Group #33003950 — subgroups

Subgroups — #33003950

Order 18688.

314 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 97 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×#17988404	C₂	1	1	yes	maximal, characteristic
2	#22611650	C₂	1	1	yes	maximal, characteristic
3	C₂×#17988364	C₂	1	1	yes	maximal, characteristic
4	#22610800	C₂	1	1	yes	maximal, characteristic
5	#22610685	C₂	1	1	yes	maximal, characteristic
6	#22608029	C₂	1	1	yes	maximal, characteristic
7	C₇₃×#1386	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₂₉₂	C₂²	1	1	yes	characteristic
9	C₂×#14556531	C₂²	1	1	yes	characteristic
10	C₂×#14556527	C₂²	1	1	yes	characteristic
11	#17988614	—	2	1	no	—
12	C₂×#14556514	—	2	1	no	—
13	C₂×#14556501	C₂²	1	1	yes	characteristic
14	#17988492	—	2	1	no	—
15	#17988404	—	2	2	no	—
16	#17988390	C₄	1	4	yes	complemented
17	#17988364	—	2	2	no	—
18	#17988346	—	2	1	no	—
19	C₂×M₃₂×C₇₃	C₂²	1	1	yes	characteristic
20	#427×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×#106×C₇₃	C₂²	1	1	yes	characteristic
22	C₂²×Dic₁₄₆	—	2	1	no	—
23	C₂×Dic₂₉₂	—	2	1	no	—
24	C₂×Dic₂₉₂	—	2	1	no	—
25	C₂×Dic₂₉₂	—	2	1	no	—
26	C₂×Dic₂₉₂	—	2	1	no	—
27	C₂×Dic₂₉₂	—	2	1	no	—
28	C₂×Dic₂₉₂	C₂×C₄	1	2	yes	—
29	C₂×#11924012	—	2	1	no	—
30	C₂²×#10596831	D₄	1	1	yes	characteristic
31	C₂×C₄×Dic₇₃	D₄	1	1	yes	characteristic
32	#14556531	—	2	1	no	—
33	#14556531	—	2	1	no	—
34	C₂×#11924003	C₂×C₄	1	2	yes	—
35	#14556527	—	2	1	no	—
36	#14556527	—	2	1	no	—
37	C₄⋊#10596831	—	4	2	no	—
38	#14556514	—	4	2	no	—
39	#14556501	—	2	1	no	—
40	#14556501	—	2	1	no	—
41	#14556498	—	4	2	no	—
42	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
43	#117×C₇₃	—	2	1	no	—
44	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
45	M₃₂×C₇₃	—	2	1	no	—
46	M₃₂×C₇₃	D₄	1	2	yes	—
47	C₂×C₁₆×C₇₃	—	2	1	no	—
48	#107×C₇₃	C₂×C₄	1	2	yes	—
49	#106×C₇₃	—	2	1	no	—
50	#106×C₇₃	—	2	1	no	—
51	#106×C₇₃	—	2	1	no	—
52	C₂×Dic₁₄₆	—	2	2	no	—
53	C₂×Dic₁₄₆	—	4	1	no	—
54	C₂×Dic₁₄₆	—	4	1	no	—
55	C₂×Dic₁₄₆	—	4	1	no	—
56	C₂×Dic₁₄₆	—	4	1	no	—
57	C₂×Dic₁₄₆	—	4	1	no	—
58	C₂²×Dic₇₃	—	2	1	no	—
59	C₂²×Dic₇₃	—	4	1	no	—
60	Dic₂₉₂	—	2	2	no	—
61	Dic₂₉₂	—	2	2	no	—
62	Dic₂₉₂	—	4	1	no	—
63	Dic₂₉₂	—	4	1	no	—
64	#11924012	—	4	1	no	—
65	#11924012	—	4	1	no	—
66	C₂×#10596831	—	2	1	no	—
67	C₂×#10596831	—	2	1	no	—
68	C₂×#10596831	—	2	1	no	—
69	C₂×#10596831	—	4	1	no	—
70	C₄×Dic₇₃	—	2	1	no	—
71	C₄×Dic₇₃	—	2	1	no	—
72	#11924003	—	2	2	no	—
73	C₂²×C₄×C₇₃	—	4	1	no	—
74	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
75	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
76	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
77	C₂×C₈×C₇₃	#41	1	1	yes	characteristic
