Group #33004409 — subgroups

Subgroups — #33004409

Order 18688.

442 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 123 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	C₂×#17988417	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#17988400	C₂	1	2	yes	maximal, complemented
3	#22611527	C₂	1	1	yes	maximal, characteristic, complemented
4	#22610842	C₂	1	2	yes	maximal, complemented
5	C₂²×D₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#14556531	C₂²	1	1	yes	characteristic
7	C₂×#14556527	C₂²	1	2	yes	—
8	#17988592	—	2	2	no	—
9	C₂×#14556508	—	2	2	no	—
10	#17988542	C₂²	1	1	yes	characteristic
11	#17988417	—	2	2	no	—
12	#17988400	—	2	4	no	—
13	#17988362	—	2	1	no	—
14	C₁₆×Dic₇₃	—	2	1	no	—
15	C₂²×D₈×C₇₃	C₂²	1	2	yes	—
16	C₂×D₁₆×C₇₃	—	2	1	no	—
17	C₂×D₁₆×C₇₃	—	2	1	no	—
18	C₂×D₁₆×C₇₃	—	2	2	no	—
19	C₂×D₁₆×C₇₃	C₄	1	4	yes	complemented
20	C₂²×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×#11924012	—	2	2	no	—
22	C₂×#11924012	D₄	1	1	yes	characteristic
23	#14556550	D₄	1	1	yes	characteristic
24	#14556531	—	2	1	no	—
25	#14556531	D₄	1	2	yes	—
26	C₂×#11924003	—	2	1	no	—
27	#14556527	—	2	2	no	—
28	#14556527	—	2	2	no	—
29	#14556512	—	4	4	no	—
30	#14556508	—	4	4	no	—
31	#14556501	—	2	1	no	—
32	C₈×Dic₇₃	—	2	1	no	—
33	C₂²×D₄×C₇₃	—	2	2	no	—
34	C₂×D₈×C₇₃	—	2	2	no	—
35	C₂×D₈×C₇₃	—	2	2	no	—
36	C₂×D₈×C₇₃	—	2	2	no	—
37	C₂×D₈×C₇₃	—	2	2	no	—
38	C₂×D₈×C₇₃	—	2	2	no	—
39	C₂×D₈×C₇₃	C₂×C₄	1	4	yes	—
40	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
41	D₁₆×C₇₃	—	2	4	no	—
42	D₁₆×C₇₃	—	2	4	no	—
43	C₂×C₁₆×C₇₃	C₂×C₄	1	2	yes	—
44	C₂×C₁₆×C₇₃	D₄	1	1	yes	characteristic
45	C₂×C₁₆×C₇₃	D₄	1	1	yes	characteristic
46	C₂×C₁₆×C₇₃	D₄	1	2	yes	—
47	#11924012	—	2	1	no	—
48	#11924012	—	4	2	no	—
49	#11924012	—	4	2	no	—
50	#11924012	D₈	1	2	yes	—
51	C₂×#10596831	—	2	1	no	—
52	C₂×#10596831	—	4	2	no	—
53	C₄⋊Dic₇₃	D₈	1	2	yes	—
54	C₂²⋊Dic₇₃	—	2	1	no	—
55	C₄×Dic₇₃	—	2	1	no	—
56	#11924003	—	2	2	no	—
57	C₂⁴×C₇₃	—	4	2	no	—
58	C₂×D₄×C₇₃	—	2	4	no	—
59	C₂×D₄×C₇₃	—	4	2	no	—
60	C₂×D₄×C₇₃	—	4	2	no	—
61	C₂×D₄×C₇₃	—	4	2	no	—
62	C₂×D₄×C₇₃	—	4	2	no	—
63	C₂×D₄×C₇₃	—	4	2	no	—
64	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
65	D₈×C₇₃	—	2	4	no	—
66	D₈×C₇₃	—	2	4	no	—
67	D₈×C₇₃	—	4	2	no	—
68	D₈×C₇₃	—	4	2	no	—
69	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
70	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
71	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
72	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
