Group #32988996 — subgroups

Subgroups — #32988996

Order 18688.

504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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	#22610879	C₂	1	2	yes	maximal
2	#22610732	C₂	1	1	yes	maximal, characteristic
3	#22607814	C₂	1	1	yes	maximal, characteristic
4	#22607772	C₂	1	2	yes	maximal
5	C₇₃×#2551	C₂	1	1	yes	maximal, characteristic
6	C₂×#14556591	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊#10596831	C₂²	1	2	yes	—
8	C₂×#14556514	—	2	2	no	—
9	C₂×C₄×#10596831	C₂²	1	1	yes	characteristic
10	#17988349	—	2	2	no	—
11	#17988349	—	2	2	no	—
12	C₂×C₄⋊Q₈×C₇₃	—	2	2	no	—
13	#395×C₇₃	—	2	2	no	—
14	#389×C₇₃	—	2	2	no	—
15	#384×C₇₃	C₂²	1	1	yes	characteristic
16	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
17	C₂²×Dic₁₄₆	—	2	1	no	—
18	C₂²×#10596831	—	2	1	no	—
19	C₂²×#10596831	—	2	2	no	—
20	#14556591	—	2	2	no	—
21	#14556591	—	2	1	no	—
22	#14556591	Q₈	1	2	yes	complemented
23	C₂×C₄⋊Dic₇₃	—	2	2	no	—
24	C₄⋊#10596831	—	2	2	no	—
25	C₄⋊#10596831	—	2	2	no	—
26	#14556514	—	4	4	no	—
27	C₄×#10596831	—	2	2	no	—
28	C₂²×Q₈×C₇₃	—	2	2	no	—
29	C₄⋊Q₈×C₇₃	—	4	4	no	—
30	C₄⋊Q₈×C₇₃	—	4	4	no	—
31	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
32	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
33	C₂×C₄⋊C₄×C₇₃	D₄	1	2	yes	—
34	C₂×C₄⋊C₄×C₇₃	D₄	1	2	yes	—
35	C₂×C₄⋊C₄×C₇₃	D₄	1	2	yes	—
36	C₂×C₄²×C₇₃	—	2	2	no	—
37	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
38	#95×C₇₃	—	2	2	no	—
39	#95×C₇₃	—	2	2	no	—
40	C₂×Dic₁₄₆	—	2	2	no	—
41	C₂×Dic₁₄₆	—	4	2	no	—
42	C₂×Dic₁₄₆	—	4	2	no	—
43	C₂×Dic₁₄₆	—	4	1	no	—
44	C₂²×Dic₇₃	—	4	1	no	—
45	C₂×#10596831	—	2	2	no	—
46	C₂×#10596831	—	4	1	no	—
47	C₂×#10596831	—	4	1	no	—
48	C₂×#10596831	—	4	2	no	—
49	C₂×#10596831	—	4	2	no	—
50	C₂×#10596831	—	4	2	no	—
51	C₄⋊Dic₇₃	—	2	4	no	—
52	C₄⋊Dic₇₃	—	4	2	no	—
53	C₂×Q₈×C₇₃	—	4	8	no	—
54	C₂×Q₈×C₇₃	—	8	2	no	—
55	C₂²×C₄×C₇₃	—	2	2	no	—
56	C₂²×C₄×C₇₃	—	2	2	no	—
57	C₂²×C₄×C₇₃	—	2	2	no	—
58	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
60	C₄⋊C₄×C₇₃	—	2	2	no	—
61	C₄⋊C₄×C₇₃	—	2	2	no	—
62	C₄⋊C₄×C₇₃	—	4	2	no	—
63	C₄⋊C₄×C₇₃	—	4	8	no	—
64	C₄⋊C₄×C₇₃	—	4	2	no	—
65	C₄⋊C₄×C₇₃	—	4	2	no	—
66	C₄⋊C₄×C₇₃	SD₁₆	1	4	yes	—
67	C₄⋊C₄×C₇₃	Q₁₆	1	4	yes	—
68	C₄²×C₇₃	—	4	2	no	—
69	C₄²×C₇₃	—	4	2	no	—
70	C₄²×C₇₃	C₂×Q₈	1	1	yes	characteristic
71	C₄²×C₇₃	#41	1	2	yes	—
72	C₄²×C₇₃	#41	1	1	yes	characteristic
