Group #34011297 — subgroups

Subgroups — #34011297

Order 18688.

378 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 88 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	#22626290	C₂	1	1	yes	maximal, characteristic, complemented
2	#22625852	C₂	1	1	yes	maximal, characteristic, complemented
3	#22624917	C₂	1	4	yes	maximal, complemented
4	#22620508	C₂	1	1	yes	maximal, characteristic
5	#17989533	—	2	1	no	—
6	#17989508	—	2	1	no	—
7	#17989482	C₂²	1	2	yes	—
8	C₄×#11924031	—	2	1	no	—
9	#17989461	—	2	1	no	—
10	#17989461	C₂²	1	2	yes	—
11	#17989135	—	2	1	no	—
12	#17988992	C₄	1	1	yes	characteristic, complemented
13	#17988933	—	2	1	no	—
14	#17988820	—	2	1	no	—
15	#17988820	C₂²	1	2	yes	—
16	D₈×Dic₇₃	—	2	1	no	—
17	D₈×Dic₇₃	C₄	1	2	yes	complemented
18	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
19	#493×C₇₃	C₄	1	1	yes	characteristic, complemented
20	C₂×C₄⋊#64408	—	2	2	no	—
21	C₂×C₄⋊#64408	—	4	1	no	—
22	C₂×C₄⋊#64408	—	4	1	no	—
23	C₂×#11924031	—	2	2	no	—
24	C₂×#11924027	—	4	1	no	—
25	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
26	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
27	#14556591	—	2	1	no	—
28	#14556578	—	4	1	no	—
29	#14556562	—	2	2	no	—
30	#14556562	—	4	1	no	—
31	D₄×Dic₇₃	—	2	2	no	—
32	D₄×Dic₇₃	—	4	1	no	—
33	C₄²×D₇₃	D₄	1	1	yes	characteristic
34	#14556525	—	2	1	no	—
35	#14556525	C₂×C₄	1	2	yes	—
36	#14556512	—	2	2	no	—
37	#14556512	—	2	2	no	—
38	C₄×#10596831	D₄	1	1	yes	characteristic
39	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
40	C₈×Dic₇₃	D₄	1	1	yes	characteristic
41	C₂×D₈×C₇₃	—	2	1	no	—
42	C₂×D₈×C₇₃	C₂×C₄	1	2	yes	—
43	#127×C₇₃	—	2	1	no	—
44	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
45	C₂²×#64408	—	4	2	no	—
46	C₄⋊#64408	—	4	2	no	—
47	C₄⋊#64408	—	4	2	no	—
48	C₄⋊#64408	—	8	2	no	—
49	C₄⋊#64408	—	8	2	no	—
50	#11924031	—	4	2	no	—
51	#11924027	—	8	2	no	—
52	#11924027	—	8	2	no	—
53	C₂×Dic₁₄₆	—	4	1	no	—
54	C₂×C₂²⋊D₇₃	—	4	2	no	—
55	C₂²×Dic₇₃	—	4	2	no	—
56	C₂×C₄×D₇₃	D₈	1	1	yes	characteristic
57	C₂×C₄×D₇₃	D₈	1	1	yes	characteristic
58	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
59	C₂×#10596831	C₂²⋊C₄	1	1	yes	characteristic
60	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
61	C₈×D₇₃	—	4	1	no	—
62	C₈×D₇₃	—	4	1	no	—
63	C₄⋊Dic₇₃	—	2	2	no	—
64	C₄⋊Dic₇₃	—	4	1	no	—
65	C₂²⋊Dic₇₃	—	4	2	no	—
66	C₂²⋊Dic₇₃	—	4	2	no	—
67	C₄×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
68	C₄×Dic₇₃	SD₁₆	1	1	yes	characteristic
69	C₄×Dic₇₃	SD₁₆	1	1	yes	characteristic
70	C₂×D₄×C₇₃	—	2	2	no	—
71	C₂×D₄×C₇₃	—	4	1	no	—
