Group #28506655 — subgroups

Subgroups — #28506655

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	C₂×#16837219	C₂	1	1	yes	maximal, characteristic
2	#21425815	C₂	1	1	yes	maximal, characteristic
3	C₂×#16837179	C₂	1	1	yes	maximal, characteristic
4	#21424965	C₂	1	1	yes	maximal, characteristic
5	#21424850	C₂	1	1	yes	maximal, characteristic
6	#21422194	C₂	1	1	yes	maximal, characteristic
7	C₅₉×#1386	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₂₃₆	C₂²	1	1	yes	characteristic
9	C₂×#14273667	C₂²	1	1	yes	characteristic
10	C₂×#14273663	C₂²	1	1	yes	characteristic
11	#16837429	—	2	1	no	—
12	C₂×#14273650	—	2	1	no	—
13	C₂×#14273637	C₂²	1	1	yes	characteristic
14	#16837307	—	2	1	no	—
15	#16837219	—	2	2	no	—
16	#16837205	C₄	1	4	yes	complemented
17	#16837179	—	2	2	no	—
18	#16837161	—	2	1	no	—
19	C₂×M₃₂×C₅₉	C₂²	1	1	yes	characteristic
20	C₅₉×#427	C₂²	1	1	yes	characteristic
21	C₂×#106×C₅₉	C₂²	1	1	yes	characteristic
22	C₂²×Dic₁₁₈	—	2	1	no	—
23	C₂×Dic₂₃₆	—	2	1	no	—
24	C₂×Dic₂₃₆	—	2	1	no	—
25	C₂×Dic₂₃₆	—	2	1	no	—
26	C₂×Dic₂₃₆	—	2	1	no	—
27	C₂×Dic₂₃₆	—	2	1	no	—
28	C₂×Dic₂₃₆	C₂×C₄	1	2	yes	—
29	C₂×#11745664	—	2	1	no	—
30	C₂²×C₅₉⋊C₈	D₄	1	1	yes	characteristic
31	C₂×C₄×Dic₅₉	D₄	1	1	yes	characteristic
32	#14273667	—	2	1	no	—
33	#14273667	—	2	1	no	—
34	C₂×C₅₉⋊C₁₆	C₂×C₄	1	2	yes	—
35	#14273663	—	2	1	no	—
36	#14273663	—	2	1	no	—
37	C₄⋊(C₅₉⋊C₈)	—	4	2	no	—
38	#14273650	—	4	2	no	—
39	#14273637	—	2	1	no	—
40	#14273637	—	2	1	no	—
41	C₅₉⋊#95	—	4	2	no	—
42	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
43	#117×C₅₉	—	2	1	no	—
44	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
45	M₃₂×C₅₉	—	2	1	no	—
46	M₃₂×C₅₉	D₄	1	2	yes	—
47	C₂×C₁₆×C₅₉	—	2	1	no	—
48	#107×C₅₉	C₂×C₄	1	2	yes	—
49	#106×C₅₉	—	2	1	no	—
50	#106×C₅₉	—	2	1	no	—
51	#106×C₅₉	—	2	1	no	—
52	C₂²×C₄×C₅₉	—	4	1	no	—
53	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
54	C₂²×Dic₅₉	—	2	1	no	—
55	C₂²×Dic₅₉	—	4	1	no	—
56	C₂×Dic₁₁₈	—	2	2	no	—
57	C₂×Dic₁₁₈	—	4	1	no	—
58	C₂×Dic₁₁₈	—	4	1	no	—
59	C₂×Dic₁₁₈	—	4	1	no	—
60	C₂×Dic₁₁₈	—	4	1	no	—
61	C₂×Dic₁₁₈	—	4	1	no	—
62	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
63	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
64	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
65	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
66	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
67	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
