Group #33292541 — subgroups

Subgroups — C₂×#22617971 #33292541

Order 18688.

3666 conjugacy classes of subgroups; only the 667 normal subgroups are shown.

normal subgroups only

This group has 3666 conjugacy classes of subgroups — too many to draw. Only its 667 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	C₂²×#14556588	C₂	1	1	yes	maximal, characteristic, complemented
2	#22617971	C₂	1	16	yes	maximal, direct product factor
3	C₂×#17988504	C₂	1	6	yes	maximal, complemented
4	C₂×#17988496	C₂	1	6	yes	maximal, complemented
5	C₂×#17988455	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#126×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×D₂₉₂	C₂²	1	6	yes	—
8	C₂³×C₂²⋊D₇₃	C₂²	1	4	yes	—
9	C₂×#14556588	—	2	8	no	—
10	C₂×#14556588	C₂²	1	8	yes	complemented
11	C₂²×#11924005	C₂²	1	12	yes	—
12	#17988504	C₂²	1	48	yes	complemented
13	#17988496	C₂²	1	48	yes	complemented
14	#17988455	C₂²	1	8	yes	complemented
15	C₂×#14556498	C₂²	1	6	yes	—
16	C₂×#126×C₇₃	—	2	8	no	—
17	C₂×#126×C₇₃	C₂²	1	8	yes	complemented
18	C₂²×C₄⋊C₄×C₇₃	C₂²	1	3	yes	—
19	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	3	yes	—
20	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
21	C₂⁴×D₇₃	C₂³	1	4	yes	—
22	C₂²×D₂₉₂	—	2	24	no	—
23	C₂²×D₂₉₂	—	4	24	no	—
24	C₂²×D₂₉₂	C₂³	1	24	yes	—
25	C₂²×C₂²⋊D₇₃	—	4	24	no	—
26	C₂²×C₂²⋊D₇₃	C₂³	1	16	yes	—
27	C₂³×Dic₇₃	C₂³	1	4	yes	—
28	#14556588	—	2	32	no	—
29	C₂×#11924005	—	4	24	no	—
30	C₂×#11924005	C₂³	1	48	yes	—
31	#14556498	C₂³	1	24	yes	—
32	C₂⁵×C₇₃	C₂³	1	1	yes	characteristic
33	C₂³×C₄×C₇₃	C₂³	1	3	yes	—
34	C₂³×C₄×C₇₃	C₂³	1	3	yes	—
35	#126×C₇₃	—	2	32	no	—
36	C₂×C₄⋊C₄×C₇₃	—	2	12	no	—
37	C₂×C₄⋊C₄×C₇₃	C₂³	1	12	yes	—
38	C₂×C₂²⋊C₄×C₇₃	—	2	12	no	—
39	C₂×C₂²⋊C₄×C₇₃	C₂³	1	12	yes	—
40	C₂×C₄²×C₇₃	D₄	1	8	yes	complemented
41	C₂×C₄²×C₇₃	C₂³	1	4	yes	—
42	C₂³×D₇₃	—	2	8	no	—
43	C₂³×D₇₃	—	2	24	no	—
44	C₂³×D₇₃	—	2	24	no	—
45	C₂³×D₇₃	C₂⁴	1	8	yes	—
46	C₂×D₂₉₂	—	2	48	no	—
47	C₂×D₂₉₂	—	4	48	no	—
48	C₂×D₂₉₂	—	4	96	no	—
49	C₂×C₂²⋊D₇₃	—	4	48	no	—
50	C₂×C₂²⋊D₇₃	—	4	64	no	—
51	C₂²×Dic₇₃	—	2	24	no	—
52	C₂²×Dic₇₃	C₂⁴	1	8	yes	—
53	#11924005	—	4	48	no	—
54	C₂⁴×C₇₃	—	2	2	no	—
55	C₂⁴×C₇₃	—	2	12	no	—
56	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
