Group #16927599 — subgroups

Subgroups — #16927599

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	#14528922	C₂	1	1	yes	maximal, characteristic, complemented
3	#14527459	C₂	1	2	yes	maximal
4	#14526659	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₇×#335	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	2	yes	—
13	#11762833	C₂²	1	1	yes	characteristic
14	#11762775	—	2	1	no	—
15	#11762574	—	2	1	no	—
16	#11762574	—	2	1	no	—
17	#11762554	—	2	2	no	—
18	#11762552	—	2	2	no	—
19	C₂×C₁₇×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
21	C₁₇×#335	—	2	1	no	—
22	C₁₇×#335	—	2	1	no	—
23	C₂×#63252	—	2	1	no	—
24	C₂²×C₈×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	C₂×#63223	—	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	C₂×C₈×C₁₇	—	2	2	no	—
64	C₂×C₈×C₁₇	—	2	2	no	—
65	C₂×C₈×C₁₇	—	4	2	no	—
66	C₂×C₈×C₁₇	—	8	2	no	—
67	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
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	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
72	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
73	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₁₇	#41	1	1	yes	characteristic
75	#63227	—	2	2	no	—
76	#63227	—	2	2	no	—
77	C₄⋊Dic₁₇	—	2	1	no	—
78	C₄⋊Dic₁₇	C₄⋊C₄	1	2	yes	—
79	#63223	—	4	2	no	—
80	#63223	—	4	2	no	—
81	#63223	—	4	2	no	—
82	C₂×#3622	—	2	2	no	—
83	C₂×#3622	—	4	2	no	—
84	#63218	—	4	4	no	—
85	C₈×D₁₇	—	4	4	no	—
86	#8688	—	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	1	no	—
90	C₂×C₄×C₁₇	—	2	1	no	—
91	C₂×C₄×C₁₇	—	4	1	no	—
92	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
94	C₂×C₄×C₁₇	#117	1	1	yes	characteristic
95	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
96	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
97	C₂×C₄×C₁₇	C₂²⋊Q₈	1	1	yes	characteristic
98	C₂×C₄×C₁₇	#135	1	2	yes	—
99	C₂×C₄×C₁₇	AGL(1,ℤ/8)	1	2	yes	—
100	C₂²⋊D₁₇	—	4	4	no	—
101	C₂×Dic₁₇	—	2	2	no	—
102	D₆₈	—	4	2	no	—
103	D₆₈	—	4	2	no	—
104	D₆₈	—	4	1	no	—
105	D₆₈	—	4	1	no	—
106	C₄×D₁₇	—	4	2	no	—
107	C₄×D₁₇	—	4	2	no	—
108	Dic₃₄	—	4	2	no	—
109	C₈×C₁₇	—	2	1	no	—
110	C₈×C₁₇	—	2	1	no	—
111	C₈×C₁₇	—	2	1	no	—
112	C₈×C₁₇	—	2	1	no	—
113	C₈×C₁₇	—	8	2	no	—
114	#3622	—	4	2	no	—
115	#3622	—	8	2	no	—
