Group #32990784 — subgroups

Subgroups — #32990784

Order 18688.

294 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 93 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	#22610904	C₂	1	1	yes	maximal, characteristic
2	#22610106	C₂	1	1	yes	maximal, characteristic
3	#22608615	C₂	1	1	yes	maximal, characteristic
4	#22608611	C₂	1	1	yes	maximal, characteristic
5	#22607790	C₂	1	1	yes	maximal, characteristic
6	#22607790	C₂	1	1	yes	maximal, characteristic
7	C₇₃×#1281	C₂	1	1	yes	maximal, characteristic
8	C₂×#14556591	C₂²	1	1	yes	characteristic
9	C₂×#14556527	—	2	1	no	—
10	C₂×#14556527	—	2	1	no	—
11	#17988611	C₂²	1	1	yes	characteristic
12	#17988611	C₂²	1	1	yes	characteristic
13	#17988453	C₂²	1	1	yes	characteristic
14	#17988350	—	2	1	no	—
15	#17988350	—	2	1	no	—
16	#17988335	—	2	2	no	—
17	#17988334	—	2	2	no	—
18	#431×C₇₃	C₂²	1	1	yes	characteristic
19	#431×C₇₃	C₂²	1	1	yes	characteristic
20	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
21	C₂²×Dic₁₄₆	—	2	1	no	—
22	C₂×#11924012	—	2	1	no	—
23	C₂×#11924012	—	2	1	no	—
24	#14556591	—	2	1	no	—
25	#14556591	—	2	1	no	—
26	#14556591	—	2	1	no	—
27	#14556591	D₄	1	2	yes	—
28	C₂×C₄⋊Dic₇₃	—	2	1	no	—
29	C₂×C₄⋊Dic₇₃	—	2	1	no	—
30	C₂×C₄⋊Dic₇₃	—	2	1	no	—
31	#14556527	—	4	2	no	—
32	#14556527	—	4	2	no	—
33	C₄⋊#10596831	—	2	1	no	—
34	C₄⋊#10596831	—	2	1	no	—
35	C₄⋊#10596831	—	2	1	no	—
36	C₄⋊#10596831	—	2	1	no	—
37	#14556498	—	2	1	no	—
38	#14556498	—	2	1	no	—
39	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
40	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
42	C₄⋊C₈×C₇₃	—	2	1	no	—
43	C₄⋊C₈×C₇₃	—	2	1	no	—
44	C₂²⋊C₈×C₇₃	—	2	1	no	—
45	C₂²⋊C₈×C₇₃	—	2	1	no	—
46	#97×C₇₃	—	2	1	no	—
47	#97×C₇₃	—	2	1	no	—
48	C₄×C₈×C₇₃	—	2	1	no	—
49	C₄×C₈×C₇₃	—	2	1	no	—
50	C₂×Dic₁₄₆	—	2	2	no	—
51	C₂×Dic₁₄₆	—	4	1	no	—
52	C₂×Dic₁₄₆	—	8	2	no	—
53	C₂²×Dic₇₃	—	4	1	no	—
54	C₂²×Dic₇₃	—	4	1	no	—
55	#11924012	—	4	1	no	—
56	#11924012	—	4	1	no	—
57	#11924012	—	4	1	no	—
