Group #21436816 — subgroups

Subgroups — #21436816

Order 7552.

372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 123 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	#16838125	C₂	1	1	yes	maximal, characteristic, complemented
2	Q₈×D₂₃₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#16837762	C₂	1	2	yes	maximal, complemented
4	#16837753	C₂	1	1	yes	maximal, characteristic, complemented
5	#16837698	C₂	1	2	yes	maximal, complemented
6	#16837683	C₂	1	1	yes	maximal, characteristic, complemented
7	#16837618	C₂	1	2	yes	maximal
8	#16837608	C₂	1	1	yes	maximal, characteristic, complemented
9	#16837504	C₂	1	2	yes	maximal, complemented
10	C₄×D₄₇₂	C₂	1	1	yes	maximal, characteristic
11	C₅₉×#446	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₈×D₅₉	—	2	1	no	—
13	C₂×#11745660	C₂²	1	2	yes	—
14	C₂×D₄₇₂	C₂²	1	1	yes	characteristic
15	#14273727	C₂²	1	1	yes	characteristic
16	#14273727	C₂²	1	1	yes	characteristic
17	#14273727	C₂²	1	2	yes	—
18	#14273722	—	2	2	no	—
19	#14273715	C₂²	1	2	yes	—
20	#14273707	—	2	1	no	—
21	#14273707	—	2	2	no	—
22	#14273703	—	2	1	no	—
23	C₄×Dic₁₁₈	C₂²	1	2	yes	—
24	C₄×D₂₃₆	C₂²	1	1	yes	characteristic
25	C₄×D₂₃₆	C₂²	1	1	yes	characteristic
26	C₄×D₂₃₆	C₂²	1	2	yes	—
27	#14273685	—	2	1	no	—
28	#14273661	C₂²	1	2	yes	—
29	#14273661	C₂²	1	1	yes	characteristic
30	#14273652	C₂²	1	2	yes	—
31	#14273652	C₂²	1	2	yes	—
32	#14273652	C₂²	1	2	yes	—
33	#14273649	C₂²	1	2	yes	—
34	#14273649	C₂²	1	1	yes	characteristic
35	#14273649	C₂²	1	1	yes	characteristic
36	C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
37	C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
38	C₄⋊C₈×C₅₉	C₂²	1	2	yes	—
39	#97×C₅₉	C₂²	1	2	yes	—
40	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
41	C₂×Q₈×C₅₉	D₄	1	1	yes	characteristic
42	Q₈×D₅₉	—	4	4	no	—
43	C₂×D₂₃₆	C₂³	1	1	yes	characteristic
44	C₂×D₂₃₆	C₂³	1	1	yes	characteristic
45	C₂×C₄×D₅₉	—	2	1	no	—
46	C₂×C₄×D₅₉	—	2	2	no	—
47	C₂×C₄×D₅₉	—	2	1	no	—
48	C₂×Dic₁₁₈	—	2	2	no	—
49	C₂×Dic₁₁₈	—	2	1	no	—
50	C₂×Dic₁₁₈	C₂³	1	2	yes	—
51	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
52	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
53	C₂×C₈×C₅₉	C₂³	1	2	yes	—
54	C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
55	C₄⋊C₄×C₅₉	D₄	1	2	yes	—
56	C₄²×C₅₉	C₂³	1	1	yes	characteristic
57	C₄²×C₅₉	C₂³	1	2	yes	—
58	(C₂×D₅₉)⋊C₄	—	2	2	no	—
59	(C₂×D₅₉)⋊C₄	—	2	2	no	—
60	(C₂×D₅₉)⋊C₄	—	2	1	no	—
61	(C₂×D₅₉)⋊C₄	—	2	1	no	—
62	(C₂×D₅₉)⋊C₄	—	2	2	no	—
