Group #28363749 — subgroups

Subgroups — #28363749

Order 13952.

260 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 117 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×C₄⋊#11724784	C₂	1	1	yes	maximal, characteristic
2	C₂×#16812628	C₂	1	1	yes	maximal, characteristic
3	C₂×#16812628	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×Dic₁₀₉	C₂	1	1	yes	maximal, characteristic
5	C₄×#13182008	C₂	1	1	yes	maximal, characteristic
6	#20294780	C₂	1	1	yes	maximal, characteristic
7	#336×C₁₀₉	C₂	1	1	yes	maximal, characteristic
8	C₂²×#11724784	C₂²	1	1	yes	characteristic
9	C₂²×#11724784	C₂²	1	1	yes	characteristic
10	C₂×#13182008	C₄	1	1	yes	characteristic
11	C₂×#13182008	C₄	1	1	yes	characteristic
12	C₂×C₄×Dic₁₀₉	C₂²	1	1	yes	characteristic
13	C₂×C₄×Dic₁₀₉	C₂²	1	1	yes	characteristic
14	C₄⋊#11724784	—	2	2	no	—
15	#16812628	—	2	2	no	—
16	#16812628	—	2	2	no	—
17	C₈×Dic₁₀₉	—	2	2	no	—
18	#16812606	C₄	1	1	yes	characteristic
19	#16812606	C₄	1	1	yes	characteristic
20	C₂²×C₈×C₁₀₉	C₂²	1	1	yes	characteristic
21	C₂²×C₈×C₁₀₉	C₂²	1	1	yes	characteristic
22	C₂×C₄²×C₁₀₉	C₂²	1	1	yes	characteristic
23	C₂²×Dic₁₀₉	C₂×C₄	1	1	yes	characteristic
24	C₂²×Dic₁₀₉	C₂×C₄	1	1	yes	characteristic
25	C₂²×Dic₁₀₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×Dic₁₀₉	C₂×C₄	1	1	yes	characteristic
27	C₂×#11724784	—	2	1	no	—
28	C₂×#11724784	—	2	1	no	—
29	C₂×#11724784	—	2	1	no	—
30	C₂×#11724784	—	2	1	no	—
31	C₂×#11724784	—	2	1	no	—
32	C₂×#11724784	D₄	1	2	yes	—
33	#13182008	—	2	2	no	—
34	#13182008	C₈	1	4	yes	complemented
35	C₄×Dic₁₀₉	—	2	1	no	—
36	C₄×Dic₁₀₉	—	2	1	no	—
37	C₄×Dic₁₀₉	D₄	1	2	yes	—
38	C₄×Dic₁₀₉	Q₈	1	2	yes	—
39	C₂²×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
42	C₂×C₈×C₁₀₉	—	2	1	no	—
43	C₂×C₈×C₁₀₉	—	2	1	no	—
44	C₂×C₈×C₁₀₉	—	2	1	no	—
45	C₂×C₈×C₁₀₉	—	2	1	no	—
46	C₂×C₈×C₁₀₉	—	2	1	no	—
47	C₂×C₈×C₁₀₉	Q₈	1	2	yes	—
48	C₄²×C₁₀₉	—	2	1	no	—
49	C₄²×C₁₀₉	—	2	1	no	—
50	C₂³×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₄×C₁₀₉	—	2	1	no	—
52	C₂×C₄×C₁₀₉	—	2	1	no	—
53	C₂×C₄×C₁₀₉	—	2	1	no	—
54	C₂×C₄×C₁₀₉	—	2	1	no	—
55	C₂×C₄×C₁₀₉	—	2	1	no	—
56	C₂×C₄×C₁₀₉	C₂×C₈	1	2	yes	—
57	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
58	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
59	C₂×C₄×C₁₀₉	C₂×Q₈	1	1	yes	characteristic
