Group #22610127 — subgroups

Subgroups — #22610127

Order 9344.

316 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 99 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×#14556549	C₂	1	1	yes	maximal, characteristic
2	C₂×#14556522	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#14556503	C₂	1	1	yes	maximal, characteristic
4	#17988444	C₂	1	1	yes	maximal, characteristic
5	#17988350	C₂	1	1	yes	maximal, characteristic, complemented
6	#17988349	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#107×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×D₇₃	C₂²	1	1	yes	characteristic
9	C₂²×#10596831	C₂²	1	1	yes	characteristic
10	#14556549	—	2	2	no	—
11	#14556549	—	2	2	no	—
12	C₂×C₄⋊Dic₇₃	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Dic₇₃	C₂²	1	1	yes	characteristic
14	C₂×#11924005	—	2	1	no	—
15	C₂×#11924005	—	2	1	no	—
16	C₂×C₄×Dic₇₃	—	2	1	no	—
17	#14556522	—	2	2	no	—
18	#14556503	C₄	1	4	yes	complemented
19	#14556498	—	2	1	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	#107×C₇₃	—	2	2	no	—
24	C₂³×D₇₃	D₄	1	1	yes	characteristic
25	C₂²×Dic₇₃	—	2	1	no	—
26	C₂²×Dic₇₃	—	2	1	no	—
27	C₂²×Dic₇₃	D₄	1	1	yes	characteristic
28	C₂×C₄×D₇₃	—	2	1	no	—
29	C₂×C₄×D₇₃	—	2	1	no	—
30	C₂×C₄×D₇₃	—	2	1	no	—
31	C₂×C₄×D₇₃	—	2	1	no	—
32	C₂×C₄×D₇₃	C₂×C₄	1	2	yes	—
33	C₂×C₄×D₇₃	Q₈	1	2	yes	—
34	C₂×#10596831	—	2	1	no	—
35	C₂×#10596831	—	2	1	no	—
36	C₂×#10596831	C₂×C₄	1	2	yes	—
37	C₄⋊Dic₇₃	—	2	1	no	—
38	C₄⋊Dic₇₃	—	2	1	no	—
39	C₄⋊Dic₇₃	—	2	1	no	—
40	C₄⋊Dic₇₃	D₄	1	2	yes	—
41	#11924005	—	2	4	no	—
42	#11924005	—	4	2	no	—
43	C₄×Dic₇₃	—	2	4	no	—
44	C₂²×C₄×C₇₃	—	2	1	no	—
45	C₂²×C₄×C₇₃	—	2	1	no	—
46	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
47	C₂×C₈×C₇₃	—	2	1	no	—
48	C₂×C₈×C₇₃	—	2	1	no	—
49	C₂×C₈×C₇₃	C₂×C₄	1	2	yes	—
50	C₄⋊C₄×C₇₃	—	2	1	no	—
51	C₄⋊C₄×C₇₃	—	2	1	no	—
52	C₄⋊C₄×C₇₃	—	2	1	no	—
53	C₄⋊C₄×C₇₃	D₄	1	2	yes	—
54	C₂³×C₇₃	C₂×D₄	1	1	yes	characteristic
55	C₂²×D₇₃	—	2	1	no	—
56	C₂²×D₇₃	—	2	1	no	—
57	C₂²×D₇₃	—	2	1	no	—
58	C₂²×D₇₃	—	2	1	no	—
59	C₂²×D₇₃	—	2	1	no	—
60	C₂²×D₇₃	—	2	1	no	—
61	C₂²×D₇₃	C₄⋊C₄	1	2	yes	—
62	C₂×C₄×C₇₃	—	2	2	no	—
63	C₂×C₄×C₇₃	—	4	1	no	—
64	C₂×C₄×C₇₃	—	4	1	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	C₂²×C₄	1	1	yes	characteristic
69	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
70	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
71	C₂×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
72	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
73	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
