Group #32983385 — subgroups

Subgroups — #32983385

Order 18688.

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

normal subgroups only

This group has 466 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	#22619016	C₂	1	1	yes	maximal, characteristic
2	#22609927	C₂	1	1	yes	maximal, characteristic
3	#22608612	C₂	1	2	yes	maximal
4	#22607834	C₂	1	2	yes	maximal
5	C₇₃×#2567	C₂	1	1	yes	maximal, characteristic
6	#17988718	—	2	4	no	—
7	#17988644	—	2	2	no	—
8	#17988640	C₂²	1	2	yes	—
9	#17988611	C₂²	1	2	yes	—
10	C₂×#14556510	—	2	1	no	—
11	#17988356	—	2	1	no	—
12	#17988336	—	2	4	no	—
13	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
15	#395×C₇₃	C₄	1	4	yes	—
16	#391×C₇₃	—	2	1	no	—
17	#389×C₇₃	—	2	2	no	—
18	#384×C₇₃	—	2	1	no	—
19	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
20	C₂×#11924012	—	2	2	no	—
21	C₄⋊#10596831	—	2	4	no	—
22	C₄⋊#10596831	—	2	2	no	—
23	C₄⋊#10596831	—	2	2	no	—
24	C₄⋊#10596831	D₄	1	4	yes	—
25	#14556510	—	4	2	no	—
26	C₂²⋊#10596831	—	2	2	no	—
27	#14556502	—	2	4	no	—
28	C₄×#10596831	—	2	2	no	—
29	C₂²×Q₈×C₇₃	C₂×C₄	1	2	yes	—
30	C₂²×Q₈×C₇₃	D₄	1	1	yes	characteristic
31	C₄⋊Q₈×C₇₃	—	2	2	no	—
32	C₄⋊Q₈×C₇₃	—	2	2	no	—
33	C₄×Q₈×C₇₃	—	2	2	no	—
34	C₄×Q₈×C₇₃	—	2	2	no	—
35	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
36	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
37	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
38	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
39	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
40	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₇₃	—	2	1	no	—
42	C₂×C₄²×C₇₃	D₄	1	2	yes	—
43	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
44	#95×C₇₃	—	2	4	no	—
45	#95×C₇₃	C₂×C₄	1	2	yes	—
46	#11924012	—	4	2	no	—
47	#11924012	—	4	2	no	—
48	C₂×#10596831	—	2	4	no	—
49	C₂×#10596831	—	4	2	no	—
50	C₂×Q₈×C₇₃	—	2	2	no	—
51	C₂×Q₈×C₇₃	—	2	1	no	—
52	C₂×Q₈×C₇₃	—	2	1	no	—
53	C₂×Q₈×C₇₃	—	2	2	no	—
54	C₂×Q₈×C₇₃	—	2	4	no	—
55	C₂×Q₈×C₇₃	—	8	2	no	—
56	C₂²×C₄×C₇₃	—	2	2	no	—
57	C₂²×C₄×C₇₃	—	2	2	no	—
58	C₂²×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
59	C₂²×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
60	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
61	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
62	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
63	C₄⋊C₄×C₇₃	—	2	4	no	—
64	C₄⋊C₄×C₇₃	—	2	4	no	—
65	C₄⋊C₄×C₇₃	—	2	2	no	—
66	C₄⋊C₄×C₇₃	—	4	1	no	—
