

C₂×C₄

#10587583

yes

characteristic

236

C₂×C₄

C₂×#63227

yes

characteristic

237

C₂×C₄

#10587624

yes

characteristic

238

C₂×C₄

#10587635

yes

—

239

C₂×C₄

#10587636

yes

—

240

C₈

—

241

C₈

—

242

C₈

—

243

C₈

—

244

C₈

—

245

C₈

—

246

C₈

—

136

—

247

C₂²

—

248

C₂²

—

249

C₂²

—

250

C₂²

—

251

C₂²

—

252

C₂²

#11762666

yes

characteristic

253

C₂²

#11763106

yes

—

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

—

258

C₄

#11762803

yes

characteristic

259

C₄

#11762813

yes

characteristic

260

C₄

#11763021

yes

—

261

C₄

#11763073

yes

—

262

C₂

—

263

C₂

—

136

—

264

C₂

#14528791

yes

characteristic

265

C₂

#14528831

yes

characteristic

266

C₂

#14528840

yes

characteristic

	subgroup	G/H
center	C₂²	#11762666
commutator	C₄²×C₁₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₇
Fitting	C₁₇×#1837	C₂
socle	C₂²×C₁₇	#380
prime radical	#11763359	C₂²
cosocle	C₂×C₄²×C₁₇	C₂³
hypercenter	#1837	D₁₇
hypocenter	C₁₇	#8686
LCS	G ▷ C₄²×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1837

subgroup

G/H

center

C₂²

#11762666

commutator

C₄²×C₁₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₇

Fitting

C₁₇×#1837

C₂

C₂²×C₁₇

C₂²

C₂×C₄²×C₁₇

C₂³

D₁₇

C₁₇

G ▷ C₄²×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1837

N	H ≅ G/N	type
2. C₂×#11762560	C₂	semidirect
4. #14526658	C₂	semidirect
5. C₁₇×#1837	C₂	semidirect
115. #1837	D₁₇	semidirect
185. C₁₇	#8686	semidirect

H ≅ G/N

type

2. C₂×#11762560

C₂

semidirect

4. #14526658

C₂

semidirect

5. C₁₇×#1837

C₂

semidirect

115. #1837

D₁₇

semidirect

185. C₁₇

#8686

semidirect

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

subgroup	index
#14537497	2
C₂×#11762560	2
#14527462	2
#14526658	2
C₁₇×#1837	2
#8686	17

subgroup

index

C₁₇×#1837

Subgroups — #16927585

Conjugacy classes of subgroups

Complements

Maximal subgroups