Group #22611066 — subgroups

Subgroups — #22611066

Order 9344.

326 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 87 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×#14556590	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14556513	C₂	1	1	yes	maximal, characteristic
3	C₂×#14556511	C₂	1	1	yes	maximal, characteristic
4	#17988488	C₂	1	1	yes	maximal, characteristic
5	#17988349	C₂	1	1	yes	maximal, characteristic, complemented
6	#17988341	C₂	1	1	yes	maximal, characteristic, complemented
7	#340×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×Dic₁₄₆	—	2	1	no	—
9	C₂²×D₂₉₂	C₂²	1	1	yes	characteristic
10	C₂²×#10596831	C₂²	1	1	yes	characteristic
11	#14556590	—	2	2	no	—
12	#14556590	—	2	2	no	—
13	C₂×C₄⋊Dic₇₃	C₂²	1	1	yes	characteristic
14	C₂×#11924007	—	2	1	no	—
15	C₂×#11924005	—	2	1	no	—
16	C₂×#11924005	—	2	1	no	—
17	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
18	#14556513	—	2	2	no	—
19	#14556511	—	2	2	no	—
20	C₂²×C₈×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
23	C₂³×D₇₃	—	2	1	no	—
24	C₂×Dic₁₄₆	—	2	4	no	—
25	C₂×Dic₁₄₆	—	4	2	no	—
26	C₂×Dic₁₄₆	—	4	2	no	—
27	C₂×D₂₉₂	—	2	1	no	—
28	C₂×D₂₉₂	—	2	1	no	—
29	C₂×D₂₉₂	—	2	1	no	—
30	C₂×D₂₉₂	—	2	1	no	—
31	C₂×D₂₉₂	—	2	1	no	—
32	C₂×D₂₉₂	Q₈	1	2	yes	complemented
33	C₂²×Dic₇₃	—	2	1	no	—
34	C₂²×Dic₇₃	D₄	1	1	yes	characteristic
35	C₂²×Dic₇₃	D₄	1	1	yes	characteristic
36	C₂×#10596831	—	2	1	no	—
37	C₂×#10596831	—	2	1	no	—
38	C₂×#10596831	—	2	1	no	—
39	C₄⋊Dic₇₃	—	2	1	no	—
40	C₄⋊Dic₇₃	D₄	1	2	yes	—
41	#11924007	—	2	4	no	—
42	#11924005	—	4	2	no	—
43	#11924005	—	4	2	no	—
44	C₄×Dic₇₃	—	2	1	no	—
45	C₄×Dic₇₃	—	2	1	no	—
46	C₂²×C₄×C₇₃	—	2	1	no	—
47	C₂²×C₄×C₇₃	—	2	1	no	—
48	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
49	C₂×C₈×C₇₃	—	2	1	no	—
50	C₂×C₈×C₇₃	—	2	1	no	—
51	C₂×C₈×C₇₃	—	2	1	no	—
52	C₄⋊C₄×C₇₃	—	2	1	no	—
53	C₄⋊C₄×C₇₃	—	2	1	no	—
54	C₄⋊C₄×C₇₃	—	2	1	no	—
55	C₄⋊C₄×C₇₃	D₄	1	2	yes	—
56	C₂³×C₇₃	C₂×D₄	1	1	yes	characteristic
57	C₂²×D₇₃	—	2	2	no	—
58	C₂²×D₇₃	—	4	1	no	—
59	C₂²×D₇₃	—	4	1	no	—
60	C₂²×D₇₃	—	4	1	no	—
61	C₂²×D₇₃	—	4	1	no	—
62	C₂²×D₇₃	—	4	1	no	—
63	C₂²×D₇₃	—	4	1	no	—
64	C₂×C₄×C₇₃	—	2	2	no	—
65	C₂×C₄×C₇₃	—	4	1	no	—
66	C₂×C₄×C₇₃	—	4	1	no	—
67	C₂×C₄×C₇₃	—	4	1	no	—
68	C₂×C₄×C₇₃	—	4	1	no	—
69	C₂×C₄×C₇₃	—	4	1	no	—
70	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
71	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
72	C₂×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
73	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
74	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
