Group #32988997 — subgroups

Subgroups — #32988997

Order 18688.

504 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 131 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	#22614960	C₂	1	1	yes	maximal, characteristic
2	#22610880	C₂	1	2	yes	maximal
3	#22607814	C₂	1	1	yes	maximal, characteristic
4	#22607771	C₂	1	2	yes	maximal
5	C₇₃×#1956	C₂	1	1	yes	maximal, characteristic
6	C₂×#14556590	—	2	2	no	—
7	C₂×C₄⋊#10596831	C₂²	1	2	yes	—
8	#17988507	—	2	2	no	—
9	#17988483	—	2	2	no	—
10	C₄×C₄⋊Dic₇₃	C₂²	1	2	yes	—
11	#17988349	—	2	2	no	—
12	#17988349	—	2	2	no	—
13	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×#103×C₇₃	—	2	2	no	—
15	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
16	#384×C₇₃	C₂²	1	1	yes	characteristic
17	C₂²×Dic₁₄₆	—	2	2	no	—
18	C₂²×#10596831	—	2	2	no	—
19	#14556590	—	4	4	no	—
20	#14556590	—	4	4	no	—
21	C₂×C₄⋊Dic₇₃	D₄	1	2	yes	—
22	C₂×C₄⋊Dic₇₃	D₄	1	2	yes	—
23	C₂×#11924007	—	2	4	no	—
24	C₂×C₄×Dic₇₃	—	2	2	no	—
25	C₄⋊#10596831	—	2	2	no	—
26	C₄⋊#10596831	—	2	2	no	—
27	#14556498	—	2	2	no	—
28	#14556498	—	2	2	no	—
29	C₂²×Q₈×C₇₃	—	2	1	no	—
30	C₂²×C₈×C₇₃	—	2	1	no	—
31	C₄⋊Q₈×C₇₃	—	2	2	no	—
32	C₄⋊Q₈×C₇₃	—	2	1	no	—
33	C₄⋊Q₈×C₇₃	Q₈	1	2	yes	complemented
34	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
35	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
36	C₂×C₄⋊C₄×C₇₃	D₄	1	2	yes	—
37	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
38	#103×C₇₃	—	4	4	no	—
39	C₄×C₈×C₇₃	—	2	2	no	—
40	C₂×Dic₁₄₆	—	4	8	no	—
41	C₂×Dic₁₄₆	—	8	2	no	—
42	C₂²×Dic₇₃	—	2	2	no	—
43	C₂²×Dic₇₃	—	2	2	no	—
44	C₂×#10596831	—	4	2	no	—
45	C₂×#10596831	—	4	2	no	—
46	C₂×#10596831	—	4	2	no	—
47	C₄⋊Dic₇₃	—	2	2	no	—
48	C₄⋊Dic₇₃	—	2	2	no	—
49	C₄⋊Dic₇₃	SD₁₆	1	4	yes	—
50	C₄⋊Dic₇₃	Q₁₆	1	4	yes	—
51	#11924007	—	4	8	no	—
52	C₄×Dic₇₃	—	4	2	no	—
53	C₄×Dic₇₃	—	4	2	no	—
54	C₂×Q₈×C₇₃	—	2	2	no	—
55	C₂×Q₈×C₇₃	—	4	2	no	—
56	C₂×Q₈×C₇₃	—	4	2	no	—
57	C₂×Q₈×C₇₃	—	4	1	no	—
58	C₂²×C₄×C₇₃	—	2	2	no	—
59	C₂²×C₄×C₇₃	—	4	1	no	—
60	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
61	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
62	C₂×C₈×C₇₃	—	2	2	no	—
63	C₂×C₈×C₇₃	—	4	1	no	—
64	C₂×C₈×C₇₃	—	4	1	no	—
