Group #32997473 — subgroups

Subgroups — #32997473

Order 18688.

306 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 85 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	#22620515	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₁₆×D₇₃	C₂	1	1	yes	maximal, characteristic
3	#22608693	C₂	1	1	yes	maximal, characteristic
4	#22607987	C₂	1	1	yes	maximal, characteristic, complemented
5	#22607985	C₂	1	1	yes	maximal, characteristic, complemented
6	#22607980	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#1362	C₂	1	1	yes	maximal, characteristic, complemented
8	#17989142	—	2	1	no	—
9	C₂×C₁₆×D₇₃	—	2	1	no	—
10	#17988992	C₂²	1	1	yes	characteristic
11	#17988937	—	2	1	no	—
12	#17988825	—	2	1	no	—
13	#17988825	C₄	1	2	yes	—
14	Q₁₆×Dic₇₃	—	2	1	no	—
15	Q₁₆×Dic₇₃	C₄	1	2	yes	—
16	#17988643	—	2	1	no	—
17	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
18	C₄⋊#11924003	C₂²	1	1	yes	characteristic
19	#17988405	—	2	1	no	—
20	#17988340	C₂²	1	1	yes	characteristic
21	#17988337	—	2	1	no	—
22	#494×C₇₃	C₂²	1	1	yes	characteristic
23	C₄⋊C₁₆×C₇₃	C₂²	1	1	yes	characteristic
24	#335×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
26	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
27	#14556591	—	2	1	no	—
28	#14556582	—	4	1	no	—
29	#14556571	—	4	1	no	—
30	#14556567	—	2	2	no	—
31	Q₈×Dic₇₃	—	2	2	no	—
32	#14556556	—	4	1	no	—
33	#14556549	—	4	1	no	—
34	C₄²×D₇₃	D₄	1	1	yes	characteristic
35	C₂×#11924003	—	2	1	no	—
36	C₁₆×D₇₃	—	4	2	no	—
37	#14556525	—	2	1	no	—
38	#14556525	C₂×C₄	1	2	yes	—
39	C₄⋊#10596831	—	2	1	no	—
40	#14556515	—	2	2	no	—
41	#14556515	—	2	2	no	—
42	#14556503	—	4	1	no	—
43	#14556501	—	4	1	no	—
44	C₄×#10596831	D₄	1	1	yes	characteristic
45	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
46	C₈×Dic₇₃	D₄	1	1	yes	characteristic
47	C₂×Q₁₆×C₇₃	—	2	1	no	—
48	C₂×Q₁₆×C₇₃	C₂×C₄	1	2	yes	—
49	C₄⋊Q₈×C₇₃	—	2	1	no	—
50	C₂×C₁₆×C₇₃	—	2	1	no	—
51	C₄⋊C₈×C₇₃	—	2	1	no	—
52	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
53	C₂×Dic₁₄₆	—	4	1	no	—
54	C₂×C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
55	C₂×C₄×D₇₃	D₈	1	1	yes	characteristic
56	C₂×C₄×D₇₃	SD₁₆	1	1	yes	characteristic
57	C₂×#10596831	—	4	1	no	—
58	C₂×#10596831	C₂²⋊C₄	1	1	yes	characteristic
59	C₂×#10596831	C₂²⋊C₄	1	1	yes	characteristic
60	C₈×D₇₃	—	2	1	no	—
61	C₈×D₇₃	—	2	1	no	—
62	C₈×D₇₃	—	4	1	no	—
63	C₄⋊Dic₇₃	—	2	2	no	—
64	C₄⋊Dic₇₃	—	4	1	no	—
65	C₄⋊Dic₇₃	—	4	2	no	—
66	#11924007	—	4	2	no	—
67	#11924005	—	4	2	no	—
68	C₄×Dic₇₃	—	4	2	no	—
69	C₄×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
70	C₄×Dic₇₃	D₈	1	1	yes	characteristic
