Group #33005576 — subgroups

Subgroups — #33005576

Order 18688.

482 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 113 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×#17988405	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#17988388	C₂	1	2	yes	maximal, complemented
3	#22610798	C₂	1	2	yes	maximal, complemented
4	#22608023	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×#11924003	C₂²	1	1	yes	characteristic
7	C₂×#14556525	C₂²	1	2	yes	—
8	C₂×#14556512	—	2	2	no	—
9	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
10	#17988490	—	2	2	no	—
11	#17988405	—	2	2	no	—
12	#17988388	—	2	4	no	—
13	C₂²×D₈×C₇₃	C₂²	1	2	yes	—
14	C₂×D₁₆×C₇₃	—	2	4	no	—
15	C₂×D₁₆×C₇₃	—	2	2	no	—
16	C₂²×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
17	C₂²×#10596831	D₄	1	1	yes	characteristic
18	C₂×C₄⋊Dic₇₃	—	2	2	no	—
19	C₂×C₂²⋊Dic₇₃	—	4	2	no	—
20	C₂×C₂²⋊Dic₇₃	—	4	2	no	—
21	C₂×C₄×Dic₇₃	D₄	1	1	yes	characteristic
22	C₂×#11924003	—	2	2	no	—
23	C₂×#11924003	—	2	1	no	—
24	#14556525	—	2	2	no	—
25	#14556525	—	2	2	no	—
26	#14556512	—	4	4	no	—
27	C₈×Dic₇₃	—	2	1	no	—
28	C₈×Dic₇₃	—	2	1	no	—
29	C₂²×D₄×C₇₃	—	2	2	no	—
30	C₂×D₈×C₇₃	—	2	2	no	—
31	C₂×D₈×C₇₃	—	2	2	no	—
32	C₂×D₈×C₇₃	—	2	2	no	—
33	C₂×D₈×C₇₃	—	2	2	no	—
34	C₂×D₈×C₇₃	—	2	2	no	—
35	C₂×D₈×C₇₃	D₄	1	4	yes	—
36	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
37	D₁₆×C₇₃	—	2	8	no	—
38	C₂×C₁₆×C₇₃	—	2	2	no	—
39	C₂×C₁₆×C₇₃	D₄	1	2	yes	—
40	C₂²×Dic₇₃	—	4	2	no	—
41	C₂²×Dic₇₃	D₈	1	1	yes	characteristic
42	C₂²×Dic₇₃	D₈	1	1	yes	characteristic
43	C₂×#10596831	—	2	1	no	—
44	C₂×#10596831	—	2	2	no	—
45	C₄⋊Dic₇₃	—	4	2	no	—
46	C₄⋊Dic₇₃	—	4	2	no	—
47	C₂²⋊Dic₇₃	—	8	4	no	—
48	C₂²⋊Dic₇₃	—	8	4	no	—
49	C₄×Dic₇₃	—	2	1	no	—
50	C₄×Dic₇₃	—	2	1	no	—
51	#11924003	—	4	1	no	—
52	C₂⁴×C₇₃	—	4	2	no	—
53	C₂×D₄×C₇₃	—	2	4	no	—
54	C₂×D₄×C₇₃	—	4	2	no	—
55	C₂×D₄×C₇₃	—	4	2	no	—
56	C₂×D₄×C₇₃	—	4	2	no	—
57	C₂×D₄×C₇₃	—	4	2	no	—
58	C₂×D₄×C₇₃	—	4	2	no	—
59	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
60	D₈×C₇₃	—	2	4	no	—
61	D₈×C₇₃	—	2	4	no	—
62	D₈×C₇₃	—	4	2	no	—
63	D₈×C₇₃	—	4	2	no	—
64	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
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	2	yes	—
68	C₁₆×C₇₃	—	2	2	no	—
69	C₂³×C₇₃	—	4	4	no	—
70	C₂³×C₇₃	—	8	2	no	—
71	C₂³×C₇₃	—	8	2	no	—
