Group #33053736 — subgroups

Subgroups — #33053736

Order 18688.

938 conjugacy classes of subgroups; only the 395 normal subgroups are shown.

normal subgroups only

This group has 938 conjugacy classes of subgroups — too many to draw. Only its 395 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	#22619012	C₂	1	1	yes	maximal, characteristic
2	#22612852	C₂	1	1	yes	maximal, characteristic
3	#22608495	C₂	1	6	yes	maximal
4	#22608430	C₂	1	6	yes	maximal
5	C₇₃×#3502	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×Dic₇₃	—	2	1	no	—
7	Q₈×#10596831	—	2	4	no	—
8	#17988640	C₂²	1	6	yes	—
9	#17988486	—	2	3	no	—
10	#17988453	C₂²	1	3	yes	—
11	C₄×C₄⋊Dic₇₃	C₂²	1	3	yes	—
12	#17988324	C₂²	1	4	yes	—
13	#17988324	C₂²	1	12	yes	—
14	Q₈²×C₇₃	C₄	1	4	yes	complemented
15	#557×C₇₃	—	2	4	no	—
16	#557×C₇₃	C₄	1	4	yes	complemented
17	#544×C₇₃	—	2	3	no	—
18	#533×C₇₃	C₂²	1	6	yes	—
19	#519×C₇₃	—	2	1	no	—
20	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
21	Q₈×Dic₇₃	—	4	4	no	—
22	C₂×C₄⋊Dic₇₃	—	2	3	no	—
23	C₂×C₄⋊Dic₇₃	—	2	3	no	—
24	C₂×C₄×Dic₇₃	—	2	3	no	—
25	C₄⋊#10596831	—	2	6	no	—
26	C₂²⋊#10596831	C₂³	1	4	yes	—
27	C₄×#10596831	—	2	6	no	—
28	#14556498	—	2	3	no	—
29	#14556498	C₂³	1	1	yes	characteristic
30	#14556498	C₂³	1	3	yes	—
31	C₂²×Q₈×C₇₃	D₄	1	1	yes	characteristic
32	C₄⋊Q₈×C₇₃	—	2	12	no	—
33	C₄⋊Q₈×C₇₃	C₂×C₄	1	6	yes	—
34	C₄⋊Q₈×C₇₃	C₂×C₄	1	6	yes	—
35	#125×C₇₃	—	2	12	no	—
36	#125×C₇₃	—	2	6	no	—
37	C₂²⋊Q₈×C₇₃	—	2	6	no	—
38	C₂²⋊Q₈×C₇₃	C₂³	1	4	yes	—
39	C₄×Q₈×C₇₃	—	2	4	no	—
40	C₄×Q₈×C₇₃	—	2	4	no	—
41	C₄×Q₈×C₇₃	—	2	6	no	—
42	C₄×Q₈×C₇₃	C₂×C₄	1	12	yes	—
43	C₄×Q₈×C₇₃	C₂×C₄	1	4	yes	—
44	C₄×Q₈×C₇₃	D₄	1	4	yes	—
45	#117×C₇₃	—	2	6	no	—
46	C₂×C₄⋊C₄×C₇₃	D₄	1	3	yes	—
47	C₂×C₄²×C₇₃	C₂³	1	3	yes	—
48	C₂²×Dic₇₃	—	2	1	no	—
49	C₂²×Dic₇₃	—	2	3	no	—
50	C₂×#10596831	—	2	4	no	—
51	C₄⋊Dic₇₃	—	4	6	no	—
52	C₄⋊Dic₇₃	—	4	6	no	—
53	C₄×Dic₇₃	—	4	6	no	—
54	C₂×Q₈×C₇₃	—	2	6	no	—
55	C₂×Q₈×C₇₃	C₂²⋊C₄	1	4	yes	—
56	C₂×Q₈×C₇₃	SD₁₆	1	4	yes	—
57	C₂×Q₈×C₇₃	Q₁₆	1	4	yes	—
58	C₂×Q₈×C₇₃	C₂²×C₄	1	4	yes	—
59	C₂²×C₄×C₇₃	C₂×D₄	1	3	yes	—
60	C₂²×C₄×C₇₃	C₂×D₄	1	3	yes	—
61	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
62	C₄⋊C₄×C₇₃	—	2	6	no	—
63	C₄⋊C₄×C₇₃	—	2	6	no	—
64	C₄⋊C₄×C₇₃	—	2	6	no	—
65	C₄⋊C₄×C₇₃	—	2	12	no	—
66	C₄⋊C₄×C₇₃	—	2	4	no	—
67	C₄⋊C₄×C₇₃	C₂²⋊C₄	1	12	yes	—
