Group #32943330 — subgroups

Subgroups — C₇₃×#33926 #32943330

Order 18688.

506 conjugacy classes of subgroups; only the 218 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 218 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	C₇₃×#3395	C₂	1	1	yes	maximal, characteristic, complemented
2	Q₈×D₈×C₇₃	C₂	1	1	yes	maximal, characteristic
3	C₇₃×#2241	C₂	1	3	yes	maximal, complemented
4	C₇₃×#2225	C₂	1	3	yes	maximal, complemented
5	C₇₃×#2208	C₂	1	3	yes	maximal
6	Q₈×C₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×SD₃₂×C₇₃	C₂	1	3	yes	maximal
8	#557×C₇₃	—	2	1	no	—
9	D₄×Q₈×C₇₃	—	2	1	no	—
10	C₂×SD₃₂×C₇₃	C₂²	1	3	yes	—
11	#500×C₇₃	C₂²	1	3	yes	—
12	#494×C₇₃	C₂²	1	3	yes	—
13	#474×C₇₃	—	2	3	no	—
14	#462×C₇₃	—	2	3	no	—
15	C₈×Q₈×C₇₃	C₂²	1	1	yes	characteristic
16	C₄×Q₁₆×C₇₃	C₂²	1	3	yes	—
17	C₄×D₈×C₇₃	C₂²	1	3	yes	—
18	#367×C₇₃	C₂²	1	3	yes	—
19	C₄⋊C₁₆×C₇₃	C₂²	1	3	yes	—
20	#358×C₇₃	C₂²	1	6	yes	—
21	#358×C₇₃	C₂²	1	3	yes	—
22	#357×C₇₃	C₂²	1	1	yes	characteristic
23	C₄×C₁₆×C₇₃	C₂²	1	3	yes	—
24	C₂²×Q₈×C₇₃	—	4	1	no	—
25	C₂×Q₁₆×C₇₃	—	2	3	no	—
26	C₂×Q₁₆×C₇₃	C₂³	1	3	yes	—
27	C₂×D₈×C₇₃	C₂³	1	1	yes	characteristic
28	C₄⋊Q₈×C₇₃	—	2	3	no	—
29	C₄⋊Q₈×C₇₃	—	2	3	no	—
30	#125×C₇₃	—	4	3	no	—
31	C₂²⋊Q₈×C₇₃	—	4	3	no	—
32	C₄×Q₈×C₇₃	—	2	3	no	—
33	C₄×Q₈×C₇₃	—	4	1	no	—
34	C₄×Q₈×C₇₃	D₄	1	1	yes	characteristic
35	C₄×D₄×C₇₃	—	2	3	no	—
36	SD₃₂×C₇₃	—	2	6	no	—
37	C₂×C₁₆×C₇₃	C₂³	1	3	yes	—
38	C₂×C₁₆×C₇₃	C₂³	1	1	yes	characteristic
39	#107×C₇₃	—	2	3	no	—
40	#107×C₇₃	C₂³	1	3	yes	—
41	#107×C₇₃	C₂³	1	1	yes	characteristic
42	C₄⋊C₈×C₇₃	D₄	1	3	yes	—
43	#103×C₇₃	—	2	3	no	—
44	#102×C₇₃	—	2	3	no	—
45	C₄×C₈×C₇₃	C₂³	1	3	yes	—
46	C₂×Q₈×C₇₃	—	2	3	no	—
47	C₂×Q₈×C₇₃	—	4	3	no	—
48	C₂×Q₈×C₇₃	—	8	4	no	—
49	C₂×Q₈×C₇₃	D₈	1	1	yes	characteristic
50	C₂×D₄×C₇₃	—	2	1	no	—
51	C₂²×C₄×C₇₃	—	4	3	no	—
52	Q₁₆×C₇₃	—	2	3	no	—
53	Q₁₆×C₇₃	—	2	3	no	—
54	Q₁₆×C₇₃	—	8	3	no	—
55	D₈×C₇₃	—	2	1	no	—
56	D₈×C₇₃	#41	1	2	yes	—
57	C₂×C₈×C₇₃	C₂×D₄	1	3	yes	—
58	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
59	C₄⋊C₄×C₇₃	—	2	3	no	—
60	C₄⋊C₄×C₇₃	—	2	1	no	—
61	C₄⋊C₄×C₇₃	—	4	3	no	—
