Group #33004143 — subgroups

Subgroups — #33004143

Order 18688.

522 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 159 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×C₈×D₂₉₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊#11924003	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#17988366	C₂	1	4	yes	maximal, complemented
4	C₂×#346×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₈×D₇₃	C₂²	1	2	yes	—
6	C₂×C₄×D₂₉₂	C₄	1	1	yes	characteristic
7	C₂²×#11924003	C₂²	1	2	yes	—
8	C₈×D₂₉₂	—	2	2	no	—
9	C₈×D₂₉₂	—	2	2	no	—
10	C₂×C₄⋊#10596831	C₄	1	1	yes	characteristic
11	C₂×#14556503	C₄	1	2	yes	—
12	C₄⋊#11924003	—	2	2	no	—
13	#17988366	—	2	8	no	—
14	C₂²×C₁₆×C₇₃	C₂²	1	2	yes	—
15	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
16	#346×C₇₃	—	2	2	no	—
17	C₂²×D₂₉₂	C₈	1	1	yes	characteristic
18	C₂²×C₄×D₇₃	C₂×C₄	1	2	yes	—
19	C₂²×#10596831	C₂×C₄	1	2	yes	—
20	C₂×C₈×D₇₃	—	2	4	no	—
21	C₂×C₈×D₇₃	—	2	2	no	—
22	C₂×C₈×D₇₃	—	2	2	no	—
23	C₂×C₈×D₇₃	—	2	4	no	—
24	C₄×D₂₉₂	—	2	2	no	—
25	C₄×D₂₉₂	—	2	2	no	—
26	C₂×C₄⋊Dic₇₃	C₈	1	1	yes	characteristic
27	C₂×#11924005	C₈	1	2	yes	—
28	C₂×#11924003	—	2	4	no	—
29	C₂×#11924003	—	2	2	no	—
30	C₄⋊#10596831	—	2	2	no	—
31	#14556503	—	2	4	no	—
32	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
34	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
35	C₂×C₁₆×C₇₃	—	2	2	no	—
36	C₂×C₁₆×C₇₃	—	2	2	no	—
37	C₂×C₁₆×C₇₃	D₄	1	4	yes	complemented
38	C₄×C₈×C₇₃	D₄	1	2	yes	—
39	C₄×C₈×C₇₃	D₄	1	2	yes	—
40	C₂³×D₇₃	C₂×C₈	1	2	yes	—
41	C₂×D₂₉₂	—	2	4	no	—
42	C₂×D₂₉₂	—	2	2	no	—
43	C₂²×Dic₇₃	C₂×C₈	1	2	yes	—
44	C₂×C₄×D₇₃	—	2	2	no	—
45	C₂×C₄×D₇₃	—	2	4	no	—
46	C₂×C₄×D₇₃	—	2	2	no	—
47	C₂×C₄×D₇₃	—	2	4	no	—
48	C₂×#10596831	—	2	2	no	—
49	C₂×#10596831	—	2	4	no	—
50	C₈×D₇₃	—	4	4	no	—
51	C₈×D₇₃	—	4	2	no	—
52	C₈×D₇₃	—	4	2	no	—
53	C₄⋊Dic₇₃	—	2	2	no	—
54	#11924005	—	2	4	no	—
55	#11924003	—	4	2	no	—
56	C₂²×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
57	C₂²×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
58	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
59	C₂×C₈×C₇₃	—	2	2	no	—
60	C₂×C₈×C₇₃	C₂²⋊C₄	1	2	yes	—
61	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
62	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
63	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
64	C₂×C₈×C₇₃	#41	1	2	yes	—
65	C₄²×C₇₃	C₂²⋊C₄	1	2	yes	—
66	C₄²×C₇₃	M₁₆	1	2	yes	—
