Group #28506565 — subgroups

Subgroups — #28506565

Order 15104.

320 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 105 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	C₂×#16837225	C₂	1	1	yes	maximal, characteristic
2	C₂×#16837218	C₂	1	1	yes	maximal, characteristic
3	#21424968	C₂	1	1	yes	maximal, characteristic
4	#21423982	C₂	1	1	yes	maximal, characteristic
5	#21422201	C₂	1	1	yes	maximal, characteristic
6	#21422175	C₂	1	1	yes	maximal, characteristic
7	C₅₉×#2141	C₂	1	1	yes	maximal, characteristic
8	C₂×#14273667	C₂²	1	1	yes	characteristic
9	C₂×#14273663	C₂²	1	1	yes	characteristic
10	C₂×#14273659	C₂²	1	1	yes	characteristic
11	C₂×#14273651	—	2	1	no	—
12	#16837358	—	2	1	no	—
13	C₂×#14273637	C₂²	1	1	yes	characteristic
14	#16837309	—	2	1	no	—
15	#16837225	—	2	2	no	—
16	#16837218	—	2	2	no	—
17	#16837161	—	2	1	no	—
18	C₂²×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
19	C₂×M₃₂×C₅₉	C₂²	1	1	yes	characteristic
20	C₅₉×#427	C₂²	1	1	yes	characteristic
21	C₅₉×#358	C₄	1	4	yes	complemented
22	C₂×#11745664	—	2	1	no	—
23	C₂²×C₅₉⋊C₈	D₄	1	1	yes	characteristic
24	C₂×C₄⋊Dic₅₉	—	2	1	no	—
25	C₂×C₄×Dic₅₉	D₄	1	1	yes	characteristic
26	#14273667	—	2	1	no	—
27	#14273667	—	2	1	no	—
28	C₂×C₅₉⋊C₁₆	—	2	1	no	—
29	#14273663	—	2	1	no	—
30	#14273663	D₄	1	2	yes	—
31	#14273659	—	2	1	no	—
32	#14273659	—	2	1	no	—
33	#14273651	—	4	2	no	—
34	#14273638	—	4	1	no	—
35	#14273637	—	2	1	no	—
36	#14273637	—	2	1	no	—
37	C₄×C₅₉⋊C₈	—	4	1	no	—
38	C₅₉⋊#95	—	4	2	no	—
39	C₂²×Q₈×C₅₉	—	2	1	no	—
40	C₂×Q₁₆×C₅₉	—	2	1	no	—
41	C₂×Q₁₆×C₅₉	—	2	1	no	—
42	C₂×Q₁₆×C₅₉	—	2	1	no	—
43	C₂×Q₁₆×C₅₉	—	2	1	no	—
44	C₂×Q₁₆×C₅₉	—	2	1	no	—
45	C₂×Q₁₆×C₅₉	C₂×C₄	1	2	yes	—
46	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
47	#117×C₅₉	—	2	1	no	—
48	M₃₂×C₅₉	—	2	1	no	—
49	M₃₂×C₅₉	—	2	1	no	—
50	C₂×C₁₆×C₅₉	C₂×C₄	1	2	yes	—
51	#107×C₅₉	C₂×C₄	1	2	yes	—
52	#106×C₅₉	—	2	1	no	—
53	C₂×Q₈×C₅₉	—	2	2	no	—
54	C₂×Q₈×C₅₉	—	4	1	no	—
55	C₂×Q₈×C₅₉	—	4	1	no	—
56	C₂×Q₈×C₅₉	—	4	1	no	—
57	C₂×Q₈×C₅₉	—	4	1	no	—
58	C₂×Q₈×C₅₉	—	4	1	no	—
59	C₂²×C₄×C₅₉	—	4	1	no	—
60	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
61	C₂²×Dic₅₉	—	2	1	no	—
62	C₂²×Dic₅₉	—	4	1	no	—
63	Q₁₆×C₅₉	—	2	2	no	—
64	Q₁₆×C₅₉	—	2	2	no	—
65	Q₁₆×C₅₉	—	4	1	no	—
66	Q₁₆×C₅₉	—	4	1	no	—
67	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
68	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
69	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
70	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
71	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
72	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
73	C₄⋊C₄×C₅₉	—	2	2	no	—
74	C₂²⋊C₄×C₅₉	—	4	1	no	—
75	C₄²×C₅₉	—	4	1	no	—
76	C₄⋊Dic₅₉	—	4	1	no	—
