Group #28506651 — subgroups

Subgroups — #28506651

Order 15104.

314 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 97 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	#21425816	C₂	1	1	yes	maximal, characteristic
2	C₂×#16837179	C₂	1	1	yes	maximal, characteristic
3	#21424968	C₂	1	1	yes	maximal, characteristic
4	#21424847	C₂	1	1	yes	maximal, characteristic
5	#21422202	C₂	1	1	yes	maximal, characteristic
6	#21422196	C₂	1	1	yes	maximal, characteristic
7	C₂×C₅₉×#362	C₂	1	1	yes	maximal, characteristic
8	C₂×#14273667	C₂²	1	1	yes	characteristic
9	#16837440	C₂²	1	1	yes	characteristic
10	C₂×#14273659	C₂²	1	1	yes	characteristic
11	#16837430	—	2	1	no	—
12	C₂×#14273651	—	2	1	no	—
13	C₂×#14273637	C₂²	1	1	yes	characteristic
14	#16837309	—	2	1	no	—
15	#16837206	C₄	1	4	yes	complemented
16	#16837179	—	2	2	no	—
17	#16837163	—	2	1	no	—
18	C₂²×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
19	C₂×M₃₂×C₅₉	C₂²	1	1	yes	characteristic
20	C₂×#108×C₅₉	C₂²	1	1	yes	characteristic
21	C₅₉×#362	—	2	2	no	—
22	C₂²×C₅₉⋊C₈	D₄	1	1	yes	characteristic
23	#14273686	—	2	1	no	—
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	C₂×C₄	1	2	yes	—
29	#14273661	C₂×C₄	1	2	yes	—
30	#14273659	—	2	1	no	—
31	#14273659	—	2	1	no	—
32	#14273659	—	2	1	no	—
33	Dic₅₉⋊C₈	—	4	2	no	—
34	#14273651	—	4	2	no	—
35	#14273637	—	2	1	no	—
36	#14273637	—	2	1	no	—
37	C₅₉⋊#95	—	4	2	no	—
38	C₂²×Q₈×C₅₉	—	2	1	no	—
39	C₂×Q₁₆×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	C₂×C₄	1	2	yes	—
45	C₂×M₁₆×C₅₉	—	2	1	no	—
46	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
47	M₃₂×C₅₉	—	2	1	no	—
48	M₃₂×C₅₉	D₄	1	2	yes	—
49	C₂×C₁₆×C₅₉	—	2	1	no	—
50	#108×C₅₉	—	2	1	no	—
51	#108×C₅₉	—	2	1	no	—
52	C₂×Q₈×C₅₉	—	2	2	no	—
53	C₂×Q₈×C₅₉	—	4	1	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	C₂²×C₄×C₅₉	—	4	1	no	—
59	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
60	C₂²×Dic₅₉	—	2	1	no	—
61	C₂²×Dic₅₉	—	4	1	no	—
62	Q₁₆×C₅₉	—	2	2	no	—
63	Q₁₆×C₅₉	—	2	2	no	—
64	Q₁₆×C₅₉	—	4	1	no	—
65	Q₁₆×C₅₉	—	4	1	no	—
66	M₁₆×C₅₉	—	4	1	no	—
67	M₁₆×C₅₉	—	4	1	no	—
68	C₂×C₈×C₅₉	—	4	1	no	—
69	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
70	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
71	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
72	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
73	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
74	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
75	C₂²⋊Dic₅₉	—	4	1	no	—
76	C₄⋊Dic₅₉	—	2	2	no	—
77	C₄⋊Dic₅₉	—	4	1	no	—
78	C₄⋊Dic₅₉	—	4	1	no	—
79	C₄×Dic₅₉	—	2	1	no	—
80	C₄×Dic₅₉	—	2	1	no	—