63	C₄⋊Dic₅₉	—	2	1	no	—
64	C₄⋊Dic₅₉	—	2	2	no	—
65	C₄⋊Dic₅₉	—	2	1	no	—
66	C₄⋊Dic₅₉	—	2	1	no	—
67	C₄⋊Dic₅₉	C₂³	1	2	yes	—
68	C₄⋊Dic₅₉	C₂³	1	1	yes	characteristic
69	C₄⋊Dic₅₉	C₂³	1	1	yes	characteristic
70	Dic₅₉⋊C₄	—	2	2	no	—
71	C₄×Dic₅₉	—	2	2	no	—
72	D₄₇₂	—	2	2	no	—
73	#11745660	—	2	4	no	—
74	C₂²×D₅₉	—	2	1	no	—
75	C₂²×D₅₉	—	2	1	no	—
76	Q₈×C₅₉	—	2	2	no	—
77	C₂×C₄×C₅₉	C₂×D₄	1	2	yes	—
78	C₂×C₄×C₅₉	C₂×D₄	1	2	yes	—
79	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
80	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
81	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
82	C₂×Dic₅₉	—	2	1	no	—
83	C₂×Dic₅₉	—	2	2	no	—
84	C₂×Dic₅₉	—	2	1	no	—
85	C₂×Dic₅₉	—	2	2	no	—
86	D₂₃₆	—	2	1	no	—
87	D₂₃₆	—	2	1	no	—
88	D₂₃₆	—	2	1	no	—
89	D₂₃₆	#41	1	2	yes	—
90	C₄×D₅₉	—	4	4	no	—
91	C₄×D₅₉	—	4	2	no	—
92	C₄×D₅₉	—	4	2	no	—
93	Dic₁₁₈	—	2	2	no	—
94	Dic₁₁₈	—	2	2	no	—
95	Dic₁₁₈	—	4	4	no	—
96	Dic₁₁₈	—	4	2	no	—
97	C₈×C₅₉	—	2	2	no	—
98	C₈×C₅₉	—	2	1	no	—
99	C₈×C₅₉	—	2	1	no	—
100	C₂²×C₅₉	C₂²×D₄	1	1	yes	characteristic
101	C₂×D₅₉	—	2	2	no	—
102	C₂×D₅₉	—	4	1	no	—
103	C₂×D₅₉	—	4	1	no	—
104	C₂×D₅₉	—	4	1	no	—
105	C₂×D₅₉	—	4	1	no	—
106	C₂×D₅₉	—	4	1	no	—
107	C₄×C₅₉	—	2	2	no	—
108	C₄×C₅₉	—	2	2	no	—
109	C₄×C₅₉	—	2	1	no	—
110	C₄×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
111	C₄×C₅₉	C₂×#41	1	1	yes	characteristic
112	C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
113	Dic₅₉	—	4	2	no	—
114	Dic₅₉	—	4	1	no	—
115	Dic₅₉	—	4	2	no	—
116	Dic₅₉	—	4	1	no	—
117	#3367	—	59	1	no	maximal, Sylow
118	C₂×C₅₉	#548	1	1	yes	characteristic
119	C₂×C₅₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
120	C₂×C₅₉	#578	1	1	yes	characteristic
121	D₅₉	—	4	2	no	—
122	D₅₉	—	8	1	no	—
123	#556	—	59	1	no	—
124	D₄×Q₈	—	59	1	no	—
125	#489	—	59	2	no	—
126	#487	—	59	1	no	—
127	#477	—	59	2	no	—
128	#474	—	59	1	no	—
129	#463	—	59	2	no	—
130	#461	—	59	1	no	—
131	#446	D₅₉	1	1	yes	characteristic, complemented
132	#440	—	59	2	no	—
133	C₄×D₈	—	59	1	no	—
134	C₅₉	#3367	1	1	yes	characteristic, complemented, Sylow
135	C₂²×Q₈	—	118	1	no	—
136	C₂×SD₁₆	—	59	2	no	—
137	C₂×D₈	—	59	1	no	—
138	C₄⋊Q₈	—	59	1	no	—
139	C₄⋊Q₈	—	59	2	no	—
140	C₄⋊Q₈	—	59	1	no	—
141	#126	—	118	2	no	—
142	#124	—	59	2	no	—
143	C₂²⋊Q₈	—	118	1	no	—
144	C₂²⋊Q₈	—	118	1	no	—
145	C₂²⋊Q₈	—	118	2	no	—
146	C₄×Q₈	—	59	2	no	—
147	C₄×Q₈	C₂×D₅₉	1	1	yes	characteristic
148	C₄×D₄	—	59	1	no	—
149	C₄×D₄	—	59	2	no	—
150	C₄×D₄	—	59	1	no	—
151	#117	—	118	1	no	—
152	#107	—	59	1	no	—
153	#107	—	59	2	no	—