74	C₂×Dic₇₃	—	2	1	no	—
75	C₂×Dic₇₃	—	2	1	no	—
76	C₂×Dic₇₃	—	2	2	no	—
77	C₂×Dic₇₃	—	4	1	no	—
78	C₂×Dic₇₃	—	4	1	no	—
79	C₂×Dic₇₃	—	4	1	no	—
80	C₂×Dic₇₃	—	4	1	no	—
81	C₂×Dic₇₃	—	4	1	no	—
82	C₂×Dic₇₃	C₄⋊C₄	1	2	yes	—
83	C₄×D₇₃	—	2	2	no	—
84	C₄×D₇₃	—	2	2	no	—
85	C₄×D₇₃	—	2	2	no	—
86	C₄×D₇₃	—	2	2	no	—
87	C₈×C₇₃	—	2	2	no	—
88	#10596831	—	2	2	no	—
89	C₂²×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
90	C₂²×C₇₃	#120	1	1	yes	characteristic
91	C₂²×C₇₃	#123	1	1	yes	characteristic
92	C₂²×C₇₃	#135	1	1	yes	characteristic
93	C₂²×C₇₃	#135	1	1	yes	characteristic
94	C₂²×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
95	C₂²×C₇₃	#137	1	1	yes	characteristic
96	C₂×D₇₃	—	2	2	no	—
97	C₂×D₇₃	—	2	2	no	—
98	C₂×D₇₃	—	2	2	no	—
99	C₂×D₇₃	—	4	1	no	—
100	C₂×D₇₃	—	4	1	no	—
101	C₂×D₇₃	—	4	1	no	—
102	C₂×D₇₃	—	4	1	no	—
103	C₄×C₇₃	—	4	2	no	—
104	C₄×C₇₃	—	8	1	no	—
105	C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
106	C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
107	C₄×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
108	C₄×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
109	Dic₇₃	—	2	2	no	—
110	Dic₇₃	—	4	2	no	—
111	Dic₇₃	—	8	1	no	—
112	C₂×C₇₃	#385	1	1	yes	characteristic
113	C₂×C₇₃	#427	1	1	yes	characteristic
114	C₂×C₇₃	#428	1	1	yes	characteristic
115	C₂×C₇₃	#449	1	1	yes	characteristic
116	C₂×C₇₃	#452	1	1	yes	characteristic
117	C₂×C₇₃	#482	1	1	yes	characteristic
118	C₂×C₇₃	#485	1	1	yes	characteristic
119	D₇₃	—	4	2	no	—
120	#1854	—	73	1	no	maximal, Sylow
121	C₇₃	#1854	1	1	yes	characteristic, complemented, Sylow
122	C₂×#117	—	73	1	no	—
123	C₂×#107	D₇₃	1	1	yes	characteristic, complemented
124	C₂×#106	—	73	1	no	—
125	C₂×C₂²⋊C₈	—	73	1	no	—
126	#380	—	73	1	no	—
127	#340	—	73	1	no	—
128	#340	—	73	1	no	—
129	C₂³×C₄	—	73	1	no	—
130	C₂²×C₈	—	73	1	no	—
131	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
132	#117	—	146	2	no	—
133	#117	—	146	2	no	—
134	C₂×C₄⋊C₄	—	73	1	no	—
135	C₂×C₄⋊C₄	—	73	1	no	—
136	C₂×C₄⋊C₄	C₂×D₇₃	1	1	yes	characteristic
137	C₂×C₄⋊C₄	C₂×D₇₃	1	1	yes	characteristic
138	C₂×C₂²⋊C₄	—	146	1	no	—
139	C₂×C₂²⋊C₄	—	146	1	no	—
140	C₂×C₄²	—	146	1	no	—
141	#107	—	2	2	no	—
142	#106	—	146	2	no	—
143	C₂²⋊C₈	—	73	4	no	—
144	#95	—	146	1	no	—
145	C₂⁴	—	73	1	no	—
146	C₂²×C₄	—	2	1	no	—
147	C₂²×C₄	—	2	1	no	—
148	C₂²×C₄	—	73	1	no	—
149	C₂²×C₄	—	73	2	no	—
150	C₂²×C₄	—	73	2	no	—
151	C₂²×C₄	—	146	1	no	—
152	C₂²×C₄	—	146	1	no	—
153	C₂²×C₄	—	146	1	no	—
154	C₂²×C₄	—	146	1	no	—
155	C₂²×C₄	—	146	1	no	—