73	C₂³×C₇₃	#120	1	1	yes	characteristic
74	Q₈×C₇₃	—	8	8	no	—
75	C₂×C₄×C₇₃	—	2	1	no	—
76	C₂×C₄×C₇₃	—	2	1	no	—
77	C₂×C₄×C₇₃	—	2	4	no	—
78	C₂×C₄×C₇₃	—	2	4	no	—
79	C₂×C₄×C₇₃	—	4	2	no	—
80	C₂×C₄×C₇₃	—	4	2	no	—
81	C₂×C₄×C₇₃	—	4	2	no	—
82	C₂×C₄×C₇₃	—	4	2	no	—
83	C₂×C₄×C₇₃	—	4	4	no	—
84	C₂×C₄×C₇₃	—	4	2	no	—
85	C₂×C₄×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
86	C₂×C₄×C₇₃	C₂²⋊Q₈	1	2	yes	—
87	C₂×C₄×C₇₃	#124	1	1	yes	characteristic
88	C₂×C₄×C₇₃	#124	1	2	yes	—
89	C₂×C₄×C₇₃	C₂×SD₁₆	1	2	yes	—
90	C₂×C₄×C₇₃	C₂×Q₁₆	1	2	yes	—
91	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
92	C₂×C₄×C₇₃	#137	1	2	yes	—
93	C₂×Dic₇₃	—	4	2	no	—
94	C₂×Dic₇₃	—	8	1	no	—
95	C₂×Dic₇₃	—	8	1	no	—
96	Dic₁₄₆	—	4	4	no	—
97	Dic₁₄₆	—	8	2	no	—
98	#10596831	—	4	2	no	—
99	#10596831	—	8	2	no	—
100	C₂²×C₇₃	#393	1	1	yes	characteristic
101	C₂²×C₇₃	#450	1	2	yes	—
102	C₂²×C₇₃	#451	1	2	yes	—
103	C₂²×C₇₃	#453	1	1	yes	characteristic
104	C₂²×C₇₃	#454	1	1	yes	characteristic
105	C₄×C₇₃	—	2	1	no	—
106	C₄×C₇₃	—	2	1	no	—
107	C₄×C₇₃	—	4	4	no	—
108	C₄×C₇₃	—	4	4	no	—
109	C₄×C₇₃	—	8	2	no	—
110	C₄×C₇₃	#475	1	2	yes	—
111	C₄×C₇₃	#477	1	2	yes	—
112	C₄×C₇₃	#487	1	2	yes	—
113	C₄×C₇₃	#489	1	2	yes	—
114	Dic₇₃	—	8	2	no	—
115	#10349	—	73	1	no	maximal, Sylow
116	C₂×C₇₃	#1629	1	1	yes	characteristic
117	C₂×C₇₃	#1633	1	1	yes	characteristic
118	C₂×C₇₃	#1637	1	2	yes	—
119	C₂×C₇₃	#2024	1	2	yes	—
120	C₂×C₇₃	#2027	1	1	yes	characteristic
121	#2551	D₇₃	1	1	yes	characteristic
122	#1987	—	73	2	no	—
123	#1956	—	73	1	no	—
124	#1296	—	73	1	no	—
125	#1279	—	73	2	no	—
126	C₇₃	#10349	1	1	yes	characteristic, complemented, Sylow
127	C₂×C₄⋊Q₈	—	2	2	no	—
128	C₂×C₄⋊Q₈	—	73	1	no	—
129	C₂×C₄⋊C₈	—	73	2	no	—
130	C₂×#103	—	146	2	no	—
131	C₂×C₄×C₈	—	73	1	no	—
132	#395	—	2	2	no	—
133	#389	—	2	2	no	—
134	#384	C₂×D₇₃	1	1	yes	characteristic
135	C₄×C₄⋊C₄	C₂×D₇₃	1	2	yes	—
136	#340	—	146	2	no	—
137	#340	—	146	2	no	—
138	C₂²×Q₈	—	2	2	no	—
139	C₂²×Q₈	—	146	1	no	—
140	C₂²×C₈	—	146	2	no	—
141	C₂²×C₈	—	146	1	no	—
142	C₄⋊Q₈	—	4	4	no	—
143	C₄⋊Q₈	—	4	4	no	—
144	C₄⋊Q₈	—	73	2	no	—
145	C₄⋊Q₈	—	146	1	no	—
146	C₄⋊Q₈	—	146	2	no	—
147	C₂×C₄⋊C₄	—	2	4	no	—
148	C₂×C₄⋊C₄	—	2	2	no	—
149	C₂×C₄⋊C₄	—	146	2	no	—
150	C₂×C₄⋊C₄	C₂²⋊D₇₃	1	2	yes	—
151	C₂×C₄⋊C₄	C₂²⋊D₇₃	1	2	yes	—
152	C₂×C₄⋊C₄	C₂²⋊D₇₃	1	2	yes	—
153	C₂×C₄²	—	2	2	no	—
154	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
