Group #33004383 — subgroups

Subgroups — #33004383

Order 18688.

430 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 139 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	C₂²×Dic₅₈₄	C₂	1	1	yes	maximal, characteristic
2	C₂×#17988415	C₂	1	1	yes	maximal, characteristic
3	C₂×#17988392	C₂	1	2	yes	maximal
4	#22610792	C₂	1	2	yes	maximal
5	C₂×#346×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₂₉₂	C₂²	1	2	yes	—
7	C₂×Dic₅₈₄	—	2	2	no	—
8	C₂×Dic₅₈₄	—	2	2	no	—
9	C₂×Dic₅₈₄	C₄	1	4	yes	complemented
10	C₂×#14556525	C₂²	1	2	yes	—
11	C₂×#14556516	—	2	2	no	—
12	#17988493	—	2	2	no	—
13	#17988415	—	2	2	no	—
14	#17988392	—	2	4	no	—
15	C₂²×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
16	C₂²×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
18	#346×C₇₃	—	2	2	no	—
19	C₂²×Dic₁₄₆	—	2	2	no	—
20	C₂×Dic₂₉₂	—	2	2	no	—
21	C₂×Dic₂₉₂	—	2	2	no	—
22	C₂×Dic₂₉₂	—	2	2	no	—
23	C₂×Dic₂₉₂	—	2	2	no	—
24	C₂×Dic₂₉₂	—	2	2	no	—
25	C₂×Dic₂₉₂	C₂×C₄	1	4	yes	—
26	C₂×C₄⋊Dic₇₃	—	2	2	no	—
27	Dic₅₈₄	—	2	8	no	—
28	#14556525	—	2	2	no	—
29	#14556525	—	2	2	no	—
30	#14556516	—	4	4	no	—
31	#14556498	—	4	4	no	—
32	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
33	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
34	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
35	C₂×C₁₆×C₇₃	—	2	1	no	—
36	C₂×C₁₆×C₇₃	—	2	1	no	—
37	C₂×C₁₆×C₇₃	C₂×C₄	1	2	yes	—
38	C₂×C₁₆×C₇₃	D₄	1	2	yes	—
39	C₂×C₁₆×C₇₃	D₄	1	2	yes	—
40	C₂×C₁₆×C₇₃	D₄	1	2	yes	—
41	C₄×C₈×C₇₃	—	2	1	no	—
42	C₄×C₈×C₇₃	—	2	1	no	—
43	C₂×Dic₁₄₆	—	2	4	no	—
44	C₂×Dic₁₄₆	—	4	2	no	—
45	C₂×Dic₁₄₆	—	4	2	no	—
46	C₂×Dic₁₄₆	—	4	2	no	—
47	C₂×Dic₁₄₆	—	4	2	no	—
48	C₂×Dic₁₄₆	—	4	2	no	—
49	C₂²×Dic₇₃	—	4	2	no	—
50	C₂²×Dic₇₃	—	4	2	no	—
51	Dic₂₉₂	—	2	4	no	—
52	Dic₂₉₂	—	2	4	no	—
53	Dic₂₉₂	—	4	2	no	—
54	Dic₂₉₂	—	4	2	no	—
55	C₄⋊Dic₇₃	—	4	2	no	—
56	C₄⋊Dic₇₃	—	4	2	no	—
57	C₂²×C₄×C₇₃	D₈	1	2	yes	—
58	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
59	C₂×C₈×C₇₃	—	2	1	no	—
60	C₂×C₈×C₇₃	—	2	1	no	—
61	C₂×C₈×C₇₃	D₈	1	2	yes	—
62	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
63	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
64	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
65	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
66	C₂×C₈×C₇₃	#41	1	1	yes	characteristic
67	C₂×C₈×C₇₃	#41	1	1	yes	characteristic
68	C₄²×C₇₃	—	2	1	no	—
69	C₄²×C₇₃	—	2	1	no	—
70	C₁₆×C₇₃	—	2	2	no	—
