Group #28506138 — subgroups

Subgroups — #28506138

Order 15104.

490 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 127 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	#21433744	C₂	1	1	yes	maximal, characteristic
2	#21425813	C₂	1	2	yes	maximal, complemented
3	#21424142	C₂	1	1	yes	maximal, characteristic, complemented
4	#21422198	C₂	1	2	yes	maximal, complemented
5	C₅₉×#3407	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₄₇₂	C₂²	1	1	yes	characteristic
7	#16837966	—	2	1	no	—
8	#16837655	C₄	1	4	yes	complemented
9	#16837638	—	2	2	no	—
10	#16837440	C₂²	1	2	yes	—
11	#16837440	C₂²	1	1	yes	characteristic
12	#16837408	—	2	1	no	—
13	#16837376	—	2	1	no	—
14	#16837204	—	2	4	no	—
15	#16837159	—	2	1	no	—
16	C₂×#131×C₅₉	C₂²	1	1	yes	characteristic
17	C₅₉×#504	—	2	4	no	—
18	C₂×M₃₂×C₅₉	—	2	2	no	—
19	C₂×M₃₂×C₅₉	C₂²	1	2	yes	—
20	C₂²×D₂₃₆	—	2	1	no	—
21	C₂×D₄₇₂	—	2	2	no	—
22	C₂×D₄₇₂	—	2	2	no	—
23	C₂×D₄₇₂	—	2	1	no	—
24	C₂×D₄₇₂	C₂×C₄	1	2	yes	—
25	#14273723	—	4	1	no	—
26	#14273716	—	4	1	no	—
27	#14273701	—	2	4	no	—
28	#14273695	—	4	2	no	—
29	#14273686	—	2	1	no	—
30	#14273686	—	2	2	no	—
31	#14273661	—	2	1	no	—
32	#14273661	—	2	2	no	—
33	#14273659	—	2	2	no	—
34	#14273659	C₂×C₄	1	2	yes	—
35	#14273649	—	2	4	no	—
36	#14273642	—	4	2	no	—
37	C₂×#41×C₅₉	D₄	1	1	yes	characteristic
38	#131×C₅₉	—	2	2	no	—
39	#131×C₅₉	—	2	2	no	—
40	C₂×M₁₆×C₅₉	C₂×C₄	1	2	yes	—
41	C₂×M₁₆×C₅₉	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₅₉	D₄	1	2	yes	—
43	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
44	M₃₂×C₅₉	—	2	4	no	—
45	M₃₂×C₅₉	—	2	2	no	—
46	M₃₂×C₅₉	—	2	2	no	—
47	C₂×C₁₆×C₅₉	—	2	4	no	—
48	C₂×C₁₆×C₅₉	D₄	1	4	yes	complemented
49	C₂³×D₅₉	—	4	1	no	—
50	#41×C₅₉	—	2	2	no	—
51	#41×C₅₉	—	2	2	no	—
52	C₂×Q₈×C₅₉	SD₁₆	1	1	yes	characteristic
53	C₂×D₄×C₅₉	D₈	1	2	yes	—
54	C₂×D₄×C₅₉	SD₁₆	1	1	yes	characteristic
55	C₂²×C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
56	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
57	C₂×C₂²⋊D₅₉	—	4	4	no	—
58	C₂×D₂₃₆	—	2	2	no	—
59	C₂×D₂₃₆	—	4	2	no	—
60	C₂×D₂₃₆	—	4	2	no	—
61	C₂×D₂₃₆	—	4	1	no	—
62	M₁₆×C₅₉	—	2	2	no	—
63	M₁₆×C₅₉	—	2	4	no	—
64	C₂×C₈×C₅₉	—	2	2	no	—
65	C₂×C₈×C₅₉	—	2	2	no	—
66	C₂×C₈×C₅₉	C₂²⋊C₄	1	2	yes	—
67	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
68	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
69	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
70	C₂×C₈×C₅₉	#41	1	2	yes	—
71	C₂²⋊Dic₅₉	—	4	1	no	—