62	C₄⋊C₄×C₇₃	—	4	3	no	—
63	C₄⋊C₄×C₇₃	—	4	3	no	—
64	C₄⋊C₄×C₇₃	—	4	3	no	—
65	C₄⋊C₄×C₇₃	D₈	1	3	yes	—
66	C₂²⋊C₄×C₇₃	—	4	3	no	—
67	C₄²×C₇₃	—	4	3	no	—
68	C₄²×C₇₃	C₂×D₄	1	3	yes	—
69	C₁₆×C₇₃	—	2	3	no	—
70	C₁₆×C₇₃	—	2	1	no	—
71	C₂³×C₇₃	—	4	1	no	—
72	Q₈×C₇₃	—	4	3	no	—
73	Q₈×C₇₃	—	4	3	no	—
74	Q₈×C₇₃	—	8	6	no	—
75	Q₈×C₇₃	SD₃₂	1	4	yes	complemented
76	D₄×C₇₃	—	2	2	no	—
77	D₄×C₇₃	—	4	1	no	—
78	C₂×C₄×C₇₃	—	4	1	no	—
79	C₂×C₄×C₇₃	—	4	3	no	—
80	C₂×C₄×C₇₃	—	4	3	no	—
81	C₂×C₄×C₇₃	—	8	6	no	—
82	C₂×C₄×C₇₃	C₂×D₈	1	3	yes	—
83	C₂×C₄×C₇₃	C₂×D₈	1	3	yes	—
84	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
85	C₈×C₇₃	—	2	3	no	—
86	C₈×C₇₃	C₂×#41	1	1	yes	characteristic
87	C₈×C₇₃	2₋¹⁺⁴	1	1	yes	characteristic
88	C₂²×C₇₃	—	4	2	no	—
89	C₂²×C₇₃	—	8	1	no	—
90	C₂²×C₇₃	—	8	1	no	—
91	C₂²×C₇₃	C₂²×D₈	1	1	yes	characteristic
92	C₄×C₇₃	—	2	3	no	—
93	C₄×C₇₃	—	8	3	no	—
94	C₄×C₇₃	—	8	3	no	—
95	C₄×C₇₃	—	8	1	no	—
96	C₄×C₇₃	C₂×SD₃₂	1	6	yes	—
97	C₄×C₇₃	#548	1	1	yes	characteristic
98	C₄×C₇₃	#577	1	1	yes	characteristic
99	#33926	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
100	C₂×C₇₃	—	8	2	no	—
101	C₂×C₇₃	#3358	1	1	yes	characteristic
102	C₂×C₇₃	C₂²×SD₃₂	1	1	yes	characteristic
103	C₂×C₇₃	#3417	1	1	yes	characteristic
104	#3395	C₂×C₇₃	1	1	yes	characteristic, complemented
105	Q₈×D₈	C₂×C₇₃	1	1	yes	characteristic
106	#2241	C₂×C₇₃	1	3	yes	complemented
107	#2225	C₂×C₇₃	1	3	yes	complemented
108	#2208	C₂×C₇₃	1	3	yes	—
109	Q₈×C₁₆	C₂×C₇₃	1	1	yes	characteristic, complemented
110	C₄×SD₃₂	C₂×C₇₃	1	3	yes	—
111	C₇₃	#33926	1	1	yes	characteristic, direct product factor, Sylow
112	#557	—	2	1	no	—
113	D₄×Q₈	—	2	1	no	—
114	C₂×SD₃₂	C₂²×C₇₃	1	3	yes	—
115	#500	C₂²×C₇₃	1	3	yes	—
116	#494	C₂²×C₇₃	1	3	yes	—
117	#474	—	2	3	no	—
118	#462	—	2	3	no	—
119	C₈×Q₈	C₂²×C₇₃	1	1	yes	characteristic
120	C₄×Q₁₆	C₂²×C₇₃	1	3	yes	—
121	C₄×D₈	C₂²×C₇₃	1	3	yes	—
122	#367	C₂²×C₇₃	1	3	yes	—
123	C₄⋊C₁₆	C₂²×C₇₃	1	3	yes	—
124	#358	C₂²×C₇₃	1	3	yes	—
125	#358	C₂²×C₇₃	1	6	yes	—
126	#357	C₂²×C₇₃	1	1	yes	characteristic
127	C₄×C₁₆	C₂²×C₇₃	1	3	yes	—
128	C₂²×Q₈	—	4	1	no	—
129	C₂×Q₁₆	—	2	3	no	—
