Group #34012396 — subgroups

Subgroups — #34012396

Order 18688.

494 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 128 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×#17989484	C₂	1	2	yes	maximal
2	C₂×#17989480	C₂	1	2	yes	maximal, complemented
3	#22624975	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×#11924011	C₂	1	1	yes	maximal, characteristic
5	C₂×#14556665	C₂²	1	4	yes	—
6	#17989484	C₄	1	8	yes	complemented
7	#17989480	—	2	4	no	—
8	C₂²×#11924011	C₄	1	1	yes	characteristic
9	C₂²×#11924011	C₂²	1	1	yes	characteristic
10	C₂×C₄²×D₇₃	C₄	1	1	yes	characteristic
11	C₄×#11924011	—	2	4	no	—
12	C₂×#14556501	C₄	1	1	yes	characteristic
13	C₂×#14556501	C₂²	1	1	yes	characteristic
14	C₂×C₄×#10596831	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₇₃	C₄	1	1	yes	characteristic
16	#14556665	—	2	4	no	—
17	#14556665	C₂×C₄	1	8	yes	complemented
18	C₂×#11924031	—	2	4	no	—
19	C₂²×C₄×D₇₃	—	2	1	no	—
20	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
21	C₂×#11924011	—	2	2	no	—
22	C₂×#11924011	—	2	2	no	—
23	C₂×#11924011	—	2	2	no	—
24	C₂×#11924011	—	2	2	no	—
25	C₂×#11924011	—	2	2	no	—
26	C₂×#11924011	C₂×C₄	1	4	yes	—
27	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
28	C₂²×#10596831	C₂³	1	1	yes	characteristic
29	C₂×C₄×Dic₇₃	—	2	1	no	—
30	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
31	C₄²×D₇₃	—	2	2	no	—
32	C₄²×D₇₃	—	2	2	no	—
33	#14556501	—	2	2	no	—
34	#14556501	D₄	1	4	yes	—
35	C₄×#10596831	—	2	2	no	—
36	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
39	C₄×C₈×C₇₃	—	2	2	no	—
40	#11924031	—	2	8	no	—
41	C₂³×D₇₃	M₁₆	1	1	yes	characteristic
42	C₂²×Dic₇₃	—	2	1	no	—
43	C₂²×Dic₇₃	M₁₆	1	1	yes	characteristic
44	C₂×C₄×D₇₃	—	2	1	no	—
45	C₂×C₄×D₇₃	—	2	1	no	—
46	C₂×C₄×D₇₃	—	2	1	no	—
47	C₂×C₄×D₇₃	—	2	1	no	—
48	C₂×C₄×D₇₃	—	2	4	no	—
49	C₂×C₄×D₇₃	—	4	4	no	—
50	C₂×C₄×D₇₃	C₄²	1	2	yes	—
51	C₂×C₄×D₇₃	M₁₆	1	2	yes	—
52	#11924011	—	2	8	no	—
53	#11924011	—	2	8	no	—
54	C₂×#10596831	—	2	1	no	—
55	C₂×#10596831	—	2	1	no	—
56	C₂×#10596831	M₁₆	1	2	yes	—
57	C₂×#10596831	C₂²×C₄	1	2	yes	—
58	C₂×#10596831	C₂×D₄	1	2	yes	—
59	C₂×#10596831	#41	1	2	yes	—
60	C₄×Dic₇₃	—	2	4	no	—
61	C₄×Dic₇₃	—	2	1	no	—
62	C₄×Dic₇₃	C₂²⋊C₄	1	2	yes	—
63	C₂²×C₄×C₇₃	—	2	1	no	—
64	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
65	C₂×C₈×C₇₃	—	2	1	no	—
66	C₂×C₈×C₇₃	—	2	1	no	—
67	C₂×C₈×C₇₃	—	2	1	no	—
68	C₂×C₈×C₇₃	—	2	1	no	—
69	C₂×C₈×C₇₃	C₄²	1	2	yes	—
70	C₂×C₈×C₇₃	C₂²⋊C₄	1	2	yes	—
