Group #32983402 — subgroups

Subgroups — #32983402

Order 18688.

450 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 115 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	#22619016	C₂	1	1	yes	maximal, characteristic
2	#22615143	C₂	1	1	yes	maximal, characteristic
3	#22608617	C₂	1	2	yes	maximal
4	#22607832	C₂	1	2	yes	maximal
5	C₇₃×#1801	C₂	1	1	yes	maximal, characteristic
6	C₂×#14556591	C₂²	1	1	yes	characteristic
7	#17988718	—	2	4	no	—
8	#17988644	—	2	2	no	—
9	#17988640	C₂²	1	2	yes	—
10	#17988526	C₄	1	4	yes	—
11	#17988494	—	2	1	no	—
12	#17988493	—	2	2	no	—
13	#17988452	—	2	1	no	—
14	C₄×C₄⋊Dic₇₃	C₂²	1	1	yes	characteristic
15	#17988332	—	2	4	no	—
16	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
17	#423×C₇₃	C₂²	1	2	yes	—
18	C₂×#101×C₇₃	—	2	1	no	—
19	#343×C₇₃	—	2	1	no	—
20	C₂²×Dic₁₄₆	—	2	1	no	—
21	#14556591	—	2	2	no	—
22	#14556591	—	2	2	no	—
23	C₂×C₄⋊Dic₇₃	—	2	1	no	—
24	C₂×C₄⋊Dic₇₃	—	2	1	no	—
25	C₂×C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
26	C₂×C₄×Dic₇₃	—	2	1	no	—
27	C₄⋊#10596831	—	2	4	no	—
28	C₄⋊#10596831	D₄	1	4	yes	—
29	C₂²⋊#10596831	—	2	2	no	—
30	#14556502	—	2	4	no	—
31	C₄×#10596831	—	2	2	no	—
32	#14556498	—	2	4	no	—
33	#14556498	—	2	4	no	—
34	#14556498	C₂×C₄	1	2	yes	—
35	C₂²×Q₈×C₇₃	D₄	1	1	yes	characteristic
36	C₂×M₁₆×C₇₃	—	2	2	no	—
37	C₄×Q₈×C₇₃	—	2	2	no	—
38	C₄×Q₈×C₇₃	—	2	2	no	—
39	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
40	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₇₃	D₄	1	2	yes	—
42	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
43	C₄⋊C₈×C₇₃	—	2	2	no	—
44	C₄⋊C₈×C₇₃	—	2	2	no	—
45	#101×C₇₃	—	4	2	no	—
46	C₂×Dic₁₄₆	—	4	4	no	—
47	C₂×Dic₁₄₆	—	4	1	no	—
48	C₂×Dic₁₄₆	—	4	1	no	—
49	C₂²×Dic₇₃	—	2	2	no	—
50	C₂²×Dic₇₃	—	2	2	no	—
51	C₂×#10596831	—	2	4	no	—
52	C₄⋊Dic₇₃	—	2	4	no	—
53	C₄⋊Dic₇₃	—	4	2	no	—
54	C₄⋊Dic₇₃	—	4	2	no	—
55	C₄×Dic₇₃	—	4	1	no	—
56	C₄×Dic₇₃	—	4	1	no	—
57	C₂×Q₈×C₇₃	—	2	2	no	—
58	C₂×Q₈×C₇₃	—	2	1	no	—
59	C₂×Q₈×C₇₃	—	2	2	no	—
60	C₂×Q₈×C₇₃	—	2	1	no	—
61	C₂²×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
62	C₂²×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
63	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
66	M₁₆×C₇₃	—	4	2	no	—
67	M₁₆×C₇₃	—	4	2	no	—
68	C₂×C₈×C₇₃	—	4	2	no	—
69	C₄⋊C₄×C₇₃	—	2	4	no	—
70	C₄⋊C₄×C₇₃	—	2	2	no	—
71	C₄²×C₇₃	—	2	2	no	—