78	C₂×C₈×C₇₃	#41	1	1	yes	characteristic
79	C₂×C₈×C₇₃	#41	1	1	yes	characteristic
80	C₂×C₈×C₇₃	#41	1	1	yes	characteristic
81	C₄⋊C₄×C₇₃	—	2	2	no	—
82	C₄⋊C₄×C₇₃	—	4	1	no	—
83	C₄⋊C₄×C₇₃	—	4	1	no	—
84	C₂²⋊C₄×C₇₃	—	4	1	no	—
85	C₄²×C₇₃	—	4	1	no	—
86	C₁₆×C₇₃	—	2	2	no	—
87	C₂³×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
88	C₂×C₄×C₇₃	—	4	2	no	—
89	C₂×C₄×C₇₃	—	8	2	no	—
90	C₂×C₄×C₇₃	—	8	1	no	—
91	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
92	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
93	C₂×C₄×C₇₃	#124	1	1	yes	characteristic
94	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
95	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
96	C₂×C₄×C₇₃	#137	1	1	yes	characteristic
97	C₂×Dic₇₃	—	4	2	no	—
98	C₂×Dic₇₃	—	4	2	no	—
99	C₂×Dic₇₃	—	4	1	no	—
100	C₂×Dic₇₃	—	8	1	no	—
101	C₂×Dic₇₃	—	8	1	no	—
102	Dic₁₄₆	—	4	2	no	—
103	Dic₁₄₆	—	4	2	no	—
104	Dic₁₄₆	—	8	1	no	—
105	Dic₁₄₆	—	8	1	no	—
106	C₈×C₇₃	#117	1	1	yes	characteristic
107	C₈×C₇₃	C₄×D₄	1	1	yes	characteristic
108	C₈×C₇₃	#123	1	1	yes	characteristic
109	C₈×C₇₃	#126	1	1	yes	characteristic
110	#10596831	—	4	1	no	—
111	#10596831	—	8	1	no	—
112	C₂²×C₇₃	—	2	2	no	—
113	C₂²×C₇₃	#442	1	1	yes	characteristic
114	C₂²×C₇₃	#468	1	1	yes	characteristic
115	C₂²×C₇₃	#490	1	1	yes	characteristic
116	C₄×C₇₃	—	8	2	no	—
117	C₄×C₇₃	—	16	1	no	—
118	C₄×C₇₃	#388	1	1	yes	characteristic
119	C₄×C₇₃	#440	1	1	yes	characteristic
120	C₄×C₇₃	#469	1	1	yes	characteristic
121	C₄×C₇₃	#489	1	1	yes	characteristic
122	Dic₇₃	—	8	1	no	—
123	Dic₇₃	—	8	2	no	—
124	#13154	—	73	1	no	maximal, Sylow
125	C₂×C₇₃	—	2	1	no	—
126	C₂×C₇₃	—	2	1	no	—
127	C₂×C₇₃	#1936	1	1	yes	characteristic
128	C₂×C₇₃	#2180	1	2	yes	—
129	C₂×#362	—	73	1	no	—
130	#2141	—	73	1	no	—
131	C₂×#347	—	73	1	no	—
132	#1971	—	73	1	no	—
133	#1946	—	73	1	no	—
134	#1386	D₇₃	1	1	yes	characteristic
135	#1383	—	73	1	no	—
136	C₇₃	#13154	1	1	yes	characteristic, complemented, Sylow
137	C₂²×Q₁₆	—	73	1	no	—
138	C₂×M₃₂	—	73	1	no	—
139	C₂×M₃₂	C₂×D₇₃	1	1	yes	characteristic
140	C₂×#108	—	73	1	no	—
141	#427	C₂×D₇₃	1	1	yes	characteristic
142	C₂×#106	C₂×D₇₃	1	1	yes	characteristic
143	#424	—	146	1	no	—
144	C₂×#103	—	146	1	no	—
145	C₂×#97	—	73	1	no	—
146	#391	—	146	1	no	—
147	#362	—	146	2	no	—
148	#358	—	73	4	no	—
149	#347	—	146	2	no	—
150	#339	—	146	1	no	—
151	C₂²×Q₈	—	146	1	no	—
152	C₂×Q₁₆	—	73	2	no	—
153	C₂×Q₁₆	—	146	1	no	—
154	C₂×Q₁₆	—	146	1	no	—
155	C₂×Q₁₆	—	146	1	no	—
156	C₂×Q₁₆	—	146	1	no	—
157	C₂×Q₁₆	—	146	1	no	—
158	C₂×M₁₆	—	146	1	no	—
159	C₂²×C₈	—	73	1	no	—
160	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
161	#117	—	2	1	no	—
162	C₂×C₄⋊C₄	—	2	1	no	—
163	C₂×C₄²	—	73	1	no	—
164	M₃₂	—	2	1	no	—