65	C₄⋊C₄×C₇₃	—	2	4	no	—
66	C₄⋊C₄×C₇₃	—	4	2	no	—
67	C₄⋊C₄×C₇₃	—	4	2	no	—
68	C₄⋊C₄×C₇₃	—	4	2	no	—
69	C₄⋊C₄×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	—	4	4	no	—
75	Q₈×C₇₃	—	8	2	no	—
76	C₂×C₄×C₇₃	—	2	1	no	—
77	C₂×C₄×C₇₃	—	2	1	no	—
78	C₂×C₄×C₇₃	—	4	2	no	—
79	C₂×C₄×C₇₃	—	4	4	no	—
80	C₂×C₄×C₇₃	—	4	2	no	—
81	C₂×C₄×C₇₃	—	8	1	no	—
82	C₂×C₄×C₇₃	—	8	1	no	—
83	C₂×C₄×C₇₃	C₂²⋊Q₈	1	2	yes	—
84	C₂×C₄×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
85	C₂×C₄×C₇₃	#124	1	2	yes	—
86	C₂×C₄×C₇₃	#124	1	1	yes	characteristic
87	C₂×C₄×C₇₃	C₂×SD₁₆	1	2	yes	—
88	C₂×C₄×C₇₃	C₂×Q₁₆	1	2	yes	—
89	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
90	C₂×C₄×C₇₃	#137	1	2	yes	—
91	C₂×Dic₇₃	—	2	4	no	—
92	C₂×Dic₇₃	—	2	4	no	—
93	C₂×Dic₇₃	—	4	2	no	—
94	C₂×Dic₇₃	—	4	2	no	—
95	C₂×Dic₇₃	—	4	2	no	—
96	C₂×Dic₇₃	—	4	2	no	—
97	Dic₁₄₆	—	8	8	no	—
98	C₈×C₇₃	—	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	—	8	2	no	—
108	C₄×C₇₃	—	8	2	no	—
109	C₄×C₇₃	#475	1	2	yes	—
110	C₄×C₇₃	#477	1	2	yes	—
111	C₄×C₇₃	#487	1	2	yes	—
112	C₄×C₇₃	#489	1	2	yes	—
113	Dic₇₃	—	4	4	no	—
114	Dic₇₃	—	4	4	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	—	73	1	no	—
122	#1987	—	73	2	no	—
123	#1956	D₇₃	1	1	yes	characteristic
124	#1296	—	73	1	no	—
125	#1279	—	73	2	no	—
126	C₇₃	#10349	1	1	yes	characteristic, complemented, Sylow
127	C₂×C₄⋊Q₈	—	146	2	no	—
128	C₂×C₄⋊Q₈	C₂×D₇₃	1	1	yes	characteristic
129	C₂×C₄⋊C₈	—	73	2	no	—
130	C₂×#103	—	2	2	no	—
131	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
132	#395	—	146	2	no	—
133	#389	—	146	2	no	—
134	#384	C₂×D₇₃	1	1	yes	characteristic
135	C₄×C₄⋊C₄	—	73	2	no	—
136	#340	—	146	2	no	—
137	#340	—	146	2	no	—
138	C₂²×Q₈	—	2	1	no	—
139	C₂²×Q₈	—	146	2	no	—
140	C₂²×C₈	—	2	1	no	—
141	C₂²×C₈	—	146	2	no	—
142	C₄⋊Q₈	—	2	2	no	—
143	C₄⋊Q₈	—	2	1	no	—
144	C₄⋊Q₈	—	292	4	no	—
145	C₄⋊Q₈	—	292	4	no	—
146	C₄⋊Q₈	Dic₁₄₆	1	2	yes	complemented
147	C₂×C₄⋊C₄	—	2	2	no	—
148	C₂×C₄⋊C₄	—	2	2	no	—
149	C₂×C₄⋊C₄	—	73	2	no	—
150	C₂×C₄⋊C₄	—	73	2	no	—
151	C₂×C₄⋊C₄	—	146	4	no	—
152	C₂×C₄⋊C₄	C₂²⋊D₇₃	1	2	yes	—
153	C₂×C₄²	—	146	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	—	4	4	no	—
158	C₄×C₈	—	2	2	no	—
159	#95	—	146	2	no	—
