Group #28493493 — subgroups

Subgroups — #28493493

Order 15104.

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

normal subgroups only

This group has 294 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	#21425068	C₂	1	1	yes	maximal, characteristic
2	#21424270	C₂	1	1	yes	maximal, characteristic
3	#21422782	C₂	1	1	yes	maximal, characteristic
4	#21422776	C₂	1	1	yes	maximal, characteristic
5	#21421954	C₂	1	1	yes	maximal, characteristic
6	#21421940	C₂	1	1	yes	maximal, characteristic
7	C₅₉×#1286	C₂	1	1	yes	maximal, characteristic
8	C₂×#14273727	C₂²	1	1	yes	characteristic
9	#16837455	C₂²	1	1	yes	characteristic
10	C₂×#14273662	—	2	1	no	—
11	C₂×#14273662	—	2	1	no	—
12	#16837426	C₂²	1	1	yes	characteristic
13	C₂×#14273638	C₂²	1	1	yes	characteristic
14	#16837164	—	2	1	no	—
15	#16837164	—	2	1	no	—
16	#16837150	—	2	2	no	—
17	#16837147	—	2	2	no	—
18	C₅₉×#431	C₂²	1	1	yes	characteristic
19	C₅₉×#423	C₂²	1	1	yes	characteristic
20	C₅₉×#382	C₂²	1	1	yes	characteristic
21	C₂²×Dic₁₁₈	—	2	1	no	—
22	C₂×#11745664	—	2	1	no	—
23	C₂²×C₅₉⋊C₈	D₄	1	1	yes	characteristic
24	C₂²×C₅₉⋊C₈	D₄	1	1	yes	characteristic
25	#14273727	—	2	1	no	—
26	#14273727	—	2	1	no	—
27	#14273727	—	2	1	no	—
28	#14273727	D₄	1	2	yes	—
29	C₂×C₄⋊Dic₅₉	—	2	1	no	—
30	C₂×C₄⋊Dic₅₉	—	2	1	no	—
31	#14273662	—	4	2	no	—
32	#14273662	—	4	2	no	—
33	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
34	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
35	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
36	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
37	#14273638	—	2	1	no	—
38	#14273638	—	2	1	no	—
39	C₄×C₅₉⋊C₈	—	2	1	no	—
40	C₂×M₁₆×C₅₉	—	2	1	no	—
41	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
42	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
43	C₄⋊C₈×C₅₉	—	2	1	no	—
44	C₄⋊C₈×C₅₉	—	2	1	no	—
45	C₄⋊C₈×C₅₉	—	2	1	no	—
46	C₂²⋊C₈×C₅₉	—	2	1	no	—
47	C₄×C₈×C₅₉	—	2	1	no	—
48	#95×C₅₉	—	2	1	no	—
49	#95×C₅₉	—	2	1	no	—