58	#11924012	—	4	1	no	—
59	C₂×#10596831	—	4	1	no	—
60	C₂×#10596831	—	4	1	no	—
61	C₄⋊Dic₇₃	—	2	2	no	—
62	C₄⋊Dic₇₃	—	2	2	no	—
63	C₄⋊Dic₇₃	—	4	1	no	—
64	C₄⋊Dic₇₃	—	4	1	no	—
65	C₄⋊Dic₇₃	—	4	1	no	—
66	C₄⋊Dic₇₃	—	4	1	no	—
67	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
69	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
70	C₂×C₈×C₇₃	—	2	1	no	—
71	C₂×C₈×C₇₃	—	2	1	no	—
72	C₂×C₈×C₇₃	—	2	1	no	—
73	C₂×C₈×C₇₃	—	2	1	no	—
74	C₂×C₈×C₇₃	—	4	1	no	—
75	C₂×C₈×C₇₃	—	4	1	no	—
76	C₂×C₈×C₇₃	SD₁₆	1	2	yes	—
77	C₂×C₈×C₇₃	Q₁₆	1	2	yes	—
78	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
79	C₄²×C₇₃	#41	1	1	yes	characteristic
80	C₄²×C₇₃	#41	1	1	yes	characteristic
81	C₄²×C₇₃	#41	1	1	yes	characteristic
82	C₂³×C₇₃	#124	1	1	yes	characteristic
83	C₂×C₄×C₇₃	—	4	1	no	—
84	C₂×C₄×C₇₃	—	4	1	no	—
85	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
86	C₂×C₄×C₇₃	#123	1	1	yes	characteristic
87	C₂×C₄×C₇₃	#123	1	1	yes	characteristic
88	C₂×C₄×C₇₃	#123	1	1	yes	characteristic
89	C₂×C₄×C₇₃	#126	1	1	yes	characteristic
90	C₂×C₄×C₇₃	#126	1	1	yes	characteristic
91	C₂×C₄×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
92	C₂×C₄×C₇₃	C₂×Q₁₆	1	1	yes	characteristic
93	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
94	C₂×C₄×C₇₃	#137	1	1	yes	characteristic
95	C₂×Dic₇₃	—	4	2	no	—
96	C₂×Dic₇₃	—	8	2	no	—
97	C₂×Dic₇₃	—	8	1	no	—
98	C₂×Dic₇₃	—	8	1	no	—
99	C₂×Dic₇₃	—	8	1	no	—
100	Dic₁₄₆	—	8	2	no	—
101	Dic₁₄₆	—	8	2	no	—
102	C₈×C₇₃	—	2	2	no	—
103	C₈×C₇₃	—	2	2	no	—
104	C₈×C₇₃	—	8	1	no	—
105	C₈×C₇₃	—	8	1	no	—
106	#10596831	—	8	1	no	—
107	#10596831	—	8	1	no	—
108	C₂²×C₇₃	—	2	1	no	—
109	C₂²×C₇₃	—	2	1	no	—
110	C₂²×C₇₃	#397	1	1	yes	characteristic
111	C₂²×C₇₃	#487	1	1	yes	characteristic
112	C₂²×C₇₃	#489	1	1	yes	characteristic
113	C₄×C₇₃	—	2	1	no	—
114	C₄×C₇₃	—	2	1	no	—
115	C₄×C₇₃	—	2	1	no	—
116	C₄×C₇₃	—	2	1	no	—
117	C₄×C₇₃	#460	1	1	yes	characteristic
118	C₄×C₇₃	#462	1	1	yes	characteristic
119	C₄×C₇₃	#483	1	1	yes	characteristic
