Group #28481849 — subgroups

Subgroups — #28481849

Order 15104.

358 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 119 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×#16837532	C₂	1	1	yes	maximal, characteristic
2	#21424234	C₂	1	1	yes	maximal, characteristic
3	#21422526	C₂	1	2	yes	maximal
4	#21421992	C₂	1	2	yes	maximal
5	C₅₉×#1564	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₁₁₈	C₂²	1	1	yes	characteristic
7	#16837532	—	2	1	no	—
8	#16837532	—	2	1	no	—
9	#16837532	C₄	1	2	yes	—
10	#16837532	C₄	1	2	yes	—
11	#16837426	C₂²	1	2	yes	—
12	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×Dic₅₉⋊C₈	—	2	1	no	—
14	C₂×#14273637	—	2	1	no	—
15	#16837167	—	2	1	no	—
16	#16837167	—	2	1	no	—
17	#16837134	—	2	4	no	—
18	C₅₉×#431	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
20	C₅₉×#335	—	2	1	no	—
21	C₅₉×#334	—	2	1	no	—
22	C₂²×Dic₁₁₈	Q₈	1	1	yes	characteristic
23	C₂×#11745664	—	2	2	no	—
24	C₂²×C₅₉⋊C₈	—	2	1	no	—
25	C₄×Dic₁₁₈	—	2	1	no	—
26	C₄×Dic₁₁₈	—	2	1	no	—
27	C₄×Dic₁₁₈	C₂×C₄	1	2	yes	—
28	C₄×Dic₁₁₈	D₄	1	2	yes	—
29	C₂×C₄⋊Dic₅₉	Q₈	1	1	yes	characteristic
30	C₂×Dic₅₉⋊C₄	—	2	1	no	—
31	C₂×C₄×Dic₅₉	—	2	1	no	—
32	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
33	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
34	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
35	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
36	Dic₅₉⋊C₈	—	2	2	no	—
37	Dic₅₉⋊C₈	—	2	2	no	—
38	#14273637	—	2	2	no	—
39	#14273637	—	2	2	no	—
40	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
43	C₄⋊C₈×C₅₉	—	2	2	no	—
44	C₂²⋊C₈×C₅₉	—	2	2	no	—
45	C₄×C₈×C₅₉	—	2	2	no	—
46	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
47	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
48	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
49	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
50	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
52	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
53	C₂²×Dic₅₉	—	2	1	no	—
54	C₂²×Dic₅₉	—	2	1	no	—
55	C₂×Dic₁₁₈	—	2	1	no	—
56	C₂×Dic₁₁₈	—	4	2	no	—
57	C₂×Dic₁₁₈	C₄⋊C₄	1	2	yes	—
58	C₂×C₈×C₅₉	—	2	2	no	—
59	C₂×C₈×C₅₉	—	2	2	no	—
60	C₂×C₈×C₅₉	—	4	2	no	—
61	C₂×C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
62	C₂×C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
63	C₂×C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
64	C₂×C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
65	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
66	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
67	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
68	C₄²×C₅₉	#41	1	1	yes	characteristic
69	C₄⋊Dic₅₉	—	2	1	no	—
70	C₄⋊Dic₅₉	C₄⋊C₄	1	2	yes	—
71	Dic₅₉⋊C₄	—	2	2	no	—
72	Dic₅₉⋊C₄	—	2	2	no	—
