Group #28493709 — subgroups

Subgroups — #28493709

Order 15104.

316 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 95 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	#21425078	C₂	1	1	yes	maximal, characteristic
2	#21424249	C₂	1	1	yes	maximal, characteristic
3	#21422871	C₂	1	1	yes	maximal, characteristic
4	#21422870	C₂	1	1	yes	maximal, characteristic
5	#21422499	C₂	1	1	yes	maximal, characteristic
6	#21421924	C₂	1	1	yes	maximal, characteristic
7	C₅₉×#1481	C₂	1	1	yes	maximal, characteristic
8	#16837455	C₂²	1	1	yes	characteristic
9	#16837426	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×Dic₅₉⋊C₈	—	2	2	no	—
12	#16837248	C₂²	1	1	yes	characteristic
13	#16837161	—	2	2	no	—
14	#16837155	—	2	2	no	—
15	#16837154	—	2	2	no	—
16	Q₈⋊(C₅₉⋊C₈)	—	2	2	no	—
17	C₅₉×#533	C₂²	1	1	yes	characteristic
18	C₅₉×#431	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
20	C₅₉×Q₈⋊C₈	—	2	2	no	—
21	C₂×#11745664	—	2	1	no	—
22	C₂²×C₅₉⋊C₈	—	2	1	no	—
23	C₂×C₄×Dic₅₉	D₄	1	2	yes	—
24	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
25	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
26	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
27	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
28	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
29	Dic₅₉⋊C₈	—	4	4	no	—
30	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
31	C₄×C₅₉⋊C₈	D₄	1	2	yes	—
32	C₅₉⋊#95	—	2	1	no	—
33	C₅₉⋊#95	—	2	1	no	—
34	C₂²×C₈×C₅₉	—	2	1	no	—
35	C₄⋊Q₈×C₅₉	Q₈	1	1	yes	characteristic
36	C₄⋊Q₈×C₅₉	Q₈	1	1	yes	characteristic
37	#125×C₅₉	—	2	1	no	—
38	C₂²⋊Q₈×C₅₉	—	2	1	no	—
39	C₂²⋊Q₈×C₅₉	—	2	1	no	—
40	C₄×Q₈×C₅₉	—	2	1	no	—
41	C₄×Q₈×C₅₉	—	2	1	no	—
42	#117×C₅₉	—	2	1	no	—
43	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
44	C₄⋊C₈×C₅₉	—	2	1	no	—
45	C₄⋊C₈×C₅₉	—	2	1	no	—
46	C₄⋊C₈×C₅₉	—	2	1	no	—
47	C₂²⋊C₈×C₅₉	—	2	1	no	—
48	C₄×C₈×C₅₉	D₄	1	2	yes	—
49	C₂×Q₈×C₅₉	—	2	1	no	—
50	C₂×Q₈×C₅₉	—	2	1	no	—
51	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
53	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
54	C₂²×Dic₅₉	—	2	2	no	—
55	C₂×C₈×C₅₉	—	2	2	no	—
56	C₂×C₈×C₅₉	—	4	1	no	—
57	C₂×C₈×C₅₉	—	4	2	no	—
58	C₄⋊C₄×C₅₉	—	2	1	no	—
59	C₄⋊C₄×C₅₉	—	2	1	no	—
60	C₄⋊C₄×C₅₉	—	2	1	no	—
61	C₄⋊C₄×C₅₉	—	2	1	no	—
62	C₄⋊C₄×C₅₉	—	4	1	no	—
63	C₄⋊C₄×C₅₉	—	4	1	no	—
64	C₂²⋊C₄×C₅₉	—	4	1	no	—
65	C₄²×C₅₉	—	4	1	no	—
66	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