72	C₂³×C₇₃	—	8	2	no	—
73	C₂³×C₇₃	—	8	2	no	—
74	C₂³×C₇₃	—	8	2	no	—
75	C₂³×C₇₃	—	8	2	no	—
76	C₂³×C₇₃	C₂×D₈	1	1	yes	characteristic
77	D₄×C₇₃	—	4	4	no	—
78	D₄×C₇₃	—	4	4	no	—
79	D₄×C₇₃	—	8	2	no	—
80	D₄×C₇₃	—	8	2	no	—
81	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
82	C₂×C₄×C₇₃	#121	1	2	yes	—
83	C₂×C₄×C₇₃	#135	1	1	yes	characteristic
84	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
85	C₂×Dic₇₃	—	2	1	no	—
86	C₂×Dic₇₃	—	2	1	no	—
87	C₂×Dic₇₃	—	2	1	no	—
88	C₂×Dic₇₃	—	2	2	no	—
89	C₂×Dic₇₃	—	8	2	no	—
90	C₂×Dic₇₃	—	8	2	no	—
91	C₂×Dic₇₃	—	8	2	no	—
92	C₂×Dic₇₃	D₁₆	1	2	yes	complemented
93	C₈×C₇₃	#120	1	1	yes	characteristic
94	C₈×C₇₃	#123	1	2	yes	—
95	C₈×C₇₃	#124	1	1	yes	characteristic
96	#10596831	—	4	1	no	—
97	C₂²×C₇₃	—	8	4	no	—
98	C₂²×C₇₃	—	8	4	no	—
99	C₂²×C₇₃	—	8	4	no	—
100	C₂²×C₇₃	—	16	2	no	—
101	C₂²×C₇₃	—	16	2	no	—
102	C₂²×C₇₃	—	16	2	no	—
103	C₂²×C₇₃	—	16	2	no	—
104	C₂²×C₇₃	#459	1	2	yes	—
105	C₂²×C₇₃	#466	1	1	yes	characteristic
106	C₂²×C₇₃	C₂×D₁₆	1	1	yes	characteristic
107	C₂²×C₇₃	#508	1	1	yes	characteristic
108	C₂²×C₇₃	#509	1	2	yes	—
109	C₄×C₇₃	#394	1	1	yes	characteristic
110	C₄×C₇₃	#463	1	2	yes	—
111	C₄×C₇₃	#469	1	1	yes	characteristic
112	Dic₇₃	—	2	2	no	—
113	Dic₇₃	—	4	1	no	—
114	Dic₇₃	—	16	2	no	—
115	#13448	—	73	1	no	maximal, Sylow
116	C₂×C₇₃	—	16	4	no	—
117	C₂×C₇₃	#2054	1	1	yes	characteristic
118	C₂×C₇₃	#2206	1	2	yes	—
119	C₂×C₇₃	#2210	1	2	yes	—
120	C₂×C₇₃	#2215	1	1	yes	characteristic
121	C₂×C₇₃	#2218	1	1	yes	characteristic
122	C₂²×D₁₆	D₇₃	1	1	yes	characteristic
123	C₂×C₄⋊C₁₆	—	73	1	no	—
124	C₂×#357	—	73	2	no	—
125	#1970	—	73	2	no	—
126	#1380	—	73	1	no	—
127	C₇₃	#13448	1	1	yes	characteristic, complemented, Sylow
128	C₂²×D₈	C₂×D₇₃	1	2	yes	—
129	C₂×D₁₆	—	2	4	no	—
130	C₂×D₁₆	—	2	2	no	—
131	C₂²×C₁₆	—	73	1	no	—
132	C₂²×C₁₆	C₂×D₇₃	1	1	yes	characteristic
133	C₂×#107	—	73	2	no	—
134	C₂×#102	—	146	2	no	—
135	C₂×C₄×C₈	—	73	1	no	—
136	#390	—	146	2	no	—
137	C₄⋊C₁₆	—	146	2	no	—
138	#357	—	146	4	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	C₂²⋊D₇₃	1	4	yes	—
146	C₂²×C₈	—	73	1	no	—
147	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
148	C₂×C₄⋊C₄	—	146	2	no	—
149	C₂×C₂²⋊C₄	—	292	2	no	—
150	C₂×C₂²⋊C₄	—	292	2	no	—
151	C₂×C₄²	—	73	1	no	—
152	D₁₆	—	2	8	no	—
153	C₂×C₁₆	—	2	2	no	—
154	C₂×C₁₆	—	146	2	no	—