116	#2931	—	17	1	no	—
117	#1837	—	17	1	no	—
118	C₂×#335	D₁₇	1	1	yes	characteristic, complemented
119	#1547	—	17	2	no	—
120	#1292	—	17	2	no	—
121	C₂²×C₁₇	—	2	1	no	—
122	C₂²×C₁₇	—	2	1	no	—
123	C₂²×C₁₇	#380	1	1	yes	characteristic
124	C₂²×C₁₇	#478	1	2	yes	—
125	C₂×D₁₇	—	4	2	no	—
126	C₂×D₁₇	—	4	2	no	—
127	C₂×D₁₇	—	4	2	no	—
128	C₄×C₁₇	—	2	1	no	—
129	C₄×C₁₇	—	2	1	no	—
130	C₄×C₁₇	—	2	1	no	—
131	C₄×C₁₇	#416	1	1	yes	characteristic
132	C₄×C₁₇	#418	1	1	yes	characteristic
133	C₄×C₁₇	#463	1	2	yes	—
134	C₄×C₁₇	#472	1	1	yes	characteristic
135	C₄×C₁₇	#473	1	1	yes	characteristic
136	Dic₁₇	—	4	2	no	—
137	C₂×#131	—	34	1	no	—
138	#532	—	17	1	no	—
139	#436	—	17	2	no	—
140	#436	—	34	1	no	—
141	C₈×D₄	—	17	2	no	—
142	C₈×D₄	—	34	1	no	—
143	#423	—	17	1	no	—
144	#423	—	17	2	no	—
145	C₂×C₄⋊C₈	C₂×D₁₇	1	2	yes	—
146	#408	—	34	1	no	—
147	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
148	#341	—	34	1	no	—
149	#341	—	34	1	no	—
150	#335	—	2	1	no	—
151	#335	—	2	1	no	—
152	#332	—	34	2	no	—
153	#331	—	34	2	no	—
154	C₂×C₁₇	—	2	2	no	—
155	C₂×C₁₇	#1804	1	1	yes	characteristic
156	C₂×C₁₇	#1813	1	1	yes	characteristic
157	C₂×C₁₇	#1816	1	1	yes	characteristic
158	D₁₇	—	8	2	no	—
159	C₂×#41	—	34	1	no	—
160	#131	—	68	4	no	—
161	C₂×M₁₆	—	34	1	no	—
162	C₂×M₁₆	—	34	2	no	—
163	C₂×M₁₆	—	34	2	no	—
164	C₂²×C₈	—	2	2	no	—
165	C₂²×C₈	—	34	2	no	—
166	C₂²×C₈	D₆₈	1	1	yes	characteristic
167	C₂²×C₈	D₆₈	1	1	yes	characteristic
168	C₄⋊Q₈	—	17	1	no	—
169	#127	—	17	1	no	—
170	#124	—	34	1	no	—
171	#121	—	17	2	no	—
172	#121	—	34	1	no	—
173	C₄×D₄	—	17	2	no	—
174	C₄×D₄	—	34	1	no	—
175	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
176	C₄⋊C₈	—	2	2	no	—
177	C₄⋊C₈	—	2	2	no	—
178	C₄⋊C₈	—	17	2	no	—
179	C₄⋊C₈	—	34	2	no	—
180	C₄⋊C₈	—	34	2	no	—
181	C₄⋊C₈	—	34	1	no	—
182	C₂²⋊C₈	—	34	2	no	—
183	C₂²⋊C₈	—	34	2	no	—
184	C₄×C₈	C₄×D₁₇	1	1	yes	characteristic
185	C₄×C₈	C₄×D₁₇	1	1	yes	characteristic
186	C₄×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
187	C₄×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
188	C₁₇	#8688	1	1	yes	characteristic, complemented, Sylow
189	#41	—	68	2	no	—
190	#41	—	68	2	no	—
191	C₂×Q₈	—	34	1	no	—
192	C₂×D₄	—	17	2	no	—
193	C₂×D₄	—	34	2	no	—
194	C₂×D₄	—	34	1	no	—
195	C₂×D₄	—	34	1	no	—
196	C₂²×C₄	—	34	2	no	—