71	C₁₆×C₇₃	C₂²⋊C₄	1	4	yes	—
72	C₂³×C₇₃	C₂×D₈	1	1	yes	characteristic
73	C₂×C₄×C₇₃	—	2	2	no	—
74	C₂×C₄×C₇₃	—	2	4	no	—
75	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
76	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
77	C₂×C₄×C₇₃	#127	1	1	yes	characteristic
78	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
79	C₂×C₄×C₇₃	#135	1	1	yes	characteristic
80	C₂×C₄×C₇₃	#135	1	1	yes	characteristic
81	C₂×Dic₇₃	—	4	4	no	—
82	C₂×Dic₇₃	—	8	2	no	—
83	C₂×Dic₇₃	—	8	2	no	—
84	C₂×Dic₇₃	—	8	2	no	—
85	C₂×Dic₇₃	—	8	4	no	—
86	Dic₁₄₆	—	4	4	no	—
87	Dic₁₄₆	—	4	4	no	—
88	Dic₁₄₆	—	8	2	no	—
89	Dic₁₄₆	—	8	2	no	—
90	C₈×C₇₃	—	2	2	no	—
91	C₈×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
92	C₈×C₇₃	C₄×D₄	1	1	yes	characteristic
93	C₈×C₇₃	#121	1	1	yes	characteristic
94	C₈×C₇₃	#124	1	1	yes	characteristic
95	C₂²×C₇₃	C₄×D₈	1	1	yes	characteristic
96	C₂²×C₇₃	#466	1	1	yes	characteristic
97	C₂²×C₇₃	#493	1	1	yes	characteristic
98	C₂²×C₇₃	#510	1	4	yes	—
99	C₄×C₇₃	—	4	2	no	—
100	C₄×C₇₃	#390	1	1	yes	characteristic
101	C₄×C₇₃	C₄×D₈	1	1	yes	characteristic
102	C₄×C₇₃	#466	1	1	yes	characteristic
103	C₄×C₇₃	#495	1	1	yes	characteristic
104	Dic₇₃	—	8	4	no	—
105	Dic₇₃	—	16	2	no	—
106	#13240	—	73	1	no	maximal, Sylow
107	C₂×C₇₃	#1970	1	1	yes	characteristic
108	C₂×C₇₃	#2176	1	2	yes	—
109	C₂×C₇₃	#2219	1	2	yes	—
110	C₂×C₇₃	#2251	1	2	yes	—
111	C₂²×Q₃₂	—	73	1	no	—
112	C₂×#367	—	73	1	no	—
113	C₂×#358	—	73	2	no	—
114	C₂×#346	D₇₃	1	1	yes	characteristic
115	#1969	—	73	2	no	—
116	C₇₃	#13240	1	1	yes	characteristic, complemented, Sylow
117	C₂²×Q₁₆	—	73	2	no	—
118	C₂×Q₃₂	—	73	4	no	—
119	C₂×Q₃₂	—	146	2	no	—
120	C₂×Q₃₂	—	146	2	no	—
121	C₂²×C₁₆	C₂×D₇₃	1	1	yes	characteristic
122	C₂²×C₁₆	C₂×D₇₃	1	1	yes	characteristic
123	C₂×#107	—	73	2	no	—
124	C₂×#103	—	146	2	no	—
125	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
126	#391	—	146	2	no	—
127	#367	—	146	2	no	—
128	#358	—	146	4	no	—
129	#346	—	2	2	no	—
130	C₂²×Q₈	—	146	2	no	—
131	C₂×Q₁₆	—	73	4	no	—
132	C₂×Q₁₆	—	146	2	no	—
133	C₂×Q₁₆	—	146	2	no	—
134	C₂×Q₁₆	—	146	2	no	—
135	C₂×Q₁₆	—	146	2	no	—
136	C₂×Q₁₆	—	146	2	no	—
137	C₂²×C₈	D₂₉₂	1	1	yes	characteristic
138	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
139	C₂×C₄⋊C₄	—	146	2	no	—
140	C₂×C₄²	D₂₉₂	1	1	yes	characteristic
141	Q₃₂	—	146	8	no	—
142	C₂×C₁₆	—	2	1	no	—
143	C₂×C₁₆	—	2	1	no	—
144	C₂×C₁₆	C₄×D₇₃	1	2	yes	—
