Group #21424435 — subgroups

Subgroups — #21424435

Order 7552.

338 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 107 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	C₂²×#11745672	C₂	1	1	yes	maximal, characteristic
2	C₂×Q₈×Dic₅₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#14273652	C₂	1	1	yes	maximal, characteristic
4	#16837307	C₂	1	1	yes	maximal, characteristic
5	#16837164	C₂	1	1	yes	maximal, characteristic
6	#16837156	C₂	1	1	yes	maximal, characteristic
7	C₂×#103×C₅₉	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₁₁₈	C₂²	1	1	yes	characteristic
9	C₂×#11745672	—	2	2	no	—
10	C₂×#11745672	—	2	2	no	—
11	C₂×#11745672	C₄	1	4	yes	complemented
12	C₂²×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
13	Q₈×Dic₅₉	—	2	2	no	—
14	Q₈×Dic₅₉	—	2	2	no	—
15	C₂×C₄⋊Dic₅₉	—	2	1	no	—
16	C₂×C₄⋊Dic₅₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×Dic₅₉	—	2	1	no	—
18	C₂×C₄×Dic₅₉	C₂²	1	1	yes	characteristic
19	#14273652	—	2	2	no	—
20	C₅₉⋊#95	—	2	1	no	—
21	C₅₉⋊#95	—	2	1	no	—
22	C₂²×Q₈×C₅₉	C₂²	1	1	yes	characteristic
23	C₂²×C₈×C₅₉	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
25	#103×C₅₉	—	2	2	no	—
26	C₂×Q₈×C₅₉	—	2	1	no	—
27	C₂×Q₈×C₅₉	—	2	1	no	—
28	C₂×Q₈×C₅₉	—	2	1	no	—
29	C₂×Q₈×C₅₉	C₂×C₄	1	2	yes	—
30	C₂×Q₈×C₅₉	D₄	1	2	yes	—
31	C₂×Q₈×C₅₉	D₄	1	2	yes	—
32	C₂²×C₄×C₅₉	—	2	1	no	—
33	C₂²×C₄×C₅₉	—	2	1	no	—
34	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
35	C₂²×Dic₅₉	—	2	1	no	—
36	C₂²×Dic₅₉	—	2	1	no	—
37	C₂²×Dic₅₉	D₄	1	1	yes	characteristic
38	C₂²×Dic₅₉	D₄	1	1	yes	characteristic
39	C₂×Dic₁₁₈	—	2	1	no	—
40	C₂×Dic₁₁₈	—	2	1	no	—
41	C₂×Dic₁₁₈	—	2	1	no	—
42	C₂×Dic₁₁₈	—	2	1	no	—
43	C₂×Dic₁₁₈	—	2	1	no	—
44	C₂×Dic₁₁₈	C₂×C₄	1	2	yes	—
45	C₂×C₈×C₅₉	—	2	1	no	—
46	C₂×C₈×C₅₉	—	2	1	no	—
47	C₂×C₈×C₅₉	—	2	1	no	—
48	C₄⋊C₄×C₅₉	—	2	1	no	—
49	C₄⋊C₄×C₅₉	—	2	1	no	—
50	#11745672	—	2	8	no	—
51	C₄⋊Dic₅₉	—	2	4	no	—
52	C₄⋊Dic₅₉	—	2	1	no	—
53	C₄⋊Dic₅₉	D₄	1	2	yes	—
54	C₄×Dic₅₉	—	2	4	no	—
55	C₄×Dic₅₉	—	2	1	no	—
56	C₄×Dic₅₉	—	2	1	no	—
57	C₂×C₅₉⋊C₈	—	2	1	no	—
58	C₂×C₅₉⋊C₈	—	2	1	no	—
59	C₂×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
60	C₂³×C₅₉	C₂×D₄	1	1	yes	characteristic
61	Q₈×C₅₉	—	2	2	no	—
62	Q₈×C₅₉	—	2	2	no	—
63	Q₈×C₅₉	—	2	2	no	—
64	Q₈×C₅₉	C₂²⋊C₄	1	4	yes	—
65	C₂×C₄×C₅₉	—	2	2	no	—
66	C₂×C₄×C₅₉	—	2	2	no	—
67	C₂×C₄×C₅₉	—	2	2	no	—
68	C₂×C₄×C₅₉	—	4	1	no	—
69	C₂×C₄×C₅₉	—	4	1	no	—
70	C₂×C₄×C₅₉	—	4	1	no	—
71	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
72	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