155	C₂×C₁₆	—	146	1	no	—
156	C₂×C₁₆	C₂²⋊D₇₃	1	2	yes	—
157	#107	—	146	2	no	—
158	#107	—	146	2	no	—
159	#102	—	292	4	no	—
160	C₄×C₈	—	146	1	no	—
161	C₄×C₈	—	146	1	no	—
162	C₂⁴	—	4	2	no	—
163	C₂×D₄	—	2	4	no	—
164	C₂×D₄	—	4	2	no	—
165	C₂×D₄	—	4	2	no	—
166	C₂×D₄	—	4	2	no	—
167	C₂×D₄	—	4	2	no	—
168	C₂×D₄	—	4	2	no	—
169	C₂²×C₄	—	292	2	no	—
170	C₂²×C₄	—	73	1	no	—
171	C₂²×C₄	—	73	1	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	C₂×C₈	—	146	1	no	—
178	C₂×C₈	—	146	2	no	—
179	C₂×C₈	C₂×C₂²⋊D₇₃	1	2	yes	—
180	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
181	C₂×C₈	#11924027	1	1	yes	characteristic
182	C₂×C₈	#11924027	1	2	yes	—
183	C₄⋊C₄	—	292	2	no	—
184	C₄⋊C₄	—	292	2	no	—
185	C₂²⋊C₄	—	584	4	no	—
186	C₂²⋊C₄	—	584	4	no	—
187	C₄²	—	146	1	no	—
188	C₄²	—	146	1	no	—
189	C₁₆	—	2	2	no	—
190	C₁₆	—	292	1	no	—
191	C₂³	—	4	4	no	—
192	C₂³	—	8	2	no	—
193	C₂³	—	8	2	no	—
194	C₂³	—	8	2	no	—
195	C₂³	—	8	2	no	—
196	C₂³	—	8	2	no	—
197	C₂³	—	8	2	no	—
198	C₂³	D₈×D₇₃	1	1	yes	characteristic
199	D₄	—	4	4	no	—
200	D₄	—	4	4	no	—
201	D₄	—	8	2	no	—
202	D₄	—	8	2	no	—
203	C₂×C₄	—	584	2	no	—
204	C₂×C₄	—	584	2	no	—
205	C₂×C₄	—	584	2	no	—
206	C₂×C₄	—	73	2	no	—
207	C₂×C₄	—	146	2	no	—
208	C₂×C₄	—	146	1	no	—
209	C₂×C₄	—	146	1	no	—
210	C₂×C₄	—	146	1	no	—
211	C₂×C₄	#14556562	1	1	yes	characteristic
212	C₂×C₄	#14556563	1	2	yes	—
213	C₂×C₄	#14556610	1	1	yes	characteristic
214	C₂×C₄	#14556615	1	2	yes	—
215	C₈	—	292	1	no	—
216	C₈	#14556560	1	1	yes	characteristic
217	C₈	#14556572	1	2	yes	—
218	C₈	#14556578	1	1	yes	characteristic
219	C₂²	—	8	4	no	—
220	C₂²	—	8	4	no	—
221	C₂²	—	8	4	no	—
222	C₂²	—	16	2	no	—
223	C₂²	—	16	2	no	—
224	C₂²	—	16	2	no	—
225	C₂²	—	16	2	no	—
226	C₂²	#17988780	1	2	yes	—
227	C₂²	#17988820	1	1	yes	characteristic
228	C₂²	D₁₆×D₇₃	1	1	yes	characteristic
229	C₂²	#17989016	1	1	yes	characteristic
230	C₂²	#17989021	1	2	yes	—
231	C₄	—	292	1	no	—
232	C₄	—	1168	2	no	—
233	C₄	—	146	2	no	—
234	C₄	#17988501	1	1	yes	characteristic
235	C₄	#17988800	1	2	yes	—
236	C₄	#17988837	1	1	yes	characteristic
237	C₂	—	16	4	no	—
238	C₂	#22611239	1	1	yes	characteristic
239	C₂	#22611964	1	2	yes	—
240	C₂	#22611984	1	2	yes	—
241	C₂	#22612014	1	1	yes	characteristic
242	C₂	#22612031	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17988405

