Group #33004403 — subgroups

Subgroups — #33004403

Order 18688.

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

normal subgroups only

This group has 402 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	C₂²×Dic₅₈₄	C₂	1	1	yes	maximal, characteristic
2	C₂×#17988417	C₂	1	1	yes	maximal, characteristic
3	C₂×#17988404	C₂	1	2	yes	maximal
4	#22610846	C₂	1	2	yes	maximal
5	C₇₃×#2108	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₂₉₂	C₂²	1	2	yes	—
7	C₂×Dic₅₈₄	—	2	2	no	—
8	C₂×Dic₅₈₄	—	2	1	no	—
9	C₂×Dic₅₈₄	—	2	1	no	—
10	C₂×Dic₅₈₄	C₄	1	4	yes	complemented
11	C₂×#14556527	C₂²	1	2	yes	—
12	#17988595	—	2	2	no	—
13	C₂×#14556509	—	2	2	no	—
14	#17988417	—	2	2	no	—
15	#17988404	—	2	4	no	—
16	C₂×M₃₂×C₇₃	C₂²	1	1	yes	characteristic
17	C₂²×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
18	#405×C₇₃	C₂²	1	1	yes	characteristic
19	#346×C₇₃	—	2	1	no	—
20	C₄×C₁₆×C₇₃	—	2	1	no	—
21	C₂²×Dic₁₄₆	—	2	2	no	—
22	C₂×Dic₂₉₂	—	2	2	no	—
23	C₂×Dic₂₉₂	—	2	2	no	—
24	C₂×Dic₂₉₂	—	2	2	no	—
25	C₂×Dic₂₉₂	—	2	2	no	—
26	C₂×Dic₂₉₂	—	2	2	no	—
27	C₂×Dic₂₉₂	C₂×C₄	1	4	yes	—
28	C₂×#11924012	—	2	2	no	—
29	Dic₅₈₄	—	2	4	no	—
30	Dic₅₈₄	—	2	4	no	—
31	#14556527	—	2	2	no	—
32	#14556527	—	2	2	no	—
33	#14556514	—	4	4	no	—
34	#14556509	—	4	4	no	—
35	C₂×M₁₆×C₇₃	D₄	1	1	yes	characteristic
36	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
37	#117×C₇₃	D₄	1	1	yes	characteristic
38	M₃₂×C₇₃	—	2	1	no	—
39	M₃₂×C₇₃	D₄	1	2	yes	—
40	C₂×C₁₆×C₇₃	—	2	1	no	—
41	C₂×C₁₆×C₇₃	C₂×C₄	1	2	yes	—
42	C₂×C₁₆×C₇₃	D₄	1	2	yes	—
43	C₂×C₁₆×C₇₃	D₄	1	1	yes	characteristic
44	C₂×C₁₆×C₇₃	D₄	1	1	yes	characteristic
45	#97×C₇₃	—	2	1	no	—
46	C₄×C₈×C₇₃	—	2	1	no	—
47	C₂×Dic₁₄₆	—	2	4	no	—
48	C₂×Dic₁₄₆	—	4	2	no	—
49	C₂×Dic₁₄₆	—	4	2	no	—
50	C₂×Dic₁₄₆	—	4	2	no	—
51	C₂×Dic₁₄₆	—	4	2	no	—
52	C₂×Dic₁₄₆	—	4	2	no	—
53	C₂²×Dic₇₃	—	4	2	no	—
54	Dic₂₉₂	—	2	4	no	—
55	Dic₂₉₂	—	2	4	no	—
56	Dic₂₉₂	—	4	2	no	—
57	Dic₂₉₂	—	4	2	no	—
58	#11924012	—	4	2	no	—
59	#11924012	—	4	2	no	—
60	C₂×#10596831	—	4	2	no	—
61	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
62	M₁₆×C₇₃	—	2	1	no	—
63	M₁₆×C₇₃	D₈	1	2	yes	—
64	C₂×C₈×C₇₃	—	2	1	no	—
65	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
66	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
67	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
68	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