130	C₂×Q₁₆	C₂³×C₇₃	1	3	yes	—
131	C₂×D₈	C₂³×C₇₃	1	1	yes	characteristic
132	C₄⋊Q₈	—	2	3	no	—
133	C₄⋊Q₈	—	2	3	no	—
134	#125	—	4	3	no	—
135	C₂²⋊Q₈	—	4	3	no	—
136	C₄×Q₈	—	2	3	no	—
137	C₄×Q₈	—	4	1	no	—
138	C₄×Q₈	D₄×C₇₃	1	1	yes	characteristic
139	C₄×D₄	—	2	3	no	—
140	SD₃₂	—	2	6	no	—
141	C₂×C₁₆	C₂³×C₇₃	1	1	yes	characteristic
142	C₂×C₁₆	C₂³×C₇₃	1	3	yes	—
143	#107	—	2	3	no	—
144	#107	C₂³×C₇₃	1	1	yes	characteristic
145	#107	C₂³×C₇₃	1	3	yes	—
146	C₄⋊C₈	D₄×C₇₃	1	3	yes	—
147	#103	—	2	3	no	—
148	#102	—	2	3	no	—
149	C₄×C₈	C₂³×C₇₃	1	3	yes	—
150	C₂×Q₈	—	2	3	no	—
151	C₂×Q₈	—	4	3	no	—
152	C₂×Q₈	—	8	4	no	—
153	C₂×Q₈	D₈×C₇₃	1	1	yes	characteristic
154	C₂×D₄	—	2	1	no	—
155	C₂²×C₄	—	4	3	no	—
156	Q₁₆	—	2	3	no	—
157	Q₁₆	—	2	3	no	—
158	Q₁₆	—	8	3	no	—
159	D₈	—	2	1	no	—
160	D₈	#41×C₇₃	1	2	yes	—
161	C₂×C₈	C₂×D₄×C₇₃	1	3	yes	—
162	C₂×C₈	C₂⁴×C₇₃	1	1	yes	characteristic
163	C₄⋊C₄	—	2	3	no	—
164	C₄⋊C₄	—	2	1	no	—
165	C₄⋊C₄	—	4	3	no	—
166	C₄⋊C₄	—	4	3	no	—
167	C₄⋊C₄	—	4	3	no	—
168	C₄⋊C₄	—	4	3	no	—
169	C₄⋊C₄	D₈×C₇₃	1	3	yes	—
170	C₂²⋊C₄	—	4	3	no	—
171	C₄²	—	4	3	no	—
172	C₄²	C₂×D₄×C₇₃	1	3	yes	—
173	C₁₆	—	2	3	no	—
174	C₁₆	—	2	1	no	—
175	C₂³	—	4	1	no	—
176	Q₈	—	4	3	no	—
177	Q₈	—	4	3	no	—
178	Q₈	—	8	6	no	—
179	Q₈	SD₃₂×C₇₃	1	4	yes	complemented
180	D₄	—	2	2	no	—
181	D₄	—	4	1	no	—
182	C₂×C₄	—	4	1	no	—
183	C₂×C₄	—	4	3	no	—
184	C₂×C₄	—	4	3	no	—
185	C₂×C₄	—	8	6	no	—
186	C₂×C₄	C₂×D₈×C₇₃	1	3	yes	—
187	C₂×C₄	C₂×D₈×C₇₃	1	3	yes	—
188	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
189	C₈	—	2	3	no	—
190	C₈	C₂×#41×C₇₃	1	1	yes	characteristic
191	C₈	2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
192	C₂²	—	4	2	no	—
193	C₂²	—	8	1	no	—
194	C₂²	—	8	1	no	—
195	C₂²	C₂²×D₈×C₇₃	1	1	yes	characteristic
196	C₄	—	2	3	no	—
197	C₄	—	8	3	no	—
198	C₄	—	8	3	no	—
199	C₄	—	8	1	no	—
200	C₄	C₂×SD₃₂×C₇₃	1	6	yes	—
201	C₄	#548×C₇₃	1	1	yes	characteristic
202	C₄	#577×C₇₃	1	1	yes	characteristic
203	C₂	—	8	2	no	—
204	C₂	C₇₃×#3358	1	1	yes	characteristic
205	C₂	C₂²×SD₃₂×C₇₃	1	1	yes	characteristic
206	C₂	C₇₃×#3417	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₇₃×#3395

