Group #28493821 — subgroups

Subgroups — #28493821

Order 15104.

264 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 87 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	#21424817	C₂	1	1	yes	maximal, characteristic
2	#21424270	C₂	1	1	yes	maximal, characteristic
3	#21421998	C₂	1	1	yes	maximal, characteristic
4	#21421997	C₂	1	1	yes	maximal, characteristic
5	#21421993	C₂	1	1	yes	maximal, characteristic
6	#21421926	C₂	1	1	yes	maximal, characteristic
7	C₅₉×#1301	C₂	1	1	yes	maximal, characteristic
8	#16837455	C₂²	1	1	yes	characteristic
9	C₂×#14273662	—	2	1	no	—
10	C₂×#14273662	—	2	1	no	—
11	#16837426	C₂²	1	1	yes	characteristic
12	C₂×Dic₅₉⋊C₈	—	2	1	no	—
13	C₂×#14273638	C₂²	1	1	yes	characteristic
14	C₄×C₄⋊Dic₅₉	C₂²	1	1	yes	characteristic
15	#16837156	—	2	1	no	—
16	C₅₉×#431	C₂²	1	1	yes	characteristic
17	C₅₉×#423	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
19	C₂×#11745664	—	2	1	no	—
20	C₂²×C₅₉⋊C₈	D₄	1	1	yes	characteristic
21	C₂²×C₅₉⋊C₈	D₄	1	1	yes	characteristic
22	C₂×C₄⋊Dic₅₉	—	2	1	no	—
23	C₂×C₄×Dic₅₉	—	2	1	no	—
24	#14273662	—	4	2	no	—
25	#14273662	—	4	2	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	2	no	—
30	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
31	#14273638	—	2	1	no	—
32	#14273638	—	2	1	no	—
33	C₄×C₅₉⋊C₈	—	2	1	no	—
34	C₅₉⋊#95	Q₈	1	1	yes	characteristic
35	C₅₉⋊#95	Q₈	1	1	yes	characteristic
36	C₂×M₁₆×C₅₉	—	2	1	no	—
37	C₂²×C₈×C₅₉	—	2	1	no	—
38	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
39	C₄⋊C₈×C₅₉	—	2	1	no	—
40	C₄⋊C₈×C₅₉	—	2	1	no	—
41	C₄⋊C₈×C₅₉	—	2	1	no	—
42	C₄⋊C₈×C₅₉	—	2	1	no	—
43	C₄⋊C₈×C₅₉	—	2	1	no	—
44	C₂²⋊C₈×C₅₉	—	2	1	no	—
45	C₄×C₈×C₅₉	—	2	1	no	—
46	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
47	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
48	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
49	C₂²×Dic₅₉	—	2	1	no	—
50	C₂²×Dic₅₉	—	2	1	no	—
51	M₁₆×C₅₉	—	4	1	no	—
52	M₁₆×C₅₉	—	4	1	no	—
53	C₂×C₈×C₅₉	—	4	1	no	—
54	C₂×C₈×C₅₉	—	4	1	no	—
55	C₂×C₈×C₅₉	—	4	1	no	—
56	C₂×C₈×C₅₉	—	4	1	no	—
57	C₂×C₈×C₅₉	—	4	1	no	—
58	C₄²×C₅₉	#41	1	1	yes	characteristic
59	C₄²×C₅₉	#41	1	1	yes	characteristic
60	C₄²×C₅₉	#41	1	1	yes	characteristic
61	C₄²×C₅₉	#41	1	1	yes	characteristic
62	C₄⋊Dic₅₉	—	4	2	no	—
63	C₄×Dic₅₉	—	4	1	no	—
64	C₄×Dic₅₉	—	4	1	no	—
65	#11745664	—	4	1	no	—
66	#11745664	—	4	1	no	—
67	C₂×C₅₉⋊C₈	—	2	1	no	—
68	C₂×C₅₉⋊C₈	—	2	1	no	—
69	C₂×C₅₉⋊C₈	—	2	1	no	—
70	C₂×C₅₉⋊C₈	—	2	1	no	—
71	C₂×C₅₉⋊C₈	—	4	1	no	—
72	C₂×C₅₉⋊C₈	—	4	1	no	—