160	#95	—	146	2	no	—
161	C₂×Q₈	—	2	2	no	—
162	C₂×Q₈	—	4	2	no	—
163	C₂×Q₈	—	4	2	no	—
164	C₂×Q₈	—	4	1	no	—
165	C₂×Q₈	—	292	8	no	—
166	C₂×Q₈	—	584	2	no	—
167	C₂²×C₄	—	2	2	no	—
168	C₂²×C₄	—	4	1	no	—
169	C₂²×C₄	—	146	2	no	—
170	C₂²×C₄	—	146	2	no	—
171	C₂²×C₄	D₄×D₇₃	1	2	yes	—
172	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
173	C₂×C₈	—	2	2	no	—
174	C₂×C₈	—	4	1	no	—
175	C₂×C₈	—	4	1	no	—
176	C₂×C₈	—	292	2	no	—
177	C₂×C₈	—	292	2	no	—
178	C₂×C₈	—	292	2	no	—
179	C₄⋊C₄	—	2	4	no	—
180	C₄⋊C₄	—	4	2	no	—
181	C₄⋊C₄	—	4	2	no	—
182	C₄⋊C₄	—	4	2	no	—
183	C₄⋊C₄	—	4	2	no	—
184	C₄⋊C₄	—	292	8	no	—
185	C₄⋊C₄	—	73	4	no	—
186	C₄⋊C₄	—	73	4	no	—
187	C₄⋊C₄	—	146	2	no	—
188	C₄⋊C₄	—	146	2	no	—
189	C₄²	—	292	2	no	—
190	C₄²	—	292	2	no	—
191	C₄²	C₂×Dic₁₄₆	1	1	yes	characteristic
192	C₄²	#11924027	1	2	yes	—
193	C₄²	#11924028	1	1	yes	characteristic
194	C₂³	#14556559	1	1	yes	characteristic
195	Q₈	—	4	4	no	—
196	Q₈	—	8	2	no	—
197	Q₈	—	584	8	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	4	4	no	—
201	C₂×C₄	—	4	2	no	—
202	C₂×C₄	—	4	2	no	—
203	C₂×C₄	—	8	1	no	—
204	C₂×C₄	—	8	1	no	—
205	C₂×C₄	—	292	2	no	—
206	C₂×C₄	—	292	2	no	—
207	C₂×C₄	—	292	2	no	—
208	C₂×C₄	—	292	2	no	—
209	C₂×C₄	—	146	4	no	—
210	C₂×C₄	—	146	4	no	—
211	C₂×C₄	#14556568	1	2	yes	—
212	C₂×C₄	#14556570	1	1	yes	characteristic
213	C₂×C₄	#14556577	1	2	yes	—
214	C₂×C₄	#14556578	1	1	yes	characteristic
215	C₂×C₄	SD₁₆×D₇₃	1	2	yes	—
216	C₂×C₄	Q₁₆×D₇₃	1	2	yes	—
217	C₂×C₄	#14556618	1	2	yes	—
218	C₂×C₄	#14556623	1	2	yes	—
219	C₈	—	4	2	no	—
220	C₈	—	584	2	no	—
221	C₂²	#17988499	1	1	yes	characteristic
222	C₂²	#17988736	1	2	yes	—
223	C₂²	#17988741	1	2	yes	—
224	C₂²	#17988754	1	1	yes	characteristic
225	C₂²	#17988759	1	1	yes	characteristic
226	C₄	—	2	1	no	—
227	C₄	—	2	1	no	—
228	C₄	—	8	2	no	—
229	C₄	—	8	2	no	—
230	C₄	—	292	4	no	—
231	C₄	—	292	4	no	—
232	C₄	#17988870	1	2	yes	—
233	C₄	#17988880	1	2	yes	—
234	C₄	#17988936	1	2	yes	—
235	C₄	#17988948	1	2	yes	—
236	C₂	#22609045	1	1	yes	characteristic
237	C₂	#22609069	1	1	yes	characteristic
238	C₂	#22609093	1	2	yes	—
239	C₂	#22611070	1	2	yes	—
240	C₂	#22611087	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22614960