69	C₂×C₈×C₇₃	#41	1	1	yes	characteristic
70	C₂×C₈×C₇₃	#41	1	1	yes	characteristic
71	C₄⋊C₄×C₇₃	D₈	1	2	yes	—
72	C₂²⋊C₄×C₇₃	—	2	1	no	—
73	C₄²×C₇₃	—	2	1	no	—
74	C₁₆×C₇₃	—	2	2	no	—
75	C₁₆×C₇₃	C₂²⋊C₄	1	2	yes	—
76	C₁₆×C₇₃	C₂²⋊C₄	1	2	yes	—
77	C₂³×C₇₃	#135	1	1	yes	characteristic
78	C₂×C₄×C₇₃	—	2	2	no	—
79	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
80	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
81	C₂×C₄×C₇₃	#127	1	1	yes	characteristic
82	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
83	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
84	C₂×C₄×C₇₃	#135	1	1	yes	characteristic
85	C₂×Dic₇₃	—	4	4	no	—
86	C₂×Dic₇₃	—	8	2	no	—
87	C₂×Dic₇₃	—	8	2	no	—
88	Dic₁₄₆	—	4	4	no	—
89	Dic₁₄₆	—	4	4	no	—
90	Dic₁₄₆	—	8	2	no	—
91	Dic₁₄₆	—	8	2	no	—
92	C₈×C₇₃	—	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	—	8	2	no	—
98	C₂²×C₇₃	—	2	2	no	—
99	C₂²×C₇₃	C₄×D₈	1	1	yes	characteristic
100	C₂²×C₇₃	#466	1	1	yes	characteristic
101	C₂²×C₇₃	#495	1	1	yes	characteristic
102	C₄×C₇₃	—	4	2	no	—
103	C₄×C₇₃	#390	1	1	yes	characteristic
104	C₄×C₇₃	C₄×D₈	1	1	yes	characteristic
105	C₄×C₇₃	#466	1	1	yes	characteristic
106	C₄×C₇₃	#493	1	1	yes	characteristic
107	Dic₇₃	—	8	4	no	—
108	#13244	—	73	1	no	maximal, Sylow
109	C₂×C₇₃	—	2	1	no	—
110	C₂×C₇₃	—	2	1	no	—
111	C₂×C₇₃	#1970	1	1	yes	characteristic
112	C₂×C₇₃	#2222	1	2	yes	—
113	C₂²×Q₃₂	—	73	1	no	—
114	C₂×#368	—	73	1	no	—
115	C₂×#362	—	73	2	no	—
116	#2108	D₇₃	1	1	yes	characteristic
117	#1979	—	73	2	no	—
118	C₇₃	#13244	1	1	yes	characteristic, complemented, Sylow
119	C₂²×Q₁₆	—	73	2	no	—
120	C₂×Q₃₂	—	73	4	no	—
121	C₂×Q₃₂	—	146	2	no	—
122	C₂×Q₃₂	—	146	1	no	—
123	C₂×Q₃₂	—	146	1	no	—
124	C₂×M₃₂	C₂×D₇₃	1	1	yes	characteristic
125	C₂²×C₁₆	C₂×D₇₃	1	1	yes	characteristic
126	C₂×#108	—	73	2	no	—
127	#419	—	146	2	no	—
128	C₂×#101	—	146	2	no	—
129	#405	C₂×D₇₃	1	1	yes	characteristic
130	#368	—	146	2	no	—
131	#362	—	146	4	no	—
132	#346	—	2	1	no	—
133	C₄×C₁₆	—	2	1	no	—
134	C₂²×Q₈	—	146	2	no	—
135	C₂×Q₁₆	—	73	4	no	—
136	C₂×Q₁₆	—	146	2	no	—
137	C₂×Q₁₆	—	146	2	no	—
138	C₂×Q₁₆	—	146	2	no	—
139	C₂×Q₁₆	—	146	2	no	—
140	C₂×Q₁₆	—	146	2	no	—
141	C₂×M₁₆	—	146	2	no	—
142	C₂×M₁₆	D₂₉₂	1	1	yes	characteristic
143	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
144	#117	D₂₉₂	1	1	yes	characteristic
145	Q₃₂	—	146	4	no	—
146	Q₃₂	—	146	4	no	—
147	M₃₂	—	2	1	no	—
148	M₃₂	D₂₉₂	1	2	yes	—
149	C₂×C₁₆	—	2	1	no	—