68	C₄⋊C₄×C₇₃	C₂²×C₄	1	4	yes	—
69	C₂²⋊C₄×C₇₃	—	2	4	no	—
70	C₄²×C₇₃	—	2	12	no	—
71	C₄²×C₇₃	C₂²×C₄	1	6	yes	—
72	C₄²×C₇₃	C₂×D₄	1	6	yes	—
73	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
74	Q₈×C₇₃	—	4	4	no	—
75	Q₈×C₇₃	—	8	6	no	—
76	Q₈×C₇₃	#103	1	16	yes	—
77	C₂×C₄×C₇₃	—	2	4	no	—
78	C₂×C₄×C₇₃	—	2	4	no	—
79	C₂×C₄×C₇₃	—	4	3	no	—
80	C₂×C₄×C₇₃	—	4	1	no	—
81	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	6	yes	—
82	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	6	yes	—
83	C₂×C₄×C₇₃	C₂×SD₁₆	1	6	yes	—
84	C₂×C₄×C₇₃	C₂×Q₁₆	1	6	yes	—
85	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
86	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
87	C₂×Dic₇₃	—	2	2	no	—
88	C₂×Dic₇₃	—	4	1	no	—
89	C₂×Dic₇₃	—	4	1	no	—
90	C₂×Dic₇₃	—	4	3	no	—
91	C₂×Dic₇₃	—	4	3	no	—
92	C₂×Dic₇₃	—	4	3	no	—
93	#10596831	—	4	4	no	—
94	C₂²×C₇₃	—	2	1	no	—
95	C₂²×C₇₃	—	2	1	no	—
96	C₂²×C₇₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
97	C₂²×C₇₃	C₂²×SD₁₆	1	1	yes	characteristic
98	C₂²×C₇₃	C₂²×Q₁₆	1	1	yes	characteristic
99	C₄×C₇₃	—	2	1	no	—
100	C₄×C₇₃	—	2	1	no	—
101	C₄×C₇₃	—	2	6	no	—
102	C₄×C₇₃	—	4	4	no	—
103	C₄×C₇₃	—	4	4	no	—
104	C₄×C₇₃	C₂×#103	1	12	yes	—
105	Dic₇₃	—	4	2	no	—
106	Dic₇₃	—	8	3	no	—
107	#17619	—	73	1	no	maximal, Sylow
108	C₂×C₇₃	—	2	1	no	—
109	C₂×C₇₃	—	2	1	no	—
110	C₂×C₇₃	#2884	1	1	yes	characteristic
111	C₂×C₇₃	C₂²×#103	1	1	yes	characteristic
112	C₂×C₇₃	#2901	1	1	yes	characteristic
113	#3502	D₇₃	1	1	yes	characteristic
114	#2982	—	73	1	no	—
115	#2351	—	73	1	no	—
116	#1518	—	73	6	no	—
117	#1503	—	73	6	no	—
118	C₇₃	#17619	1	1	yes	characteristic, complemented, Sylow
119	Q₈²	Dic₇₃	1	4	yes	complemented
120	#557	—	2	4	no	—
121	#557	Dic₇₃	1	4	yes	complemented
122	#544	—	2	3	no	—
123	#533	C₂×D₇₃	1	6	yes	—
124	#519	—	2	1	no	—
125	C₂×C₄×Q₈	—	146	1	no	—
126	C₂×C₄×Q₈	C₂×D₇₃	1	1	yes	characteristic
127	C₈×Q₈	—	146	4	no	—
128	#431	—	73	6	no	—
129	#389	—	146	3	no	—
130	#382	—	73	3	no	—
131	C₄×C₄⋊C₄	—	73	3	no	—
132	#328	—	73	4	no	—
133	#328	—	73	12	no	—
134	C₂²×Q₈	C₂²⋊D₇₃	1	1	yes	characteristic
135	C₄⋊Q₈	—	2	12	no	—
136	C₄⋊Q₈	C₂×Dic₇₃	1	6	yes	—
137	C₄⋊Q₈	C₂×Dic₇₃	1	6	yes	—
138	#125	—	2	12	no	—
139	#125	—	2	6	no	—
140	C₂²⋊Q₈	—	2	6	no	—
141	C₂²⋊Q₈	C₂²×D₇₃	1	4	yes	—
142	C₄×Q₈	—	2	4	no	—
143	C₄×Q₈	—	2	4	no	—
144	C₄×Q₈	—	2	6	no	—
145	C₄×Q₈	—	292	4	no	—