145	C₂×C₁₆	D₂₉₂	1	2	yes	—
146	C₂×C₁₆	D₂₉₂	1	2	yes	—
147	C₂×C₁₆	C₂²⋊D₇₃	1	2	yes	—
148	#107	—	146	2	no	—
149	#107	—	146	2	no	—
150	#103	—	292	4	no	—
151	C₄×C₈	—	2	1	no	—
152	C₄×C₈	—	2	1	no	—
153	#95	—	292	4	no	—
154	C₂×Q₈	—	292	2	no	—
155	C₂×Q₈	—	292	2	no	—
156	C₂×Q₈	—	292	2	no	—
157	C₂×Q₈	—	292	2	no	—
158	C₂×Q₈	—	292	2	no	—
159	C₂×Q₈	—	146	4	no	—
160	C₂²×C₄	—	292	2	no	—
161	C₂²×C₄	—	292	2	no	—
162	C₂²×C₄	D₅₈₄	1	2	yes	—
163	C₂²×C₄	C₂×D₂₉₂	1	1	yes	characteristic
164	Q₁₆	—	292	2	no	—
165	Q₁₆	—	292	2	no	—
166	Q₁₆	—	146	4	no	—
167	Q₁₆	—	146	4	no	—
168	C₂×C₈	—	2	1	no	—
169	C₂×C₈	—	2	1	no	—
170	C₂×C₈	D₅₈₄	1	2	yes	—
171	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
172	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
173	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
174	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
175	C₂×C₈	#11924028	1	1	yes	characteristic
176	C₂×C₈	#11924028	1	1	yes	characteristic
177	C₄⋊C₄	—	292	2	no	—
178	C₄⋊C₄	—	292	2	no	—
179	C₄²	—	2	1	no	—
180	C₄²	—	2	1	no	—
181	C₁₆	—	2	2	no	—
182	C₁₆	#11924005	1	4	yes	—
183	C₂³	C₂×D₅₈₄	1	1	yes	characteristic
184	Q₈	—	292	4	no	—
185	Q₈	—	292	4	no	—
186	Q₈	—	584	2	no	—
187	Q₈	—	584	2	no	—
188	C₂×C₄	—	2	4	no	—
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	292	4	no	—
191	C₂×C₄	—	584	2	no	—
192	C₂×C₄	—	584	2	no	—
193	C₂×C₄	—	584	2	no	—
194	C₂×C₄	—	584	4	no	—
195	C₂×C₄	C₄×D₂₉₂	1	1	yes	characteristic
196	C₂×C₄	#14556565	1	1	yes	characteristic
197	C₂×C₄	#14556588	1	1	yes	characteristic
198	C₂×C₄	C₂×D₅₈₄	1	1	yes	characteristic
199	C₂×C₄	#14556613	1	1	yes	characteristic
200	C₂×C₄	#14556613	1	1	yes	characteristic
201	C₈	—	2	2	no	—
202	C₈	C₂×#11924005	1	1	yes	characteristic
203	C₈	C₄×D₂₉₂	1	1	yes	characteristic
204	C₈	#14556565	1	1	yes	characteristic
205	C₈	#14556579	1	1	yes	characteristic
206	C₂²	C₄×D₅₈₄	1	1	yes	characteristic
207	C₂²	#17988823	1	1	yes	characteristic
208	C₂²	#17988964	1	1	yes	characteristic
209	C₂²	#17989030	1	4	yes	—
210	C₄	—	4	2	no	—
211	C₄	—	584	4	no	—
212	C₄	—	1168	2	no	—
213	C₄	#17988489	1	1	yes	characteristic
214	C₄	C₄×D₅₈₄	1	1	yes	characteristic
215	C₄	#17988823	1	1	yes	characteristic
216	C₄	#17988971	1	1	yes	characteristic
217	C₂	#22610797	1	1	yes	characteristic
218	C₂	#22611803	1	2	yes	—
219	C₂	#22612039	1	2	yes	—
220	C₂	#22612202	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₅₈₄