72	C₂×D₄×C₇₃	—	4	1	no	—
73	D₈×C₇₃	—	4	2	no	—
74	D₈×C₇₃	—	4	2	no	—
75	C₂×C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
76	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
77	C₄²×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
78	C₂³×C₇₃	—	4	2	no	—
79	C₂²×D₇₃	C₂×D₈	1	1	yes	characteristic
80	C₂×#64408	—	8	2	no	—
81	C₂×#64408	—	8	2	no	—
82	C₂×#64408	—	8	2	no	—
83	D₄×C₇₃	—	4	2	no	—
84	D₄×C₇₃	—	4	2	no	—
85	D₄×C₇₃	—	8	2	no	—
86	D₄×C₇₃	—	8	2	no	—
87	C₂×C₄×C₇₃	#102	1	1	yes	characteristic
88	C₂×C₄×C₇₃	#102	1	1	yes	characteristic
89	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
90	C₂²⋊D₇₃	—	8	2	no	—
91	C₂²⋊D₇₃	—	8	2	no	—
92	C₂×Dic₇₃	—	4	2	no	—
93	C₂×Dic₇₃	—	8	4	no	—
94	C₂×Dic₇₃	#102	1	1	yes	characteristic
95	C₂×Dic₇₃	#102	1	1	yes	characteristic
96	C₂×Dic₇₃	C₂×SD₁₆	1	1	yes	characteristic
97	C₄×D₇₃	—	2	2	no	—
98	C₄×D₇₃	—	2	1	no	—
99	C₄×D₇₃	—	2	1	no	—
100	C₄×D₇₃	D₁₆	1	2	yes	—
101	C₄×D₇₃	SD₃₂	1	2	yes	—
102	Dic₁₄₆	—	8	2	no	—
103	C₈×C₇₃	—	2	1	no	—
104	C₈×C₇₃	—	2	1	no	—
105	#10596831	—	2	1	no	—
106	#10596831	—	2	1	no	—
107	C₂²×C₇₃	—	8	2	no	—
108	C₂²×C₇₃	—	8	2	no	—
109	C₂²×C₇₃	—	8	2	no	—
110	C₂²×C₇₃	C₂×#102	1	1	yes	characteristic
111	C₂×D₇₃	—	2	1	no	—
112	C₂×D₇₃	—	2	1	no	—
113	C₂×D₇₃	C₂×D₁₆	1	1	yes	characteristic
114	C₂×D₇₃	C₂×SD₃₂	1	1	yes	characteristic
115	#64408	—	16	2	no	—
116	C₄×C₇₃	#357	1	2	yes	—
117	C₄×C₇₃	#360	1	2	yes	—
118	C₄×C₇₃	#410	1	1	yes	characteristic
119	C₄×C₇₃	#421	1	1	yes	characteristic
120	Dic₇₃	—	2	1	no	—
121	Dic₇₃	—	2	1	no	—
122	Dic₇₃	—	8	2	no	—
123	Dic₇₃	#357	1	2	yes	—
124	#11856	—	73	1	no	maximal, Sylow
125	C₂×C₇₃	—	16	2	no	—
126	C₂×C₇₃	#1517	1	1	yes	characteristic
127	C₂×C₇₃	C₂×#357	1	1	yes	characteristic
128	C₂×C₇₃	C₂×#360	1	1	yes	characteristic
129	D₇₃	—	2	1	no	—
130	D₇₃	—	2	1	no	—
131	#3169	—	73	1	no	—
132	#2162	—	73	1	no	—
133	#1834	—	73	1	no	—
134	#1347	—	73	4	no	—
135	C₇₃	#11856	1	1	yes	characteristic, complemented, Sylow
136	#532	—	146	1	no	—
137	#500	—	73	1	no	—
138	#493	#64408	1	1	yes	characteristic, complemented
139	#486	—	146	1	no	—
140	#466	—	73	2	no	—
141	#466	—	146	1	no	—
142	C₄×D₈	—	73	2	no	—
143	C₄×D₈	—	146	1	no	—
144	C₂×C₄×C₈	—	73	1	no	—
145	#384	—	146	1	no	—
146	C₄⋊C₁₆	—	146	1	no	—
147	C₂²⋊C₁₆	—	73	2	no	—
148	C₄×C₁₆	—	146	1	no	—
149	#340	—	73	2	no	—
150	#340	—	146	1	no	—
151	C₂×#41	—	292	1	no	—
152	C₂×D₈	—	2	1	no	—
153	C₂×D₈	C₂×#64408	1	2	yes	—
154	C₂²×C₈	—	73	1	no	—
155	C₂²×C₈	—	73	1	no	—
156	C₄⋊Q₈	—	146	1	no	—
157	#127	—	2	1	no	—
158	#124	—	292	1	no	—
159	#121	—	292	1	no	—
160	#121	—	146	2	no	—