150	C₂×C₁₆	C₄×D₇₃	1	2	yes	—
151	C₂×C₁₆	D₂₉₂	1	2	yes	—
152	C₂×C₁₆	C₂²⋊D₇₃	1	1	yes	characteristic
153	C₂×C₁₆	C₂²⋊D₇₃	1	1	yes	characteristic
154	#108	—	146	2	no	—
155	#108	—	146	2	no	—
156	#103	—	292	4	no	—
157	#101	—	292	4	no	—
158	#97	—	2	1	no	—
159	C₄×C₈	—	2	1	no	—
160	C₂×Q₈	—	292	2	no	—
161	C₂×Q₈	—	292	2	no	—
162	C₂×Q₈	—	292	2	no	—
163	C₂×Q₈	—	292	2	no	—
164	C₂×Q₈	—	292	2	no	—
165	C₂×Q₈	—	146	4	no	—
166	C₂²×C₄	—	292	2	no	—
167	C₂²×C₄	C₂×D₂₉₂	1	1	yes	characteristic
168	Q₁₆	—	292	2	no	—
169	Q₁₆	—	292	2	no	—
170	Q₁₆	—	146	4	no	—
171	Q₁₆	—	146	4	no	—
172	M₁₆	—	2	1	no	—
173	M₁₆	—	292	2	no	—
174	M₁₆	—	292	2	no	—
175	M₁₆	D₅₈₄	1	2	yes	—
176	C₂×C₈	—	2	1	no	—
177	C₂×C₈	—	292	2	no	—
178	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
179	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
180	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
181	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
182	C₂×C₈	#11924028	1	1	yes	characteristic
183	C₂×C₈	#11924028	1	1	yes	characteristic
184	C₄⋊C₄	D₅₈₄	1	2	yes	—
185	C₂²⋊C₄	—	2	1	no	—
186	C₄²	—	2	1	no	—
187	C₁₆	—	2	2	no	—
188	C₁₆	#11924005	1	2	yes	—
189	C₁₆	#11924005	1	2	yes	—
190	C₂³	#14556613	1	1	yes	characteristic
191	Q₈	—	292	4	no	—
192	Q₈	—	292	4	no	—
193	Q₈	—	584	2	no	—
194	Q₈	—	584	2	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	292	4	no	—
197	C₂×C₄	—	584	2	no	—
198	C₂×C₄	—	584	2	no	—
199	C₂×C₄	C₄×D₂₉₂	1	1	yes	characteristic
200	C₂×C₄	#14556565	1	1	yes	characteristic
201	C₂×C₄	#14556588	1	1	yes	characteristic
202	C₂×C₄	C₂×D₅₈₄	1	1	yes	characteristic
203	C₂×C₄	C₂×D₅₈₄	1	1	yes	characteristic
204	C₂×C₄	#14556613	1	1	yes	characteristic
205	C₈	—	2	2	no	—
206	C₈	—	584	2	no	—
207	C₈	C₂×#11924005	1	1	yes	characteristic
208	C₈	C₄×D₂₉₂	1	1	yes	characteristic
209	C₈	#14556565	1	1	yes	characteristic
210	C₈	#14556579	1	1	yes	characteristic
211	C₂²	—	2	2	no	—
212	C₂²	C₄×D₅₈₄	1	1	yes	characteristic
213	C₂²	#17988823	1	1	yes	characteristic
214	C₂²	#17988971	1	1	yes	characteristic
215	C₄	—	4	2	no	—
216	C₄	—	584	4	no	—
217	C₄	#17988489	1	1	yes	characteristic
218	C₄	C₄×D₅₈₄	1	1	yes	characteristic
219	C₄	#17988823	1	1	yes	characteristic
220	C₄	#17988964	1	1	yes	characteristic
221	C₂	—	2	1	no	—
222	C₂	—	2	1	no	—
223	C₂	#22610797	1	1	yes	characteristic
224	C₂	#22612056	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₅₈₄

