Group #28481915 — subgroups

Subgroups — #28481915

Order 15104.

350 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 115 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	#21433030	C₂	1	1	yes	maximal, characteristic
2	#21422844	C₂	1	1	yes	maximal, characteristic
3	#21422659	C₂	1	2	yes	maximal
4	#21421954	C₂	1	2	yes	maximal
5	C₅₉×#1835	C₂	1	1	yes	maximal, characteristic
6	#16837959	C₂²	1	1	yes	characteristic
7	#16837532	—	2	1	no	—
8	#16837532	C₄	1	2	yes	complemented
9	C₈×Dic₁₁₈	—	2	1	no	—
10	C₈×Dic₁₁₈	C₄	1	2	yes	complemented
11	#16837455	C₂²	1	2	yes	—
12	#16837428	—	2	1	no	—
13	#16837426	C₂²	1	1	yes	characteristic
14	#16837357	—	2	1	no	—
15	#16837155	—	2	1	no	—
16	#16837153	—	2	1	no	—
17	#16837138	—	2	4	no	—
18	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
19	C₅₉×#382	C₂²	1	2	yes	—
20	C₅₉×#340	—	2	1	no	—
21	C₅₉×#340	—	2	1	no	—
22	C₂×#11745664	—	2	1	no	—
23	#14273727	Q₈	1	1	yes	characteristic
24	#14273727	Q₈	1	1	yes	characteristic
25	#14273719	—	2	1	no	—
26	#14273706	—	2	1	no	—
27	#14273706	D₄	1	2	yes	—
28	C₄×Dic₁₁₈	—	2	1	no	—
29	C₄×Dic₁₁₈	C₂×C₄	1	2	yes	—
30	#14273686	—	2	1	no	—
31	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
32	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
33	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
34	Dic₅₉⋊C₈	—	2	2	no	—
35	Dic₅₉⋊C₈	—	2	2	no	—
36	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
37	#14273637	—	2	2	no	—
38	C₄×C₅₉⋊C₈	—	2	2	no	—
39	C₈×Dic₅₉	—	2	2	no	—
40	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
42	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
43	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
44	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
45	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
46	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
47	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
48	#95×C₅₉	—	2	2	no	—
49	#95×C₅₉	—	2	2	no	—
50	C₂²×C₄×C₅₉	—	4	2	no	—
51	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
54	C₂×Dic₁₁₈	—	2	1	no	—
55	C₂×Dic₁₁₈	C₄⋊C₄	1	2	yes	—
56	C₂×C₈×C₅₉	—	2	2	no	—
57	C₂×C₈×C₅₉	—	2	2	no	—
58	C₂×C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
59	C₂×C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
60	C₂×C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
61	C₂×C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
62	C₄⋊C₄×C₅₉	—	4	2	no	—
63	C₄⋊C₄×C₅₉	—	4	2	no	—
64	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
65	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
66	C₄²×C₅₉	C₂×Q₈	1	1	yes	characteristic
67	C₄²×C₅₉	#41	1	1	yes	characteristic