C₂

yes

maximal, characteristic

#22610880

C₂

yes

maximal

#22607814

C₂

yes

maximal, characteristic

#22607771

C₂

yes

maximal

C₇₃×#1956

C₂

yes

maximal, characteristic

C₂×#14556590

—

C₂×C₄⋊#10596831

C₂²

yes

—

#17988507

—

#17988483

—

C₄×C₄⋊Dic₇₃

C₂²

yes

—

#17988349

—

#17988349

—

C₂×C₄⋊Q₈×C₇₃

C₂²

yes

characteristic

C₂×#103×C₇₃

—

C₂×C₄×C₈×C₇₃

C₂²

yes

characteristic

#384×C₇₃

C₂²

yes

characteristic

C₂²×Dic₁₄₆

—

C₂²×#10596831

—

#14556590

—

#14556590

—

C₂×C₄⋊Dic₇₃

D₄

yes

—

C₂×C₄⋊Dic₇₃

D₄

yes

—

C₂×#11924007

—

C₂×C₄×Dic₇₃

—

—

—

—

—

C₂²×Q₈×C₇₃

—

C₂²×C₈×C₇₃

—

C₄⋊Q₈×C₇₃

—

C₄⋊Q₈×C₇₃

—

C₄⋊Q₈×C₇₃

Q₈

yes

complemented

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

D₄

yes

—

C₂×C₄²×C₇₃

C₂³

yes

characteristic

#103×C₇₃

—

C₄×C₈×C₇₃

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

C₂×#10596831

—

C₂×#10596831

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

SD₁₆

yes

—

C₄⋊Dic₇₃

Q₁₆

yes

—

#11924007

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂×D₄

yes

—

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

C₂×Q₈

yes

characteristic

C₄²×C₇₃

#41

yes

—

C₄²×C₇₃

yes

C₂³×C₇₃

yes

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

C₂²⋊Q₈

yes

—

C₂×C₄×C₇₃

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₇₃

#124

yes

—

C₂×C₄×C₇₃

#124

yes

characteristic

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

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

C₈×C₇₃

—

#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

#475

yes

—

110

C₄×C₇₃

#477

yes

—

111

C₄×C₇₃

#487

yes

—

112

C₄×C₇₃

#489

yes

—

113

Dic₇₃

—

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

—

122

#1987

—

123

#1956

D₇₃

yes

characteristic

124

#1296

—

125

#1279

—

126

C₇₃

#10349

yes

characteristic, complemented, Sylow

127

C₂×C₄⋊Q₈

—

146

—

128

C₂×C₄⋊Q₈

C₂×D₇₃

yes

characteristic

129

C₂×C₄⋊C₈

—

130

C₂×#103

—

131

C₂×C₄×C₈

C₂×D₇₃

yes

characteristic

132

#395

—

146

—

133

#389

—

146

—

134

#384

C₂×D₇₃

yes

characteristic

135

C₄×C₄⋊C₄

—

136

#340

—

146

—

137

#340

—

146

—

138

C₂²×Q₈

—

139

C₂²×Q₈

—

146

—

140

C₂²×C₈

—

141

C₂²×C₈

—

146

—

142

C₄⋊Q₈

—

143

C₄⋊Q₈

—

144

C₄⋊Q₈

—

292

—

145

C₄⋊Q₈

—

292

—

146

C₄⋊Q₈

Dic₁₄₆

yes

complemented

147

C₂×C₄⋊C₄

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

—

146

—

152

C₂×C₄⋊C₄

C₂²⋊D₇₃

yes

—

153

C₂×C₄²

—

146

—

154

C₂×C₄²

C₂²×D₇₃

yes

characteristic

155

C₄⋊C₈

—

146

—

156

C₄⋊C₈

—

146

—

157

#103

—

158

C₄×C₈

—

159

#95

—

146

—

160

#95

—

