Group #21436971 — subgroups

Subgroups — #21436971

Order 7552.

338 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 133 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	#16838130	C₂	1	1	yes	maximal, characteristic, complemented
2	#16837801	C₂	1	2	yes	maximal, complemented
3	#16837798	C₂	1	1	yes	maximal, characteristic, complemented
4	#16837706	C₂	1	2	yes	maximal, complemented
5	#16837702	C₂	1	2	yes	maximal
6	#16837694	C₂	1	1	yes	maximal, characteristic, complemented
7	#16837682	C₂	1	1	yes	maximal, characteristic
8	Q₈×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#11745670	C₂	1	1	yes	maximal, characteristic
10	C₄×#11745670	C₂	1	2	yes	maximal
11	C₅₉×#554	C₂	1	1	yes	maximal, characteristic
12	C₂×#11745670	C₂²	1	1	yes	characteristic
13	#14273727	C₂²	1	1	yes	characteristic
14	#14273725	—	2	1	no	—
15	#14273719	C₂²	1	2	yes	—
16	#14273717	—	2	2	no	—
17	C₄×Dic₁₁₈	C₂²	1	1	yes	characteristic
18	C₄×Dic₁₁₈	C₂²	1	2	yes	—
19	#14273692	—	2	1	no	—
20	#14273660	C₂²	1	2	yes	—
21	#14273660	C₂²	1	2	yes	—
22	#14273658	C₂²	1	2	yes	—
23	#14273658	C₂²	1	2	yes	—
24	#14273658	C₂²	1	1	yes	characteristic
25	C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
26	C₄⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
27	#14273650	C₂²	1	2	yes	—
28	#14273650	C₂²	1	1	yes	characteristic
29	#14273648	C₂²	1	2	yes	—
30	#14273648	C₂²	1	1	yes	characteristic
31	C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
32	C₄×C₅₉⋊C₈	C₂²	1	2	yes	—
33	C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
34	#125×C₅₉	C₂²	1	2	yes	—
35	C₂²⋊Q₈×C₅₉	—	2	1	no	—
36	C₂²⋊Q₈×C₅₉	—	2	2	no	—
37	C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
38	C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
39	C₄×D₄×C₅₉	C₂²	1	2	yes	—
40	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
41	C₂×Q₈×C₅₉	—	2	1	no	—
42	C₂×Q₈×C₅₉	D₄	1	1	yes	characteristic
43	C₂×D₄×C₅₉	C₂³	1	1	yes	characteristic
44	C₂²×C₄×C₅₉	—	2	1	no	—
45	C₂²×C₄×C₅₉	—	2	2	no	—
46	C₂×Dic₁₁₈	—	2	1	no	—
47	C₂×Dic₁₁₈	C₂³	1	1	yes	characteristic
48	C₄⋊C₄×C₅₉	—	2	2	no	—
49	C₄⋊C₄×C₅₉	—	2	1	no	—
50	C₄⋊C₄×C₅₉	—	2	2	no	—
51	C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
52	C₄⋊C₄×C₅₉	D₄	1	2	yes	—
53	C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
54	C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
55	C₂²⋊C₄×C₅₉	—	2	1	no	—
56	C₂²⋊C₄×C₅₉	—	2	2	no	—
57	C₄²×C₅₉	C₂³	1	2	yes	—