68	C₂²⋊Dic₅₉	—	2	2	no	—
69	C₄⋊Dic₅₉	—	2	1	no	—
70	C₄⋊Dic₅₉	—	2	1	no	—
71	C₄⋊Dic₅₉	—	2	1	no	—
72	C₄⋊Dic₅₉	C₄⋊C₄	1	2	yes	—
73	Dic₅₉⋊C₄	—	2	2	no	—
74	Dic₅₉⋊C₄	—	2	2	no	—
75	C₄×Dic₅₉	—	2	2	no	—
76	#11745664	—	4	2	no	—
77	C₂×C₅₉⋊C₈	—	2	2	no	—
78	C₂×C₅₉⋊C₈	—	4	2	no	—
79	C₂³×C₅₉	#121	1	1	yes	characteristic
80	C₂×C₄×C₅₉	—	4	1	no	—
81	C₂×C₄×C₅₉	—	4	1	no	—
82	C₂×C₄×C₅₉	—	8	2	no	—
83	C₂×C₄×C₅₉	—	8	2	no	—
84	C₂×C₄×C₅₉	—	8	2	no	—
85	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
86	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
87	C₂×C₄×C₅₉	#117	1	1	yes	characteristic
88	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
89	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
90	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
91	C₂×C₄×C₅₉	#135	1	2	yes	—
92	C₂×C₄×C₅₉	#137	1	2	yes	—
93	C₂×Dic₅₉	—	2	2	no	—
94	C₂×Dic₅₉	—	2	2	no	—
95	Dic₁₁₈	—	4	2	no	—
96	Dic₁₁₈	—	4	2	no	—
97	C₈×C₅₉	—	2	1	no	—
98	C₈×C₅₉	—	2	1	no	—
99	C₈×C₅₉	—	2	1	no	—
100	C₈×C₅₉	—	2	1	no	—
101	C₅₉⋊C₈	—	4	2	no	—
102	C₅₉⋊C₈	—	8	2	no	—
103	#8679	—	59	1	no	maximal, Sylow
104	C₂²×C₅₉	—	2	1	no	—
105	C₂²×C₅₉	—	2	1	no	—
106	C₂²×C₅₉	#380	1	1	yes	characteristic
107	C₂²×C₅₉	#464	1	2	yes	—
108	C₄×C₅₉	—	2	1	no	—
109	C₄×C₅₉	—	2	1	no	—
110	C₄×C₅₉	—	2	1	no	—
111	C₄×C₅₉	—	2	1	no	—
112	C₄×C₅₉	—	16	2	no	—
113	C₄×C₅₉	#416	1	1	yes	characteristic
114	C₄×C₅₉	#419	1	1	yes	characteristic
115	C₄×C₅₉	#479	1	2	yes	—
116	Dic₅₉	—	4	2	no	—
117	Dic₅₉	—	4	2	no	—
118	#2960	—	59	1	no	—
119	#1835	D₅₉	1	1	yes	characteristic
120	#1564	—	59	1	no	—
121	#1518	—	59	2	no	—
122	#1286	—	59	2	no	—
123	C₂×C₅₉	—	2	2	no	—
124	C₂×C₅₉	#1805	1	1	yes	characteristic
125	C₂×C₅₉	#1812	1	1	yes	characteristic
126	C₂×C₅₉	#1814	1	1	yes	characteristic
127	#533	—	59	1	no	—
128	#446	—	59	2	no	—
129	#446	—	118	1	no	—
130	C₈×Q₈	—	59	2	no	—
131	C₈×Q₈	—	118	1	no	—
132	#431	—	59	2	no	—
133	#424	—	118	1	no	—
134	#423	—	59	1	no	—
135	#405	—	118	1	no	—
136	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
137	#382	C₂×D₅₉	1	2	yes	—
138	#340	—	2	1	no	—
139	#340	—	2	1	no	—
140	#335	—	118	1	no	—
141	#334	—	118	1	no	—
142	#328	—	118	4	no	—
143	C₅₉	#8679	1	1	yes	characteristic, complemented, Sylow
144	C₂×M₁₆	—	118	1	no	—
145	C₂²×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
146	C₂²×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
147	C₄⋊Q₈	—	59	1	no	—
148	C₄⋊Q₈	—	59	1	no	—
149	#125	—	118	1	no	—
150	C₂²⋊Q₈	—	59	2	no	—
151	C₂²⋊Q₈	—	118	1	no	—
152	C₄×Q₈	—	59	2	no	—
153	C₄×Q₈	—	118	1	no	—
154	#117	—	118	1	no	—
155	C₂×C₄⋊C₄	—	2	2	no	—
156	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
157	C₄⋊C₈	—	59	2	no	—
