Group #33005058 — subgroups

Subgroups — #33005058

Order 18688.

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

normal subgroups only

This group has 418 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	C₂×#17988989	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#17988388	C₂	1	2	yes	maximal
3	#22608022	C₂	1	2	yes	maximal, complemented
4	#22608009	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#1970	C₂	1	1	yes	maximal, characteristic
6	C₂×#14556583	—	2	1	no	—
7	C₂²×#11924003	C₂²	1	2	yes	—
8	#17988989	—	2	4	no	—
9	C₂×#14556525	C₂²	1	2	yes	—
10	C₂×#14556523	—	2	1	no	—
11	#17988388	—	2	4	no	—
12	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic
13	C₂×#107×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×#102×C₇₃	—	2	1	no	—
15	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
16	#390×C₇₃	—	2	1	no	—
17	#14556583	—	2	4	no	—
18	#14556583	—	4	2	no	—
19	C₂×C₄⋊Dic₇₃	—	2	2	no	—
20	C₂×#11924007	—	4	2	no	—
21	C₂×#11924003	—	2	2	no	—
22	C₂×#11924003	—	2	2	no	—
23	C₂×#11924003	—	2	2	no	—
24	#14556525	—	2	2	no	—
25	#14556525	D₄	1	4	yes	—
26	#14556523	—	2	4	no	—
27	C₂²×D₄×C₇₃	—	2	1	no	—
28	C₂×D₈×C₇₃	—	2	2	no	—
29	C₂×D₈×C₇₃	—	2	2	no	—
30	C₂×D₈×C₇₃	—	2	1	no	—
31	C₂×D₈×C₇₃	Q₈	1	2	yes	—
32	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
33	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
34	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
35	C₂×C₂²⋊C₄×C₇₃	—	4	2	no	—
36	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
37	#107×C₇₃	—	2	2	no	—
38	#102×C₇₃	—	4	2	no	—
39	C₄×C₈×C₇₃	—	2	2	no	—
40	C₂²×Dic₇₃	—	4	2	no	—
41	C₄⋊Dic₇₃	—	2	4	no	—
42	C₄⋊Dic₇₃	—	4	2	no	—
43	#11924007	—	4	8	no	—
44	#11924003	—	4	2	no	—
45	C₂⁴×C₇₃	—	4	1	no	—
46	C₂×D₄×C₇₃	—	2	2	no	—
47	C₂×D₄×C₇₃	—	4	1	no	—
48	C₂×D₄×C₇₃	—	4	1	no	—
49	C₂×D₄×C₇₃	—	4	1	no	—
50	C₂×D₄×C₇₃	—	4	1	no	—
51	C₂×D₄×C₇₃	—	4	1	no	—
52	C₂²×C₄×C₇₃	—	4	1	no	—
53	C₂²×C₄×C₇₃	D₈	1	2	yes	—
54	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
55	D₈×C₇₃	—	2	4	no	—
56	D₈×C₇₃	—	4	2	no	—
57	C₂×C₈×C₇₃	—	2	1	no	—
58	C₂×C₈×C₇₃	—	2	1	no	—
59	C₂×C₈×C₇₃	SD₁₆	1	2	yes	—
60	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
61	C₂×C₈×C₇₃	C₂×Q₈	1	1	yes	characteristic
62	C₂×C₈×C₇₃	#41	1	2	yes	—
63	C₂×C₈×C₇₃	#41	1	1	yes	characteristic
64	C₄⋊C₄×C₇₃	—	4	1	no	—
65	C₄⋊C₄×C₇₃	—	4	1	no	—
66	C₂²⋊C₄×C₇₃	—	8	4	no	—
67	C₄²×C₇₃	—	2	1	no	—
68	C₄²×C₇₃	—	2	1	no	—
69	C₂³×C₇₃	—	4	2	no	—
70	C₂³×C₇₃	—	8	1	no	—