60	C₂×C₄×C₁₀₉	C₂×Q₈	1	1	yes	characteristic
61	C₂×C₄×C₁₀₉	#41	1	1	yes	characteristic
62	C₂×C₄×C₁₀₉	#41	1	1	yes	characteristic
63	C₂×Dic₁₀₉	—	2	1	no	—
64	C₂×Dic₁₀₉	—	2	1	no	—
65	C₂×Dic₁₀₉	—	2	1	no	—
66	C₂×Dic₁₀₉	—	2	1	no	—
67	C₂×Dic₁₀₉	—	2	1	no	—
68	C₂×Dic₁₀₉	—	2	1	no	—
69	C₂×Dic₁₀₉	—	2	1	no	—
70	C₂×Dic₁₀₉	C₄⋊C₄	1	2	yes	—
71	C₂×Dic₁₀₉	C₄⋊C₄	1	2	yes	—
72	C₂×Dic₁₀₉	C₂×C₈	1	2	yes	—
73	C₂×Dic₁₀₉	C₂×C₈	1	2	yes	—
74	C₂×Dic₁₀₉	M₁₆	1	2	yes	—
75	C₈×C₁₀₉	—	2	2	no	—
76	C₈×C₁₀₉	—	4	1	no	—
77	#11724784	—	2	2	no	—
78	#11724784	—	4	1	no	—
79	C₂²×C₁₀₉	C₂×C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₁₀₉	C₄×D₄	1	1	yes	characteristic
81	C₂²×C₁₀₉	C₄×Q₈	1	1	yes	characteristic
82	C₂²×C₁₀₉	C₂²×C₈	1	1	yes	characteristic
83	C₂²×C₁₀₉	C₂×M₁₆	1	1	yes	characteristic
84	C₂²×C₁₀₉	#131	1	1	yes	characteristic
85	C₂²×C₁₀₉	#131	1	1	yes	characteristic
86	C₄×C₁₀₉	—	2	2	no	—
87	C₄×C₁₀₉	—	4	1	no	—
88	C₄×C₁₀₉	#121	1	1	yes	characteristic
89	C₄×C₁₀₉	C₂²⋊Q₈	1	1	yes	characteristic
90	C₄×C₁₀₉	#125	1	1	yes	characteristic
91	C₄×C₁₀₉	C₄⋊Q₈	1	1	yes	characteristic
92	Dic₁₀₉	—	2	2	no	—
93	Dic₁₀₉	—	2	2	no	—
94	Dic₁₀₉	—	4	1	no	—
95	Dic₁₀₉	C₄⋊C₈	1	4	yes	complemented
96	C₂×C₁₀₉	#389	1	1	yes	characteristic
97	C₂×C₁₀₉	C₂×C₄⋊C₈	1	1	yes	characteristic
98	C₂×C₁₀₉	#424	1	1	yes	characteristic
99	C₂×C₁₀₉	C₈×D₄	1	1	yes	characteristic
100	C₂×C₁₀₉	#436	1	1	yes	characteristic
101	C₂×C₁₀₉	C₈×Q₈	1	1	yes	characteristic
102	C₂×C₁₀₉	#446	1	1	yes	characteristic
103	#1939	—	109	1	no	maximal, Sylow
104	C₁₀₉	#1939	1	1	yes	characteristic, complemented, Sylow
105	C₂×C₄⋊C₈	—	109	1	no	—
106	C₂×C₄⋊C₈	—	109	1	no	—
107	C₂×C₄⋊C₈	—	109	1	no	—
108	C₂×C₄×C₈	—	109	1	no	—
109	C₄×C₄⋊C₄	—	109	1	no	—
110	#336	—	109	1	no	—
111	#336	D₁₀₉	1	1	yes	characteristic
112	C₂²×C₈	—	109	1	no	—
113	C₂²×C₈	—	109	1	no	—
114	C₂²×C₈	C₂×D₁₀₉	1	1	yes	characteristic
115	C₂²×C₈	C₂×D₁₀₉	1	1	yes	characteristic
116	C₂×C₄⋊C₄	—	109	1	no	—
117	C₂×C₄⋊C₄	—	109	1	no	—
118	C₂×C₄²	—	109	1	no	—
119	C₂×C₄²	—	109	1	no	—
120	C₂×C₄²	C₂×D₁₀₉	1	1	yes	characteristic
121	C₄⋊C₈	—	218	2	no	—
122	C₄⋊C₈	—	218	2	no	—
123	C₄⋊C₈	—	218	2	no	—
124	C₄×C₈	—	218	2	no	—
125	#95	—	109	1	no	—
126	#95	—	109	1	no	—
127	C₂²×C₄	—	109	1	no	—
128	C₂²×C₄	—	109	1	no	—
129	C₂²×C₄	—	109	1	no	—
130	C₂²×C₄	—	109	1	no	—
131	C₂²×C₄	C₄×D₁₀₉	1	1	yes	characteristic
