Group #28507159 — subgroups

Subgroups — #28507159

Order 15104.

494 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 159 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×#16837782	C₂	1	1	yes	maximal, characteristic
2	C₂×#16837207	C₂	1	4	yes	maximal
3	C₄×#14273661	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅₉×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₂₃₆	—	2	1	no	—
6	C₂²×Dic₂₃₆	C₂²	1	2	yes	—
7	C₂×#14273727	—	2	1	no	—
8	#16837782	—	2	2	no	—
9	#16837782	C₄	1	4	yes	complemented
10	C₂×#14273661	C₂²	1	2	yes	—
11	C₄×C₄⋊Dic₅₉	—	2	1	no	—
12	#16837207	—	2	8	no	—
13	#16837165	—	2	1	no	—
14	C₂²×C₁₆×C₅₉	C₂²	1	2	yes	—
15	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
16	C₅₉×C₄⋊C₁₆	—	2	2	no	—
17	C₂²×Dic₁₁₈	—	2	2	no	—
18	C₂×Dic₂₃₆	—	2	4	no	—
19	C₂×Dic₂₃₆	—	2	4	no	—
20	C₂×Dic₂₃₆	—	2	4	no	—
21	C₂×Dic₂₃₆	—	2	2	no	—
22	C₂×Dic₂₃₆	—	4	4	no	—
23	C₂×Dic₂₃₆	C₂×C₄	1	4	yes	—
24	#14273727	—	2	4	no	—
25	#14273727	—	4	2	no	—
26	C₂×C₄⋊Dic₅₉	—	2	2	no	—
27	C₂×C₄⋊Dic₅₉	—	4	1	no	—
28	C₂×C₄⋊Dic₅₉	—	4	1	no	—
29	C₂×C₄×Dic₅₉	—	4	1	no	—
30	#14273661	—	2	2	no	—
31	#14273661	D₄	1	4	yes	—
32	C₅₉⋊#95	—	4	1	no	—
33	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
34	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
35	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
36	C₂×C₁₆×C₅₉	—	2	2	no	—
37	C₂×C₁₆×C₅₉	—	2	4	no	—
38	C₄×C₈×C₅₉	C₂×C₄	1	2	yes	—
39	C₄×C₈×C₅₉	D₄	1	2	yes	—
40	C₂²×C₄×C₅₉	D₈	1	1	yes	characteristic
41	C₂²×C₄×C₅₉	D₈	1	1	yes	characteristic
42	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
43	C₂²×Dic₅₉	—	4	2	no	—
44	C₂²×Dic₅₉	—	4	2	no	—
45	C₂×Dic₁₁₈	—	2	4	no	—
46	C₂×Dic₁₁₈	—	4	4	no	—
47	C₂×Dic₁₁₈	—	4	4	no	—
48	C₂×Dic₁₁₈	—	4	2	no	—
49	C₂×C₈×C₅₉	—	2	2	no	—
50	C₂×C₈×C₅₉	C₂²⋊C₄	1	2	yes	—
51	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
52	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
53	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
54	C₂×C₈×C₅₉	#41	1	2	yes	—
55	C₄²×C₅₉	C₂²⋊C₄	1	2	yes	—
56	C₄²×C₅₉	SD₁₆	1	2	yes	—
57	C₄⋊Dic₅₉	—	2	4	no	—
58	C₄⋊Dic₅₉	—	4	4	no	—
59	C₄⋊Dic₅₉	—	4	4	no	—
60	C₄⋊Dic₅₉	—	4	2	no	—
61	C₄×Dic₅₉	—	8	2	no	—
62	Dic₂₃₆	—	2	8	no	—
63	Dic₂₃₆	—	4	8	no	—
64	Dic₂₃₆	—	4	2	no	—
65	Dic₂₃₆	—	4	2	no	—
66	C₁₆×C₅₉	—	4	2	no	—
67	C₂³×C₅₉	C₂×D₈	1	1	yes	characteristic
68	C₂×C₄×C₅₉	—	2	2	no	—
69	C₂×C₄×C₅₉	#102	1	2	yes	—
70	C₂×C₄×C₅₉	#102	1	2	yes	—
71	C₂×C₄×C₅₉	SD₃₂	1	2	yes	—
72	C₂×C₄×C₅₉	Q₃₂	1	2	yes	—
73	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
74	C₂×C₄×C₅₉	#121	1	2	yes	—
75	C₂×C₄×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
76	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
77	C₂×Dic₅₉	—	4	4	no	—
78	C₂×Dic₅₉	—	4	4	no	—
79	C₂×Dic₅₉	—	8	4	no	—
80	C₂×Dic₅₉	—	8	2	no	—
81	C₂×Dic₅₉	—	8	2	no	—
82	Dic₁₁₈	—	4	4	no	—
83	Dic₁₁₈	—	4	4	no	—
84	Dic₁₁₈	—	8	4	no	—
85	C₈×C₅₉	—	2	2	no	—
86	C₈×C₅₉	C₄×D₄	1	2	yes	—
87	C₈×C₅₉	#124	1	1	yes	characteristic
88	C₈×C₅₉	#127	1	1	yes	characteristic
89	#13253	—	59	1	no	maximal, Sylow
90	C₂²×C₅₉	C₂×#102	1	1	yes	characteristic
91	C₂²×C₅₉	#459	1	2	yes	—
92	C₂²×C₅₉	C₂×SD₃₂	1	1	yes	characteristic
93	C₂²×C₅₉	C₂×Q₃₂	1	1	yes	characteristic
94	C₂²×C₅₉	#510	1	2	yes	—
95	C₄×C₅₉	—	2	2	no	—
96	C₄×C₅₉	#358	1	4	yes	complemented
97	C₄×C₅₉	#390	1	1	yes	characteristic
98	C₄×C₅₉	#418	1	1	yes	characteristic
99	C₄×C₅₉	#460	1	2	yes	—
100	Dic₅₉	—	8	4	no	—
101	Dic₅₉	—	8	4	no	—
102	C₂×#494	—	59	1	no	—