71	C₄²×C₇₃	—	2	1	no	—
72	C₄²×C₇₃	M₁₆	1	2	yes	—
73	C₂³×C₇₃	C₂×M₁₆	1	1	yes	characteristic
74	C₂²×D₇₃	—	2	1	no	—
75	C₂²×D₇₃	—	2	1	no	—
76	C₂²×D₇₃	—	4	2	no	—
77	C₂²×D₇₃	#97	1	2	yes	—
78	C₂×C₄×C₇₃	—	2	4	no	—
79	C₂×C₄×C₇₃	—	2	2	no	—
80	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
81	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₄×C₇₃	#117	1	1	yes	characteristic
83	C₂×C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
84	C₂×C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
85	C₂×C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
86	C₂×Dic₇₃	—	2	1	no	—
87	C₂×Dic₇₃	—	2	1	no	—
88	C₂×Dic₇₃	—	2	2	no	—
89	C₂×Dic₇₃	—	4	2	no	—
90	C₂×Dic₇₃	#97	1	2	yes	—
91	C₄×D₇₃	—	2	2	no	—
92	C₄×D₇₃	—	2	2	no	—
93	C₄×D₇₃	—	2	2	no	—
94	C₄×D₇₃	—	2	2	no	—
95	C₄×D₇₃	—	4	8	no	—
96	C₈×C₇₃	—	2	2	no	—
97	C₈×C₇₃	—	2	2	no	—
98	#10596831	—	2	2	no	—
99	#10596831	C₄×D₄	1	4	yes	—
100	C₂²×C₇₃	—	2	2	no	—
101	C₂²×C₇₃	C₂×#97	1	1	yes	characteristic
102	C₂²×C₇₃	#407	1	1	yes	characteristic
103	C₂²×C₇₃	#432	1	1	yes	characteristic
104	C₂×D₇₃	—	2	2	no	—
105	C₂×D₇₃	—	4	2	no	—
106	C₂×D₇₃	—	4	2	no	—
107	C₂×D₇₃	—	4	2	no	—
108	C₄×C₇₃	—	2	4	no	—
109	C₄×C₇₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
110	C₄×C₇₃	C₄×M₁₆	1	1	yes	characteristic
111	C₄×C₇₃	#407	1	1	yes	characteristic
112	C₄×C₇₃	#432	1	1	yes	characteristic
113	Dic₇₃	—	2	2	no	—
114	Dic₇₃	—	4	2	no	—
115	#12607	—	73	1	no	maximal, Sylow
116	C₂×C₇₃	—	2	1	no	—
117	C₂×C₇₃	—	2	1	no	—
118	C₂×C₇₃	#1749	1	1	yes	characteristic
119	C₂×C₇₃	#2165	1	2	yes	—
120	D₇₃	—	4	2	no	—
121	C₂×C₄×M₁₆	—	73	1	no	—
122	C₂×#349	—	73	2	no	—
123	C₂×#347	—	73	2	no	—
124	#1376	—	73	2	no	—
125	C₇₃	#12607	1	1	yes	characteristic, complemented, Sylow
126	C₂²×M₁₆	—	73	1	no	—
127	C₂²×M₁₆	—	73	1	no	—
128	C₂²×C₄²	—	73	1	no	—
129	C₂×M₃₂	—	73	4	no	—
130	C₄×M₁₆	—	146	4	no	—
131	C₂×#97	—	73	1	no	—
132	C₂×#97	—	73	1	no	—
133	C₂×C₄×C₈	—	73	1	no	—
134	C₂×C₄×C₈	#64408	1	1	yes	characteristic
135	#349	—	73	8	no	—
136	#347	—	146	4	no	—
137	C₂³×C₄	—	73	1	no	—
138	C₂³×C₄	—	146	1	no	—
139	C₂×M₁₆	—	73	4	no	—
140	C₂×M₁₆	—	146	2	no	—
141	C₂×M₁₆	—	146	2	no	—
142	C₂×M₁₆	—	146	2	no	—
143	C₂×M₁₆	—	146	2	no	—
144	C₂×M₁₆	—	146	2	no	—
145	C₂²×C₈	—	73	1	no	—
146	C₂²×C₈	—	73	1	no	—
147	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
148	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
149	C₂×C₄²	—	73	1	no	—
150	C₂×C₄²	—	146	2	no	—
151	C₂×C₄²	—	146	1	no	—