77	C₄⋊Dic₅₉	—	4	1	no	—
78	C₄×Dic₅₉	—	2	1	no	—
79	C₄×Dic₅₉	—	2	1	no	—
80	#11745664	—	2	2	no	—
81	#11745664	—	4	1	no	—
82	C₂×C₅₉⋊C₈	—	2	1	no	—
83	C₂×C₅₉⋊C₈	—	2	1	no	—
84	C₂×C₅₉⋊C₈	—	4	1	no	—
85	C₂×C₅₉⋊C₈	SD₁₆	1	2	yes	—
86	C₁₆×C₅₉	—	2	2	no	—
87	C₅₉⋊C₁₆	—	4	1	no	—
88	C₂³×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
89	Q₈×C₅₉	—	4	2	no	—
90	Q₈×C₅₉	—	4	2	no	—
91	Q₈×C₅₉	—	8	1	no	—
92	Q₈×C₅₉	—	8	1	no	—
93	C₂×C₄×C₅₉	—	4	2	no	—
94	C₂×C₄×C₅₉	—	4	2	no	—
95	C₂×C₄×C₅₉	—	8	1	no	—
96	C₂×C₄×C₅₉	—	8	1	no	—
97	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
98	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
99	C₂×C₄×C₅₉	#123	1	1	yes	characteristic
100	C₂×C₄×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
101	C₂×C₄×C₅₉	#135	1	1	yes	characteristic
102	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
103	C₂×Dic₅₉	—	4	2	no	—
104	C₂×Dic₅₉	—	4	1	no	—
105	C₂×Dic₅₉	—	8	2	no	—
106	C₂×Dic₅₉	—	8	1	no	—
107	C₈×C₅₉	#117	1	1	yes	characteristic
108	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
109	C₈×C₅₉	#124	1	1	yes	characteristic
110	C₈×C₅₉	#126	1	1	yes	characteristic
111	C₅₉⋊C₈	—	2	2	no	—
112	C₅₉⋊C₈	—	4	2	no	—
113	#13141	—	59	1	no	maximal, Sylow
114	C₂²×C₅₉	—	2	2	no	—
115	C₂²×C₅₉	#442	1	1	yes	characteristic
116	C₂²×C₅₉	#460	1	1	yes	characteristic
117	C₂²×C₅₉	#482	1	1	yes	characteristic
118	C₄×C₅₉	—	8	2	no	—
119	C₄×C₅₉	—	8	2	no	—
120	C₄×C₅₉	#388	1	1	yes	characteristic
121	C₄×C₅₉	C₄×SD₁₆	1	1	yes	characteristic
122	C₄×C₅₉	#463	1	1	yes	characteristic
123	C₄×C₅₉	#481	1	1	yes	characteristic
124	Dic₅₉	—	8	1	no	—
125	Dic₅₉	—	16	1	no	—
126	C₂×#365	—	59	1	no	—
127	C₂×#362	—	59	1	no	—
128	#2141	D₅₉	1	1	yes	characteristic
129	#1971	—	59	1	no	—
130	#1773	—	59	1	no	—
131	#1386	—	59	1	no	—
132	#1375	—	59	1	no	—
133	C₂×C₅₉	—	2	1	no	—
134	C₂×C₅₉	—	2	1	no	—
135	C₂×C₅₉	#1926	1	1	yes	characteristic
136	C₂×C₅₉	#2180	1	2	yes	—
137	C₂²×Q₁₆	C₂×D₅₉	1	1	yes	characteristic
138	C₂×M₃₂	—	59	1	no	—
139	C₂×M₃₂	C₂×D₅₉	1	1	yes	characteristic
140	C₂×#108	—	59	1	no	—
141	#427	C₂×D₅₉	1	1	yes	characteristic
142	C₂×#106	—	59	1	no	—
143	C₂×#103	—	118	1	no	—
144	#405	—	118	1	no	—
145	C₂×#97	—	59	1	no	—
146	#391	—	118	1	no	—
147	#365	—	118	2	no	—
148	#362	—	118	2	no	—
149	#358	Dic₅₉	1	4	yes	complemented
150	#339	—	118	1	no	—
151	C₅₉	#13141	1	1	yes	characteristic, complemented, Sylow
152	C₂²×Q₈	—	2	1	no	—
153	C₂×Q₁₆	—	2	1	no	—
154	C₂×Q₁₆	—	2	1	no	—
155	C₂×Q₁₆	—	2	1	no	—
156	C₂×Q₁₆	—	2	1	no	—
157	C₂×Q₁₆	—	2	1	no	—
158	C₂×Q₁₆	C₂×Dic₅₉	1	2	yes	—
159	C₂×M₁₆	—	118	1	no	—
160	C₂²×C₈	—	59	1	no	—
161	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
162	#117	—	2	1	no	—
163	C₂×C₄⋊C₄	—	118	1	no	—
164	C₂×C₄²	—	59	1	no	—