71	C₂³×C₇₃	—	8	1	no	—
72	C₂³×C₇₃	—	8	2	no	—
73	C₂³×C₇₃	—	8	2	no	—
74	C₂³×C₇₃	C₂×D₈	1	1	yes	characteristic
75	D₄×C₇₃	—	4	2	no	—
76	D₄×C₇₃	—	4	2	no	—
77	D₄×C₇₃	—	8	1	no	—
78	D₄×C₇₃	—	8	1	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	—	8	1	no	—
83	C₂×C₄×C₇₃	—	8	2	no	—
84	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
85	C₂×C₄×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
86	C₂×C₄×C₇₃	#124	1	1	yes	characteristic
87	C₂×C₄×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
88	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
89	C₂×C₄×C₇₃	#137	1	1	yes	characteristic
90	C₂×Dic₇₃	—	4	4	no	—
91	C₂×Dic₇₃	—	8	2	no	—
92	C₂×Dic₇₃	—	8	2	no	—
93	C₈×C₇₃	—	2	2	no	—
94	C₈×C₇₃	C₂²⋊Q₈	1	2	yes	—
95	C₈×C₇₃	#124	1	2	yes	—
96	C₂²×C₇₃	—	8	4	no	—
97	C₂²×C₇₃	—	8	2	no	—
98	C₂²×C₇₃	—	16	2	no	—
99	C₂²×C₇₃	—	16	1	no	—
100	C₂²×C₇₃	—	16	1	no	—
101	C₂²×C₇₃	#447	1	1	yes	characteristic
102	C₂²×C₇₃	#474	1	1	yes	characteristic
103	C₂²×C₇₃	#486	1	1	yes	characteristic
104	C₂²×C₇₃	#508	1	2	yes	—
105	C₂²×C₇₃	#509	1	2	yes	—
106	C₄×C₇₃	—	4	2	no	—
107	C₄×C₇₃	—	16	1	no	—
108	C₄×C₇₃	#393	1	1	yes	characteristic
109	C₄×C₇₃	#448	1	1	yes	characteristic
110	C₄×C₇₃	#476	1	1	yes	characteristic
111	C₄×C₇₃	#489	1	1	yes	characteristic
112	Dic₇₃	—	8	4	no	—
113	#13365	—	73	1	no	maximal, Sylow
114	C₂×C₇₃	—	16	2	no	—
115	C₂×C₇₃	#2023	1	1	yes	characteristic
116	C₂×C₇₃	#2186	1	2	yes	—
117	C₂×C₇₃	#2228	1	2	yes	—
118	C₂×C₇₃	#2242	1	1	yes	characteristic
119	C₂×C₇₃	#2244	1	1	yes	characteristic
120	C₂×#499	—	73	1	no	—
121	C₂×#357	—	73	2	no	—
122	#1970	D₇₃	1	1	yes	characteristic
123	#1380	—	73	2	no	—
124	#1374	—	73	1	no	—
125	C₇₃	#13365	1	1	yes	characteristic, complemented, Sylow
126	C₂²×D₈	C₂×D₇₃	1	1	yes	characteristic
127	C₂×#125	—	146	1	no	—
128	C₂²×C₁₆	—	73	2	no	—
129	#499	—	146	4	no	—
130	C₂×#107	—	73	2	no	—
131	C₂×#107	C₂×D₇₃	1	1	yes	characteristic
132	C₂×#106	—	146	1	no	—
133	C₂×#102	—	2	1	no	—
134	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
135	#390	—	2	1	no	—
136	#357	—	146	4	no	—
137	C₂²×D₄	—	2	1	no	—
138	C₂×D₈	—	2	2	no	—
139	C₂×D₈	—	2	2	no	—
140	C₂×D₈	—	2	1	no	—
141	C₂×D₈	Dic₁₄₆	1	2	yes	—
142	C₂²×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
143	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
144	#125	—	292	2	no	—
145	#125	—	146	4	no	—
146	C₂×C₄⋊C₄	—	2	1	no	—
147	C₂×C₄⋊C₄	—	292	2	no	—
148	C₂×C₄⋊C₄	—	146	2	no	—
149	C₂×C₂²⋊C₄	—	4	2	no	—