C₂

yes

maximal, characteristic, complemented

Q₈×D₈×C₇₃

C₂

yes

maximal, characteristic

C₇₃×#2241

C₂

yes

maximal, complemented

C₇₃×#2225

C₂

yes

maximal, complemented

C₇₃×#2208

C₂

yes

maximal

Q₈×C₁₆×C₇₃

C₂

yes

maximal, characteristic, complemented

C₄×SD₃₂×C₇₃

C₂

yes

maximal

#557×C₇₃

—

D₄×Q₈×C₇₃

—

C₂×SD₃₂×C₇₃

C₂²

yes

—

#500×C₇₃

C₂²

yes

—

#494×C₇₃

C₂²

yes

—

#474×C₇₃

—

#462×C₇₃

—

C₈×Q₈×C₇₃

C₂²

yes

characteristic

C₄×Q₁₆×C₇₃

C₂²

yes

—

C₄×D₈×C₇₃

C₂²

yes

—

#367×C₇₃

C₂²

yes

—

C₄⋊C₁₆×C₇₃

C₂²

yes

—

#358×C₇₃

C₂²

yes

—

#358×C₇₃

C₂²

yes

—

#357×C₇₃

C₂²

yes

characteristic

C₄×C₁₆×C₇₃

C₂²

yes

—

C₂²×Q₈×C₇₃

—

C₂×Q₁₆×C₇₃

—

C₂×Q₁₆×C₇₃

C₂³

yes

—

C₂×D₈×C₇₃

C₂³

yes

characteristic

C₄⋊Q₈×C₇₃

—

C₄⋊Q₈×C₇₃

—

#125×C₇₃

—

C₂²⋊Q₈×C₇₃

—

C₄×Q₈×C₇₃

—

C₄×Q₈×C₇₃

—

C₄×Q₈×C₇₃

D₄

yes

characteristic

C₄×D₄×C₇₃

—

SD₃₂×C₇₃

—

C₂×C₁₆×C₇₃

C₂³

yes

—

C₂×C₁₆×C₇₃

C₂³

yes

characteristic

#107×C₇₃

—

#107×C₇₃

C₂³

yes

—

#107×C₇₃

C₂³

yes

characteristic

C₄⋊C₈×C₇₃

D₄

yes

—

#103×C₇₃

—

#102×C₇₃

—

C₄×C₈×C₇₃

C₂³

yes

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

D₈

yes

characteristic

C₂×D₄×C₇₃

—

C₂²×C₄×C₇₃

—

Q₁₆×C₇₃

—

Q₁₆×C₇₃

—

Q₁₆×C₇₃

—

D₈×C₇₃

—

D₈×C₇₃

#41

yes

—

C₂×C₈×C₇₃

C₂×D₄

yes

—

C₂×C₈×C₇₃

C₂⁴

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

D₈

yes

—

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

C₂×D₄

yes

—

C₁₆×C₇₃

—

C₁₆×C₇₃

—

C₂³×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

SD₃₂

yes

complemented

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₈

yes

—

C₂×C₄×C₇₃

C₂×D₈

yes

—

C₂×C₄×C₇₃

C₂²×D₄

yes

characteristic

C₈×C₇₃

—

C₈×C₇₃

C₂×#41

yes

characteristic

C₈×C₇₃

2₋¹⁺⁴

yes

characteristic

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂²×D₈

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₂×SD₃₂

yes

—

C₄×C₇₃

yes

C₄×C₇₃

yes

C₇₃

yes

maximal, characteristic, direct product factor, Sylow

100

C₂×C₇₃

—

101

C₂×C₇₃

#3358

yes

characteristic