68	C₄⋊C₄×C₅₉	—	2	2	no	—
69	C₄⋊C₄×C₅₉	—	4	1	no	—
70	C₄⋊C₄×C₅₉	—	4	1	no	—
71	C₂²⋊C₄×C₅₉	—	4	1	no	—
72	C₄²×C₅₉	—	4	1	no	—
73	C₄×Dic₅₉	—	2	1	no	—
74	C₄×Dic₅₉	—	2	1	no	—
75	#11745664	—	4	1	no	—
76	#11745664	—	4	1	no	—
77	C₂×C₅₉⋊C₈	—	2	1	no	—
78	C₂×C₅₉⋊C₈	—	2	1	no	—
79	C₂×C₅₉⋊C₈	—	2	1	no	—
80	C₂×C₅₉⋊C₈	—	4	1	no	—
81	Dic₂₃₆	—	2	2	no	—
82	Dic₂₃₆	—	2	2	no	—
83	Dic₂₃₆	—	4	1	no	—
84	Dic₂₃₆	—	4	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	C₂×C₄×C₅₉	—	4	2	no	—
89	C₂×C₄×C₅₉	—	8	2	no	—
90	C₂×C₄×C₅₉	—	8	1	no	—
91	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
92	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
93	C₂×C₄×C₅₉	#124	1	1	yes	characteristic
94	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
95	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
96	C₂×C₄×C₅₉	#137	1	1	yes	characteristic
97	C₂×Dic₅₉	—	4	2	no	—
98	C₂×Dic₅₉	—	4	2	no	—
99	C₂×Dic₅₉	—	4	1	no	—
100	C₂×Dic₅₉	—	8	1	no	—
101	C₂×Dic₅₉	—	8	1	no	—
102	Dic₁₁₈	—	4	2	no	—
103	Dic₁₁₈	—	4	2	no	—
104	Dic₁₁₈	—	8	1	no	—
105	Dic₁₁₈	—	8	1	no	—
106	C₈×C₅₉	#117	1	1	yes	characteristic
107	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
108	C₈×C₅₉	#123	1	1	yes	characteristic
109	C₈×C₅₉	#126	1	1	yes	characteristic
110	C₅₉⋊C₈	—	4	1	no	—
111	C₅₉⋊C₈	—	8	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	—	16	1	no	—
119	C₄×C₅₉	#388	1	1	yes	characteristic
120	C₄×C₅₉	#440	1	1	yes	characteristic
121	C₄×C₅₉	#469	1	1	yes	characteristic
122	C₄×C₅₉	#489	1	1	yes	characteristic
123	Dic₅₉	—	8	1	no	—
124	Dic₅₉	—	8	2	no	—
125	C₂×#362	—	59	1	no	—
126	#2141	—	59	1	no	—
127	C₂×#347	—	59	1	no	—
128	#1971	—	59	1	no	—
129	#1946	—	59	1	no	—
130	#1386	D₅₉	1	1	yes	characteristic
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	—	59	1	no	—
137	C₂×M₃₂	—	59	1	no	—
138	C₂×M₃₂	C₂×D₅₉	1	1	yes	characteristic
139	C₂×#108	—	59	1	no	—
140	#427	C₂×D₅₉	1	1	yes	characteristic
141	C₂×#106	C₂×D₅₉	1	1	yes	characteristic
142	#424	—	118	1	no	—
143	C₂×#103	—	118	1	no	—
144	C₂×#97	—	59	1	no	—
145	#391	—	118	1	no	—
146	#362	—	118	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	—	118	1	no	—
152	C₂×Q₁₆	—	59	2	no	—
153	C₂×Q₁₆	—	118	1	no	—
154	C₂×Q₁₆	—	118	1	no	—
155	C₂×Q₁₆	—	118	1	no	—
156	C₂×Q₁₆	—	118	1	no	—
157	C₂×Q₁₆	—	118	1	no	—
158	C₂×M₁₆	—	118	1	no	—
159	C₂²×C₈	—	59	1	no	—
160	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
161	#117	—	2	1	no	—