72	C₄²×C₇₃	—	2	2	no	—
73	C₄²×C₇₃	C₂×D₄	1	2	yes	—
74	C₄²×C₇₃	#41	1	2	yes	—
75	C₂³×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
76	Q₈×C₇₃	—	4	2	no	—
77	Q₈×C₇₃	—	4	2	no	—
78	C₂×C₄×C₇₃	—	2	2	no	—
79	C₂×C₄×C₇₃	—	2	2	no	—
80	C₂×C₄×C₇₃	—	2	2	no	—
81	C₂×C₄×C₇₃	—	2	2	no	—
82	C₂×C₄×C₇₃	—	2	2	no	—
83	C₂×C₄×C₇₃	—	4	1	no	—
84	C₂×C₄×C₇₃	—	4	2	no	—
85	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
86	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
87	C₂×C₄×C₇₃	#121	1	2	yes	—
88	C₂×C₄×C₇₃	#123	1	1	yes	characteristic
89	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
90	C₂×C₄×C₇₃	#137	1	2	yes	—
91	C₂×C₄×C₇₃	#137	1	1	yes	characteristic
92	C₂×Dic₇₃	—	4	2	no	—
93	C₂×Dic₇₃	—	4	2	no	—
94	C₂×Dic₇₃	—	4	4	no	—
95	C₂×Dic₇₃	—	4	2	no	—
96	C₂×Dic₇₃	—	4	2	no	—
97	Dic₁₄₆	—	8	2	no	—
98	Dic₁₄₆	—	8	2	no	—
99	C₈×C₇₃	—	8	2	no	—
100	#10596831	—	4	4	no	—
101	C₂²×C₇₃	—	2	1	no	—
102	C₂²×C₇₃	—	2	1	no	—
103	C₂²×C₇₃	#386	1	1	yes	characteristic
104	C₂²×C₇₃	#417	1	1	yes	characteristic
105	C₂²×C₇₃	#419	1	1	yes	characteristic
106	C₄×C₇₃	—	2	1	no	—
107	C₄×C₇₃	—	2	2	no	—
108	C₄×C₇₃	—	4	2	no	—
109	C₄×C₇₃	—	4	2	no	—
110	C₄×C₇₃	#454	1	2	yes	—
111	C₄×C₇₃	#468	1	2	yes	—
112	C₄×C₇₃	#470	1	2	yes	—
113	Dic₇₃	—	8	2	no	—
114	Dic₇₃	—	8	2	no	—
115	#9404	—	73	1	no	maximal, Sylow
116	C₂×C₇₃	—	2	1	no	—
117	C₂×C₇₃	—	2	1	no	—
118	C₂×C₇₃	#1888	1	1	yes	characteristic
119	C₂×C₇₃	#1894	1	1	yes	characteristic
120	C₂×C₇₃	#1915	1	1	yes	characteristic
121	#2983	—	73	1	no	—
122	#2568	—	73	1	no	—
123	#1801	D₇₃	1	1	yes	characteristic
124	#1549	—	73	2	no	—
125	#1303	—	73	2	no	—
126	C₇₃	#9404	1	1	yes	characteristic, complemented, Sylow
127	C₂×C₄⋊Q₈	—	73	1	no	—
128	C₂×C₄×Q₈	C₂×D₇₃	1	1	yes	characteristic
129	#446	—	146	4	no	—
130	#432	—	146	2	no	—
131	#431	—	73	2	no	—
132	#423	C₂×D₇₃	1	2	yes	—
133	C₂×#101	—	2	1	no	—
134	#400	—	73	4	no	—
135	#391	—	146	1	no	—
136	#391	—	146	2	no	—
137	#382	—	146	1	no	—
138	C₄×C₄⋊C₄	—	73	1	no	—
139	#343	—	2	1	no	—
140	#332	—	146	4	no	—
141	C₂²×Q₈	—	146	1	no	—
142	C₂²×Q₈	C₂²⋊D₇₃	1	1	yes	characteristic
143	C₂×M₁₆	—	2	2	no	—
144	C₄⋊Q₈	—	146	2	no	—
145	C₄⋊Q₈	—	146	2	no	—
146	C₄×Q₈	—	2	2	no	—
147	C₄×Q₈	—	2	2	no	—
148	C₂×C₄⋊C₄	—	73	2	no	—
149	C₂×C₄⋊C₄	—	146	1	no	—
150	C₂×C₄⋊C₄	—	146	1	no	—
151	C₂×C₄⋊C₄	C₄×D₇₃	1	2	yes	—