103	C₂×C₄⋊C₁₆	D₅₉	1	1	yes	characteristic
104	C₂×#358	—	59	4	no	—
105	C₄×#107	—	59	1	no	—
106	C₂×C₅₉	#1982	1	1	yes	characteristic
107	C₂×C₅₉	C₂×#358	1	1	yes	characteristic
108	C₂×C₅₉	#2141	1	1	yes	characteristic
109	C₂×C₅₉	#2208	1	2	yes	—
110	C₂×C₅₉	#2209	1	2	yes	—
111	C₂²×Q₁₆	—	59	2	no	—
112	C₂²×Q₁₆	—	118	1	no	—
113	C₂×C₄⋊Q₈	—	118	1	no	—
114	C₂²×C₁₆	C₂×D₅₉	1	2	yes	—
115	#494	—	59	4	no	—
116	#494	—	118	2	no	—
117	C₂×#107	—	59	2	no	—
118	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
119	C₄×C₄⋊C₄	—	118	1	no	—
120	C₄⋊C₁₆	—	2	2	no	—
121	#358	—	118	8	no	—
122	#340	—	118	1	no	—
123	C₅₉	#13253	1	1	yes	characteristic, complemented, Sylow
124	C₂²×Q₈	—	118	2	no	—
125	C₂×Q₁₆	—	59	4	no	—
126	C₂×Q₁₆	—	118	4	no	—
127	C₂×Q₁₆	—	118	4	no	—
128	C₂×Q₁₆	—	118	4	no	—
129	C₂×Q₁₆	—	118	2	no	—
130	C₂×Q₁₆	—	236	4	no	—
131	C₂²×C₈	D₂₃₆	1	1	yes	characteristic
132	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
133	C₄⋊Q₈	—	118	4	no	—
134	C₄⋊Q₈	—	236	2	no	—
135	C₂×C₄⋊C₄	—	118	2	no	—
136	C₂×C₄⋊C₄	—	236	1	no	—
137	C₂×C₄⋊C₄	—	236	1	no	—
138	C₂×C₄²	—	236	1	no	—
139	C₂×C₄²	D₂₃₆	1	1	yes	characteristic
140	C₂×C₁₆	—	2	4	no	—
141	C₂×C₁₆	—	2	2	no	—
142	#107	—	59	4	no	—
143	#107	—	118	2	no	—
144	C₄×C₈	C₄×D₅₉	1	2	yes	—
145	C₄×C₈	C₂²⋊D₅₉	1	2	yes	—
146	#95	—	236	1	no	—
147	C₂×Q₈	—	118	4	no	—
148	C₂×Q₈	—	236	4	no	—
149	C₂×Q₈	—	236	4	no	—
150	C₂×Q₈	—	236	2	no	—
151	C₂²×C₄	—	236	2	no	—
152	C₂²×C₄	—	236	2	no	—
153	C₂²×C₄	D₄₇₂	1	1	yes	characteristic
154	C₂²×C₄	D₄₇₂	1	1	yes	characteristic
155	C₂²×C₄	C₂×D₂₃₆	1	1	yes	characteristic
156	Q₁₆	—	118	8	no	—
157	Q₁₆	—	236	8	no	—
158	Q₁₆	—	236	2	no	—
159	Q₁₆	—	236	2	no	—
160	C₂×C₈	—	2	2	no	—
161	C₂×C₈	(C₂×D₅₉)⋊C₄	1	2	yes	—
162	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
163	C₂×C₈	D₄×D₅₉	1	2	yes	—
164	C₂×C₈	#11745689	1	2	yes	—
165	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
166	C₄⋊C₄	—	118	4	no	—
167	C₄⋊C₄	—	236	4	no	—
168	C₄⋊C₄	—	236	4	no	—
169	C₄⋊C₄	—	236	2	no	—
170	C₄²	—	472	2	no	—
171	C₄²	#11745660	1	2	yes	—
172	C₄²	(C₂×D₅₉)⋊C₄	1	2	yes	—
173	C₁₆	—	4	2	no	—
174	C₂³	C₂×D₄₇₂	1	1	yes	characteristic
175	Q₈	—	472	4	no	—
176	Q₈	—	236	4	no	—
177	Q₈	—	236	4	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	472	2	no	—
180	C₂×C₄	—	472	2	no	—
181	C₂×C₄	—	472	4	no	—
182	C₂×C₄	—	236	4	no	—
183	C₂×C₄	—	236	4	no	—
184	C₂×C₄	#14273649	1	2	yes	—
185	C₂×C₄	#14273649	1	2	yes	—
186	C₂×C₄	#14273672	1	2	yes	—
187	C₂×C₄	Dic₄₇₂	1	2	yes	—
188	C₂×C₄	C₂×(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
189	C₂×C₄	#14273702	1	2	yes	—
190	C₂×C₄	C₂×#11745660	1	1	yes	characteristic
191	C₂×C₄	#14273755	1	2	yes	—
192	C₈	—	2	2	no	—
193	C₈	#14273689	1	2	yes	—
194	C₈	#14273716	1	1	yes	characteristic
195	C₈	#14273723	1	1	yes	characteristic
196	C₂²	C₂×#14273649	1	1	yes	characteristic
197	C₂²	#16837598	1	2	yes	—
198	C₂²	C₂×#14273672	1	1	yes	characteristic
199	C₂²	C₂×Dic₄₇₂	1	1	yes	characteristic
200	C₂²	#16837845	1	2	yes	—
201	C₄	—	2	2	no	—
202	C₄	—	472	4	no	—
203	C₄	—	472	4	no	—
204	C₄	#16837207	1	4	yes	complemented
205	C₄	#16837303	1	1	yes	characteristic
206	C₄	#16837408	1	1	yes	characteristic
207	C₄	#16837603	1	2	yes	—
208	C₂	#21425022	1	1	yes	characteristic
209	C₂	C₂×#16837207	1	1	yes	characteristic
210	C₂	#21425817	1	1	yes	characteristic
211	C₂	#21426142	1	2	yes	—
212	C₂	#21426147	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#16837782