73	C₂×C₈×C₇₃	#41	1	1	yes	characteristic
74	C₂×C₈×C₇₃	#41	1	1	yes	characteristic
75	C₁₆×C₇₃	C₂²⋊C₄	1	2	yes	—
76	C₁₆×C₇₃	C₂²⋊C₄	1	2	yes	—
77	C₂³×C₇₃	—	4	4	no	—
78	C₂³×C₇₃	—	8	2	no	—
79	C₂³×C₇₃	—	8	2	no	—
80	C₂³×C₇₃	—	16	4	no	—
81	C₂³×C₇₃	#135	1	1	yes	characteristic
82	D₄×C₇₃	—	4	4	no	—
83	D₄×C₇₃	—	4	4	no	—
84	D₄×C₇₃	—	8	2	no	—
85	D₄×C₇₃	—	8	2	no	—
86	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
87	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
88	C₂×C₄×C₇₃	#127	1	1	yes	characteristic
89	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
90	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
91	C₂×C₄×C₇₃	#135	1	1	yes	characteristic
92	C₂×Dic₇₃	—	2	2	no	—
93	C₈×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
94	C₈×C₇₃	C₄×D₄	1	1	yes	characteristic
95	C₈×C₇₃	#121	1	1	yes	characteristic
96	C₈×C₇₃	#124	1	1	yes	characteristic
97	#10596831	—	2	2	no	—
98	#10596831	—	8	2	no	—
99	C₂²×C₇₃	—	2	2	no	—
100	C₂²×C₇₃	—	8	4	no	—
101	C₂²×C₇₃	—	16	4	no	—
102	C₂²×C₇₃	—	16	4	no	—
103	C₂²×C₇₃	—	16	4	no	—
104	C₂²×C₇₃	C₄×D₈	1	1	yes	characteristic
105	C₂²×C₇₃	#466	1	1	yes	characteristic
106	C₂²×C₇₃	#495	1	1	yes	characteristic
107	C₄×C₇₃	#390	1	1	yes	characteristic
108	C₄×C₇₃	C₄×D₈	1	1	yes	characteristic
109	C₄×C₇₃	#466	1	1	yes	characteristic
110	C₄×C₇₃	#493	1	1	yes	characteristic
111	Dic₇₃	—	4	2	no	—
112	#13245	—	73	1	no	maximal, Sylow
113	C₂×C₇₃	—	2	1	no	—
114	C₂×C₇₃	—	2	1	no	—
115	C₂×C₇₃	—	16	4	no	—
116	C₂×C₇₃	#1970	1	1	yes	characteristic
117	C₂×C₇₃	#2221	1	2	yes	—
118	C₂²×D₁₆	D₇₃	1	1	yes	characteristic
119	C₂×#368	—	73	1	no	—
120	C₂×#361	—	73	2	no	—
121	#2108	—	73	1	no	—
122	#1978	—	73	2	no	—
123	C₇₃	#13245	1	1	yes	characteristic, complemented, Sylow
124	C₂²×D₈	C₂×D₇₃	1	2	yes	—
125	C₂×D₁₆	—	2	1	no	—
126	C₂×D₁₆	—	2	1	no	—
127	C₂×D₁₆	—	2	2	no	—
128	C₂×D₁₆	Dic₇₃	1	4	yes	complemented
129	C₂×M₃₂	—	73	1	no	—
130	C₂²×C₁₆	C₂×D₇₃	1	1	yes	characteristic
131	C₂×#108	—	73	2	no	—
132	#418	—	146	2	no	—
133	C₂×#100	—	146	2	no	—
134	#405	—	73	1	no	—
135	#368	—	146	2	no	—
136	#361	—	146	4	no	—
137	#346	—	146	1	no	—
138	C₄×C₁₆	—	146	1	no	—
139	C₂²×D₄	—	2	2	no	—
140	C₂×D₈	—	2	2	no	—
141	C₂×D₈	—	2	2	no	—
142	C₂×D₈	—	2	2	no	—
143	C₂×D₈	—	2	2	no	—
144	C₂×D₈	—	2	2	no	—
145	C₂×D₈	C₂×Dic₇₃	1	4	yes	—
146	C₂×M₁₆	—	73	1	no	—
147	C₂×M₁₆	—	146	2	no	—
148	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
149	#117	—	73	1	no	—
150	D₁₆	—	2	4	no	—
151	D₁₆	—	2	4	no	—
152	M₃₂	—	73	2	no	—