75	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
76	C₂×Dic₇₃	—	2	1	no	—
77	C₂×Dic₇₃	—	2	1	no	—
78	C₂×Dic₇₃	—	2	1	no	—
79	C₂×Dic₇₃	—	2	1	no	—
80	C₂×Dic₇₃	—	2	2	no	—
81	C₂×Dic₇₃	—	4	1	no	—
82	C₂×Dic₇₃	—	4	1	no	—
83	C₂×Dic₇₃	D₈	1	2	yes	—
84	C₂×Dic₇₃	SD₁₆	1	2	yes	—
85	D₂₉₂	—	2	2	no	—
86	D₂₉₂	—	2	2	no	—
87	D₂₉₂	—	4	1	no	—
88	D₂₉₂	—	4	1	no	—
89	Dic₁₄₆	—	4	8	no	—
90	C₈×C₇₃	—	4	1	no	—
91	#10596831	—	4	1	no	—
92	C₂²×C₇₃	#120	1	1	yes	characteristic
93	C₂²×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
94	C₂²×C₇₃	#124	1	1	yes	characteristic
95	C₂²×C₇₃	C₂×D₈	1	1	yes	characteristic
96	C₂²×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
97	C₂²×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
98	C₂²×C₇₃	#137	1	1	yes	characteristic
99	C₂×D₇₃	—	4	2	no	—
100	C₂×D₇₃	—	4	2	no	—
101	C₂×D₇₃	—	4	2	no	—
102	C₂×D₇₃	—	8	1	no	—
103	C₂×D₇₃	—	8	1	no	—
104	C₂×D₇₃	—	8	1	no	—
105	C₂×D₇₃	—	8	1	no	—
106	C₄×C₇₃	—	4	2	no	—
107	C₄×C₇₃	—	8	1	no	—
108	C₄×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
109	C₄×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
110	C₄×C₇₃	#124	1	1	yes	characteristic
111	C₄×C₇₃	#124	1	1	yes	characteristic
112	Dic₇₃	—	2	2	no	—
113	Dic₇₃	—	2	2	no	—
114	Dic₇₃	—	4	2	no	—
115	C₂×C₇₃	#393	1	1	yes	characteristic
116	C₂×C₇₃	#447	1	1	yes	characteristic
117	C₂×C₇₃	#448	1	1	yes	characteristic
118	C₂×C₇₃	#474	1	1	yes	characteristic
119	C₂×C₇₃	#476	1	1	yes	characteristic
120	C₂×C₇₃	#486	1	1	yes	characteristic
121	C₂×C₇₃	#489	1	1	yes	characteristic
122	D₇₃	—	8	2	no	—
123	#2023	—	73	1	no	maximal, Sylow
124	C₇₃	#2023	1	1	yes	characteristic, complemented, Sylow
125	C₂×C₄⋊Q₈	—	73	1	no	—
126	C₂×#102	—	73	1	no	—
127	C₂×#102	—	73	1	no	—
128	#390	—	73	1	no	—
129	#340	—	73	1	no	—
130	#340	D₇₃	1	1	yes	characteristic, complemented
131	#336	—	73	1	no	—
132	C₂²×Q₈	—	146	1	no	—
133	C₂²×D₄	—	73	1	no	—
134	C₂²×C₈	—	73	1	no	—
135	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
136	C₄⋊Q₈	—	146	2	no	—
137	C₄⋊Q₈	—	146	2	no	—
138	C₂×C₄⋊C₄	—	73	1	no	—
139	C₂×C₄⋊C₄	—	146	1	no	—
140	C₂×C₄⋊C₄	C₂×D₇₃	1	1	yes	characteristic
141	C₂×C₄⋊C₄	C₂×D₇₃	1	1	yes	characteristic
142	C₂×C₂²⋊C₄	—	146	1	no	—
143	C₂×C₂²⋊C₄	—	146	1	no	—
144	C₂×C₄²	—	73	1	no	—
145	#102	—	146	2	no	—
146	#102	—	146	2	no	—
147	C₂⁴	—	146	1	no	—
148	C₂×Q₈	—	292	2	no	—
149	C₂×Q₈	—	292	2	no	—
150	C₂×Q₈	—	146	4	no	—
151	C₂×D₄	—	73	2	no	—
152	C₂×D₄	—	146	1	no	—
153	C₂×D₄	—	146	1	no	—
154	C₂×D₄	—	146	1	no	—
155	C₂×D₄	—	146	1	no	—
156	C₂×D₄	—	146	1	no	—
157	C₂²×C₄	—	2	1	no	—
158	C₂²×C₄	—	2	1	no	—