152	C₂×C₄⋊C₄	C₂²⋊D₇₃	1	1	yes	characteristic
153	C₂×C₄²	—	146	1	no	—
154	C₂×C₄²	D₂₉₂	1	2	yes	—
155	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
156	C₄⋊C₈	—	2	2	no	—
157	C₄⋊C₈	—	2	2	no	—
158	C₄⋊C₈	—	73	4	no	—
159	C₄⋊C₈	—	146	4	no	—
160	#101	—	4	2	no	—
161	C₂²⋊C₈	—	146	2	no	—
162	#97	—	146	4	no	—
163	C₄×C₈	—	146	2	no	—
164	#95	—	73	2	no	—
165	#95	—	146	4	no	—
166	#95	—	146	4	no	—
167	C₂×Q₈	—	2	2	no	—
168	C₂×Q₈	—	2	1	no	—
169	C₂×Q₈	—	2	2	no	—
170	C₂×Q₈	—	2	1	no	—
171	C₂×Q₈	—	292	4	no	—
172	C₂×Q₈	—	292	1	no	—
173	C₂×Q₈	—	292	1	no	—
174	C₂²×C₄	—	146	2	no	—
175	C₂²×C₄	—	146	2	no	—
176	C₂²×C₄	#11924005	1	2	yes	—
177	C₂²×C₄	#11924005	1	2	yes	—
178	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
179	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
180	C₂²×C₄	C₂×D₂₉₂	1	1	yes	characteristic
181	M₁₆	—	4	2	no	—
182	M₁₆	—	4	2	no	—
183	C₂×C₈	—	4	2	no	—
184	C₂×C₈	—	146	4	no	—
185	C₄⋊C₄	—	2	4	no	—
186	C₄⋊C₄	—	2	2	no	—
187	C₄⋊C₄	—	292	2	no	—
188	C₄⋊C₄	—	292	2	no	—
189	C₄⋊C₄	—	146	4	no	—
190	C₄²	—	2	2	no	—
191	C₄²	—	2	2	no	—
192	C₄²	—	292	1	no	—
193	C₄²	—	292	1	no	—
194	C₄²	D₄×D₇₃	1	2	yes	—
195	C₄²	#11924027	1	2	yes	—
196	C₂³	C₂×#11924005	1	1	yes	characteristic
197	Q₈	—	4	2	no	—
198	Q₈	—	4	2	no	—
199	Q₈	—	584	2	no	—
200	Q₈	—	584	2	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	4	2	no	—
208	C₂×C₄	—	292	2	no	—
209	C₂×C₄	—	292	4	no	—
210	C₂×C₄	—	292	2	no	—
211	C₂×C₄	—	292	2	no	—
212	C₂×C₄	—	292	2	no	—
213	C₂×C₄	#14556551	1	2	yes	—
214	C₂×C₄	#14556561	1	1	yes	characteristic
215	C₂×C₄	#14556563	1	2	yes	—
216	C₂×C₄	#14556575	1	1	yes	characteristic
217	C₂×C₄	#14556617	1	1	yes	characteristic
218	C₂×C₄	#14556621	1	2	yes	—
219	C₂×C₄	#14556622	1	1	yes	characteristic
220	C₈	—	8	2	no	—
221	C₈	—	292	4	no	—
222	C₂²	—	2	1	no	—
223	C₂²	—	2	1	no	—
224	C₂²	#17988464	1	1	yes	characteristic
225	C₂²	#17988586	1	1	yes	characteristic
226	C₂²	#17988595	1	1	yes	characteristic
227	C₄	—	2	2	no	—
228	C₄	—	2	1	no	—
229	C₄	—	4	2	no	—
230	C₄	—	4	2	no	—
231	C₄	—	584	2	no	—
232	C₄	—	584	2	no	—
233	C₄	#17988762	1	2	yes	—
234	C₄	#17988831	1	2	yes	—
235	C₄	#17988843	1	2	yes	—
236	C₂	—	2	1	no	—
237	C₂	—	2	1	no	—
238	C₂	#22610332	1	1	yes	characteristic
239	C₂	#22610362	1	1	yes	characteristic
240	C₂	#22610481	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22619016