67	C₁₆×C₇₃	—	2	4	no	—
68	C₂³×C₇₃	C₂²×C₈	1	1	yes	characteristic
69	C₂²×D₇₃	—	2	2	no	—
70	C₂²×D₇₃	—	2	4	no	—
71	C₂²×D₇₃	—	2	2	no	—
72	C₂²×D₇₃	—	2	4	no	—
73	C₂²×D₇₃	M₃₂	1	4	yes	—
74	C₂×C₄×C₇₃	—	2	2	no	—
75	C₂×C₄×C₇₃	—	2	2	no	—
76	C₂×C₄×C₇₃	C₂²⋊C₈	1	2	yes	—
77	C₂×C₄×C₇₃	C₂²⋊C₈	1	2	yes	—
78	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
79	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
80	C₂×C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
81	C₂×C₄×C₇₃	#131	1	2	yes	—
82	C₂×Dic₇₃	—	2	2	no	—
83	C₂×Dic₇₃	—	2	4	no	—
84	D₂₉₂	—	2	8	no	—
85	C₄×D₇₃	—	4	2	no	—
86	C₄×D₇₃	—	4	2	no	—
87	C₄×D₇₃	—	4	4	no	—
88	C₈×C₇₃	—	2	2	no	—
89	C₈×C₇₃	#121	1	2	yes	—
90	C₈×C₇₃	#124	1	1	yes	characteristic
91	C₈×C₇₃	#127	1	1	yes	characteristic
92	#10596831	—	4	2	no	—
93	C₂²×C₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
94	C₂²×C₇₃	C₈×D₄	1	2	yes	—
95	C₂²×C₇₃	C₂×M₃₂	1	2	yes	—
96	C₂²×C₇₃	#504	1	2	yes	—
97	C₂×D₇₃	—	2	4	no	—
98	C₂×D₇₃	—	2	8	no	—
99	C₂×D₇₃	—	4	2	no	—
100	C₂×D₇₃	—	4	4	no	—
101	C₂×D₇₃	—	4	2	no	—
102	C₄×C₇₃	—	2	2	no	—
103	C₄×C₇₃	—	2	2	no	—
104	C₄×C₇₃	#390	1	1	yes	characteristic
105	C₄×C₇₃	#408	1	1	yes	characteristic
106	C₄×C₇₃	#436	1	2	yes	—
107	Dic₇₃	—	4	2	no	—
108	#13190	—	73	1	no	maximal, Sylow
109	C₂×C₇₃	#1954	1	1	yes	characteristic
110	C₂×C₇₃	#2112	1	1	yes	characteristic
111	C₂×C₇₃	#2113	1	1	yes	characteristic
112	C₂×C₇₃	#2168	1	4	yes	—
113	D₇₃	—	4	4	no	—
114	C₂×C₈×D₄	—	73	1	no	—
115	C₂×C₄⋊C₁₆	—	73	1	no	—
116	C₂×C₂²⋊C₁₆	—	73	4	no	—
117	C₂×#346	D₇₃	1	1	yes	characteristic, complemented
118	C₇₃	#13190	1	1	yes	characteristic, complemented, Sylow
119	C₂³×C₈	—	73	2	no	—
120	C₂×C₄×D₄	—	73	1	no	—
121	C₂²×C₁₆	—	73	2	no	—
122	C₂²×C₁₆	C₂×D₇₃	1	2	yes	—
123	C₈×D₄	—	146	2	no	—
124	C₈×D₄	—	146	2	no	—
125	C₂×C₄⋊C₈	—	73	1	no	—
126	C₂×C₂²⋊C₈	—	73	2	no	—
127	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
128	C₄⋊C₁₆	—	146	2	no	—
129	C₂²⋊C₁₆	—	146	8	no	—
130	#346	—	2	2	no	—
131	C₂²×D₄	—	73	1	no	—
132	C₂³×C₄	—	73	2	no	—
133	C₂²×C₈	—	73	2	no	—
134	C₂²×C₈	—	146	2	no	—
135	C₂²×C₈	—	146	4	no	—
136	C₂²×C₈	—	146	2	no	—
137	C₂²×C₈	—	146	4	no	—
138	C₂²×C₈	C₄×D₇₃	1	1	yes	characteristic
139	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
140	C₄×D₄	—	146	2	no	—
141	C₄×D₄	—	146	2	no	—
142	C₂×C₄⋊C₄	—	73	1	no	—
143	C₂×C₂²⋊C₄	—	73	2	no	—
144	C₂×C₄²	C₄×D₇₃	1	1	yes	characteristic