156	C₂²×C₄	—	146	1	no	—
157	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
158	C₂×C₈	—	2	1	no	—
159	C₂×C₈	—	2	1	no	—
160	C₂×C₈	—	73	2	no	—
161	C₂×C₈	—	146	1	no	—
162	C₂×C₈	—	146	1	no	—
163	C₂×C₈	C₄×D₇₃	1	2	yes	—
164	C₄⋊C₄	—	2	1	no	—
165	C₄⋊C₄	—	2	1	no	—
166	C₄⋊C₄	—	2	1	no	—
167	C₄⋊C₄	—	73	2	no	—
168	C₄⋊C₄	—	146	1	no	—
169	C₄⋊C₄	—	146	1	no	—
170	C₄⋊C₄	—	146	1	no	—
171	C₄⋊C₄	C₂²⋊D₇₃	1	2	yes	—
172	C₂²⋊C₄	—	292	2	no	—
173	C₂²⋊C₄	—	146	4	no	—
174	C₄²	—	146	4	no	—
175	C₂³	—	73	2	no	—
176	C₂³	—	146	1	no	—
177	C₂³	—	146	1	no	—
178	C₂³	—	146	1	no	—
179	C₂³	—	146	1	no	—
180	C₂³	—	146	1	no	—
181	C₂³	—	146	1	no	—
182	C₂³	D₄×D₇₃	1	1	yes	characteristic
183	C₂×C₄	—	2	2	no	—
184	C₂×C₄	—	4	1	no	—
185	C₂×C₄	—	4	1	no	—
186	C₂×C₄	—	4	1	no	—
187	C₂×C₄	—	4	1	no	—
188	C₂×C₄	—	4	1	no	—
189	C₂×C₄	—	292	1	no	—
190	C₂×C₄	—	292	1	no	—
191	C₂×C₄	—	292	1	no	—
192	C₂×C₄	—	292	1	no	—
193	C₂×C₄	—	292	1	no	—
194	C₂×C₄	—	73	2	no	—
195	C₂×C₄	—	146	2	no	—
196	C₂×C₄	—	146	1	no	—
197	C₂×C₄	—	146	1	no	—
198	C₂×C₄	—	146	2	no	—
199	C₂×C₄	—	146	2	no	—
200	C₂×C₄	—	146	2	no	—
201	C₂×C₄	—	146	2	no	—
202	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
203	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
204	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
205	C₂×C₄	Q₈×D₇₃	1	1	yes	characteristic
206	C₂×C₄	#11924028	1	1	yes	characteristic
207	C₂×C₄	#11924029	1	1	yes	characteristic
208	C₈	—	2	2	no	—
209	C₈	—	146	2	no	—
210	C₂²	—	292	1	no	—
211	C₂²	—	292	1	no	—
212	C₂²	—	292	1	no	—
213	C₂²	—	292	1	no	—
214	C₂²	—	146	2	no	—
215	C₂²	—	146	2	no	—
216	C₂²	—	146	2	no	—
217	C₂²	C₄⋊C₄×D₇₃	1	1	yes	characteristic
218	C₂²	#14556559	1	1	yes	characteristic
219	C₂²	#14556576	1	1	yes	characteristic
220	C₂²	#14556610	1	1	yes	characteristic
221	C₂²	#14556614	1	1	yes	characteristic
222	C₂²	#14556615	1	1	yes	characteristic
223	C₂²	#14556623	1	1	yes	characteristic
224	C₄	—	4	2	no	—
225	C₄	—	8	1	no	—
226	C₄	—	292	2	no	—
227	C₄	—	584	1	no	—
228	C₄	—	146	2	no	—
229	C₄	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
230	C₄	#14556553	1	1	yes	characteristic
231	C₄	#14556567	1	1	yes	characteristic
232	C₄	#14556569	1	1	yes	characteristic
233	C₂	—	292	2	no	—
234	C₂	#17988458	1	1	yes	characteristic
235	C₂	#17988624	1	1	yes	characteristic
236	C₂	#17988628	1	1	yes	characteristic
237	C₂	#17988729	1	1	yes	characteristic
238	C₂	#17988748	1	1	yes	characteristic
239	C₂	#17988914	1	1	yes	characteristic
240	C₂	#17988930	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556549