165	M₃₂	—	2	1	no	—
166	M₃₂	—	2	1	no	—
167	M₃₂	—	118	1	no	—
168	M₃₂	—	118	1	no	—
169	C₂×C₁₆	—	118	1	no	—
170	C₂×C₁₆	C₂×Dic₅₉	1	2	yes	—
171	#108	—	59	2	no	—
172	#108	—	118	1	no	—
173	#107	C₂×Dic₅₉	1	2	yes	—
174	#106	—	2	1	no	—
175	#106	—	118	1	no	—
176	#106	—	118	1	no	—
177	#103	—	236	2	no	—
178	#97	—	118	1	no	—
179	#97	—	118	1	no	—
180	#97	—	236	1	no	—
181	C₄×C₈	—	236	1	no	—
182	#95	—	236	2	no	—
183	C₂×Q₈	—	2	2	no	—
184	C₂×Q₈	—	4	1	no	—
185	C₂×Q₈	—	4	1	no	—
186	C₂×Q₈	—	4	1	no	—
187	C₂×Q₈	—	4	1	no	—
188	C₂×Q₈	—	4	1	no	—
189	C₂²×C₄	—	4	1	no	—
190	C₂²×C₄	—	118	1	no	—
191	C₂²×C₄	—	236	1	no	—
192	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
193	Q₁₆	—	2	2	no	—
194	Q₁₆	—	2	2	no	—
195	Q₁₆	—	4	1	no	—
196	Q₁₆	—	4	1	no	—
197	M₁₆	—	118	2	no	—
198	M₁₆	—	236	1	no	—
199	C₂×C₈	—	59	2	no	—
200	C₂×C₈	—	118	1	no	—
201	C₂×C₈	—	118	1	no	—
202	C₂×C₈	—	236	1	no	—
203	C₂×C₈	#11745685	1	1	yes	characteristic
204	C₂×C₈	#11745685	1	1	yes	characteristic
205	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
206	C₂×C₈	#11745687	1	1	yes	characteristic
207	C₂×C₈	#11745687	1	1	yes	characteristic
208	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
209	C₄⋊C₄	—	2	2	no	—
210	C₄⋊C₄	—	236	1	no	—
211	C₄⋊C₄	—	236	1	no	—
212	C₂²⋊C₄	—	4	1	no	—
213	C₄²	—	4	1	no	—
214	C₄²	—	118	1	no	—
215	C₄²	—	118	1	no	—
216	C₁₆	—	2	2	no	—
217	C₁₆	—	236	1	no	—
218	C₂³	#14273751	1	1	yes	characteristic
219	Q₈	—	4	2	no	—
220	Q₈	—	4	2	no	—
221	Q₈	—	8	1	no	—
222	Q₈	—	8	1	no	—
223	C₂×C₄	—	4	2	no	—
224	C₂×C₄	—	4	2	no	—
225	C₂×C₄	—	8	1	no	—
226	C₂×C₄	—	8	1	no	—
227	C₂×C₄	—	472	2	no	—
228	C₂×C₄	—	472	1	no	—
229	C₂×C₄	—	236	2	no	—
230	C₂×C₄	—	236	1	no	—
231	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
232	C₂×C₄	#14273700	1	1	yes	characteristic
233	C₂×C₄	#14273709	1	1	yes	characteristic
234	C₂×C₄	SD₁₆×D₅₉	1	1	yes	characteristic
235	C₂×C₄	#14273748	1	1	yes	characteristic
236	C₂×C₄	#14273751	1	1	yes	characteristic
237	C₈	—	118	2	no	—
238	C₈	—	236	2	no	—
239	C₈	#14273686	1	1	yes	characteristic
240	C₈	D₄×Dic₅₉	1	1	yes	characteristic
241	C₈	#14273713	1	1	yes	characteristic
242	C₈	#14273720	1	1	yes	characteristic
243	C₂²	—	2	2	no	—
244	C₂²	#16837514	1	1	yes	characteristic
245	C₂²	#16837601	1	1	yes	characteristic
246	C₂²	#16837725	1	1	yes	characteristic
247	C₄	—	8	2	no	—
248	C₄	—	8	2	no	—
249	C₄	—	944	1	no	—
250	C₄	—	472	1	no	—
251	C₄	#16837295	1	1	yes	characteristic
252	C₄	SD₁₆×Dic₅₉	1	1	yes	characteristic
253	C₄	#16837616	1	1	yes	characteristic
254	C₄	#16837719	1	1	yes	characteristic
255	C₂	—	2	1	no	—
256	C₂	—	2	1	no	—
257	C₂	#21424725	1	1	yes	characteristic
258	C₂	#21425988	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#16837225

