Group #25303154 — subgroups

Subgroups — C₂×#19142635 #25303154

Order 11008.

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×#13063322	C₂	1	1	yes	maximal, characteristic, complemented
2	#19142635	C₂	1	16	yes	maximal, direct product factor
3	C₂×#14582816	C₂	1	6	yes	maximal, complemented
4	C₂×#14582808	C₂	1	6	yes	maximal, complemented
5	C₂×#14582767	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#126×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×D₁₇₂	C₂²	1	6	yes	—
8	C₂³×C₂²⋊D₄₃	C₂²	1	4	yes	—
9	C₂×#13063322	—	2	8	no	—
10	C₂×#13063322	C₂²	1	8	yes	complemented
11	C₂²×(C₂×D₄₃)⋊C₄	C₂²	1	12	yes	—
12	#14582816	C₂²	1	48	yes	complemented
13	#14582808	C₂²	1	48	yes	complemented
14	#14582767	C₂²	1	8	yes	complemented
15	C₂×C₄₃⋊#95	C₂²	1	6	yes	—
16	C₂×#126×C₄₃	—	2	8	no	—
17	C₂×#126×C₄₃	C₂²	1	8	yes	complemented
18	C₂²×C₄⋊C₄×C₄₃	C₂²	1	3	yes	—
19	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	3	yes	—
20	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
21	C₂⁴×D₄₃	C₂³	1	4	yes	—
22	C₂²×D₁₇₂	—	2	24	no	—
23	C₂²×D₁₇₂	—	4	24	no	—
24	C₂²×D₁₇₂	C₂³	1	24	yes	—
25	C₂²×C₂²⋊D₄₃	—	4	24	no	—
26	C₂²×C₂²⋊D₄₃	C₂³	1	16	yes	—
27	C₂³×Dic₄₃	C₂³	1	4	yes	—
28	#13063322	—	2	32	no	—
29	C₂×(C₂×D₄₃)⋊C₄	—	4	24	no	—
30	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	48	yes	—
31	C₄₃⋊#95	C₂³	1	24	yes	—
32	C₂⁵×C₄₃	C₂³	1	1	yes	characteristic
33	C₂³×C₄×C₄₃	C₂³	1	3	yes	—
34	C₂³×C₄×C₄₃	C₂³	1	3	yes	—
35	#126×C₄₃	—	2	32	no	—
36	C₂×C₄⋊C₄×C₄₃	—	2	12	no	—
37	C₂×C₄⋊C₄×C₄₃	C₂³	1	12	yes	—
38	C₂×C₂²⋊C₄×C₄₃	—	2	12	no	—
39	C₂×C₂²⋊C₄×C₄₃	C₂³	1	12	yes	—
40	C₂×C₄²×C₄₃	D₄	1	8	yes	complemented
41	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
42	C₂⁴×C₄₃	—	2	2	no	—
43	C₂⁴×C₄₃	—	2	12	no	—
44	C₂⁴×C₄₃	C₂⁴	1	2	yes	—
45	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
46	C₂³×D₄₃	—	2	8	no	—
47	C₂³×D₄₃	—	2	24	no	—
48	C₂³×D₄₃	—	2	24	no	—
49	C₂³×D₄₃	C₂⁴	1	8	yes	—
50	C₂²×C₄×C₄₃	—	2	6	no	—
51	C₂²×C₄×C₄₃	—	2	12	no	—
52	C₂²×C₄×C₄₃	—	2	12	no	—
53	C₂²×C₄×C₄₃	C₂×D₄	1	12	yes	—
54	C₂²×C₄×C₄₃	C₂⁴	1	6	yes	—
55	C₂²×C₄×C₄₃	C₂⁴	1	6	yes	—
56	C₂×C₂²⋊D₄₃	—	4	48	no	—
57	C₂×C₂²⋊D₄₃	—	4	64	no	—
58	C₂²×Dic₄₃	—	2	24	no	—
