Group #32985023 — subgroups

Subgroups — #32985023

Order 18688.

478 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 163 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	#22618309	C₂	1	1	yes	maximal, characteristic
2	#22610048	C₂	1	1	yes	maximal, characteristic
3	C₂×#17988335	C₂	1	2	yes	maximal
4	C₂×#17988332	C₂	1	2	yes	maximal
5	C₄×C₄⋊C₈×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#14556591	C₂²	1	1	yes	characteristic
7	C₂×#14556591	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊#10596831	C₂²	1	2	yes	—
9	#17988493	—	2	2	no	—
10	#17988493	C₄	1	4	yes	—
11	#17988453	—	2	1	no	—
12	#17988453	—	2	1	no	—
13	#17988342	—	2	2	no	—
14	#17988335	—	2	4	no	—
15	#17988332	—	2	4	no	—
16	C₂×C₄⋊C₈×C₇₃	C₂²	1	2	yes	—
17	C₂×C₄×C₈×C₇₃	—	2	1	no	—
18	C₄³×C₇₃	C₂²	1	1	yes	characteristic
19	#336×C₇₃	—	2	1	no	—
20	C₂²×Dic₁₄₆	—	2	1	no	—
21	C₂²×Dic₁₄₆	C₂×C₄	1	2	yes	—
22	C₂²×#10596831	—	2	2	no	—
23	#14556591	—	2	2	no	—
24	#14556591	—	2	2	no	—
25	#14556591	—	2	2	no	—
26	#14556591	—	2	2	no	—
27	C₂×C₄⋊Dic₇₃	—	2	1	no	—
28	C₂×C₄⋊Dic₇₃	—	2	1	no	—
29	C₂×C₄⋊Dic₇₃	—	2	1	no	—
30	C₂×C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
31	C₄⋊#10596831	—	2	2	no	—
32	C₄⋊#10596831	—	2	2	no	—
33	#14556498	—	2	4	no	—
34	#14556498	—	2	4	no	—
35	C₂²×C₈×C₇₃	—	2	2	no	—
36	C₂×C₄²×C₇₃	C₂×C₄	1	2	yes	—
37	C₂×C₄²×C₇₃	D₄	1	2	yes	—
38	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
41	C₄⋊C₈×C₇₃	—	2	2	no	—
42	C₄⋊C₈×C₇₃	D₄	1	4	yes	—
43	C₄×C₈×C₇₃	—	4	2	no	—
44	C₂×Dic₁₄₆	—	2	4	no	—
45	C₂×Dic₁₄₆	—	4	1	no	—
46	C₂×Dic₁₄₆	—	4	1	no	—
47	C₂×Dic₁₄₆	—	4	4	no	—
48	C₂×Dic₁₄₆	—	4	4	no	—
49	C₂²×Dic₇₃	—	2	2	no	—
50	C₂²×Dic₇₃	—	2	2	no	—
51	C₂×#10596831	—	4	2	no	—
52	C₂×#10596831	—	4	4	no	—
53	C₄⋊Dic₇₃	—	2	4	no	—
54	C₄⋊Dic₇₃	—	4	2	no	—
55	C₄⋊Dic₇₃	—	4	2	no	—
56	C₄⋊Dic₇₃	—	4	1	no	—
57	C₄⋊Dic₇₃	—	4	1	no	—
58	C₂²×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
59	C₂²×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
60	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
61	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
62	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
63	C₂×C₈×C₇₃	—	2	4	no	—
64	C₂×C₈×C₇₃	—	4	2	no	—
65	C₂×C₈×C₇₃	—	4	2	no	—
66	C₄²×C₇₃	—	2	4	no	—
67	C₄²×C₇₃	—	2	2	no	—
68	C₄²×C₇₃	—	4	2	no	—
69	C₄²×C₇₃	SD₁₆	1	2	yes	—
70	C₄²×C₇₃	Q₁₆	1	2	yes	—