102

C₂×C₇₃

C₂²×SD₃₂

yes

characteristic

103

C₂×C₇₃

#3417

yes

characteristic

104

#3395

C₂×C₇₃

yes

characteristic, complemented

105

Q₈×D₈

C₂×C₇₃

yes

characteristic

106

#2241

C₂×C₇₃

yes

complemented

107

#2225

C₂×C₇₃

yes

complemented

108

#2208

C₂×C₇₃

yes

—

109

Q₈×C₁₆

C₂×C₇₃

yes

characteristic, complemented

110

C₄×SD₃₂

C₂×C₇₃

yes

—

111

C₇₃

#33926

yes

characteristic, direct product factor, Sylow

112

#557

—

113

D₄×Q₈

—

114

C₂×SD₃₂

C₂²×C₇₃

yes

—

115

#500

C₂²×C₇₃

yes

—

116

#494

C₂²×C₇₃

yes

—

117

#474

—

118

#462

—

119

C₈×Q₈

C₂²×C₇₃

yes

characteristic

120

C₄×Q₁₆

C₂²×C₇₃

yes

—

121

C₄×D₈

C₂²×C₇₃

yes

—

122

#367

C₂²×C₇₃

yes

—

123

C₄⋊C₁₆

C₂²×C₇₃

yes

—

124

#358

C₂²×C₇₃

yes

—

125

#358

C₂²×C₇₃

yes

—

126

#357

C₂²×C₇₃

yes

characteristic

127

C₄×C₁₆

C₂²×C₇₃

yes

—

128

C₂²×Q₈

—

129

C₂×Q₁₆

—

130

C₂×Q₁₆

C₂³×C₇₃

yes

—

131

C₂×D₈

C₂³×C₇₃

yes

characteristic

132

C₄⋊Q₈

—

133

C₄⋊Q₈

—

134

#125

—

135

C₂²⋊Q₈

—

136

C₄×Q₈

—

137

C₄×Q₈

—

138

C₄×Q₈

D₄×C₇₃

yes

characteristic

139

C₄×D₄

—

140

SD₃₂

—

141

C₂×C₁₆

C₂³×C₇₃

yes

characteristic

142

C₂×C₁₆

C₂³×C₇₃

yes

—

143

#107

—

144

#107

C₂³×C₇₃

yes

characteristic

145

#107

C₂³×C₇₃

yes

—

146

C₄⋊C₈

D₄×C₇₃

yes

—

147

#103

—

148

#102

—

149

C₄×C₈

C₂³×C₇₃

yes

—

150

C₂×Q₈

—

151

C₂×Q₈

—

152

C₂×Q₈

—

153

C₂×Q₈

D₈×C₇₃

yes

characteristic

154

C₂×D₄

—

155

C₂²×C₄

—

156

Q₁₆

—

157

Q₁₆

—

158

Q₁₆

—

159

D₈

—

160

D₈

#41×C₇₃

yes

—

161

C₂×C₈

C₂×D₄×C₇₃

yes

—

162

C₂×C₈

C₂⁴×C₇₃

yes

characteristic

163

C₄⋊C₄

—

164

C₄⋊C₄

—

165

C₄⋊C₄

—

166

C₄⋊C₄

—

167

C₄⋊C₄

—

168

C₄⋊C₄

—

169

C₄⋊C₄

D₈×C₇₃

yes

—

170

C₂²⋊C₄

—

171

C₄²

—

172

C₄²

C₂×D₄×C₇₃

yes

—

173

C₁₆

—

174

C₁₆

—

175

C₂³

—

176

Q₈

—

177

Q₈

—

178

Q₈

—

179

Q₈

SD₃₂×C₇₃

yes

complemented

180

D₄

—

181

D₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

C₂×D₈×C₇₃

yes

—

187

C₂×C₄

C₂×D₈×C₇₃

yes

—

188

C₂×C₄

