Group #16933488 — subgroups

Subgroups — #16933488

Order 4352.

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

normal subgroups only

This group has 422 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	#14539370	C₂	1	1	yes	maximal, characteristic
2	#14529727	C₂	1	2	yes	maximal
3	#14527282	C₂	1	2	yes	maximal
4	#14527073	C₂	1	1	yes	maximal, characteristic
5	C₄×C₁₇×#106	C₂	1	1	yes	maximal, characteristic
6	#11763366	C₂²	1	2	yes	—
7	#11763214	C₄	1	1	yes	characteristic, complemented
8	#11763189	C₄	1	1	yes	characteristic, complemented
9	#11763160	C₄	1	2	yes	complemented
10	#11763050	—	2	1	no	—
11	#11763050	—	2	1	no	—
12	C₄×Dic₆₈	—	2	1	no	—
13	C₄×Dic₆₈	—	2	1	no	—
14	#11762862	C₂²	1	1	yes	characteristic
15	C₄×#63223	C₂²	1	1	yes	characteristic
16	#11762569	—	2	4	no	—
17	#11762545	—	2	4	no	—
18	#11762531	—	2	1	no	—
19	#11762530	—	2	1	no	—
20	C₂×C₁₇×#106	—	2	1	no	—
21	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
22	C₄×C₄⋊C₄×C₁₇	C₂²	1	2	yes	—
23	C₁₇×#340	—	2	1	no	—
24	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
26	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
27	C₂×C₄²×C₁₇	—	2	2	no	—
28	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
29	#10587612	—	2	2	no	—
30	#10587610	—	2	2	no	—
31	#10587610	—	2	2	no	—
32	C₂×#63223	D₄	1	2	yes	—
33	C₂×Dic₆₈	—	2	1	no	—
34	C₂×Dic₆₈	—	2	1	no	—
35	#10587556	—	2	2	no	—
36	#10587555	C₂×C₄	1	2	yes	—
37	#10587555	C₂×C₄	1	2	yes	—
38	C₄×Dic₃₄	—	2	2	no	—
39	C₄×Dic₃₄	—	2	2	no	—
40	C₁₇×#106	—	2	4	no	—
41	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
42	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₁₇	D₄	1	1	yes	characteristic
44	C₄×C₈×C₁₇	D₄	1	1	yes	characteristic
45	C₁₇×#95	—	2	2	no	—
46	C₂²⋊#3622	D₄	1	2	yes	—
47	#10587489	—	2	1	no	—
48	#10587489	—	2	1	no	—
49	#10587487	—	2	2	no	—
50	#10587487	—	2	2	no	—
51	C₄⋊#3622	—	2	1	no	—
52	#10587474	—	2	1	no	—
53	C₄×#3622	—	2	1	no	—
54	C₄×#3622	—	2	1	no	—
55	C₂²×C₄×C₁₇	—	4	2	no	—
56	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
59	C₂×Dic₃₄	—	2	2	no	—
60	C₂×Dic₃₄	—	2	2	no	—
61	C₂×C₈×C₁₇	—	2	2	no	—
62	C₂×C₈×C₁₇	—	4	1	no	—
63	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
64	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
65	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
66	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
67	C₄⋊C₄×C₁₇	—	2	4	no	—
68	C₄⋊C₄×C₁₇	—	4	2	no	—
69	C₄²×C₁₇	—	4	4	no	—
70	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
71	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
72	C₄²×C₁₇	#41	1	1	yes	characteristic
73	C₄²×C₁₇	#41	1	1	yes	characteristic