197	C₂²×C₄	C₂×D₆₈	1	1	yes	characteristic
198	C₂²×C₄	#63254	1	1	yes	characteristic
199	C₂²×C₄	Q₈×D₁₇	1	1	yes	characteristic
200	M₁₆	—	68	4	no	—
201	M₁₆	—	68	2	no	—
202	M₁₆	—	68	2	no	—
203	M₁₆	—	68	2	no	—
204	C₂×C₈	—	2	2	no	—
205	C₂×C₈	—	2	2	no	—
206	C₂×C₈	—	4	2	no	—
207	C₂×C₈	—	8	2	no	—
208	C₂×C₈	—	34	2	no	—
209	C₂×C₈	—	68	4	no	—
210	C₂×C₈	—	68	2	no	—
211	C₂×C₈	#63227	1	1	yes	characteristic
212	C₂×C₈	#63227	1	1	yes	characteristic
213	C₂×C₈	#63227	1	1	yes	characteristic
214	C₂×C₈	#63227	1	1	yes	characteristic
215	C₄⋊C₄	—	17	2	no	—
216	C₄⋊C₄	—	34	1	no	—
217	C₂²⋊C₄	—	34	2	no	—
218	C₂²⋊C₄	—	34	2	no	—
219	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
220	C₄²	D₄×D₁₇	1	1	yes	characteristic
221	C₄²	#63256	1	1	yes	characteristic
222	C₄²	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
223	C₂³	—	34	2	no	—
224	C₂³	#10587583	1	1	yes	characteristic
225	Q₈	—	68	2	no	—
226	D₄	—	68	2	no	—
227	D₄	—	68	4	no	—
228	D₄	—	68	2	no	—
229	D₄	—	68	1	no	—
230	D₄	—	68	1	no	—
231	C₂×C₄	—	2	1	no	—
232	C₂×C₄	—	2	1	no	—
233	C₂×C₄	—	4	1	no	—
234	C₂×C₄	—	34	2	no	—
235	C₂×C₄	—	68	2	no	—
236	C₂×C₄	—	68	2	no	—
237	C₂×C₄	C₄⋊C₄×D₁₇	1	1	yes	characteristic
238	C₂×C₄	#10587578	1	1	yes	characteristic
239	C₂×C₄	#10587581	1	1	yes	characteristic
240	C₂×C₄	#10587590	1	2	yes	—
241	C₂×C₄	#10587594	1	2	yes	—
242	C₂×C₄	C₂×#63227	1	1	yes	characteristic
243	C₂×C₄	#10587624	1	1	yes	characteristic
244	C₂×C₄	#10587632	1	1	yes	characteristic
245	C₈	—	2	1	no	—
246	C₈	—	2	1	no	—
247	C₈	—	2	1	no	—
248	C₈	—	2	1	no	—
249	C₈	—	8	2	no	—
250	C₈	—	68	2	no	—
251	C₈	—	136	2	no	—
252	C₂²	—	2	1	no	—
253	C₂²	—	2	1	no	—
254	C₂²	—	68	2	no	—
255	C₂²	—	68	2	no	—
256	C₂²	—	68	2	no	—
257	C₂²	#11762666	1	1	yes	characteristic
258	C₂²	#11763110	1	2	yes	—
259	C₄	—	2	1	no	—
260	C₄	—	2	1	no	—
261	C₄	—	2	1	no	—
262	C₄	—	68	2	no	—
263	C₄	#11762806	1	1	yes	characteristic
264	C₄	#11762815	1	1	yes	characteristic
265	C₄	#11763025	1	2	yes	—
266	C₄	#11763076	1	1	yes	characteristic
267	C₄	#11763081	1	1	yes	characteristic
268	C₂	—	2	2	no	—
269	C₂	—	136	2	no	—
270	C₂	#14528795	1	1	yes	characteristic
271	C₂	#14528831	1	1	yes	characteristic
272	C₂	#14528849	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14537497