58	C₄²×C₅₉	C₂³	1	1	yes	characteristic
59	#11745670	Q₈	1	4	yes	complemented
60	C₄⋊Dic₅₉	—	2	1	no	—
61	C₄⋊Dic₅₉	C₂³	1	2	yes	—
62	C₄⋊Dic₅₉	C₂³	1	1	yes	characteristic
63	Dic₅₉⋊C₄	—	2	2	no	—
64	Dic₅₉⋊C₄	—	2	1	no	—
65	Dic₅₉⋊C₄	—	2	2	no	—
66	Dic₅₉⋊C₄	—	2	2	no	—
67	C₄×Dic₅₉	—	2	2	no	—
68	C₄×Dic₅₉	—	2	1	no	—
69	C₂×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
70	C₂×C₅₉⋊C₈	C₂³	1	2	yes	—
71	C₂×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
72	C₂³×C₅₉	—	2	1	no	—
73	Q₈×C₅₉	—	2	2	no	—
74	Q₈×C₅₉	—	8	1	no	—
75	D₄×C₅₉	—	2	1	no	—
76	D₄×C₅₉	C₂×Q₈	1	2	yes	—
77	C₂×C₄×C₅₉	—	2	1	no	—
78	C₂×C₄×C₅₉	—	2	2	no	—
79	C₂×C₄×C₅₉	—	4	2	no	—
80	C₂×C₄×C₅₉	—	8	2	no	—
81	C₂×C₄×C₅₉	C₂×D₄	1	2	yes	—
82	C₂×C₄×C₅₉	C₂×D₄	1	2	yes	—
83	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
84	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
85	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
86	C₂×Dic₅₉	—	2	1	no	—
87	C₂×Dic₅₉	—	2	1	no	—
88	C₂×Dic₅₉	—	2	2	no	—
89	Dic₁₁₈	—	2	1	no	—
90	Dic₁₁₈	—	4	2	no	—
91	Dic₁₁₈	C₂×Q₈	1	2	yes	—
92	C₅₉⋊C₈	—	2	1	no	—
93	C₅₉⋊C₈	—	2	2	no	—
94	C₅₉⋊C₈	C₂×Q₈	1	2	yes	—
95	C₂²×C₅₉	—	2	2	no	—
96	C₂²×C₅₉	—	4	1	no	—
97	C₂²×C₅₉	—	4	1	no	—
98	C₂²×C₅₉	C₂²×D₄	1	1	yes	characteristic
99	C₄×C₅₉	—	2	2	no	—
100	C₄×C₅₉	—	2	2	no	—
101	C₄×C₅₉	—	2	1	no	—
102	C₄×C₅₉	—	4	1	no	—
103	C₄×C₅₉	—	4	2	no	—
104	C₄×C₅₉	#135	1	2	yes	—
105	C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
106	C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
107	Dic₅₉	—	2	2	no	—
108	Dic₅₉	—	4	2	no	—
109	Dic₅₉	—	4	1	no	—
110	#3381	—	59	1	no	maximal, Sylow
111	C₂×C₅₉	—	4	2	no	—
112	C₂×C₅₉	D₄×Q₈	1	1	yes	characteristic
113	C₂×C₅₉	C₂×#135	1	1	yes	characteristic
114	C₂×C₅₉	#577	1	1	yes	characteristic
115	#557	—	59	1	no	—
116	#554	D₅₉	1	1	yes	characteristic
117	#499	—	59	2	no	—
118	#498	—	59	1	no	—
119	#479	—	59	2	no	—
120	#478	—	59	2	no	—
121	#477	—	59	1	no	—
122	#474	—	59	1	no	—
123	C₈×Q₈	—	59	1	no	—
124	C₄×SD₁₆	—	59	1	no	—
125	C₄×SD₁₆	—	59	2	no	—
126	C₅₉	#3381	1	1	yes	characteristic, complemented, Sylow
127	C₂×SD₁₆	—	59	1	no	—
128	C₄⋊Q₈	—	59	1	no	—
129	C₄⋊Q₈	—	118	1	no	—
130	C₄⋊Q₈	C₂×D₅₉	1	1	yes	characteristic
131	#125	—	59	2	no	—
132	#125	—	118	2	no	—
133	#125	C₂×D₅₉	1	2	yes	—
134	C₂²⋊Q₈	—	2	1	no	—
135	C₂²⋊Q₈	—	2	2	no	—
136	C₄×Q₈	—	59	1	no	—
137	C₄×Q₈	—	59	2	no	—
138	C₄×Q₈	—	118	1	no	—
139	C₄×Q₈	C₂×D₅₉	1	1	yes	characteristic
