Group #33003438 — subgroups

Subgroups — #33003438

Order 18688.

458 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 127 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	#22619586	C₂	1	1	yes	maximal, characteristic
2	#22611652	C₂	1	2	yes	maximal, complemented
3	#22609977	C₂	1	1	yes	maximal, characteristic
4	#22608033	C₂	1	2	yes	maximal, complemented
5	C₇₃×#3407	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₂₉₂	C₂²	1	1	yes	characteristic
7	#17989158	—	2	1	no	—
8	#17988845	C₄	1	4	yes	complemented
9	#17988828	—	2	2	no	—
10	#17988625	C₂²	1	2	yes	—
11	#17988625	C₂²	1	1	yes	characteristic
12	#17988597	—	2	1	no	—
13	#17988561	—	2	1	no	—
14	#17988392	—	2	4	no	—
15	#17988344	—	2	1	no	—
16	C₂×#131×C₇₃	C₂²	1	1	yes	characteristic
17	#504×C₇₃	—	2	4	no	—
18	C₂×M₃₂×C₇₃	—	2	2	no	—
19	C₂×M₃₂×C₇₃	C₂²	1	2	yes	—
20	C₂²×Dic₁₄₆	—	2	1	no	—
21	C₂×Dic₂₉₂	—	2	2	no	—
22	C₂×Dic₂₉₂	—	2	1	no	—
23	C₂×Dic₂₉₂	—	2	2	no	—
24	C₂×Dic₂₉₂	C₂×C₄	1	2	yes	—
25	#14556589	—	4	1	no	—
26	#14556578	—	4	1	no	—
27	#14556572	—	4	2	no	—
28	#14556570	—	2	4	no	—
29	#14556550	—	2	1	no	—
30	#14556550	—	2	2	no	—
31	#14556525	—	2	1	no	—
32	#14556525	—	2	2	no	—
33	#14556523	—	2	2	no	—
34	#14556523	C₂×C₄	1	2	yes	—
35	#14556516	—	2	4	no	—
36	#14556506	—	4	2	no	—
37	C₂×#41×C₇₃	D₄	1	1	yes	characteristic
38	#131×C₇₃	—	2	2	no	—
39	#131×C₇₃	—	2	2	no	—
40	C₂×M₁₆×C₇₃	C₂×C₄	1	2	yes	—
41	C₂×M₁₆×C₇₃	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₇₃	D₄	1	2	yes	—
43	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
44	M₃₂×C₇₃	—	2	4	no	—
45	M₃₂×C₇₃	—	2	2	no	—
46	M₃₂×C₇₃	—	2	2	no	—
47	C₂×C₁₆×C₇₃	—	2	4	no	—
48	C₂×C₁₆×C₇₃	D₄	1	4	yes	—
49	C₂×Dic₁₄₆	—	2	2	no	—
50	C₂×Dic₁₄₆	—	4	2	no	—
51	C₂×Dic₁₄₆	—	4	2	no	—
52	C₂×Dic₁₄₆	—	4	1	no	—
53	C₂²×Dic₇₃	—	4	1	no	—
54	Dic₂₉₂	—	2	4	no	—
55	Dic₂₉₂	—	4	1	no	—
56	Dic₂₉₂	—	4	1	no	—
57	C₄⋊Dic₇₃	—	2	2	no	—
58	C₄⋊Dic₇₃	—	4	2	no	—
59	#11924007	—	4	4	no	—
60	C₂²⋊Dic₇₃	—	4	4	no	—
61	C₂²⋊Dic₇₃	—	4	1	no	—
62	C₂²⋊Dic₇₃	—	4	2	no	—
63	C₄×Dic₇₃	—	4	1	no	—
64	C₄×Dic₇₃	—	4	2	no	—
65	#41×C₇₃	—	2	2	no	—
66	#41×C₇₃	—	2	2	no	—
67	C₂×Q₈×C₇₃	SD₁₆	1	1	yes	characteristic
68	C₂×D₄×C₇₃	D₈	1	2	yes	—
69	C₂×D₄×C₇₃	SD₁₆	1	1	yes	characteristic
70	C₂²×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
71	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
72	M₁₆×C₇₃	—	2	2	no	—
73	M₁₆×C₇₃	—	2	4	no	—