81	C₄×Dic₅₉	—	4	1	no	—
82	C₂×C₅₉⋊C₈	—	2	1	no	—
83	C₂×C₅₉⋊C₈	—	2	1	no	—
84	C₂×C₅₉⋊C₈	—	2	1	no	—
85	C₁₆×C₅₉	—	2	2	no	—
86	C₅₉⋊C₁₆	—	2	2	no	—
87	C₂³×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
88	Q₈×C₅₉	—	4	2	no	—
89	Q₈×C₅₉	—	4	2	no	—
90	Q₈×C₅₉	—	8	1	no	—
91	Q₈×C₅₉	—	8	1	no	—
92	C₂×C₄×C₅₉	—	4	2	no	—
93	C₂×C₄×C₅₉	—	8	1	no	—
94	C₂×C₄×C₅₉	—	8	1	no	—
95	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
96	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
97	C₂×C₄×C₅₉	#124	1	1	yes	characteristic
98	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
99	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
100	C₂×C₄×C₅₉	#137	1	1	yes	characteristic
101	C₂×Dic₅₉	—	4	2	no	—
102	C₂×Dic₅₉	—	4	2	no	—
103	C₂×Dic₅₉	—	4	1	no	—
104	C₂×Dic₅₉	—	8	2	no	—
105	C₂×Dic₅₉	—	8	1	no	—
106	C₈×C₅₉	—	8	1	no	—
107	C₈×C₅₉	#117	1	1	yes	characteristic
108	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
109	C₈×C₅₉	#123	1	1	yes	characteristic
110	C₈×C₅₉	#126	1	1	yes	characteristic
111	C₅₉⋊C₈	—	4	1	no	—
112	#13154	—	59	1	no	maximal, Sylow
113	C₂²×C₅₉	—	2	2	no	—
114	C₂²×C₅₉	#442	1	1	yes	characteristic
115	C₂²×C₅₉	#468	1	1	yes	characteristic
116	C₂²×C₅₉	#490	1	1	yes	characteristic
117	C₄×C₅₉	—	8	2	no	—
118	C₄×C₅₉	#388	1	1	yes	characteristic
119	C₄×C₅₉	#440	1	1	yes	characteristic
120	C₄×C₅₉	#469	1	1	yes	characteristic
121	C₄×C₅₉	#489	1	1	yes	characteristic
122	Dic₅₉	—	8	1	no	—
123	Dic₅₉	—	8	2	no	—
124	Dic₅₉	—	16	1	no	—
125	C₂×#362	D₅₉	1	1	yes	characteristic
126	#2141	—	59	1	no	—
127	C₂×#347	—	59	1	no	—
128	#1971	—	59	1	no	—
129	#1946	—	59	1	no	—
130	#1386	—	59	1	no	—
131	#1383	—	59	1	no	—
132	C₂×C₅₉	—	2	1	no	—
133	C₂×C₅₉	—	2	1	no	—
134	C₂×C₅₉	#1936	1	1	yes	characteristic
135	C₂×C₅₉	#2180	1	2	yes	—
136	C₂²×Q₁₆	C₂×D₅₉	1	1	yes	characteristic
137	C₂×M₃₂	—	59	1	no	—
138	C₂×M₃₂	C₂×D₅₉	1	1	yes	characteristic
139	C₂×#108	C₂×D₅₉	1	1	yes	characteristic
140	#427	—	59	1	no	—
141	C₂×#106	—	59	1	no	—
142	#424	—	118	1	no	—
143	C₂×#103	—	118	1	no	—
144	C₂×#97	—	59	1	no	—
145	#391	—	118	1	no	—
146	#362	—	2	2	no	—
147	#358	—	59	4	no	—
148	#347	—	118	2	no	—
149	#339	—	118	1	no	—
150	C₅₉	#13154	1	1	yes	characteristic, complemented, Sylow
151	C₂²×Q₈	—	2	1	no	—
152	C₂×Q₁₆	—	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	C₄×D₅₉	1	2	yes	—
158	C₂×M₁₆	—	2	1	no	—
159	C₂²×C₈	—	59	1	no	—
160	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
161	#117	—	118	1	no	—
162	C₂×C₄⋊C₄	—	118	1	no	—
163	C₂×C₄²	—	59	1	no	—
164	M₃₂	—	2	1	no	—
165	M₃₂	—	118	1	no	—
166	M₃₂	—	118	1	no	—
167	M₃₂	C₂²⋊D₅₉	1	2	yes	—
168	C₂×C₁₆	—	2	1	no	—