154	C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
155	C₄⋊C₈	C₂×D₅₉	1	2	yes	—
156	#103	—	59	2	no	—
157	#103	—	59	2	no	—
158	#103	—	59	2	no	—
159	#102	—	59	1	no	—
160	#102	—	59	1	no	—
161	#102	—	59	2	no	—
162	#97	C₂×D₅₉	1	2	yes	—
163	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
164	C₂×Q₈	—	59	2	no	—
165	C₂×Q₈	—	118	2	no	—
166	C₂×Q₈	—	118	1	no	—
167	C₂×Q₈	—	236	4	no	—
168	C₂×Q₈	D₂₃₆	1	1	yes	characteristic
169	C₂×D₄	—	59	1	no	—
170	C₂×D₄	—	59	1	no	—
171	C₂²×C₄	—	118	1	no	—
172	C₂²×C₄	—	118	2	no	—
173	C₂²×C₄	—	118	1	no	—
174	SD₁₆	—	118	4	no	—
175	D₈	—	118	2	no	—
176	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
177	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
178	C₂×C₈	C₂²×D₅₉	1	2	yes	—
179	C₄⋊C₄	—	59	1	no	—
180	C₄⋊C₄	—	59	2	no	—
181	C₄⋊C₄	—	59	1	no	—
182	C₄⋊C₄	—	118	1	no	—
183	C₄⋊C₄	—	118	2	no	—
184	C₄⋊C₄	—	118	2	no	—
185	C₄⋊C₄	—	118	1	no	—
186	C₄⋊C₄	—	118	1	no	—
187	C₄⋊C₄	D₂₃₆	1	1	yes	characteristic
188	C₄⋊C₄	D₂₃₆	1	2	yes	—
189	C₂²⋊C₄	—	118	2	no	—
190	C₂²⋊C₄	—	118	2	no	—
191	C₂²⋊C₄	—	118	1	no	—
192	C₂²⋊C₄	—	118	1	no	—
193	C₂²⋊C₄	—	118	2	no	—
194	C₄²	—	118	2	no	—
195	C₄²	C₂²×D₅₉	1	1	yes	characteristic
196	C₄²	C₂²×D₅₉	1	2	yes	—
197	C₂³	—	118	1	no	—
198	C₂³	—	118	1	no	—
199	Q₈	—	2	2	no	—
200	Q₈	—	118	2	no	—
201	Q₈	—	118	2	no	—
202	Q₈	—	236	4	no	—
203	Q₈	—	236	2	no	—
204	D₄	—	59	2	no	—
205	D₄	—	118	1	no	—
206	D₄	—	118	1	no	—
207	D₄	—	118	1	no	—
208	C₂×C₄	—	118	1	no	—
209	C₂×C₄	—	118	2	no	—
210	C₂×C₄	—	118	2	no	—
211	C₂×C₄	—	118	1	no	—
212	C₂×C₄	—	236	4	no	—
213	C₂×C₄	—	236	2	no	—
214	C₂×C₄	—	236	2	no	—
215	C₂×C₄	C₂×D₂₃₆	1	2	yes	—
216	C₂×C₄	C₂×D₂₃₆	1	1	yes	characteristic
217	C₂×C₄	C₂×D₂₃₆	1	2	yes	—
218	C₂×C₄	C₂×D₂₃₆	1	1	yes	characteristic
219	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
220	C₈	—	2	1	no	—
221	C₈	—	2	2	no	—
222	C₈	—	2	1	no	—
223	C₂²	—	118	2	no	—
224	C₂²	—	236	1	no	—
225	C₂²	—	236	1	no	—
226	C₂²	—	236	1	no	—
227	C₂²	—	236	1	no	—
228	C₂²	—	236	1	no	—
229	C₂²	C₂²×D₂₃₆	1	1	yes	characteristic
230	C₄	—	2	2	no	—
231	C₄	—	2	2	no	—
232	C₄	—	2	1	no	—
233	C₄	—	236	2	no	—
234	C₄	—	236	1	no	—
235	C₄	—	236	1	no	—
236	C₄	—	236	2	no	—
237	C₄	#14273755	1	2	yes	—
238	C₄	#41×D₅₉	1	1	yes	characteristic
239	C₄	#14273775	1	1	yes	characteristic
240	C₂	—	472	1	no	—
241	C₂	—	236	2	no	—
242	C₂	#16838064	1	1	yes	characteristic
243	C₂	C₂×#14273755	1	1	yes	characteristic
244	C₂	#16838219	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16838125

