Group #33004357 — subgroups

Subgroups — #33004357

Order 18688.

438 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 135 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×#17988390	C₂	1	2	yes	maximal
3	C₂×C₁₆×Dic₇₃	C₂	1	1	yes	maximal, characteristic
4	#22610790	C₂	1	2	yes	maximal
5	C₂×#366×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	C₂²×#11924003	C₂²	1	1	yes	characteristic
11	C₂×#14556514	—	2	2	no	—
12	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
13	#17988492	—	2	2	no	—
14	#17988390	—	2	4	no	—
15	C₁₆×Dic₇₃	—	2	2	no	—
16	C₂²×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×#107×C₇₃	C₂²	1	2	yes	—
18	#366×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	C₂²×#10596831	D₄	1	1	yes	characteristic
27	C₂×C₄×Dic₇₃	D₄	1	1	yes	characteristic
28	Dic₅₈₄	—	2	8	no	—
29	C₂×#11924003	—	2	1	no	—
30	C₂×#11924003	—	2	1	no	—
31	C₂×#11924003	D₄	1	2	yes	—
32	#14556514	—	4	4	no	—
33	C₈×Dic₇₃	—	2	1	no	—
34	C₈×Dic₇₃	—	2	1	no	—
35	#14556498	—	4	4	no	—
36	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
37	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
38	C₂×C₁₆×C₇₃	C₂×C₄	1	2	yes	—
39	C₂×C₁₆×C₇₃	D₄	1	2	yes	—
40	C₂×C₁₆×C₇₃	D₄	1	2	yes	—
41	#107×C₇₃	—	2	2	no	—
42	#107×C₇₃	—	2	2	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	D₈	1	2	yes	—
51	Dic₂₉₂	—	2	4	no	—
52	Dic₂₉₂	—	2	4	no	—
53	Dic₂₉₂	—	4	2	no	—
54	Dic₂₉₂	—	4	2	no	—
55	C₂×#10596831	—	2	1	no	—
56	C₂×#10596831	—	2	1	no	—
57	C₂×#10596831	D₈	1	2	yes	—
58	C₄×Dic₇₃	—	2	1	no	—
59	C₄×Dic₇₃	—	2	1	no	—
60	#11924003	—	2	2	no	—
61	C₂²×C₄×C₇₃	—	4	2	no	—
62	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
63	C₂×C₈×C₇₃	C₂²×C₄	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	C₂×D₄	1	1	yes	characteristic
67	C₂×C₈×C₇₃	#41	1	1	yes	characteristic
68	C₂×C₈×C₇₃	#41	1	1	yes	characteristic
69	C₄⋊C₄×C₇₃	—	4	2	no	—
70	C₄⋊C₄×C₇₃	—	4	2	no	—
71	C₁₆×C₇₃	C₂²⋊C₄	1	4	yes	—
72	C₂³×C₇₃	C₂×D₈	1	1	yes	characteristic
73	C₂×C₄×C₇₃	—	8	2	no	—
74	C₂×C₄×C₇₃	—	8	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	—	2	2	no	—
82	C₂×Dic₇₃	—	2	2	no	—
83	C₂×Dic₇₃	—	4	4	no	—