71	C₄²×C₇₃	C₂×D₄	1	2	yes	—
72	C₄²×C₇₃	#41	1	2	yes	—
73	C₂³×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
74	C₂×C₄×C₇₃	—	2	2	no	—
75	C₂×C₄×C₇₃	—	2	2	no	—
76	C₂×C₄×C₇₃	—	2	2	no	—
77	C₂×C₄×C₇₃	—	2	2	no	—
78	C₂×C₄×C₇₃	—	2	2	no	—
79	C₂×C₄×C₇₃	—	2	2	no	—
80	C₂×C₄×C₇₃	#103	1	4	yes	—
81	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
82	C₂×C₄×C₇₃	#121	1	2	yes	—
83	C₂×C₄×C₇₃	#124	1	1	yes	characteristic
84	C₂×C₄×C₇₃	#127	1	1	yes	characteristic
85	C₂×C₄×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
86	C₂×C₄×C₇₃	C₂×Q₁₆	1	1	yes	characteristic
87	C₂×C₄×C₇₃	#135	1	4	yes	—
88	C₂×C₄×C₇₃	#137	1	2	yes	—
89	C₂×Dic₇₃	—	4	2	no	—
90	C₂×Dic₇₃	—	4	2	no	—
91	C₂×Dic₇₃	—	4	4	no	—
92	C₂×Dic₇₃	—	4	4	no	—
93	Dic₁₄₆	—	8	2	no	—
94	Dic₁₄₆	—	8	2	no	—
95	Dic₁₄₆	—	8	4	no	—
96	C₈×C₇₃	—	4	4	no	—
97	#10596831	—	8	2	no	—
98	C₂²×C₇₃	#390	1	1	yes	characteristic
99	C₂²×C₇₃	#413	1	2	yes	—
100	C₂²×C₇₃	C₂×#103	1	1	yes	characteristic
101	C₂²×C₇₃	#416	1	2	yes	—
102	C₂²×C₇₃	#419	1	1	yes	characteristic
103	C₄×C₇₃	—	2	4	no	—
104	C₄×C₇₃	—	2	2	no	—
105	C₄×C₇₃	—	4	2	no	—
106	C₄×C₇₃	#461	1	2	yes	—
107	C₄×C₇₃	#462	1	2	yes	—
108	C₄×C₇₃	#488	1	2	yes	—
109	C₄×C₇₃	#495	1	2	yes	—
110	Dic₇₃	—	8	2	no	—
111	Dic₇₃	—	8	2	no	—
112	#9693	—	73	1	no	maximal, Sylow
113	C₂×C₇₃	#1542	1	2	yes	—
114	C₂×C₇₃	#1554	1	2	yes	—
115	C₂×C₇₃	#1958	1	1	yes	characteristic
116	C₂×C₇₃	#1967	1	1	yes	characteristic
117	C₂×C₇₃	#1981	1	1	yes	characteristic
118	#2862	—	73	1	no	—
119	#1831	—	73	1	no	—
120	C₄×C₄⋊C₈	D₇₃	1	1	yes	characteristic
121	C₂×#333	—	73	2	no	—
122	C₂×#332	—	73	2	no	—
123	C₇₃	#9693	1	1	yes	characteristic, complemented, Sylow
124	C₂×C₄⋊Q₈	—	73	1	no	—
125	C₂×C₄⋊Q₈	—	73	1	no	—
126	C₂×C₄⋊C₈	—	73	2	no	—
127	C₂×C₄⋊C₈	C₂×D₇₃	1	2	yes	—
128	C₂×C₄×C₈	—	2	1	no	—
129	#391	—	73	4	no	—
130	#391	—	146	2	no	—
131	#382	—	146	1	no	—
132	#382	—	146	1	no	—
133	C₄³	C₂×D₇₃	1	1	yes	characteristic
134	#336	—	2	1	no	—
135	#336	—	146	2	no	—
136	#333	—	146	4	no	—
137	#332	—	146	4	no	—
138	C₂²×Q₈	—	73	2	no	—
139	C₂²×Q₈	—	146	1	no	—
140	C₂²×C₈	—	2	2	no	—
141	C₂²×C₈	—	146	2	no	—
142	C₄⋊Q₈	—	146	2	no	—
143	C₄⋊Q₈	—	146	2	no	—
144	C₄⋊Q₈	—	146	2	no	—
145	C₄⋊Q₈	—	146	2	no	—
146	C₂×C₄⋊C₄	—	73	2	no	—
147	C₂×C₄⋊C₄	—	146	1	no	—
148	C₂×C₄⋊C₄	—	146	1	no	—
149	C₂×C₄⋊C₄	—	146	1	no	—
150	C₂×C₄²	C₄×D₇₃	1	2	yes	—
151	C₂×C₄²	D₂₉₂	1	2	yes	—