140	C₄×D₄	C₂×D₅₉	1	1	yes	characteristic
141	C₄×D₄	C₂×D₅₉	1	2	yes	—
142	C₂×C₄⋊C₄	—	2	1	no	—
143	#107	—	59	2	no	—
144	#107	—	59	2	no	—
145	#106	—	59	2	no	—
146	#106	—	59	1	no	—
147	#106	—	59	2	no	—
148	C₄⋊C₈	—	59	1	no	—
149	C₄⋊C₈	—	59	2	no	—
150	#103	—	59	2	no	—
151	#103	—	59	1	no	—
152	#102	—	59	2	no	—
153	#102	—	59	1	no	—
154	C₄×C₈	—	59	1	no	—
155	C₄×C₈	—	59	2	no	—
156	C₂×Q₈	—	2	1	no	—
157	C₂×Q₈	—	59	1	no	—
158	C₂×Q₈	—	118	1	no	—
159	C₂×Q₈	C₂²⋊D₅₉	1	1	yes	characteristic
160	C₂×D₄	C₂²×D₅₉	1	1	yes	characteristic
161	C₂²×C₄	—	2	1	no	—
162	C₂²×C₄	—	2	2	no	—
163	SD₁₆	—	59	4	no	—
164	C₂×C₈	—	59	1	no	—
165	C₂×C₈	—	59	1	no	—
166	C₂×C₈	—	59	2	no	—
167	C₄⋊C₄	—	2	2	no	—
168	C₄⋊C₄	—	2	1	no	—
169	C₄⋊C₄	—	2	2	no	—
170	C₄⋊C₄	—	59	2	no	—
171	C₄⋊C₄	—	59	1	no	—
172	C₄⋊C₄	—	118	1	no	—
173	C₄⋊C₄	—	118	2	no	—
174	C₄⋊C₄	—	118	2	no	—
175	C₄⋊C₄	—	118	2	no	—
176	C₄⋊C₄	—	118	1	no	—
177	C₄⋊C₄	C₂²⋊D₅₉	1	1	yes	characteristic
178	C₄⋊C₄	C₂²⋊D₅₉	1	2	yes	—
179	C₄⋊C₄	C₂²×D₅₉	1	2	yes	—
180	C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
181	C₂²⋊C₄	—	2	1	no	—
182	C₂²⋊C₄	—	2	2	no	—
183	C₄²	—	118	2	no	—
184	C₄²	—	118	1	no	—
185	C₄²	C₂²×D₅₉	1	2	yes	—
186	C₄²	C₂²×D₅₉	1	1	yes	characteristic
187	C₂³	—	2	1	no	—
188	Q₈	—	2	2	no	—
189	Q₈	—	8	1	no	—
190	Q₈	—	59	2	no	—
191	Q₈	—	118	1	no	—
192	Q₈	—	236	2	no	—
193	D₄	—	2	1	no	—
194	D₄	Q₈×D₅₉	1	2	yes	—
195	C₂×C₄	—	2	1	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	8	2	no	—
199	C₂×C₄	—	118	1	no	—
200	C₂×C₄	—	118	1	no	—
201	C₂×C₄	—	118	2	no	—
202	C₂×C₄	C₂×C₂²⋊D₅₉	1	2	yes	—
203	C₂×C₄	C₂×C₂²⋊D₅₉	1	2	yes	—
204	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
205	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
206	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
207	C₈	—	59	2	no	—
208	C₈	—	118	1	no	—
209	C₈	—	118	2	no	—
210	C₂²	—	2	2	no	—
211	C₂²	—	4	1	no	—
212	C₂²	—	4	1	no	—
213	C₂²	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
214	C₄	—	2	2	no	—
215	C₄	—	2	2	no	—
216	C₄	—	2	1	no	—
217	C₄	—	4	1	no	—
218	C₄	—	4	2	no	—
219	C₄	—	118	2	no	—
220	C₄	—	236	2	no	—
221	C₄	—	236	1	no	—
222	C₄	#14273747	1	2	yes	—
223	C₄	C₂×Q₈×D₅₉	1	1	yes	characteristic
224	C₄	#14273775	1	1	yes	characteristic
225	C₂	—	4	2	no	—
226	C₂	Q₈×C₂²⋊D₅₉	1	1	yes	characteristic
227	C₂	C₂×#14273747	1	1	yes	characteristic
228	C₂	#16838213	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16838130