84	C₂×Dic₇₃	—	8	2	no	—
85	C₂×Dic₇₃	—	8	2	no	—
86	C₂×Dic₇₃	Q₃₂	1	4	yes	complemented
87	Dic₁₄₆	—	4	4	no	—
88	Dic₁₄₆	—	4	4	no	—
89	Dic₁₄₆	—	8	2	no	—
90	Dic₁₄₆	—	8	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	#10596831	—	2	2	no	—
96	C₂²×C₇₃	C₄×D₈	1	1	yes	characteristic
97	C₂²×C₇₃	#466	1	1	yes	characteristic
98	C₂²×C₇₃	#493	1	1	yes	characteristic
99	C₂²×C₇₃	C₂×Q₃₂	1	2	yes	—
100	C₂²×C₇₃	#508	1	2	yes	—
101	C₄×C₇₃	—	16	2	no	—
102	C₄×C₇₃	#390	1	1	yes	characteristic
103	C₄×C₇₃	C₄×D₈	1	1	yes	characteristic
104	C₄×C₇₃	#466	1	1	yes	characteristic
105	C₄×C₇₃	#495	1	1	yes	characteristic
106	Dic₇₃	—	2	4	no	—
107	Dic₇₃	—	8	4	no	—
108	#13236	—	73	1	no	maximal, Sylow
109	C₂×C₇₃	#1970	1	1	yes	characteristic
110	C₂×C₇₃	C₄×Q₃₂	1	2	yes	—
111	C₂×C₇₃	#2216	1	2	yes	—
112	C₂×C₇₃	#2247	1	1	yes	characteristic
113	C₂×C₇₃	#2249	1	1	yes	characteristic
114	C₂²×Q₃₂	—	73	1	no	—
115	C₂×#366	D₇₃	1	1	yes	characteristic
116	C₂×#358	—	73	2	no	—
117	C₂×C₄×C₁₆	—	73	1	no	—
118	#1969	—	73	2	no	—
119	C₇₃	#13236	1	1	yes	characteristic, complemented, Sylow
120	C₂²×Q₁₆	—	73	2	no	—
121	C₂×Q₃₂	—	73	4	no	—
122	C₂×Q₃₂	—	146	2	no	—
123	C₂×Q₃₂	—	146	2	no	—
124	C₂²×C₁₆	—	73	1	no	—
125	C₂²×C₁₆	C₂×D₇₃	1	1	yes	characteristic
126	C₂×#107	C₂×D₇₃	1	2	yes	—
127	C₂×#103	—	146	2	no	—
128	C₂×C₄×C₈	—	73	1	no	—
129	#391	—	146	2	no	—
130	#366	—	2	2	no	—
131	#358	—	146	4	no	—
132	C₄×C₁₆	—	146	2	no	—
133	C₂²×Q₈	—	146	2	no	—
134	C₂×Q₁₆	—	73	4	no	—
135	C₂×Q₁₆	—	146	2	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	C₂²×C₈	—	73	1	no	—
141	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
142	C₂×C₄⋊C₄	—	2	2	no	—
143	C₂×C₄²	—	73	1	no	—
144	Q₃₂	—	146	8	no	—
145	C₂×C₁₆	—	73	2	no	—
146	C₂×C₁₆	—	146	1	no	—
147	C₂×C₁₆	—	146	1	no	—
148	C₂×C₁₆	C₄×D₇₃	1	2	yes	—
149	C₂×C₁₆	D₂₉₂	1	2	yes	—
150	C₂×C₁₆	C₂²⋊D₇₃	1	2	yes	—
151	#107	—	2	2	no	—
152	#107	—	2	2	no	—
153	#103	—	292	4	no	—
154	C₄×C₈	—	146	1	no	—
155	C₄×C₈	—	146	1	no	—
156	#95	—	292	4	no	—
157	C₂×Q₈	—	292	2	no	—
158	C₂×Q₈	—	292	2	no	—
159	C₂×Q₈	—	292	2	no	—
160	C₂×Q₈	—	292	2	no	—
161	C₂×Q₈	—	292	2	no	—
162	C₂×Q₈	—	146	4	no	—
163	C₂²×C₄	—	4	2	no	—