169	C₂×C₁₆	—	59	2	no	—
170	#108	—	2	1	no	—
171	#108	—	2	1	no	—
172	#107	—	59	2	no	—
173	#106	—	118	1	no	—
174	#106	—	118	1	no	—
175	#106	—	118	1	no	—
176	C₄⋊C₈	—	236	2	no	—
177	#103	—	236	2	no	—
178	#97	—	118	1	no	—
179	#97	—	118	1	no	—
180	#95	—	236	2	no	—
181	C₂×Q₈	—	2	2	no	—
182	C₂×Q₈	—	4	1	no	—
183	C₂×Q₈	—	4	1	no	—
184	C₂×Q₈	—	4	1	no	—
185	C₂×Q₈	—	4	1	no	—
186	C₂×Q₈	—	4	1	no	—
187	C₂²×C₄	—	4	1	no	—
188	C₂²×C₄	—	118	1	no	—
189	C₂²×C₄	—	236	1	no	—
190	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
191	Q₁₆	—	2	2	no	—
192	Q₁₆	—	2	2	no	—
193	Q₁₆	—	4	1	no	—
194	Q₁₆	—	4	1	no	—
195	M₁₆	—	4	1	no	—
196	M₁₆	—	4	1	no	—
197	C₂×C₈	—	4	1	no	—
198	C₂×C₈	—	118	1	no	—
199	C₂×C₈	—	118	1	no	—
200	C₂×C₈	—	118	1	no	—
201	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
202	C₂×C₈	#11745685	1	1	yes	characteristic
203	C₂×C₈	#11745687	1	1	yes	characteristic
204	C₂×C₈	#11745687	1	1	yes	characteristic
205	C₂×C₈	#11745687	1	1	yes	characteristic
206	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
207	C₄⋊C₄	—	118	2	no	—
208	C₄⋊C₄	—	236	1	no	—
209	C₄⋊C₄	—	236	1	no	—
210	C₂²⋊C₄	—	236	1	no	—
211	C₄²	—	118	1	no	—
212	C₄²	—	118	1	no	—
213	C₄²	—	236	1	no	—
214	C₁₆	—	2	2	no	—
215	C₁₆	—	118	2	no	—
216	C₂³	#14273754	1	1	yes	characteristic
217	Q₈	—	4	2	no	—
218	Q₈	—	4	2	no	—
219	Q₈	—	8	1	no	—
220	Q₈	—	8	1	no	—
221	C₂×C₄	—	4	2	no	—
222	C₂×C₄	—	8	1	no	—
223	C₂×C₄	—	8	1	no	—
224	C₂×C₄	—	472	2	no	—
225	C₂×C₄	—	472	1	no	—
226	C₂×C₄	—	236	2	no	—
227	C₂×C₄	—	236	1	no	—
228	C₂×C₄	—	236	2	no	—
229	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
230	C₂×C₄	#14273698	1	1	yes	characteristic
231	C₂×C₄	#14273713	1	1	yes	characteristic
232	C₂×C₄	#14273751	1	1	yes	characteristic
233	C₂×C₄	#14273751	1	1	yes	characteristic
234	C₂×C₄	#14273756	1	1	yes	characteristic
235	C₈	—	8	1	no	—
236	C₈	—	236	1	no	—
237	C₈	#14273683	1	1	yes	characteristic
238	C₈	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
239	C₈	#14273708	1	1	yes	characteristic
240	C₈	#14273720	1	1	yes	characteristic
241	C₂²	—	2	2	no	—
242	C₂²	#16837511	1	1	yes	characteristic
243	C₂²	#16837645	1	1	yes	characteristic
244	C₂²	#16837765	1	1	yes	characteristic
245	C₄	—	8	2	no	—
246	C₄	—	944	1	no	—
247	C₄	—	472	1	no	—
248	C₄	—	472	2	no	—
249	C₄	#16837290	1	1	yes	characteristic
250	C₄	#16837499	1	1	yes	characteristic
251	C₄	#16837652	1	1	yes	characteristic
252	C₄	#16837760	1	1	yes	characteristic
253	C₂	—	2	1	no	—
254	C₂	—	2	1	no	—
255	C₂	#21424790	1	1	yes	characteristic
256	C₂	#21425990	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#21425816

