Group #25249180 — subgroups

Subgroups — #25249180

Order 11008.

910 conjugacy classes of subgroups; only the 299 normal subgroups are shown.

normal subgroups only

This group has 910 conjugacy classes of subgroups — too many to draw. Only its 299 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×#14583302	C₂	1	2	yes	maximal
2	C₂×#14583295	C₂	1	2	yes	maximal
3	#19142973	C₂	1	1	yes	maximal, characteristic
4	#19134761	C₂	1	8	yes	maximal
5	C₄×#13063236	C₂	1	1	yes	maximal, characteristic
6	C₄₃×#2868	C₂	1	1	yes	maximal, characteristic
7	C₂×#13063325	C₂²	1	1	yes	characteristic
8	C₂×#13063325	C₂²	1	1	yes	characteristic
9	#14583302	—	2	8	no	—
10	#14583295	—	2	8	no	—
11	C₂×#13063258	C₂²	1	8	yes	—
12	C₂×#13063256	C₂²	1	8	yes	—
13	C₂×#13063236	C₂²	1	4	yes	—
14	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
15	#14582805	—	2	2	no	—
16	#14582805	—	2	2	no	—
17	#14582765	C₂²	1	4	yes	—
18	C₂×C₄⋊Q₈×C₄₃	—	2	2	no	—
19	C₂×C₄⋊Q₈×C₄₃	C₂²	1	2	yes	—
20	C₄₃×#384	—	2	2	no	—
21	C₄₃×#384	C₂²	1	4	yes	—
22	C₄³×C₄₃	C₂²	1	1	yes	characteristic
23	C₂²×Dic₈₆	—	2	1	no	—
24	C₂²×Dic₈₆	—	2	1	no	—
25	C₂²×C₄₃⋊C₈	C₂³	1	4	yes	—
26	#13063325	—	2	4	no	—
27	#13063325	—	2	4	no	—
28	C₂×C₄⋊Dic₄₃	—	2	1	no	—
29	C₂×C₄⋊Dic₄₃	—	2	1	no	—
30	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
31	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
32	#13063258	—	2	16	no	—
33	#13063256	—	2	16	no	—
34	#13063236	Q₈	1	16	yes	complemented
35	C₄×C₄₃⋊C₈	D₄	1	8	yes	—
36	C₄₃⋊#95	—	2	8	no	—
37	C₂²×Q₈×C₄₃	—	2	2	no	—
38	C₄⋊Q₈×C₄₃	—	2	4	no	—
39	C₄⋊Q₈×C₄₃	—	2	4	no	—
40	C₄⋊Q₈×C₄₃	—	4	8	no	—
41	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
42	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
43	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
44	C₂×C₄²×C₄₃	D₄	1	2	yes	—
45	C₂×C₄²×C₄₃	D₄	1	2	yes	—
46	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
47	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
48	C₂×Q₈×C₄₃	—	4	4	no	—
49	C₂×Q₈×C₄₃	—	4	8	no	—
50	C₂²×C₄×C₄₃	—	2	4	no	—
51	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
52	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
55	C₂²×Dic₄₃	—	2	2	no	—
56	C₂²×Dic₄₃	—	2	2	no	—
57	C₂×Dic₈₆	—	4	2	no	—
58	C₂×Dic₈₆	—	4	2	no	—
59	C₂×Dic₈₆	—	4	4	no	—
60	C₂×Dic₈₆	—	4	4	no	—
61	C₄⋊C₄×C₄₃	—	2	4	no	—