59	C₂²×Dic₄₃	C₂⁴	1	8	yes	—
60	C₂×D₁₇₂	—	2	48	no	—
61	C₂×D₁₇₂	—	4	48	no	—
62	C₂×D₁₇₂	—	4	96	no	—
63	C₄⋊C₄×C₄₃	—	2	24	no	—
64	C₂²⋊C₄×C₄₃	—	2	24	no	—
65	C₄²×C₄₃	C₂×D₄	1	16	yes	complemented
66	(C₂×D₄₃)⋊C₄	—	4	48	no	—
67	C₂³×C₄₃	—	2	2	no	—
68	C₂³×C₄₃	—	2	12	no	—
69	C₂³×C₄₃	—	4	12	no	—
70	C₂³×C₄₃	—	4	16	no	—
71	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
72	C₂³×C₄₃	H(5,𝔽₂)	1	12	yes	—
73	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
74	C₂²×D₄₃	—	2	8	no	—
75	C₂²×D₄₃	—	2	24	no	—
76	C₂²×D₄₃	—	2	24	no	—
77	C₂²×D₄₃	—	4	48	no	—
78	C₂²×D₄₃	—	4	16	no	—
79	C₂²×D₄₃	—	4	48	no	—
80	C₂×C₄×C₄₃	—	2	24	no	—
81	C₂×C₄×C₄₃	—	2	12	no	—
82	C₂×C₄×C₄₃	—	2	6	no	—
83	C₂×C₄×C₄₃	—	2	12	no	—
84	C₂×C₄×C₄₃	—	4	12	no	—
85	C₂×C₄×C₄₃	C₂²×D₄	1	12	yes	—
86	C₂²⋊D₄₃	—	4	64	no	—
87	C₂×Dic₄₃	—	2	24	no	—
88	C₂×Dic₄₃	—	4	16	no	—
89	D₁₇₂	—	4	96	no	—
90	C₂×#2818	—	43	1	no	maximal, Sylow
91	C₂²×C₄₃	—	4	6	no	—
92	C₂²×C₄₃	—	4	8	no	—
93	C₂²×C₄₃	—	8	8	no	—
94	C₂²×C₄₃	#535	1	12	yes	—
95	C₂²×C₄₃	#560	1	16	yes	—
96	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
97	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	6	yes	—
98	C₂×D₄₃	—	4	24	no	—
99	C₂×D₄₃	—	4	24	no	—
100	C₂×D₄₃	—	4	8	no	—
101	C₂×D₄₃	—	8	32	no	—
102	C₄×C₄₃	—	2	12	no	—
103	C₄×C₄₃	—	4	6	no	—
104	Dic₄₃	—	4	8	no	—
105	C₂²×#127	—	43	1	no	—
106	C₂²×#126	D₄₃	1	1	yes	characteristic, complemented
107	#2818	—	43	16	no	—
108	C₂×#394	—	43	6	no	—
109	C₂×#392	—	43	6	no	—
110	C₂×#383	—	43	1	no	—
111	C₂×C₄₃	—	8	2	no	—
112	C₂×C₄₃	#2818	1	8	yes	complemented
113	C₂×C₄₃	C₂×#535	1	3	yes	—
114	C₂×C₄₃	C₂×#560	1	4	yes	—
115	D₄₃	—	8	8	no	—
116	C₂³×D₄	—	43	4	no	—
117	C₂³×D₄	—	43	6	no	—
118	C₂×#127	—	43	8	no	—
119	C₂×#127	—	86	8	no	—
120	C₂×#126	—	2	8	no	—
121	C₂×#126	C₂×D₄₃	1	8	yes	complemented
122	C₂²×C₄⋊C₄	C₂×D₄₃	1	3	yes	—
123	C₂²×C₂²⋊C₄	—	43	12	no	—
124	C₂²×C₂²⋊C₄	C₂×D₄₃	1	3	yes	—
125	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
126	#394	—	43	48	no	—
127	#392	—	43	48	no	—
128	#383	—	43	8	no	—
129	C₂×#95	—	43	6	no	—
130	C₄₃	C₂×#2818	1	1	yes	characteristic, complemented, Sylow
131	C₂⁵	—	43	4	no	—
132	C₂⁵	C₂²×D₄₃	1	1	yes	characteristic
133	C₂²×D₄	—	43	16	no	—