73	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
74	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
75	C₂×C₄×C₅₉	#41	1	1	yes	characteristic
76	C₂×C₄×C₅₉	#41	1	1	yes	characteristic
77	C₂×Dic₅₉	—	2	1	no	—
78	C₂×Dic₅₉	—	2	1	no	—
79	C₂×Dic₅₉	—	2	2	no	—
80	C₂×Dic₅₉	—	2	1	no	—
81	C₂×Dic₅₉	—	2	2	no	—
82	C₂×Dic₅₉	—	2	1	no	—
83	C₂×Dic₅₉	—	2	1	no	—
84	C₂×Dic₅₉	—	4	1	no	—
85	C₂×Dic₅₉	—	4	1	no	—
86	C₂×Dic₅₉	—	4	1	no	—
87	C₂×Dic₅₉	—	4	1	no	—
88	C₂×Dic₅₉	Q₁₆	1	2	yes	complemented
89	Dic₁₁₈	—	2	2	no	—
90	Dic₁₁₈	—	2	2	no	—
91	Dic₁₁₈	—	4	1	no	—
92	Dic₁₁₈	—	4	1	no	—
93	C₈×C₅₉	—	4	1	no	—
94	C₅₉⋊C₈	—	2	2	no	—
95	C₂²×C₅₉	C₄×D₄	1	1	yes	characteristic
96	C₂²×C₅₉	#120	1	1	yes	characteristic
97	C₂²×C₅₉	#121	1	1	yes	characteristic
98	C₂²×C₅₉	C₂×Q₁₆	1	1	yes	characteristic
99	C₂²×C₅₉	#135	1	1	yes	characteristic
100	C₂²×C₅₉	#137	1	1	yes	characteristic
101	C₂²×C₅₉	#137	1	1	yes	characteristic
102	C₄×C₅₉	—	2	4	no	—
103	C₄×C₅₉	—	8	1	no	—
104	C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
105	C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
106	C₄×C₅₉	#121	1	1	yes	characteristic
107	C₄×C₅₉	#123	1	1	yes	characteristic
108	Dic₅₉	—	2	2	no	—
109	Dic₅₉	—	4	2	no	—
110	Dic₅₉	—	4	1	no	—
111	Dic₅₉	—	4	2	no	—
112	#1878	—	59	1	no	maximal, Sylow
113	C₂×C₅₉	#386	1	1	yes	characteristic
114	C₂×C₅₉	C₄×Q₁₆	1	1	yes	characteristic
115	C₂×C₅₉	#441	1	1	yes	characteristic
116	C₂×C₅₉	#451	1	1	yes	characteristic
117	C₂×C₅₉	#452	1	1	yes	characteristic
118	C₂×C₅₉	#462	1	1	yes	characteristic
119	C₂×C₅₉	#464	1	1	yes	characteristic
120	C₂²×Q₁₆	—	59	1	no	—
121	C₂×C₄×Q₈	—	59	1	no	—
122	C₂×#103	—	59	1	no	—
123	C₂×#103	D₅₉	1	1	yes	characteristic
124	#391	—	59	1	no	—
125	#340	—	59	1	no	—
126	#336	—	59	1	no	—
127	C₅₉	#1878	1	1	yes	characteristic, complemented, Sylow
128	C₂²×Q₈	—	59	1	no	—
129	C₂²×Q₈	C₂×D₅₉	1	1	yes	characteristic
130	C₂×Q₁₆	—	59	4	no	—
131	C₂×Q₁₆	—	118	2	no	—
132	C₂×Q₁₆	—	118	2	no	—
133	C₂²×C₈	—	59	1	no	—
134	C₂²×C₈	C₂×D₅₉	1	1	yes	characteristic
135	C₄×Q₈	—	118	2	no	—
136	C₄×Q₈	—	118	2	no	—
137	C₂×C₄⋊C₄	—	59	1	no	—
138	C₂×C₄⋊C₄	—	118	1	no	—
139	C₂×C₄⋊C₄	C₂×D₅₉	1	1	yes	characteristic
140	C₂×C₄²	—	59	1	no	—
141	C₂×C₄²	—	118	1	no	—
142	#103	—	2	2	no	—
143	#103	—	118	2	no	—
144	#95	—	118	1	no	—
145	#95	—	118	1	no	—
146	C₂×Q₈	—	2	1	no	—
147	C₂×Q₈	—	2	1	no	—
148	C₂×Q₈	—	2	1	no	—
149	C₂×Q₈	—	59	2	no	—
150	C₂×Q₈	—	118	1	no	—
151	C₂×Q₈	—	118	1	no	—
152	C₂×Q₈	—	118	1	no	—
153	C₂×Q₈	—	118	1	no	—
154	C₂×Q₈	—	118	1	no	—