C₂

yes

maximal, characteristic

C₂×#17988415

C₂

yes

maximal, characteristic

C₂×#17988392

C₂

yes

maximal

#22610792

C₂

yes

maximal

C₂×#346×C₇₃

C₂

yes

maximal, characteristic

C₂²×Dic₂₉₂

C₂²

yes

—

C₂×Dic₅₈₄

—

C₂×Dic₅₈₄

—

C₂×Dic₅₈₄

C₄

yes

complemented

C₂×#14556525

C₂²

yes

—

—

—

—

—

C₂²×C₁₆×C₇₃

C₂²

yes

characteristic

C₂²×C₁₆×C₇₃

C₂²

yes

characteristic

C₂×C₄×C₈×C₇₃

C₂²

yes

characteristic

#346×C₇₃

—

C₂²×Dic₁₄₆

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

C₂×C₄

yes

—

C₂×C₄⋊Dic₇₃

—

Dic₅₈₄

—

—

—

—

—

C₂²×C₈×C₇₃

D₄

yes

characteristic

C₂²×C₈×C₇₃

C₂³

yes

characteristic

C₂×C₄²×C₇₃

D₄

yes

characteristic

C₂×C₁₆×C₇₃

—

C₂×C₁₆×C₇₃

—

C₂×C₁₆×C₇₃

C₂×C₄

yes

—

C₂×C₁₆×C₇₃

D₄

yes

—

C₂×C₁₆×C₇₃

D₄

yes

—

C₂×C₁₆×C₇₃

D₄

yes

—

C₄×C₈×C₇₃

—

C₄×C₈×C₇₃

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

Dic₂₉₂

—

Dic₂₉₂

—

Dic₂₉₂

—

Dic₂₉₂

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₂²×C₄×C₇₃

D₈

yes

—

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

D₈

yes

—

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

C₄²×C₇₃

—

C₄²×C₇₃

—

C₁₆×C₇₃

—

C₁₆×C₇₃

C₂²⋊C₄

yes

—

C₂³×C₇₃

C₂×D₈

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₄×D₄

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

C₂×D₈

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

—

C₈×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₈×C₇₃

C₄×D₄

yes

C₈×C₇₃

yes

C₈×C₇₃

yes

C₂²×C₇₃

C₄×D₈

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

—

C₄×C₇₃

—

100

C₄×C₇₃

#390

yes

characteristic

101

C₄×C₇₃

C₄×D₈

yes

characteristic

102

C₄×C₇₃

#466

yes

characteristic

103

C₄×C₇₃

#495

yes

characteristic

104

Dic₇₃

—

105

Dic₇₃

—

106

#13240

—

maximal, Sylow

107

C₂×C₇₃

#1970

yes

characteristic

108

C₂×C₇₃

#2176

yes

—

109

C₂×C₇₃

#2219

yes

—

110

C₂×C₇₃

#2251

yes

—

111

C₂²×Q₃₂

—

112

C₂×#367

—

113

C₂×#358

—

114

C₂×#346

D₇₃

yes

characteristic

115

#1969

—

116

C₇₃

#13240

yes

characteristic, complemented, Sylow

117

C₂²×Q₁₆

—

118

C₂×Q₃₂

—

119

C₂×Q₃₂

—

146

—

120

C₂×Q₃₂

—

146

—

121

C₂²×C₁₆

C₂×D₇₃

yes

characteristic

122

C₂²×C₁₆

C₂×D₇₃

yes

characteristic

123

C₂×#107

—

124

C₂×#103

—

146

—

125

C₂×C₄×C₈

C₂×D₇₃

yes

characteristic

126

#391

—

146

—

127

#367

—

146

—

128

#358

—

146

—

129

#346

—

130

C₂²×Q₈

—

146

—

131

C₂×Q₁₆

—

132

C₂×Q₁₆

—

146

—

133

C₂×Q₁₆

—

146

—

134

C₂×Q₁₆

—

146

—

135

C₂×Q₁₆

—

146

—

136

C₂×Q₁₆

—

146

—

137

C₂²×C₈

D₂₉₂

yes

characteristic

138

C₂²×C₈

C₂²×D₇₃

yes

characteristic

139

C₂×C₄⋊C₄

—

146

—

140

C₂×C₄²

D₂₉₂

yes

characteristic

141

Q₃₂

—

146

—

142

C₂×C₁₆

—

143

C₂×C₁₆

—

144

C₂×C₁₆

C₄×D₇₃

yes

—

145

C₂×C₁₆

D₂₉₂

yes

—

146

C₂×C₁₆

D₂₉₂

yes

—

147

C₂×C₁₆

C₂²⋊D₇₃

yes

—

148

#107

—

146

—

149

#107

—

146

—

150

#103

—

292

—

151

C₄×C₈

—

152

C₄×C₈

—

153