152	C₂×C₄²	—	146	2	no	—
153	C₂×C₄²	C₂×#64408	1	1	yes	characteristic
154	M₃₂	—	73	8	no	—
155	M₃₂	—	146	4	no	—
156	C₂×C₁₆	—	146	4	no	—
157	#97	—	73	4	no	—
158	#97	—	146	2	no	—
159	C₄×C₈	—	2	2	no	—
160	C₄×C₈	—	146	2	no	—
161	C₂⁴	—	73	1	no	—
162	C₂²×C₄	—	2	1	no	—
163	C₂²×C₄	—	292	4	no	—
164	C₂²×C₄	—	73	1	no	—
165	C₂²×C₄	—	73	2	no	—
166	C₂²×C₄	—	73	2	no	—
167	C₂²×C₄	—	146	4	no	—
168	C₂²×C₄	—	146	1	no	—
169	C₂²×C₄	—	146	1	no	—
170	C₂²×C₄	—	146	1	no	—
171	C₂²×C₄	—	146	1	no	—
172	C₂²×C₄	—	146	1	no	—
173	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
174	M₁₆	—	146	8	no	—
175	M₁₆	—	146	8	no	—
176	C₂×C₈	—	2	1	no	—
177	C₂×C₈	—	2	1	no	—
178	C₂×C₈	—	2	1	no	—
179	C₂×C₈	—	2	1	no	—
180	C₂×C₈	—	73	2	no	—
181	C₂×C₈	—	73	2	no	—
182	C₂×C₈	—	73	2	no	—
183	C₂×C₈	—	73	2	no	—
184	C₂×C₈	—	146	1	no	—
185	C₂×C₈	—	146	1	no	—
186	C₂×C₈	C₄×#64408	1	2	yes	—
187	C₂×C₈	C₂²⋊#64408	1	2	yes	—
188	C₄²	—	2	1	no	—
189	C₄²	—	73	2	no	—
190	C₄²	—	146	4	no	—
191	C₄²	—	146	1	no	—
192	C₄²	#11924038	1	2	yes	—
193	C₁₆	—	146	8	no	—
194	C₂³	—	292	2	no	—
195	C₂³	—	73	2	no	—
196	C₂³	—	146	1	no	—
197	C₂³	—	146	1	no	—
198	C₂³	D₇₃⋊M₁₆	1	1	yes	characteristic
199	C₂×C₄	—	2	4	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	292	8	no	—
202	C₂×C₄	—	292	2	no	—
203	C₂×C₄	—	73	2	no	—
204	C₂×C₄	—	146	2	no	—
205	C₂×C₄	—	146	1	no	—
206	C₂×C₄	—	146	1	no	—
207	C₂×C₄	—	146	2	no	—
208	C₂×C₄	—	146	2	no	—
209	C₂×C₄	—	146	2	no	—
210	C₂×C₄	—	146	2	no	—
211	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
212	C₂×C₄	C₂×C₂²⋊#64408	1	1	yes	characteristic
213	C₂×C₄	#14556670	1	1	yes	characteristic
214	C₂×C₄	D₇₃⋊M₁₆	1	1	yes	characteristic
215	C₂×C₄	D₇₃⋊M₁₆	1	1	yes	characteristic
216	C₂×C₄	C₂×#11924038	1	1	yes	characteristic
217	C₈	—	2	2	no	—
218	C₈	—	2	2	no	—
219	C₈	—	73	4	no	—
220	C₈	—	146	2	no	—
221	C₂²	—	2	2	no	—
222	C₂²	—	292	2	no	—
223	C₂²	—	292	2	no	—
224	C₂²	—	292	2	no	—
225	C₂²	—	146	2	no	—
226	C₂²	#17989546	1	1	yes	characteristic
227	C₂²	#17989558	1	1	yes	characteristic
228	C₂²	#17989610	1	1	yes	characteristic
229	C₄	—	2	4	no	—
230	C₄	—	292	2	no	—
231	C₄	—	146	2	no	—
232	C₄	C₄×C₂²⋊#64408	1	1	yes	characteristic
233	C₄	C₄×#11924038	1	1	yes	characteristic
234	C₄	#17989559	1	1	yes	characteristic
235	C₄	#17989609	1	1	yes	characteristic
236	C₂	—	2	1	no	—
237	C₂	—	2	1	no	—
238	C₂	—	292	2	no	—
239	C₂	#22625658	1	1	yes	characteristic
240	C₂	#22626303	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17989484