74	C₂²⋊Dic₁₇	—	4	2	no	—
75	C₄⋊Dic₁₇	—	2	2	no	—
76	C₄⋊Dic₁₇	—	2	2	no	—
77	C₄⋊Dic₁₇	—	2	2	no	—
78	C₄⋊Dic₁₇	—	2	2	no	—
79	#63225	—	4	2	no	—
80	#63225	—	4	2	no	—
81	C₄×Dic₁₇	—	4	2	no	—
82	#63223	—	2	4	no	—
83	C₂×#3622	—	2	2	no	—
84	C₂×#3622	—	2	2	no	—
85	Dic₆₈	—	4	2	no	—
86	Dic₆₈	—	4	2	no	—
87	#9720	—	17	1	no	maximal, Sylow
88	C₂³×C₁₇	#127	1	1	yes	characteristic
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	—	4	4	no	—
93	C₂×C₄×C₁₇	—	8	2	no	—
94	C₂×C₄×C₁₇	—	8	2	no	—
95	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
97	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
98	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
99	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
100	C₂×C₄×C₁₇	#124	1	1	yes	characteristic
101	C₂×C₄×C₁₇	#137	1	4	yes	—
102	C₂×Dic₁₇	—	4	2	no	—
103	C₂×Dic₁₇	—	4	2	no	—
104	Dic₃₄	—	4	2	no	—
105	Dic₃₄	—	4	2	no	—
106	Dic₃₄	—	8	2	no	—
107	C₈×C₁₇	—	2	1	no	—
108	C₈×C₁₇	—	2	1	no	—
109	C₈×C₁₇	—	2	1	no	—
110	C₈×C₁₇	#104	1	2	yes	—
111	#3622	—	4	2	no	—
112	#3622	—	4	2	no	—
113	#3170	—	17	1	no	—
114	#1986	—	17	2	no	—
115	C₄×#106	D₁₇	1	1	yes	characteristic
116	#1503	—	17	2	no	—
117	#1451	—	17	1	no	—
118	C₂²×C₁₇	—	2	1	no	—
119	C₂²×C₁₇	—	2	1	no	—
120	C₂²×C₁₇	#390	1	1	yes	characteristic
121	C₂²×C₁₇	#497	1	2	yes	—
122	C₄×C₁₇	—	2	1	no	—
123	C₄×C₁₇	—	2	1	no	—
124	C₄×C₁₇	—	2	1	no	—
125	C₄×C₁₇	—	8	4	no	—
126	C₄×C₁₇	C₂×#104	1	1	yes	characteristic
127	C₄×C₁₇	#421	1	1	yes	characteristic
128	C₄×C₁₇	#441	1	2	yes	—
129	C₄×C₁₇	#470	1	2	yes	—
130	Dic₁₇	—	8	2	no	—
131	Dic₁₇	—	8	2	no	—
132	#533	—	17	2	no	—
133	#500	—	17	1	no	—
134	#494	—	17	1	no	—
135	#487	—	17	2	no	—
136	#467	—	34	1	no	—
137	#467	—	34	1	no	—
138	C₄×Q₁₆	—	34	1	no	—
139	C₄×Q₁₆	—	34	1	no	—
140	#431	—	17	1	no	—
141	C₂×#106	—	2	1	no	—
142	C₄×M₁₆	—	17	1	no	—
143	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
144	C₄×C₄⋊C₄	C₂×D₁₇	1	2	yes	—
145	#340	—	2	1	no	—
146	#339	—	34	4	no	—
147	#328	—	34	4	no	—
148	#322	—	34	1	no	—
149	#322	—	34	1	no	—
150	C₂×C₁₇	—	2	2	no	—
151	C₂×C₁₇	#1971	1	1	yes	characteristic
152	C₂×C₁₇	#1976	1	1	yes	characteristic
153	C₂×C₁₇	#1980	1	1	yes	characteristic
154	C₂×Q₁₆	—	34	1	no	—
155	C₂×Q₁₆	—	34	1	no	—
156	C₂×M₁₆	—	17	2	no	—
157	C₂²×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
158	C₂²×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
159	C₄⋊Q₈	—	17	2	no	—
160	C₄⋊Q₈	—	17	2	no	—
161	#125	—	34	2	no	—
162	C₂²⋊Q₈	—	34	2	no	—
163	C₂²⋊Q₈	—	34	2	no	—
164	C₄×Q₈	—	34	2	no	—
165	C₄×Q₈	—	34	2	no	—
166	#117	—	34	2	no	—
167	C₂×C₄⋊C₄	—	2	2	no	—
168	C₂×C₄²	—	2	2	no	—
169	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
170	#107	—	34	1	no	—