50	C₂²×C₄×C₅₉	—	4	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	—	4	1	no	—
55	C₂×Dic₁₁₈	—	2	2	no	—
56	C₂×Dic₁₁₈	—	4	1	no	—
57	C₂×Dic₁₁₈	—	8	2	no	—
58	M₁₆×C₅₉	—	4	1	no	—
59	M₁₆×C₅₉	—	4	1	no	—
60	C₂×C₈×C₅₉	—	4	1	no	—
61	C₂×C₈×C₅₉	—	4	1	no	—
62	C₄⋊C₄×C₅₉	—	4	1	no	—
63	C₄⋊C₄×C₅₉	—	4	1	no	—
64	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
65	C₄²×C₅₉	#41	1	1	yes	characteristic
66	C₄²×C₅₉	#41	1	1	yes	characteristic
67	C₄²×C₅₉	#41	1	1	yes	characteristic
68	C₄⋊Dic₅₉	—	2	2	no	—
69	C₄⋊Dic₅₉	—	2	2	no	—
70	C₄⋊Dic₅₉	—	4	1	no	—
71	C₄⋊Dic₅₉	—	4	1	no	—
72	#11745664	—	4	1	no	—
73	#11745664	—	4	1	no	—
74	C₂×C₅₉⋊C₈	—	2	1	no	—
75	C₂×C₅₉⋊C₈	—	2	1	no	—
76	C₂×C₅₉⋊C₈	—	2	1	no	—
77	C₂×C₅₉⋊C₈	—	2	1	no	—
78	C₂×C₅₉⋊C₈	—	4	1	no	—
79	C₂×C₅₉⋊C₈	—	4	1	no	—
80	C₂×C₅₉⋊C₈	SD₁₆	1	2	yes	—
81	C₂×C₅₉⋊C₈	Q₁₆	1	2	yes	—
82	C₂³×C₅₉	#124	1	1	yes	characteristic
83	C₂×C₄×C₅₉	—	4	1	no	—
84	C₂×C₄×C₅₉	—	4	1	no	—
85	C₂×C₄×C₅₉	—	8	1	no	—
86	C₂×C₄×C₅₉	—	8	1	no	—
87	C₂×C₄×C₅₉	—	8	1	no	—
88	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
89	C₂×C₄×C₅₉	#123	1	1	yes	characteristic
90	C₂×C₄×C₅₉	#123	1	1	yes	characteristic
91	C₂×C₄×C₅₉	#123	1	1	yes	characteristic
92	C₂×C₄×C₅₉	#126	1	1	yes	characteristic
93	C₂×C₄×C₅₉	#126	1	1	yes	characteristic
94	C₂×C₄×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
95	C₂×C₄×C₅₉	C₂×Q₁₆	1	1	yes	characteristic
96	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
97	C₂×C₄×C₅₉	#137	1	1	yes	characteristic
98	C₂×Dic₅₉	—	4	2	no	—
99	C₂×Dic₅₉	—	8	2	no	—
100	Dic₁₁₈	—	8	2	no	—
101	Dic₁₁₈	—	8	2	no	—
102	C₈×C₅₉	—	8	1	no	—
103	C₈×C₅₉	—	8	1	no	—
104	C₅₉⋊C₈	—	2	2	no	—
105	C₅₉⋊C₈	—	2	2	no	—
106	C₅₉⋊C₈	—	8	1	no	—
107	C₅₉⋊C₈	—	8	1	no	—
108	#10633	—	59	1	no	maximal, Sylow
109	C₂²×C₅₉	—	2	1	no	—
110	C₂²×C₅₉	—	2	1	no	—
111	C₂²×C₅₉	#397	1	1	yes	characteristic
112	C₂²×C₅₉	#487	1	1	yes	characteristic
113	C₂²×C₅₉	#489	1	1	yes	characteristic
114	C₄×C₅₉	—	2	1	no	—
115	C₄×C₅₉	—	2	1	no	—
116	C₄×C₅₉	—	2	1	no	—
117	C₄×C₅₉	—	2	1	no	—
118	C₄×C₅₉	—	16	1	no	—