#95

—

292

—

154

C₂×Q₈

—

292

—

155

C₂×Q₈

—

292

—

156

C₂×Q₈

—

292

—

157

C₂×Q₈

—

292

—

158

C₂×Q₈

—

292

—

159

C₂×Q₈

—

146

—

160

C₂²×C₄

—

292

—

161

C₂²×C₄

—

292

—

162

C₂²×C₄

D₅₈₄

yes

—

163

C₂²×C₄

C₂×D₂₉₂

yes

characteristic

164

Q₁₆

—

292

—

165

Q₁₆

—

292

—

166

Q₁₆

—

146

—

167

Q₁₆

—

146

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

D₅₈₄

yes

—

171

C₂×C₈

C₂×C₄×D₇₃

yes

characteristic

172

C₂×C₈

C₂×C₂²⋊D₇₃

yes

characteristic

173

C₂×C₈

C₂×D₂₉₂

yes

characteristic

174

C₂×C₈

C₂×D₂₉₂

yes

characteristic

175

C₂×C₈

#11924028

yes

characteristic

176

C₂×C₈

#11924028

yes

characteristic

177

C₄⋊C₄

—

292

—

178

C₄⋊C₄

—

292

—

179

C₄²

—

180

C₄²

—

181

C₁₆

—

182

C₁₆

#11924005

yes

—

183

C₂³

C₂×D₅₈₄

yes

characteristic

184

Q₈

—

292

—

185

Q₈

—

292

—

186

Q₈

—

584

—

187

Q₈

—

584

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

292

—

191

C₂×C₄

—

584

—

192

C₂×C₄

—

584

—

193

C₂×C₄

—

584

—

194

C₂×C₄

—

584

—

195

C₂×C₄

C₄×D₂₉₂

yes

characteristic

196

C₂×C₄

#14556565

yes

characteristic

197

C₂×C₄

#14556588

yes

characteristic

198

C₂×C₄

C₂×D₅₈₄

yes

characteristic

199

C₂×C₄

#14556613

yes

characteristic

200

C₂×C₄

#14556613

yes

characteristic

201

C₈

—

202

C₈

C₂×#11924005

yes

characteristic

203

C₈

C₄×D₂₉₂

yes

characteristic

204

C₈

#14556565

yes

characteristic

205

C₈

#14556579

yes

characteristic

206

C₂²

C₄×D₅₈₄

yes

characteristic

207

C₂²

#17988823

yes

characteristic

208

C₂²

#17988964

yes

characteristic

209

C₂²

#17989030

yes

—

210

C₄

—

211

C₄

—

584

—

212

C₄

—

1168

—

213

C₄

#17988489

yes

characteristic

214

C₄

C₄×D₅₈₄

yes

characteristic

215

C₄

#17988823

yes

characteristic

216

C₄

#17988971

yes

characteristic

217

C₂

#22610797

yes

characteristic

218

C₂

#22611803

yes

—

219

C₂

#22612039

yes

—

220

C₂

#22612202

yes

—

	subgroup	G/H
center	C₂³	C₂×D₅₈₄
commutator	C₂×C₈×C₇₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₇₃
Fitting	C₂×#346×C₇₃	C₂
socle, prime radical	C₂³×C₇₃	C₂×D₈
cosocle	C₂²×C₈×C₇₃	C₂³
hypercenter	C₂×#346	D₇₃
hypocenter	C₇₃	#13240
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#346

subgroup

G/H

center

C₂³

C₂×D₅₈₄

commutator

C₂×C₈×C₇₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₇₃

Fitting

C₂×#346×C₇₃

C₂

socle, prime radical

C₂³×C₇₃

C₂×D₈

cosocle

C₂²×C₈×C₇₃

C₂³

D₇₃

C₇₃

G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#346

N	H ≅ G/N	type
9. C₂×Dic₅₈₄	C₄	semidirect
116. C₇₃	#13240	semidirect

H ≅ G/N

type

9. C₂×Dic₅₈₄

C₄

semidirect

116. C₇₃

#13240

semidirect

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

subgroup	index
C₂²×Dic₅₈₄	2
C₂×#17988415	2
C₂×#17988392	2
#22610792	2
C₂×#346×C₇₃	2
#13240	73

subgroup

index

C₂²×Dic₅₈₄

C₂×#346×C₇₃

Subgroups — #33004383

Conjugacy classes of subgroups

Complements

Maximal subgroups