67	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
68	C₄²×C₅₉	C₂×Q₈	1	1	yes	characteristic
69	C₄²×C₅₉	#41	1	1	yes	characteristic
70	C₄×Dic₅₉	—	2	2	no	—
71	C₄×Dic₅₉	Q₁₆	1	4	yes	—
72	#11745664	—	4	2	no	—
73	C₂×C₅₉⋊C₈	—	2	2	no	—
74	C₂×C₅₉⋊C₈	—	4	1	no	—
75	C₂×C₅₉⋊C₈	—	4	1	no	—
76	C₂×C₅₉⋊C₈	—	4	2	no	—
77	C₂³×C₅₉	#123	1	1	yes	characteristic
78	Q₈×C₅₉	—	4	2	no	—
79	Q₈×C₅₉	—	4	2	no	—
80	C₂×C₄×C₅₉	—	4	1	no	—
81	C₂×C₄×C₅₉	—	4	1	no	—
82	C₂×C₄×C₅₉	—	4	1	no	—
83	C₂×C₄×C₅₉	—	4	1	no	—
84	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
85	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
86	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
87	C₂×C₄×C₅₉	#123	1	1	yes	characteristic
88	C₂×C₄×C₅₉	#123	1	1	yes	characteristic
89	C₂×C₄×C₅₉	#127	1	1	yes	characteristic
90	C₂×C₄×C₅₉	C₂×Q₁₆	1	2	yes	—
91	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
92	C₂×Dic₅₉	—	2	4	no	—
93	C₂×Dic₅₉	—	4	2	no	—
94	C₂×Dic₅₉	—	4	2	no	—
95	C₈×C₅₉	—	4	2	no	—
96	C₈×C₅₉	—	8	1	no	—
97	C₅₉⋊C₈	—	4	2	no	—
98	C₅₉⋊C₈	—	8	1	no	—
99	C₅₉⋊C₈	—	8	1	no	—
100	#10668	—	59	1	no	maximal, Sylow
101	C₂²×C₅₉	—	2	1	no	—
102	C₂²×C₅₉	—	2	1	no	—
103	C₂²×C₅₉	#399	1	1	yes	characteristic
104	C₂²×C₅₉	#484	1	2	yes	—
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	—	8	1	no	—
110	C₄×C₅₉	—	8	1	no	—
111	C₄×C₅₉	#477	1	2	yes	—
112	C₄×C₅₉	#494	1	1	yes	characteristic
113	C₄×C₅₉	#496	1	1	yes	characteristic
114	Dic₅₉	—	4	4	no	—
115	#1995	—	59	1	no	—
116	#1843	—	59	1	no	—
117	#1571	—	59	1	no	—
118	#1571	—	59	1	no	—
119	#1481	—	59	1	no	—
120	#1481	D₅₉	1	1	yes	characteristic
121	#1274	—	59	1	no	—
122	C₂×C₅₉	—	2	2	no	—
123	C₂×C₅₉	#2095	1	1	yes	characteristic
124	C₂×C₅₉	#2098	1	1	yes	characteristic
125	C₂×C₅₉	#2098	1	1	yes	characteristic
126	#533	C₂×D₅₉	1	1	yes	characteristic
127	#431	—	59	1	no	—
128	#431	C₂×D₅₉	1	1	yes	characteristic
129	#423	—	59	1	no	—
130	C₂×C₄⋊C₈	—	59	1	no	—
131	C₂×C₄⋊C₈	—	118	2	no	—
132	C₂×C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
133	#376	—	59	1	no	—
134	#339	—	118	2	no	—
135	#335	—	118	2	no	—
136	#335	—	118	2	no	—
137	Q₈⋊C₈	—	2	2	no	—
138	Q₈⋊C₈	—	118	2	no	—
139	C₅₉	#10668	1	1	yes	characteristic, complemented, Sylow
140	C₂×M₁₆	—	118	1	no	—
141	C₂²×C₈	—	2	1	no	—
142	C₂²×C₈	—	118	1	no	—
143	C₄⋊Q₈	Dic₁₁₈	1	1	yes	characteristic
144	C₄⋊Q₈	Dic₁₁₈	1	1	yes	characteristic
145	#125	—	2	1	no	—
146	C₂²⋊Q₈	—	2	1	no	—
147	C₂²⋊Q₈	—	2	1	no	—
148	C₄×Q₈	—	2	1	no	—
149	C₄×Q₈	—	2	1	no	—