C₂

yes

maximal, characteristic

C₂×#14556522

C₂

yes

maximal, characteristic, complemented

C₂×#14556503

C₂

yes

maximal, characteristic

#17988444

C₂

yes

maximal, characteristic

#17988350

C₂

yes

maximal, characteristic, complemented

#17988349

C₂

yes

maximal, characteristic, complemented

C₂×#107×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₇₃

C₂²

yes

characteristic

C₂²×#10596831

C₂²

yes

characteristic

#14556549

—

#14556549

—

C₂×C₄⋊Dic₇₃

C₂²

yes

characteristic

C₂×C₄⋊Dic₇₃

C₂²

yes

characteristic

C₂×#11924005

—

C₂×#11924005

—

C₂×C₄×Dic₇₃

—

#14556522

—

#14556503

C₄

yes

complemented

#14556498

—

C₂²×C₈×C₇₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₇₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₇₃

C₂²

yes

characteristic

#107×C₇₃

—

C₂³×D₇₃

D₄

yes

characteristic

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

D₄

yes

characteristic

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

C₂×C₄

yes

—

C₂×C₄×D₇₃

Q₈

yes

—

C₂×#10596831

—

C₂×#10596831

—

C₂×#10596831

C₂×C₄

yes

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

D₄

yes

—

#11924005

—

#11924005

—

C₄×Dic₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂×C₄

yes

—

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

C₄⋊C₄

yes

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

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×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₄⋊C₄