165	M₃₂	—	146	1	no	—
166	M₃₂	—	146	1	no	—
167	M₃₂	D₂₉₂	1	2	yes	—
168	C₂×C₁₆	—	2	1	no	—
169	C₂×C₁₆	—	73	2	no	—
170	#108	—	146	1	no	—
171	#108	—	146	1	no	—
172	#107	C₄×D₇₃	1	2	yes	—
173	#106	—	2	1	no	—
174	#106	—	2	1	no	—
175	#106	—	2	1	no	—
176	C₄⋊C₈	—	292	2	no	—
177	#103	—	292	2	no	—
178	#97	—	146	1	no	—
179	#97	—	146	1	no	—
180	#95	—	292	2	no	—
181	C₂×Q₈	—	292	1	no	—
182	C₂×Q₈	—	292	1	no	—
183	C₂×Q₈	—	292	1	no	—
184	C₂×Q₈	—	292	1	no	—
185	C₂×Q₈	—	292	1	no	—
186	C₂×Q₈	—	146	2	no	—
187	C₂²×C₄	—	4	1	no	—
188	C₂²×C₄	—	292	1	no	—
189	C₂²×C₄	—	146	1	no	—
190	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
191	Q₁₆	—	292	1	no	—
192	Q₁₆	—	292	1	no	—
193	Q₁₆	—	146	2	no	—
194	Q₁₆	—	146	2	no	—
195	M₁₆	—	292	1	no	—
196	M₁₆	—	292	1	no	—
197	C₂×C₈	—	292	1	no	—
198	C₂×C₈	—	146	1	no	—
199	C₂×C₈	—	146	1	no	—
200	C₂×C₈	—	146	1	no	—
201	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
202	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
203	C₂×C₈	#11924027	1	1	yes	characteristic
204	C₂×C₈	#11924027	1	1	yes	characteristic
205	C₂×C₈	#11924028	1	1	yes	characteristic
206	C₂×C₈	#11924029	1	1	yes	characteristic
207	C₄⋊C₄	—	2	2	no	—
208	C₄⋊C₄	—	4	1	no	—
209	C₄⋊C₄	—	4	1	no	—
210	C₂²⋊C₄	—	4	1	no	—
211	C₄²	—	4	1	no	—
212	C₄²	—	146	1	no	—
213	C₄²	—	146	1	no	—
214	C₁₆	—	2	2	no	—
215	C₁₆	—	146	2	no	—
216	C₂³	#14556615	1	1	yes	characteristic
217	Q₈	—	292	2	no	—
218	Q₈	—	292	2	no	—
219	Q₈	—	584	1	no	—
220	Q₈	—	584	1	no	—
221	C₂×C₄	—	4	2	no	—
222	C₂×C₄	—	8	2	no	—
223	C₂×C₄	—	8	1	no	—
224	C₂×C₄	—	292	2	no	—
225	C₂×C₄	—	292	2	no	—
226	C₂×C₄	—	292	1	no	—
227	C₂×C₄	—	584	1	no	—
228	C₂×C₄	—	584	1	no	—
229	C₂×C₄	#14556551	1	1	yes	characteristic
230	C₂×C₄	#14556566	1	1	yes	characteristic
231	C₂×C₄	#14556577	1	1	yes	characteristic
232	C₂×C₄	#14556618	1	1	yes	characteristic
233	C₂×C₄	#14556618	1	1	yes	characteristic
234	C₂×C₄	#14556623	1	1	yes	characteristic
235	C₈	—	292	1	no	—
236	C₈	—	584	1	no	—
237	C₈	#14556549	1	1	yes	characteristic
238	C₈	C₄×D₂₉₂	1	1	yes	characteristic
239	C₈	#14556575	1	1	yes	characteristic
240	C₈	#14556586	1	1	yes	characteristic
241	C₂²	—	2	2	no	—
242	C₂²	#17988696	1	1	yes	characteristic
243	C₂²	#17988834	1	1	yes	characteristic
244	C₂²	#17988950	1	1	yes	characteristic
245	C₄	—	8	2	no	—
246	C₄	—	16	1	no	—
247	C₄	—	584	1	no	—
248	C₄	—	584	2	no	—
249	C₄	#17988479	1	1	yes	characteristic
250	C₄	#17988690	1	1	yes	characteristic
251	C₄	#17988841	1	1	yes	characteristic
252	C₄	#17988948	1	1	yes	characteristic
253	C₂	—	2	1	no	—
254	C₂	—	2	1	no	—
255	C₂	#22610629	1	1	yes	characteristic
256	C₂	#22611819	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17988404