150	#117	—	2	1	no	—
151	C₂×C₄²	—	59	2	no	—
152	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
153	C₄⋊C₈	—	2	1	no	—
154	C₄⋊C₈	—	2	1	no	—
155	C₄⋊C₈	—	2	1	no	—
156	C₄⋊C₈	—	118	1	no	—
157	C₄⋊C₈	—	118	1	no	—
158	C₄⋊C₈	—	118	1	no	—
159	C₄⋊C₈	—	118	1	no	—
160	C₄⋊C₈	—	118	1	no	—
161	C₄⋊C₈	—	236	4	no	—
162	C₂²⋊C₈	—	2	1	no	—
163	C₂²⋊C₈	—	118	1	no	—
164	C₄×C₈	—	59	2	no	—
165	C₄×C₈	C₂²⋊D₅₉	1	2	yes	—
166	#95	—	118	1	no	—
167	#95	—	118	1	no	—
168	C₂×Q₈	—	2	1	no	—
169	C₂×Q₈	—	2	1	no	—
170	C₂²×C₄	—	118	2	no	—
171	C₂²×C₄	#11745685	1	1	yes	characteristic
172	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
173	C₂²×C₄	#11745687	1	1	yes	characteristic
174	M₁₆	—	236	2	no	—
175	C₂×C₈	—	2	2	no	—
176	C₂×C₈	—	4	1	no	—
177	C₂×C₈	—	4	2	no	—
178	C₂×C₈	—	118	2	no	—
179	C₂×C₈	—	236	1	no	—
180	C₂×C₈	—	236	1	no	—
181	C₂×C₈	—	236	2	no	—
182	C₄⋊C₄	—	2	1	no	—
183	C₄⋊C₄	—	2	1	no	—
184	C₄⋊C₄	—	2	1	no	—
185	C₄⋊C₄	—	2	1	no	—
186	C₄⋊C₄	—	4	1	no	—
187	C₄⋊C₄	—	4	1	no	—
188	C₂²⋊C₄	—	4	1	no	—
189	C₄²	—	4	1	no	—
190	C₄²	—	59	4	no	—
191	C₄²	—	118	2	no	—
192	C₄²	C₂×Dic₁₁₈	1	1	yes	characteristic
193	C₄²	D₄×D₅₉	1	1	yes	characteristic
194	C₄²	#11745687	1	1	yes	characteristic
195	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
196	C₂³	#14273709	1	1	yes	characteristic
197	Q₈	—	4	2	no	—
198	Q₈	—	4	2	no	—
199	C₂×C₄	—	4	1	no	—
200	C₂×C₄	—	4	1	no	—
201	C₂×C₄	—	4	1	no	—
202	C₂×C₄	—	4	1	no	—
203	C₂×C₄	—	118	4	no	—
204	C₂×C₄	—	236	2	no	—
205	C₂×C₄	—	236	2	no	—
206	C₂×C₄	#14273704	1	1	yes	characteristic
207	C₂×C₄	#14273704	1	1	yes	characteristic
208	C₂×C₄	#14273706	1	1	yes	characteristic
209	C₂×C₄	#14273708	1	1	yes	characteristic
210	C₂×C₄	#14273709	1	1	yes	characteristic
211	C₂×C₄	#14273723	1	1	yes	characteristic
212	C₂×C₄	Q₁₆×D₅₉	1	2	yes	—
213	C₂×C₄	#14273754	1	2	yes	—
214	C₈	—	4	2	no	—
215	C₈	—	8	1	no	—
216	C₈	—	472	1	no	—
217	C₈	—	472	1	no	—
218	C₈	—	236	2	no	—
219	C₂²	—	2	1	no	—
220	C₂²	—	2	1	no	—
221	C₂²	#16837338	1	1	yes	characteristic
222	C₂²	#16837736	1	2	yes	—
223	C₄	—	2	1	no	—
224	C₄	—	2	1	no	—
225	C₄	—	2	1	no	—
226	C₄	—	2	1	no	—
227	C₄	—	8	1	no	—
228	C₄	—	8	1	no	—
229	C₄	—	236	4	no	—
230	C₄	#16837695	1	2	yes	—
231	C₄	#16837780	1	1	yes	characteristic
232	C₄	#16837788	1	1	yes	characteristic
233	C₂	—	2	2	no	—
234	C₂	#21425632	1	1	yes	characteristic
235	C₂	#21425649	1	1	yes	characteristic
236	C₂	#21425651	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#21425078