162	C₂×C₄⋊C₄	—	2	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	D₂₃₆	1	2	yes	—
168	C₂×C₁₆	—	2	1	no	—
169	C₂×C₁₆	—	59	2	no	—
170	#108	—	118	1	no	—
171	#108	—	118	1	no	—
172	#107	C₄×D₅₉	1	2	yes	—
173	#106	—	2	1	no	—
174	#106	—	2	1	no	—
175	#106	—	2	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	—	118	2	no	—
182	C₂×Q₈	—	236	1	no	—
183	C₂×Q₈	—	236	1	no	—
184	C₂×Q₈	—	236	1	no	—
185	C₂×Q₈	—	236	1	no	—
186	C₂×Q₈	—	236	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	—	118	2	no	—
192	Q₁₆	—	118	2	no	—
193	Q₁₆	—	236	1	no	—
194	Q₁₆	—	236	1	no	—
195	M₁₆	—	236	1	no	—
196	M₁₆	—	236	1	no	—
197	C₂×C₈	—	118	1	no	—
198	C₂×C₈	—	118	1	no	—
199	C₂×C₈	—	118	1	no	—
200	C₂×C₈	—	236	1	no	—
201	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
202	C₂×C₈	C₂×D₂₃₆	1	1	yes	characteristic
203	C₂×C₈	#11745685	1	1	yes	characteristic
204	C₂×C₈	#11745687	1	1	yes	characteristic
205	C₂×C₈	#11745687	1	1	yes	characteristic
206	C₂×C₈	#11745689	1	1	yes	characteristic
207	C₄⋊C₄	—	2	2	no	—
208	C₄⋊C₄	—	4	1	no	—
209	C₄⋊C₄	—	4	1	no	—
210	C₂²⋊C₄	—	4	1	no	—
211	C₄²	—	4	1	no	—
212	C₄²	—	118	1	no	—
213	C₄²	—	118	1	no	—
214	C₁₆	—	2	2	no	—
215	C₁₆	—	118	2	no	—
216	C₂³	#14273751	1	1	yes	characteristic
217	Q₈	—	472	1	no	—
218	Q₈	—	472	1	no	—
219	Q₈	—	236	2	no	—
220	Q₈	—	236	2	no	—
221	C₂×C₄	—	4	2	no	—
222	C₂×C₄	—	8	2	no	—
223	C₂×C₄	—	8	1	no	—
224	C₂×C₄	—	472	1	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	#14273702	1	1	yes	characteristic
231	C₂×C₄	#14273713	1	1	yes	characteristic
232	C₂×C₄	#14273754	1	1	yes	characteristic
233	C₂×C₄	#14273754	1	1	yes	characteristic
234	C₂×C₄	#14273759	1	1	yes	characteristic
235	C₈	—	472	1	no	—
236	C₈	—	236	1	no	—
237	C₈	#14273685	1	1	yes	characteristic
238	C₈	C₄×D₂₃₆	1	1	yes	characteristic
239	C₈	#14273711	1	1	yes	characteristic
240	C₈	#14273722	1	1	yes	characteristic
241	C₂²	—	2	2	no	—
242	C₂²	#16837511	1	1	yes	characteristic
243	C₂²	#16837649	1	1	yes	characteristic
244	C₂²	#16837765	1	1	yes	characteristic
245	C₄	—	8	2	no	—
246	C₄	—	16	1	no	—
247	C₄	—	472	1	no	—
248	C₄	—	472	2	no	—
249	C₄	#16837294	1	1	yes	characteristic
250	C₄	#16837505	1	1	yes	characteristic
251	C₄	#16837656	1	1	yes	characteristic
252	C₄	#16837763	1	1	yes	characteristic
253	C₂	—	2	1	no	—
254	C₂	—	2	1	no	—
255	C₂	#21424794	1	1	yes	characteristic
256	C₂	#21425984	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#16837219