62	C₄⋊C₄×C₄₃	—	2	4	no	—
63	C₄⋊C₄×C₄₃	—	4	16	no	—
64	C₄⋊C₄×C₄₃	—	4	4	no	—
65	C₄²×C₄₃	—	2	4	no	—
66	C₄²×C₄₃	—	2	4	no	—
67	C₄²×C₄₃	C₂×D₄	1	4	yes	—
68	C₄²×C₄₃	C₂×Q₈	1	8	yes	—
69	C₄⋊Dic₄₃	—	2	4	no	—
70	C₄⋊Dic₄₃	—	2	4	no	—
71	C₄⋊Dic₄₃	—	4	2	no	—
72	C₄⋊Dic₄₃	—	4	2	no	—
73	C₂×C₄₃⋊C₈	C₂×D₄	1	8	yes	—
74	C₂×C₄₃⋊C₈	C₂×Q₈	1	16	yes	—
75	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
76	Q₈×C₄₃	—	8	8	no	—
77	C₂×C₄×C₄₃	—	2	4	no	—
78	C₂×C₄×C₄₃	—	2	4	no	—
79	C₂×C₄×C₄₃	—	4	4	no	—
80	C₂×C₄×C₄₃	—	4	8	no	—
81	C₂×C₄×C₄₃	#127	1	2	yes	—
82	C₂×C₄×C₄₃	#127	1	2	yes	—
83	C₂×C₄×C₄₃	C₄⋊Q₈	1	8	yes	—
84	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	4	yes	—
85	C₂×C₄×C₄₃	#137	1	4	yes	—
86	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
87	C₂×C₄×C₄₃	C₂²×Q₈	1	4	yes	—
88	C₂×Dic₄₃	—	4	2	no	—
89	C₂×Dic₄₃	—	4	2	no	—
90	C₂×Dic₄₃	—	4	4	no	—
91	C₂×Dic₄₃	—	4	4	no	—
92	Dic₈₆	—	8	4	no	—
93	Dic₈₆	—	8	4	no	—
94	C₄₃⋊C₈	C₄⋊Q₈	1	16	yes	complemented
95	#33314	—	43	1	no	maximal, Sylow
96	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
97	C₂²×C₄₃	C₂×C₄⋊Q₈	1	2	yes	—
98	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
99	C₂²×C₄₃	C₂×#137	1	2	yes	—
100	C₄×C₄₃	—	2	8	no	—
101	C₄×C₄₃	—	8	4	no	—
102	C₄×C₄₃	#496	1	4	yes	—
103	C₄×C₄₃	#497	1	4	yes	—
104	C₄×C₄₃	C₂×C₄⋊Q₈	1	4	yes	—
105	Dic₄₃	—	8	2	no	—
106	Dic₄₃	—	8	2	no	—
107	C₂×#500	—	43	2	no	—
108	C₂×#498	—	43	2	no	—
109	#2868	D₄₃	1	1	yes	characteristic
110	#2862	—	43	1	no	—
111	#1847	—	43	8	no	—
112	C₄×#97	—	43	1	no	—
113	C₂×C₄₃	#2868	1	1	yes	characteristic
114	C₂×C₄₃	C₂×#496	1	1	yes	characteristic
115	C₂×C₄₃	C₂×#497	1	1	yes	characteristic
116	C₂×C₄₃	#3165	1	4	yes	—
117	C₂×C₄⋊Q₈	—	2	2	no	—
118	C₂×C₄⋊Q₈	—	43	1	no	—
119	C₂×C₄⋊Q₈	—	43	1	no	—
120	C₂×C₄⋊Q₈	C₂×D₄₃	1	2	yes	—
121	#500	—	86	8	no	—
122	#498	—	86	8	no	—
123	C₂×#107	—	43	8	no	—
124	C₂×#106	—	43	8	no	—
125	C₂×#97	—	43	4	no	—
126	C₂×C₄×C₈	—	43	2	no	—
127	#391	—	86	2	no	—
128	#391	—	86	2	no	—
129	#384	—	2	2	no	—
130	#384	C₂×D₄₃	1	4	yes	—
131	#382	—	43	4	no	—
132	C₄³	C₂×D₄₃	1	1	yes	characteristic
133	C₄₃	#33314	1	1	yes	characteristic, complemented, Sylow
134	C₂²×Q₈	—	2	2	no	—
135	C₂²×Q₈	—	86	1	no	—
136	C₂²×Q₈	—	86	1	no	—
137	C₂²×C₈	—	43	4	no	—
138	C₄⋊Q₈	—	2	4	no	—
139	C₄⋊Q₈	—	2	4	no	—
140	C₄⋊Q₈	—	4	8	no	—
141	C₄⋊Q₈	—	86	4	no	—