145	C₂×C₁₆	—	2	2	no	—
146	C₂×C₁₆	—	2	2	no	—
147	C₂×C₁₆	—	146	4	no	—
148	C₂×C₁₆	—	146	2	no	—
149	C₂×C₁₆	D₂₉₂	1	4	yes	complemented
150	C₄⋊C₈	—	146	2	no	—
151	C₂²⋊C₈	—	146	4	no	—
152	C₄×C₈	D₂₉₂	1	2	yes	—
153	C₄×C₈	C₂²⋊D₇₃	1	2	yes	—
154	C₂⁴	—	73	2	no	—
155	C₂×D₄	—	146	4	no	—
156	C₂×D₄	—	146	2	no	—
157	C₂²×C₄	—	73	2	no	—
158	C₂²×C₄	—	146	2	no	—
159	C₂²×C₄	—	146	4	no	—
160	C₂²×C₄	—	146	2	no	—
161	C₂²×C₄	—	146	4	no	—
162	C₂²×C₄	C₈×D₇₃	1	1	yes	characteristic
163	C₂²×C₄	C₈×D₇₃	1	1	yes	characteristic
164	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
165	C₂×C₈	—	2	2	no	—
166	C₂×C₈	—	292	4	no	—
167	C₂×C₈	—	292	2	no	—
168	C₂×C₈	—	292	2	no	—
169	C₂×C₈	—	146	2	no	—
170	C₂×C₈	—	146	4	no	—
171	C₂×C₈	#11924005	1	2	yes	—
172	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
173	C₂×C₈	C₂×D₂₉₂	1	2	yes	—
174	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
175	C₂×C₈	#11924028	1	2	yes	—
176	C₄⋊C₄	—	146	2	no	—
177	C₂²⋊C₄	—	146	4	no	—
178	C₄²	#11924005	1	2	yes	—
179	C₄²	#11924011	1	2	yes	—
180	C₁₆	—	2	4	no	—
181	C₁₆	—	292	2	no	—
182	C₂³	—	73	4	no	—
183	C₂³	—	146	4	no	—
184	C₂³	—	146	2	no	—
185	C₂³	—	146	4	no	—
186	C₂³	—	146	2	no	—
187	C₂³	C₂×C₈×D₇₃	1	1	yes	characteristic
188	D₄	—	146	8	no	—
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	292	4	no	—
192	C₂×C₄	—	292	2	no	—
193	C₂×C₄	—	292	2	no	—
194	C₂×C₄	—	146	4	no	—
195	C₂×C₄	—	146	2	no	—
196	C₂×C₄	#14556503	1	2	yes	—
197	C₂×C₄	#14556503	1	2	yes	—
198	C₂×C₄	C₂×#11924005	1	1	yes	characteristic
199	C₂×C₄	C₄×D₂₉₂	1	2	yes	—
200	C₂×C₄	C₂×#11924011	1	1	yes	characteristic
201	C₂×C₄	#14556597	1	2	yes	—
202	C₈	—	2	2	no	—
203	C₈	—	292	2	no	—
204	C₈	#14556565	1	2	yes	—
205	C₈	#14556579	1	1	yes	characteristic
206	C₈	#14556588	1	1	yes	characteristic
207	C₂²	—	292	2	no	—
208	C₂²	—	292	4	no	—
209	C₂²	—	292	2	no	—
210	C₂²	—	146	8	no	—
211	C₂²	—	146	4	no	—
212	C₂²	C₂×#14556503	1	1	yes	characteristic
213	C₂²	C₈×D₂₉₂	1	2	yes	—
214	C₂²	M₃₂×D₇₃	1	2	yes	—
215	C₂²	#17989005	1	2	yes	—
216	C₄	—	2	2	no	—
217	C₄	—	2	2	no	—
218	C₄	—	292	2	no	—
219	C₄	#17988489	1	1	yes	characteristic
220	C₄	#17988553	1	1	yes	characteristic
221	C₄	#17988666	1	2	yes	—
222	C₂	—	292	4	no	—
223	C₂	#22610725	1	1	yes	characteristic
224	C₂	#22611541	1	1	yes	characteristic
225	C₂	#22611546	1	1	yes	characteristic
226	C₂	#22611758	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₈×D₂₉₂