C₂

yes

maximal, characteristic

#21425815

C₂

yes

maximal, characteristic

C₂×#16837179

C₂

yes

maximal, characteristic

#21424965

C₂

yes

maximal, characteristic

#21424850

C₂

yes

maximal, characteristic

#21422194

C₂

yes

maximal, characteristic

C₅₉×#1386

C₂

yes

maximal, characteristic

C₂²×Dic₂₃₆

C₂²

yes

characteristic

C₂×#14273667

C₂²

yes

characteristic

C₂×#14273663

C₂²

yes

—

—

C₂²

yes

—

—

C₄

yes

complemented

#16837179

—

#16837161

—

C₂×M₃₂×C₅₉

C₂²

yes

characteristic

C₅₉×#427

C₂²

yes

characteristic

C₂×#106×C₅₉

C₂²

yes

characteristic

C₂²×Dic₁₁₈

—

C₂×Dic₂₃₆

—

C₂×Dic₂₃₆

—

C₂×Dic₂₃₆

—

C₂×Dic₂₃₆

—

C₂×Dic₂₃₆

—

C₂×Dic₂₃₆

C₂×C₄

yes

—

C₂×#11745664

—

C₂²×C₅₉⋊C₈

D₄

yes

characteristic

C₂×C₄×Dic₅₉

D₄

yes

characteristic

#14273667

—

#14273667

—

C₂×C₅₉⋊C₁₆

C₂×C₄

yes

—

#14273663

—

#14273663

—

C₄⋊(C₅₉⋊C₈)

—

#14273650

—

#14273637

—

#14273637

—

C₅₉⋊#95

—

C₂²×C₈×C₅₉

C₂³

yes

characteristic

#117×C₅₉

—

C₂×C₄⋊C₄×C₅₉

—

M₃₂×C₅₉

—

M₃₂×C₅₉

D₄

yes

—

C₂×C₁₆×C₅₉

—

#107×C₅₉

C₂×C₄

yes

—

#106×C₅₉

—

#106×C₅₉

—

#106×C₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂²×Dic₅₉

—

C₂²×Dic₅₉

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

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

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₂²⋊C₄×C₅₉

—

C₄²×C₅₉

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

#11745664

—

#11745664

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

Dic₂₃₆

—

Dic₂₃₆

—

Dic₂₃₆

—

Dic₂₃₆

—

C₁₆×C₅₉

—

C₅₉⋊C₁₆

—

C₂³×C₅₉

AGL(1,ℤ/8)