C₂

yes

maximal, characteristic

#22615143

C₂

yes

maximal, characteristic

#22608617

C₂

yes

maximal

#22607832

C₂

yes

maximal

C₇₃×#1801

C₂

yes

maximal, characteristic

C₂×#14556591

C₂²

yes

—

—

C₂²

yes

—

#17988526

C₄

yes

—

#17988494

—

#17988493

—

#17988452

—

C₄×C₄⋊Dic₇₃

C₂²

yes

characteristic

#17988332

—

C₂×C₄×Q₈×C₇₃

C₂²

yes

characteristic

#423×C₇₃

C₂²

yes

—

C₂×#101×C₇₃

—

#343×C₇₃

—

C₂²×Dic₁₄₆

—

#14556591

—

#14556591

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

C₂×C₄

yes

—

C₂×C₄×Dic₇₃

—

C₄⋊#10596831

—

C₄⋊#10596831

D₄

yes

—

—

—

—

—

—

C₂×C₄

yes

—

C₂²×Q₈×C₇₃

D₄

yes

characteristic

C₂×M₁₆×C₇₃

—

C₄×Q₈×C₇₃

—

C₄×Q₈×C₇₃

—

C₂×C₄⋊C₄×C₇₃

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₇₃

D₄

yes

characteristic

C₂×C₄²×C₇₃

D₄

yes

—

C₂×C₄²×C₇₃

C₂³

yes

characteristic

C₄⋊C₈×C₇₃

—

C₄⋊C₈×C₇₃

—

#101×C₇₃

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂²×C₄×C₇₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