155	C₄⋊C₈	—	146	2	no	—
156	C₄⋊C₈	—	146	2	no	—
157	#103	—	292	4	no	—
158	C₄×C₈	—	146	2	no	—
159	#95	—	2	2	no	—
160	#95	—	2	2	no	—
161	C₂×Q₈	—	4	8	no	—
162	C₂×Q₈	—	8	2	no	—
163	C₂×Q₈	—	292	2	no	—
164	C₂×Q₈	—	292	2	no	—
165	C₂×Q₈	—	292	1	no	—
166	C₂×Q₈	—	146	2	no	—
167	C₂²×C₄	—	2	2	no	—
168	C₂²×C₄	—	2	2	no	—
169	C₂²×C₄	—	2	2	no	—
170	C₂²×C₄	—	292	1	no	—
171	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
172	C₂²×C₄	C₂×C₂²⋊D₇₃	1	2	yes	—
173	C₂×C₈	—	292	1	no	—
174	C₂×C₈	—	292	1	no	—
175	C₂×C₈	—	292	2	no	—
176	C₂×C₈	—	292	2	no	—
177	C₂×C₈	—	292	2	no	—
178	C₂×C₈	—	146	2	no	—
179	C₄⋊C₄	—	2	2	no	—
180	C₄⋊C₄	—	2	2	no	—
181	C₄⋊C₄	—	4	2	no	—
182	C₄⋊C₄	—	4	8	no	—
183	C₄⋊C₄	—	4	2	no	—
184	C₄⋊C₄	—	4	2	no	—
185	C₄⋊C₄	—	292	2	no	—
186	C₄⋊C₄	—	146	4	no	—
187	C₄⋊C₄	#11924016	1	4	yes	—
188	C₄⋊C₄	#11924018	1	4	yes	—
189	C₄²	—	4	2	no	—
190	C₄²	—	4	2	no	—
191	C₄²	Q₈×D₇₃	1	1	yes	characteristic
192	C₄²	#11924029	1	2	yes	—
193	C₄²	#11924029	1	1	yes	characteristic
194	C₂³	#14556560	1	1	yes	characteristic
195	Q₈	—	8	8	no	—
196	Q₈	—	292	4	no	—
197	Q₈	—	584	2	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	2	4	no	—
201	C₂×C₄	—	2	4	no	—
202	C₂×C₄	—	4	2	no	—
203	C₂×C₄	—	4	2	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	—	4	2	no	—
206	C₂×C₄	—	4	4	no	—
207	C₂×C₄	—	4	2	no	—
208	C₂×C₄	—	292	2	no	—
209	C₂×C₄	—	584	1	no	—
210	C₂×C₄	—	584	1	no	—
211	C₂×C₄	#14556567	1	1	yes	characteristic
212	C₂×C₄	#14556567	1	2	yes	—
213	C₂×C₄	#14556580	1	1	yes	characteristic
214	C₂×C₄	#14556580	1	2	yes	—
215	C₂×C₄	C₂×#11924016	1	2	yes	—
216	C₂×C₄	C₂×#11924018	1	2	yes	—
217	C₂×C₄	#14556617	1	2	yes	—
218	C₂×C₄	#14556622	1	2	yes	—
219	C₈	—	292	2	no	—
220	C₈	—	584	2	no	—
221	C₂²	#17988498	1	1	yes	characteristic
222	C₂²	#17988738	1	2	yes	—
223	C₂²	#17988743	1	2	yes	—
224	C₂²	#17988755	1	1	yes	characteristic
225	C₂²	#17988760	1	1	yes	characteristic
226	C₄	—	2	1	no	—
227	C₄	—	2	1	no	—
228	C₄	—	4	4	no	—
229	C₄	—	4	4	no	—
230	C₄	—	8	2	no	—
231	C₄	—	584	2	no	—
232	C₄	#17988869	1	2	yes	—
233	C₄	#17988879	1	2	yes	—
234	C₄	#17988939	1	2	yes	—
235	C₄	#17988949	1	2	yes	—
236	C₂	#22609047	1	1	yes	characteristic
237	C₂	#22609071	1	1	yes	characteristic
238	C₂	#22609096	1	2	yes	—
239	C₂	#22611069	1	2	yes	—
240	C₂	#22611084	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22610879