153	M₃₂	—	146	1	no	—
154	C₂×C₁₆	—	146	1	no	—
155	C₂×C₁₆	C₂×Dic₇₃	1	2	yes	—
156	C₂×C₁₆	C₂²⋊D₇₃	1	1	yes	characteristic
157	C₂×C₁₆	C₂²⋊D₇₃	1	1	yes	characteristic
158	C₂×C₁₆	C₂²⋊D₇₃	1	2	yes	—
159	#108	—	146	2	no	—
160	#108	—	146	2	no	—
161	#102	—	292	4	no	—
162	#100	—	292	4	no	—
163	#97	—	146	1	no	—
164	C₄×C₈	—	146	1	no	—
165	C₂⁴	—	4	2	no	—
166	C₂×D₄	—	2	4	no	—
167	C₂×D₄	—	4	2	no	—
168	C₂×D₄	—	4	2	no	—
169	C₂×D₄	—	4	2	no	—
170	C₂×D₄	—	4	2	no	—
171	C₂×D₄	—	4	2	no	—
172	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
173	D₈	—	2	4	no	—
174	D₈	—	2	4	no	—
175	D₈	—	4	2	no	—
176	D₈	—	4	2	no	—
177	M₁₆	—	292	2	no	—
178	M₁₆	—	292	2	no	—
179	M₁₆	—	73	2	no	—
180	M₁₆	—	146	1	no	—
181	C₂×C₈	—	292	2	no	—
182	C₂×C₈	—	146	1	no	—
183	C₂×C₈	C₂²×Dic₇₃	1	1	yes	characteristic
184	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
185	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
186	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
187	C₂×C₈	#11924027	1	1	yes	characteristic
188	C₂×C₈	#11924027	1	1	yes	characteristic
189	C₄⋊C₄	—	73	2	no	—
190	C₂²⋊C₄	—	146	1	no	—
191	C₄²	—	146	1	no	—
192	C₁₆	—	146	2	no	—
193	C₁₆	C₂²⋊Dic₇₃	1	2	yes	—
194	C₁₆	C₂²⋊Dic₇₃	1	2	yes	—
195	C₂³	—	4	4	no	—
196	C₂³	—	8	2	no	—
197	C₂³	—	8	2	no	—
198	C₂³	—	16	4	no	—
199	C₂³	#14556610	1	1	yes	characteristic
200	D₄	—	4	4	no	—
201	D₄	—	4	4	no	—
202	D₄	—	8	2	no	—
203	D₄	—	8	2	no	—
204	C₂×C₄	—	146	2	no	—
205	C₂×C₄	D₄×Dic₇₃	1	1	yes	characteristic
206	C₂×C₄	#14556562	1	1	yes	characteristic
207	C₂×C₄	#14556587	1	1	yes	characteristic
208	C₂×C₄	D₈×D₇₃	1	1	yes	characteristic
209	C₂×C₄	D₈×D₇₃	1	1	yes	characteristic
210	C₂×C₄	#14556610	1	1	yes	characteristic
211	C₈	—	584	2	no	—
212	C₈	—	146	2	no	—
213	C₈	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
214	C₈	D₄×Dic₇₃	1	1	yes	characteristic
215	C₈	#14556562	1	1	yes	characteristic
216	C₈	#14556578	1	1	yes	characteristic
217	C₂²	—	2	2	no	—
218	C₂²	—	8	4	no	—
219	C₂²	—	16	4	no	—
220	C₂²	—	16	4	no	—
221	C₂²	—	16	4	no	—
222	C₂²	D₈×Dic₇₃	1	1	yes	characteristic
223	C₂²	#17988820	1	1	yes	characteristic
224	C₂²	#17988970	1	1	yes	characteristic
225	C₄	—	292	2	no	—
226	C₄	#17988490	1	1	yes	characteristic
227	C₄	D₈×Dic₇₃	1	1	yes	characteristic
228	C₄	#17988820	1	1	yes	characteristic
229	C₄	#17988962	1	1	yes	characteristic
230	C₂	—	2	1	no	—
231	C₂	—	2	1	no	—
232	C₂	—	16	4	no	—
233	C₂	#22610798	1	1	yes	characteristic
234	C₂	#22612048	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17988417