158	C₄⋊C₈	—	118	2	no	—
159	C₄⋊C₈	—	118	2	no	—
160	C₄⋊C₈	—	118	1	no	—
161	C₄⋊C₈	—	118	2	no	—
162	C₂²⋊C₈	—	118	2	no	—
163	#97	—	118	2	no	—
164	C₄×C₈	—	118	2	no	—
165	C₄×C₈	—	118	2	no	—
166	C₄×C₈	C₄×D₅₉	1	1	yes	characteristic
167	C₄×C₈	C₄×D₅₉	1	1	yes	characteristic
168	C₄×C₈	D₂₃₆	1	1	yes	characteristic
169	C₄×C₈	D₂₃₆	1	1	yes	characteristic
170	#95	—	2	2	no	—
171	#95	—	2	2	no	—
172	C₂×Q₈	—	59	2	no	—
173	C₂×Q₈	—	118	1	no	—
174	C₂²×C₄	—	4	2	no	—
175	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
176	C₂²×C₄	#11745687	1	1	yes	characteristic
177	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
178	M₁₆	—	236	2	no	—
179	C₂×C₈	—	2	2	no	—
180	C₂×C₈	—	2	2	no	—
181	C₂×C₈	—	118	2	no	—
182	C₂×C₈	—	236	2	no	—
183	C₂×C₈	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
184	C₂×C₈	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
185	C₂×C₈	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
186	C₂×C₈	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
187	C₄⋊C₄	—	4	2	no	—
188	C₄⋊C₄	—	4	2	no	—
189	C₄⋊C₄	—	59	2	no	—
190	C₄⋊C₄	—	118	2	no	—
191	C₄⋊C₄	—	118	2	no	—
192	C₄⋊C₄	—	118	1	no	—
193	C₄⋊C₄	—	118	1	no	—
194	C₄⋊C₄	—	118	1	no	—
195	C₂²⋊C₄	—	118	2	no	—
196	C₄²	—	118	2	no	—
197	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
198	C₄²	C₂×D₂₃₆	1	1	yes	characteristic
199	C₄²	Q₈×D₅₉	1	1	yes	characteristic
200	C₄²	#11745689	1	1	yes	characteristic
201	C₂³	#14273698	1	1	yes	characteristic
202	Q₈	—	236	2	no	—
203	Q₈	—	236	2	no	—
204	C₂×C₄	—	4	1	no	—
205	C₂×C₄	—	4	1	no	—
206	C₂×C₄	—	8	2	no	—
207	C₂×C₄	—	8	2	no	—
208	C₂×C₄	—	8	2	no	—
209	C₂×C₄	—	118	2	no	—
210	C₂×C₄	—	118	2	no	—
211	C₂×C₄	C₂×(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
212	C₂×C₄	C₄⋊C₄×D₅₉	1	1	yes	characteristic
213	C₂×C₄	#14273685	1	1	yes	characteristic
214	C₂×C₄	#14273702	1	1	yes	characteristic
215	C₂×C₄	#14273703	1	1	yes	characteristic
216	C₂×C₄	#14273707	1	1	yes	characteristic
217	C₂×C₄	#14273747	1	2	yes	—
218	C₂×C₄	#14273757	1	2	yes	—
219	C₈	—	2	1	no	—
220	C₈	—	2	1	no	—
221	C₈	—	2	1	no	—
222	C₈	—	2	1	no	—
223	C₈	—	472	2	no	—
224	C₈	—	236	2	no	—
225	C₂²	—	2	1	no	—
226	C₂²	—	2	1	no	—
227	C₂²	#16837259	1	1	yes	characteristic
228	C₂²	#16837621	1	2	yes	—
229	C₄	—	2	1	no	—
230	C₄	—	2	1	no	—
231	C₄	—	2	1	no	—
232	C₄	—	2	1	no	—
233	C₄	—	16	2	no	—
234	C₄	—	236	2	no	—
235	C₄	—	236	2	no	—
236	C₄	#16837396	1	1	yes	characteristic
237	C₄	#16837410	1	1	yes	characteristic
238	C₄	#16837706	1	2	yes	—
239	C₂	—	2	2	no	—
240	C₂	#21424108	1	1	yes	characteristic
241	C₂	#21424139	1	1	yes	characteristic
242	C₂	#21424147	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#21433030