134	C₂²×D₄	—	43	24	no	—
135	C₂²×D₄	—	86	24	no	—
136	C₂²×D₄	—	172	24	no	—
137	C₂²×D₄	—	172	24	no	—
138	C₂³×C₄	—	43	4	no	—
139	C₂³×C₄	C₂²×D₄₃	1	3	yes	—
140	C₂³×C₄	C₂²×D₄₃	1	3	yes	—
141	#127	—	86	32	no	—
142	#126	—	2	32	no	—
143	C₂×C₄⋊C₄	—	2	12	no	—
144	C₂×C₄⋊C₄	C₂²×D₄₃	1	12	yes	—
145	C₂×C₂²⋊C₄	—	2	12	no	—
146	C₂×C₂²⋊C₄	—	43	48	no	—
147	C₂×C₂²⋊C₄	—	172	24	no	—
148	C₂×C₂²⋊C₄	C₂²×D₄₃	1	12	yes	—
149	C₂×C₄²	C₂²⋊D₄₃	1	8	yes	complemented
150	C₂×C₄²	C₂²×D₄₃	1	4	yes	—
151	#95	—	43	24	no	—
152	C₂⁴	—	2	2	no	—
153	C₂⁴	—	2	12	no	—
154	C₂⁴	—	43	8	no	—
155	C₂⁴	—	86	8	no	—
156	C₂⁴	—	86	24	no	—
157	C₂⁴	—	86	24	no	—
158	C₂⁴	C₂³×D₄₃	1	2	yes	—
159	C₂⁴	C₂³×D₄₃	1	1	yes	characteristic
160	C₂×D₄	—	86	48	no	—
161	C₂×D₄	—	172	48	no	—
162	C₂×D₄	—	172	96	no	—
163	C₂×D₄	—	172	48	no	—
164	C₂×D₄	—	172	64	no	—
165	C₂²×C₄	—	2	12	no	—
166	C₂²×C₄	—	2	6	no	—
167	C₂²×C₄	—	2	12	no	—
168	C₂²×C₄	—	43	8	no	—
169	C₂²×C₄	—	86	24	no	—
170	C₂²×C₄	C₂×C₂²⋊D₄₃	1	12	yes	—
171	C₂²×C₄	C₂³×D₄₃	1	6	yes	—
172	C₂²×C₄	C₂³×D₄₃	1	6	yes	—
173	C₄⋊C₄	—	2	24	no	—
174	C₂²⋊C₄	—	2	24	no	—
175	C₂²⋊C₄	—	172	48	no	—
176	C₄²	C₂×C₂²⋊D₄₃	1	16	yes	complemented
177	C₂³	—	2	2	no	—
178	C₂³	—	2	12	no	—
179	C₂³	—	4	16	no	—
180	C₂³	—	4	12	no	—
181	C₂³	—	86	8	no	—
182	C₂³	—	86	24	no	—
183	C₂³	—	86	24	no	—
184	C₂³	—	172	16	no	—
185	C₂³	—	172	48	no	—
186	C₂³	—	172	48	no	—
187	C₂³	C₂²×C₂²⋊D₄₃	1	2	yes	—
188	C₂³	#13063371	1	12	yes	—
189	C₂³	C₂⁴×D₄₃	1	1	yes	characteristic
190	D₄	—	172	96	no	—
191	D₄	—	172	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	—	86	24	no	—
198	C₂×C₄	—	172	16	no	—
199	C₂×C₄	C₂²×C₂²⋊D₄₃	1	12	yes	—
200	C₂²	—	4	6	no	—
201	C₂²	—	4	8	no	—
202	C₂²	—	8	8	no	—
203	C₂²	—	344	32	no	—
204	C₂²	—	172	24	no	—
205	C₂²	—	172	8	no	—
206	C₂²	—	172	24	no	—
207	C₂²	#14583463	1	12	yes	—
208	C₂²	#14583640	1	16	yes	—
209	C₂²	C₂³×C₂²⋊D₄₃	1	1	yes	characteristic
210	C₂²	C₂×#13063371	1	6	yes	—
211	C₄	—	2	12	no	—
212	C₄	—	4	6	no	—
213	C₄	—	172	8	no	—
214	C₂	—	8	2	no	—
215	C₂	—	344	8	no	—
216	C₂	#19142635	1	8	yes	direct product factor
217	C₂	C₂×#14583463	1	3	yes	—
218	C₂	C₂×#14583640	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#13063322