C₂

yes

maximal, characteristic

C₂×#17988417

C₂

yes

maximal, characteristic

C₂×#17988404

C₂

yes

maximal

#22610846

C₂

yes

maximal

C₇₃×#2108

C₂

yes

maximal, characteristic

C₂²×Dic₂₉₂

C₂²

yes

—

C₂×Dic₅₈₄

—

C₂×Dic₅₈₄

—

C₂×Dic₅₈₄

—

C₂×Dic₅₈₄

C₄

yes

complemented

C₂×#14556527

C₂²

yes

—

—

—

—

—

C₂×M₃₂×C₇₃

C₂²

yes

characteristic

C₂²×C₁₆×C₇₃

C₂²

yes

characteristic

#405×C₇₃

C₂²

yes

characteristic

#346×C₇₃

—

C₄×C₁₆×C₇₃

—

C₂²×Dic₁₄₆

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

C₂×C₄

yes

—

C₂×#11924012

—

Dic₅₈₄

—

Dic₅₈₄

—

—

—

—

—

C₂×M₁₆×C₇₃

D₄

yes

characteristic

C₂²×C₈×C₇₃

C₂³

yes

characteristic

#117×C₇₃

D₄

yes

characteristic

M₃₂×C₇₃

—

M₃₂×C₇₃

D₄

yes

—

C₂×C₁₆×C₇₃

—

C₂×C₁₆×C₇₃

C₂×C₄

yes

—

C₂×C₁₆×C₇₃

D₄

yes

—

C₂×C₁₆×C₇₃

D₄

yes

characteristic

C₂×C₁₆×C₇₃

D₄

yes

characteristic

#97×C₇₃

—

C₄×C₈×C₇₃

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂²×Dic₇₃

—

Dic₂₉₂

—

Dic₂₉₂

—

Dic₂₉₂

—

Dic₂₉₂

—

#11924012

—

#11924012

—

C₂×#10596831

—

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

M₁₆×C₇₃

—

M₁₆×C₇₃

D₈

yes

—

C₂×C₈×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

C₄⋊C₄×C₇₃

D₈

yes

—

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₁₆×C₇₃

—

C₁₆×C₇₃

C₂²⋊C₄

yes

—

C₁₆×C₇₃

C₂²⋊C₄

yes

—

C₂³×C₇₃

#135

yes

characteristic

C₂×C₄×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

—

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

—

C₂²×C₇₃

C₄×D₈

yes

characteristic

100

C₂²×C₇₃

#466

yes

characteristic

101

C₂²×C₇₃

#495

yes

characteristic

102

C₄×C₇₃

—

103

C₄×C₇₃

#390

yes

characteristic

104

C₄×C₇₃

C₄×D₈

yes

characteristic

105

C₄×C₇₃

#466

yes

characteristic

106

C₄×C₇₃

#493

yes

characteristic

107

Dic₇₃

—

108

#13244

—

maximal, Sylow

109

C₂×C₇₃

—

110

C₂×C₇₃

—

111

C₂×C₇₃

#1970

yes

characteristic

112

C₂×C₇₃

#2222

yes

—

113

C₂²×Q₃₂

—

114

C₂×#368

—

115

C₂×#362

—

116

#2108

D₇₃

yes

characteristic

117

#1979

—

118

C₇₃

#13244

yes

characteristic, complemented, Sylow

119

C₂²×Q₁₆

—

120

C₂×Q₃₂

—

121

C₂×Q₃₂

—

146

—

122

C₂×Q₃₂

—

146

—

123

C₂×Q₃₂

—

146

—

124

C₂×M₃₂

C₂×D₇₃

yes

characteristic

125

C₂²×C₁₆

C₂×D₇₃

yes

characteristic

126

C₂×#108

—

127

#419

—

146

—

128

C₂×#101

—

146

—

129

#405

C₂×D₇₃

yes

characteristic

130

#368

—

146

—

131

#362

—

146

—

132

#346

—

133

C₄×C₁₆

—

134

C₂²×Q₈

—

146

—

135

C₂×Q₁₆

—

136

C₂×Q₁₆

—

146

—

137

C₂×Q₁₆

—

146

—

138

C₂×Q₁₆

—

146

—

139

C₂×Q₁₆

—

146

—

140

C₂×Q₁₆

—

146

—

141

C₂×M₁₆

—

146

—

142

C₂×M₁₆

D₂₉₂

yes

characteristic

143

C₂²×C₈

C₂²×D₇₃

yes

characteristic

144

#117

D₂₉₂

yes

characteristic

145

Q₃₂

—

146

—

146

Q₃₂

—

146

—

147

M₃₂

—

148

M₃₂

D₂₉₂

yes

—

149

C₂×C₁₆

—

150

C₂×C₁₆

C₄×D₇₃

yes

—

151

C₂×C₁₆

D₂₉₂

yes

—

152

C₂×C₁₆

C₂²⋊D₇₃

yes

characteristic

153

C₂×C₁₆

C₂²⋊D₇₃