C₂

yes

maximal, characteristic

C₂×#16837207

C₂

yes

maximal

C₄×#14273661

C₂

yes

maximal, characteristic

C₂×C₅₉×C₄⋊C₁₆

C₂

yes

maximal, characteristic

C₂²×Dic₂₃₆

—

C₂²×Dic₂₃₆

C₂²

yes

—

C₂×#14273727

—

#16837782

—

#16837782

C₄

yes

complemented

C₂×#14273661

C₂²

yes

—

C₄×C₄⋊Dic₅₉

—

#16837207

—

#16837165

—

C₂²×C₁₆×C₅₉

C₂²

yes

—

C₂×C₄×C₈×C₅₉

C₂²

yes

characteristic

C₅₉×C₄⋊C₁₆

—

C₂²×Dic₁₁₈

—

C₂×Dic₂₃₆

—

C₂×Dic₂₃₆

—

C₂×Dic₂₃₆

—

C₂×Dic₂₃₆

—

C₂×Dic₂₃₆

—

C₂×Dic₂₃₆

C₂×C₄

yes

—

#14273727

—

#14273727

—

C₂×C₄⋊Dic₅₉

—

C₂×C₄⋊Dic₅₉

—

C₂×C₄⋊Dic₅₉

—

C₂×C₄×Dic₅₉

—

#14273661

—

#14273661

D₄

yes

—

C₅₉⋊#95

—

C₂²×C₈×C₅₉

D₄

yes

characteristic

C₂²×C₈×C₅₉

C₂³

yes

characteristic

C₂×C₄²×C₅₉

D₄

yes

characteristic

C₂×C₁₆×C₅₉

—

C₂×C₁₆×C₅₉

—

C₄×C₈×C₅₉

C₂×C₄

yes

—

C₄×C₈×C₅₉

D₄

yes

—

C₂²×C₄×C₅₉

D₈

yes

characteristic

C₂²×C₄×C₅₉

D₈

yes

characteristic

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂²×Dic₅₉

—

C₂²×Dic₅₉

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

C₂²⋊C₄

yes

—

C₂×C₈×C₅₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₅₉

C₂×D₄

yes

—

C₂×C₈×C₅₉

C₂×D₄

yes

characteristic

C₂×C₈×C₅₉

#41

yes

—

C₄²×C₅₉

C₂²⋊C₄

yes

—

C₄²×C₅₉

SD₁₆

yes

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄×Dic₅₉

—

Dic₂₃₆

—

Dic₂₃₆

—

Dic₂₃₆

—

Dic₂₃₆

—

C₁₆×C₅₉

—

C₂³×C₅₉

C₂×D₈

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

#102

yes

—

C₂×C₄×C₅₉

#102

yes

—

C₂×C₄×C₅₉

SD₃₂

yes

—

C₂×C₄×C₅₉

Q₃₂

yes

—

C₂×C₄×C₅₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₅₉

#121

yes

—

C₂×C₄×C₅₉

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₅₉

AGL(1,ℤ/8)

