Group #32980944 — subgroups

Subgroups — #32980944

Order 18688.

502 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 103 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	#22619002	C₂	1	1	yes	maximal, characteristic, complemented
2	#22608593	C₂	1	1	yes	maximal, characteristic, complemented
3	#22608400	C₂	1	2	yes	maximal, complemented
4	#22607830	C₂	1	2	yes	maximal, complemented
5	C₇₃×#3150	C₂	1	1	yes	maximal, characteristic
6	#17988659	—	2	4	no	—
7	#17988644	C₂²	1	2	yes	—
8	#17988640	C₂²	1	2	yes	—
9	#17988554	—	2	2	no	—
10	#17988336	—	2	1	no	—
11	#17988331	—	2	1	no	—
12	D₄⋊#10596831	—	2	4	no	—
13	C₂×#135×C₇₃	—	2	2	no	—
14	#532×C₇₃	C₂²	1	1	yes	characteristic
15	#532×C₇₃	C₂²	1	1	yes	characteristic
16	#497×C₇₃	—	2	1	no	—
17	#497×C₇₃	C₄	1	2	yes	—
18	#496×C₇₃	—	2	1	no	—
19	#496×C₇₃	C₄	1	2	yes	—
20	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×#11924012	—	2	2	no	—
22	C₂²×#10596831	—	2	2	no	—
23	C₄⋊#10596831	—	2	2	no	—
24	C₄⋊#10596831	D₄	1	4	yes	—
25	C₂²⋊#10596831	—	2	4	no	—
26	C₂²⋊#10596831	—	2	2	no	—
27	C₂²⋊#10596831	—	2	2	no	—
28	#14556502	—	2	2	no	—
29	C₄×#10596831	—	2	2	no	—
30	C₂×#41×C₇₃	—	2	1	no	—
31	C₂×#41×C₇₃	D₄	1	2	yes	—
32	#135×C₇₃	—	4	4	no	—
33	#135×C₇₃	—	4	4	no	—
34	C₂×Q₁₆×C₇₃	—	2	2	no	—
35	C₂×SD₁₆×C₇₃	—	2	2	no	—
36	C₂×SD₁₆×C₇₃	—	2	2	no	—
37	C₂×D₈×C₇₃	—	2	2	no	—
38	C₂²×C₈×C₇₃	—	2	1	no	—
39	C₄⋊Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
40	C₄⋊Q₈×C₇₃	D₄	1	1	yes	characteristic
41	#127×C₇₃	C₂×C₄	1	1	yes	characteristic
42	#127×C₇₃	D₄	1	1	yes	characteristic
43	#124×C₇₃	—	2	1	no	—
44	#124×C₇₃	C₂×C₄	1	2	yes	—
45	#121×C₇₃	—	2	2	no	—
46	#121×C₇₃	—	2	2	no	—
47	C₄×D₄×C₇₃	—	2	2	no	—
48	C₄×D₄×C₇₃	—	2	2	no	—
49	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
50	#97×C₇₃	—	2	1	no	—
51	#97×C₇₃	C₂×C₄	1	2	yes	—
52	#11924012	—	8	2	no	—
53	C₂×#10596831	—	2	4	no	—
54	C₂×#10596831	—	4	2	no	—
55	C₂×#10596831	—	8	2	no	—
56	#41×C₇₃	—	4	2	no	—
57	#41×C₇₃	—	4	2	no	—
58	#41×C₇₃	—	4	2	no	—
59	#41×C₇₃	—	4	2	no	—
60	C₂×Q₈×C₇₃	—	2	1	no	—
61	C₂×Q₈×C₇₃	C₂²⋊C₄	1	2	yes	—
62	C₂×D₄×C₇₃	—	2	2	no	—
63	C₂×D₄×C₇₃	—	2	1	no	—
64	C₂×D₄×C₇₃	—	2	2	no	—
65	C₂×D₄×C₇₃	—	2	2	no	—
66	C₂×D₄×C₇₃	—	4	1	no	—
67	C₂×D₄×C₇₃	C₂²⋊C₄	1	2	yes	—
68	C₂²×C₄×C₇₃	—	2	2	no	—
69	C₂²×C₄×C₇₃	—	4	1	no	—
70	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₇₃	#41	1	2	yes	—
72	Q₁₆×C₇₃	—	4	4	no	—
73	SD₁₆×C₇₃	—	4	4	no	—
74	SD₁₆×C₇₃	—	4	4	no	—
75	D₈×C₇₃	—	4	4	no	—