C₂

yes

maximal, characteristic

C₂×#16837179

C₂

yes

maximal, characteristic

#21424968

C₂

yes

maximal, characteristic

#21424847

C₂

yes

maximal, characteristic

#21422202

C₂

yes

maximal, characteristic

#21422196

C₂

yes

maximal, characteristic

C₂×C₅₉×#362

C₂

yes

maximal, characteristic

C₂×#14273667

C₂²

yes

characteristic

#16837440

C₂²

yes

characteristic

C₂×#14273659

C₂²

yes

—

—

C₂²

yes

characteristic

#16837309

—

#16837206

C₄

yes

complemented

#16837179

—

#16837163

—

C₂²×Q₁₆×C₅₉

C₂²

yes

characteristic

C₂×M₃₂×C₅₉

C₂²

yes

characteristic

C₂×#108×C₅₉

C₂²

yes

characteristic

C₅₉×#362

—

C₂²×C₅₉⋊C₈

D₄

yes

characteristic

#14273686

—

C₂×C₄⋊Dic₅₉

—

C₂×C₄×Dic₅₉

D₄

yes

characteristic

#14273667

—

#14273667

—

C₂×C₅₉⋊C₁₆

C₂×C₄

yes

—

#14273661

C₂×C₄

yes

—

#14273659

—

#14273659

—

#14273659

—

Dic₅₉⋊C₈

—

#14273651

—

#14273637

—

#14273637

—

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

—

C₂×M₁₆×C₅₉

—

C₂²×C₈×C₅₉

C₂³

yes

characteristic

M₃₂×C₅₉

—

M₃₂×C₅₉

D₄

yes

—

C₂×C₁₆×C₅₉

—

#108×C₅₉

—

#108×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

—

M₁₆×C₅₉

—

M₁₆×C₅₉

—

C₂×C₈×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

C₂²⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

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

C₄×D₄

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

100

C₂×C₄×C₅₉

#137

yes

characteristic

101

C₂×Dic₅₉

—

102

C₂×Dic₅₉

—

103

C₂×Dic₅₉

—

104

C₂×Dic₅₉

—

105

C₂×Dic₅₉

—

106

C₈×C₅₉

—

107

C₈×C₅₉

#117

yes

characteristic

108

C₈×C₅₉

C₄×D₄

yes

characteristic

109

C₈×C₅₉

#123

yes

characteristic

110

C₈×C₅₉

#126

yes

characteristic

111

C₅₉⋊C₈

—

112

#13154

—

maximal, Sylow

113

C₂²×C₅₉

—

114

C₂²×C₅₉

#442

yes

characteristic

115

C₂²×C₅₉

#468

yes

characteristic

116

C₂²×C₅₉

#490

yes

characteristic

117

C₄×C₅₉

—

118

C₄×C₅₉

#388

yes

characteristic

119

C₄×C₅₉

#440

yes

characteristic

120

C₄×C₅₉

#469

yes

characteristic

121

C₄×C₅₉

#489

yes

characteristic

122

Dic₅₉

—

123

Dic₅₉

—

124

Dic₅₉

—

125

C₂×#362

D₅₉

yes

characteristic

126

#2141

—

127

C₂×#347

—

128

#1971

—

129

#1946

—

130

#1386

—

131

#1383

—

132

C₂×C₅₉

—

133

C₂×C₅₉

—

134

C₂×C₅₉

#1936

yes

characteristic

135

C₂×C₅₉

#2180

yes

—

136

C₂²×Q₁₆

C₂×D₅₉

yes

characteristic

137

C₂×M₃₂

—

138

C₂×M₃₂

C₂×D₅₉

yes

characteristic

139

C₂×#108

C₂×D₅₉

yes

characteristic

140

#427

—

141

C₂×#106

—

142

#424

—

118

—

143

C₂×#103

—

118

—

144

C₂×#97

—

145

#391

—

118

—

146

#362

—

147

#358

—

148

#347

—

118

—

149

#339

—

118

—

150

C₅₉

#13154

yes

characteristic, complemented, Sylow

151

C₂²×Q₈

—

152

C₂×Q₁₆

—

153

C₂×Q₁₆

—

154

C₂×Q₁₆

—

155

C₂×Q₁₆

—

156

C₂×Q₁₆

—

157

C₂×Q₁₆

C₄×D₅₉

yes

—

158

C₂×M₁₆

—

159

C₂²×C₈

—

160

C₂²×C₈

C₂²×D₅₉

yes

characteristic

161

#117

—

118

—

162

C₂×C₄⋊C₄

—

118

—

163

C₂×C₄²

—

164

M₃₂

—

165

M₃₂

—

118

—

166

M₃₂

—

118

—

167

M₃₂

C₂²⋊D₅₉

yes

—

168

C₂×C₁₆

—

169