73	C₂×C₅₉⋊C₈	SD₁₆	1	2	yes	—
74	C₂×C₅₉⋊C₈	Q₁₆	1	2	yes	—
75	C₂³×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
76	C₂×C₄×C₅₉	—	4	1	no	—
77	C₂×C₄×C₅₉	—	4	1	no	—
78	C₂×C₄×C₅₉	#123	1	1	yes	characteristic
79	C₂×C₄×C₅₉	#124	1	1	yes	characteristic
80	C₂×C₄×C₅₉	#125	1	1	yes	characteristic
81	C₂×C₄×C₅₉	#125	1	1	yes	characteristic
82	C₂×C₄×C₅₉	#126	1	1	yes	characteristic
83	C₂×C₄×C₅₉	#126	1	1	yes	characteristic
84	C₂×C₄×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
85	C₂×C₄×C₅₉	C₂×Q₁₆	1	1	yes	characteristic
86	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
87	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
88	C₂×Dic₅₉	—	2	2	no	—
89	C₂×Dic₅₉	—	4	1	no	—
90	C₂×Dic₅₉	—	4	1	no	—
91	C₂×Dic₅₉	—	4	1	no	—
92	C₂×Dic₅₉	—	4	1	no	—
93	C₂×Dic₅₉	—	4	1	no	—
94	C₈×C₅₉	—	8	1	no	—
95	C₈×C₅₉	—	8	1	no	—
96	C₈×C₅₉	—	8	1	no	—
97	C₅₉⋊C₈	—	2	2	no	—
98	C₅₉⋊C₈	—	2	2	no	—
99	C₅₉⋊C₈	—	8	1	no	—
100	C₅₉⋊C₈	—	8	1	no	—
101	#10688	—	59	1	no	maximal, Sylow
102	C₂²×C₅₉	—	2	1	no	—
103	C₂²×C₅₉	—	2	1	no	—
104	C₂²×C₅₉	#400	1	1	yes	characteristic
105	C₂²×C₅₉	#476	1	1	yes	characteristic
106	C₂²×C₅₉	#477	1	1	yes	characteristic
107	C₄×C₅₉	—	2	1	no	—
108	C₄×C₅₉	—	2	1	no	—
109	C₄×C₅₉	—	2	1	no	—
110	C₄×C₅₉	—	2	1	no	—
111	C₄×C₅₉	#481	1	1	yes	characteristic
112	C₄×C₅₉	#484	1	1	yes	characteristic
113	C₄×C₅₉	#487	1	1	yes	characteristic
114	C₄×C₅₉	#490	1	1	yes	characteristic
115	Dic₅₉	—	4	2	no	—
116	Dic₅₉	—	8	1	no	—
117	#1940	—	59	1	no	—
118	#1849	—	59	1	no	—
119	#1303	—	59	1	no	—
120	#1303	—	59	1	no	—
121	#1301	—	59	1	no	—
122	#1301	D₅₉	1	1	yes	characteristic
123	#1275	—	59	1	no	—
124	C₂×C₅₉	—	2	1	no	—
125	C₂×C₅₉	—	2	1	no	—
126	C₂×C₅₉	#2100	1	1	yes	characteristic
127	C₂×C₅₉	#2102	1	1	yes	characteristic
128	C₂×C₅₉	#2103	1	1	yes	characteristic
129	#431	—	59	1	no	—
130	#431	C₂×D₅₉	1	1	yes	characteristic
131	C₂×#108	—	118	1	no	—
132	C₂×#108	—	118	1	no	—
133	#423	—	59	1	no	—
134	#423	C₂×D₅₉	1	1	yes	characteristic
135	C₂×C₄⋊C₈	—	118	1	no	—
136	C₂×C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
137	C₂×#97	—	59	1	no	—
138	C₄×C₄⋊C₄	—	59	1	no	—
139	#336	—	118	1	no	—
140	C₅₉	#10688	1	1	yes	characteristic, complemented, Sylow
141	C₂×M₁₆	—	2	1	no	—
142	C₂×M₁₆	—	118	1	no	—
143	C₂²×C₈	—	2	1	no	—
144	C₂²×C₈	—	59	1	no	—
145	C₂²×C₈	—	59	1	no	—
146	C₂×C₄⋊C₄	—	118	1	no	—
147	C₂×C₄²	—	118	1	no	—
148	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
149	#108	—	236	2	no	—
150	#108	—	236	2	no	—
151	C₄⋊C₈	—	2	1	no	—
152	C₄⋊C₈	—	2	1	no	—