71	C₄×Dic₇₃	SD₁₆	1	1	yes	characteristic
72	#11924003	—	4	1	no	—
73	C₂×Q₈×C₇₃	—	2	2	no	—
74	Q₁₆×C₇₃	—	4	2	no	—
75	Q₁₆×C₇₃	—	4	1	no	—
76	Q₁₆×C₇₃	—	4	1	no	—
77	C₂×C₈×C₇₃	—	4	1	no	—
78	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
79	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
80	C₄⋊C₄×C₇₃	—	4	1	no	—
81	C₄⋊C₄×C₇₃	—	4	1	no	—
82	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
83	C₁₆×C₇₃	—	4	1	no	—
84	C₂²×D₇₃	#102	1	1	yes	characteristic
85	Q₈×C₇₃	—	4	2	no	—
86	Q₈×C₇₃	—	4	2	no	—
87	C₂×C₄×C₇₃	—	4	2	no	—
88	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
90	C₂×C₄×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
91	C₂×Dic₇₃	—	4	2	no	—
92	C₂×Dic₇₃	#102	1	1	yes	characteristic
93	C₂×Dic₇₃	#102	1	1	yes	characteristic
94	C₂×Dic₇₃	#102	1	1	yes	characteristic
95	C₄×D₇₃	—	2	2	no	—
96	C₄×D₇₃	—	2	1	no	—
97	C₄×D₇₃	—	2	1	no	—
98	C₄×D₇₃	—	2	1	no	—
99	C₄×D₇₃	—	2	1	no	—
100	Dic₁₄₆	—	8	1	no	—
101	Dic₁₄₆	—	8	1	no	—
102	C₈×C₇₃	—	2	1	no	—
103	C₈×C₇₃	—	8	1	no	—
104	C₈×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
105	C₈×C₇₃	#137	1	1	yes	characteristic
106	#10596831	—	2	1	no	—
107	#10596831	—	2	1	no	—
108	#10596831	—	8	1	no	—
109	C₂²×C₇₃	C₂×#102	1	1	yes	characteristic
110	C₂×D₇₃	—	2	1	no	—
111	C₂×D₇₃	—	2	1	no	—
112	C₂×D₇₃	#362	1	2	yes	—
113	C₄×C₇₃	—	2	1	no	—
114	C₄×C₇₃	—	8	2	no	—
115	C₄×C₇₃	#413	1	1	yes	characteristic
116	C₄×C₇₃	#417	1	1	yes	characteristic
117	C₄×C₇₃	#508	1	1	yes	characteristic
118	C₄×C₇₃	#508	1	1	yes	characteristic
119	Dic₇₃	—	2	1	no	—
120	Dic₇₃	—	2	1	no	—
121	Dic₇₃	—	2	1	no	—
122	Dic₇₃	—	8	2	no	—
123	#11984	—	73	1	no	maximal, Sylow
124	C₂×C₇₃	#1547	1	1	yes	characteristic
125	C₂×C₇₃	#2138	1	1	yes	characteristic
126	C₂×C₇₃	C₂×#362	1	1	yes	characteristic
127	D₇₃	—	2	2	no	—
128	#3170	—	73	1	no	—
129	C₂×C₄⋊C₁₆	—	73	1	no	—
130	#1568	—	73	1	no	—
131	#1364	—	73	1	no	—
132	#1364	—	73	1	no	—
133	#1362	—	73	1	no	—
134	#1362	D₇₃	1	1	yes	characteristic, complemented
135	C₇₃	#11984	1	1	yes	characteristic, complemented, Sylow
136	#533	—	146	1	no	—
137	C₂²×C₁₆	—	146	1	no	—
138	#500	—	73	1	no	—
139	#494	C₂×D₇₃	1	1	yes	characteristic
140	#487	—	146	1	no	—
141	#467	—	73	2	no	—
142	#467	—	146	1	no	—
143	C₄×Q₁₆	—	73	2	no	—
144	C₄×Q₁₆	—	146	1	no	—
145	#432	—	146	1	no	—
146	C₂×C₄×C₈	—	73	1	no	—
147	C₄⋊C₁₆	—	73	1	no	—
148	C₄⋊C₁₆	—	146	1	no	—
149	C₄⋊C₁₆	C₂×D₇₃	1	1	yes	characteristic
150	#335	—	73	1	no	—
151	#335	C₂×D₇₃	1	1	yes	characteristic
152	#334	—	146	1	no	—
153	C₂×Q₁₆	—	2	1	no	—
154	C₂×Q₁₆	C₄×D₇₃	1	2	yes	—
155	C₂²×C₈	—	73	1	no	—
156	C₂²×C₈	—	73	1	no	—