yes

characteristic

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

C₂×C₄×C₅₉

yes

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

100

C₂×Dic₅₉

—

101

C₂×Dic₅₉

—

102

Dic₁₁₈

—

103

Dic₁₁₈

—

104

Dic₁₁₈

—

105

Dic₁₁₈

—

106

C₈×C₅₉

#117

yes

characteristic

107

C₈×C₅₉

C₄×D₄

yes

characteristic

108

C₈×C₅₉

#123

yes

characteristic

109

C₈×C₅₉

#126

yes

characteristic

110

C₅₉⋊C₈

—

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

—

119

C₄×C₅₉

#388

yes

characteristic

120

C₄×C₅₉

#440

yes

characteristic

121

C₄×C₅₉

#469

yes

characteristic

122

C₄×C₅₉

#489

yes

characteristic

123

Dic₅₉

—

124

Dic₅₉

—

125

C₂×#362

—

126

#2141

—

127

C₂×#347

—

128

#1971

—

129

#1946

—

130

#1386

D₅₉

yes

characteristic

131

#1383

—

132

C₂×C₅₉

—

133

C₂×C₅₉

—

134

C₂×C₅₉

#1936

yes

characteristic

135

C₂×C₅₉

#2180

yes

—

136

C₂²×Q₁₆

—

137

C₂×M₃₂

—

138

C₂×M₃₂

C₂×D₅₉

yes

characteristic

139

C₂×#108

—

140

#427

C₂×D₅₉

yes

characteristic

141

C₂×#106

C₂×D₅₉

yes

characteristic

142

#424

—

118

—

143

C₂×#103

—

118

—

144

C₂×#97

—

145

#391

—

118

—

146

#362

—

118

—

147

#358

—

148

#347

—

118

—

149

#339

—

118

—

150

C₅₉

#13154

yes

characteristic, complemented, Sylow

151

C₂²×Q₈

—

118

—

152

C₂×Q₁₆

—

153

C₂×Q₁₆

—

118

—

154

C₂×Q₁₆

—

118

—

155

C₂×Q₁₆

—

118

—

156

C₂×Q₁₆

—

118

—

157

C₂×Q₁₆

—

118

—

158

C₂×M₁₆

—

118

—

159

C₂²×C₈

—

160

C₂²×C₈

C₂²×D₅₉

yes

characteristic

161

#117

—

162

C₂×C₄⋊C₄

—

163

C₂×C₄²

—

164

M₃₂

—

165

M₃₂

—

118

—

166

M₃₂

—

118

—

167

M₃₂

D₂₃₆

yes

—

168

C₂×C₁₆

—

169

C₂×C₁₆

—

170

#108

—

118

—

171

#108

—

118

—

172

#107

C₄×D₅₉

yes

—

173

#106

—

174

#106

—

175

#106

—

176

C₄⋊C₈

—

236

—

177

#103

—

236

—

178

#97

—

118

—

179

#97

—

118

—

180

#95

—

236

—

181

C₂×Q₈

—

118

—

182

C₂×Q₈

—

236

—

183

C₂×Q₈

—

236

—

184

C₂×Q₈

—

236

—

185

C₂×Q₈

—

236

—

186

C₂×Q₈

—

236

—

187

C₂²×C₄

—

188

C₂²×C₄

—

118

—

189

C₂²×C₄

—

236

—

190

C₂²×C₄

D₄×D₅₉

yes

characteristic

191

Q₁₆

—

118

—

192

Q₁₆

—

118

—

193

Q₁₆

—

236

—

194

Q₁₆

—

236

—

195

M₁₆

—

236

—

196

M₁₆

—

236

—

197

C₂×C₈

—

118

—

198

C₂×C₈

—

118

—

199

C₂×C₈

—

118

—

200

C₂×C₈

—

236

—

201

C₂×C₈

C₂×C₄×D₅₉

yes

characteristic

202

C₂×C₈

C₂×D₂₃₆

yes

characteristic

203

C₂×C₈

#11745685

yes

characteristic

204

C₂×C₈

#11745687

yes

characteristic

205

C₂×C₈

#11745687

yes

characteristic

206

C₂×C₈

#11745689

yes

characteristic

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

210

C₂²⋊C₄

—

211

C₄²

—

212

C₄²

—

118

—

213

C₄²

—

118

—

214

C₁₆

—

215

C₁₆

—

118

—

216

C₂³

#14273751

yes

characteristic

217

Q₈

—

472

—

218

Q₈

—

472

—

219

Q₈

—

236

—

220

Q₈

—

236

—

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

#14273702

yes

characteristic

231

C₂×C₄

#14273713

yes

characteristic

232

C₂×C₄

#14273754

yes

characteristic

233

C₂×C₄

#14273754

yes

characteristic

234

C₂×C₄

#14273759

yes

characteristic

235

C₈

—

472

—

236

C₈

—

236

—

237

C₈

#14273685

yes

characteristic

238

C₈

C₄×D₂₃₆

yes

characteristic

239

C₈

#14273711

yes

characteristic

240

C₈

#14273722

yes

characteristic

241

C₂²

—

242

C₂²

#16837511

yes

characteristic

243

C₂²

#16837649

yes

characteristic

244

C₂²

#16837765

yes

characteristic

245

C₄

—

246

C₄

—

247

C₄

—

472

—

248

C₄

—

472

—

249

C₄

#16837294

yes

characteristic

250

C₄

#16837505

yes

characteristic

251

C₄

#16837656

yes

characteristic

252

C₄

#16837763

yes

characteristic

253

C₂

—

254

C₂

—

255

C₂

#21424794

yes

characteristic

256

C₂

#21425984

yes

—

	subgroup	G/H
center	C₂²	#16837511
commutator	C₂×C₈×C₅₉	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₅₉
Fitting	C₅₉×#1386	C₂
socle	C₂²×C₅₉	#442
prime radical	C₂³×C₅₉	AGL(1,ℤ/8)
cosocle	C₂²×C₈×C₅₉	C₂³
hypercenter	#1386	D₅₉
hypocenter	C₅₉	#13154
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1386

subgroup

G/H

center

C₂²

#16837511

commutator

C₂×C₈×C₅₉

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₅₉

Fitting

C₅₉×#1386

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 ◁ #1386

N	H ≅ G/N	type
16. #16837205	C₄	semidirect
150. C₅₉	#13154	semidirect

H ≅ G/N

type

16. #16837205

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
C₂×#16837219	2
#21425815	2
C₂×#16837179	2
#21424965	2
#21424850	2
#21422194	2
C₅₉×#1386	2
#13154	59

subgroup

index

C₅₉×#1386

Subgroups — #28506655

Conjugacy classes of subgroups

Complements

Maximal subgroups