72	C₂²⋊Dic₅₉	—	4	2	no	—
73	(C₂×D₅₉)⋊C₄	—	4	4	no	—
74	C₄⋊Dic₅₉	—	2	2	no	—
75	C₄⋊Dic₅₉	—	4	2	no	—
76	C₄×Dic₅₉	—	4	1	no	—
77	C₄×Dic₅₉	—	4	2	no	—
78	D₄₇₂	—	2	4	no	—
79	D₄₇₂	—	4	1	no	—
80	D₄₇₂	—	4	1	no	—
81	C₁₆×C₅₉	—	2	4	no	—
82	C₂³×C₅₉	#102	1	2	yes	—
83	C₂³×C₅₉	C₂×D₈	1	1	yes	characteristic
84	C₂²×D₅₉	—	4	2	no	—
85	C₂²×D₅₉	—	8	2	no	—
86	C₂²×D₅₉	—	16	2	no	—
87	Q₈×C₅₉	—	2	2	no	—
88	D₄×C₅₉	—	2	4	no	—
89	D₄×C₅₉	—	2	2	no	—
90	C₂×C₄×C₅₉	—	2	2	no	—
91	C₂×C₄×C₅₉	—	2	2	no	—
92	C₂×C₄×C₅₉	#102	1	2	yes	—
93	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₄×C₅₉	#121	1	2	yes	—
95	C₂×C₄×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
96	C₂×C₄×C₅₉	#135	1	2	yes	—
97	C₂²⋊D₅₉	—	16	4	no	—
98	C₂×Dic₅₉	—	4	2	no	—
99	C₂×Dic₅₉	—	8	2	no	—
100	D₂₃₆	—	4	2	no	—
101	D₂₃₆	—	4	2	no	—
102	D₂₃₆	—	8	2	no	—
103	C₈×C₅₉	—	2	2	no	—
104	C₈×C₅₉	C₄×D₄	1	2	yes	—
105	C₈×C₅₉	#120	1	1	yes	characteristic
106	C₈×C₅₉	#123	1	1	yes	characteristic
107	#13074	—	59	1	no	maximal, Sylow
108	C₂²×C₅₉	—	2	2	no	—
109	C₂²×C₅₉	—	4	1	no	—
110	C₂²×C₅₉	—	4	2	no	—
111	C₂²×C₅₉	C₂×#102	1	1	yes	characteristic
112	C₂²×C₅₉	#466	1	2	yes	—
113	C₂×D₅₉	—	8	4	no	—
114	C₂×D₅₉	—	8	2	no	—
115	C₂×D₅₉	—	16	4	no	—
116	C₄×C₅₉	—	2	2	no	—
117	C₄×C₅₉	#386	1	1	yes	characteristic
118	C₄×C₅₉	#416	1	1	yes	characteristic
119	C₄×C₅₉	#465	1	2	yes	—
120	Dic₅₉	—	8	2	no	—
121	Dic₅₉	—	16	2	no	—
122	#3407	D₅₉	1	1	yes	characteristic, complemented
123	#3058	—	59	1	no	—
124	#2140	—	59	2	no	—
125	#1812	—	59	1	no	—
126	#1384	—	59	2	no	—
127	C₂×C₅₉	—	2	1	no	—
128	C₂×C₅₉	—	2	2	no	—
129	C₂×C₅₉	—	4	2	no	—
130	C₂×C₅₉	#1893	1	1	yes	characteristic
131	D₅₉	—	16	2	no	—
132	C₂²×D₈	—	59	1	no	—
133	C₂×#131	C₂×D₅₉	1	1	yes	characteristic
134	#535	—	118	1	no	—
135	#504	—	2	4	no	—
136	C₂×M₃₂	—	2	2	no	—
137	C₂×M₃₂	C₂×D₅₉	1	2	yes	—
138	#469	—	59	4	no	—
139	#466	—	118	2	no	—
140	#427	—	59	1	no	—
141	#427	—	59	2	no	—
142	#418	—	118	1	no	—
143	#410	—	118	1	no	—
144	#357	—	118	4	no	—
145	H(3,ℤ/4)	—	118	1	no	—
146	C₅₉	#13074	1	1	yes	characteristic, complemented, Sylow
147	C₂×#41	D₂₃₆	1	1	yes	characteristic
148	C₂²×D₄	—	118	1	no	—
149	C₂×D₈	—	59	2	no	—
150	C₂×D₈	—	118	2	no	—
151	C₂×D₈	—	118	2	no	—
152	C₂×D₈	—	118	1	no	—
153	#131	—	2	2	no	—
154	#131	—	2	2	no	—
155	C₂×M₁₆	C₄×D₅₉	1	2	yes	—
156	C₂×M₁₆	D₂₃₆	1	1	yes	characteristic
157	C₂²×C₈	C₂²⋊D₅₉	1	2	yes	—
158	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
159	#127	—	236	1	no	—
160	#124	—	236	1	no	—
161	#121	—	118	4	no	—