119	C₄×C₅₉	#460	1	1	yes	characteristic
120	C₄×C₅₉	#462	1	1	yes	characteristic
121	C₄×C₅₉	#483	1	1	yes	characteristic
122	C₄×C₅₉	#484	1	1	yes	characteristic
123	Dic₅₉	—	8	2	no	—
124	#1993	—	59	1	no	—
125	#1849	—	59	1	no	—
126	#1549	—	59	1	no	—
127	#1548	—	59	1	no	—
128	#1286	—	59	1	no	—
129	#1286	D₅₉	1	1	yes	characteristic
130	#1281	—	59	1	no	—
131	C₂×C₅₉	—	2	1	no	—
132	C₂×C₅₉	—	2	1	no	—
133	C₂×C₅₉	#2072	1	1	yes	characteristic
134	C₂×C₅₉	#2081	1	1	yes	characteristic
135	C₂×C₅₉	#2082	1	1	yes	characteristic
136	C₂×C₄⋊Q₈	—	59	1	no	—
137	#431	—	59	1	no	—
138	#431	C₂×D₅₉	1	1	yes	characteristic
139	C₂×#108	—	118	1	no	—
140	C₂×#108	—	118	1	no	—
141	#423	—	59	1	no	—
142	#423	C₂×D₅₉	1	1	yes	characteristic
143	C₂×#97	—	59	1	no	—
144	#382	C₂×D₅₉	1	1	yes	characteristic
145	#340	—	118	1	no	—
146	#340	—	118	1	no	—
147	#333	—	118	2	no	—
148	#332	—	118	2	no	—
149	C₅₉	#10633	1	1	yes	characteristic, complemented, Sylow
150	C₂²×Q₈	—	118	1	no	—
151	C₂×M₁₆	—	2	1	no	—
152	C₂×M₁₆	—	118	1	no	—
153	C₂²×C₈	—	59	1	no	—
154	C₂²×C₈	—	59	1	no	—
155	C₄⋊Q₈	—	59	2	no	—
156	C₄⋊Q₈	—	118	1	no	—
157	C₄⋊Q₈	—	118	1	no	—
158	C₄⋊Q₈	—	118	1	no	—
159	C₂×C₄⋊C₄	—	2	1	no	—
160	C₂×C₄⋊C₄	—	118	1	no	—
161	C₂×C₄⋊C₄	—	118	1	no	—
162	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
163	#108	—	236	2	no	—
164	#108	—	236	2	no	—
165	C₄⋊C₈	—	2	1	no	—
166	C₄⋊C₈	—	2	1	no	—
167	C₄⋊C₈	—	2	1	no	—
168	C₄⋊C₈	—	118	1	no	—
169	C₄⋊C₈	—	118	1	no	—
170	C₄⋊C₈	—	118	1	no	—
171	C₂²⋊C₈	—	2	1	no	—
172	C₂²⋊C₈	—	118	1	no	—
173	#97	—	118	1	no	—
174	#97	—	118	1	no	—
175	C₄×C₈	—	2	1	no	—
176	C₄×C₈	—	118	1	no	—
177	#95	—	2	1	no	—
178	#95	—	2	1	no	—
179	C₂×Q₈	—	118	2	no	—
180	C₂×Q₈	—	472	2	no	—
181	C₂×Q₈	—	236	1	no	—
182	C₂²×C₄	—	4	1	no	—
183	C₂²×C₄	—	236	1	no	—
184	C₂²×C₄	#11745685	1	1	yes	characteristic
185	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
186	C₂²×C₄	#11745687	1	1	yes	characteristic
187	M₁₆	—	4	1	no	—
188	M₁₆	—	4	1	no	—
189	M₁₆	—	236	1	no	—