M₁₆×C₇₃

—

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

C₂×D₄

yes

—

C₄²×C₇₃

#41

yes

—

C₂³×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₄×D₄

yes

—

C₂×C₄×C₇₃

#120

yes

characteristic

C₂×C₄×C₇₃

#121

yes

—

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

—

C₂×C₄×C₇₃

#137

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

—

100

#10596831

—

101

C₂²×C₇₃

—

102

C₂²×C₇₃

—

103

C₂²×C₇₃

#386

yes

characteristic

104

C₂²×C₇₃

#417

yes

characteristic

105

C₂²×C₇₃

#419

yes

characteristic

106

C₄×C₇₃

—

107

C₄×C₇₃

—

108

C₄×C₇₃

—

109

C₄×C₇₃

—

110

C₄×C₇₃

#454

yes

—

111

C₄×C₇₃

#468

yes

—

112

C₄×C₇₃

#470

yes

—

113

Dic₇₃

—

114

Dic₇₃

—

115

#9404

—

maximal, Sylow

116

C₂×C₇₃

—

117

C₂×C₇₃

—

118

C₂×C₇₃

#1888

yes

characteristic

119

C₂×C₇₃

#1894

yes

characteristic

120

C₂×C₇₃

#1915

yes

characteristic

121

#2983

—

122

#2568

—

123

#1801

D₇₃

yes

characteristic

124

#1549

—

125

#1303

—

126

C₇₃

#9404

yes

characteristic, complemented, Sylow

127

C₂×C₄⋊Q₈

—

128

C₂×C₄×Q₈

C₂×D₇₃

yes

characteristic

129

#446

—

146

—

130

#432

—

146

—

131

#431

—

132

#423

C₂×D₇₃

yes

—

133

C₂×#101

—

134

#400

—

135

#391

—

146

—

136

#391

—

146

—

137

#382

—

146

—

138

C₄×C₄⋊C₄

—

139

#343

—

140

#332

—

146

—

141

C₂²×Q₈

—

146

—

142

C₂²×Q₈

C₂²⋊D₇₃

yes

characteristic

143

C₂×M₁₆

—

144

C₄⋊Q₈

—

146

—

145

C₄⋊Q₈

—

146

—

146

C₄×Q₈

—

147

C₄×Q₈

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

—

146

—

150

C₂×C₄⋊C₄

—

146

—

151

C₂×C₄⋊C₄

C₄×D₇₃

yes

—

152

C₂×C₄⋊C₄

C₂²⋊D₇₃

yes

characteristic

153

C₂×C₄²

—

146

—

154

C₂×C₄²

D₂₉₂

yes

—

155

C₂×C₄²

C₂²×D₇₃

yes

characteristic

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

146

—

160

#101

—

161

C₂²⋊C₈

—

146

—

162

#97

—

146

—

163

C₄×C₈

—

146

—

164

#95

—

165

#95

—

146

—

166

#95

—

146

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

—

292

—

172

C₂×Q₈

—

292

—

173

C₂×Q₈

—

292

—

174

C₂²×C₄

—

146

—

175

C₂²×C₄

—

146

—

176

C₂²×C₄

#11924005

yes

—

177

C₂²×C₄

#11924005

yes

—

178

C₂²×C₄

C₂×C₄×D₇₃

yes

characteristic

179

C₂²×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

180

C₂²×C₄

C₂×D₂₉₂

yes

characteristic

181

M₁₆

—

182

M₁₆

—

183

C₂×C₈

—

184

C₂×C₈

—

146

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

292

—

188

C₄⋊C₄

—

292

—

189

C₄⋊C₄

—

146

—

190

C₄²

—

191

C₄²

—

192

C₄²

—

292

—

193

C₄²

—

292

—

194

C₄²

D₄×D₇₃

yes

—

195

C₄²

#11924027

yes

—

196

C₂³

C₂×#11924005

yes

characteristic

197

Q₈

—

198

Q₈

—

199

Q₈

—

584

—

200

Q₈

—

584

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

292

—

209

C₂×C₄

—

292

—

210

C₂×C₄

—

292

—

211

C₂×C₄

—

292

—

212

C₂×C₄

—

292

—

213

C₂×C₄

#14556551

yes

—

214

C₂×C₄

#14556561

yes

characteristic

215

C₂×C₄

#14556563

yes

—

216

C₂×C₄

#14556575

yes

characteristic

217

C₂×C₄

#14556617

yes

characteristic

218

C₂×C₄

#14556621

yes

—

219

C₂×C₄

#14556622

yes

characteristic

220

C₈

—

221

C₈

—

292

—

222

C₂²

—

223

C₂²

—

224

C₂²

#17988464

yes

characteristic

225

C₂²

#17988586

yes

characteristic

226

C₂²

#17988595

yes

characteristic

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

584

—

232

C₄

—

584

—

233

C₄

#17988762

yes

—

234

C₄

#17988831

yes

—

235

C₄

#17988843

yes

—

236

C₂

—

237

C₂

—

238

C₂

#22610332

yes

characteristic

239

C₂

#22610362

yes

characteristic

240

C₂

#22610481

yes

characteristic

	subgroup	G/H
center	C₂²	#17988464
commutator	C₂²×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₃
Fitting	C₇₃×#1801	C₂
socle	C₂²×C₇₃	#386
prime radical	C₂³×C₇₃	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₇₃	C₂³
hypercenter	#1801	D₇₃
hypocenter	C₇₃	#9404
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1801

subgroup

G/H

center

C₂²

#17988464

commutator

C₂²×C₄×C₇₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₃

Fitting

C₇₃×#1801

C₂

socle

C₂²×C₇₃

#386

prime radical

C₂³×C₇₃

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₇₃

C₂³

D₇₃

C₇₃

G ▷ C₂²×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1801

N	H ≅ G/N	type
126. C₇₃	#9404	semidirect

H ≅ G/N

type

126. C₇₃

#9404

semidirect

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

subgroup	index
#22619016	2
#22615143	2
#22608617	2
#22607832	2
C₇₃×#1801	2
#9404	73

subgroup

index

C₇₃×#1801

Subgroups — #32983402

Conjugacy classes of subgroups

Complements

Maximal subgroups