C₂

yes

maximal, characteristic, complemented

Q₈×D₂₃₆

C₂

yes

maximal, characteristic, complemented

#16837762

C₂

yes

maximal, complemented

#16837753

C₂

yes

maximal, characteristic, complemented

#16837698

C₂

yes

maximal, complemented

#16837683

C₂

yes

maximal, characteristic, complemented

#16837618

C₂

yes

maximal

#16837608

C₂

yes

maximal, characteristic, complemented

#16837504

C₂

yes

maximal, complemented

C₄×D₄₇₂

C₂

yes

maximal, characteristic

C₅₉×#446

C₂

yes

maximal, characteristic, complemented

C₂×Q₈×D₅₉

—

C₂×#11745660

C₂²

yes

—

C₂×D₄₇₂

C₂²

yes

characteristic

#14273727

C₂²

yes

characteristic

#14273727

C₂²

yes

characteristic

#14273727

C₂²

yes

—

#14273722

—

#14273715

C₂²

yes

—

#14273707

—

#14273707

—

#14273703

—

C₄×Dic₁₁₈

C₂²

yes

—

C₄×D₂₃₆

C₂²

yes

characteristic

C₄×D₂₃₆

C₂²

yes

characteristic

C₄×D₂₃₆

C₂²

yes

—

#14273685

—

#14273661

C₂²

yes

—

#14273661

C₂²

yes

characteristic

#14273652

C₂²

yes

—

#14273652

C₂²

yes

—

#14273652

C₂²

yes

—

#14273649

C₂²

yes

—

#14273649

C₂²

yes

characteristic

#14273649

C₂²

yes

characteristic

C₄×Q₈×C₅₉

C₂²

yes

characteristic

C₄⋊C₈×C₅₉

C₂²

yes

characteristic

C₄⋊C₈×C₅₉

C₂²

yes

—

#97×C₅₉

C₂²

yes

—

C₄×C₈×C₅₉

C₂²

yes

characteristic

C₂×Q₈×C₅₉

D₄

yes

characteristic

Q₈×D₅₉

—

C₂×D₂₃₆

C₂³

yes

characteristic

C₂×D₂₃₆

C₂³

yes

characteristic

C₂×C₄×D₅₉

—

C₂×C₄×D₅₉

—

C₂×C₄×D₅₉

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

C₂³

yes

—

C₂×C₈×C₅₉

C₂³

yes

characteristic

C₂×C₈×C₅₉

C₂³

yes

characteristic

C₂×C₈×C₅₉

C₂³

yes

—

C₄⋊C₄×C₅₉

D₄

yes

characteristic

C₄⋊C₄×C₅₉

D₄

yes

—

C₄²×C₅₉

C₂³

yes

characteristic

C₄²×C₅₉

C₂³

yes

—

(C₂×D₅₉)⋊C₄

—

(C₂×D₅₉)⋊C₄

—

(C₂×D₅₉)⋊C₄

—

(C₂×D₅₉)⋊C₄

—

(C₂×D₅₉)⋊C₄

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

C₂³

yes

—

C₄⋊Dic₅₉

C₂³

yes

characteristic

C₄⋊Dic₅₉

C₂³

yes

characteristic

Dic₅₉⋊C₄

—

C₄×Dic₅₉

—

D₄₇₂

—

#11745660

—

C₂²×D₅₉

—

C₂²×D₅₉

—

Q₈×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

—

C₂×Dic₅₉

—

D₂₃₆

—

D₂₃₆

—

D₂₃₆

—

D₂₃₆

#41

yes

—

C₄×D₅₉

—

C₄×D₅₉

—

C₄×D₅₉

—

Dic₁₁₈

—

Dic₁₁₈

—

Dic₁₁₈

—

Dic₁₁₈

—

C₈×C₅₉

—

C₈×C₅₉

—

C₈×C₅₉

—

100

C₂²×C₅₉

C₂²×D₄

yes

characteristic

101

C₂×D₅₉

—

102

C₂×D₅₉

—

103

C₂×D₅₉

—

104

C₂×D₅₉

—

105

C₂×D₅₉

—

106

C₂×D₅₉

—

107

C₄×C₅₉

—

108

C₄×C₅₉

—

109

C₄×C₅₉

—

110

C₄×C₅₉

AGL(1,ℤ/8)

yes

—

111

C₄×C₅₉

C₂×#41

yes

characteristic

112

C₄×C₅₉

2₋¹⁺⁴

yes

characteristic

113

Dic₅₉

—

114

Dic₅₉

—

115

Dic₅₉

—

116

Dic₅₉

—

117

#3367

—

maximal, Sylow

118

C₂×C₅₉

#548

yes

characteristic

119

C₂×C₅₉

C₂×AGL(1,ℤ/8)