C₂×C₁₆

—

170

#108

—

171

#108

—

172

#107

—

173

#106

—

118

—

174

#106

—

118

—

175

#106

—

118

—

176

C₄⋊C₈

—

236

—

177

#103

—

236

—

178

#97

—

118

—

179

#97

—

118

—

180

#95

—

236

—

181

C₂×Q₈

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂²×C₄

—

188

C₂²×C₄

—

118

—

189

C₂²×C₄

—

236

—

190

C₂²×C₄

D₄×D₅₉

yes

characteristic

191

Q₁₆

—

192

Q₁₆

—

193

Q₁₆

—

194

Q₁₆

—

195

M₁₆

—

196

M₁₆

—

197

C₂×C₈

—

198

C₂×C₈

—

118

—

199

C₂×C₈

—

118

—

200

C₂×C₈

—

118

—

201

C₂×C₈

C₂×C₄×D₅₉

yes

characteristic

202

C₂×C₈

#11745685

yes

characteristic

203

C₂×C₈

#11745687

yes

characteristic

204

C₂×C₈

#11745687

yes

characteristic

205

C₂×C₈

#11745687

yes

characteristic

206

C₂×C₈

C₂×C₂²⋊D₅₉

yes

characteristic

207

C₄⋊C₄

—

118

—

208

C₄⋊C₄

—

236

—

209

C₄⋊C₄

—

236

—

210

C₂²⋊C₄

—

236

—

211

C₄²

—

118

—

212

C₄²

—

118

—

213

C₄²

—

236

—

214

C₁₆

—

215

C₁₆

—

118

—

216

C₂³

#14273754

yes

characteristic

217

Q₈

—

218

Q₈

—

219

Q₈

—

220

Q₈

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

472

—

225

C₂×C₄

—

472

—

226

C₂×C₄

—

236

—

227

C₂×C₄

—

236

—

228

C₂×C₄

—

236

—

229

C₂×C₄

(C₂²⋊D₅₉)⋊C₄

yes

characteristic

230

C₂×C₄

#14273698

yes

characteristic

231

C₂×C₄

#14273713

yes

characteristic

232

C₂×C₄

#14273751

yes

characteristic

233

C₂×C₄

#14273751

yes

characteristic

234

C₂×C₄

#14273756

yes

characteristic

235

C₈

—

236

C₈

—

236

—

237

C₈

#14273683

yes

characteristic

238

C₈

C₄×C₂²⋊D₅₉

yes

characteristic

239

C₈

#14273708

yes

characteristic

240

C₈

#14273720

yes

characteristic

241

C₂²

—

242

C₂²

#16837511

yes

characteristic

243

C₂²

#16837645

yes

characteristic

244

C₂²

#16837765

yes

characteristic

245

C₄

—

246

C₄

—

944

—

247

C₄

—

472

—

248

C₄

—

472

—

249

C₄

#16837290

yes

characteristic

250

C₄

#16837499

yes

characteristic

251

C₄

#16837652

yes

characteristic

252

C₄

#16837760

yes

characteristic

253

C₂

—

254

C₂

—

255

C₂

#21424790

yes

characteristic

256

C₂

#21425990

yes

—

	subgroup	G/H
center	C₂²	#16837511
commutator	C₂×C₈×C₅₉	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₅₉
Fitting	C₂×C₅₉×#362	C₂
socle	C₂²×C₅₉	#442
prime radical	C₂³×C₅₉	AGL(1,ℤ/8)
cosocle	C₂²×C₈×C₅₉	C₂³
hypercenter	C₂×#362	D₅₉
hypocenter	C₅₉	#13154
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#362

subgroup

G/H

center

C₂²

#16837511

commutator

C₂×C₈×C₅₉

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₅₉

Fitting

C₂×C₅₉×#362

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 ◁ C₂×#362

N	H ≅ G/N	type
15. #16837206	C₄	semidirect
150. C₅₉	#13154	semidirect

H ≅ G/N

type

15. #16837206

C₄

semidirect

150. C₅₉

#13154

semidirect

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

subgroup	index
#21425816	2
C₂×#16837179	2
#21424968	2
#21424847	2
#21422202	2
#21422196	2
C₂×C₅₉×#362	2
#13154	59

subgroup

index

C₂×C₅₉×#362

Subgroups — #28506651

Conjugacy classes of subgroups

Complements

Maximal subgroups