142	C₄⋊Q₈	—	86	4	no	—
143	C₂×C₄⋊C₄	—	2	8	no	—
144	C₂×C₄⋊C₄	—	2	2	no	—
145	C₂×C₄⋊C₄	—	43	2	no	—
146	C₂×C₄⋊C₄	—	43	2	no	—
147	C₂×C₄⋊C₄	—	86	1	no	—
148	C₂×C₄⋊C₄	—	86	1	no	—
149	C₂×C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
150	C₂×C₄²	C₂²⋊D₄₃	1	2	yes	—
151	C₂×C₄²	C₂²⋊D₄₃	1	2	yes	—
152	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
153	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
154	#107	—	86	16	no	—
155	#106	—	86	16	no	—
156	#97	—	43	16	no	—
157	C₄×C₈	—	43	8	no	—
158	#95	—	86	8	no	—
159	C₂×Q₈	—	4	4	no	—
160	C₂×Q₈	—	4	8	no	—
161	C₂×Q₈	—	172	2	no	—
162	C₂×Q₈	—	172	2	no	—
163	C₂×Q₈	—	172	4	no	—
164	C₂×Q₈	—	172	4	no	—
165	C₂²×C₄	—	2	4	no	—
166	C₂²×C₄	—	86	2	no	—
167	C₂²×C₄	—	86	2	no	—
168	C₂²×C₄	C₂×C₂²⋊D₄₃	1	4	yes	—
169	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
170	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
171	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
172	C₂×C₈	—	43	8	no	—
173	C₂×C₈	—	43	16	no	—
174	C₄⋊C₄	—	2	4	no	—
175	C₄⋊C₄	—	2	4	no	—
176	C₄⋊C₄	—	4	16	no	—
177	C₄⋊C₄	—	4	4	no	—
178	C₄⋊C₄	—	86	4	no	—
179	C₄⋊C₄	—	86	4	no	—
180	C₄⋊C₄	—	172	2	no	—
181	C₄⋊C₄	—	172	2	no	—
182	C₄²	—	2	4	no	—
183	C₄²	—	2	4	no	—
184	C₄²	D₄×D₄₃	1	4	yes	—
185	C₄²	Q₈×D₄₃	1	8	yes	—
186	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
187	Q₈	—	8	8	no	—
188	Q₈	—	344	4	no	—
189	Q₈	—	344	4	no	—
190	C₂×C₄	—	2	4	no	—
191	C₂×C₄	—	2	4	no	—
192	C₂×C₄	—	4	8	no	—
193	C₂×C₄	—	4	4	no	—
194	C₂×C₄	—	172	4	no	—
195	C₂×C₄	—	172	4	no	—
196	C₂×C₄	—	172	2	no	—
197	C₂×C₄	—	172	2	no	—
198	C₂×C₄	#13063321	1	2	yes	—
199	C₂×C₄	#13063321	1	2	yes	—
200	C₂×C₄	#13063323	1	8	yes	—
201	C₂×C₄	#13063351	1	4	yes	—
202	C₂×C₄	#13063356	1	4	yes	—
203	C₂×C₄	C₂×D₄×D₄₃	1	2	yes	—
204	C₂×C₄	C₂×Q₈×D₄₃	1	4	yes	—
205	C₈	—	43	16	no	—
206	C₂²	C₂×#13063321	1	1	yes	characteristic
207	C₂²	C₂×#13063323	1	2	yes	—
208	C₂²	C₂×#13063351	1	2	yes	—
209	C₂²	C₂×#13063356	1	2	yes	—
210	C₄	—	2	8	no	—
211	C₄	—	8	4	no	—
212	C₄	—	344	2	no	—
213	C₄	—	344	2	no	—
214	C₄	#14583286	1	4	yes	—
215	C₄	#14583291	1	4	yes	—
216	C₄	C₄⋊Q₈×D₄₃	1	4	yes	—
217	C₂	#19142991	1	1	yes	characteristic
218	C₂	C₂×#14583286	1	1	yes	characteristic
219	C₂	C₂×#14583291	1	1	yes	characteristic
220	C₂	#19145137	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14583302