190	M₁₆	—	236	1	no	—
191	C₂×C₈	—	4	1	no	—
192	C₂×C₈	—	4	1	no	—
193	C₂×C₈	—	59	2	no	—
194	C₂×C₈	—	59	2	no	—
195	C₂×C₈	—	118	1	no	—
196	C₂×C₈	—	118	1	no	—
197	C₂×C₈	—	118	1	no	—
198	C₂×C₈	—	118	1	no	—
199	C₂×C₈	—	236	1	no	—
200	C₂×C₈	—	236	1	no	—
201	C₄⋊C₄	—	4	1	no	—
202	C₄⋊C₄	—	4	1	no	—
203	C₄⋊C₄	—	118	2	no	—
204	C₄⋊C₄	—	118	2	no	—
205	C₄⋊C₄	—	236	1	no	—
206	C₄⋊C₄	—	236	1	no	—
207	C₄²	#11745685	1	1	yes	characteristic
208	C₄²	#11745685	1	1	yes	characteristic
209	C₄²	D₄×D₅₉	1	1	yes	characteristic
210	C₄²	#11745689	1	1	yes	characteristic
211	C₂³	#14273713	1	1	yes	characteristic
212	Q₈	—	472	2	no	—
213	Q₈	—	472	2	no	—
214	C₂×C₄	—	4	1	no	—
215	C₂×C₄	—	4	1	no	—
216	C₂×C₄	—	8	1	no	—
217	C₂×C₄	—	8	1	no	—
218	C₂×C₄	—	8	1	no	—
219	C₂×C₄	—	472	2	no	—
220	C₂×C₄	—	236	2	no	—
221	C₂×C₄	#14273700	1	1	yes	characteristic
222	C₂×C₄	#14273709	1	1	yes	characteristic
223	C₂×C₄	#14273712	1	1	yes	characteristic
224	C₂×C₄	#14273712	1	1	yes	characteristic
225	C₂×C₄	#14273721	1	1	yes	characteristic
226	C₂×C₄	#14273722	1	1	yes	characteristic
227	C₂×C₄	SD₁₆×D₅₉	1	1	yes	characteristic
228	C₂×C₄	Q₁₆×D₅₉	1	1	yes	characteristic
229	C₂×C₄	#14273751	1	1	yes	characteristic
230	C₂×C₄	#14273756	1	1	yes	characteristic
231	C₈	—	8	1	no	—
232	C₈	—	8	1	no	—
233	C₈	—	118	2	no	—
234	C₈	—	118	2	no	—
235	C₈	—	472	1	no	—
236	C₈	—	472	1	no	—
237	C₂²	—	2	1	no	—
238	C₂²	—	2	1	no	—
239	C₂²	#16837331	1	1	yes	characteristic
240	C₂²	#16837751	1	1	yes	characteristic
241	C₂²	#16837760	1	1	yes	characteristic
242	C₄	—	2	1	no	—
243	C₄	—	2	1	no	—
244	C₄	—	2	1	no	—
245	C₄	—	2	1	no	—
246	C₄	—	16	1	no	—
247	C₄	—	472	2	no	—
248	C₄	#16837601	1	1	yes	characteristic
249	C₄	#16837611	1	1	yes	characteristic
250	C₄	#16837734	1	1	yes	characteristic
251	C₄	#16837739	1	1	yes	characteristic
252	C₂	—	2	1	no	—
253	C₂	—	2	1	no	—
254	C₂	#21425508	1	1	yes	characteristic
255	C₂	#21425559	1	1	yes	characteristic
256	C₂	#21425565	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#21425068