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	—	236	2	no	—
160	C₂²⋊C₈	—	2	1	no	—
161	C₂²⋊C₈	—	118	1	no	—
162	#97	—	118	1	no	—
163	#97	—	118	1	no	—
164	C₄×C₈	—	2	1	no	—
165	C₄×C₈	—	118	1	no	—
166	#95	—	59	1	no	—
167	#95	—	59	1	no	—
168	C₂²×C₄	—	118	1	no	—
169	C₂²×C₄	—	118	1	no	—
170	C₂²×C₄	#11745685	1	1	yes	characteristic
171	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
172	C₂²×C₄	Q₈×D₅₉	1	1	yes	characteristic
173	M₁₆	—	4	1	no	—
174	M₁₆	—	4	1	no	—
175	M₁₆	—	236	1	no	—
176	M₁₆	—	236	1	no	—
177	C₂×C₈	—	4	1	no	—
178	C₂×C₈	—	4	1	no	—
179	C₂×C₈	—	4	1	no	—
180	C₂×C₈	—	4	1	no	—
181	C₂×C₈	—	4	1	no	—
182	C₂×C₈	—	59	2	no	—
183	C₂×C₈	—	59	2	no	—
184	C₂×C₈	—	118	1	no	—
185	C₂×C₈	—	118	1	no	—
186	C₂×C₈	—	118	1	no	—
187	C₂×C₈	—	118	1	no	—
188	C₂×C₈	—	236	1	no	—
189	C₂×C₈	—	236	1	no	—
190	C₄⋊C₄	—	236	2	no	—
191	C₄²	—	236	1	no	—
192	C₄²	—	236	1	no	—
193	C₄²	#11745685	1	1	yes	characteristic
194	C₄²	#11745685	1	1	yes	characteristic
195	C₄²	#11745687	1	1	yes	characteristic
196	C₄²	#11745687	1	1	yes	characteristic
197	C₂³	#14273705	1	1	yes	characteristic
198	C₂×C₄	—	4	1	no	—
199	C₂×C₄	—	4	1	no	—
200	C₂×C₄	—	118	2	no	—
201	C₂×C₄	—	236	1	no	—
202	C₂×C₄	—	236	1	no	—
203	C₂×C₄	—	236	1	no	—
204	C₂×C₄	—	236	1	no	—
205	C₂×C₄	—	236	1	no	—
206	C₂×C₄	#14273709	1	1	yes	characteristic
207	C₂×C₄	#14273713	1	1	yes	characteristic
208	C₂×C₄	#14273717	1	1	yes	characteristic
209	C₂×C₄	#14273717	1	1	yes	characteristic
210	C₂×C₄	#14273720	1	1	yes	characteristic
211	C₂×C₄	#14273721	1	1	yes	characteristic
212	C₂×C₄	SD₁₆×D₅₉	1	1	yes	characteristic
213	C₂×C₄	Q₁₆×D₅₉	1	1	yes	characteristic
214	C₂×C₄	#14273751	1	1	yes	characteristic
215	C₂×C₄	#14273754	1	1	yes	characteristic
216	C₈	—	8	1	no	—
217	C₈	—	8	1	no	—
218	C₈	—	8	1	no	—
219	C₈	—	118	2	no	—
220	C₈	—	118	2	no	—
221	C₈	—	472	1	no	—
222	C₈	—	472	1	no	—
223	C₂²	—	2	1	no	—
224	C₂²	—	2	1	no	—
225	C₂²	#16837343	1	1	yes	characteristic
226	C₂²	#16837691	1	1	yes	characteristic
227	C₂²	#16837696	1	1	yes	characteristic
228	C₄	—	2	1	no	—
229	C₄	—	2	1	no	—
230	C₄	—	2	1	no	—
231	C₄	—	2	1	no	—
232	C₄	—	472	1	no	—
233	C₄	—	236	2	no	—
234	C₄	#16837719	1	1	yes	characteristic
235	C₄	#16837736	1	1	yes	characteristic
236	C₄	#16837751	1	1	yes	characteristic
237	C₄	#16837765	1	1	yes	characteristic
238	C₂	—	2	1	no	—
239	C₂	—	2	1	no	—
240	C₂	#21425661	1	1	yes	characteristic
241	C₂	#21425673	1	1	yes	characteristic
242	C₂	#21425678	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#21424817