C₂

yes

maximal, characteristic, complemented

C₂×#17988400

C₂

yes

maximal, complemented

#22611527

C₂

yes

maximal, characteristic, complemented

#22610842

C₂

yes

maximal, complemented

C₂²×D₁₆×C₇₃

C₂

yes

maximal, characteristic

C₂×#14556531

C₂²

yes

characteristic

C₂×#14556527

C₂²

yes

—

#17988592

—

C₂×#14556508

—

#17988542

C₂²

yes

—

—

—

C₁₆×Dic₇₃

—

C₂²×D₈×C₇₃

C₂²

yes

—

C₂×D₁₆×C₇₃

—

C₂×D₁₆×C₇₃

—

C₂×D₁₆×C₇₃

—

C₂×D₁₆×C₇₃

C₄

yes

complemented

C₂²×C₁₆×C₇₃

C₂²

yes

characteristic

C₂×#11924012

—

C₂×#11924012

D₄

yes

characteristic

#14556550

D₄

yes

characteristic

#14556531

—

#14556531

D₄

yes

—

—

—

—

—

—

—

C₈×Dic₇₃

—

C₂²×D₄×C₇₃

—

C₂×D₈×C₇₃

—

C₂×D₈×C₇₃

—

C₂×D₈×C₇₃

—

C₂×D₈×C₇₃

—

C₂×D₈×C₇₃

—

C₂×D₈×C₇₃

C₂×C₄

yes

—

C₂²×C₈×C₇₃

C₂³

yes

characteristic

D₁₆×C₇₃

—

D₁₆×C₇₃

—

C₂×C₁₆×C₇₃

C₂×C₄

yes

—

C₂×C₁₆×C₇₃

D₄

yes

characteristic

C₂×C₁₆×C₇₃

D₄

yes

characteristic

C₂×C₁₆×C₇₃

D₄

yes

—

—

—

—

D₈

yes

—

C₂×#10596831

—

C₂×#10596831

—

C₄⋊Dic₇₃

D₈

yes

—

C₂²⋊Dic₇₃

—

C₄×Dic₇₃

—

#11924003

—

C₂⁴×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

D₈×C₇₃

—

D₈×C₇₃

—

D₈×C₇₃

—

D₈×C₇₃

—

C₂×C₈×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×D₄

yes

characteristic

C₂×C₈×C₇₃

C₂×D₄

yes

characteristic

C₂×C₈×C₇₃

C₂×D₄

yes

C₂×C₈×C₇₃

yes

C₂×C₈×C₇₃

yes

C₁₆×C₇₃

C₂²⋊C₄

yes

—

C₁₆×C₇₃

C₂²⋊C₄

yes

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

#135

yes

characteristic

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

C₄×D₄

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

C₂×D₈

yes

characteristic

C₂×C₄×C₇₃

C₂×D₈

yes

characteristic

C₂×C₄×C₇₃

#135

yes

characteristic

C₂×Dic₇₃

—

C₈×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₈×C₇₃

C₄×D₄

yes

C₈×C₇₃

yes

C₈×C₇₃

yes

—

—

C₂²×C₇₃

—

100

C₂²×C₇₃

—

101

C₂²×C₇₃

—

102

C₂²×C₇₃

—

103

C₂²×C₇₃

—

104

C₂²×C₇₃

C₄×D₈

yes

characteristic

105

C₂²×C₇₃

#466

yes

characteristic

106

C₂²×C₇₃

#495

yes

characteristic

107

C₄×C₇₃

#390

yes

characteristic

108

C₄×C₇₃

C₄×D₈

yes

characteristic

109

C₄×C₇₃

#466

yes

characteristic

110

C₄×C₇₃

#493

yes