C₂

yes

maximal

C₂×#17989480

C₂

yes

maximal, complemented

#22624975

C₂

yes

maximal, complemented

C₂×C₄×#11924011

C₂

yes

maximal, characteristic

C₂×#14556665

C₂²

yes

—

#17989484

C₄

yes

complemented

#17989480

—

C₂²×#11924011

C₄

yes

characteristic

C₂²×#11924011

C₂²

yes

characteristic

C₂×C₄²×D₇₃

C₄

yes

characteristic

C₄×#11924011

—

C₂×#14556501

C₄

yes

characteristic

C₂×#14556501

C₂²

yes

characteristic

C₂×C₄×#10596831

C₂²

yes

characteristic

C₂×C₄×C₈×C₇₃

C₄

yes

characteristic

#14556665

—

#14556665

C₂×C₄

yes

complemented

C₂×#11924031

—

C₂²×C₄×D₇₃

—

C₂²×C₄×D₇₃

C₂×C₄

yes

—

—

—

—

—

C₂×C₄

yes

—

C₂²×#10596831

C₂×C₄

yes

characteristic

C₂²×#10596831

C₂³

yes

characteristic

C₂×C₄×Dic₇₃

—

C₂×C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄²×D₇₃

—

C₄²×D₇₃

—

#14556501

—

#14556501

D₄

yes

—

C₄×#10596831

—

C₂²×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₇₃

C₂×C₄

yes

characteristic

C₄×C₈×C₇₃

—

#11924031

—

C₂³×D₇₃

M₁₆

yes

characteristic

C₂²×Dic₇₃

—

C₂²×Dic₇₃

M₁₆

yes

characteristic

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

C₄²

yes

—

C₂×C₄×D₇₃

M₁₆

yes

—

—

—

—

—

M₁₆

yes

—

C₂×#10596831

C₂²×C₄

yes

—

C₂×#10596831

C₂×D₄

yes

—

C₂×#10596831

#41

yes

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₄²

yes

—

C₂×C₈×C₇₃

C₂²⋊C₄

yes

—

C₄²×C₇₃

—

C₄²×C₇₃

M₁₆

yes

—

C₂³×C₇₃

C₂×M₁₆

yes

characteristic

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

#97

yes

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

#117

yes

characteristic

C₂×C₄×C₇₃

C₂×M₁₆

yes

characteristic

C₂×C₄×C₇₃

C₂×M₁₆

yes

characteristic

C₂×C₄×C₇₃

C₂×M₁₆

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

#97

yes

—

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

C₈×C₇₃

—

C₈×C₇₃

—

#10596831

—

#10596831

C₄×D₄

yes

—

100

C₂²×C₇₃

—

101

C₂²×C₇₃

C₂×#97

yes

characteristic

102

C₂²×C₇₃

#407

yes

characteristic

103

C₂²×C₇₃

#432

yes

characteristic

104

C₂×D₇₃

—

105

C₂×D₇₃

—

106

C₂×D₇₃

—

107

C₂×D₇₃

—

108

C₄×C₇₃

—

109

C₄×C₇₃

C₄×C₂²⋊C₄

yes

characteristic

110

C₄×C₇₃

C₄×M₁₆

yes

characteristic

111

C₄×C₇₃

#407

yes

characteristic

112

C₄×C₇₃

#432

yes

characteristic

113

Dic₇₃

—

114

Dic₇₃

—

115

#12607

—

maximal, Sylow

116

C₂×C₇₃

—

117

C₂×C₇₃

—

118

C₂×C₇₃

#1749

yes

characteristic

119

C₂×C₇₃

#2165

yes

—

120

D₇₃

—

121

C₂×C₄×M₁₆

—

122

C₂×#349

—

123

C₂×#347

—

124

#1376

—

125

C₇₃

#12607

yes

characteristic, complemented, Sylow

126

C₂²×M₁₆

—

127

C₂²×M₁₆

—

128

C₂²×C₄²

—

129

C₂×M₃₂

—

130

C₄×M₁₆

—

146

—

131

C₂×#97

—

132

C₂×#97

—

133

C₂×C₄×C₈

—

134

C₂×C₄×C₈

#64408

yes

characteristic

135

#349

—

136

#347

—

146

—

137

C₂³×C₄

—

138

C₂³×C₄

—

146

—

139

C₂×M₁₆

—

140

C₂×M₁₆

—

146

—

141

C₂×M₁₆

—

146

—

142

C₂×M₁₆

—

146

—

143

C₂×M₁₆

—

146

—

144

C₂×M₁₆

—

146

—

145

C₂²×C₈

—

146

C₂²×C₈

—

147

C₂²×C₈

C₂×#64408

yes

characteristic

148

C₂²×C₈

C₂×#64408

yes

characteristic

149

C₂×C₄²

—

150

C₂×C₄²

—

146

—

151

C₂×C₄²