C₂

yes

maximal, characteristic

#21424270

C₂

yes

maximal, characteristic

#21422782

C₂

yes

maximal, characteristic

#21422776

C₂

yes

maximal, characteristic

#21421954

C₂

yes

maximal, characteristic

#21421940

C₂

yes

maximal, characteristic

C₅₉×#1286

C₂

yes

maximal, characteristic

C₂×#14273727

C₂²

yes

characteristic

#16837455

C₂²

yes

—

—

C₂²

yes

characteristic

C₂×#14273638

C₂²

yes

—

—

—

—

C₅₉×#431

C₂²

yes

characteristic

C₅₉×#423

C₂²

yes

characteristic

C₅₉×#382

C₂²

yes

characteristic

C₂²×Dic₁₁₈

—

C₂×#11745664

—

C₂²×C₅₉⋊C₈

D₄

yes

characteristic

C₂²×C₅₉⋊C₈

D₄

yes

—

—

—

D₄

yes

—

C₂×C₄⋊Dic₅₉

—

C₂×C₄⋊Dic₅₉

—

#14273662

—

#14273662

—

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

—

C₂²⋊(C₅₉⋊C₈)

—

#14273638

—

#14273638

—

C₄×C₅₉⋊C₈

—

C₂×M₁₆×C₅₉

—

C₂×C₄⋊C₄×C₅₉

—

C₂×C₄²×C₅₉

C₂³

yes

characteristic

C₄⋊C₈×C₅₉

—

C₄⋊C₈×C₅₉

—

C₄⋊C₈×C₅₉

—

C₂²⋊C₈×C₅₉

—

C₄×C₈×C₅₉

—

#95×C₅₉

—

#95×C₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

C₂×D₄

yes

C₂²×C₄×C₅₉

yes

C₂²×C₄×C₅₉

yes

C₂²×Dic₅₉

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

M₁₆×C₅₉

—

M₁₆×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄²×C₅₉

C₂×D₄

yes

C₄²×C₅₉

yes

C₄²×C₅₉

yes

C₄²×C₅₉

yes

C₄⋊Dic₅₉

—

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

#124

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

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

—

100

Dic₁₁₈

—

101

Dic₁₁₈

—

102

C₈×C₅₉

—

103

C₈×C₅₉

—

104

C₅₉⋊C₈

—

105

C₅₉⋊C₈

—

106

C₅₉⋊C₈

—

107

C₅₉⋊C₈

—

108

#10633

—

maximal, Sylow

109

C₂²×C₅₉

—

110

C₂²×C₅₉

—

111

C₂²×C₅₉

#397

yes

characteristic

112

C₂²×C₅₉

#487

yes

characteristic

113

C₂²×C₅₉

#489

yes

characteristic

114

C₄×C₅₉

—

115

C₄×C₅₉

—

116

C₄×C₅₉

—

117

C₄×C₅₉

—

118

C₄×C₅₉

—

119

C₄×C₅₉

#460

yes

characteristic

120

C₄×C₅₉

#462

yes

characteristic

121

C₄×C₅₉

#483

yes

characteristic

122

C₄×C₅₉

#484

yes

characteristic

123

Dic₅₉

—

124

#1993

—

125

#1849

—

126

#1549

—

127

#1548

—

128

#1286

—

129

#1286

D₅₉

yes

characteristic

130

#1281

—

131

C₂×C₅₉

—

132

C₂×C₅₉

—

133

C₂×C₅₉

#2072

yes

characteristic

134

C₂×C₅₉

#2081

yes

characteristic

135

C₂×C₅₉

#2082

yes

characteristic

136

C₂×C₄⋊Q₈

—

137

#431

—

138

#431

C₂×D₅₉

yes

characteristic

139

C₂×#108

—

118

—

140

C₂×#108

—

118

—

141

#423

—

142

#423

C₂×D₅₉

yes

characteristic

143

C₂×#97

—

144

#382

C₂×D₅₉

yes

characteristic

145

#340

—

118

—

146

#340

—

118

—

147

#333

—

118

—

148

#332

—

118

—

149

C₅₉

#10633

yes

characteristic, complemented, Sylow

150

C₂²×Q₈

—

118

—

151

C₂×M₁₆

—

152

C₂×M₁₆

—

118

—

153

C₂²×C₈

—

154

C₂²×C₈

—

155

C₄⋊Q₈

—

156

C₄⋊Q₈

—

118

—

157

C₄⋊Q₈

—

118

—

158

C₄⋊Q₈

—

118

—

159

C₂×C₄⋊C₄

—

160

C₂×C₄⋊C₄

—

118

—

161

C₂×C₄⋊C₄

—

118

—

162

C₂×C₄²

C₂²×D₅₉

yes

characteristic

163

#108

—

236

—

164

#108

—

236

—

165

C₄⋊C₈

—

166

C₄⋊C₈

—

167

C₄⋊C₈

—

168

C₄⋊C₈