characteristic

111

Dic₇₃

—

112

#13245

—

maximal, Sylow

113

C₂×C₇₃

—

114

C₂×C₇₃

—

115

C₂×C₇₃

—

116

C₂×C₇₃

#1970

yes

characteristic

117

C₂×C₇₃

#2221

yes

—

118

C₂²×D₁₆

D₇₃

yes

characteristic

119

C₂×#368

—

120

C₂×#361

—

121

#2108

—

122

#1978

—

123

C₇₃

#13245

yes

characteristic, complemented, Sylow

124

C₂²×D₈

C₂×D₇₃

yes

—

125

C₂×D₁₆

—

126

C₂×D₁₆

—

127

C₂×D₁₆

—

128

C₂×D₁₆

Dic₇₃

yes

complemented

129

C₂×M₃₂

—

130

C₂²×C₁₆

C₂×D₇₃

yes

characteristic

131

C₂×#108

—

132

#418

—

146

—

133

C₂×#100

—

146

—

134

#405

—

135

#368

—

146

—

136

#361

—

146

—

137

#346

—

146

—

138

C₄×C₁₆

—

146

—

139

C₂²×D₄

—

140

C₂×D₈

—

141

C₂×D₈

—

142

C₂×D₈

—

143

C₂×D₈

—

144

C₂×D₈

—

145

C₂×D₈

C₂×Dic₇₃

yes

—

146

C₂×M₁₆

—

147

C₂×M₁₆

—

146

—

148

C₂²×C₈

C₂²×D₇₃

yes

characteristic

149

#117

—

150

D₁₆

—

151

D₁₆

—

152

M₃₂

—

153

M₃₂

—

146

—

154

C₂×C₁₆

—

146

—

155

C₂×C₁₆

C₂×Dic₇₃

yes

—

156

C₂×C₁₆

C₂²⋊D₇₃

yes

characteristic

157

C₂×C₁₆

C₂²⋊D₇₃

yes

characteristic

158

C₂×C₁₆

C₂²⋊D₇₃

yes

—

159

#108

—

146

—

160

#108

—

146

—

161

#102

—

292

—

162

#100

—

292

—

163

#97

—

146

—

164

C₄×C₈

—

146

—

165

C₂⁴

—

166

C₂×D₄

—

167

C₂×D₄

—

168

C₂×D₄

—

169

C₂×D₄

—

170

C₂×D₄

—

171

C₂×D₄

—

172

C₂²×C₄

D₄×D₇₃

yes

characteristic

173

D₈

—

174

D₈

—

175

D₈

—

176

D₈

—

177

M₁₆

—

292

—

178

M₁₆

—

292

—

179

M₁₆

—

180

M₁₆

—

146

—

181

C₂×C₈

—

292

—

182

C₂×C₈

—

146

—

183

C₂×C₈

C₂²×Dic₇₃

yes

characteristic

184

C₂×C₈

D₄×D₇₃

yes

characteristic

185

C₂×C₈

C₂×C₂²⋊D₇₃

yes

characteristic

186

C₂×C₈

C₂×C₂²⋊D₇₃

yes

characteristic

187

C₂×C₈

#11924027

yes

characteristic

188

C₂×C₈

#11924027

yes

characteristic

189

C₄⋊C₄

—

190

C₂²⋊C₄

—

146

—

191

C₄²

—

146

—

192

C₁₆

—

146

—

193

C₁₆

C₂²⋊Dic₇₃

yes

—

194

C₁₆

C₂²⋊Dic₇₃

yes

—

195

C₂³

—

196

C₂³

—

197

C₂³

—

198

C₂³

—

199

C₂³

#14556610

yes

characteristic

200

D₄

—

201

D₄

—

202

D₄

—

203

D₄

—

204

C₂×C₄

—

146

—

205

C₂×C₄

D₄×Dic₇₃

yes

characteristic

206

C₂×C₄

#14556562