yes

characteristic

154

#108

—

146

—

155

#108

—

146

—

156

#103

—

292

—

157

#101

—

292

—

158

#97

—

159

C₄×C₈

—

160

C₂×Q₈

—

292

—

161

C₂×Q₈

—

292

—

162

C₂×Q₈

—

292

—

163

C₂×Q₈

—

292

—

164

C₂×Q₈

—

292

—

165

C₂×Q₈

—

146

—

166

C₂²×C₄

—

292

—

167

C₂²×C₄

C₂×D₂₉₂

yes

characteristic

168

Q₁₆

—

292

—

169

Q₁₆

—

292

—

170

Q₁₆

—

146

—

171

Q₁₆

—

146

—

172

M₁₆

—

173

M₁₆

—

292

—

174

M₁₆

—

292

—

175

M₁₆

D₅₈₄

yes

—

176

C₂×C₈

—

177

C₂×C₈

—

292

—

178

C₂×C₈

C₂×C₄×D₇₃

yes

characteristic

179

C₂×C₈

C₂×C₂²⋊D₇₃

yes

characteristic

180

C₂×C₈

C₂×D₂₉₂

yes

characteristic

181

C₂×C₈

C₂×D₂₉₂

yes

characteristic

182

C₂×C₈

#11924028

yes

characteristic

183

C₂×C₈

#11924028

yes

characteristic

184

C₄⋊C₄

D₅₈₄

yes

—

185

C₂²⋊C₄

—

186

C₄²

—

187

C₁₆

—

188

C₁₆

#11924005

yes

—

189

C₁₆

#11924005

yes

—

190

C₂³

#14556613

yes

characteristic

191

Q₈

—

292

—

192

Q₈

—

292

—

193

Q₈

—

584

—

194

Q₈

—

584

—

195

C₂×C₄

—

196

C₂×C₄

—

292

—

197

C₂×C₄

—

584

—

198

C₂×C₄

—

584

—

199

C₂×C₄

C₄×D₂₉₂

yes

characteristic

200

C₂×C₄

#14556565

yes

characteristic

201

C₂×C₄

#14556588

yes

characteristic

202

C₂×C₄

C₂×D₅₈₄

yes

characteristic

203

C₂×C₄

C₂×D₅₈₄

yes

characteristic

204

C₂×C₄

#14556613

yes

characteristic

205

C₈

—

206

C₈

—

584

—

207

C₈

C₂×#11924005

yes

characteristic

208

C₈

C₄×D₂₉₂

yes

characteristic

209

C₈

#14556565

yes

characteristic

210

C₈

#14556579

yes

characteristic

211

C₂²

—

212

C₂²

C₄×D₅₈₄

yes

characteristic

213

C₂²

#17988823

yes

characteristic

214

C₂²

#17988971

yes

characteristic

215

C₄

—

216

C₄

—

584

—

217

C₄

#17988489

yes

characteristic

218

C₄

C₄×D₅₈₄

yes

characteristic

219

C₄

#17988823

yes

characteristic

220

C₄

#17988964

yes

characteristic

221

C₂

—

222

C₂

—

223

C₂

#22610797

yes

characteristic

224

C₂

#22612056

yes

—

	subgroup	G/H
center	C₂²	#17988823
commutator	C₂×C₈×C₇₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₇₃
Fitting	C₇₃×#2108	C₂
socle	C₂²×C₇₃	#466
prime radical	C₂³×C₇₃	#135
cosocle	C₂²×C₈×C₇₃	C₂³
hypercenter	#2108	D₇₃
hypocenter	C₇₃	#13244
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #405 ◁ #2108

subgroup

G/H

center

C₂²

#17988823

commutator

C₂×C₈×C₇₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₇₃

Fitting

C₇₃×#2108

C₂

C₂²×C₇₃

C₂³×C₇₃

C₂²×C₈×C₇₃

C₂³

D₇₃

C₇₃

G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #405 ◁ #2108

N	H ≅ G/N	type
10. C₂×Dic₅₈₄	C₄	semidirect
118. C₇₃	#13244	semidirect

H ≅ G/N

type

10. C₂×Dic₅₈₄

C₄

semidirect

118. C₇₃

#13244

semidirect

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

subgroup	index
C₂²×Dic₅₈₄	2
C₂×#17988417	2
C₂×#17988404	2
#22610846	2
C₇₃×#2108	2
#13244	73

subgroup

index

C₂²×Dic₅₈₄

C₇₃×#2108

Subgroups — #33004403

Conjugacy classes of subgroups

Complements

Maximal subgroups