C₂

yes

maximal

#22610732

C₂

yes

maximal, characteristic

#22607814

C₂

yes

maximal, characteristic

#22607772

C₂

yes

maximal

C₇₃×#2551

C₂

yes

maximal, characteristic

C₂×#14556591

C₂²

yes

characteristic

C₂×C₄⋊#10596831

C₂²

yes

—

C₂×#14556514

—

C₂×C₄×#10596831

C₂²

yes

characteristic

#17988349

—

#17988349

—

C₂×C₄⋊Q₈×C₇₃

—

#395×C₇₃

—

#389×C₇₃

—

#384×C₇₃

C₂²

yes

characteristic

C₄×C₄⋊C₄×C₇₃

C₂²

yes

—

C₂²×Dic₁₄₆

—

—

—

—

—

Q₈

yes

complemented

C₂×C₄⋊Dic₇₃

—

—

—

—

—

C₂²×Q₈×C₇₃

—

C₄⋊Q₈×C₇₃

—

C₄⋊Q₈×C₇₃

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

D₄

yes

—

C₂×C₄⋊C₄×C₇₃

D₄

yes

—

C₂×C₄⋊C₄×C₇₃

D₄

yes

—

C₂×C₄²×C₇₃

—

C₂×C₄²×C₇₃

C₂³

yes

characteristic

#95×C₇₃

—

#95×C₇₃

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂²×Dic₇₃

—

—

—

—

—

—

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₃

C₂×D₄

yes

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

SD₁₆

yes

—

C₄⋊C₄×C₇₃

Q₁₆

yes

—

C₄²×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

C₂×Q₈

yes

characteristic

C₄²×C₇₃

#41

yes

—

C₄²×C₇₃

yes

C₂³×C₇₃

yes

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

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₇₃

C₂²⋊Q₈

yes

—

C₂×C₄×C₇₃

#124

yes

characteristic

C₂×C₄×C₇₃

#124

yes

—

C₂×C₄×C₇₃

C₂×SD₁₆

yes

—

C₂×C₄×C₇₃

C₂×Q₁₆

yes

—

C₂×C₄×C₇₃

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₇₃

#137

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

#10596831

—

#10596831

—

100

C₂²×C₇₃

#393

yes

characteristic

101

C₂²×C₇₃

#450

yes

—

102

C₂²×C₇₃

#451

yes

—

103

C₂²×C₇₃

#453

yes

characteristic

104

C₂²×C₇₃

#454

yes

characteristic

105

C₄×C₇₃

—

106

C₄×C₇₃

—

107

C₄×C₇₃

—

108

C₄×C₇₃

—

109

C₄×C₇₃

—

110

C₄×C₇₃

#475

yes

—

111

C₄×C₇₃

#477

yes

—

112

C₄×C₇₃

#487

yes

—

113

C₄×C₇₃

#489

yes

—

114

Dic₇₃

—

115

#10349

—

maximal, Sylow

116

C₂×C₇₃

#1629

yes

characteristic

117

C₂×C₇₃

#1633

yes

characteristic

118

C₂×C₇₃

#1637

yes

—

119

C₂×C₇₃

#2024

yes

—

120

C₂×C₇₃

#2027

yes

characteristic

121

#2551

D₇₃

yes

characteristic

122

#1987

—

123

#1956

—

124

#1296

—

125

#1279

—

126

C₇₃

#10349

yes

characteristic, complemented, Sylow

127

C₂×C₄⋊Q₈

—

128

C₂×C₄⋊Q₈

—

129

C₂×C₄⋊C₈

—

130

C₂×#103

—

146

—

131

C₂×C₄×C₈

—

132

#395

—

133

#389

—

134

#384

C₂×D₇₃

yes

characteristic

135

C₄×C₄⋊C₄

C₂×D₇₃

yes

—

136

#340

—

146

—

137

#340

—

146

—

138

C₂²×Q₈

—

139

C₂²×Q₈

—

146

—

140

C₂²×C₈

—

146

—

141

C₂²×C₈

—

146

—

142

C₄⋊Q₈

—

143

C₄⋊Q₈

—

144

C₄⋊Q₈

—

145

C₄⋊Q₈

—

146

—

146

C₄⋊Q₈

—

146

—

147

C₂×C₄⋊C₄

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

—

146

—

150

C₂×C₄⋊C₄

C₂²⋊D₇₃

yes

—

151

C₂×C₄⋊C₄

C₂²⋊D₇₃

yes

—