57	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
58	C₂²×C₄×C₇₃	—	2	12	no	—
59	C₂²×C₄×C₇₃	—	2	6	no	—
60	C₂²×C₄×C₇₃	—	2	12	no	—
61	C₂²×C₄×C₇₃	C₂×D₄	1	12	yes	—
62	C₂²×C₄×C₇₃	C₂⁴	1	6	yes	—
63	C₂²×C₄×C₇₃	C₂⁴	1	6	yes	—
64	C₄⋊C₄×C₇₃	—	2	24	no	—
65	C₂²⋊C₄×C₇₃	—	2	24	no	—
66	C₄²×C₇₃	C₂×D₄	1	16	yes	complemented
67	C₂³×C₇₃	—	2	2	no	—
68	C₂³×C₇₃	—	2	12	no	—
69	C₂³×C₇₃	—	4	12	no	—
70	C₂³×C₇₃	—	4	16	no	—
71	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
72	C₂³×C₇₃	H(5,𝔽₂)	1	12	yes	—
73	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
74	C₂²×D₇₃	—	2	8	no	—
75	C₂²×D₇₃	—	2	24	no	—
76	C₂²×D₇₃	—	2	24	no	—
77	C₂²×D₇₃	—	4	48	no	—
78	C₂²×D₇₃	—	4	16	no	—
79	C₂²×D₇₃	—	4	48	no	—
80	C₂×C₄×C₇₃	—	2	24	no	—
81	C₂×C₄×C₇₃	—	2	12	no	—
82	C₂×C₄×C₇₃	—	2	6	no	—
83	C₂×C₄×C₇₃	—	2	12	no	—
84	C₂×C₄×C₇₃	—	4	12	no	—
85	C₂×C₄×C₇₃	C₂²×D₄	1	12	yes	—
86	C₂²⋊D₇₃	—	4	64	no	—
87	C₂×Dic₇₃	—	2	24	no	—
88	C₂×Dic₇₃	—	4	16	no	—
89	D₂₉₂	—	4	96	no	—
90	C₂²×C₇₃	—	4	6	no	—
91	C₂²×C₇₃	—	4	8	no	—
92	C₂²×C₇₃	—	8	8	no	—
93	C₂²×C₇₃	#535	1	12	yes	—
94	C₂²×C₇₃	#560	1	16	yes	—
95	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
96	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	6	yes	—
97	C₂×D₇₃	—	4	24	no	—
98	C₂×D₇₃	—	4	8	no	—
99	C₂×D₇₃	—	4	24	no	—
100	C₂×D₇₃	—	8	32	no	—
101	C₄×C₇₃	—	2	12	no	—
102	C₄×C₇₃	—	4	6	no	—
103	Dic₇₃	—	4	8	no	—
104	C₂×#2818	—	73	1	no	maximal, Sylow
105	C₂×C₇₃	—	8	2	no	—
106	C₂×C₇₃	#2818	1	8	yes	complemented
107	C₂×C₇₃	C₂×#535	1	3	yes	—
108	C₂×C₇₃	C₂×#560	1	4	yes	—
109	D₇₃	—	8	8	no	—
110	C₂²×#127	—	73	1	no	—
111	C₂²×#126	D₇₃	1	1	yes	characteristic, complemented
112	#2818	—	73	16	no	—
113	C₂×#394	—	73	6	no	—
114	C₂×#392	—	73	6	no	—
115	C₂×#383	—	73	1	no	—
116	C₇₃	C₂×#2818	1	1	yes	characteristic, complemented, Sylow
117	C₂³×D₄	—	73	4	no	—
118	C₂³×D₄	—	73	6	no	—
119	C₂×#127	—	73	8	no	—
120	C₂×#127	—	146	8	no	—
121	C₂×#126	—	2	8	no	—
122	C₂×#126	C₂×D₇₃	1	8	yes	complemented
123	C₂²×C₄⋊C₄	C₂×D₇₃	1	3	yes	—
124	C₂²×C₂²⋊C₄	—	73	12	no	—
125	C₂²×C₂²⋊C₄	C₂×D₇₃	1	3	yes	—
126	C₂²×C₄²	C₂×D₇₃	1	1	yes	characteristic
127	#394	—	73	48	no	—
128	#392	—	73	48	no	—
129	#383	—	73	8	no	—
130	C₂×#95	—	73	6	no	—
131	C₂⁵	—	73	4	no	—
132	C₂⁵	C₂²×D₇₃	1	1	yes	characteristic
133	C₂²×D₄	—	292	24	no	—
