Group #28481682 — subgroups

Subgroups — #28481682

Order 15104.

320 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 103 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	#21433030	C₂	1	1	yes	maximal, characteristic
2	#21422859	C₂	1	1	yes	maximal, characteristic
3	#21422733	C₂	1	2	yes	maximal
4	#21422006	C₂	1	2	yes	maximal
5	C₅₉×#1568	C₂	1	1	yes	maximal, characteristic
6	#16837959	C₂²	1	1	yes	characteristic
7	#16837532	—	2	1	no	—
8	#16837532	—	2	1	no	—
9	C₈×Dic₁₁₈	—	2	1	no	—
10	C₈×Dic₁₁₈	—	2	1	no	—
11	#16837459	C₂²	1	2	yes	—
12	#16837428	C₄	1	2	yes	—
13	#16837426	C₂²	1	1	yes	characteristic
14	#16837357	C₄	1	2	yes	—
15	#16837155	—	2	1	no	—
16	#16837153	—	2	1	no	—
17	#16837143	—	2	4	no	—
18	C₅₉×#432	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
20	C₅₉×#335	—	2	1	no	—
21	C₅₉×#334	—	2	1	no	—
22	C₂×#11745664	C₂×C₄	1	2	yes	—
23	#14273727	Q₈	1	1	yes	characteristic
24	#14273727	Q₈	1	1	yes	characteristic
25	#14273719	D₄	1	2	yes	—
26	#14273706	—	2	1	no	—
27	#14273706	—	2	1	no	—
28	C₄×Dic₁₁₈	—	2	1	no	—
29	C₄×Dic₁₁₈	—	2	1	no	—
30	#14273686	C₂×C₄	1	2	yes	—
31	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
32	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
33	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
34	Dic₅₉⋊C₈	—	2	2	no	—
35	Dic₅₉⋊C₈	—	2	2	no	—
36	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
37	#14273638	—	2	2	no	—
38	#14273637	—	2	2	no	—
39	C₈×Dic₅₉	—	2	2	no	—
40	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
43	C₄⋊C₈×C₅₉	—	2	2	no	—
44	C₂²⋊C₈×C₅₉	—	2	2	no	—
45	#97×C₅₉	—	2	2	no	—
46	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
47	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
48	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
49	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
50	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
51	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
52	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
53	C₂×Dic₁₁₈	—	2	1	no	—
54	C₂×Dic₁₁₈	—	2	1	no	—
55	C₂×C₈×C₅₉	—	2	2	no	—
56	C₂×C₈×C₅₉	—	4	1	no	—
57	C₂×C₈×C₅₉	—	4	2	no	—
58	C₂×C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
59	C₂×C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
60	C₂×C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
61	C₂×C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
62	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
63	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
64	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
65	C₄²×C₅₉	C₂×Q₈	1	1	yes	characteristic
66	C₂²⋊Dic₅₉	—	2	2	no	—
67	C₄⋊Dic₅₉	—	2	1	no	—
68	C₄⋊Dic₅₉	—	2	1	no	—
69	C₄⋊Dic₅₉	C₄⋊C₄	1	2	yes	—
70	C₄⋊Dic₅₉	C₄⋊C₄	1	2	yes	—
71	Dic₅₉⋊C₄	—	2	2	no	—
72	Dic₅₉⋊C₄	—	2	2	no	—
73	C₄×Dic₅₉	—	2	2	no	—
74	#11745664	—	4	2	no	—
75	C₂×C₅₉⋊C₈	—	2	2	no	—
76	C₂×C₅₉⋊C₈	—	4	2	no	—
77	C₂³×C₅₉	#117	1	1	yes	characteristic
78	C₂×C₄×C₅₉	—	2	1	no	—
79	C₂×C₄×C₅₉	—	2	1	no	—
80	C₂×C₄×C₅₉	—	4	1	no	—
81	C₂×C₄×C₅₉	—	4	1	no	—
82	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
85	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
86	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
87	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
88	C₂×Dic₅₉	—	2	2	no	—
89	C₂×Dic₅₉	—	2	2	no	—
90	Dic₁₁₈	—	4	2	no	—
91	Dic₁₁₈	—	4	2	no	—
92	C₈×C₅₉	—	2	1	no	—
93	C₈×C₅₉	—	2	1	no	—
94	C₈×C₅₉	—	2	1	no	—
95	C₈×C₅₉	—	8	2	no	—
96	C₈×C₅₉	#101	1	2	yes	—
97	C₅₉⋊C₈	—	4	2	no	—
98	C₅₉⋊C₈	—	8	2	no	—
99	#8631	—	59	1	no	maximal, Sylow
100	C₂²×C₅₉	—	2	1	no	—
101	C₂²×C₅₉	—	2	1	no	—
102	C₂²×C₅₉	—	2	1	no	—
103	C₂²×C₅₉	#380	1	1	yes	characteristic
104	C₄×C₅₉	—	2	1	no	—
105	C₄×C₅₉	—	2	1	no	—
106	C₄×C₅₉	—	2	1	no	—
107	C₄×C₅₉	—	2	1	no	—
108	C₄×C₅₉	—	2	1	no	—
109	C₄×C₅₉	C₂×#101	1	1	yes	characteristic