157	C₄⋊Q₈	—	2	1	no	—
158	C₄⋊Q₈	—	146	1	no	—
159	#125	—	292	1	no	—
160	C₂²⋊Q₈	—	292	1	no	—
161	C₂²⋊Q₈	—	146	2	no	—
162	C₄×Q₈	—	292	1	no	—
163	C₄×Q₈	—	146	2	no	—
164	#117	—	292	1	no	—
165	C₂×C₄²	—	73	1	no	—
166	C₂×C₁₆	—	2	1	no	—
167	C₂×C₁₆	—	292	2	no	—
168	C₂×C₁₆	—	146	1	no	—
169	#107	—	73	2	no	—
170	#107	—	146	1	no	—
171	C₄⋊C₈	—	2	1	no	—
172	C₄⋊C₈	—	146	1	no	—
173	#103	—	146	2	no	—
174	#103	—	146	2	no	—
175	C₂²⋊C₈	—	292	1	no	—
176	#97	—	292	1	no	—
177	C₄×C₈	—	73	1	no	—
178	C₄×C₈	—	73	1	no	—
179	C₄×C₈	—	73	1	no	—
180	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
181	C₂×Q₈	—	2	2	no	—
182	C₂×Q₈	—	292	1	no	—
183	C₂²×C₄	—	73	1	no	—
184	C₂²×C₄	—	73	1	no	—
185	C₂²×C₄	—	73	1	no	—
186	Q₁₆	—	4	2	no	—
187	Q₁₆	—	4	1	no	—
188	Q₁₆	—	4	1	no	—
189	C₂×C₈	—	4	1	no	—
190	C₂×C₈	—	292	1	no	—
191	C₂×C₈	—	292	1	no	—
192	C₂×C₈	—	73	1	no	—
193	C₂×C₈	—	73	1	no	—
194	C₂×C₈	—	146	1	no	—
195	C₂×C₈	—	146	1	no	—
196	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
197	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
198	C₄⋊C₄	—	4	1	no	—
199	C₄⋊C₄	—	4	1	no	—
200	C₄⋊C₄	—	292	2	no	—
201	C₄⋊C₄	—	292	2	no	—
202	C₄⋊C₄	—	292	1	no	—
203	C₄⋊C₄	—	146	2	no	—
204	C₂²⋊C₄	—	292	2	no	—
205	C₄²	—	292	2	no	—
206	C₄²	—	73	1	no	—
207	C₄²	—	73	1	no	—
208	C₄²	—	73	1	no	—
209	C₄²	D₄×D₇₃	1	1	yes	characteristic
210	C₁₆	—	4	1	no	—
211	C₁₆	—	292	1	no	—
212	C₂³	—	73	1	no	—
213	Q₈	—	4	2	no	—
214	Q₈	—	4	2	no	—
215	Q₈	—	584	1	no	—
216	Q₈	—	584	1	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	292	2	no	—
219	C₂×C₄	—	73	1	no	—
220	C₂×C₄	—	73	1	no	—
221	C₂×C₄	—	73	1	no	—
222	C₂×C₄	—	146	2	no	—
223	C₂×C₄	—	146	1	no	—
224	C₂×C₄	—	146	1	no	—
225	C₂×C₄	—	146	1	no	—
226	C₂×C₄	—	146	1	no	—
227	C₂×C₄	C₂²⋊C₄×D₇₃	1	1	yes	characteristic
228	C₂×C₄	D₈×D₇₃	1	1	yes	characteristic
229	C₂×C₄	SD₁₆×D₇₃	1	1	yes	characteristic
230	C₈	—	2	1	no	—
231	C₈	—	8	1	no	—
232	C₈	—	584	1	no	—
233	C₈	—	146	1	no	—
234	C₈	—	146	1	no	—
235	C₈	#14556615	1	1	yes	characteristic
236	C₈	#14556620	1	1	yes	characteristic
237	C₂²	—	73	2	no	—
238	C₂²	—	146	1	no	—
239	C₂²	—	146	1	no	—
240	C₂²	#102×D₇₃	1	1	yes	characteristic
241	C₄	—	2	1	no	—
242	C₄	—	8	2	no	—
243	C₄	—	584	2	no	—
244	C₄	—	146	1	no	—
245	C₄	—	146	1	no	—
246	C₄	—	146	1	no	—
247	C₄	#17988568	1	1	yes	characteristic
248	C₄	#17988585	1	1	yes	characteristic
249	C₄	#17989018	1	1	yes	characteristic
250	C₄	#17989020	1	1	yes	characteristic
251	C₂	—	146	2	no	—
252	C₂	#22608605	1	1	yes	characteristic
253	C₂	#22611637	1	1	yes	characteristic
254	C₂	#362×D₇₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22620515