164	C₂²×C₄	—	292	2	no	—
165	C₂²×C₄	—	73	2	no	—
166	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
167	Q₁₆	—	292	2	no	—
168	Q₁₆	—	292	2	no	—
169	Q₁₆	—	146	4	no	—
170	Q₁₆	—	146	4	no	—
171	C₂×C₈	—	73	2	no	—
172	C₂×C₈	—	146	1	no	—
173	C₂×C₈	—	146	1	no	—
174	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
175	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
176	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
177	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
178	C₂×C₈	#11924029	1	1	yes	characteristic
179	C₂×C₈	#11924029	1	1	yes	characteristic
180	C₄⋊C₄	—	4	2	no	—
181	C₄⋊C₄	—	4	2	no	—
182	C₄²	—	146	1	no	—
183	C₄²	—	146	1	no	—
184	C₁₆	—	146	2	no	—
185	C₁₆	#11924005	1	4	yes	—
186	C₂³	D₈×D₇₃	1	1	yes	characteristic
187	Q₈	—	292	4	no	—
188	Q₈	—	292	4	no	—
189	Q₈	—	584	2	no	—
190	Q₈	—	584	2	no	—
191	C₂×C₄	—	8	2	no	—
192	C₂×C₄	—	8	4	no	—
193	C₂×C₄	—	292	4	no	—
194	C₂×C₄	—	584	2	no	—
195	C₂×C₄	—	584	2	no	—
196	C₂×C₄	—	73	4	no	—
197	C₂×C₄	—	146	2	no	—
198	C₂×C₄	—	146	2	no	—
199	C₂×C₄	#14556553	1	1	yes	characteristic
200	C₂×C₄	#14556566	1	1	yes	characteristic
201	C₂×C₄	#14556587	1	1	yes	characteristic
202	C₂×C₄	D₈×D₇₃	1	1	yes	characteristic
203	C₂×C₄	#14556614	1	1	yes	characteristic
204	C₂×C₄	#14556614	1	1	yes	characteristic
205	C₈	—	146	2	no	—
206	C₈	C₂×#11924005	1	1	yes	characteristic
207	C₈	#14556553	1	1	yes	characteristic
208	C₈	#14556566	1	1	yes	characteristic
209	C₈	#14556580	1	1	yes	characteristic
210	C₂²	#17988669	1	1	yes	characteristic
211	C₂²	#17988824	1	1	yes	characteristic
212	C₂²	#17988962	1	1	yes	characteristic
213	C₂²	Q₃₂×D₇₃	1	2	yes	—
214	C₂²	#17989016	1	2	yes	—
215	C₄	—	16	2	no	—
216	C₄	—	584	4	no	—
217	C₄	—	146	4	no	—
218	C₄	#17988488	1	1	yes	characteristic
219	C₄	#17988669	1	1	yes	characteristic
220	C₄	#17988824	1	1	yes	characteristic
221	C₄	#17988972	1	1	yes	characteristic
222	C₂	#22610795	1	1	yes	characteristic
223	C₂	#22611789	1	2	yes	—
224	C₂	#22612023	1	2	yes	—
225	C₂	#22612182	1	1	yes	characteristic
226	C₂	#22612189	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₅₈₄