134	C₂²×D₄	—	292	24	no	—
135	C₂²×D₄	—	73	16	no	—
136	C₂²×D₄	—	73	24	no	—
137	C₂²×D₄	—	146	24	no	—
138	C₂³×C₄	—	73	4	no	—
139	C₂³×C₄	C₂²×D₇₃	1	3	yes	—
140	C₂³×C₄	C₂²×D₇₃	1	3	yes	—
141	#127	—	146	32	no	—
142	#126	—	2	32	no	—
143	C₂×C₄⋊C₄	—	2	12	no	—
144	C₂×C₄⋊C₄	C₂²×D₇₃	1	12	yes	—
145	C₂×C₂²⋊C₄	—	2	12	no	—
146	C₂×C₂²⋊C₄	—	292	24	no	—
147	C₂×C₂²⋊C₄	—	73	48	no	—
148	C₂×C₂²⋊C₄	C₂²×D₇₃	1	12	yes	—
149	C₂×C₄²	C₂²⋊D₇₃	1	8	yes	complemented
150	C₂×C₄²	C₂²×D₇₃	1	4	yes	—
151	#95	—	73	24	no	—
152	C₂⁴	—	2	2	no	—
153	C₂⁴	—	2	12	no	—
154	C₂⁴	—	73	8	no	—
155	C₂⁴	—	146	8	no	—
156	C₂⁴	—	146	24	no	—
157	C₂⁴	—	146	24	no	—
158	C₂⁴	C₂³×D₇₃	1	2	yes	—
159	C₂⁴	C₂³×D₇₃	1	1	yes	characteristic
160	C₂×D₄	—	292	96	no	—
161	C₂×D₄	—	292	48	no	—
162	C₂×D₄	—	292	64	no	—
163	C₂×D₄	—	292	48	no	—
164	C₂×D₄	—	146	48	no	—
165	C₂²×C₄	—	2	12	no	—
166	C₂²×C₄	—	2	6	no	—
167	C₂²×C₄	—	2	12	no	—
168	C₂²×C₄	—	73	8	no	—
169	C₂²×C₄	—	146	24	no	—
170	C₂²×C₄	C₂×C₂²⋊D₇₃	1	12	yes	—
171	C₂²×C₄	C₂³×D₇₃	1	6	yes	—
172	C₂²×C₄	C₂³×D₇₃	1	6	yes	—
173	C₄⋊C₄	—	2	24	no	—
174	C₂²⋊C₄	—	2	24	no	—
175	C₂²⋊C₄	—	292	48	no	—
176	C₄²	C₂×C₂²⋊D₇₃	1	16	yes	complemented
177	C₂³	—	2	2	no	—
178	C₂³	—	2	12	no	—
179	C₂³	—	4	12	no	—
180	C₂³	—	4	16	no	—
181	C₂³	—	292	48	no	—
182	C₂³	—	292	16	no	—
183	C₂³	—	292	48	no	—
184	C₂³	—	146	8	no	—
185	C₂³	—	146	24	no	—
186	C₂³	—	146	24	no	—
187	C₂³	C₂²×C₂²⋊D₇₃	1	2	yes	—
188	C₂³	#14556637	1	12	yes	—
189	C₂³	C₂⁴×D₇₃	1	1	yes	characteristic
190	D₄	—	292	96	no	—
191	D₄	—	292	64	no	—
192	C₂×C₄	—	2	24	no	—
193	C₂×C₄	—	2	12	no	—
194	C₂×C₄	—	2	6	no	—
195	C₂×C₄	—	2	12	no	—
196	C₂×C₄	—	4	12	no	—
197	C₂×C₄	—	292	16	no	—
198	C₂×C₄	—	146	24	no	—
199	C₂×C₄	C₂²×C₂²⋊D₇₃	1	12	yes	—
200	C₂²	—	4	6	no	—
201	C₂²	—	4	8	no	—
202	C₂²	—	8	8	no	—
203	C₂²	—	292	24	no	—
204	C₂²	—	292	8	no	—
205	C₂²	—	292	24	no	—
206	C₂²	—	584	32	no	—
207	C₂²	#17989151	1	12	yes	—
208	C₂²	#17989328	1	16	yes	—
209	C₂²	C₂³×C₂²⋊D₇₃	1	1	yes	characteristic
210	C₂²	C₂×#14556637	1	6	yes	—
211	C₄	—	2	12	no	—
212	C₄	—	4	6	no	—
213	C₄	—	292	8	no	—
214	C₂	—	8	2	no	—
215	C₂	—	584	8	no	—
216	C₂	#22617971	1	8	yes	direct product factor
217	C₂	C₂×#17989151	1	3	yes	—
218	C₂	C₂×#17989328	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#14556588