74	C₂×C₈×C₇₃	—	2	2	no	—
75	C₂×C₈×C₇₃	—	2	2	no	—
76	C₂×C₈×C₇₃	C₂²⋊C₄	1	2	yes	—
77	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
78	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
79	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
80	C₂×C₈×C₇₃	#41	1	2	yes	—
81	C₁₆×C₇₃	—	2	4	no	—
82	C₂³×C₇₃	#102	1	2	yes	—
83	C₂³×C₇₃	C₂×D₈	1	1	yes	characteristic
84	Q₈×C₇₃	—	2	2	no	—
85	D₄×C₇₃	—	2	4	no	—
86	D₄×C₇₃	—	2	2	no	—
87	C₂×C₄×C₇₃	—	2	2	no	—
88	C₂×C₄×C₇₃	—	2	2	no	—
89	C₂×C₄×C₇₃	#102	1	2	yes	—
90	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₄×C₇₃	#121	1	2	yes	—
92	C₂×C₄×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
93	C₂×C₄×C₇₃	#135	1	2	yes	—
94	C₂×Dic₇₃	—	4	2	no	—
95	C₂×Dic₇₃	—	4	2	no	—
96	C₂×Dic₇₃	—	8	2	no	—
97	C₂×Dic₇₃	—	8	2	no	—
98	Dic₁₄₆	—	4	2	no	—
99	Dic₁₄₆	—	4	2	no	—
100	Dic₁₄₆	—	8	2	no	—
101	C₈×C₇₃	—	2	2	no	—
102	C₈×C₇₃	C₄×D₄	1	2	yes	—
103	C₈×C₇₃	#120	1	1	yes	characteristic
104	C₈×C₇₃	#123	1	1	yes	characteristic
105	C₂²×C₇₃	—	2	2	no	—
106	C₂²×C₇₃	—	4	1	no	—
107	C₂²×C₇₃	—	4	2	no	—
108	C₂²×C₇₃	C₂×#102	1	1	yes	characteristic
109	C₂²×C₇₃	#466	1	2	yes	—
110	C₄×C₇₃	—	2	2	no	—
111	C₄×C₇₃	#386	1	1	yes	characteristic
112	C₄×C₇₃	#416	1	1	yes	characteristic
113	C₄×C₇₃	#465	1	2	yes	—
114	Dic₇₃	—	8	2	no	—
115	Dic₇₃	—	8	2	no	—
116	Dic₇₃	—	16	2	no	—
117	#13075	—	73	1	no	maximal, Sylow
118	C₂×C₇₃	—	2	1	no	—
119	C₂×C₇₃	—	2	2	no	—
120	C₂×C₇₃	—	4	2	no	—
121	C₂×C₇₃	#1893	1	1	yes	characteristic
122	#3407	D₇₃	1	1	yes	characteristic
123	#3059	—	73	1	no	—
124	#2141	—	73	2	no	—
125	#1812	—	73	1	no	—
126	#1384	—	73	2	no	—
127	C₇₃	#13075	1	1	yes	characteristic, complemented, Sylow
128	C₂²×Q₁₆	—	73	1	no	—
129	C₂×#131	C₂×D₇₃	1	1	yes	characteristic
130	#536	—	146	1	no	—
131	#504	—	2	4	no	—
132	C₂×M₃₂	—	2	2	no	—
133	C₂×M₃₂	C₂×D₇₃	1	2	yes	—
134	#470	—	73	4	no	—
135	#467	—	146	2	no	—
136	#427	—	73	1	no	—
137	#427	—	73	2	no	—
138	#419	—	146	1	no	—
139	#410	—	146	1	no	—
140	#358	—	146	4	no	—
141	H(3,ℤ/4)	—	146	1	no	—
142	C₂×#41	D₂₉₂	1	1	yes	characteristic
143	C₂²×Q₈	—	146	1	no	—
144	C₂×Q₁₆	—	73	2	no	—
145	C₂×Q₁₆	—	146	1	no	—
146	C₂×Q₁₆	—	146	2	no	—
147	C₂×Q₁₆	—	146	2	no	—
148	#131	—	2	2	no	—
149	#131	—	2	2	no	—
150	C₂×M₁₆	C₄×D₇₃	1	2	yes	—
151	C₂×M₁₆	D₂₉₂	1	1	yes	characteristic
152	C₂²×C₈	C₂²⋊D₇₃	1	2	yes	—
153	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
154	C₄⋊Q₈	—	292	1	no	—