146	C₄×Q₈	C₂×Dic₇₃	1	12	yes	—
147	C₄×Q₈	C₂×Dic₇₃	1	4	yes	—
148	C₄×Q₈	C₂²⋊D₇₃	1	4	yes	—
149	#117	—	2	6	no	—
150	C₂×C₄⋊C₄	—	146	3	no	—
151	C₂×C₄⋊C₄	—	146	3	no	—
152	C₂×C₄⋊C₄	C₂²⋊D₇₃	1	3	yes	—
153	C₂×C₄²	—	146	3	no	—
154	C₂×C₄²	C₂²×D₇₃	1	3	yes	—
155	C₄⋊C₈	—	146	6	no	—
156	C₂²⋊C₈	—	73	4	no	—
157	C₄×C₈	—	146	6	no	—
158	#95	—	73	1	no	—
159	#95	—	73	3	no	—
160	#95	—	146	3	no	—
161	C₂×Q₈	—	2	6	no	—
162	C₂×Q₈	C₂²⋊Dic₇₃	1	4	yes	—
163	C₂×Q₈	#11924015	1	4	yes	—
164	C₂×Q₈	#11924018	1	4	yes	—
165	C₂×Q₈	C₂²×Dic₇₃	1	4	yes	—
166	C₂²×C₄	—	146	3	no	—
167	C₂²×C₄	—	146	1	no	—
168	C₂²×C₄	C₂×C₂²⋊D₇₃	1	3	yes	—
169	C₂²×C₄	C₂×C₂²⋊D₇₃	1	3	yes	—
170	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
171	C₂×C₈	—	146	4	no	—
172	C₄⋊C₄	—	2	6	no	—
173	C₄⋊C₄	—	2	6	no	—
174	C₄⋊C₄	—	2	6	no	—
175	C₄⋊C₄	—	2	12	no	—
176	C₄⋊C₄	—	2	4	no	—
177	C₄⋊C₄	—	292	6	no	—
178	C₄⋊C₄	—	292	6	no	—
179	C₄⋊C₄	C₂²⋊Dic₇₃	1	12	yes	—
180	C₄⋊C₄	C₂²×Dic₇₃	1	4	yes	—
181	C₂²⋊C₄	—	2	4	no	—
182	C₄²	—	2	12	no	—
183	C₄²	—	292	6	no	—
184	C₄²	C₂²×Dic₇₃	1	6	yes	—
185	C₄²	C₂×C₂²⋊D₇₃	1	6	yes	—
186	C₂³	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
187	Q₈	—	4	4	no	—
188	Q₈	—	8	6	no	—
189	Q₈	#14556515	1	16	yes	—
190	C₂×C₄	—	2	4	no	—
191	C₂×C₄	—	2	4	no	—
192	C₂×C₄	—	4	3	no	—
193	C₂×C₄	—	4	1	no	—
194	C₂×C₄	—	292	1	no	—
195	C₂×C₄	—	292	1	no	—
196	C₂×C₄	—	292	3	no	—
197	C₂×C₄	—	292	3	no	—
198	C₂×C₄	—	292	3	no	—
199	C₂×C₄	—	146	2	no	—
200	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	6	yes	—
201	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	6	yes	—
202	C₂×C₄	C₂×#11924015	1	6	yes	—
203	C₂×C₄	C₂×#11924018	1	6	yes	—
204	C₂×C₄	C₂³×Dic₇₃	1	1	yes	characteristic
205	C₂×C₄	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
206	C₈	—	292	4	no	—
207	C₂²	—	2	1	no	—
208	C₂²	—	2	1	no	—
209	C₂²	C₂²×C₂²⋊Dic₇₃	1	1	yes	characteristic
210	C₂²	C₂²×#11924015	1	1	yes	characteristic
211	C₂²	C₂²×#11924018	1	1	yes	characteristic
212	C₄	—	2	1	no	—
213	C₄	—	2	1	no	—
214	C₄	—	2	6	no	—
215	C₄	—	4	4	no	—
216	C₄	—	4	4	no	—
217	C₄	—	292	2	no	—
218	C₄	—	584	3	no	—
219	C₄	C₂×#14556515	1	12	yes	—
220	C₂	—	2	1	no	—
221	C₂	—	2	1	no	—
222	C₂	#22618395	1	1	yes	characteristic
223	C₂	C₂²×#14556515	1	1	yes	characteristic
224	C₂	#22618478	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22619012