C₂

yes

maximal, characteristic

#21422844

C₂

yes

maximal, characteristic

#21422659

C₂

yes

maximal

#21421954

C₂

yes

maximal

C₅₉×#1835

C₂

yes

maximal, characteristic

#16837959

C₂²

yes

characteristic

#16837532

—

#16837532

C₄

yes

complemented

C₈×Dic₁₁₈

—

C₈×Dic₁₁₈

C₄

yes

complemented

#16837455

C₂²

yes

—

#16837428

—

#16837426

C₂²

yes

—

—

—

—

C₂×C₄×C₈×C₅₉

C₂²

yes

characteristic

C₅₉×#382

C₂²

yes

—

C₅₉×#340

—

C₅₉×#340

—

C₂×#11745664

—

#14273727

Q₈

yes

characteristic

#14273727

Q₈

yes

—

—

D₄

yes

—

C₄×Dic₁₁₈

—

C₄×Dic₁₁₈

C₂×C₄

yes

—

#14273686

—

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

C₂×C₄

yes

—

Dic₅₉⋊C₈

—

Dic₅₉⋊C₈

—

C₂²⋊(C₅₉⋊C₈)

—

#14273637

—

C₄×C₅₉⋊C₈

—

C₈×Dic₅₉

—

C₂²×C₈×C₅₉

D₄

yes

characteristic

C₂²×C₈×C₅₉

D₄

yes

characteristic

C₂×C₄⋊C₄×C₅₉

—

C₂×C₄²×C₅₉

C₂³

yes

characteristic

C₄×C₈×C₅₉

C₂×C₄

yes

characteristic

C₄×C₈×C₅₉

C₂×C₄

yes

characteristic

C₄×C₈×C₅₉

D₄

yes

characteristic

C₄×C₈×C₅₉

D₄

yes

characteristic

#95×C₅₉

—

#95×C₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₅₉

#41

yes

characteristic

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

C₄⋊C₄

yes

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₅₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₅₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₅₉

C₂²⋊C₄

yes

characteristic

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄²×C₅₉

C₂²×C₄

yes

characteristic

C₄²×C₅₉

C₂×D₄

yes

characteristic

C₄²×C₅₉

C₂×Q₈

yes

characteristic

C₄²×C₅₉

#41

yes

characteristic

C₂²⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

C₄⋊C₄

yes

—

Dic₅₉⋊C₄

—

Dic₅₉⋊C₄

—

C₄×Dic₅₉

—

#11745664

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂³×C₅₉

#121

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₅₉

C₂×C₄⋊C₄

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₅₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₅₉