C₂

yes

maximal, characteristic

C₄⋊C₁₆×D₇₃

C₂

yes

maximal, characteristic

#22608693

C₂

yes

maximal, characteristic

#22607987

C₂

yes

maximal, characteristic, complemented

#22607985

C₂

yes

maximal, characteristic, complemented

#22607980

C₂

yes

maximal, characteristic, complemented

C₇₃×#1362

C₂

yes

maximal, characteristic, complemented

#17989142

—

C₂×C₁₆×D₇₃

—

#17988992

C₂²

yes

—

—

C₄

yes

—

Q₁₆×Dic₇₃

—

Q₁₆×Dic₇₃

C₄

yes

—

#17988643

—

C₄×C₈×D₇₃

C₂²

yes

characteristic

C₄⋊#11924003

C₂²

yes

characteristic

#17988405

—

#17988340

C₂²

yes

characteristic

#17988337

—

#494×C₇₃

C₂²

yes

characteristic

C₄⋊C₁₆×C₇₃

C₂²

yes

characteristic

#335×C₇₃

C₂²

yes

characteristic

C₂×C₈×D₇₃

C₂×C₄

yes

characteristic

C₂×C₈×D₇₃

D₄

yes

—

—

—

—

Q₈×Dic₇₃

—

#14556556

—

#14556549

—

C₄²×D₇₃

D₄

yes

characteristic

C₂×#11924003

—

C₁₆×D₇₃

—

#14556525

—

#14556525

C₂×C₄

yes

—

—

—

—

—

—

D₄

yes

characteristic

C₈×Dic₇₃

C₂×C₄

yes

characteristic

C₈×Dic₇₃

D₄

yes

characteristic

C₂×Q₁₆×C₇₃

—

C₂×Q₁₆×C₇₃

C₂×C₄

yes

—

C₄⋊Q₈×C₇₃

—

C₂×C₁₆×C₇₃

—

C₄⋊C₈×C₇₃

—

C₄×C₈×C₇₃

C₂³

yes

characteristic

C₂×Dic₁₄₆

—

C₂×C₄×D₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×D₇₃

D₈

yes

characteristic

C₂×C₄×D₇₃

SD₁₆

yes

characteristic

C₂×#10596831

—

C₂×#10596831

C₂²⋊C₄

yes

characteristic

C₂×#10596831

C₂²⋊C₄

yes

characteristic

C₈×D₇₃

—

C₈×D₇₃

—

C₈×D₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

#11924007

—

#11924005

—

C₄×Dic₇₃

—

C₄×Dic₇₃

C₂²⋊C₄

yes

characteristic

C₄×Dic₇₃

D₈

yes

characteristic

C₄×Dic₇₃

SD₁₆

yes

characteristic

#11924003

—

C₂×Q₈×C₇₃

—

Q₁₆×C₇₃

—

Q₁₆×C₇₃

—

Q₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×D₄

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

C₂×D₄

yes

characteristic

C₁₆×C₇₃

—

C₂²×D₇₃

#102

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₈

yes

characteristic

C₂×C₄×C₇₃

C₂×SD₁₆

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

yes

C₂×Dic₇₃

yes

C₂×Dic₇₃

yes

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

100

Dic₁₄₆

—

101

Dic₁₄₆

—

102

C₈×C₇₃

—

103

C₈×C₇₃

—

104

C₈×C₇₃

AGL(1,ℤ/8)