C₂

yes

maximal, characteristic, complemented

#19142635

C₂

yes

maximal, direct product factor

C₂×#14582816

C₂

yes

maximal, complemented

C₂×#14582808

C₂

yes

maximal, complemented

C₂×#14582767

C₂

yes

maximal, characteristic, complemented

C₂²×#126×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂³×D₁₇₂

C₂²

yes

—

C₂³×C₂²⋊D₄₃

C₂²

yes

—

C₂×#13063322

—

C₂×#13063322

C₂²

yes

complemented

C₂²×(C₂×D₄₃)⋊C₄

C₂²

yes

—

#14582816

C₂²

yes

complemented

#14582808

C₂²

yes

complemented

#14582767

C₂²

yes

complemented

C₂×C₄₃⋊#95

C₂²

yes

—

C₂×#126×C₄₃

—

C₂×#126×C₄₃

C₂²

yes

complemented

C₂²×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂²×C₂²⋊C₄×C₄₃

C₂²

yes

—

C₂²×C₄²×C₄₃

C₂²

yes

characteristic

C₂⁴×D₄₃

C₂³

yes

—

C₂²×D₁₇₂

—

C₂²×D₁₇₂

—

C₂²×D₁₇₂

C₂³

yes

—

C₂²×C₂²⋊D₄₃

—

C₂²×C₂²⋊D₄₃

C₂³

yes

—

C₂³×Dic₄₃

C₂³

yes

—

#13063322

—

C₂×(C₂×D₄₃)⋊C₄

—

C₂×(C₂×D₄₃)⋊C₄

C₂³

yes

—

C₄₃⋊#95

C₂³

yes

—

C₂⁵×C₄₃

C₂³

yes

characteristic

C₂³×C₄×C₄₃

C₂³

yes

—

C₂³×C₄×C₄₃

C₂³

yes

—

#126×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

C₂³

yes

—

C₂×C₂²⋊C₄×C₄₃

—

C₂×C₂²⋊C₄×C₄₃

C₂³

yes

—

C₂×C₄²×C₄₃

D₄

yes

complemented

C₂×C₄²×C₄₃

C₂³

yes

—

C₂⁴×C₄₃

—

C₂⁴×C₄₃

—

C₂⁴×C₄₃

C₂⁴

yes

—

C₂⁴×C₄₃

C₂⁴

yes

characteristic

C₂³×D₄₃

—

C₂³×D₄₃

—

C₂³×D₄₃

—

C₂³×D₄₃

C₂⁴

yes

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂²×C₄×C₄₃

C₂⁴

yes

—

C₂²×C₄×C₄₃

C₂⁴

yes

—

C₂×C₂²⋊D₄₃

—

C₂×C₂²⋊D₄₃

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

C₂⁴

yes

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

C₂×D₄

yes

complemented

(C₂×D₄₃)⋊C₄

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂²×D₄

yes

—

C₂³×C₄₃

H(5,𝔽₂)

yes

—

C₂³×C₄₃

C₂⁵

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×D₄

yes

—

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

C₂×#2818

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#535

yes

—

C₂²×C₄₃

#560

yes

—

C₂²×C₄₃

C₂³×D₄

yes

characteristic

C₂²×C₄₃

C₂×H(5,𝔽₂)