150	C₂×C₄²	C₂²⋊D₇₃	1	1	yes	characteristic
151	C₂×C₁₆	—	146	2	no	—
152	C₂×C₁₆	—	146	2	no	—
153	C₂×C₁₆	—	146	2	no	—
154	#107	—	2	2	no	—
155	#107	—	73	4	no	—
156	#107	—	146	2	no	—
157	#106	—	146	4	no	—
158	#102	—	4	2	no	—
159	C₄×C₈	—	2	2	no	—
160	C₂⁴	—	4	1	no	—
161	C₂×D₄	—	2	2	no	—
162	C₂×D₄	—	4	1	no	—
163	C₂×D₄	—	4	1	no	—
164	C₂×D₄	—	4	1	no	—
165	C₂×D₄	—	4	1	no	—
166	C₂×D₄	—	4	1	no	—
167	C₂²×C₄	—	4	1	no	—
168	C₂²×C₄	—	292	2	no	—
169	C₂²×C₄	#11924013	1	2	yes	—
170	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
171	D₈	—	2	4	no	—
172	D₈	—	4	2	no	—
173	C₂×C₈	—	2	1	no	—
174	C₂×C₈	—	2	1	no	—
175	C₂×C₈	#11924016	1	2	yes	—
176	C₂×C₈	D₄×D₇₃	1	2	yes	—
177	C₂×C₈	C₂×Dic₁₄₆	1	1	yes	characteristic
178	C₂×C₈	#11924027	1	2	yes	—
179	C₂×C₈	#11924028	1	1	yes	characteristic
180	C₄⋊C₄	—	4	1	no	—
181	C₄⋊C₄	—	4	1	no	—
182	C₄⋊C₄	—	292	8	no	—
183	C₄⋊C₄	—	292	2	no	—
184	C₄⋊C₄	—	146	4	no	—
185	C₂²⋊C₄	—	8	4	no	—
186	C₄²	—	2	1	no	—
187	C₄²	—	2	1	no	—
188	C₁₆	—	292	2	no	—
189	C₂³	—	4	2	no	—
190	C₂³	—	8	1	no	—
191	C₂³	—	8	1	no	—
192	C₂³	—	8	2	no	—
193	C₂³	—	8	2	no	—
194	C₂³	C₂×#11924013	1	1	yes	characteristic
195	D₄	—	4	2	no	—
196	D₄	—	4	2	no	—
197	D₄	—	8	1	no	—
198	D₄	—	8	1	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	8	1	no	—
203	C₂×C₄	—	8	2	no	—
204	C₂×C₄	—	292	4	no	—
205	C₂×C₄	—	584	2	no	—
206	C₂×C₄	—	584	2	no	—
207	C₂×C₄	#14556559	1	1	yes	characteristic
208	C₂×C₄	#14556570	1	1	yes	characteristic
209	C₂×C₄	#14556578	1	1	yes	characteristic
210	C₂×C₄	C₂×#11924016	1	1	yes	characteristic
211	C₂×C₄	#14556616	1	1	yes	characteristic
212	C₂×C₄	#14556621	1	1	yes	characteristic
213	C₈	—	2	2	no	—
214	C₈	#14556568	1	2	yes	—
215	C₈	#14556577	1	2	yes	—
216	C₂²	—	8	4	no	—
217	C₂²	—	8	2	no	—
218	C₂²	—	16	2	no	—
219	C₂²	—	16	1	no	—
220	C₂²	—	16	1	no	—
221	C₂²	#17988720	1	1	yes	characteristic
222	C₂²	#17988867	1	1	yes	characteristic
223	C₂²	#17988933	1	1	yes	characteristic
224	C₂²	#17989017	1	2	yes	—
225	C₂²	#17989023	1	2	yes	—
226	C₄	—	4	2	no	—
227	C₄	—	16	1	no	—
228	C₄	—	584	4	no	—
229	C₄	#17988499	1	1	yes	characteristic
230	C₄	#17988725	1	1	yes	characteristic
231	C₄	#17988877	1	1	yes	characteristic
232	C₄	#17988946	1	1	yes	characteristic
233	C₂	—	16	2	no	—
234	C₂	#22611067	1	1	yes	characteristic
235	C₂	#22611852	1	2	yes	—
236	C₂	#22612088	1	2	yes	—
237	C₂	#22612162	1	1	yes	characteristic
238	C₂	#22612172	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17988989