171	#107	—	34	1	no	—
172	#106	—	2	4	no	—
173	C₄⋊C₈	—	34	1	no	—
174	#103	—	34	2	no	—
175	#103	—	34	2	no	—
176	C₂²⋊C₈	—	17	2	no	—
177	#97	—	34	1	no	—
178	C₄×C₈	—	34	1	no	—
179	C₄×C₈	—	34	1	no	—
180	C₄×C₈	C₄×D₁₇	1	1	yes	characteristic
181	C₄×C₈	C₄×D₁₇	1	1	yes	characteristic
182	C₄×C₈	D₆₈	1	1	yes	characteristic
183	C₄×C₈	D₆₈	1	1	yes	characteristic
184	#95	—	2	2	no	—
185	C₁₇	#9720	1	1	yes	characteristic, complemented, Sylow
186	C₂×Q₈	—	34	2	no	—
187	C₂×Q₈	—	34	2	no	—
188	C₂²×C₄	—	4	2	no	—
189	C₂²×C₄	D₄×D₁₇	1	1	yes	characteristic
190	C₂²×C₄	D₄×D₁₇	1	1	yes	characteristic
191	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
192	Q₁₆	—	68	2	no	—
193	Q₁₆	—	68	2	no	—
194	M₁₆	—	34	4	no	—
195	C₂×C₈	—	2	2	no	—
196	C₂×C₈	—	4	1	no	—
197	C₂×C₈	—	34	2	no	—
198	C₂×C₈	—	34	2	no	—
199	C₂×C₈	#63227	1	1	yes	characteristic
200	C₂×C₈	#63227	1	1	yes	characteristic
201	C₂×C₈	#63227	1	1	yes	characteristic
202	C₂×C₈	#63227	1	1	yes	characteristic
203	C₄⋊C₄	—	2	4	no	—
204	C₄⋊C₄	—	4	2	no	—
205	C₄⋊C₄	—	34	2	no	—
206	C₄⋊C₄	—	34	2	no	—
207	C₄⋊C₄	—	34	2	no	—
208	C₄⋊C₄	—	34	2	no	—
209	C₄⋊C₄	—	68	2	no	—
210	C₄⋊C₄	—	68	2	no	—
211	C₂²⋊C₄	—	68	2	no	—
212	C₄²	—	4	4	no	—
213	C₄²	—	68	2	no	—
214	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
215	C₄²	C₂×D₆₈	1	1	yes	characteristic
216	C₄²	#63256	1	1	yes	characteristic
217	C₄²	#63256	1	1	yes	characteristic
218	C₂³	#10587626	1	1	yes	characteristic
219	Q₈	—	68	2	no	—
220	Q₈	—	68	2	no	—
221	Q₈	—	136	2	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	1	no	—
224	C₂×C₄	—	4	1	no	—
225	C₂×C₄	—	4	4	no	—
226	C₂×C₄	—	8	2	no	—
227	C₂×C₄	—	8	2	no	—
228	C₂×C₄	—	68	2	no	—
229	C₂×C₄	—	68	2	no	—
230	C₂×C₄	#10587579	1	1	yes	characteristic
231	C₂×C₄	#10587579	1	1	yes	characteristic
232	C₂×C₄	#10587581	1	1	yes	characteristic
233	C₂×C₄	#10587581	1	1	yes	characteristic
234	C₂×C₄	#10587601	1	4	yes	—
235	C₂×C₄	C₂×#63227	1	1	yes	characteristic
236	C₂×C₄	#10587633	1	1	yes	characteristic
237	C₈	—	2	1	no	—
238	C₈	—	2	1	no	—
239	C₈	—	2	1	no	—
240	C₈	—	68	2	no	—
241	C₈	—	68	2	no	—
242	C₈	#10587476	1	2	yes	—
243	C₂²	—	2	1	no	—
244	C₂²	—	2	1	no	—
245	C₂²	#11762710	1	1	yes	characteristic
246	C₂²	#11763200	1	2	yes	—
247	C₄	—	2	1	no	—
248	C₄	—	2	1	no	—
249	C₄	—	2	1	no	—
250	C₄	—	8	4	no	—
251	C₄	—	136	2	no	—
252	C₄	—	136	2	no	—
253	C₄	C₂×#10587476	1	1	yes	characteristic
254	C₄	#11762827	1	1	yes	characteristic
255	C₄	#11762915	1	2	yes	—
256	C₄	#11763068	1	2	yes	—
257	C₂	—	2	2	no	—
258	C₂	#14529653	1	1	yes	characteristic
259	C₂	#14529680	1	1	yes	characteristic
260	C₂	#14529702	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14539370