yes

—

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

C₂×C₄⋊C₄

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

100

C₂×D₇₃

—

101

C₂×D₇₃

—

102

C₂×D₇₃

—

103

C₄×C₇₃

—

104

C₄×C₇₃

—

105

C₄×C₇₃

C₄×D₄

yes

characteristic

106

C₄×C₇₃

C₄×D₄

yes

characteristic

107

C₄×C₇₃

C₂²⋊Q₈

yes

characteristic

108

C₄×C₇₃

C₂²⋊Q₈

yes

characteristic

109

Dic₇₃

—

110

Dic₇₃

—

111

Dic₇₃

—

112

C₂×C₇₃

#385

yes

characteristic

113

C₂×C₇₃

#427

yes

characteristic

114

C₂×C₇₃

#428

yes

characteristic

115

C₂×C₇₃

#449

yes

characteristic

116

C₂×C₇₃

#452

yes

characteristic

117

C₂×C₇₃

#482

yes

characteristic

118

C₂×C₇₃

#485

yes

characteristic

119

D₇₃

—

120

#1854

—

maximal, Sylow

121

C₇₃

#1854

yes

characteristic, complemented, Sylow

122

C₂×#117

—

123

C₂×#107

D₇₃

yes

characteristic, complemented

124

C₂×#106

—

125

C₂×C₂²⋊C₈

—

126

#380

—

127

#340

—

128

#340

—

129

C₂³×C₄

—

130

C₂²×C₈

—

131

C₂²×C₈

C₂×D₇₃

yes

characteristic

132

#117

—

146

—

133

#117

—

146

—

134

C₂×C₄⋊C₄

—

135

C₂×C₄⋊C₄

—

136

C₂×C₄⋊C₄

C₂×D₇₃

yes

characteristic

137

C₂×C₄⋊C₄

C₂×D₇₃

yes

characteristic

138

C₂×C₂²⋊C₄

—

146

—

139

C₂×C₂²⋊C₄

—

146

—

140

C₂×C₄²

—

146

—

141

#107

—

142

#106

—

146

—

143

C₂²⋊C₈

—

144

#95

—

146

—

145

C₂⁴

—

146

C₂²×C₄

—

147

C₂²×C₄

—

148

C₂²×C₄

—

149

C₂²×C₄

—

150

C₂²×C₄

—

151

C₂²×C₄

—

146

—

152

C₂²×C₄

—

146

—

153

C₂²×C₄

—

146

—

154

C₂²×C₄

—

146

—

155

C₂²×C₄

—

146

—

156

C₂²×C₄

—

146

—

157

C₂²×C₄

C₂²×D₇₃

yes

characteristic

158

C₂×C₈

—

159

C₂×C₈

—

160

C₂×C₈

—

161

C₂×C₈

—

146

—

162

C₂×C₈

—

146

—

163

C₂×C₈

C₄×D₇₃

yes

—

164

C₄⋊C₄

—

165

C₄⋊C₄

—

166

C₄⋊C₄

—

167

C₄⋊C₄

—

168

C₄⋊C₄

—

146

—

169

C₄⋊C₄

—

146

—

170

C₄⋊C₄

—

146

—

171

C₄⋊C₄

C₂²⋊D₇₃

yes

—

172

C₂²⋊C₄

—

292

—

173

C₂²⋊C₄

—

146

—

174

C₄²

—

146

—

175

C₂³

—

176

C₂³

—

146

—

177

C₂³

—

146

—

178

C₂³

—

146

—

179

C₂³

—

146

—

180

C₂³

—

146

—

181

C₂³

—

146

—

182

C₂³

D₄×D₇₃

yes

characteristic

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

292

—

190

C₂×C₄

—

292

—

191

C₂×C₄

—

292

—

192

C₂×C₄

—

292

—

193

C₂×C₄

—

292

—

194

C₂×C₄

—

195

C₂×C₄

—

146

—

196

C₂×C₄

—

146

—

197

C₂×C₄

—

146

—

198

C₂×C₄

—

146

—

199

C₂×C₄

—

146

—

200

C₂×C₄

—

146

—

201

C₂×C₄

—

146

—

202

C₂×C₄

C₂×C₄×D₇₃

yes

characteristic

203

C₂×C₄

D₄×D₇₃

yes

characteristic

204

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

205

C₂×C₄

Q₈×D₇₃

yes

characteristic

206

C₂×C₄

#11924028

yes

characteristic

207

C₂×C₄

#11924029

yes

characteristic

208

C₈

—

209

C₈

—

146

—

210

C₂²

—

292

—

211

C₂²

—

292

—

212

C₂²

—

292

—

213

C₂²

—

292

—

214

C₂²

—

146

—

215

C₂²

—

146

—

216

C₂²

—

146

—

217

C₂²

C₄⋊C₄×D₇₃

yes

characteristic

218

C₂²

#14556559

yes

characteristic

219

C₂²

#14556576

yes

characteristic

220

C₂²

#14556610

yes

characteristic

221

C₂²

#14556614

yes

characteristic

222

C₂²

#14556615

yes

characteristic

223

C₂²

#14556623

yes

characteristic

224

C₄

—

225

C₄

—

226

C₄

—

292

—

227

C₄

—

584

—

228

C₄

—

146

—

229

C₄

C₄×C₂²⋊D₇₃

yes

characteristic

230

C₄

#14556553

yes

characteristic

231

C₄

#14556567

yes

characteristic

232

C₄

#14556569

yes

characteristic

233

C₂

—

292

—

234

C₂

#17988458

yes

characteristic

235

C₂

#17988624

yes

characteristic

236

C₂

#17988628

yes

characteristic

237

C₂

#17988729

yes

characteristic

238

C₂

#17988748

yes

characteristic

239

C₂

#17988914

yes

characteristic

240

C₂

#17988930

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₇₃
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	C₂×#107×C₇₃	C₂
socle	C₂³×C₇₃	C₂×D₄
hypercenter	C₂×#107	D₇₃
hypocenter	C₇₃	#1854
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#107

subgroup

G/H

center

C₂³

D₄×D₇₃

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

C₂×#107×C₇₃

C₂

socle

C₂³×C₇₃

C₂×D₄

D₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#107

N	H ≅ G/N	type
2. C₂×#14556522	C₂	semidirect
5. #17988350	C₂	semidirect
6. #17988349	C₂	semidirect
7. C₂×#107×C₇₃	C₂	semidirect
18. #14556503	C₄	semidirect
121. C₇₃	#1854	semidirect
123. C₂×#107	D₇₃	semidirect

H ≅ G/N

type

2. C₂×#14556522

C₂

semidirect

5. #17988350

C₂

semidirect

6. #17988349

C₂

semidirect

7. C₂×#107×C₇₃

C₂

semidirect

18. #14556503

C₄

semidirect

121. C₇₃

#1854

semidirect

123. C₂×#107

D₇₃

semidirect

Subgroups — #22610127

Conjugacy classes of subgroups

Complements