67	C₄⋊C₄×C₇₃	—	4	2	no	—
68	C₄⋊C₄×C₇₃	—	4	1	no	—
69	C₄⋊C₄×C₇₃	—	8	4	no	—
70	C₄²×C₇₃	—	2	2	no	—
71	C₄²×C₇₃	—	2	2	no	—
72	C₄²×C₇₃	—	4	1	no	—
73	C₄²×C₇₃	—	4	1	no	—
74	C₄²×C₇₃	C₂×D₄	1	2	yes	—
75	C₄²×C₇₃	#41	1	2	yes	—
76	C₂³×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
77	Q₈×C₇₃	—	4	2	no	—
78	Q₈×C₇₃	—	4	2	no	—
79	Q₈×C₇₃	—	8	4	no	—
80	C₂×C₄×C₇₃	—	2	2	no	—
81	C₂×C₄×C₇₃	—	2	4	no	—
82	C₂×C₄×C₇₃	—	2	2	no	—
83	C₂×C₄×C₇₃	—	2	2	no	—
84	C₂×C₄×C₇₃	—	2	2	no	—
85	C₂×C₄×C₇₃	—	2	2	no	—
86	C₂×C₄×C₇₃	—	4	1	no	—
87	C₂×C₄×C₇₃	—	4	2	no	—
88	C₂×C₄×C₇₃	—	4	2	no	—
89	C₂×C₄×C₇₃	—	4	2	no	—
90	C₂×C₄×C₇₃	—	4	4	no	—
91	C₂×C₄×C₇₃	—	4	2	no	—
92	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
93	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
94	C₂×C₄×C₇₃	#121	1	2	yes	—
95	C₂×C₄×C₇₃	#123	1	1	yes	characteristic
96	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
97	C₂×C₄×C₇₃	#137	1	1	yes	characteristic
98	C₂×C₄×C₇₃	#137	1	2	yes	—
99	#10596831	—	4	4	no	—
100	#10596831	—	8	2	no	—
101	C₂²×C₇₃	—	2	1	no	—
102	C₂²×C₇₃	—	2	1	no	—
103	C₂²×C₇₃	#386	1	1	yes	characteristic
104	C₂²×C₇₃	#417	1	1	yes	characteristic
105	C₂²×C₇₃	#419	1	1	yes	characteristic
106	C₄×C₇₃	—	2	1	no	—
107	C₄×C₇₃	—	2	2	no	—
108	C₄×C₇₃	—	4	4	no	—
109	C₄×C₇₃	—	4	2	no	—
110	C₄×C₇₃	—	4	2	no	—
111	C₄×C₇₃	—	8	2	no	—
112	C₄×C₇₃	#456	1	2	yes	—
113	C₄×C₇₃	#468	1	2	yes	—
114	C₄×C₇₃	#470	1	2	yes	—
115	#9400	—	73	1	no	maximal, Sylow
116	C₂×C₇₃	—	2	1	no	—
117	C₂×C₇₃	—	2	1	no	—
118	C₂×C₇₃	#1886	1	1	yes	characteristic
119	C₂×C₇₃	#1894	1	1	yes	characteristic
120	C₂×C₇₃	#1914	1	1	yes	characteristic
121	#2983	—	73	1	no	—
122	#2567	D₇₃	1	1	yes	characteristic
123	#1801	—	73	1	no	—
124	#1548	—	73	2	no	—
125	#1303	—	73	2	no	—
126	C₇₃	#9400	1	1	yes	characteristic, complemented, Sylow
127	C₂×C₄⋊Q₈	C₂×D₇₃	1	1	yes	characteristic
128	C₂×C₄×Q₈	C₂×D₇₃	1	1	yes	characteristic
129	#446	—	146	4	no	—
130	#432	—	146	2	no	—
131	#431	—	73	2	no	—
132	#423	—	73	2	no	—
133	C₂×#101	—	146	1	no	—
134	#395	Dic₇₃	1	4	yes	—
135	#391	—	2	1	no	—
136	#389	—	2	2	no	—
137	#384	—	2	1	no	—
138	C₄×C₄⋊C₄	C₂×D₇₃	1	1	yes	characteristic
139	#343	—	146	1	no	—
140	#333	—	146	4	no	—
141	C₂²×Q₈	C₂×Dic₇₃	1	2	yes	—
142	C₂²×Q₈	C₂²⋊D₇₃	1	1	yes	characteristic
143	C₂×M₁₆	—	146	2	no	—
144	C₄⋊Q₈	—	2	2	no	—
145	C₄⋊Q₈	—	2	2	no	—
146	C₄×Q₈	—	2	2	no	—
147	C₄×Q₈	—	2	2	no	—
148	C₂×C₄⋊C₄	—	2	1	no	—
149	C₂×C₄⋊C₄	—	2	1	no	—
150	C₂×C₄⋊C₄	—	2	1	no	—
151	C₂×C₄⋊C₄	—	2	4	no	—