152	C₂×C₄²	C₂²⋊D₇₃	1	1	yes	characteristic
153	C₂×C₄²	C₂²⋊D₇₃	1	1	yes	characteristic
154	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
155	C₄⋊C₈	—	2	2	no	—
156	C₄⋊C₈	—	146	2	no	—
157	C₄⋊C₈	—	146	2	no	—
158	C₄⋊C₈	D₂₉₂	1	4	yes	—
159	C₄×C₈	—	4	2	no	—
160	#95	—	146	4	no	—
161	#95	—	146	4	no	—
162	C₂×Q₈	—	292	4	no	—
163	C₂×Q₈	—	292	1	no	—
164	C₂×Q₈	—	292	1	no	—
165	C₂×Q₈	—	292	4	no	—
166	C₂×Q₈	—	146	4	no	—
167	C₂²×C₄	—	146	2	no	—
168	C₂²×C₄	—	146	2	no	—
169	C₂²×C₄	#11924005	1	2	yes	—
170	C₂²×C₄	#11924005	1	2	yes	—
171	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
172	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
173	C₂²×C₄	C₂×D₂₉₂	1	1	yes	characteristic
174	C₂×C₈	—	2	4	no	—
175	C₂×C₈	—	4	2	no	—
176	C₂×C₈	—	4	2	no	—
177	C₂×C₈	—	292	2	no	—
178	C₂×C₈	—	292	4	no	—
179	C₄⋊C₄	—	292	2	no	—
180	C₄⋊C₄	—	292	2	no	—
181	C₄⋊C₄	—	292	1	no	—
182	C₄⋊C₄	—	292	1	no	—
183	C₄⋊C₄	—	146	4	no	—
184	C₄²	—	2	4	no	—
185	C₄²	—	2	2	no	—
186	C₄²	—	4	2	no	—
187	C₄²	#11924016	1	2	yes	—
188	C₄²	#11924018	1	2	yes	—
189	C₄²	C₂×D₂₉₂	1	2	yes	—
190	C₄²	#11924028	1	2	yes	—
191	C₂³	C₂×#11924005	1	1	yes	characteristic
192	Q₈	—	584	4	no	—
193	Q₈	—	584	2	no	—
194	Q₈	—	584	2	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	292	2	no	—
202	C₂×C₄	—	292	2	no	—
203	C₂×C₄	—	292	4	no	—
204	C₂×C₄	—	292	4	no	—
205	C₂×C₄	#14556514	1	4	yes	—
206	C₂×C₄	C₄×D₂₉₂	1	2	yes	—
207	C₂×C₄	#14556565	1	2	yes	—
208	C₂×C₄	#14556579	1	1	yes	characteristic
209	C₂×C₄	#14556588	1	1	yes	characteristic
210	C₂×C₄	C₂×#11924016	1	1	yes	characteristic
211	C₂×C₄	C₂×#11924018	1	1	yes	characteristic
212	C₂×C₄	#14556613	1	4	yes	—
213	C₂×C₄	#14556621	1	2	yes	—
214	C₈	—	4	4	no	—
215	C₈	—	584	2	no	—
216	C₂²	#17988489	1	1	yes	characteristic
217	C₂²	#17988569	1	2	yes	—
218	C₂²	C₂×#14556514	1	1	yes	characteristic
219	C₂²	#17988584	1	2	yes	—
220	C₂²	#17988595	1	1	yes	characteristic
221	C₄	—	2	2	no	—
222	C₄	—	2	4	no	—
223	C₄	—	4	2	no	—
224	C₄	—	584	2	no	—
225	C₄	—	584	2	no	—
226	C₄	#17988792	1	2	yes	—
227	C₄	#17988797	1	2	yes	—
228	C₄	#17988942	1	2	yes	—
229	C₄	#17988971	1	2	yes	—
230	C₂	#22608589	1	2	yes	—
231	C₂	#22608639	1	2	yes	—
232	C₂	#22610742	1	1	yes	characteristic
233	C₂	#22610780	1	1	yes	characteristic
234	C₂	#22610854	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22618309