C₂

yes

maximal, characteristic

C₂×#16837218

C₂

yes

maximal, characteristic

#21424968

C₂

yes

maximal, characteristic

#21423982

C₂

yes

maximal, characteristic

#21422201

C₂

yes

maximal, characteristic

#21422175

C₂

yes

maximal, characteristic

C₅₉×#2141

C₂

yes

maximal, characteristic

C₂×#14273667

C₂²

yes

characteristic

C₂×#14273663

C₂²

yes

characteristic

C₂×#14273659

C₂²

yes

—

—

C₂²

yes

—

—

—

—

C₂²×Q₁₆×C₅₉

C₂²

yes

characteristic

C₂×M₃₂×C₅₉

C₂²

yes

characteristic

C₅₉×#427

C₂²

yes

characteristic

C₅₉×#358

C₄

yes

complemented

C₂×#11745664

—

C₂²×C₅₉⋊C₈

D₄

yes

characteristic

C₂×C₄⋊Dic₅₉

—

C₂×C₄×Dic₅₉

D₄

yes

characteristic

#14273667

—

#14273667

—

C₂×C₅₉⋊C₁₆

—

#14273663

—

#14273663

D₄

yes

—

—

—

—

—

—

—

C₄×C₅₉⋊C₈

—

C₅₉⋊#95

—

C₂²×Q₈×C₅₉

—

C₂×Q₁₆×C₅₉

—

C₂×Q₁₆×C₅₉

—

C₂×Q₁₆×C₅₉

—

C₂×Q₁₆×C₅₉

—

C₂×Q₁₆×C₅₉

—

C₂×Q₁₆×C₅₉

C₂×C₄

yes

—

C₂²×C₈×C₅₉

C₂³

yes

characteristic

#117×C₅₉

—

M₃₂×C₅₉

—

M₃₂×C₅₉

—

C₂×C₁₆×C₅₉

C₂×C₄

yes

—

#107×C₅₉

C₂×C₄

yes

—

#106×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂²×Dic₅₉

—

C₂²×Dic₅₉

—

Q₁₆×C₅₉

—

Q₁₆×C₅₉

—

Q₁₆×C₅₉

—

Q₁₆×C₅₉

—

C₂×C₈×C₅₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₅₉

C₂×D₄

yes

C₂×C₈×C₅₉

yes

C₂×C₈×C₅₉

yes

C₂×C₈×C₅₉

yes

C₂×C₈×C₅₉

yes

C₄⋊C₄×C₅₉

—

C₂²⋊C₄×C₅₉

—

C₄²×C₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

#11745664

—

#11745664

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

SD₁₆

yes

—

C₁₆×C₅₉

—

C₅₉⋊C₁₆

—

C₂³×C₅₉

AGL(1,ℤ/8)