yes

characteristic

120

C₂×C₅₉

#578

yes

characteristic

121

D₅₉

—

122

D₅₉

—

123

#556

—

124

D₄×Q₈

—

125

#489

—

126

#487

—

127

#477

—

128

#474

—

129

#463

—

130

#461

—

131

#446

D₅₉

yes

characteristic, complemented

132

#440

—

133

C₄×D₈

—

134

C₅₉

#3367

yes

characteristic, complemented, Sylow

135

C₂²×Q₈

—

118

—

136

C₂×SD₁₆

—

137

C₂×D₈

—

138

C₄⋊Q₈

—

139

C₄⋊Q₈

—

140

C₄⋊Q₈

—

141

#126

—

118

—

142

#124

—

143

C₂²⋊Q₈

—

118

—

144

C₂²⋊Q₈

—

118

—

145

C₂²⋊Q₈

—

118

—

146

C₄×Q₈

—

147

C₄×Q₈

C₂×D₅₉

yes

characteristic

148

C₄×D₄

—

149

C₄×D₄

—

150

C₄×D₄

—

151

#117

—

118

—

152

#107

—

153

#107

—

154

C₄⋊C₈

C₂×D₅₉

yes

characteristic

155

C₄⋊C₈

C₂×D₅₉

yes

—

156

#103

—

157

#103

—

158

#103

—

159

#102

—

160

#102

—

161

#102

—

162

#97

C₂×D₅₉

yes

—

163

C₄×C₈

C₂×D₅₉

yes

characteristic

164

C₂×Q₈

—

165

C₂×Q₈

—

118

—

166

C₂×Q₈

—

118

—

167

C₂×Q₈

—

236

—

168

C₂×Q₈

D₂₃₆

yes

characteristic

169

C₂×D₄

—

170

C₂×D₄

—

171

C₂²×C₄

—

118

—

172

C₂²×C₄

—

118

—

173

C₂²×C₄

—

118

—

174

SD₁₆

—

118

—

175

D₈

—

118

—

176

C₂×C₈

C₂²×D₅₉

yes

characteristic

177

C₂×C₈

C₂²×D₅₉

yes

characteristic

178

C₂×C₈

C₂²×D₅₉

yes

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

118

—

183

C₄⋊C₄

—

118

—

184

C₄⋊C₄

—

118

—

185

C₄⋊C₄

—

118

—

186

C₄⋊C₄

—

118

—

187

C₄⋊C₄

D₂₃₆

yes

characteristic

188

C₄⋊C₄

D₂₃₆

yes

—

189

C₂²⋊C₄

—

118

—

190

C₂²⋊C₄

—

118

—

191

C₂²⋊C₄

—

118

—

192

C₂²⋊C₄

—

118

—

193

C₂²⋊C₄

—

118

—

194

C₄²

—

118

—

195

C₄²

C₂²×D₅₉

yes

characteristic

196

C₄²

C₂²×D₅₉

yes

—

197

C₂³

—

118

—

198

C₂³

—

118

—

199

Q₈

—

200

Q₈

—

118

—

201

Q₈

—

118

—

202

Q₈

—

236

—

203

Q₈

—

236

—

204

D₄

—

205

D₄

—

118

—

206

D₄

—

118

—

207

D₄

—

118

—

208

C₂×C₄

—

118

—

209

C₂×C₄

—

118

—

210

C₂×C₄

—

118

—

211

C₂×C₄

—

118

—

212

C₂×C₄

—