C₂

yes

maximal, characteristic

#21424270

C₂

yes

maximal, characteristic

#21421998

C₂

yes

maximal, characteristic

#21421997

C₂

yes

maximal, characteristic

#21421993

C₂

yes

maximal, characteristic

#21421926

C₂

yes

maximal, characteristic

C₅₉×#1301

C₂

yes

maximal, characteristic

#16837455

C₂²

yes

—

—

C₂²

yes

characteristic

C₂×Dic₅₉⋊C₈

—

C₂×#14273638

C₂²

yes

characteristic

C₄×C₄⋊Dic₅₉

C₂²

yes

characteristic

#16837156

—

C₅₉×#431

C₂²

yes

characteristic

C₅₉×#423

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₅₉

C₂²

yes

characteristic

C₂×#11745664

—

C₂²×C₅₉⋊C₈

D₄

yes

characteristic

C₂²×C₅₉⋊C₈

D₄

yes

characteristic

C₂×C₄⋊Dic₅₉

—

C₂×C₄×Dic₅₉

—

#14273662

—

#14273662

—

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

—

Dic₅₉⋊C₈

—

C₂²⋊(C₅₉⋊C₈)

—

#14273638

—

#14273638

—

C₄×C₅₉⋊C₈

—

C₅₉⋊#95

Q₈

yes

characteristic

C₅₉⋊#95

Q₈

yes

characteristic

C₂×M₁₆×C₅₉

—

C₂²×C₈×C₅₉

—

C₂×C₄²×C₅₉

C₂³

yes

characteristic

C₄⋊C₈×C₅₉

—

C₄⋊C₈×C₅₉

—

C₄⋊C₈×C₅₉

—

C₄⋊C₈×C₅₉

—

C₄⋊C₈×C₅₉

—

C₂²⋊C₈×C₅₉

—

C₄×C₈×C₅₉

—

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₅₉

C₂×Q₈

yes

characteristic

C₂²×C₄×C₅₉

#41

yes

characteristic

C₂²×Dic₅₉

—

C₂²×Dic₅₉

—

M₁₆×C₅₉

—

M₁₆×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₄²×C₅₉

yes

C₄²×C₅₉

yes

C₄²×C₅₉

yes

C₄²×C₅₉

yes

C₄⋊Dic₅₉

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

#11745664

—

#11745664

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

SD₁₆

yes

—

C₂×C₅₉⋊C₈

Q₁₆

yes

—

C₂³×C₅₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₅₉

C₂×Q₁₆

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₈×C₅₉

—

C₈×C₅₉

—

C₈×C₅₉

—

C₅₉⋊C₈

—

C₅₉⋊C₈

—

C₅₉⋊C₈

—

100

C₅₉⋊C₈

—

101

#10688

—

maximal, Sylow

102

C₂²×C₅₉

—

103

C₂²×C₅₉

—

104

C₂²×C₅₉

#400

yes

characteristic

105

C₂²×C₅₉

#476

yes

characteristic

106

C₂²×C₅₉

#477

yes

characteristic

107

C₄×C₅₉

—

108

C₄×C₅₉

—

109

C₄×C₅₉

—

110

C₄×C₅₉

—

111

C₄×C₅₉

#481

yes

characteristic

112

C₄×C₅₉

#484

yes

characteristic

113

C₄×C₅₉

#487

yes

characteristic

114

C₄×C₅₉

#490

yes

characteristic

115

Dic₅₉

—

116

Dic₅₉

—

117

#1940

—

118

#1849

—

119

#1303

—

120

#1303

—

121

#1301

—

122

#1301

D₅₉

yes

characteristic

123

#1275

—

124

C₂×C₅₉

—

125

C₂×C₅₉

—

126

C₂×C₅₉

#2100

yes

characteristic

127

C₂×C₅₉

#2102

yes

characteristic

128

C₂×C₅₉

#2103

yes

characteristic

129

#431

—

130

#431

C₂×D₅₉

yes

characteristic

131

C₂×#108

—

118

—

132

C₂×#108

—

118

—

133

#423

—

134

#423

C₂×D₅₉

yes

characteristic

135

C₂×C₄⋊C₈

—

118

—

136

C₂×C₄⋊C₈

C₂×D₅₉

yes

characteristic

137

C₂×#97

—

138

C₄×C₄⋊C₄

—

139

#336

—

118

—

140

C₅₉

#10688

yes

characteristic, complemented, Sylow

141

C₂×M₁₆

—

142

C₂×M₁₆

—

118

—

143

C₂²×C₈

—

144

C₂²×C₈

—

145

C₂²×C₈

—

146

C₂×C₄⋊C₄

—

118

—

147

C₂×C₄²

—

118

—

148

C₂×C₄²

C₂²×D₅₉

yes

characteristic

149

#108

—

236

—

150

#108

—

236

—

151

C₄⋊C₈

—

152

C₄⋊C₈

—

153

C₄⋊C₈

—

154

C₄⋊C₈

—

155