159	C₂²×C₄	—	73	1	no	—
160	C₂²×C₄	—	73	1	no	—
161	C₂²×C₄	—	146	1	no	—
162	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
163	C₂×C₈	—	2	1	no	—
164	C₂×C₈	—	2	1	no	—
165	C₂×C₈	—	2	1	no	—
166	C₂×C₈	—	146	1	no	—
167	C₂×C₈	—	146	1	no	—
168	C₂×C₈	—	146	1	no	—
169	C₄⋊C₄	—	2	1	no	—
170	C₄⋊C₄	—	2	1	no	—
171	C₄⋊C₄	—	2	1	no	—
172	C₄⋊C₄	—	73	2	no	—
173	C₄⋊C₄	—	146	4	no	—
174	C₄⋊C₄	—	146	1	no	—
175	C₄⋊C₄	D₂₉₂	1	2	yes	—
176	C₂²⋊C₄	—	292	2	no	—
177	C₂²⋊C₄	—	292	2	no	—
178	C₄²	—	146	1	no	—
179	C₄²	—	146	1	no	—
180	C₂³	—	292	1	no	—
181	C₂³	—	292	1	no	—
182	C₂³	—	292	1	no	—
183	C₂³	—	292	1	no	—
184	C₂³	—	292	1	no	—
185	C₂³	—	292	1	no	—
186	C₂³	—	146	2	no	—
187	C₂³	D₄×D₇₃	1	1	yes	characteristic
188	Q₈	—	292	8	no	—
189	D₄	—	292	1	no	—
190	D₄	—	292	1	no	—
191	D₄	—	146	2	no	—
192	D₄	—	146	2	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	4	1	no	—
195	C₂×C₄	—	4	1	no	—
196	C₂×C₄	—	4	1	no	—
197	C₂×C₄	—	4	1	no	—
198	C₂×C₄	—	4	1	no	—
199	C₂×C₄	—	292	1	no	—
200	C₂×C₄	—	292	1	no	—
201	C₂×C₄	—	73	2	no	—
202	C₂×C₄	—	73	2	no	—
203	C₂×C₄	—	146	2	no	—
204	C₂×C₄	—	146	1	no	—
205	C₂×C₄	—	146	1	no	—
206	C₂×C₄	—	146	1	no	—
207	C₂×C₄	—	146	1	no	—
208	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
209	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
210	C₂×C₄	Q₈×D₇₃	1	1	yes	characteristic
211	C₂×C₄	#11924027	1	1	yes	characteristic
212	C₂×C₄	#11924028	1	1	yes	characteristic
213	C₂×C₄	#11924028	1	1	yes	characteristic
214	C₈	—	4	1	no	—
215	C₈	—	292	1	no	—
216	C₂²	—	292	2	no	—
217	C₂²	—	292	2	no	—
218	C₂²	—	292	2	no	—
219	C₂²	—	584	1	no	—
220	C₂²	—	584	1	no	—
221	C₂²	—	584	1	no	—
222	C₂²	—	584	1	no	—
223	C₂²	#14556561	1	1	yes	characteristic
224	C₂²	#14556569	1	1	yes	characteristic
225	C₂²	#14556577	1	1	yes	characteristic
226	C₂²	D₈×D₇₃	1	1	yes	characteristic
227	C₂²	SD₁₆×D₇₃	1	1	yes	characteristic
228	C₂²	#14556618	1	1	yes	characteristic
229	C₂²	#14556623	1	1	yes	characteristic
230	C₄	—	4	2	no	—
231	C₄	—	8	1	no	—
232	C₄	—	292	2	no	—
233	C₄	—	146	2	no	—
234	C₄	—	146	2	no	—
235	C₄	#14556569	1	1	yes	characteristic
236	C₄	#14556571	1	1	yes	characteristic
237	C₄	#14556577	1	1	yes	characteristic
238	C₄	#14556579	1	1	yes	characteristic
239	C₂	—	584	2	no	—
240	C₂	#17988500	1	1	yes	characteristic
241	C₂	#17988722	1	1	yes	characteristic
242	C₂	#17988727	1	1	yes	characteristic
243	C₂	#17988866	1	1	yes	characteristic
244	C₂	#17988876	1	1	yes	characteristic
245	C₂	#17988932	1	1	yes	characteristic
246	C₂	#17988948	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556590