162	#120	—	236	2	no	—
163	#117	—	118	1	no	—
164	#117	—	118	2	no	—
165	M₃₂	—	2	4	no	—
166	M₃₂	—	2	2	no	—
167	M₃₂	—	2	2	no	—
168	C₂×C₁₆	—	2	4	no	—
169	C₂×C₁₆	C₂²⋊D₅₉	1	4	yes	complemented
170	#107	—	118	1	no	—
171	#107	—	118	2	no	—
172	#106	—	59	2	no	—
173	#106	—	118	2	no	—
174	#102	—	118	4	no	—
175	#99	—	236	2	no	—
176	C₂⁴	—	236	1	no	—
177	#41	—	2	2	no	—
178	#41	—	2	2	no	—
179	C₂×Q₈	#11745660	1	1	yes	characteristic
180	C₂×D₄	—	118	2	no	—
181	C₂×D₄	—	236	4	no	—
182	C₂×D₄	—	236	2	no	—
183	C₂×D₄	—	236	1	no	—
184	C₂×D₄	—	236	2	no	—
185	C₂×D₄	#11745660	1	1	yes	characteristic
186	C₂×D₄	D₄₇₂	1	2	yes	—
187	C₂²×C₄	(C₂×D₅₉)⋊C₄	1	2	yes	—
188	C₂²×C₄	C₂×D₂₃₆	1	1	yes	characteristic
189	D₈	—	118	4	no	—
190	D₈	—	236	1	no	—
191	D₈	—	236	1	no	—
192	M₁₆	—	2	2	no	—
193	M₁₆	—	2	4	no	—
194	C₂×C₈	—	2	2	no	—
195	C₂×C₈	—	2	2	no	—
196	C₂×C₈	(C₂×D₅₉)⋊C₄	1	2	yes	—
197	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
198	C₂×C₈	#11745685	1	2	yes	—
199	C₂×C₈	C₂×C₂²⋊D₅₉	1	2	yes	—
200	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
201	C₄⋊C₄	—	118	2	no	—
202	C₄⋊C₄	—	236	2	no	—
203	C₂²⋊C₄	—	236	2	no	—
204	C₂²⋊C₄	—	236	1	no	—
205	C₂²⋊C₄	—	236	4	no	—
206	C₄²	—	236	2	no	—
207	C₄²	—	236	1	no	—
208	C₁₆	—	2	4	no	—
209	C₂³	—	944	2	no	—
210	C₂³	—	472	2	no	—
211	C₂³	—	236	2	no	—
212	C₂³	#14273649	1	2	yes	—
213	C₂³	C₂×D₄₇₂	1	1	yes	characteristic
214	Q₈	—	2	2	no	—
215	D₄	—	2	4	no	—
216	D₄	—	2	2	no	—
217	D₄	—	944	4	no	—
218	D₄	—	472	2	no	—
219	D₄	—	236	2	no	—
220	D₄	—	236	2	no	—
221	C₂×C₄	—	2	2	no	—
222	C₂×C₄	—	2	2	no	—
223	C₂×C₄	—	472	2	no	—
224	C₂×C₄	—	236	2	no	—
225	C₂×C₄	#14273649	1	2	yes	—
226	C₂×C₄	C₂×(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
227	C₂×C₄	#14273701	1	2	yes	—
228	C₂×C₄	C₂×#11745660	1	1	yes	characteristic
229	C₂×C₄	#14273749	1	2	yes	—
230	C₈	—	2	2	no	—
231	C₈	C₄×C₂²⋊D₅₉	1	2	yes	—
232	C₈	#14273696	1	1	yes	characteristic
233	C₈	#14273710	1	1	yes	characteristic
234	C₂²	—	2	2	no	—
235	C₂²	—	4	1	no	—
236	C₂²	—	4	2	no	—
237	C₂²	—	944	4	no	—
238	C₂²	—	472	4	no	—
239	C₂²	—	472	2	no	—
240	C₂²	C₂×#14273649	1	1	yes	characteristic
241	C₂²	#16837638	1	2	yes	—
242	C₄	—	2	2	no	—
243	C₄	—	944	2	no	—
244	C₄	—	472	2	no	—
245	C₄	#16837281	1	1	yes	characteristic
246	C₄	#16837399	1	1	yes	characteristic
247	C₄	#16837631	1	2	yes	—
248	C₂	—	2	2	no	—
249	C₂	—	2	1	no	—
250	C₂	—	4	2	no	—
251	C₂	—	944	2	no	—
252	C₂	#21424524	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#21433744