152	C₂×C₄⋊C₄	C₂×Dic₇₃	1	2	yes	—
153	C₂×C₄⋊C₄	C₂²⋊D₇₃	1	1	yes	characteristic
154	C₂×C₄²	—	2	1	no	—
155	C₂×C₄²	C₂²⋊D₇₃	1	2	yes	—
156	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
157	C₄⋊C₈	—	73	4	no	—
158	C₄⋊C₈	—	146	4	no	—
159	C₄⋊C₈	—	146	2	no	—
160	C₄⋊C₈	—	146	2	no	—
161	#101	—	292	2	no	—
162	C₂²⋊C₈	—	146	2	no	—
163	#97	—	146	4	no	—
164	C₄×C₈	—	146	2	no	—
165	#95	—	2	4	no	—
166	#95	C₂×Dic₇₃	1	2	yes	—
167	C₂×Q₈	—	2	2	no	—
168	C₂×Q₈	—	2	1	no	—
169	C₂×Q₈	—	2	1	no	—
170	C₂×Q₈	—	2	2	no	—
171	C₂×Q₈	—	2	4	no	—
172	C₂×Q₈	—	8	2	no	—
173	C₂²×C₄	—	2	2	no	—
174	C₂²×C₄	—	2	2	no	—
175	C₂²×C₄	C₂²⋊Dic₇₃	1	2	yes	—
176	C₂²×C₄	C₂²⋊Dic₇₃	1	2	yes	—
177	C₂²×C₄	C₂²×Dic₇₃	1	1	yes	characteristic
178	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
179	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
180	M₁₆	—	292	2	no	—
181	M₁₆	—	292	2	no	—
182	C₂×C₈	—	292	2	no	—
183	C₂×C₈	—	146	4	no	—
184	C₄⋊C₄	—	2	4	no	—
185	C₄⋊C₄	—	2	4	no	—
186	C₄⋊C₄	—	2	2	no	—
187	C₄⋊C₄	—	4	1	no	—
188	C₄⋊C₄	—	4	2	no	—
189	C₄⋊C₄	—	4	1	no	—
190	C₄⋊C₄	—	8	4	no	—
191	C₄²	—	2	2	no	—
192	C₄²	—	2	2	no	—
193	C₄²	—	4	1	no	—
194	C₄²	—	4	1	no	—
195	C₄²	D₄×D₇₃	1	2	yes	—
196	C₄²	#11924027	1	2	yes	—
197	C₂³	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
198	Q₈	—	4	2	no	—
199	Q₈	—	4	2	no	—
200	Q₈	—	8	4	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	4	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	4	1	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	4	2	no	—
210	C₂×C₄	—	4	2	no	—
211	C₂×C₄	—	4	4	no	—
212	C₂×C₄	—	4	2	no	—
213	C₂×C₄	D₄×Dic₇₃	1	2	yes	—
214	C₂×C₄	#14556559	1	1	yes	characteristic
215	C₂×C₄	#14556563	1	2	yes	—
216	C₂×C₄	#14556572	1	1	yes	characteristic
217	C₂×C₄	#14556616	1	1	yes	characteristic
218	C₂×C₄	#14556621	1	1	yes	characteristic
219	C₂×C₄	#14556622	1	2	yes	—
220	C₈	—	292	4	no	—
221	C₈	—	584	2	no	—
222	C₂²	—	2	1	no	—
223	C₂²	—	2	1	no	—
224	C₂²	#17988467	1	1	yes	characteristic
225	C₂²	#17988588	1	1	yes	characteristic
226	C₂²	#17988596	1	1	yes	characteristic
227	C₄	—	2	2	no	—
228	C₄	—	2	1	no	—
229	C₄	—	4	4	no	—
230	C₄	—	4	2	no	—
231	C₄	—	4	2	no	—
232	C₄	—	8	2	no	—
233	C₄	#17988769	1	2	yes	—
234	C₄	#17988835	1	2	yes	—
235	C₄	#17988843	1	2	yes	—
236	C₂	—	2	1	no	—
237	C₂	—	2	1	no	—
238	C₂	#22610325	1	1	yes	characteristic
239	C₂	#22610365	1	1	yes	characteristic
240	C₂	#22610479	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22619016