155	#124	—	292	1	no	—
156	#123	—	292	2	no	—
157	C₂²⋊Q₈	—	146	4	no	—
158	#117	—	146	2	no	—
159	#117	—	146	1	no	—
160	M₃₂	—	2	4	no	—
161	M₃₂	—	2	2	no	—
162	M₃₂	—	2	2	no	—
163	C₂×C₁₆	—	2	4	no	—
164	C₂×C₁₆	C₂²⋊D₇₃	1	4	yes	—
165	#107	—	146	2	no	—
166	#107	—	146	1	no	—
167	#106	—	73	2	no	—
168	#106	—	146	2	no	—
169	#103	—	146	4	no	—
170	#99	—	292	2	no	—
171	#41	—	2	2	no	—
172	#41	—	2	2	no	—
173	C₂×Q₈	—	292	1	no	—
174	C₂×Q₈	—	292	2	no	—
175	C₂×Q₈	—	292	2	no	—
176	C₂×Q₈	—	146	2	no	—
177	C₂×Q₈	#11924017	1	1	yes	characteristic
178	C₂×D₄	D₅₈₄	1	2	yes	—
179	C₂×D₄	#11924017	1	1	yes	characteristic
180	C₂²×C₄	—	292	1	no	—
181	C₂²×C₄	#11924005	1	2	yes	—
182	C₂²×C₄	C₂×D₂₉₂	1	1	yes	characteristic
183	Q₁₆	—	292	1	no	—
184	Q₁₆	—	292	1	no	—
185	Q₁₆	—	146	4	no	—
186	M₁₆	—	2	2	no	—
187	M₁₆	—	2	4	no	—
188	C₂×C₈	—	2	2	no	—
189	C₂×C₈	—	2	2	no	—
190	C₂×C₈	#11924005	1	2	yes	—
191	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
192	C₂×C₈	C₂×C₂²⋊D₇₃	1	2	yes	—
193	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
194	C₂×C₈	#11924028	1	2	yes	—
195	C₄⋊C₄	—	292	4	no	—
196	C₄⋊C₄	—	292	2	no	—
197	C₄⋊C₄	—	146	2	no	—
198	C₂²⋊C₄	—	292	4	no	—
199	C₂²⋊C₄	—	292	1	no	—
200	C₂²⋊C₄	—	292	2	no	—
201	C₄²	—	292	1	no	—
202	C₄²	—	292	2	no	—
203	C₁₆	—	2	4	no	—
204	C₂³	#14556513	1	2	yes	—
205	C₂³	C₂×D₅₈₄	1	1	yes	characteristic
206	Q₈	—	2	2	no	—
207	Q₈	—	292	2	no	—
208	Q₈	—	292	2	no	—
209	Q₈	—	584	2	no	—
210	D₄	—	2	4	no	—
211	D₄	—	2	2	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	292	2	no	—
215	C₂×C₄	—	292	2	no	—
216	C₂×C₄	—	584	2	no	—
217	C₂×C₄	—	584	2	no	—
218	C₂×C₄	#14556513	1	2	yes	—
219	C₂×C₄	C₂×#11924005	1	1	yes	characteristic
220	C₂×C₄	#14556565	1	2	yes	—
221	C₂×C₄	C₂×#11924017	1	1	yes	characteristic
222	C₂×C₄	#14556613	1	2	yes	—
223	C₈	—	2	2	no	—
224	C₈	C₄×C₂²⋊D₇₃	1	2	yes	—
225	C₈	#14556560	1	1	yes	characteristic
226	C₈	#14556574	1	1	yes	characteristic
227	C₂²	—	2	2	no	—
228	C₂²	—	4	1	no	—
229	C₂²	—	4	2	no	—
230	C₂²	C₂×#14556513	1	1	yes	characteristic
231	C₂²	#17988823	1	2	yes	—
232	C₄	—	2	2	no	—
233	C₄	—	584	2	no	—
234	C₄	—	584	2	no	—
235	C₄	—	1168	2	no	—
236	C₄	#17988466	1	1	yes	characteristic
237	C₄	#17988584	1	1	yes	characteristic
238	C₄	#17988816	1	2	yes	—
239	C₂	—	2	1	no	—
240	C₂	—	2	2	no	—
241	C₂	—	4	2	no	—
242	C₂	#22610359	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22619586