76	C₂×C₈×C₇₃	—	2	4	no	—
77	C₂×C₈×C₇₃	—	2	2	no	—
78	C₄⋊C₄×C₇₃	—	2	2	no	—
79	C₄⋊C₄×C₇₃	—	2	2	no	—
80	C₂²⋊C₄×C₇₃	—	2	4	no	—
81	C₂²⋊C₄×C₇₃	—	4	2	no	—
82	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
83	C₄²×C₇₃	C₂×D₄	1	2	yes	—
84	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
85	C₂³×C₇₃	—	2	2	no	—
86	C₂³×C₇₃	—	4	1	no	—
87	C₂³×C₇₃	#123	1	1	yes	characteristic
88	Q₈×C₇₃	—	4	2	no	—
89	Q₈×C₇₃	—	4	2	no	—
90	D₄×C₇₃	—	4	2	no	—
91	D₄×C₇₃	—	4	2	no	—
92	D₄×C₇₃	—	4	4	no	—
93	D₄×C₇₃	—	8	2	no	—
94	D₄×C₇₃	—	8	2	no	—
95	D₄×C₇₃	—	8	1	no	—
96	D₄×C₇₃	—	8	1	no	—
97	C₂×C₄×C₇₃	—	2	2	no	—
98	C₂×C₄×C₇₃	—	2	2	no	—
99	C₂×C₄×C₇₃	—	4	2	no	—
100	C₂×C₄×C₇₃	—	4	2	no	—
101	C₂×C₄×C₇₃	—	4	2	no	—
102	C₂×C₄×C₇₃	—	4	1	no	—
103	C₂×C₄×C₇₃	—	8	2	no	—
104	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
105	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
106	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
107	C₂×C₄×C₇₃	#121	1	2	yes	—
108	C₈×C₇₃	—	2	4	no	—
109	#10596831	—	4	4	no	—
110	#10596831	—	8	2	no	—
111	C₂²×C₇₃	—	2	2	no	—
112	C₂²×C₇₃	—	2	1	no	—
113	C₂²×C₇₃	—	4	4	no	—
114	C₂²×C₇₃	—	4	2	no	—
115	C₂²×C₇₃	—	8	2	no	—
116	C₂²×C₇₃	—	8	1	no	—
117	C₂²×C₇₃	#386	1	1	yes	characteristic
118	C₄×C₇₃	—	2	2	no	—
119	C₄×C₇₃	—	2	2	no	—
120	C₄×C₇₃	—	2	1	no	—
121	C₄×C₇₃	—	4	2	no	—
122	C₄×C₇₃	—	8	1	no	—
123	C₄×C₇₃	#453	1	2	yes	—
124	#9007	—	73	1	no	maximal, Sylow
125	C₂×C₇₃	—	4	1	no	—
126	C₂×C₇₃	—	8	2	no	—
127	C₂×C₇₃	—	16	1	no	—
128	C₂×C₇₃	#1881	1	2	yes	—
129	C₂×C₇₃	#1887	1	1	yes	characteristic
130	#3150	D₇₃	1	1	yes	characteristic
131	#2980	—	73	1	no	—
132	#1543	—	73	1	no	—
133	#1496	—	73	2	no	—
134	#1302	—	73	2	no	—
135	C₇₃	#9007	1	1	yes	characteristic, complemented, Sylow
136	C₂×#135	—	2	2	no	—
137	#532	C₂×D₇₃	1	1	yes	characteristic
138	#532	C₂×D₇₃	1	1	yes	characteristic
139	#497	—	2	1	no	—
140	#497	Dic₇₃	1	2	yes	—
141	#496	—	2	1	no	—
142	#496	Dic₇₃	1	2	yes	—
143	#435	—	146	4	no	—
144	#432	—	73	2	no	—
145	#431	—	73	2	no	—
146	#408	—	146	2	no	—
147	C₂×#97	C₂×D₇₃	1	1	yes	characteristic
148	#333	—	146	1	no	—
149	#331	—	146	1	no	—
150	D₄⋊C₈	—	146	4	no	—
151	C₂×#41	—	2	1	no	—
152	C₂×#41	C₂²⋊D₇₃	1	2	yes	—
153	#135	—	4	4	no	—
154	#135	—	4	4	no	—
155	C₂×Q₁₆	—	2	2	no	—
156	C₂×SD₁₆	—	2	2	no	—
157	C₂×SD₁₆	—	2	2	no	—
158	C₂×D₈	—	2	2	no	—
159	C₂×M₁₆	—	146	2	no	—
160	C₂²×C₈	—	2	1	no	—
161	C₂²×C₈	—	146	2	no	—
162	C₄⋊Q₈	C₂×Dic₇₃	1	1	yes	characteristic
163	C₄⋊Q₈	C₂²⋊D₇₃	1	1	yes	characteristic