C₂

yes

maximal, characteristic

C₂×C₄⋊#11924003

C₂

yes

maximal, characteristic, complemented

C₂×#17988366

C₂

yes

maximal, complemented

C₂×#346×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂²×C₈×D₇₃

C₂²

yes

—

C₂×C₄×D₂₉₂

C₄

yes

characteristic

C₂²×#11924003

C₂²

yes

—

C₈×D₂₉₂

—

C₈×D₂₉₂

—

C₂×C₄⋊#10596831

C₄

yes

characteristic

C₂×#14556503

C₄

yes

—

C₄⋊#11924003

—

#17988366

—

C₂²×C₁₆×C₇₃

C₂²

yes

—

C₂×C₄×C₈×C₇₃

C₂²

yes

characteristic

#346×C₇₃

—

C₂²×D₂₉₂

C₈

yes

characteristic

C₂²×C₄×D₇₃

C₂×C₄

yes

—

C₂²×#10596831

C₂×C₄

yes

—

C₂×C₈×D₇₃

—

C₂×C₈×D₇₃

—

C₂×C₈×D₇₃

—

C₂×C₈×D₇₃

—

C₄×D₂₉₂

—

C₄×D₂₉₂

—

C₂×C₄⋊Dic₇₃

C₈

yes

characteristic

C₂×#11924005

C₈

yes

—

—

—

—

—

C₂²×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₇₃

C₂³

yes

characteristic

C₂×C₄²×C₇₃

C₂×C₄

yes

characteristic

C₂×C₁₆×C₇₃

—

C₂×C₁₆×C₇₃

—

C₂×C₁₆×C₇₃

D₄

yes

complemented

C₄×C₈×C₇₃

D₄

yes

—

C₄×C₈×C₇₃

D₄

yes

—

C₂³×D₇₃

C₂×C₈

yes

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂²×Dic₇₃

C₂×C₈

yes

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×#10596831

—

C₂×#10596831

—

C₈×D₇₃

—

C₈×D₇₃

—

C₈×D₇₃

—

C₄⋊Dic₇₃

—

#11924005

—

#11924003

—

C₂²×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂²×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂²×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂²⋊C₄