132	C₂²×C₄	C₄×D₁₀₉	1	1	yes	characteristic
133	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
134	C₂×C₈	—	2	1	no	—
135	C₂×C₈	—	2	1	no	—
136	C₂×C₈	—	2	1	no	—
137	C₂×C₈	—	2	1	no	—
138	C₂×C₈	—	2	1	no	—
139	C₂×C₈	—	109	2	no	—
140	C₂×C₈	—	218	1	no	—
141	C₂×C₈	—	218	1	no	—
142	C₂×C₈	—	218	1	no	—
143	C₂×C₈	—	218	1	no	—
144	C₂×C₈	—	218	1	no	—
145	C₂×C₈	Dic₂₁₈	1	2	yes	—
146	C₄⋊C₄	—	109	4	no	—
147	C₄⋊C₄	—	218	2	no	—
148	C₄²	—	2	1	no	—
149	C₄²	—	2	1	no	—
150	C₄²	—	109	2	no	—
151	C₄²	—	109	2	no	—
152	C₄²	—	218	1	no	—
153	C₄²	—	218	1	no	—
154	C₂³	C₂×C₄×D₁₀₉	1	1	yes	characteristic
155	C₂×C₄	—	2	1	no	—
156	C₂×C₄	—	2	1	no	—
157	C₂×C₄	—	2	1	no	—
158	C₂×C₄	—	2	1	no	—
159	C₂×C₄	—	2	1	no	—
160	C₂×C₄	—	109	2	no	—
161	C₂×C₄	—	109	2	no	—
162	C₂×C₄	—	109	2	no	—
163	C₂×C₄	—	109	2	no	—
164	C₂×C₄	—	109	2	no	—
165	C₂×C₄	—	218	1	no	—
166	C₂×C₄	—	218	1	no	—
167	C₂×C₄	—	218	1	no	—
168	C₂×C₄	—	218	1	no	—
169	C₂×C₄	—	218	1	no	—
170	C₂×C₄	—	218	1	no	—
171	C₂×C₄	—	218	1	no	—
172	C₂×C₄	C₈×D₁₀₉	1	2	yes	—
173	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
174	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
175	C₂×C₄	Q₈×D₁₀₉	1	1	yes	characteristic
176	C₂×C₄	C₂×Dic₂₁₈	1	1	yes	characteristic
177	C₂×C₄	#13182028	1	1	yes	characteristic
178	C₂×C₄	#13182029	1	1	yes	characteristic
179	C₈	—	2	2	no	—
180	C₈	—	4	1	no	—
181	C₈	—	436	1	no	—
182	C₈	—	218	2	no	—
183	C₂²	C₄⋊C₄×D₁₀₉	1	1	yes	characteristic
184	C₂²	#16812659	1	1	yes	characteristic
185	C₂²	C₄×Dic₂₁₈	1	1	yes	characteristic
186	C₂²	C₂×C₈×D₁₀₉	1	1	yes	characteristic
187	C₂²	M₁₆×D₁₀₉	1	1	yes	characteristic
188	C₂²	#16812705	1	1	yes	characteristic
189	C₂²	#16812707	1	1	yes	characteristic
190	C₄	—	2	2	no	—
191	C₄	—	4	1	no	—
192	C₄	—	109	4	no	—
193	C₄	—	436	1	no	—
194	C₄	—	218	2	no	—
195	C₄	—	218	2	no	—
196	C₄	#16812672	1	1	yes	characteristic
197	C₄	#16812676	1	1	yes	characteristic
198	C₄	#16812689	1	1	yes	characteristic
199	C₄	#16812698	1	1	yes	characteristic
200	C₂	#20294923	1	1	yes	characteristic
201	C₂	C₄⋊C₈×D₁₀₉	1	1	yes	characteristic
202	C₂	#20295051	1	1	yes	characteristic
203	C₂	#20295089	1	1	yes	characteristic
204	C₂	#20295101	1	1	yes	characteristic
205	C₂	C₈×Dic₂₁₈	1	1	yes	characteristic
206	C₂	#20295154	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊#11724784