C₂

yes

maximal, characteristic

#22611652

C₂

yes

maximal, complemented

#22609977

C₂

yes

maximal, characteristic

#22608033

C₂

yes

maximal, complemented

C₇₃×#3407

C₂

yes

maximal, characteristic

C₂²×Dic₂₉₂

C₂²

yes

characteristic

#17989158

—

#17988845

C₄

yes

complemented

#17988828

—

#17988625

C₂²

yes

—

#17988625

C₂²

yes

—

—

—

—

C₂×#131×C₇₃

C₂²

yes

characteristic

#504×C₇₃

—

C₂×M₃₂×C₇₃

—

C₂×M₃₂×C₇₃

C₂²

yes

—

C₂²×Dic₁₄₆

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

C₂×C₄

yes

—

—

—

—

—

—

—

—

—

—

C₂×C₄

yes

—

#14556516

—

#14556506

—

C₂×#41×C₇₃

D₄

yes

characteristic

#131×C₇₃

—

#131×C₇₃

—

C₂×M₁₆×C₇₃

C₂×C₄

yes

—

C₂×M₁₆×C₇₃

D₄

yes

characteristic

C₂²×C₈×C₇₃

D₄

yes

—

C₂²×C₈×C₇₃

C₂³

yes

characteristic

M₃₂×C₇₃

—

M₃₂×C₇₃

—

M₃₂×C₇₃

—

C₂×C₁₆×C₇₃

—

C₂×C₁₆×C₇₃

D₄

yes

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂²×Dic₇₃

—

Dic₂₉₂

—

Dic₂₉₂

—

Dic₂₉₂

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

#11924007

—

C₂²⋊Dic₇₃

—

C₂²⋊Dic₇₃

—

C₂²⋊Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

#41×C₇₃

—

#41×C₇₃

—

C₂×Q₈×C₇₃

SD₁₆

yes

characteristic

C₂×D₄×C₇₃

D₈

yes

—

C₂×D₄×C₇₃

SD₁₆

yes

characteristic

C₂²×C₄×C₇₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

M₁₆×C₇₃

—

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂²⋊C₄

yes

—

C₂×C₈×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×D₄

yes

—

C₂×C₈×C₇₃

C₂×D₄

yes

characteristic

C₂×C₈×C₇₃

#41

yes

—

C₁₆×C₇₃

—

C₂³×C₇₃

#102

yes

—

C₂³×C₇₃

C₂×D₈

yes

characteristic

Q₈×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

#102

yes

—

C₂×C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

#121

yes

—

C₂×C₄×C₇₃

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₇₃

#135

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

100

Dic₁₄₆

—

101

C₈×C₇₃

—

102

C₈×C₇₃

C₄×D₄

yes

—

103

C₈×C₇₃

#120

yes

characteristic

104

C₈×C₇₃

#123

yes

characteristic

105

C₂²×C₇₃

—

106

C₂²×C₇₃

—

107

C₂²×C₇₃

—

108

C₂²×C₇₃

C₂×#102

yes

characteristic

109

C₂²×C₇₃

#466

yes

—

110

C₄×C₇₃

—

111

C₄×C₇₃

#386

yes

characteristic

112

C₄×C₇₃

#416

yes

characteristic

113

C₄×C₇₃

#465

yes

—

114

Dic₇₃

—

115

Dic₇₃

—

116

Dic₇₃

—

117

#13075

—

maximal, Sylow

118

C₂×C₇₃

—

119

C₂×C₇₃

—

120

C₂×C₇₃

—

121

C₂×C₇₃

#1893

yes

characteristic

122

#3407

D₇₃

yes

characteristic

123

#3059

—

124

#2141

—

125

#1812

—

126

#1384

—

127

C₇₃

#13075

yes

characteristic, complemented, Sylow

128

C₂²×Q₁₆

—

129

C₂×#131

C₂×D₇₃

yes

characteristic

130

#536

—

146

—

131

#504

—

132

C₂×M₃₂

—

133

C₂×M₃₂

C₂×D₇₃

yes

—

134

#470

—

135

#467

—

146

—

136

#427

—

137

#427

—

138

#419

—

146

—

139

#410

—

146

—

140

#358

—

146

—

141

H(3,ℤ/4)