C₂

yes

maximal, characteristic, complemented

C₂×#14556513

C₂

yes

maximal, characteristic

C₂×#14556511

C₂

yes

maximal, characteristic

#17988488

C₂

yes

maximal, characteristic

#17988349

C₂

yes

maximal, characteristic, complemented

#17988341

C₂

yes

maximal, characteristic, complemented

#340×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂²×Dic₁₄₆

—

C₂²×D₂₉₂

C₂²

yes

characteristic

C₂²×#10596831

C₂²

yes

characteristic

#14556590

—

#14556590

—

C₂×C₄⋊Dic₇₃

C₂²

yes

—

—

—

C₂×C₄×Dic₇₃

C₂²

yes

characteristic

#14556513

—

#14556511

—

C₂²×C₈×C₇₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₇₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₇₃

C₂²

yes

characteristic

C₂³×D₇₃

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

Q₈

yes

complemented

C₂²×Dic₇₃

—

C₂²×Dic₇₃

D₄

yes

characteristic

C₂²×Dic₇₃

D₄

yes

—

—

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

D₄

yes

—

#11924007

—

#11924005

—

#11924005

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

D₄

yes

—

C₂³×C₇₃

C₂×D₄

yes

characteristic

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×Q₈

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

D₈

yes

—

C₂×Dic₇₃

SD₁₆

yes

—

D₂₉₂

—

D₂₉₂

—

D₂₉₂

—

D₂₉₂

—

Dic₁₄₆

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

#120

yes

characteristic

C₂²×C₇₃

C₂²⋊Q₈

yes

characteristic

C₂²×C₇₃

#124

yes

characteristic

C₂²×C₇₃

C₂×D₈

yes

characteristic

C₂²×C₇₃

C₂×SD₁₆

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂×D₇₃

—

100

C₂×D₇₃

—

101

C₂×D₇₃

—

102

C₂×D₇₃

—

103

C₂×D₇₃

—

104

C₂×D₇₃

—

105

C₂×D₇₃

—

106

C₄×C₇₃

—

107

C₄×C₇₃

—

108

C₄×C₇₃

C₂²⋊Q₈

yes

characteristic

109

C₄×C₇₃

C₂²⋊Q₈

yes

characteristic

110

C₄×C₇₃

#124

yes

characteristic

111

C₄×C₇₃

#124

yes

characteristic

112

Dic₇₃

—

113

Dic₇₃

—

114

Dic₇₃

—

115

C₂×C₇₃

#393

yes

characteristic

116

C₂×C₇₃

#447

yes

characteristic

117

C₂×C₇₃

#448

yes

characteristic

118

C₂×C₇₃

#474

yes

characteristic

119

C₂×C₇₃

#476

yes

characteristic

120

C₂×C₇₃

#486

yes

characteristic

121

C₂×C₇₃

#489

yes

characteristic

122

D₇₃

—

123

#2023

—

maximal, Sylow

124

C₇₃

#2023

yes

characteristic, complemented, Sylow

125

C₂×C₄⋊Q₈

—

126

C₂×#102

—

127

C₂×#102

—

128

#390

—

129

#340

—

130

#340

D₇₃

yes

characteristic, complemented

131

#336

—

132

C₂²×Q₈

—

146

—

133

C₂²×D₄

—

134

C₂²×C₈

—

135

C₂²×C₈

C₂×D₇₃

yes

characteristic

136

C₄⋊Q₈

—

146

—

137

C₄⋊Q₈

—

146

—

138

C₂×C₄⋊C₄

—

139

C₂×C₄⋊C₄

—

146

—

140

C₂×C₄⋊C₄

C₂×D₇₃

yes

characteristic

141

C₂×C₄⋊C₄

C₂×D₇₃

yes

characteristic

142

C₂×C₂²⋊C₄

—

146

—

143

C₂×C₂²⋊C₄

—

146

—

144

C₂×C₄²

—

145

#102

—

146

—

146

#102

—

146

—

147

C₂⁴

—

146

—

148

C₂×Q₈

—

292

—

149

C₂×Q₈

—

292

—

150

C₂×Q₈

—

146

—

151

C₂×D₄

—

152

C₂×D₄

—

146

—

153

C₂×D₄

—

146

—

154

C₂×D₄

—

146

—

155

C₂×D₄

—

146

—

156

C₂×D₄

—

146

—

157

C₂²×C₄

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

146

—

162