C₂

yes

maximal, characteristic

#14528922

C₂

yes

maximal, characteristic, complemented

#14527459

C₂

yes

maximal

#14526659

C₂

yes

maximal, complemented

C₂×C₁₇×#335

C₂

yes

maximal, characteristic, complemented

C₂×#10587587

—

#11763359

C₂²

yes

characteristic

#11762888

—

#11762888

C₄

yes

—

C₈×D₆₈

—

C₈×D₆₈

C₄

yes

—

#11762833

C₂²

yes

—

#11762833

C₂²

yes

—

—

—

—

—

C₂×C₁₇×C₄⋊C₈

C₂²

yes

—

C₂×C₄×C₈×C₁₇

C₂²

yes

characteristic

C₁₇×#335

—

C₁₇×#335

—

C₂×#63252

—

C₂²×C₈×C₁₇

—

C₂²×C₈×C₁₇

D₄

yes

characteristic

C₂²×C₈×C₁₇

D₄

yes

characteristic

C₂×C₄²×C₁₇

C₂³

yes

characteristic

#10587616

—

#10587616

Q₈

yes

—

—

—

—

—

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

—

C₂×C₈×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

—

#8688

—

maximal, Sylow

C₂³×C₁₇

C₂²⋊Q₈

yes

characteristic

C₂²×D₁₇

—

C₂×C₄×C₁₇

—

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

—

100

C₂²⋊D₁₇

—

101

C₂×Dic₁₇

—

102

D₆₈

—

103

D₆₈

—

104

D₆₈

—

105

D₆₈

—

106

C₄×D₁₇

—

107

C₄×D₁₇

—

108

Dic₃₄

—

109

C₈×C₁₇

—

110

C₈×C₁₇

—

111

C₈×C₁₇

—

112

C₈×C₁₇

—

113

C₈×C₁₇

—

114

#3622

—

115

#3622

—

116

#2931

—

117

#1837

—

118

C₂×#335

D₁₇

yes

characteristic, complemented

119

#1547

—

120

#1292

—

121

C₂²×C₁₇

—

122

C₂²×C₁₇

—

123

C₂²×C₁₇

#380

yes

characteristic

124

C₂²×C₁₇

#478

yes

—

125

C₂×D₁₇

—

126

C₂×D₁₇

—

127

C₂×D₁₇

—

128

C₄×C₁₇

—

129

C₄×C₁₇

—

130

C₄×C₁₇

—

131

C₄×C₁₇

#416

yes

characteristic

132

C₄×C₁₇

#418

yes

characteristic

133

C₄×C₁₇

#463

yes

—

134

C₄×C₁₇

#472

yes

characteristic

135

C₄×C₁₇

#473

yes

characteristic

136

Dic₁₇

—

137

C₂×#131

—

138

#532

—

139

#436

—

140

#436

—

141

C₈×D₄

—

142

C₈×D₄

—

143

#423

—

144

#423

—

145

C₂×C₄⋊C₈

C₂×D₁₇

yes

—

146

#408

—

147

C₂×C₄×C₈

C₂×D₁₇

yes

characteristic

148

#341

—

149

#341

—

150

#335

—

151

#335

—

152

#332

—

153

#331

—

154

C₂×C₁₇

—

155

C₂×C₁₇

#1804

yes

characteristic

156

C₂×C₁₇

#1813

yes

characteristic

157

C₂×C₁₇

#1816

yes

characteristic

158

D₁₇

—

159

C₂×#41

—

160

#131

—

161

C₂×M₁₆

—

162

C₂×M₁₆

—

163

C₂×M₁₆

—

164

C₂²×C₈

—

165

C₂²×C₈

—

166

C₂²×C₈

D₆₈

yes

characteristic

167

C₂²×C₈

D₆₈

yes

characteristic

168

C₄⋊Q₈

—

169

#127

—

170

#124

—

171

#121

—

172

#121

—

173

C₄×D₄

—

174

C₄×D₄

—

175

C₂×C₄²

C₂²×D₁₇

yes

characteristic

176

C₄⋊C₈

—

177

C₄⋊C₈

—

178

C₄⋊C₈

—

179

C₄⋊C₈

—

180

C₄⋊C₈

—

181

C₄⋊C₈

—

182

C₂²⋊C₈

—

183

C₂²⋊C₈

—

184

C₄×C₈

C₄×D₁₇

yes

characteristic

185

C₄×C₈

C₄×D₁₇

yes

characteristic

186

C₄×C₈

C₂²⋊D₁₇

yes

characteristic

187

C₄×C₈

C₂²⋊D₁₇

yes

characteristic

188

C₁₇

#8688

yes

characteristic, complemented, Sylow

189

#41

—

190

#41

—

191

C₂×Q₈

—

192

C₂×D₄

—

193

C₂×D₄

—

194

C₂×D₄

—

195

C₂×D₄

—