yes

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

Dic₁₁₈

—

Dic₁₁₈

—

Dic₁₁₈

—

C₈×C₅₉

—

C₈×C₅₉

C₄×D₄

yes

—

C₈×C₅₉

yes

C₈×C₅₉

yes

—

C₂²×C₅₉

yes

C₂²×C₅₉

yes

—

C₂²×C₅₉

C₂×SD₃₂

yes

characteristic

C₂²×C₅₉

C₂×Q₃₂

yes

characteristic

C₂²×C₅₉

#510

yes

—

C₄×C₅₉

—

C₄×C₅₉

yes

C₄×C₅₉

yes

C₄×C₅₉

yes

C₄×C₅₉

yes

—

100

Dic₅₉

—

101

Dic₅₉

—

102

C₂×#494

—

103

C₂×C₄⋊C₁₆

D₅₉

yes

characteristic

104

C₂×#358

—

105

C₄×#107

—

106

C₂×C₅₉

#1982

yes

characteristic

107

C₂×C₅₉

C₂×#358

yes

characteristic

108

C₂×C₅₉

#2141

yes

characteristic

109

C₂×C₅₉

#2208

yes

—

110

C₂×C₅₉

#2209

yes

—

111

C₂²×Q₁₆

—

112

C₂²×Q₁₆

—

118

—

113

C₂×C₄⋊Q₈

—

118

—

114

C₂²×C₁₆

C₂×D₅₉

yes

—

115

#494

—

116

#494

—

118

—

117

C₂×#107

—

118

C₂×C₄×C₈

C₂×D₅₉

yes

characteristic

119

C₄×C₄⋊C₄

—

118

—

120

C₄⋊C₁₆

—

121

#358

—

118

—

122

#340

—

118

—

123

C₅₉

#13253

yes

characteristic, complemented, Sylow

124

C₂²×Q₈

—

118

—

125

C₂×Q₁₆

—

126

C₂×Q₁₆

—

118

—

127

C₂×Q₁₆

—

118

—

128

C₂×Q₁₆

—

118

—

129

C₂×Q₁₆

—

118

—

130

C₂×Q₁₆

—

236

—

131

C₂²×C₈

D₂₃₆

yes

characteristic

132

C₂²×C₈

C₂²×D₅₉

yes

characteristic

133

C₄⋊Q₈

—

118

—

134

C₄⋊Q₈

—

236

—

135

C₂×C₄⋊C₄

—

118

—

136

C₂×C₄⋊C₄

—

236

—

137

C₂×C₄⋊C₄

—

236

—

138

C₂×C₄²

—

236

—

139

C₂×C₄²

D₂₃₆

yes

characteristic

140

C₂×C₁₆

—

141

C₂×C₁₆

—

142

#107

—

143

#107

—

118

—

144

C₄×C₈

C₄×D₅₉

yes

—

145

C₄×C₈

C₂²⋊D₅₉

yes

—

146

#95

—

236

—

147

C₂×Q₈

—

118

—

148

C₂×Q₈

—

236

—

149

C₂×Q₈

—

236

—

150

C₂×Q₈

—

236

—

151

C₂²×C₄

—

236

—

152

C₂²×C₄

—

236

—

153

C₂²×C₄

D₄₇₂

yes

characteristic

154

C₂²×C₄

D₄₇₂

yes

characteristic

155

C₂²×C₄

C₂×D₂₃₆

yes

characteristic

156

Q₁₆

—

118

—

157

Q₁₆

—

236

—

158

Q₁₆

—

236

—

159

Q₁₆

—

236

—

160

C₂×C₈

—

161

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

—

162

C₂×C₈

C₂×C₄×D₅₉

yes

characteristic

163

C₂×C₈

D₄×D₅₉

yes

—

164

C₂×C₈

#11745689

yes

—

165

C₂×C₈

C₂×C₂²⋊D₅₉

yes

characteristic

166

C₄⋊C₄

—

118

—

167

C₄⋊C₄

—

236

—

168

C₄⋊C₄

—

236

—

169

C₄⋊C₄

—

236

—

170

C₄²

—

472

—

171

C₄²

#11745660

yes

—

172

C₄²

(C₂×D₅₉)⋊C₄

yes

—

173

C₁₆

—

174

C₂³