120	C₄×C₇₃	#484	1	1	yes	characteristic
121	Dic₇₃	—	8	2	no	—
122	Dic₇₃	—	16	1	no	—
123	#10633	—	73	1	no	maximal, Sylow
124	C₂×C₇₃	—	2	1	no	—
125	C₂×C₇₃	—	2	1	no	—
126	C₂×C₇₃	#2072	1	1	yes	characteristic
127	C₂×C₇₃	#2081	1	1	yes	characteristic
128	C₂×C₇₃	#2082	1	1	yes	characteristic
129	#1993	—	73	1	no	—
130	#1849	—	73	1	no	—
131	#1549	—	73	1	no	—
132	#1548	—	73	1	no	—
133	#1286	—	73	1	no	—
134	#1286	—	73	1	no	—
135	#1281	D₇₃	1	1	yes	characteristic
136	C₇₃	#10633	1	1	yes	characteristic, complemented, Sylow
137	C₂×C₄⋊Q₈	—	73	1	no	—
138	#431	C₂×D₇₃	1	1	yes	characteristic
139	#431	C₂×D₇₃	1	1	yes	characteristic
140	C₂×#108	—	146	1	no	—
141	C₂×#108	—	146	1	no	—
142	#423	—	73	1	no	—
143	#423	—	73	1	no	—
144	C₂×#97	C₂×D₇₃	1	1	yes	characteristic
145	#382	—	73	1	no	—
146	#340	—	146	1	no	—
147	#340	—	146	1	no	—
148	#333	—	146	2	no	—
149	#332	—	146	2	no	—
150	C₂²×Q₈	—	146	1	no	—
151	C₂×M₁₆	—	146	1	no	—
152	C₂×M₁₆	—	146	1	no	—
153	C₂²×C₈	D₂₉₂	1	1	yes	characteristic
154	C₂²×C₈	D₂₉₂	1	1	yes	characteristic
155	C₄⋊Q₈	—	73	2	no	—
156	C₄⋊Q₈	—	146	1	no	—
157	C₄⋊Q₈	—	146	1	no	—
158	C₄⋊Q₈	—	146	1	no	—
159	C₂×C₄⋊C₄	—	146	1	no	—
160	C₂×C₄⋊C₄	—	146	1	no	—
161	C₂×C₄⋊C₄	—	146	1	no	—
162	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
163	#108	—	292	2	no	—
164	#108	—	292	2	no	—
165	C₄⋊C₈	—	2	1	no	—
166	C₄⋊C₈	—	2	1	no	—
167	C₄⋊C₈	—	146	1	no	—
168	C₄⋊C₈	—	146	1	no	—
169	C₄⋊C₈	—	146	1	no	—
170	C₄⋊C₈	—	146	1	no	—
171	C₂²⋊C₈	—	2	1	no	—
172	C₂²⋊C₈	—	2	1	no	—
173	#97	—	2	1	no	—
174	#97	—	2	1	no	—
175	C₄×C₈	—	2	1	no	—
176	C₄×C₈	—	2	1	no	—
177	#95	—	146	1	no	—
178	#95	—	146	1	no	—
179	C₂×Q₈	—	292	1	no	—
180	C₂×Q₈	—	584	2	no	—
181	C₂×Q₈	—	146	2	no	—
182	C₂²×C₄	—	292	1	no	—
183	C₂²×C₄	—	292	1	no	—
184	C₂²×C₄	C₂×D₂₉₂	1	1	yes	characteristic
185	C₂²×C₄	#11924028	1	1	yes	characteristic
186	C₂²×C₄	#11924028	1	1	yes	characteristic
187	M₁₆	—	292	1	no	—
188	M₁₆	—	292	1	no	—
189	M₁₆	—	292	1	no	—
190	M₁₆	—	292	1	no	—
191	C₂×C₈	—	2	1	no	—