C₂

yes

maximal, characteristic, complemented

#16837801

C₂

yes

maximal, complemented

#16837798

C₂

yes

maximal, characteristic, complemented

#16837706

C₂

yes

maximal, complemented

#16837702

C₂

yes

maximal

#16837694

C₂

yes

maximal, characteristic, complemented

#16837682

C₂

yes

maximal, characteristic

Q₈×C₅₉⋊C₈

C₂

yes

maximal, characteristic, complemented

C₄×#11745670

C₂

yes

maximal, characteristic

C₄×#11745670

C₂

yes

maximal

C₅₉×#554

C₂

yes

maximal, characteristic

C₂×#11745670

C₂²

yes

characteristic

#14273727

C₂²

yes

characteristic

#14273725

—

#14273719

C₂²

yes

—

#14273717

—

C₄×Dic₁₁₈

C₂²

yes

characteristic

C₄×Dic₁₁₈

C₂²

yes

—

#14273692

—

#14273660

C₂²

yes

—

#14273660

C₂²

yes

—

#14273658

C₂²

yes

—

#14273658

C₂²

yes

—

#14273658

C₂²

yes

characteristic

C₄⋊(C₅₉⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₅₉⋊C₈)

C₂²

yes

—

#14273650

C₂²

yes

—

#14273650

C₂²

yes

characteristic

#14273648

C₂²

yes

—

#14273648

C₂²

yes

characteristic

C₄×C₅₉⋊C₈

C₂²

yes

characteristic

C₄×C₅₉⋊C₈

C₂²

yes

—

C₄⋊Q₈×C₅₉

C₂²

yes

characteristic

#125×C₅₉

C₂²

yes

—

C₂²⋊Q₈×C₅₉

—

C₂²⋊Q₈×C₅₉

—

C₄×Q₈×C₅₉

C₂²

yes

characteristic

C₄×D₄×C₅₉

C₂²

yes

characteristic

C₄×D₄×C₅₉

C₂²

yes

—

C₂×C₄⋊C₄×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

D₄

yes

characteristic

C₂×D₄×C₅₉

C₂³

yes

characteristic

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

C₂³

yes

characteristic

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

D₄

yes

characteristic

C₄⋊C₄×C₅₉

D₄

yes

—

C₄⋊C₄×C₅₉

C₂³

yes

characteristic

C₄⋊C₄×C₅₉

C₂³

yes

—

C₂²⋊C₄×C₅₉

—

C₂²⋊C₄×C₅₉

—

C₄²×C₅₉

C₂³

yes

—

C₄²×C₅₉

C₂³

yes

characteristic

#11745670

Q₈

yes

complemented

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

C₂³

yes

—

C₄⋊Dic₅₉

C₂³

yes

characteristic

Dic₅₉⋊C₄

—

Dic₅₉⋊C₄

—

Dic₅₉⋊C₄

—

Dic₅₉⋊C₄

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

C₂×C₅₉⋊C₈

C₂³

yes

characteristic

C₂×C₅₉⋊C₈

C₂³

yes

—

C₂×C₅₉⋊C₈

C₂³

yes

characteristic

C₂³×C₅₉

—

Q₈×C₅₉

—

Q₈×C₅₉

—

D₄×C₅₉

—

D₄×C₅₉

C₂×Q₈

yes

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×D₄

yes

—

C₂×C₄×C₅₉

C₂×D₄

yes

—

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

C₂⁴

yes

characteristic

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

Dic₁₁₈

—

Dic₁₁₈

—

Dic₁₁₈

C₂×Q₈

yes

—

C₅₉⋊C₈

—

C₅₉⋊C₈

—

C₅₉⋊C₈

C₂×Q₈

yes

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

C₂²×D₄

yes

characteristic

C₄×C₅₉

—

100

C₄×C₅₉

—

101

C₄×C₅₉

—

102

C₄×C₅₉

—

103

C₄×C₅₉

—

104

C₄×C₅₉

#135

yes

—

105

C₄×C₅₉

C₂²×Q₈

yes

characteristic

106

C₄×C₅₉

2₋¹⁺⁴

yes

characteristic

107

Dic₅₉

—

108

Dic₅₉

—

109

Dic₅₉

—

110

#3381

—

maximal, Sylow

111

C₂×C₅₉

—

112

C₂×C₅₉

D₄×Q₈

yes

characteristic

113

C₂×C₅₉

C₂×#135

yes

characteristic

114

C₂×C₅₉

#577

yes

characteristic

115

#557

—

116

#554

D₅₉

yes

characteristic

117

#499

—

118

#498

—

119

#479

—

120

#478

—

121

#477

—

122

#474

—

123

C₈×Q₈

—

124

C₄×SD₁₆

—

125

C₄×SD₁₆

—

126

C₅₉

#3381

yes

characteristic, complemented, Sylow

127

C₂×SD₁₆

—

128

C₄⋊Q₈

—

129