—

146

—

142

C₂×#41

D₂₉₂

yes

characteristic

143

C₂²×Q₈

—

146

—

144

C₂×Q₁₆

—

145

C₂×Q₁₆

—

146

—

146

C₂×Q₁₆

—

146

—

147

C₂×Q₁₆

—

146

—

148

#131

—

149

#131

—

150

C₂×M₁₆

C₄×D₇₃

yes

—

151

C₂×M₁₆

D₂₉₂

yes

characteristic

152

C₂²×C₈

C₂²⋊D₇₃

yes

—

153

C₂²×C₈

C₂²×D₇₃

yes

characteristic

154

C₄⋊Q₈

—

292

—

155

#124

—

292

—

156

#123

—

292

—

157

C₂²⋊Q₈

—

146

—

158

#117

—

146

—

159

#117

—

146

—

160

M₃₂

—

161

M₃₂

—

162

M₃₂

—

163

C₂×C₁₆

—

164

C₂×C₁₆

C₂²⋊D₇₃

yes

—

165

#107

—

146

—

166

#107

—

146

—

167

#106

—

168

#106

—

146

—

169

#103

—

146

—

170

#99

—

292

—

171

#41

—

172

#41

—

173

C₂×Q₈

—

292

—

174

C₂×Q₈

—

292

—

175

C₂×Q₈

—

292

—

176

C₂×Q₈

—

146

—

177

C₂×Q₈

#11924017

yes

characteristic

178

C₂×D₄

D₅₈₄

yes

—

179

C₂×D₄

#11924017

yes

characteristic

180

C₂²×C₄

—

292

—

181

C₂²×C₄

#11924005

yes

—

182

C₂²×C₄

C₂×D₂₉₂

yes

characteristic

183

Q₁₆

—

292

—

184

Q₁₆

—

292

—

185

Q₁₆

—

146

—

186

M₁₆

—

187

M₁₆

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

#11924005

yes

—

191

C₂×C₈

C₂×C₄×D₇₃

yes

characteristic

192

C₂×C₈

C₂×C₂²⋊D₇₃

yes

—

193

C₂×C₈

C₂×C₂²⋊D₇₃

yes

characteristic

194

C₂×C₈

#11924028

yes

—

195

C₄⋊C₄

—

292

—

196

C₄⋊C₄

—

292

—

197

C₄⋊C₄

—

146

—

198

C₂²⋊C₄

—

292

—

199

C₂²⋊C₄

—

292

—

200

C₂²⋊C₄

—

292

—

201

C₄²

—

292

—

202

C₄²

—

292

—

203

C₁₆

—

204

C₂³

#14556513

yes

—

205

C₂³

C₂×D₅₈₄

yes

characteristic

206

Q₈

—

207

Q₈

—

292

—

208

Q₈

—

292

—

209

Q₈

—

584

—

210

D₄

—

211

D₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

292

—

215

C₂×C₄

—

292

—

216

C₂×C₄

—

584

—

217

C₂×C₄

—

584

—

218

C₂×C₄

#14556513

yes

—

219

C₂×C₄

C₂×#11924005

yes

characteristic

220

C₂×C₄

#14556565

yes

—

221

C₂×C₄

C₂×#11924017

yes

characteristic

222

C₂×C₄

#14556613

yes

—

223

C₈

—

224

C₈

C₄×C₂²⋊D₇₃

yes

—

225

C₈

#14556560

yes

characteristic

226

C₈

#14556574

yes

characteristic

227

C₂²

—

228

C₂²

—

229

C₂²

—

230

C₂²

C₂×#14556513

yes

characteristic

231

C₂²

#17988823

yes

—

232

C₄

—

233

C₄

—

584

—

234

C₄

—

584

—

235

C₄

—

1168

—

236

C₄

#17988466

yes

characteristic

237

C₄

#17988584

yes

characteristic

238

C₄

#17988816

yes

—

239

C₂

—

240

C₂

—

241

C₂

—

242

C₂

#22610359

yes

characteristic

	subgroup	G/H
center	C₂	#22610359
commutator	C₂×C₈×C₇₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₇₃
Fitting	C₇₃×#3407	C₂
socle	C₂×C₇₃	#1893
prime radical	C₂×#41×C₇₃	D₄
cosocle	C₂²×C₈×C₇₃	C₂³
hypercenter	#3407	D₇₃
hypocenter	C₇₃	#13075
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #3407

subgroup

G/H

center

C₂

#22610359

commutator

C₂×C₈×C₇₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₇₃

Fitting

C₇₃×#3407

C₂

socle

C₂×C₇₃

#1893

prime radical

C₂×#41×C₇₃

D₄

cosocle

C₂²×C₈×C₇₃

C₂³

D₇₃

C₇₃

G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #3407

N	H ≅ G/N	type
2. #22611652	C₂	semidirect
4. #22608033	C₂	semidirect
8. #17988845	C₄	semidirect
127. C₇₃	#13075	semidirect

H ≅ G/N

type

2. #22611652

C₂

semidirect

4. #22608033

C₂

semidirect

8. #17988845

C₄

semidirect

127. C₇₃

#13075

semidirect

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

subgroup	index
#22619586	2
#22611652	2
#22609977	2
#22608033	2
C₇₃×#3407	2
#13075	73

subgroup

index

C₇₃×#3407

Subgroups — #33003438

Conjugacy classes of subgroups

Complements

Maximal subgroups