C₂

yes

maximal, characteristic

C₂×#16812628

C₂

yes

maximal, characteristic

C₂×#16812628

C₂

yes

maximal, characteristic

C₂×C₈×Dic₁₀₉

C₂

yes

maximal, characteristic

C₄×#13182008

C₂

yes

maximal, characteristic

#20294780

C₂

yes

maximal, characteristic

#336×C₁₀₉

C₂

yes

maximal, characteristic

C₂²×#11724784

C₂²

yes

characteristic

C₂²×#11724784

C₂²

yes

characteristic

C₂×#13182008

C₄

yes

characteristic

C₂×#13182008

C₄

yes

characteristic

C₂×C₄×Dic₁₀₉

C₂²

yes

characteristic

C₂×C₄×Dic₁₀₉

C₂²

yes

—

—

—

C₈×Dic₁₀₉

—

#16812606

C₄

yes

characteristic

#16812606

C₄

yes

characteristic

C₂²×C₈×C₁₀₉

C₂²

yes

characteristic

C₂²×C₈×C₁₀₉

C₂²

yes

characteristic

C₂×C₄²×C₁₀₉

C₂²

yes

characteristic

C₂²×Dic₁₀₉

C₂×C₄

yes

characteristic

C₂²×Dic₁₀₉

C₂×C₄

yes

characteristic

C₂²×Dic₁₀₉

C₂×C₄

yes

characteristic

C₂²×Dic₁₀₉

C₂×C₄

yes

—

—

—

—

—

D₄

yes

—

#13182008

—

#13182008

C₈

yes

complemented

C₄×Dic₁₀₉

—

C₄×Dic₁₀₉

—

C₄×Dic₁₀₉

D₄

yes

—

C₄×Dic₁₀₉

Q₈

yes

—

C₂²×C₄×C₁₀₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₀₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₀₉

C₂³

yes

characteristic

C₂×C₈×C₁₀₉

—

C₂×C₈×C₁₀₉

—

C₂×C₈×C₁₀₉

—

C₂×C₈×C₁₀₉

—

C₂×C₈×C₁₀₉

—

C₂×C₈×C₁₀₉

Q₈

yes

—

C₄²×C₁₀₉

—

C₄²×C₁₀₉

—

C₂³×C₁₀₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₀₉

—

C₂×C₄×C₁₀₉

—

C₂×C₄×C₁₀₉

—

C₂×C₄×C₁₀₉

—

C₂×C₄×C₁₀₉

—

C₂×C₄×C₁₀₉

C₂×C₈

yes

—

C₂×C₄×C₁₀₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₀₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₀₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₀₉