yes

—

C₂×D₄₃

—

C₂×D₄₃

—

100

C₂×D₄₃

—

101

C₂×D₄₃

—

102

C₄×C₄₃

—

103

C₄×C₄₃

—

104

Dic₄₃

—

105

C₂²×#127

—

106

C₂²×#126

D₄₃

yes

characteristic, complemented

107

#2818

—

108

C₂×#394

—

109

C₂×#392

—

110

C₂×#383

—

111

C₂×C₄₃

—

112

C₂×C₄₃

#2818

yes

complemented

113

C₂×C₄₃

C₂×#535

yes

—

114

C₂×C₄₃

C₂×#560

yes

—

115

D₄₃

—

116

C₂³×D₄

—

117

C₂³×D₄

—

118

C₂×#127

—

119

C₂×#127

—

120

C₂×#126

—

121

C₂×#126

C₂×D₄₃

yes

complemented

122

C₂²×C₄⋊C₄

C₂×D₄₃

yes

—

123

C₂²×C₂²⋊C₄

—

124

C₂²×C₂²⋊C₄

C₂×D₄₃

yes

—

125

C₂²×C₄²

C₂×D₄₃

yes

characteristic

126

#394

—

127

#392

—

128

#383

—

129

C₂×#95

—

130

C₄₃

C₂×#2818

yes

characteristic, complemented, Sylow

131

C₂⁵

—

132

C₂⁵

C₂²×D₄₃

yes

characteristic

133

C₂²×D₄

—

134

C₂²×D₄

—

135

C₂²×D₄

—

136

C₂²×D₄

—

172

—

137

C₂²×D₄

—

172

—

138

C₂³×C₄

—

139

C₂³×C₄

C₂²×D₄₃

yes

—

140

C₂³×C₄

C₂²×D₄₃

yes

—

141

#127

—

142

#126

—

143

C₂×C₄⋊C₄

—

144

C₂×C₄⋊C₄

C₂²×D₄₃

yes

—

145

C₂×C₂²⋊C₄

—

146

C₂×C₂²⋊C₄

—

147

C₂×C₂²⋊C₄

—

172

—

148

C₂×C₂²⋊C₄

C₂²×D₄₃

yes

—

149

C₂×C₄²

C₂²⋊D₄₃

yes

complemented

150

C₂×C₄²

C₂²×D₄₃

yes

—

151

#95

—

152

C₂⁴

—

153

C₂⁴

—

154

C₂⁴

—

155

C₂⁴

—

156

C₂⁴

—

157

C₂⁴

—

158

C₂⁴

C₂³×D₄₃

yes

—

159

C₂⁴

C₂³×D₄₃

yes

characteristic

160

C₂×D₄

—

161

C₂×D₄

—

172

—

162

C₂×D₄

—

172

—

163

C₂×D₄

—

172

—

164

C₂×D₄

—

172

—

165

C₂²×C₄

—

166

C₂²×C₄

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

—

171

C₂²×C₄

C₂³×D₄₃

yes

—

172

C₂²×C₄

C₂³×D₄₃

yes

—

173

C₄⋊C₄

—

174

C₂²⋊C₄

—

175

C₂²⋊C₄

—

172

—

176

C₄²

C₂×C₂²⋊D₄₃

yes

complemented

177

C₂³

—

178

C₂³

—

179

C₂³

—

180

C₂³

—

181

C₂³

—

182

C₂³

—

183

C₂³

—

184

C₂³

—

172

—

185

C₂³

—

172

—

186

C₂³

—

172

—

187

C₂³

C₂²×C₂²⋊D₄₃

yes

—

188

C₂³

#13063371

yes

—

189

C₂³

C₂⁴×D₄₃

yes

characteristic

190

D₄

—

172

—

191

D₄

—

172

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

172

—

199

C₂×C₄

C₂²×C₂²⋊D₄₃

yes

—

200

C₂²

—

201

C₂²

—

202

C₂²

—

203

C₂²

—

344

—

204

C₂²

—

172

—

205

C₂²

—

172

—

206

C₂²

—

172

—

207

C₂²

#14583463

yes

—

208

C₂²

#14583640

yes

—

209

C₂²

C₂³×C₂²⋊D₄₃

yes

characteristic

210

C₂²