yes

—

C₂×C₈×C₇₃

C₂×D₄

yes

characteristic

C₂×C₈×C₇₃

C₂×D₄

yes

—

C₂×C₈×C₇₃

C₂×D₄

yes

characteristic

C₂×C₈×C₇₃

#41

yes

—

C₄²×C₇₃

C₂²⋊C₄

yes

—

C₄²×C₇₃

M₁₆

yes

—

C₁₆×C₇₃

—

C₂³×C₇₃

C₂²×C₈

yes

characteristic

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

M₃₂

yes

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₈

yes

—

C₂×C₄×C₇₃

C₂²⋊C₈

yes

—

C₂×C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄×D₄

yes

—

C₂×C₄×C₇₃

C₂×M₁₆

yes

characteristic

C₂×C₄×C₇₃

#131

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

D₂₉₂

—

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

C₈×C₇₃

—

C₈×C₇₃

#121

yes

—

C₈×C₇₃

yes

C₈×C₇₃

yes

—

C₂²×C₇₃

C₂×C₂²⋊C₈

yes

characteristic

C₂²×C₇₃

C₈×D₄

yes

—

C₂²×C₇₃

C₂×M₃₂

yes

—

C₂²×C₇₃

#504

yes

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

100

C₂×D₇₃

—

101

C₂×D₇₃

—

102

C₄×C₇₃

—

103

C₄×C₇₃

—

104

C₄×C₇₃

#390

yes

characteristic

105

C₄×C₇₃

#408

yes

characteristic

106

C₄×C₇₃

#436

yes

—

107

Dic₇₃

—

108

#13190

—

maximal, Sylow

109

C₂×C₇₃

#1954

yes

characteristic

110

C₂×C₇₃

#2112

yes

characteristic

111

C₂×C₇₃

#2113

yes

characteristic

112

C₂×C₇₃

#2168

yes

—

113

D₇₃

—

114

C₂×C₈×D₄

—

115

C₂×C₄⋊C₁₆

—

116

C₂×C₂²⋊C₁₆

—

117

C₂×#346

D₇₃

yes

characteristic, complemented

118

C₇₃

#13190

yes

characteristic, complemented, Sylow

119

C₂³×C₈

—

120

C₂×C₄×D₄

—

121

C₂²×C₁₆

—

122

C₂²×C₁₆

C₂×D₇₃

yes

—

123

C₈×D₄

—

146

—

124

C₈×D₄

—

146

—

125

C₂×C₄⋊C₈

—

126

C₂×C₂²⋊C₈

—

127

C₂×C₄×C₈

C₂×D₇₃

yes

characteristic

128

C₄⋊C₁₆

—

146

—

129

C₂²⋊C₁₆

—

146

—

130

#346

—

131

C₂²×D₄

—

132

C₂³×C₄

—

133

C₂²×C₈

—

134

C₂²×C₈

—

146

—

135

C₂²×C₈

—

146

—

136

C₂²×C₈

—

146

—

137

C₂²×C₈

—

146

—

138

C₂²×C₈

C₄×D₇₃

yes

characteristic

139

C₂²×C₈

C₂²×D₇₃

yes

characteristic

140

C₄×D₄

—

146

—

141

C₄×D₄

—

146

—

142

C₂×C₄⋊C₄

—

143

C₂×C₂²⋊C₄

—

144

C₂×C₄²

C₄×D₇₃

yes

characteristic

145

C₂×C₁₆

—

146

C₂×C₁₆

—

147

C₂×C₁₆

—

146

—

148

C₂×C₁₆

—

146

—

149

C₂×C₁₆

D₂₉₂

yes

complemented

150

C₄⋊C₈

—

146

—

151

C₂²⋊C₈

—

146

—

152

C₄×C₈

D₂₉₂

yes

—

153

C₄×C₈

C₂²⋊D₇₃

yes

—

154

C₂⁴

—

155

C₂×D₄

—

146

—

156

C₂×D₄

—

146

—

157

C₂²×C₄

—

158

C₂²×C₄

—

146

—

159

C₂²×C₄

—

146

—

160

C₂²×C₄

—

146

—

161

C₂²×C₄

—

146

—

162

C₂²×C₄

C₈×D₇₃

yes

characteristic

163

C₂²×C₄

C₈×D₇₃

yes

characteristic

164

C₂²×C₄

C₂×C₄×D₇₃

yes

characteristic

165

C₂×C₈

—

166

C₂×C₈

—

292

—

167

C₂×C₈

—

292

—

168

C₂×C₈

—

292

—

169

C₂×C₈

—

146

—

170

C₂×C₈

—

146

—

171

C₂×C₈

#11924005

yes

—

172

C₂×C₈