C₂

yes

maximal, characteristic, complemented

C₂×#17988388

C₂

yes

maximal, complemented

#22610798

C₂

yes

maximal, complemented

#22608023

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₆×C₇₃

C₂

yes

maximal, characteristic

C₂²×#11924003

C₂²

yes

characteristic

C₂×#14556525

C₂²

yes

—

C₂×#14556512

—

C₂×C₈×Dic₇₃

C₂²

yes

—

—

—

C₂²×D₈×C₇₃

C₂²

yes

—

C₂×D₁₆×C₇₃

—

C₂×D₁₆×C₇₃

—

C₂²×C₁₆×C₇₃

C₂²

yes

characteristic

C₂²×#10596831

D₄

yes

characteristic

C₂×C₄⋊Dic₇₃

—

C₂×C₂²⋊Dic₇₃

—

C₂×C₂²⋊Dic₇₃

—

C₂×C₄×Dic₇₃

D₄

yes

—

—

—

—

—

C₈×Dic₇₃

—

C₈×Dic₇₃

—

C₂²×D₄×C₇₃

—

C₂×D₈×C₇₃

—

C₂×D₈×C₇₃

—

C₂×D₈×C₇₃

—

C₂×D₈×C₇₃

—

C₂×D₈×C₇₃

—

C₂×D₈×C₇₃

D₄

yes

—

C₂²×C₈×C₇₃

C₂³

yes

characteristic

D₁₆×C₇₃

—

C₂×C₁₆×C₇₃

—

C₂×C₁₆×C₇₃

D₄

yes

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

D₈

yes

characteristic

C₂²×Dic₇₃

D₈

yes

characteristic

C₂×#10596831

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₂²⋊Dic₇₃

—

C₂²⋊Dic₇₃

—

C₄×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

C₂×D₄

yes

—

C₂×C₈×C₇₃

C₂×D₄

yes

C₂×C₈×C₇₃

yes

C₂×C₈×C₇₃

yes

—

C₁₆×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

C₂×D₈

yes

characteristic

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

#121

yes

characteristic

C₂×C₄×C₇₃

#121

yes

—

C₂×C₄×C₇₃

#135

yes

characteristic

C₂×C₄×C₇₃

AGL(1,ℤ/8)