C₂

yes

maximal, characteristic

#22612852

C₂

yes

maximal, characteristic

#22608495

C₂

yes

maximal

#22608430

C₂

yes

maximal

C₇₃×#3502

C₂

yes

maximal, characteristic

C₂×Q₈×Dic₇₃

—

Q₈×#10596831

—

#17988640

C₂²

yes

—

#17988486

—

#17988453

C₂²

yes

—

C₄×C₄⋊Dic₇₃

C₂²

yes

—

#17988324

C₂²

yes

—

#17988324

C₂²

yes

—

Q₈²×C₇₃

C₄

yes

complemented

#557×C₇₃

—

#557×C₇₃

C₄

yes

complemented

#544×C₇₃

—

#533×C₇₃

C₂²

yes

—

#519×C₇₃

—

C₂×C₄×Q₈×C₇₃

C₂²

yes

characteristic

Q₈×Dic₇₃

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄×Dic₇₃

—

C₄⋊#10596831

—

C₂²⋊#10596831

C₂³

yes

—

C₄×#10596831

—

#14556498

—

#14556498

C₂³

yes

characteristic

#14556498

C₂³

yes

—

C₂²×Q₈×C₇₃

D₄

yes

characteristic

C₄⋊Q₈×C₇₃

—

C₄⋊Q₈×C₇₃

C₂×C₄

yes

—

C₄⋊Q₈×C₇₃

C₂×C₄

yes

—

#125×C₇₃

—

#125×C₇₃

—

C₂²⋊Q₈×C₇₃

—

C₂²⋊Q₈×C₇₃

C₂³

yes

—

C₄×Q₈×C₇₃

—

C₄×Q₈×C₇₃

—

C₄×Q₈×C₇₃

—

C₄×Q₈×C₇₃

C₂×C₄

yes

—

C₄×Q₈×C₇₃

C₂×C₄

yes

—

C₄×Q₈×C₇₃

D₄

yes

—

#117×C₇₃

—

C₂×C₄⋊C₄×C₇₃

D₄

yes

—

C₂×C₄²×C₇₃

C₂³

yes

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄×Dic₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