C₂×C₂²⋊D₇₃

yes

characteristic

173

C₂×C₈

C₂×D₂₉₂

yes

—

174

C₂×C₈

C₂×D₂₉₂

yes

characteristic

175

C₂×C₈

#11924028

yes

—

176

C₄⋊C₄

—

146

—

177

C₂²⋊C₄

—

146

—

178

C₄²

#11924005

yes

—

179

C₄²

#11924011

yes

—

180

C₁₆

—

181

C₁₆

—

292

—

182

C₂³

—

183

C₂³

—

146

—

184

C₂³

—

146

—

185

C₂³

—

146

—

186

C₂³

—

146

—

187

C₂³

C₂×C₈×D₇₃

yes

characteristic

188

D₄

—

146

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

292

—

192

C₂×C₄

—

292

—

193

C₂×C₄

—

292

—

194

C₂×C₄

—

146

—

195

C₂×C₄

—

146

—

196

C₂×C₄

#14556503

yes

—

197

C₂×C₄

#14556503

yes

—

198

C₂×C₄

C₂×#11924005

yes

characteristic

199

C₂×C₄

C₄×D₂₉₂

yes

—

200

C₂×C₄

C₂×#11924011

yes

characteristic

201

C₂×C₄

#14556597

yes

—

202

C₈

—

203

C₈

—

292

—

204

C₈

#14556565

yes

—

205

C₈

#14556579

yes

characteristic

206

C₈

#14556588

yes

characteristic

207

C₂²

—

292

—

208

C₂²

—

292

—

209

C₂²

—

292

—

210

C₂²

—

146

—

211

C₂²

—

146

—

212

C₂²

C₂×#14556503

yes

characteristic

213

C₂²

C₈×D₂₉₂

yes

—

214

C₂²

M₃₂×D₇₃

yes

—

215

C₂²

#17989005

yes

—

216

C₄

—

217

C₄

—

218

C₄

—

292

—

219

C₄

#17988489

yes

characteristic

220

C₄

#17988553

yes

characteristic

221

C₄

#17988666

yes

—

222

C₂

—

292

—

223

C₂

#22610725

yes

characteristic

224

C₂

#22611541

yes

characteristic

225

C₂

#22611546

yes

characteristic

226

C₂

#22611758

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₇₃
commutator, socle	C₂³×C₇₃	C₂²×C₈
Fitting	C₂×#346×C₇₃	C₂
prime radical	C₂²×D₂₉₂	C₈
cosocle	C₂²×C₈×C₇₃	C₂³
hypercenter	C₂×#346	D₇₃
hypocenter	C₇₃	#13190
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×#346

subgroup

G/H

center, Frattini

C₂²×C₈

C₂²×D₇₃

commutator, socle

C₂³×C₇₃

C₂²×C₈

Fitting

C₂×#346×C₇₃

C₂

prime radical

C₂²×D₂₉₂

C₈

cosocle

C₂²×C₈×C₇₃

C₂³

D₇₃

C₇₃

G ▷ C₂³×C₇₃ ▷ C₇₃

C₁ ◁ C₂²×C₈ ◁ C₂×#346

N	H ≅ G/N	type
2. C₂×C₄⋊#11924003	C₂	semidirect
3. C₂×#17988366	C₂	semidirect
4. C₂×#346×C₇₃	C₂	semidirect
37. C₂×C₁₆×C₇₃	D₄	semidirect
117. C₂×#346	D₇₃	semidirect
118. C₇₃	#13190	semidirect
149. C₂×C₁₆	D₂₉₂	semidirect

H ≅ G/N

type

2. C₂×C₄⋊#11924003

C₂

semidirect

3. C₂×#17988366

C₂

semidirect

4. C₂×#346×C₇₃

C₂

semidirect

37. C₂×C₁₆×C₇₃

D₄

semidirect

117. C₂×#346

D₇₃

semidirect

118. C₇₃

#13190

semidirect

149. C₂×C₁₆

D₂₉₂

semidirect

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

subgroup	index
C₂×C₈×D₂₉₂	2
C₂×C₄⋊#11924003	2
C₂×#17988366	2
C₂×#346×C₇₃	2
#13190	73

subgroup

index

C₂×C₈×D₂₉₂

C₂×C₄⋊#11924003

C₂×#17988366

C₂×#346×C₇₃

#13190

Subgroups — #33004143

Conjugacy classes of subgroups

Complements

Maximal subgroups