C₄⋊C₈

—

156

C₄⋊C₈

—

118

—

157

C₄⋊C₈

—

118

—

158

C₄⋊C₈

—

118

—

159

C₄⋊C₈

—

236

—

160

C₂²⋊C₈

—

161

C₂²⋊C₈

—

118

—

162

#97

—

118

—

163

#97

—

118

—

164

C₄×C₈

—

165

C₄×C₈

—

118

—

166

#95

—

167

#95

—

168

C₂²×C₄

—

118

—

169

C₂²×C₄

—

118

—

170

C₂²×C₄

#11745685

yes

characteristic

171

C₂²×C₄

D₄×D₅₉

yes

characteristic

172

C₂²×C₄

Q₈×D₅₉

yes

characteristic

173

M₁₆

—

174

M₁₆

—

175

M₁₆

—

236

—

176

M₁₆

—

236

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

118

—

185

C₂×C₈

—

118

—

186

C₂×C₈

—

118

—

187

C₂×C₈

—

118

—

188

C₂×C₈

—

236

—

189

C₂×C₈

—

236

—

190

C₄⋊C₄

—

236

—

191

C₄²

—

236

—

192

C₄²

—

236

—

193

C₄²

#11745685

yes

characteristic

194

C₄²

#11745685

yes

characteristic

195

C₄²

#11745687

yes

characteristic

196

C₄²

#11745687

yes

characteristic

197

C₂³

#14273705

yes

characteristic

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

118

—

201

C₂×C₄

—

236

—

202

C₂×C₄

—

236

—

203

C₂×C₄

—

236

—

204

C₂×C₄

—

236

—

205

C₂×C₄

—

236

—

206

C₂×C₄

#14273709

yes

characteristic

207

C₂×C₄

#14273713

yes

characteristic

208

C₂×C₄

#14273717

yes

characteristic

209

C₂×C₄

#14273717

yes

characteristic

210

C₂×C₄

#14273720

yes

characteristic

211

C₂×C₄

#14273721

yes

characteristic

212

C₂×C₄

SD₁₆×D₅₉

yes

characteristic

213

C₂×C₄

Q₁₆×D₅₉

yes

characteristic

214

C₂×C₄

#14273751

yes

characteristic

215

C₂×C₄

#14273754

yes

characteristic

216

C₈

—

217

C₈

—

218

C₈

—

219

C₈

—

118

—

220

C₈

—

118

—

221

C₈

—

472

—

222

C₈

—

472

—

223

C₂²

—

224

C₂²

—

225

C₂²

#16837343

yes

characteristic

226

C₂²

#16837691

yes

characteristic

227

C₂²

#16837696

yes

characteristic

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

472

—

233

C₄

—

236

—

234

C₄

#16837719

yes

characteristic

235

C₄

#16837736

yes

characteristic

236

C₄

#16837751

yes

characteristic

237

C₄

#16837765

yes

characteristic

238

C₂

—

239

C₂

—

240

C₂

#21425661

yes

characteristic

241

C₂

#21425673

yes

characteristic

242

C₂

#21425678

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14273713
commutator, cosocle	C₂×C₄²×C₅₉	C₂³
Frattini	C₂×C₄²	C₂²×D₅₉
Fitting	C₅₉×#1301	C₂
socle	C₂²×C₅₉	#400
prime radical	C₂³×C₅₉	C₂²⋊Q₈
hypercenter	#1301	D₅₉
hypocenter	C₅₉	#10688
LCS	G ▷ C₂×C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1301

subgroup

G/H

center

C₂×C₄

#14273713

commutator, cosocle

C₂×C₄²×C₅₉

C₂³

Frattini

C₂×C₄²

C₂²×D₅₉

Fitting

C₅₉×#1301

C₂

socle

C₂²×C₅₉

#400

prime radical

C₂³×C₅₉

C₂²⋊Q₈

D₅₉

C₅₉

G ▷ C₂×C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1301

N	H ≅ G/N	type
140. C₅₉	#10688	semidirect

H ≅ G/N

type

140. C₅₉

#10688

semidirect

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

subgroup	index
#21424817	2
#21424270	2
#21421998	2
#21421997	2
#21421993	2
#21421926	2
C₅₉×#1301	2
#10688	59

subgroup

index

C₅₉×#1301

Subgroups — #28493821

Conjugacy classes of subgroups

Complements

Maximal subgroups