C₂²⋊C₄

yes

—

C₂×Q₈×C₇₃

SD₁₆

yes

—

C₂×Q₈×C₇₃

Q₁₆

yes

—

C₂×Q₈×C₇₃

C₂²×C₄

yes

—

C₂²×C₄×C₇₃

C₂×D₄

yes

—

C₂²×C₄×C₇₃

C₂×D₄

yes

—

C₂²×C₄×C₇₃

C₂⁴

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

C₂²⋊C₄

yes

—

C₄⋊C₄×C₇₃

C₂²×C₄

yes

—

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

C₂²×C₄

yes

—

C₄²×C₇₃

C₂×D₄

yes

—

C₂³×C₇₃

C₂²×D₄

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

#103

yes

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₂²⋊C₄

yes

—

C₂×C₄×C₇₃

C₂×C₂²⋊C₄

yes

—

C₂×C₄×C₇₃

C₂×SD₁₆

yes

—

C₂×C₄×C₇₃

C₂×Q₁₆

yes

—

C₂×C₄×C₇₃

C₂³×C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²×D₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂²×C₂²⋊C₄

yes

characteristic

C₂²×C₇₃

C₂²×SD₁₆

yes

characteristic

C₂²×C₇₃

C₂²×Q₁₆

yes

characteristic

C₄×C₇₃

—

100

C₄×C₇₃

—

101

C₄×C₇₃

—

102

C₄×C₇₃

—

103

C₄×C₇₃

—

104

C₄×C₇₃

C₂×#103

yes

—

105

Dic₇₃

—

106

Dic₇₃

—

107

#17619

—

maximal, Sylow

108

C₂×C₇₃

—

109

C₂×C₇₃

—

110

C₂×C₇₃

#2884

yes

characteristic

111

C₂×C₇₃

C₂²×#103

yes

characteristic

112

C₂×C₇₃

#2901

yes

characteristic

113

#3502

D₇₃

yes

characteristic

114

#2982

—

115

#2351

—

116

#1518

—

117

#1503

—

118

C₇₃

#17619

yes

characteristic, complemented, Sylow

119

Q₈²

Dic₇₃

yes

complemented

120

#557

—

121

#557

Dic₇₃

yes

complemented

122

#544

—

123

#533

C₂×D₇₃

yes

—

124

#519

—

125

C₂×C₄×Q₈

—

146

—

126

C₂×C₄×Q₈

C₂×D₇₃

yes

characteristic

127

C₈×Q₈

—

146

—

128

#431

—

129

#389

—

146

—

130

#382

—

131

C₄×C₄⋊C₄

—

132

#328

—

133

#328

—

134

C₂²×Q₈

C₂²⋊D₇₃

yes

characteristic

135

C₄⋊Q₈

—

136

C₄⋊Q₈

C₂×Dic₇₃

yes

—

137

C₄⋊Q₈

C₂×Dic₇₃

yes

—

138

#125

—

139

#125

—

140

C₂²⋊Q₈

—

141

C₂²⋊Q₈

C₂²×D₇₃

yes

—

142

C₄×Q₈

—

143

C₄×Q₈

—

144

C₄×Q₈

—

145

C₄×Q₈

—

292

—

146

C₄×Q₈

C₂×Dic₇₃

yes

—

147

C₄×Q₈

C₂×Dic₇₃

yes

—

148

C₄×Q₈

C₂²⋊D₇₃

yes

—

149

#117

—

150

C₂×C₄⋊C₄

—

146

—

151

C₂×C₄⋊C₄

—

146

—

152

C₂×C₄⋊C₄

C₂²⋊D₇₃

yes

—

153

C₂×C₄²

—

146

—

154

C₂×C₄²

C₂²×D₇₃

yes

—

155

C₄⋊C₈

—

146

—

156

C₂²⋊C₈

—

157

C₄×C₈

—

146

—

158

#95

—

159

#95

—

160

#95

—

146

—

161

C₂×Q₈

—

162

C₂×Q₈

C₂²⋊Dic₇₃

yes

—

163

C₂×Q₈

#11924015

yes

—

164

C₂×Q₈

#11924018

yes

—

165

C₂×Q₈

C₂²×Dic₇₃

yes

—

166

C₂²×C₄

—

146

—

167

C₂²×C₄

—

146

—

168

C₂²×C₄

C₂×C₂²⋊D₇₃

yes

—

169