73	C₄×Dic₅₉	—	2	2	no	—
74	C₄×Dic₅₉	—	2	2	no	—
75	#11745664	—	4	2	no	—
76	#11745664	—	4	2	no	—
77	C₂×C₅₉⋊C₈	—	2	2	no	—
78	C₂×C₅₉⋊C₈	—	4	2	no	—
79	C₂×C₅₉⋊C₈	—	4	2	no	—
80	C₂³×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
81	C₂×C₄×C₅₉	—	2	2	no	—
82	C₂×C₄×C₅₉	—	4	1	no	—
83	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
85	C₂×C₄×C₅₉	#117	1	1	yes	characteristic
86	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
87	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
88	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
89	C₂×C₄×C₅₉	#135	1	2	yes	—
90	C₂×C₄×C₅₉	#137	1	2	yes	—
91	C₂×Dic₅₉	—	2	2	no	—
92	C₂×Dic₅₉	—	2	2	no	—
93	C₂×Dic₅₉	—	4	2	no	—
94	C₂×Dic₅₉	—	4	2	no	—
95	Dic₁₁₈	—	2	4	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	C₈×C₅₉	—	8	2	no	—
102	C₅₉⋊C₈	—	4	2	no	—
103	C₅₉⋊C₈	—	8	2	no	—
104	#8665	—	59	1	no	maximal, Sylow
105	C₂²×C₅₉	—	2	1	no	—
106	C₂²×C₅₉	—	2	1	no	—
107	C₂²×C₅₉	#380	1	1	yes	characteristic
108	C₂²×C₅₉	#479	1	2	yes	—
109	C₄×C₅₉	—	2	1	no	—
110	C₄×C₅₉	—	2	1	no	—
111	C₄×C₅₉	—	2	1	no	—
112	C₄×C₅₉	#416	1	1	yes	characteristic
113	C₄×C₅₉	#419	1	1	yes	characteristic
114	C₄×C₅₉	#430	1	2	yes	—
115	C₄×C₅₉	#464	1	2	yes	—
116	Dic₅₉	—	4	2	no	—
117	Dic₅₉	—	4	2	no	—
118	C₂×#446	—	59	1	no	—
119	#1837	—	59	1	no	—
120	#1564	D₅₉	1	1	yes	characteristic
121	#1487	—	59	2	no	—
122	#1301	—	59	2	no	—
123	C₂×C₅₉	—	2	2	no	—
124	C₂×C₅₉	#1805	1	1	yes	characteristic
125	C₂×C₅₉	#1811	1	1	yes	characteristic
126	C₂×C₅₉	#1814	1	1	yes	characteristic
127	C₂×C₄×Q₈	—	59	1	no	—
128	#446	—	59	2	no	—
129	#446	—	59	2	no	—
130	#446	—	118	1	no	—
131	#446	—	118	1	no	—
132	#431	C₂×D₅₉	1	2	yes	—
133	#423	—	59	2	no	—
134	C₂×C₄⋊C₈	—	59	1	no	—
135	C₂×C₄⋊C₈	—	118	1	no	—
136	C₂×#97	—	118	1	no	—
137	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
138	#341	—	118	1	no	—
139	#341	—	118	1	no	—
140	#335	—	2	1	no	—
141	#334	—	2	1	no	—
142	Q₈⋊C₈	—	118	4	no	—
143	C₅₉	#8665	1	1	yes	characteristic, complemented, Sylow
144	C₂²×Q₈	—	59	1	no	—
145	C₂×M₁₆	—	118	2	no	—
146	C₂²×C₈	—	118	1	no	—
147	C₂²×C₈	D₂₃₆	1	1	yes	characteristic
148	C₂²×C₈	D₂₃₆	1	1	yes	characteristic
149	C₄×Q₈	—	59	2	no	—
150	C₄×Q₈	—	59	2	no	—
151	C₄×Q₈	—	118	1	no	—
152	C₄×Q₈	—	118	1	no	—
153	C₂×C₄⋊C₄	—	59	1	no	—
154	C₂×C₄⋊C₄	—	118	1	no	—
155	C₂×C₄²	—	118	1	no	—
156	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
157	C₄⋊C₈	—	2	2	no	—
158	C₄⋊C₈	—	59	2	no	—
159	C₄⋊C₈	—	118	2	no	—
160	C₄⋊C₈	—	118	2	no	—
161	C₄⋊C₈	—	118	2	no	—
162	C₄⋊C₈	—	118	2	no	—
163	C₄⋊C₈	—	118	1	no	—
164	C₂²⋊C₈	—	2	2	no	—
165	#97	—	118	2	no	—
166	#97	—	118	2	no	—
167	C₄×C₈	—	2	2	no	—
168	C₄×C₈	C₄×D₅₉	1	1	yes	characteristic
169	C₄×C₈	C₄×D₅₉	1	1	yes	characteristic
170	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