C₂

yes

maximal, characteristic

#21424249

C₂

yes

maximal, characteristic

#21422871

C₂

yes

maximal, characteristic

#21422870

C₂

yes

maximal, characteristic

#21422499

C₂

yes

maximal, characteristic

#21421924

C₂

yes

maximal, characteristic

C₅₉×#1481

C₂

yes

maximal, characteristic

#16837455

C₂²

yes

characteristic

#16837426

C₂²

yes

characteristic

C₂×C₄⋊(C₅₉⋊C₈)

C₂²

yes

characteristic

C₂×Dic₅₉⋊C₈

—

#16837248

C₂²

yes

—

—

—

Q₈⋊(C₅₉⋊C₈)

—

C₅₉×#533

C₂²

yes

characteristic

C₅₉×#431

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₅₉

C₂²

yes

characteristic

C₅₉×Q₈⋊C₈

—

C₂×#11745664

—

C₂²×C₅₉⋊C₈

—

C₂×C₄×Dic₅₉

D₄

yes

—

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

—

Dic₅₉⋊C₈

—

C₂²⋊(C₅₉⋊C₈)

—

C₄×C₅₉⋊C₈

D₄

yes

—

C₅₉⋊#95

—

C₅₉⋊#95

—

C₂²×C₈×C₅₉

—

C₄⋊Q₈×C₅₉

Q₈

yes

characteristic

C₄⋊Q₈×C₅₉

Q₈

yes

characteristic

#125×C₅₉

—

C₂²⋊Q₈×C₅₉

—

C₂²⋊Q₈×C₅₉

—

C₄×Q₈×C₅₉

—

C₄×Q₈×C₅₉

—

#117×C₅₉

—

C₂×C₄²×C₅₉

C₂³

yes

characteristic

C₄⋊C₈×C₅₉

—

C₄⋊C₈×C₅₉

—

C₄⋊C₈×C₅₉

—

C₂²⋊C₈×C₅₉

—

C₄×C₈×C₅₉

D₄

yes

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂²×C₄×C₅₉

C₂×D₄

yes

C₂²×C₄×C₅₉

yes

C₂²×C₄×C₅₉

yes

C₂²×Dic₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₂²⋊C₄×C₅₉

—

C₄²×C₅₉

—

C₄²×C₅₉

C₂×D₄

yes

characteristic

C₄²×C₅₉

C₂×D₄

yes

characteristic

C₄²×C₅₉

C₂×Q₈

yes

characteristic

C₄²×C₅₉

#41

yes

characteristic

C₄×Dic₅₉

—

C₄×Dic₅₉

Q₁₆

yes

—

#11745664

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂³×C₅₉

#123

yes

characteristic

Q₈×C₅₉

—

Q₈×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₅₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₅₉

C₂²⋊Q₈

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

C₂×Q₁₆

yes

—

C₂×C₄×C₅₉

AGL(1,ℤ/8)