155	C₂×Q₈	C₄×D₅₉	1	2	yes	—
156	C₂×Q₈	D₂₃₆	1	2	yes	—
157	C₂×Q₈	C₂²⋊D₅₉	1	2	yes	—
158	C₂²×C₄	—	2	1	no	—
159	C₂²×C₄	—	2	1	no	—
160	C₂²×C₄	—	59	1	no	—
161	C₂²×C₄	—	59	1	no	—
162	C₂²×C₄	—	118	1	no	—
163	C₂²×C₄	—	118	1	no	—
164	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
165	Q₁₆	—	118	8	no	—
166	C₂×C₈	—	2	1	no	—
167	C₂×C₈	—	2	1	no	—
168	C₂×C₈	—	2	1	no	—
169	C₂×C₈	—	59	2	no	—
170	C₂×C₈	—	118	1	no	—
171	C₂×C₈	—	118	1	no	—
172	C₄⋊C₄	—	2	1	no	—
173	C₄⋊C₄	—	2	1	no	—
174	C₄⋊C₄	—	59	2	no	—
175	C₄⋊C₄	—	118	4	no	—
176	C₄⋊C₄	—	118	1	no	—
177	C₄²	—	118	4	no	—
178	C₄²	—	118	1	no	—
179	C₄²	—	118	1	no	—
180	C₂³	D₄×D₅₉	1	1	yes	characteristic
181	Q₈	—	2	2	no	—
182	Q₈	—	2	2	no	—
183	Q₈	—	2	2	no	—
184	Q₈	—	118	2	no	—
185	Q₈	—	118	2	no	—
186	Q₈	—	236	1	no	—
187	Q₈	—	236	1	no	—
188	Q₈	(C₂×D₅₉)⋊C₄	1	4	yes	—
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	4	1	no	—
193	C₂×C₄	—	4	1	no	—
194	C₂×C₄	—	4	1	no	—
195	C₂×C₄	—	59	2	no	—
196	C₂×C₄	—	118	1	no	—
197	C₂×C₄	—	118	1	no	—
198	C₂×C₄	—	118	2	no	—
199	C₂×C₄	—	118	2	no	—
200	C₂×C₄	—	118	1	no	—
201	C₂×C₄	—	118	1	no	—
202	C₂×C₄	—	118	1	no	—
203	C₂×C₄	—	236	1	no	—
204	C₂×C₄	—	236	1	no	—
205	C₂×C₄	—	236	1	no	—
206	C₂×C₄	—	236	1	no	—
207	C₂×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
208	C₂×C₄	C₂×D₂₃₆	1	1	yes	characteristic
209	C₂×C₄	D₄×D₅₉	1	1	yes	characteristic
210	C₂×C₄	#11745687	1	1	yes	characteristic
211	C₂×C₄	#11745687	1	1	yes	characteristic
212	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
213	C₈	—	4	1	no	—
214	C₈	—	118	2	no	—
215	C₂²	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
216	C₂²	#14273697	1	1	yes	characteristic
217	C₂²	#14273699	1	1	yes	characteristic
218	C₂²	Q₁₆×D₅₉	1	1	yes	characteristic
219	C₂²	#14273748	1	1	yes	characteristic
220	C₂²	#14273756	1	1	yes	characteristic
221	C₂²	#14273759	1	1	yes	characteristic
222	C₄	—	2	4	no	—
223	C₄	—	8	1	no	—
224	C₄	—	118	2	no	—
225	C₄	—	236	2	no	—
226	C₄	—	236	1	no	—
227	C₄	—	236	2	no	—
228	C₄	C₂×(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
229	C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
230	C₄	#14273699	1	1	yes	characteristic
231	C₄	#14273711	1	1	yes	characteristic
232	C₂	#16837279	1	1	yes	characteristic
233	C₂	#16837494	1	1	yes	characteristic
234	C₂	#16837506	1	1	yes	characteristic
235	C₂	#16837559	1	1	yes	characteristic
236	C₂	#16837567	1	1	yes	characteristic
237	C₂	#16837610	1	1	yes	characteristic
238	C₂	#16837622	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#11745672