C₄⋊Q₈

—

118

—

130

C₄⋊Q₈

C₂×D₅₉

yes

characteristic

131

#125

—

132

#125

—

118

—

133

#125

C₂×D₅₉

yes

—

134

C₂²⋊Q₈

—

135

C₂²⋊Q₈

—

136

C₄×Q₈

—

137

C₄×Q₈

—

138

C₄×Q₈

—

118

—

139

C₄×Q₈

C₂×D₅₉

yes

characteristic

140

C₄×D₄

C₂×D₅₉

yes

characteristic

141

C₄×D₄

C₂×D₅₉

yes

—

142

C₂×C₄⋊C₄

—

143

#107

—

144

#107

—

145

#106

—

146

#106

—

147

#106

—

148

C₄⋊C₈

—

149

C₄⋊C₈

—

150

#103

—

151

#103

—

152

#102

—

153

#102

—

154

C₄×C₈

—

155

C₄×C₈

—

156

C₂×Q₈

—

157

C₂×Q₈

—

158

C₂×Q₈

—

118

—

159

C₂×Q₈

C₂²⋊D₅₉

yes

characteristic

160

C₂×D₄

C₂²×D₅₉

yes

characteristic

161

C₂²×C₄

—

162

C₂²×C₄

—

163

SD₁₆

—

164

C₂×C₈

—

165

C₂×C₈

—

166

C₂×C₈

—

167

C₄⋊C₄

—

168

C₄⋊C₄

—

169

C₄⋊C₄

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

118

—

173

C₄⋊C₄

—

118

—

174

C₄⋊C₄

—

118

—

175

C₄⋊C₄

—

118

—

176

C₄⋊C₄

—

118

—

177

C₄⋊C₄

C₂²⋊D₅₉

yes

characteristic

178

C₄⋊C₄

C₂²⋊D₅₉

yes

—

179

C₄⋊C₄

C₂²×D₅₉

yes

—

180

C₄⋊C₄

C₂²×D₅₉

yes

characteristic

181

C₂²⋊C₄

—

182

C₂²⋊C₄

—

183

C₄²

—

118

—

184

C₄²

—

118

—

185

C₄²

C₂²×D₅₉

yes

—

186

C₄²

C₂²×D₅₉

yes

characteristic

187

C₂³

—

188

Q₈

—

189

Q₈

—

190

Q₈

—

191

Q₈

—

118

—

192

Q₈

—

236

—

193

D₄

—

194

D₄

Q₈×D₅₉

yes

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

118

—

200

C₂×C₄

—

118

—

201

C₂×C₄

—

118

—

202

C₂×C₄

C₂×C₂²⋊D₅₉

yes

—

203

C₂×C₄

C₂×C₂²⋊D₅₉

yes

—

204

C₂×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

205

C₂×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

206

C₂×C₄

C₂³×D₅₉

yes

characteristic

207

C₈

—

208

C₈

—

118

—

209

C₈

—

118

—

210

C₂²

—

211

C₂²

—

212

C₂²

—

213

C₂²

C₂²×C₂²⋊D₅₉

yes

characteristic

214

C₄

—

215

C₄

—

216

C₄

—

217

C₄

—

218

C₄

—

219

C₄

—

118

—

220

C₄

—

236

—

221

C₄

—

236

—

222

C₄

#14273747

yes

—

223

C₄

C₂×Q₈×D₅₉

yes

characteristic

224

C₄

#14273775

yes

characteristic

225

C₂

—

226

C₂

Q₈×C₂²⋊D₅₉

yes

characteristic

227

C₂

C₂×#14273747

yes

characteristic

228

C₂

#16838213

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₅₉
commutator	C₂×C₄×C₅₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₅₉
Fitting	C₅₉×#554	C₂
socle	C₂²×C₅₉	C₂²×D₄
hypercenter	#554	D₅₉
hypocenter	C₅₉	#3381
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #554

subgroup

G/H

center

C₂²

C₂²×C₂²⋊D₅₉

commutator

C₂×C₄×C₅₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₅₉

Fitting

C₅₉×#554

C₂

socle

C₂²×C₅₉

C₂²×D₄

D₅₉

C₅₉

G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #554

N	H ≅ G/N	type
1. #16838130	C₂	semidirect
2. #16837801	C₂	semidirect
3. #16837798	C₂	semidirect
4. #16837706	C₂	semidirect
6. #16837694	C₂	semidirect
8. Q₈×C₅₉⋊C₈	C₂	semidirect
59. #11745670	Q₈	semidirect
126. C₅₉	#3381	semidirect

H ≅ G/N

type

1. #16838130

C₂

semidirect

2. #16837801

C₂

semidirect

3. #16837798

C₂

semidirect

4. #16837706

C₂

semidirect

6. #16837694

C₂

semidirect

8. Q₈×C₅₉⋊C₈

C₂

semidirect

59. #11745670

Q₈

semidirect

126. C₅₉

#3381

semidirect

Subgroups — #21436971

Conjugacy classes of subgroups

Complements