C₂

yes

maximal, characteristic

#21425813

C₂

yes

maximal, complemented

#21424142

C₂

yes

maximal, characteristic, complemented

#21422198

C₂

yes

maximal, complemented

C₅₉×#3407

C₂

yes

maximal, characteristic, complemented

C₂²×D₄₇₂

C₂²

yes

characteristic

#16837966

—

#16837655

C₄

yes

complemented

#16837638

—

#16837440

C₂²

yes

—

#16837440

C₂²

yes

—

—

—

—

C₂×#131×C₅₉

C₂²

yes

characteristic

C₅₉×#504

—

C₂×M₃₂×C₅₉

—

C₂×M₃₂×C₅₉

C₂²

yes

—

C₂²×D₂₃₆

—

C₂×D₄₇₂

—

C₂×D₄₇₂

—

C₂×D₄₇₂

—

C₂×D₄₇₂

C₂×C₄

yes

—

—

—

—

—

—

—

—

—

—

C₂×C₄

yes

—

#14273649

—

#14273642

—

C₂×#41×C₅₉

D₄

yes

characteristic

#131×C₅₉

—

#131×C₅₉

—

C₂×M₁₆×C₅₉

C₂×C₄

yes

—

C₂×M₁₆×C₅₉

D₄

yes

characteristic

C₂²×C₈×C₅₉

D₄

yes

—

C₂²×C₈×C₅₉

C₂³

yes

characteristic

M₃₂×C₅₉

—

M₃₂×C₅₉

—

M₃₂×C₅₉

—

C₂×C₁₆×C₅₉

—

C₂×C₁₆×C₅₉

D₄

yes

complemented

C₂³×D₅₉

—

#41×C₅₉

—

#41×C₅₉

—

C₂×Q₈×C₅₉

SD₁₆

yes

characteristic

C₂×D₄×C₅₉

D₈

yes

—

C₂×D₄×C₅₉

SD₁₆

yes

characteristic

C₂²×C₄×C₅₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×C₂²⋊D₅₉

—

C₂×D₂₃₆

—

C₂×D₂₃₆

—

C₂×D₂₃₆

—

C₂×D₂₃₆

—

M₁₆×C₅₉

—

M₁₆×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

C₂²⋊C₄

yes

—

C₂×C₈×C₅₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₅₉

C₂×D₄

yes

—

C₂×C₈×C₅₉

C₂×D₄

yes

characteristic

C₂×C₈×C₅₉

#41

yes

—

C₂²⋊Dic₅₉

—

C₂²⋊Dic₅₉

—

(C₂×D₅₉)⋊C₄

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

D₄₇₂

—

D₄₇₂

—

D₄₇₂

—

C₁₆×C₅₉

—

C₂³×C₅₉

#102

yes

—

C₂³×C₅₉

C₂×D₈

yes

characteristic

C₂²×D₅₉

—

C₂²×D₅₉

—

C₂²×D₅₉

—

Q₈×C₅₉

—

D₄×C₅₉

—

D₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

#102

yes

—

C₂×C₄×C₅₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₅₉

#121

yes

—

C₂×C₄×C₅₉

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₅₉

#135

yes

—

C₂²⋊D₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

100

D₂₃₆

—

101

D₂₃₆

—

102

D₂₃₆

—

103

C₈×C₅₉

—

104

C₈×C₅₉

C₄×D₄

yes

—

105

C₈×C₅₉

#120

yes

characteristic

106

C₈×C₅₉

yes

107

—

108

C₂²×C₅₉

—

109

C₂²×C₅₉

—

110

C₂²×C₅₉

—

111

C₂²×C₅₉

C₂×#102

yes

characteristic

112

C₂²×C₅₉

#466

yes

—

113

C₂×D₅₉

—

114

C₂×D₅₉

—

115

C₂×D₅₉

—

116

C₄×C₅₉

—

117

C₄×C₅₉

#386

yes

characteristic

118

C₄×C₅₉

#416

yes

characteristic

119

C₄×C₅₉

#465

yes

—

120

Dic₅₉

—

121

Dic₅₉

—

122

#3407

D₅₉

yes

characteristic, complemented

123

#3058

—

124

#2140

—

125

#1812

—

126

#1384

—

127

C₂×C₅₉

—

128

C₂×C₅₉

—

129

C₂×C₅₉

—

130

C₂×C₅₉

#1893

yes

characteristic

131

D₅₉

—

132

C₂²×D₈

—

133

C₂×#131

C₂×D₅₉

yes

characteristic

134

#535

—

118

—

135

#504

—

136

C₂×M₃₂

—

137

C₂×M₃₂

C₂×D₅₉

yes

—

138

#469

—

139

#466

—

118

—

140

#427

—

141

#427

—

142

#418

—

118

—

143

#410

—

118

—

144

#357

—

118

—

145

H(3,ℤ/4)