yes

characteristic

105

C₈×C₇₃

#137

yes

characteristic

106

#10596831

—

107

#10596831

—

108

#10596831

—

109

C₂²×C₇₃

C₂×#102

yes

characteristic

110

C₂×D₇₃

—

111

C₂×D₇₃

—

112

C₂×D₇₃

#362

yes

—

113

C₄×C₇₃

—

114

C₄×C₇₃

—

115

C₄×C₇₃

#413

yes

characteristic

116

C₄×C₇₃

#417

yes

characteristic

117

C₄×C₇₃

#508

yes

characteristic

118

C₄×C₇₃

#508

yes

characteristic

119

Dic₇₃

—

120

Dic₇₃

—

121

Dic₇₃

—

122

Dic₇₃

—

123

#11984

—

maximal, Sylow

124

C₂×C₇₃

#1547

yes

characteristic

125

C₂×C₇₃

#2138

yes

characteristic

126

C₂×C₇₃

C₂×#362

yes

characteristic

127

D₇₃

—

128

#3170

—

129

C₂×C₄⋊C₁₆

—

130

#1568

—

131

#1364

—

132

#1364

—

133

#1362

—

134

#1362

D₇₃

yes

characteristic, complemented

135

C₇₃

#11984

yes

characteristic, complemented, Sylow

136

#533

—

146

—

137

C₂²×C₁₆

—

146

—

138

#500

—

139

#494

C₂×D₇₃

yes

characteristic

140

#487

—

146

—

141

#467

—

142

#467

—

146

—

143

C₄×Q₁₆

—

144

C₄×Q₁₆

—

146

—

145

#432

—

146

—

146

C₂×C₄×C₈

—

147

C₄⋊C₁₆

—

148

C₄⋊C₁₆

—

146

—

149

C₄⋊C₁₆

C₂×D₇₃

yes

characteristic

150

#335

—

151

#335

C₂×D₇₃

yes

characteristic

152

#334

—

146

—

153

C₂×Q₁₆

—

154

C₂×Q₁₆

C₄×D₇₃

yes

—

155

C₂²×C₈

—

156

C₂²×C₈

—

157

C₄⋊Q₈

—

158

C₄⋊Q₈

—

146

—

159

#125

—

292

—

160

C₂²⋊Q₈

—

292

—

161

C₂²⋊Q₈

—

146

—

162

C₄×Q₈

—

292

—

163

C₄×Q₈

—

146

—

164

#117

—

292

—

165

C₂×C₄²

—

166

C₂×C₁₆

—

167

C₂×C₁₆

—

292

—

168

C₂×C₁₆

—

146

—

169

#107

—

170

#107

—

146

—

171

C₄⋊C₈

—

172

C₄⋊C₈

—

146

—

173

#103

—

146

—

174

#103

—

146

—

175

C₂²⋊C₈

—

292

—

176

#97

—

292

—

177

C₄×C₈

—

178

C₄×C₈

—

179

C₄×C₈

—

180

C₄×C₈

C₂²×D₇₃

yes

characteristic

181

C₂×Q₈

—

182

C₂×Q₈

—

292

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

Q₁₆

—

187

Q₁₆

—

188

Q₁₆

—

189

C₂×C₈

—

190

C₂×C₈

—

292

—

191

C₂×C₈

—

292

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

146

—

195

C₂×C₈

—

146

—

196

C₂×C₈

C₂×C₄×D₇₃

yes

characteristic

197

C₂×C₈

D₄×D₇₃

yes

characteristic

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₄⋊C₄

—

292

—

201

C₄⋊C₄

—

292

—

202

C₄⋊C₄

—

292

—

203

C₄⋊C₄

—

146

—

204

C₂²⋊C₄

—

292

—

205

C₄²

—

292