yes

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₈×C₅₉

—

C₈×C₅₉

—

C₅₉⋊C₈

—

C₅₉⋊C₈

—

C₅₉⋊C₈

—

100

#10668

—

maximal, Sylow

101

C₂²×C₅₉

—

102

C₂²×C₅₉

—

103

C₂²×C₅₉

#399

yes

characteristic

104

C₂²×C₅₉

#484

yes

—

105

C₄×C₅₉

—

106

C₄×C₅₉

—

107

C₄×C₅₉

—

108

C₄×C₅₉

—

109

C₄×C₅₉

—

110

C₄×C₅₉

—

111

C₄×C₅₉

#477

yes

—

112

C₄×C₅₉

#494

yes

characteristic

113

C₄×C₅₉

#496

yes

characteristic

114

Dic₅₉

—

115

#1995

—

116

#1843

—

117

#1571

—

118

#1571

—

119

#1481

—

120

#1481

D₅₉

yes

characteristic

121

#1274

—

122

C₂×C₅₉

—

123

C₂×C₅₉

#2095

yes

characteristic

124

C₂×C₅₉

#2098

yes

characteristic

125

C₂×C₅₉

#2098

yes

characteristic

126

#533

C₂×D₅₉

yes

characteristic

127

#431

—

128

#431

C₂×D₅₉

yes

characteristic

129

#423

—

130

C₂×C₄⋊C₈

—

131

C₂×C₄⋊C₈

—

118

—

132

C₂×C₄⋊C₈

C₂×D₅₉

yes

characteristic

133

#376

—

134

#339

—

118

—

135

#335

—

118

—

136

#335

—

118

—

137

Q₈⋊C₈

—

138

Q₈⋊C₈

—

118

—

139

C₅₉

#10668

yes

characteristic, complemented, Sylow

140

C₂×M₁₆

—

118

—

141

C₂²×C₈

—

142

C₂²×C₈

—

118

—

143

C₄⋊Q₈

Dic₁₁₈

yes

characteristic

144

C₄⋊Q₈

Dic₁₁₈

yes

characteristic

145

#125

—

146

C₂²⋊Q₈

—

147

C₂²⋊Q₈

—

148

C₄×Q₈

—

149

C₄×Q₈

—

150

#117

—

151

C₂×C₄²

—

152

C₂×C₄²

C₂²×D₅₉

yes

characteristic

153

C₄⋊C₈

—

154

C₄⋊C₈

—

155

C₄⋊C₈

—

156

C₄⋊C₈

—

118

—

157

C₄⋊C₈

—

118

—

158

C₄⋊C₈

—

118

—

159

C₄⋊C₈

—

118

—

160

C₄⋊C₈

—

118

—

161

C₄⋊C₈

—

236

—

162

C₂²⋊C₈

—

163

C₂²⋊C₈

—

118

—

164

C₄×C₈

—

165

C₄×C₈

C₂²⋊D₅₉

yes

—

166

#95

—

118

—

167

#95

—

118

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂²×C₄

—

118

—

171

C₂²×C₄

#11745685

yes

characteristic

172

C₂²×C₄

D₄×D₅₉

yes

characteristic

173

C₂²×C₄

#11745687

yes

characteristic

174

M₁₆

—

236

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

118

—

179

C₂×C₈

—

236

—

180

C₂×C₈

—

236

—

181

C₂×C₈

—

236

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₂²⋊C₄

—

189

C₄²

—

190

C₄²

—

191

C₄²

—

118

—

192

C₄²

C₂×Dic₁₁₈

yes

characteristic

193

C₄²

D₄×D₅₉

yes

characteristic

194

C₄²

#11745687

yes

characteristic

195

C₄²

C₂×C₂²⋊D₅₉

yes

characteristic

196

C₂³

#14273709

yes

characteristic

197

Q₈

—

198

Q₈

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

118

—

204

C₂×C₄

—

236

—

205

C₂×C₄

—

236

—

206

C₂×C₄

#14273704

yes

characteristic

207

C₂×C₄

#14273704

yes

characteristic

208

C₂×C₄

#14273706

yes

characteristic

209

C₂×C₄

#14273708

yes

characteristic

210

C₂×C₄

#14273709

yes

characteristic

211

C₂×C₄

#14273723

yes

characteristic

212

C₂×C₄

Q₁₆×D₅₉

yes

—

213

C₂×C₄

#14273754

yes

—

214

C₈

—

215

C₈

—

216

C₈

—

472

—

217

C₈

—

472

—

218

C₈

—

236

—

219

C₂²

—

220

C₂²

—

221

C₂²

#16837338

yes

characteristic

222

C₂²

#16837736

yes

—

223

C₄

—

224

C₄

—

225

C₄

—

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

236

—

230

C₄

#16837695

yes

—

231

C₄

#16837780

yes

characteristic

232

C₄

#16837788

yes

characteristic

233

C₂

—

234

C₂

#21425632

yes

characteristic

235

C₂

#21425649

yes

characteristic

236

C₂

#21425651

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14273723
commutator, cosocle	C₂×C₄²×C₅₉	C₂³
Frattini	C₂×C₄²	C₂²×D₅₉
Fitting	C₅₉×#1481	C₂
socle	C₂²×C₅₉	#399
prime radical	C₂³×C₅₉	#123
hypercenter	#1481	D₅₉
hypocenter	C₅₉	#10668
LCS	G ▷ C₂×C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1481

subgroup

G/H

center

C₂×C₄

#14273723

commutator, cosocle

C₂×C₄²×C₅₉

C₂³

Frattini

C₂×C₄²

C₂²×D₅₉

Fitting

C₅₉×#1481

C₂

C₂²×C₅₉

C₂³×C₅₉

D₅₉

C₅₉

G ▷ C₂×C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1481

N	H ≅ G/N	type
139. C₅₉	#10668	semidirect

H ≅ G/N

type

139. C₅₉

#10668

semidirect

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

subgroup	index
#21425078	2
#21424249	2
#21422871	2
#21422870	2
#21422499	2
#21421924	2
C₅₉×#1481	2
#10668	59

subgroup

index

C₅₉×#1481

Subgroups — #28493709

Conjugacy classes of subgroups

Complements

Maximal subgroups