C₂

yes

maximal

C₂×#14583295

C₂

yes

maximal

#19142973

C₂

yes

maximal, characteristic

#19134761

C₂

yes

maximal

C₄×#13063236

C₂

yes

maximal, characteristic

C₄₃×#2868

C₂

yes

maximal, characteristic

C₂×#13063325

C₂²

yes

characteristic

C₂×#13063325

C₂²

yes

—

—

C₂²

yes

—

C₂×#13063256

C₂²

yes

—

C₂×#13063236

C₂²

yes

—

C₂×C₄×C₄₃⋊C₈

C₂²

yes

—

#14582805

—

#14582805

—

#14582765

C₂²

yes

—

C₂×C₄⋊Q₈×C₄₃

—

C₂×C₄⋊Q₈×C₄₃

C₂²

yes

—

C₄₃×#384

—

C₄₃×#384

C₂²

yes

—

C₄³×C₄₃

C₂²

yes

characteristic

C₂²×Dic₈₆

—

C₂²×Dic₈₆

—

C₂²×C₄₃⋊C₈

C₂³

yes

—

#13063325

—

#13063325

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

C₂³

yes

—

C₂×C₄⋊Dic₄₃

C₂³

yes

—

#13063258

—

#13063256

—

#13063236

Q₈

yes

complemented

C₄×C₄₃⋊C₈

D₄

yes

—

C₄₃⋊#95

—

C₂²×Q₈×C₄₃

—

C₄⋊Q₈×C₄₃

—

C₄⋊Q₈×C₄₃

—

C₄⋊Q₈×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

C₂³

yes

—

C₂×C₄²×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₂×C₄²×C₄₃

C₂³

yes

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂⁴

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂×D₄

yes

—

C₄²×C₄₃

C₂×Q₈

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₂×C₄₃⋊C₈

C₂×D₄

yes

—

C₂×C₄₃⋊C₈

C₂×Q₈

yes

—

C₂³×C₄₃

C₂²×D₄

yes

characteristic

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#127

yes

—

C₂×C₄×C₄₃

#127

yes

—

C₂×C₄×C₄₃

C₄⋊Q₈

yes

—

C₂×C₄×C₄₃

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₄₃

#137

yes

—

C₂×C₄×C₄₃

C₂²×D₄

yes

—

C₂×C₄×C₄₃

C₂²×Q₈

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₄₃⋊C₈

C₄⋊Q₈

yes

—

C₂²×C₄₃

yes

C₂²×C₄₃

C₂×C₄⋊Q₈

yes

—

C₂²×C₄₃

C₂×AGL(1,ℤ/8)