C₂

yes

maximal, characteristic, complemented

#22617971

C₂

yes

maximal, direct product factor

C₂×#17988504

C₂

yes

maximal, complemented

C₂×#17988496

C₂

yes

maximal, complemented

C₂×#17988455

C₂

yes

maximal, characteristic, complemented

C₂²×#126×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂³×D₂₉₂

C₂²

yes

—

C₂³×C₂²⋊D₇₃

C₂²

yes

—

C₂×#14556588

—

C₂×#14556588

C₂²

yes

complemented

C₂²×#11924005

C₂²

yes

—

#17988504

C₂²

yes

complemented

#17988496

C₂²

yes

complemented

#17988455

C₂²

yes

complemented

C₂×#14556498

C₂²

yes

—

C₂×#126×C₇₃

—

C₂×#126×C₇₃

C₂²

yes

complemented

C₂²×C₄⋊C₄×C₇₃

C₂²

yes

—

C₂²×C₂²⋊C₄×C₇₃

C₂²

yes

—

C₂²×C₄²×C₇₃

C₂²

yes

characteristic

C₂⁴×D₇₃

C₂³

yes

—

C₂²×D₂₉₂

—

C₂²×D₂₉₂

—

C₂²×D₂₉₂

C₂³

yes

—

C₂²×C₂²⋊D₇₃

—

C₂²×C₂²⋊D₇₃

C₂³

yes

—

C₂³×Dic₇₃

C₂³

yes

—

#14556588

—

C₂×#11924005

—

C₂×#11924005

C₂³

yes

—

#14556498

C₂³

yes

—

C₂⁵×C₇₃

C₂³

yes

characteristic

C₂³×C₄×C₇₃

C₂³

yes

—

C₂³×C₄×C₇₃

C₂³

yes

—

#126×C₇₃

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

C₂³

yes

—

C₂×C₂²⋊C₄×C₇₃

—

C₂×C₂²⋊C₄×C₇₃

C₂³

yes

—

C₂×C₄²×C₇₃

D₄

yes

complemented

C₂×C₄²×C₇₃

C₂³

yes

—

C₂³×D₇₃

—

C₂³×D₇₃

—

C₂³×D₇₃

—

C₂³×D₇₃

C₂⁴

yes

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×C₂²⋊D₇₃

—

C₂×C₂²⋊D₇₃

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

C₂⁴

yes

—

#11924005

—

C₂⁴×C₇₃

—

C₂⁴×C₇₃

—

C₂⁴×C₇₃

C₂⁴

yes

—

C₂⁴×C₇₃

C₂⁴

yes

characteristic

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂×D₄

yes

—

C₂²×C₄×C₇₃

C₂⁴

yes

—

C₂²×C₄×C₇₃

C₂⁴

yes

—

C₄⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

C₂×D₄

yes

complemented

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

C₂²×D₄

yes

—

C₂³×C₇₃

H(5,𝔽₂)

yes

—

C₂³×C₇₃

C₂⁵

yes

characteristic

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²×D₄

yes

—

C₂²⋊D₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

D₂₉₂

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#535

yes

—

C₂²×C₇₃

#560

yes

—

C₂²×C₇₃

C₂³×D₄

yes

characteristic

C₂²×C₇₃

C₂×H(5,𝔽₂)