—

206

C₄²

—

207

C₄²

—

208

C₄²

—

209

C₄²

D₄×D₇₃

yes

characteristic

210

C₁₆

—

211

C₁₆

—

292

—

212

C₂³

—

213

Q₈

—

214

Q₈

—

215

Q₈

—

584

—

216

Q₈

—

584

—

217

C₂×C₄

—

218

C₂×C₄

—

292

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

146

—

223

C₂×C₄

—

146

—

224

C₂×C₄

—

146

—

225

C₂×C₄

—

146

—

226

C₂×C₄

—

146

—

227

C₂×C₄

C₂²⋊C₄×D₇₃

yes

characteristic

228

C₂×C₄

D₈×D₇₃

yes

characteristic

229

C₂×C₄

SD₁₆×D₇₃

yes

characteristic

230

C₈

—

231

C₈

—

232

C₈

—

584

—

233

C₈

—

146

—

234

C₈

—

146

—

235

C₈

#14556615

yes

characteristic

236

C₈

#14556620

yes

characteristic

237

C₂²

—

238

C₂²

—

146

—

239

C₂²

—

146

—

240

C₂²

#102×D₇₃

yes

characteristic

241

C₄

—

242

C₄

—

243

C₄

—

584

—

244

C₄

—

146

—

245

C₄

—

146

—

246

C₄

—

146

—

247

C₄

#17988568

yes

characteristic

248

C₄

#17988585

yes

characteristic

249

C₄

#17989018

yes

characteristic

250

C₄

#17989020

yes

characteristic

251

C₂

—

146

—

252

C₂

#22608605

yes

characteristic

253

C₂

#22611637

yes

characteristic

254

C₂

#362×D₇₃

yes

characteristic

	subgroup	G/H
center	C₂²	#102×D₇₃
commutator	C₂×C₈×C₇₃	C₂²×C₄
Frattini	C₄×C₈	C₂²×D₇₃
Fitting	C₇₃×#1362	C₂
socle	C₂²×C₇₃	C₂×#102
prime radical	C₂²×D₇₃	#102
cosocle	C₄×C₈×C₇₃	C₂³
hypercenter	#1362	D₇₃
hypocenter	C₇₃	#11984
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #1362

subgroup

G/H

center

C₂²

#102×D₇₃

commutator

C₂×C₈×C₇₃

C₂²×C₄

Frattini

C₄×C₈

C₂²×D₇₃

Fitting

C₇₃×#1362

C₂

C₂²×C₇₃

C₂²×D₇₃

C₄×C₈×C₇₃

C₂³

D₇₃

C₇₃

G ▷ C₂×C₈×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #1362

N	H ≅ G/N	type
4. #22607987	C₂	semidirect
5. #22607985	C₂	semidirect
6. #22607980	C₂	semidirect
7. C₇₃×#1362	C₂	semidirect
134. #1362	D₇₃	semidirect
135. C₇₃	#11984	semidirect

H ≅ G/N

type

4. #22607987

C₂

semidirect

5. #22607985

C₂

semidirect

6. #22607980

C₂

semidirect

7. C₇₃×#1362

C₂

semidirect

134. #1362

D₇₃

semidirect

135. C₇₃

#11984

semidirect

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

subgroup	index
#22620515	2
C₄⋊C₁₆×D₇₃	2
#22608693	2
#22607987	2
#22607985	2
#22607980	2
C₇₃×#1362	2
#11984	73

subgroup

index

C₄⋊C₁₆×D₇₃

C₇₃×#1362

Subgroups — #32997473

Conjugacy classes of subgroups

Complements

Maximal subgroups