C₂

yes

maximal, characteristic

C₂×#17988390

C₂

yes

maximal

C₂×C₁₆×Dic₇₃

C₂

yes

maximal, characteristic

#22610790

C₂

yes

maximal

C₂×#366×C₇₃

C₂

yes

maximal, characteristic

C₂²×Dic₂₉₂

C₂²

yes

—

C₂×Dic₅₈₄

—

C₂×Dic₅₈₄

—

C₂×Dic₅₈₄

C₄

yes

complemented

C₂²×#11924003

C₂²

yes

characteristic

C₂×#14556514

—

C₂×C₈×Dic₇₃

C₂²

yes

characteristic

#17988492

—

#17988390

—

C₁₆×Dic₇₃

—

C₂²×C₁₆×C₇₃

C₂²

yes

characteristic

C₂×#107×C₇₃

C₂²

yes

—

#366×C₇₃

—

C₂²×Dic₁₄₆

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

C₂×C₄

yes

—

C₂²×#10596831

D₄

yes

characteristic

C₂×C₄×Dic₇₃

D₄

yes

characteristic

Dic₅₈₄

—

C₂×#11924003

—

C₂×#11924003

—

C₂×#11924003

D₄

yes

—

#14556514

—

C₈×Dic₇₃

—

C₈×Dic₇₃

—

#14556498

—

C₂²×C₈×C₇₃

C₂³

yes

characteristic

C₂×C₄⋊C₄×C₇₃

—

C₂×C₁₆×C₇₃

C₂×C₄

yes

—

C₂×C₁₆×C₇₃

D₄

yes

—

C₂×C₁₆×C₇₃

D₄

yes

—

#107×C₇₃

—

#107×C₇₃

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

D₈

yes

—

Dic₂₉₂

—

Dic₂₉₂

—

Dic₂₉₂

—

Dic₂₉₂

—

C₂×#10596831

—

C₂×#10596831

—

C₂×#10596831

D₈

yes

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

#11924003

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

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

—

C₄⋊C₄×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

—

C₂×Dic₇₃

Q₃₂

yes

complemented

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

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

C₂×Q₃₂

yes

—

100

C₂²×C₇₃

#508

yes

—

101

C₄×C₇₃

—

102

C₄×C₇₃

#390

yes

characteristic

103

C₄×C₇₃

C₄×D₈

yes

characteristic

104

C₄×C₇₃

#466

yes

characteristic

105

C₄×C₇₃

#495

yes

characteristic

106

Dic₇₃

—

107

Dic₇₃

—

108

#13236

—

maximal, Sylow

109

C₂×C₇₃

#1970

yes

characteristic

110

C₂×C₇₃

C₄×Q₃₂

yes

—

111

C₂×C₇₃

#2216

yes

—

112

C₂×C₇₃

#2247

yes

characteristic

113

C₂×C₇₃

#2249

yes

characteristic

114

C₂²×Q₃₂

—

115

C₂×#366

D₇₃

yes

characteristic

116

C₂×#358

—

117

C₂×C₄×C₁₆

—

118

#1969

—

119

C₇₃

#13236

yes

characteristic, complemented, Sylow

120

C₂²×Q₁₆

—

121

C₂×Q₃₂

—

122

C₂×Q₃₂

—

146

—

123

C₂×Q₃₂

—

146

—

124

C₂²×C₁₆

—

125

C₂²×C₁₆

C₂×D₇₃

yes

characteristic

126

C₂×#107

C₂×D₇₃

yes

—

127

C₂×#103

—

146

—

128

C₂×C₄×C₈

—

129

#391

—

146

—

130

#366

—

131

#358

—

146

—

132

C₄×C₁₆

—

146

—

133

C₂²×Q₈

—

146

—

134

C₂×Q₁₆

—

135

C₂×Q₁₆

—

146

—

136

C₂×Q₁₆

—

146

—

137

C₂×Q₁₆

—

146

—

138

C₂×Q₁₆

—

146

—

139

C₂×Q₁₆

—

146

—

140

C₂²×C₈

—

141

C₂²×C₈

C₂²×D₇₃

yes

characteristic

142

C₂×C₄⋊C₄

—

143

C₂×C₄²

—

144

Q₃₂

—

146

—

145

C₂×C₁₆

—

146

C₂×C₁₆

—

146

—

147

C₂×C₁₆

—

146

—

148

C₂×C₁₆

C₄×D₇₃

yes

—

149

C₂×C₁₆

D₂₉₂

yes

—

150

C₂×C₁₆

C₂²⋊D₇₃

yes

—

151

#107

—

152

#107

—

153

#103

—

292

—

154

C₄×C₈

—

146

—

155

C₄×C₈

—

146

—

156

#95

—

292

—

157

C₂×Q₈

—

292

—

158

C₂×Q₈

—

292

—

159

C₂×Q₈

—

292

—

160

C₂×Q₈

—

292

—

161

C₂×Q₈