C₂

yes

maximal, characteristic

#22611650

C₂

yes

maximal, characteristic

C₂×#17988364

C₂

yes

maximal, characteristic

#22610800

C₂

yes

maximal, characteristic

#22610685

C₂

yes

maximal, characteristic

#22608029

C₂

yes

maximal, characteristic

C₇₃×#1386

C₂

yes

maximal, characteristic

C₂²×Dic₂₉₂

C₂²

yes

characteristic

C₂×#14556531

C₂²

yes

characteristic

C₂×#14556527

C₂²

yes

—

—

C₂²

yes

—

—

C₄

yes

complemented

#17988364

—

#17988346

—

C₂×M₃₂×C₇₃

C₂²

yes

characteristic

#427×C₇₃

C₂²

yes

characteristic

C₂×#106×C₇₃

C₂²

yes

characteristic

C₂²×Dic₁₄₆

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

C₂×C₄

yes

—

C₂×#11924012

—

C₂²×#10596831

D₄

yes

characteristic

C₂×C₄×Dic₇₃

D₄

yes

—

—

C₂×C₄

yes

—

—

—

—

—

—

—

—

C₂²×C₈×C₇₃

C₂³

yes

characteristic

#117×C₇₃

—

C₂×C₄⋊C₄×C₇₃

—

M₃₂×C₇₃

—

M₃₂×C₇₃

D₄

yes

—

C₂×C₁₆×C₇₃

—

#107×C₇₃

C₂×C₄

yes

—

#106×C₇₃

—

#106×C₇₃

—

#106×C₇₃

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

Dic₂₉₂

—

Dic₂₉₂

—

Dic₂₉₂

—

Dic₂₉₂

—

—

—

—

—

—

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

#11924003

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₈×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×D₄

yes

C₂×C₈×C₇₃

yes

C₂×C₈×C₇₃

yes

C₂×C₈×C₇₃

yes

C₂×C₈×C₇₃

yes

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₁₆×C₇₃

—

C₂³×C₇₃

AGL(1,ℤ/8)