110	C₄×C₅₉	#413	1	1	yes	characteristic
111	Dic₅₉	—	4	2	no	—
112	Dic₅₉	—	4	2	no	—
113	#2960	—	59	1	no	—
114	#1568	—	59	1	no	—
115	#1568	D₅₉	1	1	yes	characteristic
116	#1537	—	59	2	no	—
117	#1307	—	59	2	no	—
118	C₂×C₅₉	—	4	1	no	—
119	C₂×C₅₉	#1801	1	1	yes	characteristic
120	C₂×C₅₉	#1814	1	1	yes	characteristic
121	C₂×C₅₉	#1814	1	1	yes	characteristic
122	#533	—	59	1	no	—
123	#446	—	118	1	no	—
124	#446	—	118	1	no	—
125	C₈×Q₈	—	118	1	no	—
126	C₈×Q₈	—	118	1	no	—
127	#432	—	59	2	no	—
128	#432	C₂×D₅₉	1	2	yes	—
129	#424	—	59	2	no	—
130	#423	—	59	1	no	—
131	#405	—	59	2	no	—
132	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
133	#335	—	2	1	no	—
134	#335	—	118	1	no	—
135	#334	—	2	1	no	—
136	#334	—	118	1	no	—
137	#330	—	118	4	no	—
138	C₅₉	#8631	1	1	yes	characteristic, complemented, Sylow
139	C₂×M₁₆	—	59	2	no	—
140	C₂²×C₈	C₄×D₅₉	1	1	yes	characteristic
141	C₂²×C₈	C₄×D₅₉	1	1	yes	characteristic
142	C₄⋊Q₈	—	59	1	no	—
143	C₄⋊Q₈	—	59	1	no	—
144	#125	—	59	2	no	—
145	C₂²⋊Q₈	—	118	1	no	—
146	C₂²⋊Q₈	—	118	1	no	—
147	C₄×Q₈	—	118	1	no	—
148	C₄×Q₈	—	118	1	no	—
149	#117	—	59	2	no	—
150	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
151	C₄⋊C₈	—	2	2	no	—
152	C₄⋊C₈	—	118	2	no	—
153	C₄⋊C₈	—	118	2	no	—
154	C₄⋊C₈	—	118	1	no	—
155	C₄⋊C₈	—	118	2	no	—
156	C₄⋊C₈	—	118	1	no	—
157	C₂²⋊C₈	—	2	2	no	—
158	C₂²⋊C₈	—	118	2	no	—
159	#97	—	2	2	no	—
160	#97	—	118	2	no	—
161	#97	—	118	2	no	—
162	C₄×C₈	—	118	2	no	—
163	C₄×C₈	D₂₃₆	1	1	yes	characteristic
164	C₄×C₈	D₂₃₆	1	1	yes	characteristic
165	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
166	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
167	C₂×Q₈	—	118	1	no	—
168	C₂×Q₈	—	118	1	no	—
169	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
170	C₂²×C₄	#11745687	1	1	yes	characteristic
171	C₂²×C₄	#11745689	1	1	yes	characteristic
172	M₁₆	—	236	2	no	—
173	C₂×C₈	—	2	2	no	—
174	C₂×C₈	—	4	1	no	—
175	C₂×C₈	—	4	2	no	—
176	C₂×C₈	—	118	2	no	—
177	C₂×C₈	—	236	2	no	—
178	C₂×C₈	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
179	C₂×C₈	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
180	C₂×C₈	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
181	C₂×C₈	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
182	C₄⋊C₄	—	59	2	no	—
183	C₄⋊C₄	—	59	2	no	—
184	C₄⋊C₄	—	118	2	no	—
185	C₄⋊C₄	—	118	2	no	—
186	C₄⋊C₄	—	118	1	no	—
187	C₄⋊C₄	—	118	1	no	—
188	C₂²⋊C₄	—	118	2	no	—
189	C₄²	—	118	2	no	—
190	C₄²	C₂×D₂₃₆	1	1	yes	characteristic
191	C₄²	D₄×D₅₉	1	1	yes	characteristic
192	C₄²	Q₈×D₅₉	1	1	yes	characteristic
193	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
194	C₂³	#14273685	1	1	yes	characteristic
195	Q₈	—	236	2	no	—
196	Q₈	—	236	2	no	—
197	C₂×C₄	—	2	1	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	4	1	no	—
200	C₂×C₄	—	4	1	no	—
201	C₂×C₄	—	118	2	no	—
202	C₂×C₄	—	118	2	no	—
203	C₂×C₄	C₂×(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
204	C₂×C₄	C₄⋊C₄×D₅₉	1	1	yes	characteristic
205	C₂×C₄	#14273698	1	1	yes	characteristic
206	C₂×C₄	#14273702	1	1	yes	characteristic
207	C₂×C₄	#14273703	1	1	yes	characteristic
208	C₂×C₄	#14273707	1	1	yes	characteristic
209	C₈	—	2	1	no	—
210	C₈	—	2	1	no	—
211	C₈	—	2	1	no	—
212	C₈	—	8	2	no	—
213	C₈	—	472	2	no	—
214	C₈	—	236	2	no	—
215	C₈	#14273645	1	2	yes	—
216	C₂²	—	2	1	no	—
217	C₂²	—	2	1	no	—
218	C₂²	—	2	1	no	—
219	C₂²	#16837259	1	1	yes	characteristic
220	C₄	—	2	1	no	—
221	C₄	—	2	1	no	—
222	C₄	—	2	1	no	—
223	C₄	—	2	1	no	—
224	C₄	—	2	1	no	—
225	C₄	—	236	2	no	—
226	C₄	—	236	2	no	—
227	C₄	C₂×#14273645	1	1	yes	characteristic
228	C₄	#16837384	1	1	yes	characteristic
229	C₂	—	4	1	no	—
230	C₂	#21424089	1	1	yes	characteristic
231	C₂	#21424147	1	1	yes	characteristic
232	C₂	#21424151	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#21433030