C₂

yes

maximal, characteristic

C₂×Q₈×Dic₅₉

C₂

yes

maximal, characteristic

C₂×#14273652

C₂

yes

maximal, characteristic

#16837307

C₂

yes

maximal, characteristic

#16837164

C₂

yes

maximal, characteristic

#16837156

C₂

yes

maximal, characteristic

C₂×#103×C₅₉

C₂

yes

maximal, characteristic

C₂²×Dic₁₁₈

C₂²

yes

—

—

C₄

yes

complemented

C₂²×C₅₉⋊C₈

C₂²

yes

characteristic

Q₈×Dic₅₉

—

Q₈×Dic₅₉

—

C₂×C₄⋊Dic₅₉

—

C₂×C₄⋊Dic₅₉

C₂²

yes

characteristic

C₂×C₄×Dic₅₉

—

C₂×C₄×Dic₅₉

C₂²

yes

characteristic

#14273652

—

C₅₉⋊#95

—

C₅₉⋊#95

—

C₂²×Q₈×C₅₉

C₂²

yes

characteristic

C₂²×C₈×C₅₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₅₉

C₂²

yes

characteristic

#103×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

C₂×C₄

yes

—

C₂×Q₈×C₅₉

D₄

yes

—

C₂×Q₈×C₅₉

D₄

yes

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

C₂³

yes

characteristic

C₂²×Dic₅₉

—

C₂²×Dic₅₉

—

C₂²×Dic₅₉

D₄

yes

characteristic

C₂²×Dic₅₉

D₄

yes

characteristic

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

C₂×C₄

yes

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

#11745672

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

D₄

yes

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

C₂×C₄

yes

—

C₂³×C₅₉

C₂×D₄

yes

characteristic

Q₈×C₅₉

—

Q₈×C₅₉

—

Q₈×C₅₉

—

Q₈×C₅₉

C₂²⋊C₄

yes

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

C₂×D₄

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

Q₁₆

yes

complemented

Dic₁₁₈

—

Dic₁₁₈

—

Dic₁₁₈

—

Dic₁₁₈

—

C₈×C₅₉

—

C₅₉⋊C₈

—

C₂²×C₅₉

C₄×D₄

yes

C₂²×C₅₉

yes

C₂²×C₅₉

yes

C₂²×C₅₉

C₂×Q₁₆

yes

characteristic

C₂²×C₅₉

#135

yes

characteristic

100

C₂²×C₅₉

#137

yes

characteristic

101

C₂²×C₅₉

#137

yes

characteristic

102

C₄×C₅₉

—

103

C₄×C₅₉

—

104

C₄×C₅₉

C₂×C₂²⋊C₄

yes

characteristic

105

C₄×C₅₉

C₄×D₄

yes

characteristic

106

C₄×C₅₉

#121

yes

characteristic

107

C₄×C₅₉

#123

yes

characteristic

108

Dic₅₉

—

109

Dic₅₉

—

110

Dic₅₉

—

111

Dic₅₉

—

112

#1878

—

maximal, Sylow

113

C₂×C₅₉

#386

yes

characteristic

114

C₂×C₅₉

C₄×Q₁₆

yes

characteristic

115

C₂×C₅₉

#441

yes

characteristic

116

C₂×C₅₉

#451

yes

characteristic

117

C₂×C₅₉

#452

yes

characteristic

118

C₂×C₅₉

#462

yes

characteristic

119

C₂×C₅₉

#464

yes

characteristic

120

C₂²×Q₁₆

—

121

C₂×C₄×Q₈

—

122

C₂×#103

—

123

C₂×#103

D₅₉

yes

characteristic

124

#391

—

125

#340

—

126

#336

—

127

C₅₉

#1878

yes

characteristic, complemented, Sylow

128

C₂²×Q₈

—

129

C₂²×Q₈

C₂×D₅₉

yes

characteristic

130

C₂×Q₁₆

—

131

C₂×Q₁₆

—

118

—

132

C₂×Q₁₆

—

118

—

133

C₂²×C₈

—

134

C₂²×C₈

C₂×D₅₉

yes

characteristic

135

C₄×Q₈

—

118

—

136

C₄×Q₈

—

118

—

137

C₂×C₄⋊C₄

—

138

C₂×C₄⋊C₄

—

118

—

139

C₂×C₄⋊C₄

C₂×D₅₉

yes

characteristic

140

C₂×C₄²

—

141

C₂×C₄²

—

118

—

142

#103

—

143

#103

—

118

—

144

#95

—

118

—

145

#95

—

118

—

146

C₂×Q₈

—

147

C₂×Q₈

—

148