C₂

yes

maximal, characteristic

#14529727

C₂

yes

maximal

#14527282

C₂

yes

maximal

#14527073

C₂

yes

maximal, characteristic

C₄×C₁₇×#106

C₂

yes

maximal, characteristic

#11763366

C₂²

yes

—

#11763214

C₄

yes

characteristic, complemented

#11763189

C₄

yes

characteristic, complemented

#11763160

C₄

yes

complemented

#11763050

—

#11763050

—

C₄×Dic₆₈

—

C₄×Dic₆₈

—

#11762862

C₂²

yes

characteristic

C₄×#63223

C₂²

yes

—

—

—

—

C₂×C₁₇×#106

—

C₂×C₄×C₈×C₁₇

C₂²

yes

characteristic

C₄×C₄⋊C₄×C₁₇

C₂²

yes

—

C₁₇×#340

—

C₂²×C₈×C₁₇

D₄

yes

characteristic

C₂²×C₈×C₁₇

D₄

yes

characteristic

C₂×C₄⋊C₄×C₁₇

—

C₂×C₄²×C₁₇

—

C₂×C₄²×C₁₇

C₂³

yes

—

—

—

D₄

yes

—

C₂×Dic₆₈

—

C₂×Dic₆₈

—

#10587556

—

#10587555

C₂×C₄

yes

—

#10587555

C₂×C₄

yes

—

C₄×Dic₃₄

—

C₄×Dic₃₄

—

C₁₇×#106

—

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

characteristic

C₁₇×#95

—

C₂²⋊#3622

D₄

yes

—

—

—

—

—

—

—

—

—

C₂²×C₄×C₁₇

—

C₂²×C₄×C₁₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₇

C₂×D₄

yes

characteristic

C₂×Dic₃₄

—

C₂×Dic₃₄

—

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

C₄⋊C₄×C₁₇

—

C₄⋊C₄×C₁₇

—

C₄²×C₁₇

—

C₄²×C₁₇

C₂²×C₄

yes

characteristic

C₄²×C₁₇

C₂×D₄

yes

C₄²×C₁₇

yes

C₄²×C₁₇

yes

C₂²⋊Dic₁₇

—

C₄⋊Dic₁₇

—

C₄⋊Dic₁₇

—

C₄⋊Dic₁₇

—

C₄⋊Dic₁₇

—

#63225

—

#63225

—

C₄×Dic₁₇

—

#63223

—

C₂×#3622

—

C₂×#3622

—

Dic₆₈

—

Dic₆₈

—

—

C₂³×C₁₇

yes

C₂×C₄×C₁₇

—

C₂×C₄×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

100

C₂×C₄×C₁₇

#124

yes

characteristic

101

C₂×C₄×C₁₇

#137

yes

—

102

C₂×Dic₁₇

—

103

C₂×Dic₁₇

—

104

Dic₃₄

—

105

Dic₃₄

—

106

Dic₃₄

—

107

C₈×C₁₇

—

108

C₈×C₁₇

—

109

C₈×C₁₇

—

110

C₈×C₁₇

#104

yes

—

111

#3622

—

112

#3622

—

113

#3170

—

114

#1986

—

115

C₄×#106

D₁₇

yes

characteristic

116

#1503

—

117

#1451

—

118

C₂²×C₁₇

—

119

C₂²×C₁₇

—

120

C₂²×C₁₇

#390

yes

characteristic

121

C₂²×C₁₇

#497

yes

—

122

C₄×C₁₇

—

123

C₄×C₁₇

—

124

C₄×C₁₇

—

125

C₄×C₁₇

—

126

C₄×C₁₇

C₂×#104

yes

characteristic

127

C₄×C₁₇

#421

yes

characteristic

128

C₄×C₁₇

#441

yes

—

129

C₄×C₁₇

#470

yes

—

130

Dic₁₇

—

131

Dic₁₇

—

132

#533

—

133

#500

—

134

#494

—

135

#487

—

136

#467

—

137

#467

—

138

C₄×Q₁₆

—

139

C₄×Q₁₆

—

140

#431

—

141

C₂×#106

—

142

C₄×M₁₆

—

143

C₂×C₄×C₈

C₂×D₁₇

yes

characteristic

144

C₄×C₄⋊C₄

C₂×D₁₇

yes

—

145

#340

—

146

#339

—

147

#328

—

148

#322

—

149

#322

—

150

C₂×C₁₇

—

151

C₂×C₁₇

#1971

yes

characteristic

152

C₂×C₁₇

#1976

yes

characteristic

153

C₂×C₁₇

#1980

yes

characteristic

154

C₂×Q₁₆

—

155

C₂×Q₁₆

—

156

C₂×M₁₆

—

157

C₂²×C₈

C₂²⋊D₁₇

yes

characteristic

158

C₂²×C₈

C₂²⋊D₁₇

yes

characteristic

159

C₄⋊Q₈

—

160

C₄⋊Q₈

—

161

#125

—

162

C₂²⋊Q₈

—

163

C₂²⋊Q₈

—

164

C₄×Q₈

—

165

C₄×Q₈

—

166

#117

—

167

C₂×C₄⋊C₄

—

168

C₂×C₄²

—

169

C₂×C₄²

C₂²×D₁₇

yes

characteristic

170

#107

—

171

#107

—

172

#106

—

173

C₄⋊C₈

—

174