161	C₄×D₄	—	292	1	no	—
162	C₄×D₄	—	146	2	no	—
163	C₂×C₄⋊C₄	—	292	1	no	—
164	C₂×C₄⋊C₄	—	292	1	no	—
165	C₂×C₄⋊C₄	—	146	2	no	—
166	C₂×C₄²	—	73	1	no	—
167	C₂×C₁₆	—	146	2	no	—
168	#107	—	73	2	no	—
169	#107	—	146	1	no	—
170	#102	—	146	2	no	—
171	#102	—	146	2	no	—
172	C₄×C₈	—	73	1	no	—
173	C₄×C₈	—	73	1	no	—
174	C₄×C₈	—	73	1	no	—
175	C₄×C₈	C₂×#64408	1	1	yes	characteristic
176	#41	—	584	2	no	—
177	#41	—	584	2	no	—
178	C₂×Q₈	—	292	1	no	—
179	C₂×D₄	—	2	2	no	—
180	C₂×D₄	—	4	1	no	—
181	C₂×D₄	—	4	1	no	—
182	C₂×D₄	—	292	2	no	—
183	C₂²×C₄	—	292	2	no	—
184	C₂²×C₄	—	292	2	no	—
185	C₂²×C₄	—	73	1	no	—
186	C₂²×C₄	—	73	1	no	—
187	C₂²×C₄	—	73	1	no	—
188	D₈	—	4	2	no	—
189	D₈	—	4	2	no	—
190	C₂×C₈	—	292	1	no	—
191	C₂×C₈	—	292	1	no	—
192	C₂×C₈	—	73	1	no	—
193	C₂×C₈	—	73	1	no	—
194	C₂×C₈	C₂²⋊#64408	1	1	yes	characteristic
195	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
196	C₄⋊C₄	—	292	1	no	—
197	C₄⋊C₄	—	292	2	no	—
198	C₄⋊C₄	—	292	2	no	—
199	C₄⋊C₄	—	584	2	no	—
200	C₄⋊C₄	—	584	2	no	—
201	C₄⋊C₄	—	146	2	no	—
202	C₂²⋊C₄	—	292	2	no	—
203	C₂²⋊C₄	—	292	2	no	—
204	C₄²	—	73	1	no	—
205	C₄²	—	73	1	no	—
206	C₄²	—	73	1	no	—
207	C₄²	C₂²⋊#64408	1	1	yes	characteristic
208	C₁₆	—	292	2	no	—
209	C₂³	—	4	2	no	—
210	C₂³	—	73	1	no	—
211	Q₈	—	584	2	no	—
212	D₄	—	4	2	no	—
213	D₄	—	4	2	no	—
214	D₄	—	8	2	no	—
215	D₄	—	8	2	no	—
216	D₄	—	584	2	no	—
217	D₄	—	584	2	no	—
218	C₂×C₄	—	292	2	no	—
219	C₂×C₄	—	584	4	no	—
220	C₂×C₄	—	584	2	no	—
221	C₂×C₄	—	584	2	no	—
222	C₂×C₄	—	584	2	no	—
223	C₂×C₄	—	73	1	no	—
224	C₂×C₄	—	73	2	no	—
225	C₂×C₄	—	73	2	no	—
226	C₂×C₄	—	73	1	no	—
227	C₂×C₄	—	73	1	no	—
228	C₂×C₄	—	146	2	no	—
229	C₂×C₄	—	146	1	no	—
230	C₂×C₄	—	146	1	no	—
231	C₂×C₄	#14556653	1	1	yes	characteristic
232	C₂×C₄	#14556653	1	1	yes	characteristic
233	C₂×C₄	C₂×C₂²⋊#64408	1	1	yes	characteristic
234	C₈	—	2	1	no	—
235	C₈	—	2	1	no	—
236	C₈	—	146	1	no	—
237	C₈	—	146	1	no	—
238	C₂²	—	8	2	no	—
239	C₂²	—	8	2	no	—
240	C₂²	—	8	2	no	—
241	C₂²	—	73	1	no	—
242	C₂²	—	73	1	no	—
243	C₂²	—	146	1	no	—
244	C₂²	—	146	1	no	—
245	C₂²	C₂×#14556653	1	1	yes	characteristic
246	C₄	—	584	2	no	—
247	C₄	—	73	2	no	—
248	C₄	—	1168	2	no	—
249	C₄	—	146	1	no	—
250	C₄	—	146	1	no	—
251	C₄	#17989499	1	2	yes	—
252	C₄	#17989503	1	2	yes	—
253	C₄	#17989567	1	1	yes	characteristic
254	C₄	#17989585	1	1	yes	characteristic
255	C₂	—	16	2	no	—
256	C₂	—	146	1	no	—
257	C₂	—	146	1	no	—
258	C₂	#22625360	1	1	yes	characteristic
259	C₂	C₂×#17989499	1	1	yes	characteristic
260	C₂	C₂×#17989503	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22626290