yes

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

100

C₂×D₇₃

—

101

C₄×C₇₃

—

102

C₄×C₇₃

—

103

Dic₇₃

—

104

C₂×#2818

—

maximal, Sylow

105

C₂×C₇₃

—

106

C₂×C₇₃

#2818

yes

complemented

107

C₂×C₇₃

C₂×#535

yes

—

108

C₂×C₇₃

C₂×#560

yes

—

109

D₇₃

—

110

C₂²×#127

—

111

C₂²×#126

D₇₃

yes

characteristic, complemented

112

#2818

—

113

C₂×#394

—

114

C₂×#392

—

115

C₂×#383

—

116

C₇₃

C₂×#2818

yes

characteristic, complemented, Sylow

117

C₂³×D₄

—

118

C₂³×D₄

—

119

C₂×#127

—

120

C₂×#127

—

146

—

121

C₂×#126

—

122

C₂×#126

C₂×D₇₃

yes

complemented

123

C₂²×C₄⋊C₄

C₂×D₇₃

yes

—

124

C₂²×C₂²⋊C₄

—

125

C₂²×C₂²⋊C₄

C₂×D₇₃

yes

—

126

C₂²×C₄²

C₂×D₇₃

yes

characteristic

127

#394

—

128

#392

—

129

#383

—

130

C₂×#95

—

131

C₂⁵

—

132

C₂⁵

C₂²×D₇₃

yes

characteristic

133

C₂²×D₄

—

292

—

134

C₂²×D₄

—

292

—

135

C₂²×D₄

—

136

C₂²×D₄

—

137

C₂²×D₄

—

146

—

138

C₂³×C₄

—

139

C₂³×C₄

C₂²×D₇₃

yes

—

140

C₂³×C₄

C₂²×D₇₃

yes

—

141

#127

—

146

—

142

#126

—

143

C₂×C₄⋊C₄

—

144

C₂×C₄⋊C₄

C₂²×D₇₃

yes

—

145

C₂×C₂²⋊C₄

—

146

C₂×C₂²⋊C₄

—

292

—

147

C₂×C₂²⋊C₄

—

148

C₂×C₂²⋊C₄

C₂²×D₇₃

yes

—

149

C₂×C₄²

C₂²⋊D₇₃

yes

complemented

150

C₂×C₄²

C₂²×D₇₃

yes

—

151

#95

—

152

C₂⁴

—

153

C₂⁴

—

154

C₂⁴

—

155

C₂⁴

—

146

—

156

C₂⁴

—

146

—

157

C₂⁴

—

146

—

158

C₂⁴

C₂³×D₇₃

yes

—

159

C₂⁴

C₂³×D₇₃

yes

characteristic

160

C₂×D₄

—

292

—

161

C₂×D₄

—

292

—

162

C₂×D₄

—

292

—

163

C₂×D₄

—

292

—

164

C₂×D₄

—

146

—

165

C₂²×C₄

—

166

C₂²×C₄

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

—

146

—

170

C₂²×C₄

C₂×C₂²⋊D₇₃

yes

—

171

C₂²×C₄

C₂³×D₇₃

yes

—

172

C₂²×C₄

C₂³×D₇₃

yes

—

173

C₄⋊C₄

—

174

C₂²⋊C₄

—

175

C₂²⋊C₄

—

292

—

176

C₄²

C₂×C₂²⋊D₇₃

yes

complemented

177

C₂³

—

178

C₂³

—

179

C₂³

—

180

C₂³

—

181

C₂³

—

292

—

182

C₂³

—

292

—

183

C₂³

—

292

—

184

C₂³

—

146

—

185

C₂³

—

146

—

186

C₂³

—

146

—

187

C₂³

C₂²×C₂²⋊D₇₃

yes

—

188

C₂³

#14556637

yes

—

189

C₂³

C₂⁴×D₇₃

yes

characteristic

190

D₄

—

292

—

191

D₄

—

292

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

292

—

198

C₂×C₄

—

146

—

199

C₂×C₄

C₂²×C₂²⋊D₇₃

yes

—

200

C₂²

—

201

C₂²

—

202

C₂²

—

203

C₂²

—

292

—

204

C₂²

—

292

—

205

C₂²

—

292

—

206

C₂²

—

584

—

207

C₂²