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₄×D₄

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

100

C₂×Dic₇₃

—

101

C₂×Dic₇₃

—

102

Dic₁₄₆

—

103

Dic₁₄₆

—

104

Dic₁₄₆

—

105

Dic₁₄₆

—

106

C₈×C₇₃

#117

yes

characteristic

107

C₈×C₇₃

C₄×D₄

yes

characteristic

108

C₈×C₇₃

#123

yes

characteristic

109

C₈×C₇₃

#126

yes

characteristic

110

#10596831

—

111

#10596831

—

112

C₂²×C₇₃

—

113

C₂²×C₇₃

#442

yes

characteristic

114

C₂²×C₇₃

#468

yes

characteristic

115

C₂²×C₇₃

#490

yes

characteristic

116

C₄×C₇₃

—

117

C₄×C₇₃

—

118

C₄×C₇₃

#388

yes

characteristic

119

C₄×C₇₃

#440

yes

characteristic

120

C₄×C₇₃

#469

yes

characteristic

121

C₄×C₇₃

#489

yes

characteristic

122

Dic₇₃

—

123

Dic₇₃

—

124

#13154

—

maximal, Sylow

125

C₂×C₇₃

—

126

C₂×C₇₃

—

127

C₂×C₇₃

#1936

yes

characteristic

128

C₂×C₇₃

#2180

yes

—

129

C₂×#362

—

130

#2141

—

131

C₂×#347

—

132

#1971

—

133

#1946

—

134

#1386

D₇₃

yes

characteristic

135

#1383

—

136

C₇₃

#13154

yes

characteristic, complemented, Sylow

137

C₂²×Q₁₆

—

138

C₂×M₃₂

—

139

C₂×M₃₂

C₂×D₇₃

yes

characteristic

140

C₂×#108

—

141

#427

C₂×D₇₃

yes

characteristic

142

C₂×#106

C₂×D₇₃

yes

characteristic

143

#424

—

146

—

144

C₂×#103

—

146

—

145

C₂×#97

—

146

#391

—

146

—

147

#362

—

146

—

148

#358

—

149

#347

—

146

—

150

#339

—

146

—

151

C₂²×Q₈

—

146

—

152

C₂×Q₁₆

—

153

C₂×Q₁₆

—

146

—

154

C₂×Q₁₆

—

146

—

155

C₂×Q₁₆

—

146

—

156

C₂×Q₁₆

—

146

—

157

C₂×Q₁₆

—

146

—

158

C₂×M₁₆

—

146

—

159

C₂²×C₈

—

160

C₂²×C₈

C₂²×D₇₃

yes

characteristic

161

#117

—

162

C₂×C₄⋊C₄

—

163

C₂×C₄²

—

164

M₃₂

—

165

M₃₂

—

146

—

166

M₃₂

—

146

—

167

M₃₂

D₂₉₂

yes

—

168

C₂×C₁₆

—

169

C₂×C₁₆

—

170

#108

—

146

—

171

#108

—

146

—

172

#107

C₄×D₇₃

yes

—

173

#106

—

174

#106

—

175

#106

—

176

C₄⋊C₈

—

292

—

177

#103

—

292

—

178

#97

—

146

—

179

#97

—

146

—

180

#95

—

292

—

181

C₂×Q₈

—

292

—

182

C₂×Q₈

—

292

—

183

C₂×Q₈

—

292

—

184

C₂×Q₈

—

292

—

185

C₂×Q₈

—

292

—

186

C₂×Q₈

—

146

—

187

C₂²×C₄

—

188

C₂²×C₄

—

292

—

189

C₂²×C₄

—

146

—

190

C₂²×C₄

D₄×D₇₃

yes

characteristic

191

Q₁₆

—

292

—

192

Q₁₆

—

292

—

193

Q₁₆

—

146

—

194

Q₁₆

—

146

—

195

M₁₆

—

292

—

196

M₁₆

—

292

—

197

C₂×C₈

—

292

—

198

C₂×C₈

—

146

—

199

C₂×C₈

—

146

—

200

C₂×C₈

—

146

—

201

C₂×C₈

C₂×C₄×D₇₃

yes

characteristic