164	#127	C₂×Dic₇₃	1	1	yes	characteristic
165	#127	C₂²⋊D₇₃	1	1	yes	characteristic
166	#124	—	2	1	no	—
167	#124	C₂×Dic₇₃	1	2	yes	—
168	#121	—	2	2	no	—
169	#121	—	2	2	no	—
170	C₄×D₄	—	2	2	no	—
171	C₄×D₄	—	2	2	no	—
172	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
173	C₄⋊C₈	—	73	4	no	—
174	C₄⋊C₈	—	146	2	no	—
175	C₂²⋊C₈	—	146	2	no	—
176	C₂²⋊C₈	—	146	4	no	—
177	C₂²⋊C₈	—	146	2	no	—
178	#97	—	2	1	no	—
179	#97	—	146	2	no	—
180	#97	C₂×Dic₇₃	1	2	yes	—
181	C₄×C₈	—	146	2	no	—
182	#41	—	4	2	no	—
183	#41	—	4	2	no	—
184	#41	—	4	2	no	—
185	#41	—	4	2	no	—
186	C₂×Q₈	—	2	1	no	—
187	C₂×Q₈	C₂²⋊Dic₇₃	1	2	yes	—
188	C₂×D₄	—	2	2	no	—
189	C₂×D₄	—	2	1	no	—
190	C₂×D₄	—	2	2	no	—
191	C₂×D₄	—	2	2	no	—
192	C₂×D₄	—	4	1	no	—
193	C₂×D₄	C₂²⋊Dic₇₃	1	2	yes	—
194	C₂²×C₄	—	2	2	no	—
195	C₂²×C₄	—	4	1	no	—
196	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
197	C₂²×C₄	#11924027	1	2	yes	—
198	Q₁₆	—	4	4	no	—
199	SD₁₆	—	4	4	no	—
200	SD₁₆	—	4	4	no	—
201	D₈	—	4	4	no	—
202	M₁₆	—	584	2	no	—
203	C₂×C₈	—	2	4	no	—
204	C₂×C₈	—	2	2	no	—
205	C₂×C₈	—	292	2	no	—
206	C₂×C₈	—	584	2	no	—
207	C₂×C₈	—	146	4	no	—
208	C₄⋊C₄	—	2	2	no	—
209	C₄⋊C₄	—	2	2	no	—
210	C₂²⋊C₄	—	2	4	no	—
211	C₂²⋊C₄	—	4	2	no	—
212	C₄²	C₂²×Dic₇₃	1	1	yes	characteristic
213	C₄²	D₄×D₇₃	1	2	yes	—
214	C₄²	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
215	C₂³	—	2	2	no	—
216	C₂³	—	4	1	no	—
217	C₂³	#14556572	1	1	yes	characteristic
218	Q₈	—	4	2	no	—
219	Q₈	—	4	2	no	—
220	D₄	—	4	2	no	—
221	D₄	—	4	2	no	—
222	D₄	—	4	4	no	—
223	D₄	—	8	2	no	—
224	D₄	—	8	2	no	—
225	D₄	—	8	1	no	—
226	D₄	—	8	1	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	2	2	no	—
229	C₂×C₄	—	4	2	no	—
230	C₂×C₄	—	4	2	no	—
231	C₂×C₄	—	4	2	no	—
232	C₂×C₄	—	4	1	no	—
233	C₂×C₄	—	8	2	no	—
234	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
235	C₂×C₄	D₄×Dic₇₃	1	2	yes	—
236	C₂×C₄	#14556559	1	1	yes	characteristic
237	C₂×C₄	#14556563	1	2	yes	—
238	C₈	—	2	4	no	—
239	C₈	—	292	4	no	—
240	C₈	—	584	2	no	—
241	C₂²	—	2	2	no	—
242	C₂²	—	2	1	no	—
243	C₂²	—	4	4	no	—
244	C₂²	—	4	2	no	—
245	C₂²	—	8	2	no	—
246	C₂²	—	8	1	no	—
247	C₂²	#17988467	1	1	yes	characteristic
248	C₄	—	2	2	no	—
249	C₄	—	2	2	no	—
250	C₄	—	2	1	no	—
251	C₄	—	4	2	no	—
252	C₄	—	8	1	no	—
253	C₄	#17988754	1	2	yes	—
254	C₂	—	4	1	no	—
255	C₂	—	8	2	no	—
256	C₂	—	16	1	no	—
257	C₂	#22610295	1	2	yes	—
258	C₂	#22610330	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22619002