#135

yes

—

C₂×C₄×C₅₉

#137

yes

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

Dic₁₁₈

—

Dic₁₁₈

—

C₈×C₅₉

—

C₈×C₅₉

—

C₈×C₅₉

—

100

C₈×C₅₉

—

101

C₅₉⋊C₈

—

102

C₅₉⋊C₈

—

103

#8679

—

maximal, Sylow

104

C₂²×C₅₉

—

105

C₂²×C₅₉

—

106

C₂²×C₅₉

#380

yes

characteristic

107

C₂²×C₅₉

#464

yes

—

108

C₄×C₅₉

—

109

C₄×C₅₉

—

110

C₄×C₅₉

—

111

C₄×C₅₉

—

112

C₄×C₅₉

—

113

C₄×C₅₉

#416

yes

characteristic

114

C₄×C₅₉

#419

yes

characteristic

115

C₄×C₅₉

#479

yes

—

116

Dic₅₉

—

117

Dic₅₉

—

118

#2960

—

119

#1835

D₅₉

yes

characteristic

120

#1564

—

121

#1518

—

122

#1286

—

123

C₂×C₅₉

—

124

C₂×C₅₉

#1805

yes

characteristic

125

C₂×C₅₉

#1812

yes

characteristic

126

C₂×C₅₉

#1814

yes

characteristic

127

#533

—

128

#446

—

129

#446

—

118

—

130

C₈×Q₈

—

131

C₈×Q₈

—

118

—

132

#431

—

133

#424

—

118

—

134

#423

—

135

#405

—

118

—

136

C₂×C₄×C₈

C₂×D₅₉

yes

characteristic

137

#382

C₂×D₅₉

yes

—

138

#340

—

139

#340

—

140

#335

—

118

—

141

#334

—

118

—

142

#328

—

118

—

143

C₅₉

#8679

yes

characteristic, complemented, Sylow

144

C₂×M₁₆

—

118

—

145

C₂²×C₈

C₂²⋊D₅₉

yes

characteristic

146

C₂²×C₈

C₂²⋊D₅₉

yes

characteristic

147

C₄⋊Q₈

—

148

C₄⋊Q₈

—

149

#125

—

118

—

150

C₂²⋊Q₈

—

151

C₂²⋊Q₈

—

118

—

152

C₄×Q₈

—

153

C₄×Q₈

—

118

—

154

#117

—

118

—

155

C₂×C₄⋊C₄

—

156

C₂×C₄²

C₂²×D₅₉

yes

characteristic

157

C₄⋊C₈

—

158

C₄⋊C₈

—

118

—

159

C₄⋊C₈

—

118

—

160

C₄⋊C₈

—

118

—

161

C₄⋊C₈

—

118

—

162

C₂²⋊C₈

—

118

—

163

#97

—

118

—

164

C₄×C₈

—

118

—

165

C₄×C₈

—

118

—

166

C₄×C₈

C₄×D₅₉

yes

characteristic

167

C₄×C₈

C₄×D₅₉

yes

characteristic

168

C₄×C₈

D₂₃₆

yes

characteristic

169

C₄×C₈

D₂₃₆

yes

characteristic

170

#95

—

171

#95

—

172

C₂×Q₈

—

173

C₂×Q₈

—

118

—

174

C₂²×C₄

—

175

C₂²×C₄

D₄×D₅₉

yes

characteristic

176

C₂²×C₄

#11745687

yes

characteristic

177

C₂²×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

178

M₁₆

—

236

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

118

—

182

C₂×C₈

—

236

—

183

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

characteristic

184

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

characteristic

185

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

characteristic

186

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

characteristic

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

118

—

191

C₄⋊C₄

—

118

—

192

C₄⋊C₄

—

118

—

193

C₄⋊C₄

—

118

—

194

C₄⋊C₄

—

118

—

195

C₂²⋊C₄

—

118

—

196

C₄²

—

118

—

197

C₄²

C₂×C₄×D₅₉

yes

characteristic

198

C₄²

C₂×D₂₃₆

yes

characteristic

199

C₄²

Q₈×D₅₉

yes

characteristic

200

C₄²

#11745689

yes

characteristic

201

C₂³

#14273698

yes

characteristic

202

Q₈

—

236

—

203

Q₈

—

236

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

118

—

210

C₂×C₄

—

118

—

211

C₂×C₄

C₂×(C₂×D₅₉)⋊C₄

yes

characteristic

212

C₂×C₄

C₄⋊C₄×D₅₉

yes

characteristic

213

C₂×C₄

#14273685

yes

characteristic

214

C₂×C₄

#14273702

yes

characteristic

215

C₂×C₄

#14273703

yes

characteristic

216

C₂×C₄

#14273707

yes

characteristic

217

C₂×C₄

#14273747

yes

—

218

C₂×C₄

#14273757

yes

—

219

C₈

—

220

C₈

—

221

C₈

—

222

C₈

—

223

C₈

—

472

—

224

C₈

—

236

—

225

C₂²

—

226

C₂²

—

227

C₂²

#16837259

yes

characteristic

228

C₂²

#16837621

yes

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

—

236

—

235

C₄

—

236

—

236

C₄

#16837396

yes

characteristic

237

C₄

#16837410

yes

characteristic

238

C₄

#16837706

yes

—

239

C₂

—

240

C₂

#21424108

yes

characteristic

241

C₂

#21424139

yes

characteristic

242

C₂

#21424147

yes

characteristic

	subgroup	G/H
center	C₂²	#16837259
commutator	C₄²×C₅₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₅₉
Fitting	C₅₉×#1835	C₂
socle	C₂²×C₅₉	#380
prime radical	C₂³×C₅₉	#121
cosocle	C₂×C₄²×C₅₉	C₂³
hypercenter	#1835	D₅₉
hypocenter	C₅₉	#8679
LCS	G ▷ C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1835

subgroup

G/H

center

C₂²

#16837259

commutator

C₄²×C₅₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₅₉

Fitting

C₅₉×#1835

C₂

C₂²×C₅₉

C₂³×C₅₉

C₂×C₄²×C₅₉

C₂³

D₅₉

C₅₉

G ▷ C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1835

N	H ≅ G/N	type
8. #16837532	C₄	semidirect
10. C₈×Dic₁₁₈	C₄	semidirect
143. C₅₉	#8679	semidirect

H ≅ G/N

type

8. #16837532

C₄

semidirect

10. C₈×Dic₁₁₈

C₄

semidirect

143. C₅₉

#8679

semidirect

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

subgroup	index
#21433030	2
#21422844	2
#21422659	2
#21421954	2
C₅₉×#1835	2
#8679	59

subgroup

index

C₅₉×#1835

Subgroups — #28481915

Conjugacy classes of subgroups

Complements

Maximal subgroups