192	C₂×C₈	—	2	1	no	—
193	C₂×C₈	—	2	1	no	—
194	C₂×C₈	—	2	1	no	—
195	C₂×C₈	—	4	1	no	—
196	C₂×C₈	—	4	1	no	—
197	C₂×C₈	—	292	1	no	—
198	C₂×C₈	—	292	1	no	—
199	C₂×C₈	#11924017	1	2	yes	—
200	C₂×C₈	Dic₂₉₂	1	2	yes	—
201	C₄⋊C₄	—	292	1	no	—
202	C₄⋊C₄	—	292	1	no	—
203	C₄⋊C₄	—	292	1	no	—
204	C₄⋊C₄	—	292	1	no	—
205	C₄⋊C₄	—	146	2	no	—
206	C₄⋊C₄	—	146	2	no	—
207	C₄²	D₄×D₇₃	1	1	yes	characteristic
208	C₄²	#11924027	1	1	yes	characteristic
209	C₄²	#11924027	1	1	yes	characteristic
210	C₄²	#11924029	1	1	yes	characteristic
211	C₂³	#14556579	1	1	yes	characteristic
212	Q₈	—	584	2	no	—
213	Q₈	—	584	2	no	—
214	C₂×C₄	—	4	1	no	—
215	C₂×C₄	—	4	1	no	—
216	C₂×C₄	—	292	2	no	—
217	C₂×C₄	—	584	2	no	—
218	C₂×C₄	—	584	1	no	—
219	C₂×C₄	—	584	1	no	—
220	C₂×C₄	—	584	1	no	—
221	C₂×C₄	#14556566	1	1	yes	characteristic
222	C₂×C₄	#14556573	1	1	yes	characteristic
223	C₂×C₄	#14556573	1	1	yes	characteristic
224	C₂×C₄	#14556575	1	1	yes	characteristic
225	C₂×C₄	#14556586	1	1	yes	characteristic
226	C₂×C₄	#14556586	1	1	yes	characteristic
227	C₂×C₄	C₂×#11924017	1	1	yes	characteristic
228	C₂×C₄	C₂×Dic₂₉₂	1	1	yes	characteristic
229	C₂×C₄	#14556619	1	1	yes	characteristic
230	C₂×C₄	#14556624	1	1	yes	characteristic
231	C₈	—	2	2	no	—
232	C₈	—	2	2	no	—
233	C₈	—	8	1	no	—
234	C₈	—	8	1	no	—
235	C₈	—	584	1	no	—
236	C₈	—	584	1	no	—
237	C₂²	—	2	1	no	—
238	C₂²	—	2	1	no	—
239	C₂²	#17988514	1	1	yes	characteristic
240	C₂²	#17988938	1	1	yes	characteristic
241	C₂²	#17988947	1	1	yes	characteristic
242	C₄	—	2	1	no	—
243	C₄	—	2	1	no	—
244	C₄	—	2	1	no	—
245	C₄	—	2	1	no	—
246	C₄	—	584	2	no	—
247	C₄	—	1168	1	no	—
248	C₄	#17988788	1	1	yes	characteristic
249	C₄	#17988798	1	1	yes	characteristic
250	C₄	#17988918	1	1	yes	characteristic
251	C₄	#17988923	1	1	yes	characteristic
252	C₂	—	2	1	no	—
253	C₂	—	2	1	no	—
254	C₂	#22611341	1	1	yes	characteristic
255	C₂	#22611390	1	1	yes	characteristic
256	C₂	#22611397	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22610904