C₂

yes

maximal, characteristic, complemented

#22608593

C₂

yes

maximal, characteristic, complemented

#22608400

C₂

yes

maximal, complemented

#22607830

C₂

yes

maximal, complemented

C₇₃×#3150

C₂

yes

maximal, characteristic

#17988659

—

#17988644

C₂²

yes

—

#17988640

C₂²

yes

—

—

—

—

—

C₂×#135×C₇₃

—

#532×C₇₃

C₂²

yes

characteristic

#532×C₇₃

C₂²

yes

characteristic

#497×C₇₃

—

#497×C₇₃

C₄

yes

—

#496×C₇₃

—

#496×C₇₃

C₄

yes

—

C₂×#97×C₇₃

C₂²

yes

—

—

—

D₄

yes

—

—

—

—

—

—

C₂×#41×C₇₃

—

C₂×#41×C₇₃

D₄

yes

—

#135×C₇₃

—

#135×C₇₃

—

C₂×Q₁₆×C₇₃

—

C₂×SD₁₆×C₇₃

—

C₂×SD₁₆×C₇₃

—

C₂×D₈×C₇₃

—

C₂²×C₈×C₇₃

—

C₄⋊Q₈×C₇₃

C₂×C₄

yes

characteristic

C₄⋊Q₈×C₇₃

D₄

yes

characteristic

#127×C₇₃

C₂×C₄

yes

characteristic

#127×C₇₃

D₄

yes

characteristic

#124×C₇₃

—

#124×C₇₃

C₂×C₄

yes

—

#121×C₇₃

—

#121×C₇₃

—

C₄×D₄×C₇₃

—

C₄×D₄×C₇₃

—

C₂×C₄²×C₇₃

C₂³

yes

characteristic

#97×C₇₃

—

#97×C₇₃

C₂×C₄

yes

—

—

—

—

—

#41×C₇₃

—

#41×C₇₃

—

#41×C₇₃

—

#41×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

C₂²⋊C₄

yes

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₃

#41

yes

—

Q₁₆×C₇₃

—

SD₁₆×C₇₃

—

SD₁₆×C₇₃

—

D₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

C₂²×C₄

yes

characteristic

C₄²×C₇₃

C₂×D₄

yes

—

C₄²×C₇₃

C₂×D₄

yes

characteristic

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

#123

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

100

C₂×C₄×C₇₃

—

101

C₂×C₄×C₇₃

—

102

C₂×C₄×C₇₃

—

103

C₂×C₄×C₇₃

—

104

C₂×C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

105

C₂×C₄×C₇₃

C₄×D₄

yes

—

106

C₂×C₄×C₇₃

#120

yes

characteristic

107

C₂×C₄×C₇₃

#121

yes

—

108

C₈×C₇₃

—

109

#10596831

—

110

#10596831

—

111

C₂²×C₇₃

—

112

C₂²×C₇₃

—

113

C₂²×C₇₃

—

114

C₂²×C₇₃

—

115

C₂²×C₇₃

—

116

C₂²×C₇₃

—

117

C₂²×C₇₃

#386

yes

characteristic

118

C₄×C₇₃

—

119

C₄×C₇₃

—

120

C₄×C₇₃

—

121

C₄×C₇₃

—

122

C₄×C₇₃

—

123

C₄×C₇₃

#453

yes

—

124

#9007

—

maximal, Sylow

125

C₂×C₇₃

—

126

C₂×C₇₃

—

127

C₂×C₇₃

—

128

C₂×C₇₃

#1881

yes

—

129

C₂×C₇₃

#1887

yes

characteristic

130

#3150

D₇₃

yes

characteristic

131

#2980

—

132

#1543

—

133

#1496

—

134

#1302

—

135

C₇₃

#9007

yes

characteristic, complemented, Sylow

136

C₂×#135

—

137

#532

C₂×D₇₃

yes

characteristic

138

#532

C₂×D₇₃

yes

characteristic

139

#497

—

140

#497

Dic₇₃

yes

—

141

#496

—

142

#496

Dic₇₃

yes

—

143

#435

—

146

—

144

#432

—

145

#431

—

146

#408

—

146

—

147

C₂×#97

C₂×D₇₃

yes

characteristic

148

#333

—

146

—

149

#331

—

146

—

150

D₄⋊C₈

—

146

—

151

C₂×#41

—

152

C₂×#41

C₂²⋊D₇₃

yes

—

153

#135

—

154

#135

—

155

C₂×Q₁₆

—

156

C₂×SD₁₆

—

157

C₂×SD₁₆

—

158

C₂×D₈

—

159

C₂×M₁₆

—

146

—

160

C₂²×C₈

—

161

C₂²×C₈

—

146

—

162

C₄⋊Q₈

C₂×Dic₇₃

yes

characteristic

163

C₄⋊Q₈

C₂²⋊D₇₃

yes

characteristic

164

#127