C₂²×C₄

C₂²×D₇₃

yes

characteristic

163

C₂×C₈

—

164

C₂×C₈

—

165

C₂×C₈

—

166

C₂×C₈

—

146

—

167

C₂×C₈

—

146

—

168

C₂×C₈

—

146

—

169

C₄⋊C₄

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

146

—

174

C₄⋊C₄

—

146

—

175

C₄⋊C₄

D₂₉₂

yes

—

176

C₂²⋊C₄

—

292

—

177

C₂²⋊C₄

—

292

—

178

C₄²

—

146

—

179

C₄²

—

146

—

180

C₂³

—

292

—

181

C₂³

—

292

—

182

C₂³

—

292

—

183

C₂³

—

292

—

184

C₂³

—

292

—

185

C₂³

—

292

—

186

C₂³

—

146

—

187

C₂³

D₄×D₇₃

yes

characteristic

188

Q₈

—

292

—

189

D₄

—

292

—

190

D₄

—

292

—

191

D₄

—

146

—

192

D₄

—

146

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

292

—

200

C₂×C₄

—

292

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

146

—

204

C₂×C₄

—

146

—

205

C₂×C₄

—

146

—

206

C₂×C₄

—

146

—

207

C₂×C₄

—

146

—

208

C₂×C₄

D₄×D₇₃

yes

characteristic

209

C₂×C₄

C₂×D₂₉₂

yes

characteristic

210

C₂×C₄

Q₈×D₇₃

yes

characteristic

211

C₂×C₄

#11924027

yes

characteristic

212

C₂×C₄

#11924028

yes

characteristic

213

C₂×C₄

#11924028

yes

characteristic

214

C₈

—

215

C₈

—

292

—

216

C₂²

—

292

—

217

C₂²

—

292

—

218

C₂²

—

292

—

219

C₂²

—

584

—

220

C₂²

—

584

—

221

C₂²

—

584

—

222

C₂²

—

584

—

223

C₂²

#14556561

yes

characteristic

224

C₂²

#14556569

yes

characteristic

225

C₂²

#14556577

yes

characteristic

226

C₂²

D₈×D₇₃

yes

characteristic

227

C₂²

SD₁₆×D₇₃

yes

characteristic

228

C₂²

#14556618

yes

characteristic

229

C₂²

#14556623

yes

characteristic

230

C₄

—

231

C₄

—

232

C₄

—

292

—

233

C₄

—

146

—

234

C₄

—

146

—

235

C₄

#14556569

yes

characteristic

236

C₄

#14556571

yes

characteristic

237

C₄

#14556577

yes

characteristic

238

C₄

#14556579

yes

characteristic

239

C₂

—

584

—

240

C₂

#17988500

yes

characteristic

241

C₂

#17988722

yes

characteristic

242

C₂

#17988727

yes

characteristic

243

C₂

#17988866

yes

characteristic

244

C₂

#17988876

yes

characteristic

245

C₂

#17988932

yes

characteristic

246

C₂

#17988948

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₇₃
commutator	C₂²×C₄×C₇₃	C₂³
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	#340×C₇₃	C₂
socle	C₂³×C₇₃	C₂×D₄
hypercenter	#340	D₇₃
hypocenter	C₇₃	#2023
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

subgroup

G/H

center

C₂³

D₄×D₇₃

commutator

C₂²×C₄×C₇₃

C₂³

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

#340×C₇₃

C₂

socle

C₂³×C₇₃

C₂×D₄

D₇₃

C₇₃

G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

N	H ≅ G/N	type
1. C₂×#14556590	C₂	semidirect
5. #17988349	C₂	semidirect
6. #17988341	C₂	semidirect
7. #340×C₇₃	C₂	semidirect
32. C₂×D₂₉₂	Q₈	semidirect
124. C₇₃	#2023	semidirect
130. #340	D₇₃	semidirect

H ≅ G/N

type

1. C₂×#14556590

C₂

semidirect

5. #17988349

C₂

semidirect

6. #17988341

C₂

semidirect

7. #340×C₇₃

C₂

semidirect

32. C₂×D₂₉₂

Q₈

semidirect

124. C₇₃

#2023

semidirect

130. #340

D₇₃

semidirect

Subgroups — #22611066

Conjugacy classes of subgroups

Complements