C₂

yes

maximal, characteristic

#21422859

C₂

yes

maximal, characteristic

#21422733

C₂

yes

maximal

#21422006

C₂

yes

maximal

C₅₉×#1568

C₂

yes

maximal, characteristic

#16837959

C₂²

yes

characteristic

#16837532

—

#16837532

—

C₈×Dic₁₁₈

—

C₈×Dic₁₁₈

—

#16837459

C₂²

yes

—

#16837428

C₄

yes

—

#16837426

C₂²

yes

characteristic

#16837357

C₄

yes

—

#16837155

—

#16837153

—

#16837143

—

C₅₉×#432

C₂²

yes

—

C₂×C₄×C₈×C₅₉

C₂²

yes

characteristic

C₅₉×#335

—

C₅₉×#334

—

C₂×#11745664

C₂×C₄

yes

—

#14273727

Q₈

yes

characteristic

#14273727

Q₈

yes

characteristic

#14273719

D₄

yes

—

#14273706

—

#14273706

—

C₄×Dic₁₁₈

—

C₄×Dic₁₁₈

—

#14273686

C₂×C₄

yes

—

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

—

Dic₅₉⋊C₈

—

Dic₅₉⋊C₈

—

C₂²⋊(C₅₉⋊C₈)

—

#14273638

—

#14273637

—

C₈×Dic₅₉

—

C₂²×C₈×C₅₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₅₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₅₉

C₂³

yes

characteristic

C₄⋊C₈×C₅₉

—

C₂²⋊C₈×C₅₉

—

#97×C₅₉

—

C₄×C₈×C₅₉

D₄

yes

characteristic

C₄×C₈×C₅₉

D₄

yes

characteristic

C₄×C₈×C₅₉

D₄

yes

characteristic

C₄×C₈×C₅₉

D₄

yes

characteristic

C₂²×C₄×C₅₉

C₂²×C₄

yes

C₂²×C₄×C₅₉

yes

C₂²×C₄×C₅₉

yes

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₅₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₅₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₅₉