C₂

yes

maximal, characteristic

#22609927

C₂

yes

maximal, characteristic

#22608612

C₂

yes

maximal

#22607834

C₂

yes

maximal

C₇₃×#2567

C₂

yes

maximal, characteristic

#17988718

—

#17988644

—

#17988640

C₂²

yes

—

#17988611

C₂²

yes

—

C₂×#14556510

—

#17988356

—

#17988336

—

C₂×C₄⋊Q₈×C₇₃

C₂²

yes

characteristic

C₂×C₄×Q₈×C₇₃

C₂²

yes

characteristic

#395×C₇₃

C₄

yes

—

#391×C₇₃

—

#389×C₇₃

—

#384×C₇₃

—

C₄×C₄⋊C₄×C₇₃

C₂²

yes

—

—

—

—

D₄

yes

—

—

—

—

—

C₂²×Q₈×C₇₃

C₂×C₄

yes

—

C₂²×Q₈×C₇₃

D₄

yes

characteristic

C₄⋊Q₈×C₇₃

—

C₄⋊Q₈×C₇₃

—

C₄×Q₈×C₇₃

—

C₄×Q₈×C₇₃

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₇₃

D₄

yes

characteristic

C₂×C₄²×C₇₃

—

C₂×C₄²×C₇₃

D₄

yes

—

C₂×C₄²×C₇₃

C₂³

yes

characteristic

#95×C₇₃

—

#95×C₇₃

C₂×C₄

yes

—

—

—

—

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

C₂×D₄

yes

—

C₄²×C₇₃

#41

yes

—

C₂³×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₄×D₄

yes

—

C₂×C₄×C₇₃

#120

yes

characteristic

C₂×C₄×C₇₃

#121

yes

—

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

—

#10596831

—

100

#10596831

—

101

C₂²×C₇₃

—

102

C₂²×C₇₃

—

103

C₂²×C₇₃

#386

yes

characteristic

104

C₂²×C₇₃

#417

yes

characteristic

105

C₂²×C₇₃

#419

yes

characteristic

106

C₄×C₇₃

—

107

C₄×C₇₃

—

108

C₄×C₇₃

—

109

C₄×C₇₃

—

110

C₄×C₇₃

—

111

C₄×C₇₃

—

112

C₄×C₇₃

#456

yes

—

113

C₄×C₇₃

#468

yes

—

114

C₄×C₇₃

#470

yes

—

115

#9400

—

maximal, Sylow

116

C₂×C₇₃

—

117

C₂×C₇₃

—

118

C₂×C₇₃

#1886

yes

characteristic

119

C₂×C₇₃

#1894

yes

characteristic

120

C₂×C₇₃

#1914

yes

characteristic

121

#2983

—

122

#2567

D₇₃

yes

characteristic

123

#1801

—

124

#1548

—

125

#1303

—

126

C₇₃

#9400

yes

characteristic, complemented, Sylow

127

C₂×C₄⋊Q₈

C₂×D₇₃

yes

characteristic

128

C₂×C₄×Q₈

C₂×D₇₃

yes

characteristic

129

#446

—

146

—

130

#432

—

146

—

131

#431

—

132

#423

—

133

C₂×#101

—

146

—

134

#395

Dic₇₃

yes

—

135

#391

—

136

#389

—

137

#384

—

138

C₄×C₄⋊C₄

C₂×D₇₃

yes

characteristic

139

#343

—

146

—

140

#333

—

146

—

141

C₂²×Q₈

C₂×Dic₇₃

yes

—

142

C₂²×Q₈

C₂²⋊D₇₃

yes

characteristic

143

C₂×M₁₆

—

146

—

144

C₄⋊Q₈

—

145

C₄⋊Q₈

—

146

C₄×Q₈

—

147

C₄×Q₈

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄⋊C₄

C₂×Dic₇₃

yes

—

153

C₂×C₄⋊C₄

C₂²⋊D₇₃

yes

characteristic

154

C₂×C₄²

—

155

C₂×C₄²

C₂²⋊D₇₃

yes

—

156

C₂×C₄²

C₂²×D₇₃

yes

characteristic

157

C₄⋊C₈

—

158

C₄⋊C₈

—

146

—

159

C₄⋊C₈

—

146

—