152

C₂×C₄⋊C₄

C₂²⋊D₇₃

yes

—

153

C₂×C₄²

—

154

C₂×C₄²

C₂²×D₇₃

yes

characteristic

155

C₄⋊C₈

—

146

—

156

C₄⋊C₈

—

146

—

157

#103

—

292

—

158

C₄×C₈

—

146

—

159

#95

—

160

#95

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

292

—

164

C₂×Q₈

—

292

—

165

C₂×Q₈

—

292

—

166

C₂×Q₈

—

146

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

—

292

—

171

C₂²×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

172

C₂²×C₄

C₂×C₂²⋊D₇₃

yes

—

173

C₂×C₈

—

292

—

174

C₂×C₈

—

292

—

175

C₂×C₈

—

292

—

176

C₂×C₈

—

292

—

177

C₂×C₈

—

292

—

178

C₂×C₈

—

146

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

292

—

186

C₄⋊C₄

—

146

—

187

C₄⋊C₄

#11924016

yes

—

188

C₄⋊C₄

#11924018

yes

—

189

C₄²

—

190

C₄²

—

191

C₄²

Q₈×D₇₃

yes

characteristic

192

C₄²

#11924029

yes

—

193

C₄²

#11924029

yes

characteristic

194

C₂³

#14556560

yes

characteristic

195

Q₈

—

196

Q₈

—

292

—

197

Q₈

—

584

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

292

—

209

C₂×C₄

—

584

—

210

C₂×C₄

—

584

—

211

C₂×C₄

#14556567

yes

characteristic

212

C₂×C₄

#14556567

yes

—

213

C₂×C₄

#14556580

yes

characteristic

214

C₂×C₄

#14556580

yes

—

215

C₂×C₄

C₂×#11924016

yes

—

216

C₂×C₄

C₂×#11924018

yes

—

217

C₂×C₄

#14556617

yes

—

218

C₂×C₄

#14556622

yes

—

219

C₈

—

292

—

220

C₈

—

584

—

221

C₂²

#17988498

yes

characteristic

222

C₂²

#17988738

yes

—

223

C₂²

#17988743

yes

—

224

C₂²

#17988755

yes

characteristic

225

C₂²

#17988760

yes

characteristic

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

584

—

232

C₄

#17988869

yes

—

233

C₄

#17988879

yes

—

234

C₄

#17988939

yes

—

235

C₄

#17988949

yes

—

236

C₂

#22609047

yes

characteristic

237

C₂

#22609071

yes

characteristic

238

C₂

#22609096

yes

—

239

C₂

#22611069

yes

—

240

C₂

#22611084

yes

characteristic

	subgroup	G/H
center	C₂³	#14556560
commutator, cosocle	C₂×C₄²×C₇₃	C₂³
Frattini	C₂×C₄²	C₂²×D₇₃
Fitting	C₇₃×#2551	C₂
socle, prime radical	C₂³×C₇₃	#120
hypercenter	#2551	D₇₃
hypocenter	C₇₃	#10349
LCS	G ▷ C₂×C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2551

subgroup

G/H

center

C₂³

#14556560

commutator, cosocle

C₂×C₄²×C₇₃

C₂³

Frattini

C₂×C₄²

C₂²×D₇₃

Fitting

C₇₃×#2551

C₂

C₂³×C₇₃

D₇₃

C₇₃

G ▷ C₂×C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2551

N	H ≅ G/N	type
22. #14556591	Q₈	semidirect
126. C₇₃	#10349	semidirect

H ≅ G/N

type

22. #14556591

Q₈

semidirect

126. C₇₃

#10349

semidirect

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

subgroup	index
#22610879	2
#22610732	2
#22607814	2
#22607772	2
C₇₃×#2551	2
#10349	73

subgroup

index

C₇₃×#2551

Subgroups — #32988996

Conjugacy classes of subgroups

Complements

Maximal subgroups