yes

characteristic

Q₈×C₅₉

—

Q₈×C₅₉

—

Q₈×C₅₉

—

Q₈×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₄×D₄

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

100

C₂×C₄×C₅₉

C₂×SD₁₆

yes

characteristic

101

C₂×C₄×C₅₉

#135

yes

characteristic

102

C₂×C₄×C₅₉

AGL(1,ℤ/8)

yes

characteristic

103

C₂×Dic₅₉

—

104

C₂×Dic₅₉

—

105

C₂×Dic₅₉

—

106

C₂×Dic₅₉

—

107

C₈×C₅₉

#117

yes

characteristic

108

C₈×C₅₉

C₄×D₄

yes

characteristic

109

C₈×C₅₉

#124

yes

characteristic

110

C₈×C₅₉

#126

yes

characteristic

111

C₅₉⋊C₈

—

112

C₅₉⋊C₈

—

113

#13141

—

maximal, Sylow

114

C₂²×C₅₉

—

115

C₂²×C₅₉

#442

yes

characteristic

116

C₂²×C₅₉

#460

yes

characteristic

117

C₂²×C₅₉

#482

yes

characteristic

118

C₄×C₅₉

—

119

C₄×C₅₉

—

120

C₄×C₅₉

#388

yes

characteristic

121

C₄×C₅₉

C₄×SD₁₆

yes

characteristic

122

C₄×C₅₉

#463

yes

characteristic

123

C₄×C₅₉

#481

yes

characteristic

124

Dic₅₉

—

125

Dic₅₉

—

126

C₂×#365

—

127

C₂×#362

—

128

#2141

D₅₉

yes

characteristic

129

#1971

—

130

#1773

—

131

#1386

—

132

#1375

—

133

C₂×C₅₉

—

134

C₂×C₅₉

—

135

C₂×C₅₉

#1926

yes

characteristic

136

C₂×C₅₉

#2180

yes

—

137

C₂²×Q₁₆

C₂×D₅₉

yes

characteristic

138

C₂×M₃₂

—

139

C₂×M₃₂

C₂×D₅₉

yes

characteristic

140

C₂×#108

—

141

#427

C₂×D₅₉

yes

characteristic

142

C₂×#106

—

143

C₂×#103

—

118

—

144

#405

—

118

—

145

C₂×#97

—

146

#391

—

118

—

147

#365

—

118

—

148

#362

—

118

—

149

#358

Dic₅₉

yes

complemented

150

#339

—

118

—

151

C₅₉

#13141

yes

characteristic, complemented, Sylow

152

C₂²×Q₈

—

153

C₂×Q₁₆

—

154

C₂×Q₁₆

—

155

C₂×Q₁₆

—

156

C₂×Q₁₆

—

157

C₂×Q₁₆

—

158

C₂×Q₁₆

C₂×Dic₅₉

yes

—

159

C₂×M₁₆

—

118

—

160

C₂²×C₈

—

161

C₂²×C₈

C₂²×D₅₉

yes

characteristic

162

#117

—

163

C₂×C₄⋊C₄

—

118

—

164

C₂×C₄²

—

165

M₃₂

—

166

M₃₂

—

167

M₃₂

—

118

—

168

M₃₂

—

118

—

169

C₂×C₁₆

—

118

—

170

C₂×C₁₆

C₂×Dic₅₉

yes

—

171

#108

—

172

#108

—

118

—

173

#107

C₂×Dic₅₉

yes

—

174

#106

—

175

#106

—

118

—

176

#106

—

118

—

177

#103

—

236

—

178

#97

—

118

—

179

#97

—

118

—

180

#97

—

236

—

181

C₄×C₈

—

236

—

182

#95

—

236

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂×Q₈

—

188

C₂×Q₈

—

189

C₂²×C₄

—

190

C₂²×C₄

—

118

—

191

C₂²×C₄

—

236

—

192

C₂²×C₄

D₄×D₅₉

yes

characteristic

193

Q₁₆

—

194

Q₁₆

—

195

Q₁₆

—

196

Q₁₆

—

197

M₁₆

—

118

—

198

M₁₆

—

236

—

199

C₂×C₈

—

200

C₂×C₈

—

118

—

201

C₂×C₈

—

118

—

202

C₂×C₈

—

236