C₂×D₄₇₂

yes

characteristic

175

Q₈

—

472

—

176

Q₈

—

236

—

177

Q₈

—

236

—

178

C₂×C₄

—

179

C₂×C₄

—

472

—

180

C₂×C₄

—

472

—

181

C₂×C₄

—

472

—

182

C₂×C₄

—

236

—

183

C₂×C₄

—

236

—

184

C₂×C₄

#14273649

yes

—

185

C₂×C₄

#14273649

yes

—

186

C₂×C₄

#14273672

yes

—

187

C₂×C₄

Dic₄₇₂

yes

—

188

C₂×C₄

C₂×(C₂×D₅₉)⋊C₄

yes

characteristic

189

C₂×C₄

#14273702

yes

—

190

C₂×C₄

C₂×#11745660

yes

characteristic

191

C₂×C₄

#14273755

yes

—

192

C₈

—

193

C₈

#14273689

yes

—

194

C₈

#14273716

yes

characteristic

195

C₈

#14273723

yes

characteristic

196

C₂²

C₂×#14273649

yes

characteristic

197

C₂²

#16837598

yes

—

198

C₂²

C₂×#14273672

yes

characteristic

199

C₂²

C₂×Dic₄₇₂

yes

characteristic

200

C₂²

#16837845

yes

—

201

C₄

—

202

C₄

—

472

—

203

C₄

—

472

—

204

C₄

#16837207

yes

complemented

205

C₄

#16837303

yes

characteristic

206

C₄

#16837408

yes

characteristic

207

C₄

#16837603

yes

—

208

C₂

#21425022

yes

characteristic

209

C₂

C₂×#16837207

yes

characteristic

210

C₂

#21425817

yes

characteristic

211

C₂

#21426142

yes

—

212

C₂

#21426147

yes

—

	subgroup	G/H
center	C₂³	C₂×D₄₇₂
commutator	C₂×C₈×C₅₉	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₅₉
Fitting	C₂×C₅₉×C₄⋊C₁₆	C₂
socle, prime radical	C₂³×C₅₉	C₂×D₈
cosocle	C₂²×C₈×C₅₉	C₂³
hypercenter	C₂×C₄⋊C₁₆	D₅₉
hypocenter	C₅₉	#13253
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄⋊C₁₆

subgroup

G/H

center

C₂³

C₂×D₄₇₂

commutator

C₂×C₈×C₅₉

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₅₉

Fitting

C₂×C₅₉×C₄⋊C₁₆

C₂

socle, prime radical

C₂³×C₅₉

C₂×D₈

cosocle

C₂²×C₈×C₅₉

C₂³

hypercenter

C₂×C₄⋊C₁₆

D₅₉

hypocenter

C₅₉

#13253

LCS

G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄⋊C₁₆

N	H ≅ G/N	type
9. #16837782	C₄	semidirect
96. C₄×C₅₉	#358	semidirect
123. C₅₉	#13253	semidirect
204. C₄	#16837207	semidirect

H ≅ G/N

type

9. #16837782

C₄

semidirect

96. C₄×C₅₉

#358

semidirect

123. C₅₉

#13253

semidirect

204. C₄

#16837207

semidirect

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

subgroup	index
C₂×#16837782	2
C₂×#16837207	2
C₄×#14273661	2
C₂×C₅₉×C₄⋊C₁₆	2
#13253	59

subgroup

index

C₂×C₅₉×C₄⋊C₁₆

Subgroups — #28507159

Conjugacy classes of subgroups

Complements

Maximal subgroups