C₂

yes

maximal, characteristic

#22610048

C₂

yes

maximal, characteristic

C₂×#17988335

C₂

yes

maximal

C₂×#17988332

C₂

yes

maximal

C₄×C₄⋊C₈×C₇₃

C₂

yes

maximal, characteristic

C₂×#14556591

C₂²

yes

characteristic

C₂×#14556591

C₂²

yes

characteristic

C₂×C₄⋊#10596831

C₂²

yes

—

#17988493

—

#17988493

C₄

yes

—

—

—

—

—

—

C₂×C₄⋊C₈×C₇₃

C₂²

yes

—

C₂×C₄×C₈×C₇₃

—

C₄³×C₇₃

C₂²

yes

characteristic

#336×C₇₃

—

C₂²×Dic₁₄₆

—

C₂²×Dic₁₄₆

C₂×C₄

yes

—

—

—

—

—

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

C₂×C₄

yes

—

—

—

—

—

C₂²×C₈×C₇₃

—

C₂×C₄²×C₇₃

C₂×C₄

yes

—

C₂×C₄²×C₇₃

D₄

yes

—

C₂×C₄²×C₇₃

D₄

yes

characteristic

C₂×C₄²×C₇₃

D₄

yes

characteristic

C₂×C₄²×C₇₃

C₂³

yes

characteristic

C₄⋊C₈×C₇₃

—

C₄⋊C₈×C₇₃

D₄

yes

—

C₄×C₈×C₇₃

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

C₂×#10596831

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₂²×C₄×C₇₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