yes

—

C₂²×C₄₃

C₂×#137

yes

—

100

C₄×C₄₃

—

101

C₄×C₄₃

—

102

C₄×C₄₃

#496

yes

—

103

C₄×C₄₃

#497

yes

—

104

C₄×C₄₃

C₂×C₄⋊Q₈

yes

—

105

Dic₄₃

—

106

Dic₄₃

—

107

C₂×#500

—

108

C₂×#498

—

109

#2868

D₄₃

yes

characteristic

110

#2862

—

111

#1847

—

112

C₄×#97

—

113

C₂×C₄₃

#2868

yes

characteristic

114

C₂×C₄₃

C₂×#496

yes

characteristic

115

C₂×C₄₃

C₂×#497

yes

characteristic

116

C₂×C₄₃

#3165

yes

—

117

C₂×C₄⋊Q₈

—

118

C₂×C₄⋊Q₈

—

119

C₂×C₄⋊Q₈

—

120

C₂×C₄⋊Q₈

C₂×D₄₃

yes

—

121

#500

—

122

#498

—

123

C₂×#107

—

124

C₂×#106

—

125

C₂×#97

—

126

C₂×C₄×C₈

—

127

#391

—

128

#391

—

129

#384

—

130

#384

C₂×D₄₃

yes

—

131

#382

—

132

C₄³

C₂×D₄₃

yes

characteristic

133

C₄₃

#33314

yes

characteristic, complemented, Sylow

134

C₂²×Q₈

—

135

C₂²×Q₈

—

136

C₂²×Q₈

—

137

C₂²×C₈

—

138

C₄⋊Q₈

—

139

C₄⋊Q₈

—

140

C₄⋊Q₈

—

141

C₄⋊Q₈

—

142

C₄⋊Q₈

—

143

C₂×C₄⋊C₄

—

144

C₂×C₄⋊C₄

—

145

C₂×C₄⋊C₄

—

146

C₂×C₄⋊C₄

—

147

C₂×C₄⋊C₄

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

C₂²×D₄₃

yes

—

150

C₂×C₄²

C₂²⋊D₄₃

yes

—

151

C₂×C₄²

C₂²⋊D₄₃

yes

—

152

C₂×C₄²

C₂²×D₄₃

yes

characteristic

153

C₂×C₄²

C₂²×D₄₃

yes

—

154

#107

—

155

#106

—

156

#97

—

157

C₄×C₈

—

158

#95

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂×Q₈

—

172

—

162

C₂×Q₈

—

172

—

163

C₂×Q₈

—

172

—

164

C₂×Q₈

—

172

—

165

C₂²×C₄

—

166

C₂²×C₄

—

167

C₂²×C₄

—

168

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

—

169

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

170

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

171

C₂²×C₄

C₂³×D₄₃

yes

characteristic

172

C₂×C₈

—

173

C₂×C₈

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

172

—

181

C₄⋊C₄

—

172

—

182

C₄²

—

183

C₄²

—

184

C₄²

D₄×D₄₃

yes

—

185

C₄²

Q₈×D₄₃

yes

—

186

C₂³

C₂²×C₂²⋊D₄₃

yes

characteristic

187

Q₈

—

188

Q₈

—

344

—

189

Q₈

—

344

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

172

—

195

C₂×C₄

—

172

—

196

C₂×C₄

—

172

—

197

C₂×C₄

—

172

—

198

C₂×C₄

#13063321

yes

—

199

C₂×C₄

#13063321

yes

—

200

C₂×C₄

#13063323

yes

—

201

C₂×C₄

#13063351

yes

—

202

C₂×C₄

#13063356

yes

—

203

C₂×C₄

C₂×D₄×D₄₃

yes

—

204

C₂×C₄

C₂×Q₈×D₄₃

yes

—

205

C₈

—

206

C₂²

C₂×#13063321

yes

characteristic

207

C₂²

C₂×#13063323

yes

—

208

C₂²

C₂×#13063351

yes

—

209

C₂²

C₂×#13063356

yes

—

210

C₄

—

211

C₄

—

212

C₄

—

344

—

213

C₄

—

344

—

214

C₄

#14583286

yes

—

215

C₄

#14583291

yes

—

216

C₄

C₄⋊Q₈×D₄₃

yes

—

217

C₂

#19142991

yes

characteristic

218

C₂

C₂×#14583286

yes

characteristic

219

C₂

C₂×#14583291

yes

characteristic

220

C₂

#19145137

yes

—

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₃
commutator, cosocle	C₂²×C₄×C₄₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#2868	C₂
socle, prime radical	C₂³×C₄₃	C₂²×D₄
hypercenter	#2868	D₄₃
hypocenter	C₄₃	#33314
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #2868

subgroup

G/H

center

C₂³

C₂²×C₂²⋊D₄₃

commutator, cosocle

C₂²×C₄×C₄₃

C₂⁴

Frattini

C₂²×C₄

C₂³×D₄₃

Fitting

C₄₃×#2868

C₂

socle, prime radical

C₂³×C₄₃

C₂²×D₄

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #2868

N	H ≅ G/N	type
34. #13063236	Q₈	semidirect
94. C₄₃⋊C₈	C₄⋊Q₈	semidirect
133. C₄₃	#33314	semidirect

H ≅ G/N

type

34. #13063236

Q₈

semidirect

94. C₄₃⋊C₈

C₄⋊Q₈

semidirect

133. C₄₃

#33314

semidirect

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

subgroup	index
C₂×#14583302	2
C₂×#14583295	2
#19142973	2
#19134761	2
C₄×#13063236	2
C₄₃×#2868	2
#33314	43

subgroup

index

C₄₃×#2868

Subgroups — #25249180

Conjugacy classes of subgroups

Complements

Maximal subgroups