196

C₂²×C₄

—

197

C₂²×C₄

C₂×D₆₈

yes

characteristic

198

C₂²×C₄

#63254

yes

characteristic

199

C₂²×C₄

Q₈×D₁₇

yes

characteristic

200

M₁₆

—

201

M₁₆

—

202

M₁₆

—

203

M₁₆

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₂×C₈

—

208

C₂×C₈

—

209

C₂×C₈

—

210

C₂×C₈

—

211

C₂×C₈

#63227

yes

characteristic

212

C₂×C₈

#63227

yes

characteristic

213

C₂×C₈

#63227

yes

characteristic

214

C₂×C₈

#63227

yes

characteristic

215

C₄⋊C₄

—

216

C₄⋊C₄

—

217

C₂²⋊C₄

—

218

C₂²⋊C₄

—

219

C₄²

C₂×C₄×D₁₇

yes

characteristic

220

C₄²

D₄×D₁₇

yes

characteristic

221

C₄²

#63256

yes

characteristic

222

C₄²

C₂×C₂²⋊D₁₇

yes

characteristic

223

C₂³

—

224

C₂³

#10587583

yes

characteristic

225

Q₈

—

226

D₄

—

227

D₄

—

228

D₄

—

229

D₄

—

230

D₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

C₄⋊C₄×D₁₇

yes

characteristic

238

C₂×C₄

#10587578

yes

characteristic

239

C₂×C₄

#10587581

yes

characteristic

240

C₂×C₄

#10587590

yes

—

241

C₂×C₄

#10587594

yes

—

242

C₂×C₄

C₂×#63227

yes

characteristic

243

C₂×C₄

#10587624

yes

characteristic

244

C₂×C₄

#10587632

yes

characteristic

245

C₈

—

246

C₈

—

247

C₈

—

248

C₈

—

249

C₈

—

250

C₈

—

251

C₈

—

136

—

252

C₂²

—

253

C₂²

—

254

C₂²

—

255

C₂²

—

256

C₂²

—

257

C₂²

#11762666

yes

characteristic

258

C₂²

#11763110

yes

—

259

C₄

—

260

C₄

—

261

C₄

—

262

C₄

—

263

C₄

#11762806

yes

characteristic

264

C₄

#11762815

yes

characteristic

265

C₄

#11763025

yes

—

266

C₄

#11763076

yes

characteristic

267

C₄

#11763081

yes

characteristic

268

C₂

—

269

C₂

—

136

—

270

C₂

#14528795

yes

characteristic

271

C₂

#14528831

yes

characteristic

272

C₂

#14528849

yes

characteristic

	subgroup	G/H
center	C₂²	#11762666
commutator	C₄²×C₁₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₇
Fitting	C₂×C₁₇×#335	C₂
socle	C₂²×C₁₇	#380
prime radical	#11763359	C₂²
cosocle	C₂×C₄²×C₁₇	C₂³
hypercenter	C₂×#335	D₁₇
hypocenter	C₁₇	#8688
LCS	G ▷ C₄²×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#335

subgroup

G/H

center

C₂²

#11762666

commutator

C₄²×C₁₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₇

Fitting

C₂×C₁₇×#335

C₂

C₂²×C₁₇

C₂²

C₂×C₄²×C₁₇

C₂³

D₁₇

C₁₇

G ▷ C₄²×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#335

N	H ≅ G/N	type
2. #14528922	C₂	semidirect
4. #14526659	C₂	semidirect
5. C₂×C₁₇×#335	C₂	semidirect
118. C₂×#335	D₁₇	semidirect
188. C₁₇	#8688	semidirect

H ≅ G/N

type

2. #14528922

C₂

semidirect

4. #14526659

C₂

semidirect

5. C₂×C₁₇×#335

C₂

semidirect

118. C₂×#335

D₁₇

semidirect

188. C₁₇

#8688

semidirect

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

subgroup	index
#14537497	2
#14528922	2
#14527459	2
#14526659	2
C₂×C₁₇×#335	2
#8688	17

subgroup

index

C₂×C₁₇×#335

Subgroups — #16927599

Conjugacy classes of subgroups

Complements

Maximal subgroups