#103

—

175

#103

—

176

C₂²⋊C₈

—

177

#97

—

178

C₄×C₈

—

179

C₄×C₈

—

180

C₄×C₈

C₄×D₁₇

yes

characteristic

181

C₄×C₈

C₄×D₁₇

yes

characteristic

182

C₄×C₈

D₆₈

yes

characteristic

183

C₄×C₈

D₆₈

yes

characteristic

184

#95

—

185

C₁₇

#9720

yes

characteristic, complemented, Sylow

186

C₂×Q₈

—

187

C₂×Q₈

—

188

C₂²×C₄

—

189

C₂²×C₄

D₄×D₁₇

yes

characteristic

190

C₂²×C₄

D₄×D₁₇

yes

characteristic

191

C₂²×C₄

C₂×C₂²⋊D₁₇

yes

characteristic

192

Q₁₆

—

193

Q₁₆

—

194

M₁₆

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

#63227

yes

characteristic

200

C₂×C₈

#63227

yes

characteristic

201

C₂×C₈

#63227

yes

characteristic

202

C₂×C₈

#63227

yes

characteristic

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

210

C₄⋊C₄

—

211

C₂²⋊C₄

—

212

C₄²

—

213

C₄²

—

214

C₄²

C₂×C₄×D₁₇

yes

characteristic

215

C₄²

C₂×D₆₈

yes

characteristic

216

C₄²

#63256

yes

characteristic

217

C₄²

#63256

yes

characteristic

218

C₂³

#10587626

yes

characteristic

219

Q₈

—

220

Q₈

—

221

Q₈

—

136

—

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

#10587579

yes

characteristic

231

C₂×C₄

#10587579

yes

characteristic

232

C₂×C₄

#10587581

yes

characteristic

233

C₂×C₄

#10587581

yes

characteristic

234

C₂×C₄

#10587601

yes

—

235

C₂×C₄

C₂×#63227

yes

characteristic

236

C₂×C₄

#10587633

yes

characteristic

237

C₈

—

238

C₈

—

239

C₈

—

240

C₈

—

241

C₈

—

242

C₈

#10587476

yes

—

243

C₂²

—

244

C₂²

—

245

C₂²

#11762710

yes

characteristic

246

C₂²

#11763200

yes

—

247

C₄

—

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

—

136

—

252

C₄

—

136

—

253

C₄

C₂×#10587476

yes

characteristic

254

C₄

#11762827

yes

characteristic

255

C₄

#11762915

yes

—

256

C₄

#11763068

yes

—

257

C₂

—

258

C₂

#14529653

yes

characteristic

259

C₂

#14529680

yes

characteristic

260

C₂

#14529702

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10587581
commutator	C₄²×C₁₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₇
Fitting	C₄×C₁₇×#106	C₂
socle	C₂²×C₁₇	#390
prime radical	C₂³×C₁₇	#127
cosocle	C₂×C₄²×C₁₇	C₂³
hypercenter	C₄×#106	D₁₇
hypocenter	C₁₇	#9720
LCS	G ▷ C₄²×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#106

subgroup

G/H

center

C₂×C₄

#10587581

commutator

C₄²×C₁₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₇

Fitting

C₄×C₁₇×#106

C₂

C₂²×C₁₇

C₂³×C₁₇

C₂×C₄²×C₁₇

C₂³

D₁₇

C₁₇

G ▷ C₄²×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#106

N	H ≅ G/N	type
7. #11763214	C₄	semidirect
8. #11763189	C₄	semidirect
9. #11763160	C₄	semidirect
185. C₁₇	#9720	semidirect

H ≅ G/N

type

7. #11763214

C₄

semidirect

8. #11763189

C₄

semidirect

9. #11763160

C₄

semidirect

185. C₁₇

#9720

semidirect

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

subgroup	index
#14539370	2
#14529727	2
#14527282	2
#14527073	2
C₄×C₁₇×#106	2
#9720	17

subgroup

index

C₄×C₁₇×#106

Subgroups — #16933488

Conjugacy classes of subgroups

Complements

Maximal subgroups