—

292

—

162

C₂×Q₈

—

146

—

163

C₂²×C₄

—

164

C₂²×C₄

—

292

—

165

C₂²×C₄

—

166

C₂²×C₄

D₄×D₇₃

yes

characteristic

167

Q₁₆

—

292

—

168

Q₁₆

—

292

—

169

Q₁₆

—

146

—

170

Q₁₆

—

146

—

171

C₂×C₈

—

172

C₂×C₈

—

146

—

173

C₂×C₈

—

146

—

174

C₂×C₈

C₂×C₄×D₇₃

yes

characteristic

175

C₂×C₈

D₄×D₇₃

yes

characteristic

176

C₂×C₈

C₂×C₂²⋊D₇₃

yes

characteristic

177

C₂×C₈

C₂×D₂₉₂

yes

characteristic

178

C₂×C₈

#11924029

yes

characteristic

179

C₂×C₈

#11924029

yes

characteristic

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄²

—

146

—

183

C₄²

—

146

—

184

C₁₆

—

146

—

185

C₁₆

#11924005

yes

—

186

C₂³

D₈×D₇₃

yes

characteristic

187

Q₈

—

292

—

188

Q₈

—

292

—

189

Q₈

—

584

—

190

Q₈

—

584

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

292

—

194

C₂×C₄

—

584

—

195

C₂×C₄

—

584

—

196

C₂×C₄

—

197

C₂×C₄

—

146

—

198

C₂×C₄

—

146

—

199

C₂×C₄

#14556553

yes

characteristic

200

C₂×C₄

#14556566

yes

characteristic

201

C₂×C₄

#14556587

yes

characteristic

202

C₂×C₄

D₈×D₇₃

yes

characteristic

203

C₂×C₄

#14556614

yes

characteristic

204

C₂×C₄

#14556614

yes

characteristic

205

C₈

—

146

—

206

C₈

C₂×#11924005

yes

characteristic

207

C₈

#14556553

yes

characteristic

208

C₈

#14556566

yes

characteristic

209

C₈

#14556580

yes

characteristic

210

C₂²

#17988669

yes

characteristic

211

C₂²

#17988824

yes

characteristic

212

C₂²

#17988962

yes

characteristic

213

C₂²

Q₃₂×D₇₃

yes

—

214

C₂²

#17989016

yes

—

215

C₄

—

216

C₄

—

584

—

217

C₄

—

146

—

218

C₄

#17988488

yes

characteristic

219

C₄

#17988669

yes

characteristic

220

C₄

#17988824

yes

characteristic

221

C₄

#17988972

yes

characteristic

222

C₂

#22610795

yes

characteristic

223

C₂

#22611789

yes

—

224

C₂

#22612023

yes

—

225

C₂

#22612182

yes

characteristic

226

C₂

#22612189

yes

characteristic

	subgroup	G/H
center	C₂³	D₈×D₇₃
commutator	C₂×C₈×C₇₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₇₃
Fitting	C₂×#366×C₇₃	C₂
socle, prime radical	C₂³×C₇₃	C₂×D₈
cosocle	C₂²×C₈×C₇₃	C₂³
hypercenter	C₂×#366	D₇₃
hypocenter	C₇₃	#13236
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#366

subgroup

G/H

center

C₂³

D₈×D₇₃

commutator

C₂×C₈×C₇₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₇₃

Fitting

C₂×#366×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 ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#366

N	H ≅ G/N	type
9. C₂×Dic₅₈₄	C₄	semidirect
86. C₂×Dic₇₃	Q₃₂	semidirect
119. C₇₃	#13236	semidirect

H ≅ G/N

type

9. C₂×Dic₅₈₄

C₄

semidirect

86. C₂×Dic₇₃

Q₃₂

semidirect

119. C₇₃

#13236

semidirect

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

subgroup	index
C₂²×Dic₅₈₄	2
C₂×#17988390	2
C₂×C₁₆×Dic₇₃	2
#22610790	2
C₂×#366×C₇₃	2
#13236	73

subgroup

index

C₂²×Dic₅₈₄

C₂×#17988390

C₂×C₁₆×Dic₇₃

#22610790

C₂×#366×C₇₃

#13236

Subgroups — #33004357

Conjugacy classes of subgroups

Complements

Maximal subgroups