C₂²⋊C₄

yes

characteristic

C₄²×C₅₉

C₂×D₄

yes

characteristic

C₄²×C₅₉

C₂×D₄

yes

characteristic

C₄²×C₅₉

C₂×D₄

yes

characteristic

C₄²×C₅₉

C₂×Q₈

yes

characteristic

C₂²⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

C₄⋊C₄

yes

—

C₄⋊Dic₅₉

C₄⋊C₄

yes

—

Dic₅₉⋊C₄

—

Dic₅₉⋊C₄

—

C₄×Dic₅₉

—

#11745664

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂³×C₅₉

#117

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₅₉

C₂×C₄⋊C₄

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₅₉

C₂²⋊Q₈

yes

characteristic

C₂×Dic₅₉

—

C₂×Dic₅₉

—

Dic₁₁₈

—

Dic₁₁₈

—

C₈×C₅₉

—

C₈×C₅₉

—

C₈×C₅₉

—

C₈×C₅₉

—

C₈×C₅₉

#101

yes

—

C₅₉⋊C₈

—

C₅₉⋊C₈

—

#8631

—

maximal, Sylow

100

C₂²×C₅₉

—

101

C₂²×C₅₉

—

102

C₂²×C₅₉

—

103

C₂²×C₅₉

#380

yes

characteristic

104

C₄×C₅₉

—

105

C₄×C₅₉

—

106

C₄×C₅₉

—

107

C₄×C₅₉

—

108

C₄×C₅₉

—

109

C₄×C₅₉

C₂×#101

yes

characteristic

110

C₄×C₅₉

#413

yes

characteristic

111

Dic₅₉

—

112

Dic₅₉

—

113

#2960

—

114

#1568

—

115

#1568

D₅₉

yes

characteristic

116

#1537

—

117

#1307

—

118

C₂×C₅₉

—

119

C₂×C₅₉

#1801

yes

characteristic

120

C₂×C₅₉

#1814

yes

characteristic

121

C₂×C₅₉

#1814

yes

characteristic

122

#533

—

123

#446

—

118

—

124

#446

—

118

—

125

C₈×Q₈

—

118

—

126

C₈×Q₈

—

118

—

127

#432

—

128

#432

C₂×D₅₉

yes

—

129

#424

—

130

#423

—

131

#405

—

132

C₂×C₄×C₈

C₂×D₅₉

yes

characteristic

133

#335

—

134

#335

—

118

—

135

#334

—

136

#334

—

118

—

137

#330

—

118

—

138

C₅₉

#8631

yes

characteristic, complemented, Sylow

139

C₂×M₁₆

—

140

C₂²×C₈

C₄×D₅₉

yes

characteristic

141

C₂²×C₈

C₄×D₅₉

yes

characteristic

142

C₄⋊Q₈

—

143

C₄⋊Q₈

—

144

#125

—

145

C₂²⋊Q₈

—

118

—

146

C₂²⋊Q₈

—

118

—

147

C₄×Q₈

—

118

—

148

C₄×Q₈

—

118

—

149

#117

—

150

C₂×C₄²

C₂²×D₅₉

yes

characteristic

151

C₄⋊C₈

—

152

C₄⋊C₈

—

118

—

153

C₄⋊C₈

—

118

—

154

C₄⋊C₈

—

118

—

155

C₄⋊C₈

—

118

—

156

C₄⋊C₈

—

118

—

157

C₂²⋊C₈

—

158

C₂²⋊C₈

—

118

—

159

#97

—

160

#97

—

118

—

161

#97

—

118

—

162

C₄×C₈

—

118

—

163

C₄×C₈

D₂₃₆

yes

characteristic

164

C₄×C₈

D₂₃₆

yes

characteristic

165

C₄×C₈

C₂²⋊D₅₉

yes

characteristic

166

C₄×C₈

C₂²⋊D₅₉

yes

characteristic

167

C₂×Q₈

—

118

—

168

C₂×Q₈

—

118

—

169

C₂²×C₄

C₂×C₄×D₅₉

yes

characteristic

170

C₂²×C₄

#11745687

yes

characteristic

171

C₂²×C₄

#11745689

yes

characteristic

172

M₁₆

—

236

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