SD₁₆

yes

—

C₄²×C₇₃

Q₁₆

yes

—

C₄²×C₇₃

C₂×D₄

yes

—

C₄²×C₇₃

#41

yes

—

C₂³×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

#103

yes

—

C₂×C₄×C₇₃

C₄×D₄

yes

—

C₂×C₄×C₇₃

#121

yes

—

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₇₃

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₇₃

#135

yes

—

C₂×C₄×C₇₃

#137

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

#390

yes

characteristic

C₂²×C₇₃

#413

yes

—

100

C₂²×C₇₃

C₂×#103

yes

characteristic

101

C₂²×C₇₃

#416

yes

—

102

C₂²×C₇₃

#419

yes

characteristic

103

C₄×C₇₃

—

104

C₄×C₇₃

—

105

C₄×C₇₃

—

106

C₄×C₇₃

#461

yes

—

107

C₄×C₇₃

#462

yes

—

108

C₄×C₇₃

#488

yes

—

109

C₄×C₇₃

#495

yes

—

110

Dic₇₃

—

111

Dic₇₃

—

112

#9693

—

maximal, Sylow

113

C₂×C₇₃

#1542

yes

—

114

C₂×C₇₃

#1554

yes

—

115

C₂×C₇₃

#1958

yes

characteristic

116

C₂×C₇₃

#1967

yes

characteristic

117

C₂×C₇₃

#1981

yes

characteristic

118

#2862

—

119

#1831

—

120

C₄×C₄⋊C₈

D₇₃

yes

characteristic

121

C₂×#333

—

122

C₂×#332

—

123

C₇₃

#9693

yes

characteristic, complemented, Sylow

124

C₂×C₄⋊Q₈

—

125

C₂×C₄⋊Q₈

—

126

C₂×C₄⋊C₈

—

127

C₂×C₄⋊C₈

C₂×D₇₃

yes

—

128

C₂×C₄×C₈

—

129

#391

—

130

#391

—

146

—

131

#382

—

146

—

132

#382

—

146

—

133

C₄³

C₂×D₇₃

yes

characteristic

134

#336

—

135

#336

—

146

—

136

#333

—

146

—

137

#332

—

146

—

138

C₂²×Q₈

—

139

C₂²×Q₈

—

146

—

140

C₂²×C₈

—

141

C₂²×C₈

—

146

—

142

C₄⋊Q₈

—

146

—

143

C₄⋊Q₈

—

146

—

144

C₄⋊Q₈

—

146

—

145

C₄⋊Q₈

—

146

—

146

C₂×C₄⋊C₄

—

147

C₂×C₄⋊C₄

—

146

—

148

C₂×C₄⋊C₄

—

146

—

149

C₂×C₄⋊C₄

—

146

—

150

C₂×C₄²

C₄×D₇₃

yes

—

151

C₂×C₄²

D₂₉₂

yes

—

152

C₂×C₄²

C₂²⋊D₇₃

yes

characteristic

153

C₂×C₄²

C₂²⋊D₇₃

yes

characteristic

154

C₂×C₄²

C₂²×D₇₃

yes

characteristic

155

C₄⋊C₈

—

156

C₄⋊C₈

—

146

—

157

C₄⋊C₈

—

146

—

158

C₄⋊C₈

D₂₉₂

yes

—

159

C₄×C₈

—

160

#95

—

146

—

161

#95

—

146

—

162

C₂×Q₈

—

292

—

163

C₂×Q₈

—

292

—

164

C₂×Q₈

—

292

—

165

C₂×Q₈

—

292

—

166

C₂×Q₈

—

146

—

167

C₂²×C₄

—

146

—

168

C₂²×C₄

—

146

—

169

C₂²×C₄

#11924005

yes

—

170

C₂²×C₄

#11924005

yes

—

171

C₂²×C₄

C₂×C₄×D₇₃

yes

characteristic

172

C₂²×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

173

C₂²×C₄

C₂×D₂₉₂

yes

characteristic

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

292

—

178

C₂×C₈

—

292

—

179

C₄⋊C₄

—

292

—

180

C₄⋊C₄

—

292

—

181

C₄⋊C₄

—

292

—

182

C₄⋊C₄

—

292

—

183

C₄⋊C₄

—

146

—

184

C₄²

—

185

C₄²

—

186

C₄²

—

187

C₄²

#11924016

yes

—

188

C₄²

#11924018

yes

—

189

C₄²

C₂×D₂₉₂

yes

—

190

C₄²

#11924028

yes

—

191

C₂³

C₂×#11924005

yes

characteristic

192

Q₈

—

584

—

193

Q₈

—

584

—

194

Q₈

—

584

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

292

—

202

C₂×C₄

—

292

—

203

C₂×C₄

—

292

—

204

C₂×C₄

—

292

—

205

C₂×C₄

#14556514

yes

—

206

C₂×C₄

C₄×D₂₉₂

yes

—

207

C₂×C₄

#14556565

yes

—

208

C₂×C₄

#14556579

yes

characteristic

209

C₂×C₄

#14556588

yes

characteristic

210

C₂×C₄

C₂×#11924016

yes

characteristic

211

C₂×C₄

C₂×#11924018

yes

characteristic

212

C₂×C₄

#14556613

yes

—

213

C₂×C₄

#14556621

yes

—

214

C₈

—

215

C₈

—

584

—

216

C₂²

#17988489

yes

characteristic

217

C₂²

#17988569

yes

—

218

C₂²

C₂×#14556514

yes

characteristic

219

C₂²

#17988584

yes

—

220

C₂²

#17988595

yes

characteristic

221

C₄

—

222

C₄

—

223

C₄

—

224

C₄

—

584

—

225

C₄

—

584

—

226

C₄

#17988792

yes

—

227

C₄

#17988797

yes

—

228

C₄

#17988942

yes

—

229

C₄

#17988971

yes

—

230

C₂

#22608589

yes

—

231

C₂

#22608639

yes

—

232

C₂

#22610742

yes

characteristic

233

C₂

#22610780

yes

characteristic

234

C₂

#22610854

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×#11924005
commutator	C₂²×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₃
Fitting	C₄×C₄⋊C₈×C₇₃	C₂
socle, prime radical	C₂³×C₇₃	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₇₃	C₂³
hypercenter	C₄×C₄⋊C₈	D₇₃
hypocenter	C₇₃	#9693
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×C₄⋊C₈

subgroup

G/H

center

C₂³

C₂×#11924005

commutator

C₂²×C₄×C₇₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₃

Fitting

C₄×C₄⋊C₈×C₇₃

C₂

socle, prime radical

C₂³×C₇₃

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₇₃

C₂³

hypercenter

C₄×C₄⋊C₈

D₇₃

hypocenter

C₇₃

#9693

LCS

G ▷ C₂²×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×C₄⋊C₈

N	H ≅ G/N	type
123. C₇₃	#9693	semidirect

H ≅ G/N

type

123. C₇₃

#9693

semidirect

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

subgroup	index
#22618309	2
#22610048	2
C₂×#17988335	2
C₂×#17988332	2
C₄×C₄⋊C₈×C₇₃	2
#9693	73

subgroup

index

C₄×C₄⋊C₈×C₇₃

Subgroups — #32985023

Conjugacy classes of subgroups

Complements

Maximal subgroups