C₂

yes

maximal, characteristic, complemented

#22625852

C₂

yes

maximal, characteristic, complemented

#22624917

C₂

yes

maximal, complemented

#22620508

C₂

yes

maximal, characteristic

#17989533

—

#17989508

—

#17989482

C₂²

yes

—

C₄×#11924031

—

#17989461

—

#17989461

C₂²

yes

—

#17989135

—

#17988992

C₄

yes

characteristic, complemented

#17988933

—

#17988820

—

#17988820

C₂²

yes

—

D₈×Dic₇₃

—

D₈×Dic₇₃

C₄

yes

complemented

C₄×C₈×D₇₃

C₂²

yes

characteristic

#493×C₇₃

C₄

yes

characteristic, complemented

C₂×C₄⋊#64408

—

C₂×C₄⋊#64408

—

C₂×C₄⋊#64408

—

C₂×#11924031

—

C₂×#11924027

—

C₂×C₈×D₇₃

D₄

yes

characteristic

C₂×C₈×D₇₃

C₂³

yes

—

—

—

—

D₄×Dic₇₃

—

D₄×Dic₇₃

—

C₄²×D₇₃

D₄

yes

characteristic

#14556525

—

#14556525

C₂×C₄

yes

—

#14556512

—

#14556512

—

C₄×#10596831

D₄

yes

characteristic

C₈×Dic₇₃

C₂×C₄

yes

characteristic

C₈×Dic₇₃

D₄

yes

characteristic

C₂×D₈×C₇₃

—

C₂×D₈×C₇₃

C₂×C₄

yes

—

#127×C₇₃

—

C₄×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂²×#64408

—

—

—

—

—

—

—

—

C₂×Dic₁₄₆

—

C₂×C₂²⋊D₇₃

—

C₂²×Dic₇₃

—

C₂×C₄×D₇₃

D₈

yes

characteristic

C₂×C₄×D₇₃

D₈

yes

characteristic

C₂×C₄×D₇₃

C₂×D₄

yes

characteristic

C₂×#10596831

C₂²⋊C₄

yes

characteristic

C₂×#10596831

C₂×D₄

yes

characteristic

C₈×D₇₃

—

C₈×D₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₂²⋊Dic₇₃

—

C₂²⋊Dic₇₃

—

C₄×Dic₇₃

C₂²⋊C₄

yes

characteristic

C₄×Dic₇₃

SD₁₆

yes

characteristic

C₄×Dic₇₃

SD₁₆

yes

characteristic

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

D₈×C₇₃

—

D₈×C₇₃

—

C₂×C₈×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₃

C₂²×C₄

yes

characteristic

C₄²×C₇₃

C₂²⋊C₄

yes

characteristic

C₂³×C₇₃

—

C₂²×D₇₃

C₂×D₈

yes

—

—

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²⋊D₇₃

—

C₂²⋊D₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

yes

C₂×Dic₇₃

yes

C₂×Dic₇₃

C₂×SD₁₆

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

100

C₄×D₇₃

D₁₆

yes

—

101

C₄×D₇₃

SD₃₂

yes

—

102

Dic₁₄₆

—

103

C₈×C₇₃

—

104

C₈×C₇₃

—

105

#10596831

—

106

#10596831

—

107

C₂²×C₇₃

—

108

C₂²×C₇₃

—

109

C₂²×C₇₃

—

110

C₂²×C₇₃

C₂×#102

yes

characteristic

111

C₂×D₇₃

—

112

C₂×D₇₃

—

113

C₂×D₇₃

C₂×D₁₆

yes