C₂×Dic₇₃

yes

characteristic

165

#127

C₂²⋊D₇₃

yes

characteristic

166

#124

—

167

#124

C₂×Dic₇₃

yes

—

168

#121

—

169

#121

—

170

C₄×D₄

—

171

C₄×D₄

—

172

C₂×C₄²

C₂²×D₇₃

yes

characteristic

173

C₄⋊C₈

—

174

C₄⋊C₈

—

146

—

175

C₂²⋊C₈

—

146

—

176

C₂²⋊C₈

—

146

—

177

C₂²⋊C₈

—

146

—

178

#97

—

179

#97

—

146

—

180

#97

C₂×Dic₇₃

yes

—

181

C₄×C₈

—

146

—

182

#41

—

183

#41

—

184

#41

—

185

#41

—

186

C₂×Q₈

—

187

C₂×Q₈

C₂²⋊Dic₇₃

yes

—

188

C₂×D₄

—

189

C₂×D₄

—

190

C₂×D₄

—

191

C₂×D₄

—

192

C₂×D₄

—

193

C₂×D₄

C₂²⋊Dic₇₃

yes

—

194

C₂²×C₄

—

195

C₂²×C₄

—

196

C₂²×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

197

C₂²×C₄

#11924027

yes

—

198

Q₁₆

—

199

SD₁₆

—

200

SD₁₆

—

201

D₈

—

202

M₁₆

—

584

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

292

—

206

C₂×C₈

—

584

—

207

C₂×C₈

—

146

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

210

C₂²⋊C₄

—

211

C₂²⋊C₄

—

212

C₄²

C₂²×Dic₇₃

yes

characteristic

213

C₄²

D₄×D₇₃

yes

—

214

C₄²

C₂×C₂²⋊D₇₃

yes

characteristic

215

C₂³

—

216

C₂³

—

217

C₂³

#14556572

yes

characteristic

218

Q₈

—

219

Q₈

—

220

D₄

—

221

D₄

—

222

D₄

—

223

D₄

—

224

D₄

—

225

D₄

—

226

D₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

C₂×C₂²⋊Dic₇₃

yes

characteristic

235

C₂×C₄

D₄×Dic₇₃

yes

—

236

C₂×C₄

#14556559

yes

characteristic

237

C₂×C₄

#14556563

yes

—

238

C₈

—

239

C₈

—

292

—

240

C₈

—

584

—

241

C₂²

—

242

C₂²

—

243

C₂²

—

244

C₂²

—

245

C₂²

—

246

C₂²

—

247

C₂²

#17988467

yes

characteristic

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

—

252

C₄

—

253

C₄

#17988754

yes

—

254

C₂

—

255

C₂

—

256

C₂

—

257

C₂

#22610295

yes

—

258

C₂

#22610330

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14556559
commutator	C₄²×C₇₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₃
Fitting, prime radical	C₇₃×#3150	C₂
socle	C₂²×C₇₃	#386
cosocle	C₂×C₄²×C₇₃	C₂³
hypercenter	#3150	D₇₃
hypocenter	C₇₃	#9007
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3150

subgroup

G/H

center

C₂×C₄

#14556559

commutator

C₄²×C₇₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₃

Fitting, prime radical

C₇₃×#3150

C₂

socle

C₂²×C₇₃

#386

cosocle

C₂×C₄²×C₇₃

C₂³

D₇₃

C₇₃

G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3150

N	H ≅ G/N	type
1. #22619002	C₂	semidirect
2. #22608593	C₂	semidirect
3. #22608400	C₂	semidirect
4. #22607830	C₂	semidirect
135. C₇₃	#9007	semidirect

H ≅ G/N

type

1. #22619002

C₂

semidirect

2. #22608593

C₂

semidirect

3. #22608400

C₂

semidirect

4. #22607830

C₂

semidirect

135. C₇₃

#9007

semidirect

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

subgroup	index
#22619002	2
#22608593	2
#22608400	2
#22607830	2
C₇₃×#3150	2
#9007	73

subgroup

index

C₇₃×#3150

Subgroups — #32980944

Conjugacy classes of subgroups

Complements

Maximal subgroups