C₂

yes

maximal, characteristic

#22610106

C₂

yes

maximal, characteristic

#22608615

C₂

yes

maximal, characteristic

#22608611

C₂

yes

maximal, characteristic

#22607790

C₂

yes

maximal, characteristic

#22607790

C₂

yes

maximal, characteristic

C₇₃×#1281

C₂

yes

maximal, characteristic

C₂×#14556591

C₂²

yes

—

—

C₂²

yes

characteristic

#17988611

C₂²

yes

characteristic

#17988453

C₂²

yes

—

—

—

—

#431×C₇₃

C₂²

yes

characteristic

#431×C₇₃

C₂²

yes

characteristic

C₂×#97×C₇₃

C₂²

yes

characteristic

C₂²×Dic₁₄₆

—

—

—

—

—

—

D₄

yes

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

—

—

—

—

—

—

—

—

—

C₂²×C₈×C₇₃

D₄

yes

characteristic

C₂²×C₈×C₇₃

D₄

yes

characteristic

C₂×C₄²×C₇₃

C₂³

yes

characteristic

C₄⋊C₈×C₇₃

—

C₄⋊C₈×C₇₃

—

C₂²⋊C₈×C₇₃

—

C₂²⋊C₈×C₇₃

—

#97×C₇₃

—

#97×C₇₃

—

C₄×C₈×C₇₃

—

C₄×C₈×C₇₃

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

—

—

—

—

—

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₂²×C₄×C₇₃

C₂×D₄

yes

C₂²×C₄×C₇₃

yes

C₂²×C₄×C₇₃

yes

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

SD₁₆

yes

—

C₂×C₈×C₇₃

Q₁₆

yes

—

C₄²×C₇₃

C₂×D₄

yes

C₄²×C₇₃

yes

C₄²×C₇₃

yes

C₄²×C₇₃

yes

C₂³×C₇₃

yes

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₇₃

C₂×Q₁₆

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

100

Dic₁₄₆

—

101

Dic₁₄₆

—

102

C₈×C₇₃

—

103

C₈×C₇₃

—

104

C₈×C₇₃

—

105

C₈×C₇₃

—

106

#10596831

—

107

#10596831

—

108

C₂²×C₇₃

—

109

C₂²×C₇₃

—

110

C₂²×C₇₃

#397

yes

characteristic

111

C₂²×C₇₃

#487

yes

characteristic

112

C₂²×C₇₃

#489

yes

characteristic

113

C₄×C₇₃

—

114

C₄×C₇₃

—

115

C₄×C₇₃

—

116

C₄×C₇₃

—

117

C₄×C₇₃

#460

yes

characteristic

118

C₄×C₇₃

#462

yes

characteristic

119

C₄×C₇₃

#483

yes

characteristic

120

C₄×C₇₃

#484

yes

characteristic

121

Dic₇₃

—

122

Dic₇₃

—

123

#10633

—

maximal, Sylow

124

C₂×C₇₃

—

125

C₂×C₇₃

—

126

C₂×C₇₃

#2072

yes

characteristic

127

C₂×C₇₃

#2081

yes

characteristic

128

C₂×C₇₃

#2082

yes

characteristic

129

#1993

—

130

#1849

—

131

#1549

—

132

#1548

—

133

#1286

—

134

#1286

—

135

#1281

D₇₃

yes

characteristic

136

C₇₃

#10633

yes

characteristic, complemented, Sylow

137

C₂×C₄⋊Q₈

—

138

#431

C₂×D₇₃

yes

characteristic

139

#431

C₂×D₇₃

yes

characteristic

140

C₂×#108

—

146

—

141

C₂×#108

—

146

—

142

#423

—

143

#423

—

144

C₂×#97

C₂×D₇₃

yes

characteristic

145

#382

—

146

#340

—

146

—

147

#340

—

146

—

148

#333

—

146

—

149

#332

—

146

—

150

C₂²×Q₈

—

146

—

151

C₂×M₁₆

—

146

—

152

C₂×M₁₆

—

146

—

153

C₂²×C₈

D₂₉₂

yes

characteristic

154

C₂²×C₈

D₂₉₂

yes

characteristic

155

C₄⋊Q₈

—

156

C₄⋊Q₈

—

146

—

157

C₄⋊Q₈

—

146

—

158

C₄⋊Q₈

—

146

—

159

C₂×C₄⋊C₄

—

146

—

160

C₂×C₄⋊C₄

—

146

—

161

C₂×C₄⋊C₄

—

146

—

162

C₂×C₄²

C₂²×D₇₃

yes

characteristic

163

#108

—

292

—

164

#108

—

292

—

165

C₄⋊C₈

—

166

C₄⋊C₈

—

167

C₄⋊C₈

—

146

—

168

C₄⋊C₈

—

146

—

169

C₄⋊C₈

—

146

—

170