—

203

C₂×C₈

#11745685

yes

characteristic

204

C₂×C₈

#11745685

yes

characteristic

205

C₂×C₈

D₄×D₅₉

yes

characteristic

206

C₂×C₈

#11745687

yes

characteristic

207

C₂×C₈

#11745687

yes

characteristic

208

C₂×C₈

C₂²×Dic₅₉

yes

characteristic

209

C₄⋊C₄

—

210

C₄⋊C₄

—

236

—

211

C₄⋊C₄

—

236

—

212

C₂²⋊C₄

—

213

C₄²

—

214

C₄²

—

118

—

215

C₄²

—

118

—

216

C₁₆

—

217

C₁₆

—

236

—

218

C₂³

#14273751

yes

characteristic

219

Q₈

—

220

Q₈

—

221

Q₈

—

222

Q₈

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

472

—

228

C₂×C₄

—

472

—

229

C₂×C₄

—

236

—

230

C₂×C₄

—

236

—

231

C₂×C₄

D₄×Dic₅₉

yes

characteristic

232

C₂×C₄

#14273700

yes

characteristic

233

C₂×C₄

#14273709

yes

characteristic

234

C₂×C₄

SD₁₆×D₅₉

yes

characteristic

235

C₂×C₄

#14273748

yes

characteristic

236

C₂×C₄

#14273751

yes

characteristic

237

C₈

—

118

—

238

C₈

—

236

—

239

C₈

#14273686

yes

characteristic

240

C₈

D₄×Dic₅₉

yes

characteristic

241

C₈

#14273713

yes

characteristic

242

C₈

#14273720

yes

characteristic

243

C₂²

—

244

C₂²

#16837514

yes

characteristic

245

C₂²

#16837601

yes

characteristic

246

C₂²

#16837725

yes

characteristic

247

C₄

—

248

C₄

—

249

C₄

—

944

—

250

C₄

—

472

—

251

C₄

#16837295

yes

characteristic

252

C₄

SD₁₆×Dic₅₉

yes

characteristic

253

C₄

#16837616

yes

characteristic

254

C₄

#16837719

yes

characteristic

255

C₂

—

256

C₂

—

257

C₂

#21424725

yes

characteristic

258

C₂

#21425988

yes

—

	subgroup	G/H
center	C₂²	#16837514
commutator	C₂×C₈×C₅₉	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₅₉
Fitting	C₅₉×#2141	C₂
socle	C₂²×C₅₉	#442
prime radical	C₂³×C₅₉	AGL(1,ℤ/8)
cosocle	C₂²×C₈×C₅₉	C₂³
hypercenter	#2141	D₅₉
hypocenter	C₅₉	#13141
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #2141

subgroup

G/H

center

C₂²

#16837514

commutator

C₂×C₈×C₅₉

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₅₉

Fitting

C₅₉×#2141

C₂

C₂²×C₅₉

C₂³×C₅₉

C₂²×C₈×C₅₉

C₂³

D₅₉

C₅₉

G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #2141

N	H ≅ G/N	type
21. C₅₉×#358	C₄	semidirect
149. #358	Dic₅₉	semidirect
151. C₅₉	#13141	semidirect

H ≅ G/N

type

21. C₅₉×#358

C₄

semidirect

149. #358

Dic₅₉

semidirect

151. C₅₉

#13141

semidirect

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

subgroup	index
C₂×#16837225	2
C₂×#16837218	2
#21424968	2
#21423982	2
#21422201	2
#21422175	2
C₅₉×#2141	2
#13141	59

subgroup

index

C₅₉×#2141

Subgroups — #28506565

Conjugacy classes of subgroups

Complements

Maximal subgroups