C₂²×D₄×C₇₃

yes

characteristic

189

C₈

—

190

C₈

C₂×#41×C₇₃

yes

characteristic

191

C₈

2₋¹⁺⁴×C₇₃

yes

characteristic

192

C₂²

—

193

C₂²

—

194

C₂²

—

195

C₂²

C₂²×D₈×C₇₃

yes

characteristic

196

C₄

—

197

C₄

—

198

C₄

—

199

C₄

—

200

C₄

C₂×SD₃₂×C₇₃

yes

—

201

C₄

#548×C₇₃

yes

characteristic

202

C₄

#577×C₇₃

yes

characteristic

203

C₂

—

204

C₂

C₇₃×#3358

yes

characteristic

205

C₂

C₂²×SD₃₂×C₇₃

yes

characteristic

206

C₂

C₇₃×#3417

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₇₃
prime radical	C₂×D₈×C₇₃	C₂³
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₄×Q₈×C₇₃ ◁ C₈×Q₈×C₇₃ ◁ G

subgroup

G/H

center, socle

C₂²×C₇₃

C₂²×D₈

commutator, Frattini, cosocle

C₂×C₈

C₂⁴×C₇₃

prime radical

C₂×D₈×C₇₃

C₂³

LCS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₇₃ ◁ C₄×Q₈×C₇₃ ◁ C₈×Q₈×C₇₃ ◁ G

N	H ≅ G/N	type
1. C₇₃×#3395	C₂	semidirect
3. C₇₃×#2241	C₂	semidirect
4. C₇₃×#2225	C₂	semidirect
6. Q₈×C₁₆×C₇₃	C₂	semidirect
75. Q₈×C₇₃	SD₃₂	semidirect
99. #33926	C₇₃	direct (N × H)
104. #3395	C₂×C₇₃	semidirect
106. #2241	C₂×C₇₃	semidirect
107. #2225	C₂×C₇₃	semidirect
109. Q₈×C₁₆	C₂×C₇₃	semidirect
111. C₇₃	#33926	direct (N × H)
179. Q₈	SD₃₂×C₇₃	semidirect

H ≅ G/N

type

1. C₇₃×#3395

C₂

semidirect

3. C₇₃×#2241

C₂

semidirect

4. C₇₃×#2225

C₂

semidirect

6. Q₈×C₁₆×C₇₃

C₂

semidirect

75. Q₈×C₇₃

SD₃₂

semidirect

99. #33926

C₇₃

direct (N × H)

104. #3395

C₂×C₇₃

semidirect

106. #2241

C₂×C₇₃

semidirect

107. #2225

C₂×C₇₃

semidirect

109. Q₈×C₁₆

C₂×C₇₃

semidirect

111. C₇₃

#33926

direct (N × H)

179. Q₈

SD₃₂×C₇₃

semidirect

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

subgroup	index
C₇₃×#3395	2
Q₈×D₈×C₇₃	2
C₇₃×#2241	2
C₇₃×#2225	2
C₇₃×#2208	2
Q₈×C₁₆×C₇₃	2
C₄×SD₃₂×C₇₃	2
#33926	73

subgroup

index

C₇₃×#3395

Q₈×D₈×C₇₃

C₇₃×#2241

C₇₃×#2225

C₇₃×#2208

Q₈×C₁₆×C₇₃

C₄×SD₃₂×C₇₃

#33926

Subgroups — C₇₃×#33926 #32943330

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C73×#33926 #32943330

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#33926 #32943330