160

C₄⋊C₈

—

146

—

161

#101

—

292

—

162

C₂²⋊C₈

—

146

—

163

#97

—

146

—

164

C₄×C₈

—

146

—

165

#95

—

166

#95

C₂×Dic₇₃

yes

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

—

172

C₂×Q₈

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

C₂²⋊Dic₇₃

yes

—

176

C₂²×C₄

C₂²⋊Dic₇₃

yes

—

177

C₂²×C₄

C₂²×Dic₇₃

yes

characteristic

178

C₂²×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

179

C₂²×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

180

M₁₆

—

292

—

181

M₁₆

—

292

—

182

C₂×C₈

—

292

—

183

C₂×C₈

—

146

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄²

—

192

C₄²

—

193

C₄²

—

194

C₄²

—

195

C₄²

D₄×D₇₃

yes

—

196

C₄²

#11924027

yes

—

197

C₂³

C₂×C₂²⋊Dic₇₃

yes

characteristic

198

Q₈

—

199

Q₈

—

200

Q₈

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

D₄×Dic₇₃

yes

—

214

C₂×C₄

#14556559

yes

characteristic

215

C₂×C₄

#14556563

yes

—

216

C₂×C₄

#14556572

yes

characteristic

217

C₂×C₄

#14556616

yes

characteristic

218

C₂×C₄

#14556621

yes

characteristic

219

C₂×C₄

#14556622

yes

—

220

C₈

—

292

—

221

C₈

—

584

—

222

C₂²

—

223

C₂²

—

224

C₂²

#17988467

yes

characteristic

225

C₂²

#17988588

yes

characteristic

226

C₂²

#17988596

yes

characteristic

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

#17988769

yes

—

234

C₄

#17988835

yes

—

235

C₄

#17988843

yes

—

236

C₂

—

237

C₂

—

238

C₂

#22610325

yes

characteristic

239

C₂

#22610365

yes

characteristic

240

C₂

#22610479

yes

characteristic

	subgroup	G/H
center	C₂²	#17988467
commutator	C₂²×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₃
Fitting	C₇₃×#2567	C₂
socle	C₂²×C₇₃	#386
prime radical	C₂³×C₇₃	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₇₃	C₂³
hypercenter	#2567	D₇₃
hypocenter	C₇₃	#9400
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2567

subgroup

G/H

center

C₂²

#17988467

commutator

C₂²×C₄×C₇₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₃

Fitting

C₇₃×#2567

C₂

socle

C₂²×C₇₃

#386

prime radical

C₂³×C₇₃

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₇₃

C₂³

D₇₃

C₇₃

G ▷ C₂²×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2567

N	H ≅ G/N	type
126. C₇₃	#9400	semidirect

H ≅ G/N

type

126. C₇₃

#9400

semidirect

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

subgroup	index
#22619016	2
#22609927	2
#22608612	2
#22607834	2
C₇₃×#2567	2
#9400	73

subgroup

index

C₇₃×#2567

Subgroups — #32983385

Conjugacy classes of subgroups

Complements

Maximal subgroups