C₂×Q₈

—

149

C₂×Q₈

—

150

C₂×Q₈

—

118

—

151

C₂×Q₈

—

118

—

152

C₂×Q₈

—

118

—

153

C₂×Q₈

—

118

—

154

C₂×Q₈

—

118

—

155

C₂×Q₈

C₄×D₅₉

yes

—

156

C₂×Q₈

D₂₃₆

yes

—

157

C₂×Q₈

C₂²⋊D₅₉

yes

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

118

—

163

C₂²×C₄

—

118

—

164

C₂²×C₄

C₂²×D₅₉

yes

characteristic

165

Q₁₆

—

118

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

118

—

171

C₂×C₈

—

118

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

118

—

176

C₄⋊C₄

—

118

—

177

C₄²

—

118

—

178

C₄²

—

118

—

179

C₄²

—

118

—

180

C₂³

D₄×D₅₉

yes

characteristic

181

Q₈

—

182

Q₈

—

183

Q₈

—

184

Q₈

—

118

—

185

Q₈

—

118

—

186

Q₈

—

236

—

187

Q₈

—

236

—

188

Q₈

(C₂×D₅₉)⋊C₄

yes

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

118

—

197

C₂×C₄

—

118

—

198

C₂×C₄

—

118

—

199

C₂×C₄

—

118

—

200

C₂×C₄

—

118

—

201

C₂×C₄

—

118

—

202

C₂×C₄

—

118

—

203

C₂×C₄

—

236

—

204

C₂×C₄

—

236

—

205

C₂×C₄

—

236

—

206

C₂×C₄

—

236

—

207

C₂×C₄

C₂×C₄×D₅₉

yes

characteristic

208

C₂×C₄

C₂×D₂₃₆

yes

characteristic

209

C₂×C₄

D₄×D₅₉

yes

characteristic

210

C₂×C₄

#11745687

yes

characteristic

211

C₂×C₄

#11745687

yes

characteristic

212

C₂×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

213

C₈

—

214

C₈

—

118

—

215

C₂²

(C₂²⋊D₅₉)⋊C₄

yes

characteristic

216

C₂²

#14273697

yes

characteristic

217

C₂²

#14273699

yes

characteristic

218

C₂²

Q₁₆×D₅₉

yes

characteristic

219

C₂²

#14273748

yes

characteristic

220

C₂²

#14273756

yes

characteristic

221

C₂²

#14273759

yes

characteristic

222

C₄

—

223

C₄

—

224

C₄

—

118

—

225

C₄

—

236

—

226

C₄

—

236

—

227

C₄

—

236

—

228

C₄

C₂×(C₂×D₅₉)⋊C₄

yes

characteristic

229

C₄

(C₂²⋊D₅₉)⋊C₄

yes

characteristic

230

C₄

#14273699

yes

characteristic

231

C₄

#14273711

yes

characteristic

232

C₂

#16837279

yes

characteristic

233

C₂

#16837494

yes

characteristic

234

C₂

#16837506

yes

characteristic

235

C₂

#16837559

yes

characteristic

236

C₂

#16837567

yes

characteristic

237

C₂

#16837610

yes

characteristic

238

C₂

#16837622

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₅₉
commutator	C₂×C₄×C₅₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₅₉
Fitting	C₂×#103×C₅₉	C₂
socle	C₂³×C₅₉	C₂×D₄
hypercenter	C₂×#103	D₅₉
hypocenter	C₅₉	#1878
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#103

subgroup

G/H

center

C₂³

D₄×D₅₉

commutator

C₂×C₄×C₅₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₅₉

Fitting

C₂×#103×C₅₉

C₂

socle

C₂³×C₅₉

C₂×D₄

D₅₉

C₅₉

G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#103

N	H ≅ G/N	type
11. C₂×#11745672	C₄	semidirect
88. C₂×Dic₅₉	Q₁₆	semidirect
127. C₅₉	#1878	semidirect

H ≅ G/N

type

11. C₂×#11745672

C₄

semidirect

88. C₂×Dic₅₉

Q₁₆

semidirect

127. C₅₉

#1878

semidirect

Subgroups — #21424435

Conjugacy classes of subgroups

Complements