C₂×Q₈

yes

C₂×C₄×C₁₀₉

yes

C₂×C₄×C₁₀₉

yes

C₂×Dic₁₀₉

—

C₂×Dic₁₀₉

—

C₂×Dic₁₀₉

—

C₂×Dic₁₀₉

—

C₂×Dic₁₀₉

—

C₂×Dic₁₀₉

—

C₂×Dic₁₀₉

—

C₂×Dic₁₀₉

C₄⋊C₄

yes

—

C₂×Dic₁₀₉

C₄⋊C₄

yes

—

C₂×Dic₁₀₉

C₂×C₈

yes

—

C₂×Dic₁₀₉

C₂×C₈

yes

—

C₂×Dic₁₀₉

M₁₆

yes

—

C₈×C₁₀₉

—

C₈×C₁₀₉

—

#11724784

—

#11724784

—

C₂²×C₁₀₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₀₉

C₄×D₄

yes

characteristic

C₂²×C₁₀₉

C₄×Q₈

yes

characteristic

C₂²×C₁₀₉

C₂²×C₈

yes

characteristic

C₂²×C₁₀₉

C₂×M₁₆

yes

C₂²×C₁₀₉

yes

C₂²×C₁₀₉

yes

C₄×C₁₀₉

—

C₄×C₁₀₉

—

C₄×C₁₀₉

#121

yes

characteristic

C₄×C₁₀₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₀₉

#125

yes

characteristic

C₄×C₁₀₉

C₄⋊Q₈

yes

characteristic

Dic₁₀₉

—

Dic₁₀₉

—

Dic₁₀₉

—

Dic₁₀₉

C₄⋊C₈

yes

complemented

C₂×C₁₀₉

#389

yes

characteristic

C₂×C₁₀₉

C₂×C₄⋊C₈

yes

characteristic

C₂×C₁₀₉

#424

yes

characteristic

C₂×C₁₀₉

C₈×D₄

yes

characteristic

100

C₂×C₁₀₉

#436

yes

characteristic

101

C₂×C₁₀₉

C₈×Q₈

yes

characteristic

102

C₂×C₁₀₉

#446

yes

characteristic

103

#1939

—

109

maximal, Sylow

104

C₁₀₉

#1939

yes

characteristic, complemented, Sylow

105

C₂×C₄⋊C₈

—

109

—

106

C₂×C₄⋊C₈

—

109

—

107

C₂×C₄⋊C₈

—

109

—

108

C₂×C₄×C₈

—

109

—

109

C₄×C₄⋊C₄

—

109

—

110

#336

—

109

—

111

#336

D₁₀₉

yes

characteristic

112

C₂²×C₈

—

109

—

113

C₂²×C₈

—

109

—

114

C₂²×C₈

C₂×D₁₀₉

yes

characteristic

115

C₂²×C₈

C₂×D₁₀₉

yes

characteristic

116

C₂×C₄⋊C₄

—

109

—

117

C₂×C₄⋊C₄

—

109

—

118

C₂×C₄²

—

109

—

119

C₂×C₄²

—

109

—

120

C₂×C₄²

C₂×D₁₀₉

yes

characteristic

121

C₄⋊C₈

—

218

—

122

C₄⋊C₈

—

218

—

123

C₄⋊C₈

—

218

—

124

C₄×C₈

—

218

—

125

#95

—

109

—

126

#95

—

109

—

127

C₂²×C₄

—

109

—

128

C₂²×C₄

—

109

—

129

C₂²×C₄

—

109

—

130

C₂²×C₄

—

109

—

131

C₂²×C₄

C₄×D₁₀₉

yes

characteristic

132

C₂²×C₄

C₄×D₁₀₉

yes

characteristic

133

C₂²×C₄

C₂²×D₁₀₉

yes

characteristic

134

C₂×C₈

—

135

C₂×C₈

—

136

C₂×C₈

—

137

C₂×C₈

—

138

C₂×C₈

—

139

C₂×C₈

—

109

—

140

C₂×C₈

—

218

—

141

C₂×C₈

—

218

—

142

C₂×C₈

—

218

—

143

C₂×C₈

—

218

—

144

C₂×C₈

—

218

—

145

C₂×C₈

Dic₂₁₈

yes

—

146

C₄⋊C₄

—

109

—

147

C₄⋊C₄

—

218

—

148

C₄²

—

149

C₄²

—

150

C₄²

—

109

—

151

C₄²

—

109

—

152

C₄²

—

218

—

153

C₄²

—

218

—

154

C₂³

C₂×C₄×D₁₀₉

yes

characteristic

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