C₂

yes

maximal, characteristic, complemented

C₂×#17988388

C₂

yes

maximal

#22608022

C₂

yes

maximal, complemented

#22608009

C₂

yes

maximal, characteristic, complemented

C₇₃×#1970

C₂

yes

maximal, characteristic

C₂×#14556583

—

C₂²×#11924003

C₂²

yes

—

#17988989

—

C₂×#14556525

C₂²

yes

—

C₂×#14556523

—

#17988388

—

C₂²×D₈×C₇₃

C₂²

yes

characteristic

C₂×#107×C₇₃

C₂²

yes

characteristic

C₂×#102×C₇₃

—

C₂×C₄×C₈×C₇₃

C₂²

yes

characteristic

#390×C₇₃

—

#14556583

—

#14556583

—

C₂×C₄⋊Dic₇₃

—

—

—

—

—

—

D₄

yes

—

#14556523

—

C₂²×D₄×C₇₃

—

C₂×D₈×C₇₃

—

C₂×D₈×C₇₃

—

C₂×D₈×C₇₃

—

C₂×D₈×C₇₃

Q₈

yes

—

C₂²×C₈×C₇₃

D₄

yes

characteristic

C₂²×C₈×C₇₃

C₂³

yes

characteristic

C₂×C₄⋊C₄×C₇₃

—

C₂×C₂²⋊C₄×C₇₃

—

C₂×C₄²×C₇₃

D₄

yes

characteristic

#107×C₇₃

—

#102×C₇₃

—

C₄×C₈×C₇₃

—

C₂²×Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

#11924007

—

#11924003

—

C₂⁴×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

D₈

yes

—

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

D₈×C₇₃

—

D₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

SD₁₆

yes

—

C₂×C₈×C₇₃

C₂×D₄

yes

—

C₂×C₈×C₇₃

C₂×Q₈

yes

characteristic

C₂×C₈×C₇₃

#41

yes

—

C₂×C₈×C₇₃

#41

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₄²×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