—

118

—

146

C₅₉

#13074

yes

characteristic, complemented, Sylow

147

C₂×#41

D₂₃₆

yes

characteristic

148

C₂²×D₄

—

118

—

149

C₂×D₈

—

150

C₂×D₈

—

118

—

151

C₂×D₈

—

118

—

152

C₂×D₈

—

118

—

153

#131

—

154

#131

—

155

C₂×M₁₆

C₄×D₅₉

yes

—

156

C₂×M₁₆

D₂₃₆

yes

characteristic

157

C₂²×C₈

C₂²⋊D₅₉

yes

—

158

C₂²×C₈

C₂²×D₅₉

yes

characteristic

159

#127

—

236

—

160

#124

—

236

—

161

#121

—

118

—

162

#120

—

236

—

163

#117

—

118

—

164

#117

—

118

—

165

M₃₂

—

166

M₃₂

—

167

M₃₂

—

168

C₂×C₁₆

—

169

C₂×C₁₆

C₂²⋊D₅₉

yes

complemented

170

#107

—

118

—

171

#107

—

118

—

172

#106

—

173

#106

—

118

—

174

#102

—

118

—

175

#99

—

236

—

176

C₂⁴

—

236

—

177

#41

—

178

#41

—

179

C₂×Q₈

#11745660

yes

characteristic

180

C₂×D₄

—

118

—

181

C₂×D₄

—

236

—

182

C₂×D₄

—

236

—

183

C₂×D₄

—

236

—

184

C₂×D₄

—

236

—

185

C₂×D₄

#11745660

yes

characteristic

186

C₂×D₄

D₄₇₂

yes

—

187

C₂²×C₄

(C₂×D₅₉)⋊C₄

yes

—

188

C₂²×C₄

C₂×D₂₃₆

yes

characteristic

189

D₈

—

118

—

190

D₈

—

236

—

191

D₈

—

236

—

192

M₁₆

—

193

M₁₆

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

—

197

C₂×C₈

C₂×C₄×D₅₉

yes

characteristic

198

C₂×C₈

#11745685

yes

—

199

C₂×C₈

C₂×C₂²⋊D₅₉

yes

—

200

C₂×C₈

C₂×C₂²⋊D₅₉

yes

characteristic

201

C₄⋊C₄

—

118

—

202

C₄⋊C₄

—

236

—

203

C₂²⋊C₄

—

236

—

204

C₂²⋊C₄

—

236

—

205

C₂²⋊C₄

—

236

—

206

C₄²

—

236

—

207

C₄²

—

236

—

208

C₁₆

—

209

C₂³

—

944

—

210

C₂³

—

472

—

211

C₂³

—

236

—

212

C₂³

#14273649

yes

—

213

C₂³

C₂×D₄₇₂

yes

characteristic

214

Q₈

—

215

D₄

—

216

D₄

—

217

D₄

—

944

—

218

D₄

—

472

—

219

D₄

—

236

—

220

D₄

—

236

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

472

—

224

C₂×C₄

—

236

—

225

C₂×C₄

#14273649

yes

—

226

C₂×C₄

C₂×(C₂×D₅₉)⋊C₄

yes

characteristic

227

C₂×C₄

#14273701

yes