236

—

213

C₂×C₄

—

236

—

214

C₂×C₄

—

236

—

215

C₂×C₄

C₂×D₂₃₆

yes

—

216

C₂×C₄

C₂×D₂₃₆

yes

characteristic

217

C₂×C₄

C₂×D₂₃₆

yes

—

218

C₂×C₄

C₂×D₂₃₆

yes

characteristic

219

C₂×C₄

C₂³×D₅₉

yes

characteristic

220

C₈

—

221

C₈

—

222

C₈

—

223

C₂²

—

118

—

224

C₂²

—

236

—

225

C₂²

—

236

—

226

C₂²

—

236

—

227

C₂²

—

236

—

228

C₂²

—

236

—

229

C₂²

C₂²×D₂₃₆

yes

characteristic

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

236

—

234

C₄

—

236

—

235

C₄

—

236

—

236

C₄

—

236

—

237

C₄

#14273755

yes

—

238

C₄

#41×D₅₉

yes

characteristic

239

C₄

#14273775

yes

characteristic

240

C₂

—

472

—

241

C₂

—

236

—

242

C₂

#16838064

yes

characteristic

243

C₂

C₂×#14273755

yes

characteristic

244

C₂

#16838219

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×D₂₃₆
commutator	C₂×C₄×C₅₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₅₉
Fitting	C₅₉×#446	C₂
socle	C₂²×C₅₉	C₂²×D₄
hypercenter	#446	D₅₉
hypocenter	C₅₉	#3367
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #446

subgroup

G/H

center

C₂²

C₂²×D₂₃₆

commutator

C₂×C₄×C₅₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₅₉

Fitting

C₅₉×#446

C₂

socle

C₂²×C₅₉

C₂²×D₄

D₅₉

C₅₉

G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #446

N	H ≅ G/N	type
1. #16838125	C₂	semidirect
2. Q₈×D₂₃₆	C₂	semidirect
3. #16837762	C₂	semidirect
4. #16837753	C₂	semidirect
5. #16837698	C₂	semidirect
6. #16837683	C₂	semidirect
8. #16837608	C₂	semidirect
9. #16837504	C₂	semidirect
11. C₅₉×#446	C₂	semidirect
131. #446	D₅₉	semidirect
134. C₅₉	#3367	semidirect

H ≅ G/N

type

1. #16838125

C₂

semidirect

2. Q₈×D₂₃₆

C₂

semidirect

3. #16837762

C₂

semidirect

4. #16837753

C₂

semidirect

5. #16837698

C₂

semidirect

6. #16837683

C₂

semidirect

8. #16837608

C₂

semidirect

9. #16837504

C₂

semidirect

11. C₅₉×#446

C₂

semidirect

131. #446

D₅₉

semidirect

134. C₅₉

#3367

semidirect

Subgroups — #21436816

Conjugacy classes of subgroups

Complements