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

#120

yes

characteristic

C₂×C₄×C₇₃

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₇₃

#124

yes

characteristic

C₂×C₄×C₇₃

C₂×SD₁₆

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₈×C₇₃

—

C₈×C₇₃

C₂²⋊Q₈

yes

—

C₈×C₇₃

#124

yes

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

100

C₂²×C₇₃

—

101

C₂²×C₇₃

#447

yes

characteristic

102

C₂²×C₇₃

#474

yes

characteristic

103

C₂²×C₇₃

#486

yes

characteristic

104

C₂²×C₇₃

#508

yes

—

105

C₂²×C₇₃

#509

yes

—

106

C₄×C₇₃

—

107

C₄×C₇₃

—

108

C₄×C₇₃

#393

yes

characteristic

109

C₄×C₇₃

#448

yes

characteristic

110

C₄×C₇₃

#476

yes

characteristic

111

C₄×C₇₃

#489

yes

characteristic

112

Dic₇₃

—

113

#13365

—

maximal, Sylow

114

C₂×C₇₃

—

115

C₂×C₇₃

#2023

yes

characteristic

116

C₂×C₇₃

#2186

yes

—

117

C₂×C₇₃

#2228

yes

—

118

C₂×C₇₃

#2242

yes

characteristic

119

C₂×C₇₃

#2244

yes

characteristic

120

C₂×#499

—

121

C₂×#357

—

122

#1970

D₇₃

yes

characteristic

123

#1380

—

124

#1374

—

125

C₇₃

#13365

yes

characteristic, complemented, Sylow

126

C₂²×D₈

C₂×D₇₃

yes

characteristic

127

C₂×#125

—

146

—

128

C₂²×C₁₆

—

129

#499

—

146

—

130

C₂×#107

—

131

C₂×#107

C₂×D₇₃

yes

characteristic

132

C₂×#106

—

146

—

133

C₂×#102

—

134

C₂×C₄×C₈

C₂×D₇₃

yes

characteristic

135

#390

—

136

#357

—

146

—

137

C₂²×D₄

—

138

C₂×D₈

—

139

C₂×D₈

—

140

C₂×D₈

—

141

C₂×D₈

Dic₁₄₆

yes

—

142

C₂²×C₈

C₂²⋊D₇₃

yes

characteristic

143

C₂²×C₈

C₂²×D₇₃

yes

characteristic

144

#125

—

292

—

145

#125

—

146

—

146

C₂×C₄⋊C₄

—

147

C₂×C₄⋊C₄

—

292

—

148

C₂×C₄⋊C₄

—

146

—

149

C₂×C₂²⋊C₄

—

150

C₂×C₄²

C₂²⋊D₇₃

yes

characteristic

151

C₂×C₁₆

—

146

—

152

C₂×C₁₆

—

146

—

153

C₂×C₁₆

—

146

—

154

#107

—

155

#107

—

156

#107

—

146

—

157

#106

—

146

—

158

#102

—

159

C₄×C₈

—

160

C₂⁴

—

161

C₂×D₄

—

162

C₂×D₄

—

163

C₂×D₄

—

164

C₂×D₄

—

165

C₂×D₄

—

166

C₂×D₄

—

167

C₂²×C₄

—

168

C₂²×C₄

—

292

—

169

C₂²×C₄

#11924013

yes

—

170

C₂²×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

171

D₈

—

172

D₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

#11924016

yes

—

176

C₂×C₈

D₄×D₇₃

yes

—

177

C₂×C₈

C₂×Dic₁₄₆

yes

characteristic

178

C₂×C₈

#11924027

yes

—

179

C₂×C₈

#11924028

yes

characteristic

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

292

—

183

C₄⋊C₄

—

292

—

184

C₄⋊C₄

—

146

—

185

C₂²⋊C₄

—

186

C₄²

—

187

C₄²

—

188

C₁₆

—

292

—

189

C₂³

—

190

C₂³

—

191

C₂³

—

192

C₂³

—

193

C₂³

—

194

C₂³

C₂×#11924013

yes

characteristic

195

D₄

—

196

D₄

—

197

D₄

—

198

D₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

292

—

205

C₂×C₄

—

584

—

206

C₂×C₄

—

584

—

207

C₂×C₄

#14556559

yes

characteristic

208

C₂×C₄

#14556570

yes

characteristic

209

C₂×C₄

#14556578

yes

characteristic

210

C₂×C₄

C₂×#11924016

yes

characteristic

211

C₂×C₄

#14556616

yes

characteristic

212

C₂×C₄

#14556621

yes

characteristic

213

C₈

—

214

C₈

#14556568

yes

—

215

C₈

#14556577

yes

—

216

C₂²

—

217

C₂²

—

218

C₂²

—

219

C₂²

—

220

C₂²

—

221

C₂²

#17988720

yes

characteristic

222

C₂²

#17988867

yes

characteristic

223

C₂²

#17988933

yes

characteristic

224

C₂²

#17989017

yes

—

225

C₂²

#17989023

yes

—

226

C₄

—

227

C₄

—

228

C₄

—

584

—

229

C₄

#17988499

yes

characteristic

230

C₄

#17988725

yes

characteristic

231

C₄

#17988877

yes

characteristic

232

C₄

#17988946

yes

characteristic

233

C₂

—

234

C₂

#22611067

yes

characteristic

235

C₂

#22611852

yes

—

236

C₂

#22612088

yes

—

237

C₂

#22612162

yes

characteristic

238

C₂

#22612172

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×#11924013
commutator, cosocle	C₂²×C₈×C₇₃	C₂³
Frattini	C₂²×C₈	C₂²×D₇₃
Fitting	C₇₃×#1970	C₂
socle	C₂³×C₇₃	C₂×D₈
prime radical	C₂²×D₈×C₇₃	C₂²
hypercenter	#1970	D₇₃
hypocenter	C₇₃	#13365
LCS	G ▷ C₂²×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1970

subgroup

G/H

center

C₂³

C₂×#11924013

commutator, cosocle

C₂²×C₈×C₇₃

C₂³

Frattini

C₂²×C₈

C₂²×D₇₃

Fitting

C₇₃×#1970

C₂

socle

C₂³×C₇₃

C₂×D₈

prime radical

C₂²×D₈×C₇₃

C₂²

D₇₃

C₇₃

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

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1970

N	H ≅ G/N	type
1. C₂×#17988989	C₂	semidirect
3. #22608022	C₂	semidirect
4. #22608009	C₂	semidirect
125. C₇₃	#13365	semidirect

H ≅ G/N

type

1. C₂×#17988989

C₂

semidirect

3. #22608022

C₂

semidirect

4. #22608009

C₂

semidirect

125. C₇₃

#13365

semidirect

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

subgroup	index
C₂×#17988989	2
C₂×#17988388	2
#22608022	2
#22608009	2
C₇₃×#1970	2
#13365	73

subgroup

index

C₇₃×#1970

Subgroups — #33005058

Conjugacy classes of subgroups

Complements

Maximal subgroups