—

146

—

152

C₂×C₄²

—

146

—

153

C₂×C₄²

C₂×#64408

yes

characteristic

154

M₃₂

—

155

M₃₂

—

146

—

156

C₂×C₁₆

—

146

—

157

#97

—

158

#97

—

146

—

159

C₄×C₈

—

160

C₄×C₈

—

146

—

161

C₂⁴

—

162

C₂²×C₄

—

163

C₂²×C₄

—

292

—

164

C₂²×C₄

—

165

C₂²×C₄

—

166

C₂²×C₄

—

167

C₂²×C₄

—

146

—

168

C₂²×C₄

—

146

—

169

C₂²×C₄

—

146

—

170

C₂²×C₄

—

146

—

171

C₂²×C₄

—

146

—

172

C₂²×C₄

—

146

—

173

C₂²×C₄

C₂²×#64408

yes

characteristic

174

M₁₆

—

146

—

175

M₁₆

—

146

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

146

—

185

C₂×C₈

—

146

—

186

C₂×C₈

C₄×#64408

yes

—

187

C₂×C₈

C₂²⋊#64408

yes

—

188

C₄²

—

189

C₄²

—

190

C₄²

—

146

—

191

C₄²

—

146

—

192

C₄²

#11924038

yes

—

193

C₁₆

—

146

—

194

C₂³

—

292

—

195

C₂³

—

196

C₂³

—

146

—

197

C₂³

—

146

—

198

C₂³

D₇₃⋊M₁₆

yes

characteristic

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

292

—

202

C₂×C₄

—

292

—

203

C₂×C₄

—

204

C₂×C₄

—

146

—

205

C₂×C₄

—

146

—

206

C₂×C₄

—

146

—

207

C₂×C₄

—

146

—

208

C₂×C₄

—

146

—

209

C₂×C₄

—

146

—

210

C₂×C₄

—

146

—

211

C₂×C₄

C₂×C₄×#64408

yes

characteristic

212

C₂×C₄

C₂×C₂²⋊#64408

yes

characteristic

213

C₂×C₄

#14556670

yes

characteristic

214

C₂×C₄

D₇₃⋊M₁₆

yes

characteristic

215

C₂×C₄

D₇₃⋊M₁₆

yes

characteristic

216

C₂×C₄

C₂×#11924038

yes

characteristic

217

C₈

—

218

C₈

—

219

C₈

—

220

C₈

—

146

—

221

C₂²

—

222

C₂²

—

292

—

223

C₂²

—

292

—

224

C₂²

—

292

—

225

C₂²

—

146

—

226

C₂²

#17989546

yes

characteristic

227

C₂²

#17989558

yes

characteristic

228

C₂²

#17989610

yes

characteristic

229

C₄

—

230

C₄

—

292

—

231

C₄

—

146

—

232

C₄

C₄×C₂²⋊#64408

yes

characteristic

233

C₄

C₄×#11924038

yes

characteristic

234

C₄

#17989559

yes

characteristic

235

C₄

#17989609

yes

characteristic

236

C₂

—

237

C₂

—

238

C₂

—

292

—

239

C₂

#22625658

yes

characteristic

240

C₂

#22626303

yes

—

	subgroup	G/H
center	C₂×C₄	#14556670
commutator	C₂×C₄×C₇₃	C₂×C₄²
Frattini	C₂²×C₄	C₂²×#64408
Fitting	C₂×C₄×C₈×C₇₃	C₄
socle	C₂²×C₇₃	#432
prime radical	C₂³×D₇₃	M₁₆
cosocle	C₂²×#10596831	C₂³
hypercenter	C₂×C₄×C₈	#64408
hypocenter	C₇₃	#12607
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂×C₄

#14556670

commutator

C₂×C₄×C₇₃

C₂×C₄²

Frattini

C₂²×C₄

C₂²×#64408

Fitting

C₂×C₄×C₈×C₇₃

C₄

socle

C₂²×C₇₃

#432

prime radical

C₂³×D₇₃

M₁₆

C₂³

C₂×C₄×C₈

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

N	H ≅ G/N	type
2. C₂×#17989480	C₂	semidirect
3. #22624975	C₂	semidirect
6. #17989484	C₄	semidirect
17. #14556665	C₂×C₄	semidirect
125. C₇₃	#12607	semidirect

H ≅ G/N

type

2. C₂×#17989480

C₂

semidirect

3. #22624975

C₂

semidirect

6. #17989484

C₄

semidirect

17. #14556665

C₂×C₄

semidirect

125. C₇₃

#12607

semidirect

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

subgroup	index
C₂×#17989484	2
C₂×#17989480	2
#22624975	2
C₂×C₄×#11924011	2
#12607	73

subgroup

index

Subgroups — #34012396

Conjugacy classes of subgroups

Complements

Maximal subgroups