—

118

—

169

C₄⋊C₈

—

118

—

170

C₄⋊C₈

—

118

—

171

C₂²⋊C₈

—

172

C₂²⋊C₈

—

118

—

173

#97

—

118

—

174

#97

—

118

—

175

C₄×C₈

—

176

C₄×C₈

—

118

—

177

#95

—

178

#95

—

179

C₂×Q₈

—

118

—

180

C₂×Q₈

—

472

—

181

C₂×Q₈

—

236

—

182

C₂²×C₄

—

183

C₂²×C₄

—

236

—

184

C₂²×C₄

#11745685

yes

characteristic

185

C₂²×C₄

D₄×D₅₉

yes

characteristic

186

C₂²×C₄

#11745687

yes

characteristic

187

M₁₆

—

188

M₁₆

—

189

M₁₆

—

236

—

190

M₁₆

—

236

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

118

—

196

C₂×C₈

—

118

—

197

C₂×C₈

—

118

—

198

C₂×C₈

—

118

—

199

C₂×C₈

—

236

—

200

C₂×C₈

—

236

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₄⋊C₄

—

118

—

204

C₄⋊C₄

—

118

—

205

C₄⋊C₄

—

236

—

206

C₄⋊C₄

—

236

—

207

C₄²

#11745685

yes

characteristic

208

C₄²

#11745685

yes

characteristic

209

C₄²

D₄×D₅₉

yes

characteristic

210

C₄²

#11745689

yes

characteristic

211

C₂³

#14273713

yes

characteristic

212

Q₈

—

472

—

213

Q₈

—

472

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

472

—

220

C₂×C₄

—

236

—

221

C₂×C₄

#14273700

yes

characteristic

222

C₂×C₄

#14273709

yes

characteristic

223

C₂×C₄

#14273712

yes

characteristic

224

C₂×C₄

#14273712

yes

characteristic

225

C₂×C₄

#14273721

yes

characteristic

226

C₂×C₄

#14273722

yes

characteristic

227

C₂×C₄

SD₁₆×D₅₉

yes

characteristic

228

C₂×C₄

Q₁₆×D₅₉

yes

characteristic

229

C₂×C₄

#14273751

yes

characteristic

230

C₂×C₄

#14273756

yes

characteristic

231

C₈

—

232

C₈

—

233

C₈

—

118

—

234

C₈

—

118

—

235

C₈

—

472

—

236

C₈

—

472

—

237

C₂²

—

238

C₂²

—

239

C₂²

#16837331

yes

characteristic

240

C₂²

#16837751

yes

characteristic

241

C₂²

#16837760

yes

characteristic

242

C₄

—

243

C₄

—

244

C₄

—

245

C₄

—

246

C₄

—

247

C₄

—

472

—

248

C₄

#16837601

yes

characteristic

249

C₄

#16837611

yes

characteristic

250

C₄

#16837734

yes

characteristic

251

C₄

#16837739

yes

characteristic

252

C₂

—

253

C₂

—

254

C₂

#21425508

yes

characteristic

255

C₂

#21425559

yes

characteristic

256

C₂

#21425565

yes

characteristic

	subgroup	G/H
center	C₂²	#16837331
commutator, cosocle	C₂×C₄²×C₅₉	C₂³
Frattini	C₂×C₄²	C₂²×D₅₉
Fitting	C₅₉×#1286	C₂
socle	C₂²×C₅₉	#397
prime radical	C₂³×C₅₉	#124
hypercenter	#1286	D₅₉
hypocenter	C₅₉	#10633
LCS	G ▷ C₂×C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1286

subgroup

G/H

center

C₂²

#16837331

commutator, cosocle

C₂×C₄²×C₅₉

C₂³

Frattini

C₂×C₄²

C₂²×D₅₉

Fitting

C₅₉×#1286

C₂

C₂²×C₅₉

C₂³×C₅₉

D₅₉

C₅₉

G ▷ C₂×C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1286

N	H ≅ G/N	type
149. C₅₉	#10633	semidirect

H ≅ G/N

type

149. C₅₉

#10633

semidirect

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

subgroup	index
#21425068	2
#21424270	2
#21422782	2
#21422776	2
#21421954	2
#21421940	2
C₅₉×#1286	2
#10633	59

subgroup

index

C₅₉×#1286

Subgroups — #28493493

Conjugacy classes of subgroups

Complements

Maximal subgroups