yes

characteristic

207

C₂×C₄

#14556587

yes

characteristic

208

C₂×C₄

D₈×D₇₃

yes

characteristic

209

C₂×C₄

D₈×D₇₃

yes

characteristic

210

C₂×C₄

#14556610

yes

characteristic

211

C₈

—

584

—

212

C₈

—

146

—

213

C₈

C₂×C₂²⋊Dic₇₃

yes

characteristic

214

C₈

D₄×Dic₇₃

yes

characteristic

215

C₈

#14556562

yes

characteristic

216

C₈

#14556578

yes

characteristic

217

C₂²

—

218

C₂²

—

219

C₂²

—

220

C₂²

—

221

C₂²

—

222

C₂²

D₈×Dic₇₃

yes

characteristic

223

C₂²

#17988820

yes

characteristic

224

C₂²

#17988970

yes

characteristic

225

C₄

—

292

—

226

C₄

#17988490

yes

characteristic

227

C₄

D₈×Dic₇₃

yes

characteristic

228

C₄

#17988820

yes

characteristic

229

C₄

#17988962

yes

characteristic

230

C₂

—

231

C₂

—

232

C₂

—

233

C₂

#22610798

yes

characteristic

234

C₂

#22612048

yes

—

	subgroup	G/H
center	C₂²	#17988820
commutator	C₂×C₈×C₇₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₇₃
Fitting, prime radical	C₂²×D₁₆×C₇₃	C₂
socle	C₂²×C₇₃	#466
cosocle	C₂²×C₈×C₇₃	C₂³
hypercenter	C₂²×D₁₆	D₇₃
hypocenter	C₇₃	#13245
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×D₁₆

subgroup

G/H

center

C₂²

#17988820

commutator

C₂×C₈×C₇₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₇₃

Fitting, prime radical

C₂²×D₁₆×C₇₃

C₂

socle

C₂²×C₇₃

#466

cosocle

C₂²×C₈×C₇₃

C₂³

hypercenter

C₂²×D₁₆

D₇₃

hypocenter

C₇₃

#13245

LCS

G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×D₁₆

N	H ≅ G/N	type
1. C₂×#17988417	C₂	semidirect
2. C₂×#17988400	C₂	semidirect
3. #22611527	C₂	semidirect
4. #22610842	C₂	semidirect
19. C₂×D₁₆×C₇₃	C₄	semidirect
123. C₇₃	#13245	semidirect
128. C₂×D₁₆	Dic₇₃	semidirect

H ≅ G/N

type

1. C₂×#17988417

C₂

semidirect

2. C₂×#17988400

C₂

semidirect

3. #22611527

C₂

semidirect

4. #22610842

C₂

semidirect

19. C₂×D₁₆×C₇₃

C₄

semidirect

123. C₇₃

#13245

semidirect

128. C₂×D₁₆

Dic₇₃

semidirect

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

subgroup	index
C₂×#17988417	2
C₂×#17988400	2
#22611527	2
#22610842	2
C₂²×D₁₆×C₇₃	2
#13245	73

subgroup

index

C₂²×D₁₆×C₇₃

Subgroups — #33004409

Conjugacy classes of subgroups

Complements

Maximal subgroups