C₂²×C₄

C₂×C₂²⋊D₇₃

yes

—

170

C₂²×C₄

C₂³×D₇₃

yes

characteristic

171

C₂×C₈

—

146

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

292

—

178

C₄⋊C₄

—

292

—

179

C₄⋊C₄

C₂²⋊Dic₇₃

yes

—

180

C₄⋊C₄

C₂²×Dic₇₃

yes

—

181

C₂²⋊C₄

—

182

C₄²

—

183

C₄²

—

292

—

184

C₄²

C₂²×Dic₇₃

yes

—

185

C₄²

C₂×C₂²⋊D₇₃

yes

—

186

C₂³

C₂²×C₂²⋊D₇₃

yes

characteristic

187

Q₈

—

188

Q₈

—

189

Q₈

#14556515

yes

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

292

—

195

C₂×C₄

—

292

—

196

C₂×C₄

—

292

—

197

C₂×C₄

—

292

—

198

C₂×C₄

—

292

—

199

C₂×C₄

—

146

—

200

C₂×C₄

C₂×C₂²⋊Dic₇₃

yes

—

201

C₂×C₄

C₂×C₂²⋊Dic₇₃

yes

—

202

C₂×C₄

C₂×#11924015

yes

—

203

C₂×C₄

C₂×#11924018

yes

—

204

C₂×C₄

C₂³×Dic₇₃

yes

characteristic

205

C₂×C₄

C₂²×C₂²⋊D₇₃

yes

characteristic

206

C₈

—

292

—

207

C₂²

—

208

C₂²

—

209

C₂²

C₂²×C₂²⋊Dic₇₃

yes

characteristic

210

C₂²

C₂²×#11924015

yes

characteristic

211

C₂²

C₂²×#11924018

yes

characteristic

212

C₄

—

213

C₄

—

214

C₄

—

215

C₄

—

216

C₄

—

217

C₄

—

292

—

218

C₄

—

584

—

219

C₄

C₂×#14556515

yes

—

220

C₂

—

221

C₂

—

222

C₂

#22618395

yes

characteristic

223

C₂

C₂²×#14556515

yes

characteristic

224

C₂

#22618478

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊Dic₇₃
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₃
Fitting	C₇₃×#3502	C₂
socle	C₂²×C₇₃	C₂²×C₂²⋊C₄
prime radical	C₂³×C₇₃	C₂²×D₄
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	#3502	D₇₃
hypocenter	C₇₃	#17619
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄×Q₈ ◁ #3502

subgroup

G/H

center

C₂²

C₂²×C₂²⋊Dic₇₃

commutator

C₂×C₄×C₇₃

C₂³×C₄

Frattini

C₂²×C₄

C₂³×D₇₃

Fitting

C₇₃×#3502

C₂

socle

C₂²×C₇₃

C₂²×C₂²⋊C₄

prime radical

C₂³×C₇₃

C₂²×D₄

cosocle

C₂²×C₄×C₇₃

C₂⁴

D₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄×Q₈ ◁ #3502

N	H ≅ G/N	type
14. Q₈²×C₇₃	C₄	semidirect
16. #557×C₇₃	C₄	semidirect
118. C₇₃	#17619	semidirect
119. Q₈²	Dic₇₃	semidirect
121. #557	Dic₇₃	semidirect

H ≅ G/N

type

14. Q₈²×C₇₃

C₄

semidirect

16. #557×C₇₃

C₄

semidirect

118. C₇₃

#17619

semidirect

119. Q₈²

Dic₇₃

semidirect

121. #557

Dic₇₃

semidirect

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

subgroup	index
#22619012	2
#22612852	2
#22608495	2
#22608430	2
C₇₃×#3502	2
#17619	73

subgroup

index

C₇₃×#3502

Subgroups — #33053736

Conjugacy classes of subgroups

Complements

Maximal subgroups