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

D₁₆

yes

C₈×C₇₃

yes

C₈×C₇₃

yes

—

C₈×C₇₃

#124

yes

characteristic

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

100

C₂²×C₇₃

—

101

C₂²×C₇₃

—

102

C₂²×C₇₃

—

103

C₂²×C₇₃

—

104

C₂²×C₇₃

#459

yes

—

105

C₂²×C₇₃

#466

yes

characteristic

106

C₂²×C₇₃

C₂×D₁₆

yes

characteristic

107

C₂²×C₇₃

#508

yes

characteristic

108

C₂²×C₇₃

#509

yes

—

109

C₄×C₇₃

#394

yes

characteristic

110

C₄×C₇₃

#463

yes

—

111

C₄×C₇₃

#469

yes

characteristic

112

Dic₇₃

—

113

Dic₇₃

—

114

Dic₇₃

—

115

#13448

—

maximal, Sylow

116

C₂×C₇₃

—

117

C₂×C₇₃

#2054

yes

characteristic

118

C₂×C₇₃

#2206

yes

—

119

C₂×C₇₃

#2210

yes

—

120

C₂×C₇₃

#2215

yes

characteristic

121

C₂×C₇₃

#2218

yes

characteristic

122

C₂²×D₁₆

D₇₃

yes

characteristic

123

C₂×C₄⋊C₁₆

—

124

C₂×#357

—

125

#1970

—

126

#1380

—

127

C₇₃

#13448

yes

characteristic, complemented, Sylow

128

C₂²×D₈

C₂×D₇₃

yes

—

129

C₂×D₁₆

—

130

C₂×D₁₆

—

131

C₂²×C₁₆

—

132

C₂²×C₁₆

C₂×D₇₃

yes

characteristic

133

C₂×#107

—

134

C₂×#102

—

146

—

135

C₂×C₄×C₈

—

136

#390

—

146

—

137

C₄⋊C₁₆

—

146

—

138

#357

—

146

—

139

C₂²×D₄

—

140

C₂×D₈

—

141

C₂×D₈

—

142

C₂×D₈

—

143

C₂×D₈

—

144

C₂×D₈

—

145

C₂×D₈

C₂²⋊D₇₃

yes

—

146

C₂²×C₈

—

147

C₂²×C₈

C₂²×D₇₃

yes

characteristic

148

C₂×C₄⋊C₄

—

146

—

149

C₂×C₂²⋊C₄

—

292

—

150

C₂×C₂²⋊C₄

—

292

—

151

C₂×C₄²

—

152

D₁₆

—

153

C₂×C₁₆

—

154

C₂×C₁₆

—

146

—

155

C₂×C₁₆

—

146

—

156

C₂×C₁₆

C₂²⋊D₇₃

yes

—

157

#107

—

146

—

158

#107

—

146

—

159

#102

—

292

—

160

C₄×C₈

—

146

—

161

C₄×C₈

—

146

—

162

C₂⁴

—

163

C₂×D₄

—

164

C₂×D₄

—

165

C₂×D₄

—

166

C₂×D₄

—

167

C₂×D₄

—

168

C₂×D₄

—

169

C₂²×C₄

—

292

—

170

C₂²×C₄

—

171

C₂²×C₄

—

172

C₂²×C₄

D₄×D₇₃

yes

characteristic

173

D₈

—

174

D₈

—

175

D₈

—

176

D₈

—

177

C₂×C₈

—

146

—

178

C₂×C₈

—

146

—

179

C₂×C₈

C₂×C₂²⋊D₇₃

yes

—

180

C₂×C₈

C₂×C₂²⋊D₇₃

yes

characteristic

181

C₂×C₈

#11924027

yes

characteristic

182

C₂×C₈

#11924027

yes

—

183

C₄⋊C₄

—

292

—

184

C₄⋊C₄

—

292

—

185

C₂²⋊C₄

—

584

—

186

C₂²⋊C₄

—

584

—

187

C₄²

—

146

—

188

C₄²

—

146

—

189

C₁₆

—

190

C₁₆

—

292

—

191

C₂³

—

192

C₂³

—

193

C₂³

—

194

C₂³

—

195

C₂³

—

196

C₂³

—

197

C₂³

—

198

C₂³

D₈×D₇₃

yes

characteristic

199

D₄

—

200

D₄

—

201

D₄

—

202

D₄

—

203

C₂×C₄

—

584

—

204

C₂×C₄

—

584

—

205

C₂×C₄

—

584

—

206

C₂×C₄

—

207

C₂×C₄

—

146

—

208

C₂×C₄

—

146

—

209

C₂×C₄

—

146

—

210

C₂×C₄

—

146

—

211

C₂×C₄

#14556562

yes

characteristic

212

C₂×C₄

#14556563

yes

—

213

C₂×C₄

#14556610

yes

characteristic

214

C₂×C₄

#14556615

yes

—

215

C₈

—

292

—

216

C₈

#14556560

yes

characteristic

217

C₈

#14556572

yes

—

218

C₈

#14556578

yes

characteristic

219

C₂²

—

220

C₂²

—

221

C₂²

—

222

C₂²

—

223

C₂²

—

224

C₂²

—

225

C₂²

—

226

C₂²

#17988780

yes

—

227

C₂²

#17988820

yes

characteristic

228

C₂²

D₁₆×D₇₃

yes

characteristic

229

C₂²

#17989016

yes

characteristic

230

C₂²

#17989021

yes

—

231

C₄

—

292

—

232

C₄

—

1168

—

233

C₄

—

146

—

234

C₄

#17988501

yes

characteristic

235

C₄

#17988800

yes

—

236

C₄

#17988837

yes

characteristic

237

C₂

—

238

C₂

#22611239

yes

characteristic

239

C₂

#22611964

yes

—

240

C₂

#22611984

yes

—

241

C₂

#22612014

yes

characteristic

242

C₂

#22612031

yes

characteristic

	subgroup	G/H
center	C₂³	D₈×D₇₃
commutator, cosocle	C₂²×C₈×C₇₃	C₂³
Frattini	C₂²×C₈	C₂²×D₇₃
Fitting, prime radical	C₂²×D₁₆×C₇₃	C₂
socle	C₂³×C₇₃	C₂×D₈
hypercenter	C₂²×D₁₆	D₇₃
hypocenter	C₇₃	#13448
LCS	G ▷ C₂²×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×D₁₆

subgroup

G/H

center

C₂³

D₈×D₇₃

commutator, cosocle

C₂²×C₈×C₇₃

C₂³

Frattini

C₂²×C₈

C₂²×D₇₃

Fitting, prime radical

C₂²×D₁₆×C₇₃

C₂

socle

C₂³×C₇₃

C₂×D₈

hypercenter

C₂²×D₁₆

D₇₃

hypocenter

C₇₃

#13448

LCS

G ▷ C₂²×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×D₁₆

N	H ≅ G/N	type
1. C₂×#17988405	C₂	semidirect
2. C₂×#17988388	C₂	semidirect
3. #22610798	C₂	semidirect
4. #22608023	C₂	semidirect
92. C₂×Dic₇₃	D₁₆	semidirect
127. C₇₃	#13448	semidirect

H ≅ G/N

type

1. C₂×#17988405

C₂

semidirect

2. C₂×#17988388

C₂

semidirect

3. #22610798

C₂

semidirect

4. #22608023

C₂

semidirect

92. C₂×Dic₇₃

D₁₆

semidirect

127. C₇₃

#13448

semidirect

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

subgroup	index
C₂×#17988405	2
C₂×#17988388	2
#22610798	2
#22608023	2
C₂²×D₁₆×C₇₃	2
#13448	73

subgroup

index

C₂²×D₁₆×C₇₃

Subgroups — #33005576

Conjugacy classes of subgroups

Complements

Maximal subgroups