109

—

161

C₂×C₄

—

109

—

162

C₂×C₄

—

109

—

163

C₂×C₄

—

109

—

164

C₂×C₄

—

109

—

165

C₂×C₄

—

218

—

166

C₂×C₄

—

218

—

167

C₂×C₄

—

218

—

168

C₂×C₄

—

218

—

169

C₂×C₄

—

218

—

170

C₂×C₄

—

218

—

171

C₂×C₄

—

218

—

172

C₂×C₄

C₈×D₁₀₉

yes

—

173

C₂×C₄

D₄×D₁₀₉

yes

characteristic

174

C₂×C₄

D₄×D₁₀₉

yes

characteristic

175

C₂×C₄

Q₈×D₁₀₉

yes

characteristic

176

C₂×C₄

C₂×Dic₂₁₈

yes

characteristic

177

C₂×C₄

#13182028

yes

characteristic

178

C₂×C₄

#13182029

yes

characteristic

179

C₈

—

180

C₈

—

181

C₈

—

436

—

182

C₈

—

218

—

183

C₂²

C₄⋊C₄×D₁₀₉

yes

characteristic

184

C₂²

#16812659

yes

characteristic

185

C₂²

C₄×Dic₂₁₈

yes

characteristic

186

C₂²

C₂×C₈×D₁₀₉

yes

characteristic

187

C₂²

M₁₆×D₁₀₉

yes

characteristic

188

C₂²

#16812705

yes

characteristic

189

C₂²

#16812707

yes

characteristic

190

C₄

—

191

C₄

—

192

C₄

—

109

—

193

C₄

—

436

—

194

C₄

—

218

—

195

C₄

—

218

—

196

C₄

#16812672

yes

characteristic

197

C₄

#16812676

yes

characteristic

198

C₄

#16812689

yes

characteristic

199

C₄

#16812698

yes

characteristic

200

C₂

#20294923

yes

characteristic

201

C₂

C₄⋊C₈×D₁₀₉

yes

characteristic

202

C₂

#20295051

yes

characteristic

203

C₂

#20295089

yes

characteristic

204

C₂

#20295101

yes

characteristic

205

C₂

C₈×Dic₂₁₈

yes

characteristic

206

C₂

#20295154

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₀₉
commutator	C₂²×C₁₀₉	C₂²×C₈
Fitting	#336×C₁₀₉	C₂
socle, prime radical	C₂³×C₁₀₉	C₂²×C₄
cosocle	C₂²×C₄×C₁₀₉	C₂³
hypercenter	#336	D₁₀₉
hypocenter	C₁₀₉	#1939
LCS	G ▷ C₂²×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂²×C₄ ◁ #336

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₁₀₉

commutator

C₂²×C₁₀₉

C₂²×C₈

Fitting

#336×C₁₀₉

C₂

socle, prime radical

C₂³×C₁₀₉

C₂²×C₄

cosocle

C₂²×C₄×C₁₀₉

C₂³

D₁₀₉

C₁₀₉

G ▷ C₂²×C₁₀₉ ▷ C₁₀₉

C₁ ◁ C₂²×C₄ ◁ #336

N	H ≅ G/N	type
34. #13182008	C₈	semidirect
95. Dic₁₀₉	C₄⋊C₈	semidirect
104. C₁₀₉	#1939	semidirect

H ≅ G/N

type

34. #13182008

C₈

semidirect

95. Dic₁₀₉

C₄⋊C₈

semidirect

104. C₁₀₉

#1939

semidirect

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

subgroup	index
C₂×C₄⋊#11724784	2
C₂×#16812628	2
C₂×C₈×Dic₁₀₉	2
C₄×#13182008	2
#20294780	2
#336×C₁₀₉	2
#1939	109

subgroup

index

C₂×C₈×Dic₁₀₉

#336×C₁₀₉

109

Subgroups — #28363749

Conjugacy classes of subgroups

Complements

Maximal subgroups