C₄⋊C₈

—

146

—

171

C₂²⋊C₈

—

172

C₂²⋊C₈

—

173

#97

—

174

#97

—

175

C₄×C₈

—

176

C₄×C₈

—

177

#95

—

146

—

178

#95

—

146

—

179

C₂×Q₈

—

292

—

180

C₂×Q₈

—

584

—

181

C₂×Q₈

—

146

—

182

C₂²×C₄

—

292

—

183

C₂²×C₄

—

292

—

184

C₂²×C₄

C₂×D₂₉₂

yes

characteristic

185

C₂²×C₄

#11924028

yes

characteristic

186

C₂²×C₄

#11924028

yes

characteristic

187

M₁₆

—

292

—

188

M₁₆

—

292

—

189

M₁₆

—

292

—

190

M₁₆

—

292

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

292

—

198

C₂×C₈

—

292

—

199

C₂×C₈

#11924017

yes

—

200

C₂×C₈

Dic₂₉₂

yes

—

201

C₄⋊C₄

—

292

—

202

C₄⋊C₄

—

292

—

203

C₄⋊C₄

—

292

—

204

C₄⋊C₄

—

292

—

205

C₄⋊C₄

—

146

—

206

C₄⋊C₄

—

146

—

207

C₄²

D₄×D₇₃

yes

characteristic

208

C₄²

#11924027

yes

characteristic

209

C₄²

#11924027

yes

characteristic

210

C₄²

#11924029

yes

characteristic

211

C₂³

#14556579

yes

characteristic

212

Q₈

—

584

—

213

Q₈

—

584

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

292

—

217

C₂×C₄

—

584

—

218

C₂×C₄

—

584

—

219

C₂×C₄

—

584

—

220

C₂×C₄

—

584

—

221

C₂×C₄

#14556566

yes

characteristic

222

C₂×C₄

#14556573

yes

characteristic

223

C₂×C₄

#14556573

yes

characteristic

224

C₂×C₄

#14556575

yes

characteristic

225

C₂×C₄

#14556586

yes

characteristic

226

C₂×C₄

#14556586

yes

characteristic

227

C₂×C₄

C₂×#11924017

yes

characteristic

228

C₂×C₄

C₂×Dic₂₉₂

yes

characteristic

229

C₂×C₄

#14556619

yes

characteristic

230

C₂×C₄

#14556624

yes

characteristic

231

C₈

—

232

C₈

—

233

C₈

—

234

C₈

—

235

C₈

—

584

—

236

C₈

—

584

—

237

C₂²

—

238

C₂²

—

239

C₂²

#17988514

yes

characteristic

240

C₂²

#17988938

yes

characteristic

241

C₂²

#17988947

yes

characteristic

242

C₄

—

243

C₄

—

244

C₄

—

245

C₄

—

246

C₄

—

584

—

247

C₄

—

1168

—

248

C₄

#17988788

yes

characteristic

249

C₄

#17988798

yes

characteristic

250

C₄

#17988918

yes

characteristic

251

C₄

#17988923

yes

characteristic

252

C₂

—

253

C₂

—

254

C₂

#22611341

yes

characteristic

255

C₂

#22611390

yes

characteristic

256

C₂

#22611397

yes

characteristic

	subgroup	G/H
center	C₂²	#17988514
commutator, cosocle	C₂×C₄²×C₇₃	C₂³
Frattini	C₂×C₄²	C₂²×D₇₃
Fitting	C₇₃×#1281	C₂
socle	C₂²×C₇₃	#397
prime radical	C₂³×C₇₃	#124
hypercenter	#1281	D₇₃
hypocenter	C₇₃	#10633
LCS	G ▷ C₂×C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1281

subgroup

G/H

center

C₂²

#17988514

commutator, cosocle

C₂×C₄²×C₇₃

C₂³

Frattini

C₂×C₄²

C₂²×D₇₃

Fitting

C₇₃×#1281

C₂

C₂²×C₇₃

C₂³×C₇₃

D₇₃

C₇₃

G ▷ C₂×C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1281

N	H ≅ G/N	type
136. C₇₃	#10633	semidirect

H ≅ G/N

type

136. C₇₃

#10633

semidirect

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

subgroup	index
#22610904	2
#22610106	2
#22608615	2
#22608611	2
#22607790	2
C₇₃×#1281	2
#10633	73

subgroup

index

C₇₃×#1281

Subgroups — #32990784

Conjugacy classes of subgroups

Complements

Maximal subgroups