146

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

292

—

166

C₂×Q₈

—

584

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

—

146

—

170

C₂²×C₄

—

146

—

171

C₂²×C₄

D₄×D₇₃

yes

—

172

C₂²×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

292

—

177

C₂×C₈

—

292

—

178

C₂×C₈

—

292

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

292

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

146

—

188

C₄⋊C₄

—

146

—

189

C₄²

—

292

—

190

C₄²

—

292

—

191

C₄²

C₂×Dic₁₄₆

yes

characteristic

192

C₄²

#11924027

yes

—

193

C₄²

#11924028

yes

characteristic

194

C₂³

#14556559

yes

characteristic

195

Q₈

—

196

Q₈

—

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

—

292

—

206

C₂×C₄

—

292

—

207

C₂×C₄

—

292

—

208

C₂×C₄

—

292

—

209

C₂×C₄

—

146

—

210

C₂×C₄

—

146

—

211

C₂×C₄

#14556568

yes

—

212

C₂×C₄

#14556570

yes

characteristic

213

C₂×C₄

#14556577

yes

—

214

C₂×C₄

#14556578

yes

characteristic

215

C₂×C₄

SD₁₆×D₇₃

yes

—

216

C₂×C₄

Q₁₆×D₇₃

yes

—

217

C₂×C₄

#14556618

yes

—

218

C₂×C₄

#14556623

yes

—

219

C₈

—

220

C₈

—

584

—

221

C₂²

#17988499

yes

characteristic

222

C₂²

#17988736

yes

—

223

C₂²

#17988741

yes

—

224

C₂²

#17988754

yes

characteristic

225

C₂²

#17988759

yes

characteristic

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

292

—

231

C₄

—

292

—

232

C₄

#17988870

yes

—

233

C₄

#17988880

yes

—

234

C₄

#17988936

yes

—

235

C₄

#17988948

yes

—

236

C₂

#22609045

yes

characteristic

237

C₂

#22609069

yes

characteristic

238

C₂

#22609093

yes

—

239

C₂

#22611070

yes

—

240

C₂

#22611087

yes

characteristic

	subgroup	G/H
center	C₂³	#14556559
commutator, cosocle	C₂×C₄²×C₇₃	C₂³
Frattini	C₂×C₄²	C₂²×D₇₃
Fitting	C₇₃×#1956	C₂
socle, prime radical	C₂³×C₇₃	#120
hypercenter	#1956	D₇₃
hypocenter	C₇₃	#10349
LCS	G ▷ C₂×C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1956

subgroup

G/H

center

C₂³

#14556559

commutator, cosocle

C₂×C₄²×C₇₃

C₂³

Frattini

C₂×C₄²

C₂²×D₇₃

Fitting

C₇₃×#1956

C₂

C₂³×C₇₃

D₇₃

C₇₃

G ▷ C₂×C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1956

N	H ≅ G/N	type
33. C₄⋊Q₈×C₇₃	Q₈	semidirect
126. C₇₃	#10349	semidirect
146. C₄⋊Q₈	Dic₁₄₆	semidirect

H ≅ G/N

type

33. C₄⋊Q₈×C₇₃

Q₈

semidirect

126. C₇₃

#10349

semidirect

146. C₄⋊Q₈

Dic₁₄₆

semidirect

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

subgroup	index
#22614960	2
#22610880	2
#22607814	2
#22607771	2
C₇₃×#1956	2
#10349	73

subgroup

index

C₇₃×#1956

Subgroups — #32988997

Conjugacy classes of subgroups

Complements

Maximal subgroups