—

228

C₂×C₄

C₂×#11745660

yes

characteristic

229

C₂×C₄

#14273749

yes

—

230

C₈

—

231

C₈

C₄×C₂²⋊D₅₉

yes

—

232

C₈

#14273696

yes

characteristic

233

C₈

#14273710

yes

characteristic

234

C₂²

—

235

C₂²

—

236

C₂²

—

237

C₂²

—

944

—

238

C₂²

—

472

—

239

C₂²

—

472

—

240

C₂²

C₂×#14273649

yes

characteristic

241

C₂²

#16837638

yes

—

242

C₄

—

243

C₄

—

944

—

244

C₄

—

472

—

245

C₄

#16837281

yes

characteristic

246

C₄

#16837399

yes

characteristic

247

C₄

#16837631

yes

—

248

C₂

—

249

C₂

—

250

C₂

—

251

C₂

—

944

—

252

C₂

#21424524

yes

characteristic

	subgroup	G/H
center	C₂	#21424524
commutator	C₂×C₈×C₅₉	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₅₉
Fitting	C₅₉×#3407	C₂
socle	C₂×C₅₉	#1893
prime radical	#21433744	C₂
cosocle	C₂²×C₈×C₅₉	C₂³
hypercenter	#3407	D₅₉
hypocenter	C₅₉	#13074
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #3407

subgroup

G/H

center

C₂

#21424524

commutator

C₂×C₈×C₅₉

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₅₉

Fitting

C₅₉×#3407

C₂

C₂×C₅₉

C₂

C₂²×C₈×C₅₉

C₂³

D₅₉

C₅₉

G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #3407

N	H ≅ G/N	type
2. #21425813	C₂	semidirect
3. #21424142	C₂	semidirect
4. #21422198	C₂	semidirect
5. C₅₉×#3407	C₂	semidirect
8. #16837655	C₄	semidirect
48. C₂×C₁₆×C₅₉	D₄	semidirect
122. #3407	D₅₉	semidirect
146. C₅₉	#13074	semidirect
169. C₂×C₁₆	C₂²⋊D₅₉	semidirect

H ≅ G/N

type

2. #21425813

C₂

semidirect

3. #21424142

C₂

semidirect

4. #21422198

C₂

semidirect

5. C₅₉×#3407

C₂

semidirect

8. #16837655

C₄

semidirect

48. C₂×C₁₆×C₅₉

D₄

semidirect

122. #3407

D₅₉

semidirect

146. C₅₉

#13074

semidirect

169. C₂×C₁₆

C₂²⋊D₅₉

semidirect

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

subgroup	index
#21433744	2
#21425813	2
#21424142	2
#21422198	2
C₅₉×#3407	2
#13074	59

subgroup

index

C₅₉×#3407

Subgroups — #28506138

Conjugacy classes of subgroups

Complements

Maximal subgroups