characteristic

114

C₂×D₇₃

C₂×SD₃₂

yes

characteristic

115

#64408

—

116

C₄×C₇₃

#357

yes

—

117

C₄×C₇₃

#360

yes

—

118

C₄×C₇₃

#410

yes

characteristic

119

C₄×C₇₃

#421

yes

characteristic

120

Dic₇₃

—

121

Dic₇₃

—

122

Dic₇₃

—

123

Dic₇₃

#357

yes

—

124

#11856

—

maximal, Sylow

125

C₂×C₇₃

—

126

C₂×C₇₃

#1517

yes

characteristic

127

C₂×C₇₃

C₂×#357

yes

characteristic

128

C₂×C₇₃

C₂×#360

yes

characteristic

129

D₇₃

—

130

D₇₃

—

131

#3169

—

132

#2162

—

133

#1834

—

134

#1347

—

135

C₇₃

#11856

yes

characteristic, complemented, Sylow

136

#532

—

146

—

137

#500

—

138

#493

#64408

yes

characteristic, complemented

139

#486

—

146

—

140

#466

—

141

#466

—

146

—

142

C₄×D₈

—

143

C₄×D₈

—

146

—

144

C₂×C₄×C₈

—

145

#384

—

146

—

146

C₄⋊C₁₆

—

146

—

147

C₂²⋊C₁₆

—

148

C₄×C₁₆

—

146

—

149

#340

—

150

#340

—

146

—

151

C₂×#41

—

292

—

152

C₂×D₈

—

153

C₂×D₈

C₂×#64408

yes

—

154

C₂²×C₈

—

155

C₂²×C₈

—

156

C₄⋊Q₈

—

146

—

157

#127

—

158

#124

—

292

—

159

#121

—

292

—

160

#121

—

146

—

161

C₄×D₄

—

292

—

162

C₄×D₄

—

146

—

163

C₂×C₄⋊C₄

—

292

—

164

C₂×C₄⋊C₄

—

292

—

165

C₂×C₄⋊C₄

—

146

—

166

C₂×C₄²

—

167

C₂×C₁₆

—

146

—

168

#107

—

169

#107

—

146

—

170

#102

—

146

—

171

#102

—

146

—

172

C₄×C₈

—

173

C₄×C₈

—

174

C₄×C₈

—

175

C₄×C₈

C₂×#64408

yes

characteristic

176

#41

—

584

—

177

#41

—

584

—

178

C₂×Q₈

—

292

—

179

C₂×D₄

—

180

C₂×D₄

—

181

C₂×D₄

—

182

C₂×D₄

—

292

—

183

C₂²×C₄

—

292

—

184

C₂²×C₄

—

292

—

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

—

188

D₈

—

189

D₈

—

190

C₂×C₈

—

292

—

191

C₂×C₈

—

292

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

C₂²⋊#64408

yes

characteristic

195

C₂×C₈

C₂²×#64408

yes

characteristic

196

C₄⋊C₄

—

292

—

197

C₄⋊C₄

—

292

—

198

C₄⋊C₄

—

292

—

199

C₄⋊C₄

—

584

—

200

C₄⋊C₄

—

584

—

201

C₄⋊C₄

—

146

—

202

C₂²⋊C₄

—

292

—

203

C₂²⋊C₄

—

292

—

204

C₄²

—

205

C₄²

—

206

C₄²

—

207

C₄²

C₂²⋊#64408

yes

characteristic

208

C₁₆

—

292

—

209

C₂³

—

210

C₂³

—

211

Q₈

—

584

—

212

D₄

—

213

D₄

—

214

D₄

—

215

D₄

—

216