118

—

177

C₂×C₈

—

236

—

178

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

characteristic

179

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

characteristic

180

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

characteristic

181

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

characteristic

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

118

—

185

C₄⋊C₄

—

118

—

186

C₄⋊C₄

—

118

—

187

C₄⋊C₄

—

118

—

188

C₂²⋊C₄

—

118

—

189

C₄²

—

118

—

190

C₄²

C₂×D₂₃₆

yes

characteristic

191

C₄²

D₄×D₅₉

yes

characteristic

192

C₄²

Q₈×D₅₉

yes

characteristic

193

C₄²

C₂×C₂²⋊D₅₉

yes

characteristic

194

C₂³

#14273685

yes

characteristic

195

Q₈

—

236

—

196

Q₈

—

236

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

118

—

202

C₂×C₄

—

118

—

203

C₂×C₄

C₂×(C₂×D₅₉)⋊C₄

yes

characteristic

204

C₂×C₄

C₄⋊C₄×D₅₉

yes

characteristic

205

C₂×C₄

#14273698

yes

characteristic

206

C₂×C₄

#14273702

yes

characteristic

207

C₂×C₄

#14273703

yes

characteristic

208

C₂×C₄

#14273707

yes

characteristic

209

C₈

—

210

C₈

—

211

C₈

—

212

C₈

—

213

C₈

—

472

—

214

C₈

—

236

—

215

C₈

#14273645

yes

—

216

C₂²

—

217

C₂²

—

218

C₂²

—

219

C₂²

#16837259

yes

characteristic

220

C₄

—

221

C₄

—

222

C₄

—

223

C₄

—

224

C₄

—

225

C₄

—

236

—

226

C₄

—

236

—

227

C₄

C₂×#14273645

yes

characteristic

228

C₄

#16837384

yes

characteristic

229

C₂

—

230

C₂

#21424089

yes

characteristic

231

C₂

#21424147

yes

characteristic

232

C₂

#21424151

yes

characteristic

	subgroup	G/H
center	C₂²	#16837259
commutator	C₂²×C₄×C₅₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₅₉
Fitting	C₅₉×#1568	C₂
socle	C₂²×C₅₉	#380
prime radical	C₂³×C₅₉	#117
cosocle	C₂×C₄²×C₅₉	C₂³
hypercenter	#1568	D₅₉
hypocenter	C₅₉	#8631
LCS	G ▷ C₂²×C₄×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1568

subgroup

G/H

center

C₂²

#16837259

commutator

C₂²×C₄×C₅₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₅₉

Fitting

C₅₉×#1568

C₂

C₂²×C₅₉

C₂³×C₅₉

C₂×C₄²×C₅₉

C₂³

D₅₉

C₅₉

G ▷ C₂²×C₄×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1568

N	H ≅ G/N	type
138. C₅₉	#8631	semidirect

H ≅ G/N

type

138. C₅₉

#8631

semidirect

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

subgroup	index
#21433030	2
#21422859	2
#21422733	2
#21422006	2
C₅₉×#1568	2
#8631	59

subgroup

index

C₅₉×#1568

Subgroups — #28481682

Conjugacy classes of subgroups

Complements

Maximal subgroups