#17989151

yes

—

208

C₂²

#17989328

yes

—

209

C₂²

C₂³×C₂²⋊D₇₃

yes

characteristic

210

C₂²

C₂×#14556637

yes

—

211

C₄

—

212

C₄

—

213

C₄

—

292

—

214

C₂

—

215

C₂

—

584

—

216

C₂

#22617971

yes

direct product factor

217

C₂

C₂×#17989151

yes

—

218

C₂

C₂×#17989328

yes

—

	subgroup	G/H
center	C₂⁴	C₂³×D₇₃
commutator, cosocle	C₂³×C₇₃	C₂⁵
Frattini	C₂³	C₂⁴×D₇₃
Fitting	C₂²×#126×C₇₃	C₂
socle	C₂⁴×C₇₃	C₂⁴
hypercenter	C₂²×#126	D₇₃
hypocenter	C₇₃	C₂×#2818
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×#126

subgroup

G/H

center

C₂⁴

C₂³×D₇₃

commutator, cosocle

C₂³×C₇₃

C₂⁵

Frattini

C₂³

C₂⁴×D₇₃

Fitting

C₂²×#126×C₇₃

C₂

socle

C₂⁴×C₇₃

C₂⁴

hypercenter

C₂²×#126

D₇₃

C₇₃

G ▷ C₂³×C₇₃ ▷ C₇₃

C₁ ◁ C₂⁴ ◁ C₂²×#126

N	H ≅ G/N	type
1. C₂²×#14556588	C₂	semidirect
2. #22617971	C₂	direct (N × H)
3. C₂×#17988504	C₂	semidirect
4. C₂×#17988496	C₂	semidirect
5. C₂×#17988455	C₂	semidirect
6. C₂²×#126×C₇₃	C₂	semidirect
10. C₂×#14556588	C₂²	semidirect
12. #17988504	C₂²	semidirect
13. #17988496	C₂²	semidirect
14. #17988455	C₂²	semidirect
17. C₂×#126×C₇₃	C₂²	semidirect
40. C₂×C₄²×C₇₃	D₄	semidirect
66. C₄²×C₇₃	C₂×D₄	semidirect
106. C₂×C₇₃	#2818	semidirect
111. C₂²×#126	D₇₃	semidirect
116. C₇₃	C₂×#2818	semidirect
122. C₂×#126	C₂×D₇₃	semidirect
149. C₂×C₄²	C₂²⋊D₇₃	semidirect
176. C₄²	C₂×C₂²⋊D₇₃	semidirect
216. C₂	#22617971	direct (N × H)

H ≅ G/N

type

1. C₂²×#14556588

C₂

semidirect

2. #22617971

C₂

direct (N × H)

3. C₂×#17988504

C₂

semidirect

4. C₂×#17988496

C₂

semidirect

5. C₂×#17988455

C₂

semidirect

6. C₂²×#126×C₇₃

C₂

semidirect

10. C₂×#14556588

C₂²

semidirect

12. #17988504

C₂²

semidirect

13. #17988496

C₂²

semidirect

14. #17988455

C₂²

semidirect

17. C₂×#126×C₇₃

C₂²

semidirect

40. C₂×C₄²×C₇₃

D₄

semidirect

66. C₄²×C₇₃

C₂×D₄

semidirect

106. C₂×C₇₃

#2818

semidirect

111. C₂²×#126

D₇₃

semidirect

116. C₇₃

C₂×#2818

semidirect

122. C₂×#126

C₂×D₇₃

semidirect

149. C₂×C₄²

C₂²⋊D₇₃

semidirect

176. C₄²

C₂×C₂²⋊D₇₃

semidirect

216. C₂

#22617971

direct (N × H)

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

subgroup	index
C₂²×#14556588	2
#22617971	2
C₂×#17988504	2
C₂×#17988496	2
C₂×#17988455	2
C₂²×#126×C₇₃	2
C₂×#2818	73

subgroup

index

C₂²×#126×C₇₃

Subgroups — C₂×#22617971 #33292541

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#22617971 #33292541

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22617971 #33292541