D₄

—

584

—

217

D₄

—

584

—

218

C₂×C₄

—

292

—

219

C₂×C₄

—

584

—

220

C₂×C₄

—

584

—

221

C₂×C₄

—

584

—

222

C₂×C₄

—

584

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

146

—

229

C₂×C₄

—

146

—

230

C₂×C₄

—

146

—

231

C₂×C₄

#14556653

yes

characteristic

232

C₂×C₄

#14556653

yes

characteristic

233

C₂×C₄

C₂×C₂²⋊#64408

yes

characteristic

234

C₈

—

235

C₈

—

236

C₈

—

146

—

237

C₈

—

146

—

238

C₂²

—

239

C₂²

—

240

C₂²

—

241

C₂²

—

242

C₂²

—

243

C₂²

—

146

—

244

C₂²

—

146

—

245

C₂²

C₂×#14556653

yes

characteristic

246

C₄

—

584

—

247

C₄

—

248

C₄

—

1168

—

249

C₄

—

146

—

250

C₄

—

146

—

251

C₄

#17989499

yes

—

252

C₄

#17989503

yes

—

253

C₄

#17989567

yes

characteristic

254

C₄

#17989585

yes

characteristic

255

C₂

—

256

C₂

—

146

—

257

C₂

—

146

—

258

C₂

#22625360

yes

characteristic

259

C₂

C₂×#17989499

yes

characteristic

260

C₂

C₂×#17989503

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#14556653
commutator	C₂×C₈×C₇₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×#64408
Fitting	#493×C₇₃	C₄
socle	C₂²×C₇₃	C₂×#102
prime radical	#22620508	C₂
cosocle	C₂×C₈×D₇₃	C₂³
hypercenter	#493	#64408
hypocenter	C₇₃	#11856
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #493

subgroup

G/H

center

C₂²

C₂×#14556653

commutator

C₂×C₈×C₇₃

C₂²×C₄

Frattini

C₂×C₈

C₂²×#64408

Fitting

#493×C₇₃

C₄

C₂²×C₇₃

C₂

C₂×C₈×D₇₃

C₂³

C₇₃

G ▷ C₂×C₈×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #493

N	H ≅ G/N	type
1. #22626290	C₂	semidirect
2. #22625852	C₂	semidirect
3. #22624917	C₂	semidirect
12. #17988992	C₄	semidirect
17. D₈×Dic₇₃	C₄	semidirect
19. #493×C₇₃	C₄	semidirect
135. C₇₃	#11856	semidirect
138. #493	#64408	semidirect

H ≅ G/N

type

1. #22626290

C₂

semidirect

2. #22625852

C₂

semidirect

3. #22624917

C₂

semidirect

12. #17988992

C₄

semidirect

17. D₈×Dic₇₃

C₄

semidirect

19. #493×C₇₃

C₄

semidirect

135. C₇₃

#11856

semidirect

138. #493

#64408

semidirect

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

subgroup	index
#22626290	2
#22625852	2
#22624917	2
#22620508	2
#11856	73

subgroup

index

Subgroups — #34011297

Conjugacy classes of subgroups

Complements

Maximal subgroups