C₂×#13063371

yes

—

211

C₄

—

212

C₄

—

213

C₄

—

172

—

214

C₂

—

215

C₂

—

344

—

216

C₂

#19142635

yes

direct product factor

217

C₂

C₂×#14583463

yes

—

218

C₂

C₂×#14583640

yes

—

	subgroup	G/H
center	C₂⁴	C₂³×D₄₃
commutator, cosocle	C₂³×C₄₃	C₂⁵
Frattini	C₂³	C₂⁴×D₄₃
Fitting	C₂²×#126×C₄₃	C₂
socle	C₂⁴×C₄₃	C₂⁴
hypercenter	C₂²×#126	D₄₃
hypocenter	C₄₃	C₂×#2818
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×#126

subgroup

G/H

center

C₂⁴

C₂³×D₄₃

commutator, cosocle

C₂³×C₄₃

C₂⁵

Frattini

C₂³

C₂⁴×D₄₃

Fitting

C₂²×#126×C₄₃

C₂

socle

C₂⁴×C₄₃

C₂⁴

hypercenter

C₂²×#126

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂⁴ ◁ C₂²×#126

N	H ≅ G/N	type
1. C₂²×#13063322	C₂	semidirect
2. #19142635	C₂	direct (N × H)
3. C₂×#14582816	C₂	semidirect
4. C₂×#14582808	C₂	semidirect
5. C₂×#14582767	C₂	semidirect
6. C₂²×#126×C₄₃	C₂	semidirect
10. C₂×#13063322	C₂²	semidirect
12. #14582816	C₂²	semidirect
13. #14582808	C₂²	semidirect
14. #14582767	C₂²	semidirect
17. C₂×#126×C₄₃	C₂²	semidirect
40. C₂×C₄²×C₄₃	D₄	semidirect
65. C₄²×C₄₃	C₂×D₄	semidirect
106. C₂²×#126	D₄₃	semidirect
112. C₂×C₄₃	#2818	semidirect
121. C₂×#126	C₂×D₄₃	semidirect
130. C₄₃	C₂×#2818	semidirect
149. C₂×C₄²	C₂²⋊D₄₃	semidirect
176. C₄²	C₂×C₂²⋊D₄₃	semidirect
216. C₂	#19142635	direct (N × H)

H ≅ G/N

type

1. C₂²×#13063322

C₂

semidirect

2. #19142635

C₂

direct (N × H)

3. C₂×#14582816

C₂

semidirect

4. C₂×#14582808

C₂

semidirect

5. C₂×#14582767

C₂

semidirect

6. C₂²×#126×C₄₃

C₂

semidirect

10. C₂×#13063322

C₂²

semidirect

12. #14582816

C₂²

semidirect

13. #14582808

C₂²

semidirect

14. #14582767

C₂²

semidirect

17. C₂×#126×C₄₃

C₂²

semidirect

40. C₂×C₄²×C₄₃

D₄

semidirect

65. C₄²×C₄₃

C₂×D₄

semidirect

106. C₂²×#126

D₄₃

semidirect

112. C₂×C₄₃

#2818

semidirect

121. C₂×#126

C₂×D₄₃

semidirect

130. C₄₃

C₂×#2818

semidirect

149. C₂×C₄²

C₂²⋊D₄₃

semidirect

176. C₄²

C₂×C₂²⋊D₄₃

semidirect

216. C₂

#19142635

direct (N × H)

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

subgroup	index
C₂²×#13063322	2
#19142635	2
C₂×#14582816	2
C₂×#14582808	2
C₂×#14582767	2
C₂²×#126×C₄₃	2
C₂×#2818	43

subgroup

index

C₂²×#126×C₄₃

Subgroups — C₂×#19142635 #25303154

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#19142635 #25303154

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19142635 #25303154