202

C₂×C₈

C₂×D₂₉₂

yes

characteristic

203

C₂×C₈

#11924027

yes

characteristic

204

C₂×C₈

#11924027

yes

characteristic

205

C₂×C₈

#11924028

yes

characteristic

206

C₂×C₈

#11924029

yes

characteristic

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

210

C₂²⋊C₄

—

211

C₄²

—

212

C₄²

—

146

—

213

C₄²

—

146

—

214

C₁₆

—

215

C₁₆

—

146

—

216

C₂³

#14556615

yes

characteristic

217

Q₈

—

292

—

218

Q₈

—

292

—

219

Q₈

—

584

—

220

Q₈

—

584

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

292

—

225

C₂×C₄

—

292

—

226

C₂×C₄

—

292

—

227

C₂×C₄

—

584

—

228

C₂×C₄

—

584

—

229

C₂×C₄

#14556551

yes

characteristic

230

C₂×C₄

#14556566

yes

characteristic

231

C₂×C₄

#14556577

yes

characteristic

232

C₂×C₄

#14556618

yes

characteristic

233

C₂×C₄

#14556618

yes

characteristic

234

C₂×C₄

#14556623

yes

characteristic

235

C₈

—

292

—

236

C₈

—

584

—

237

C₈

#14556549

yes

characteristic

238

C₈

C₄×D₂₉₂

yes

characteristic

239

C₈

#14556575

yes

characteristic

240

C₈

#14556586

yes

characteristic

241

C₂²

—

242

C₂²

#17988696

yes

characteristic

243

C₂²

#17988834

yes

characteristic

244

C₂²

#17988950

yes

characteristic

245

C₄

—

246

C₄

—

247

C₄

—

584

—

248

C₄

—

584

—

249

C₄

#17988479

yes

characteristic

250

C₄

#17988690

yes

characteristic

251

C₄

#17988841

yes

characteristic

252

C₄

#17988948

yes

characteristic

253

C₂

—

254

C₂

—

255

C₂

#22610629

yes

characteristic

256

C₂

#22611819

yes

—

	subgroup	G/H
center	C₂²	#17988696
commutator	C₂×C₈×C₇₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₇₃
Fitting	C₇₃×#1386	C₂
socle	C₂²×C₇₃	#442
prime radical	C₂³×C₇₃	AGL(1,ℤ/8)
cosocle	C₂²×C₈×C₇₃	C₂³
hypercenter	#1386	D₇₃
hypocenter	C₇₃	#13154
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1386

subgroup

G/H

center

C₂²

#17988696

commutator

C₂×C₈×C₇₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₇₃

Fitting

C₇₃×#1386

C₂

C₂²×C₇₃

C₂³×C₇₃

C₂²×C₈×C₇₃

C₂³

D₇₃

C₇₃

G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1386

N	H ≅ G/N	type
16. #17988390	C₄	semidirect
136. C₇₃	#13154	semidirect

H ≅ G/N

type

16. #17988390

C₄

semidirect

136. C₇₃

#13154

semidirect

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

subgroup	index
C₂×#17988404	2
#22611650	2
C₂×#17988364	2
#22610800	2
#22610685	2
#22608029	2
C₇₃×#1386	2
#13154	73

subgroup

index

C₇₃×#1386

Subgroups — #33003950

Conjugacy classes of subgroups

Complements

Maximal subgroups