171	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
172	C₂×Q₈	—	59	2	no	—
173	C₂×Q₈	—	118	1	no	—
174	C₂×Q₈	—	236	2	no	—
175	C₂²×C₄	—	118	1	no	—
176	C₂²×C₄	—	118	1	no	—
177	C₂²×C₄	C₂×D₂₃₆	1	1	yes	characteristic
178	C₂²×C₄	#11745687	1	1	yes	characteristic
179	C₂²×C₄	Q₈×D₅₉	1	1	yes	characteristic
180	M₁₆	—	236	2	no	—
181	M₁₆	—	236	2	no	—
182	C₂×C₈	—	2	2	no	—
183	C₂×C₈	—	2	2	no	—
184	C₂×C₈	—	4	2	no	—
185	C₂×C₈	—	118	2	no	—
186	C₂×C₈	—	236	2	no	—
187	C₂×C₈	—	236	2	no	—
188	C₂×C₈	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
189	C₂×C₈	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
190	C₂×C₈	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
191	C₂×C₈	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
192	C₄⋊C₄	—	59	2	no	—
193	C₄⋊C₄	—	118	2	no	—
194	C₄⋊C₄	—	118	2	no	—
195	C₄⋊C₄	—	118	1	no	—
196	C₄²	—	118	2	no	—
197	C₄²	—	118	2	no	—
198	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
199	C₄²	D₄×D₅₉	1	1	yes	characteristic
200	C₄²	#11745689	1	1	yes	characteristic
201	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
202	C₂³	#14273707	1	1	yes	characteristic
203	Q₈	—	118	4	no	—
204	Q₈	—	236	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	118	2	no	—
208	C₂×C₄	—	118	2	no	—
209	C₂×C₄	—	236	2	no	—
210	C₂×C₄	—	236	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	#14273698	1	1	yes	characteristic
215	C₂×C₄	#14273702	1	1	yes	characteristic
216	C₂×C₄	#14273703	1	1	yes	characteristic
217	C₂×C₄	#14273749	1	2	yes	—
218	C₂×C₄	#14273760	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	—	8	2	no	—
224	C₈	—	472	2	no	—
225	C₈	—	236	2	no	—
226	C₂²	—	2	1	no	—
227	C₂²	—	2	1	no	—
228	C₂²	#16837259	1	1	yes	characteristic
229	C₂²	#16837710	1	2	yes	—
230	C₄	—	2	1	no	—
231	C₄	—	2	1	no	—
232	C₄	—	2	1	no	—
233	C₄	—	236	2	no	—
234	C₄	—	236	2	no	—
235	C₄	#16837399	1	1	yes	characteristic
236	C₄	#16837412	1	1	yes	characteristic
237	C₄	#16837449	1	2	yes	—
238	C₄	#16837625	1	2	yes	—
239	C₂	—	2	2	no	—
240	C₂	#21424112	1	1	yes	characteristic
241	C₂	#21424135	1	1	yes	characteristic
242	C₂	#21424147	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#16837532

C₂

yes

maximal, characteristic

#21424234

C₂

yes

maximal, characteristic

#21422526

C₂

yes

maximal

#21421992

C₂

yes

maximal

C₅₉×#1564

C₂

yes

maximal, characteristic

C₂×C₄×Dic₁₁₈

C₂²

yes

—

—

C₄

yes

—

#16837532

C₄

yes

—

#16837426

C₂²

yes

—

C₂×C₄⋊(C₅₉⋊C₈)

C₂²

yes

characteristic

C₂×Dic₅₉⋊C₈

—

—

—

—

—

C₅₉×#431

C₂²

yes

—

C₂×C₄×C₈×C₅₉

C₂²

yes

characteristic

C₅₉×#335

—

C₅₉×#334

—

C₂²×Dic₁₁₈

Q₈

yes

characteristic

C₂×#11745664

—

C₂²×C₅₉⋊C₈

—

C₄×Dic₁₁₈

—

C₄×Dic₁₁₈

—

C₄×Dic₁₁₈

C₂×C₄

yes

—

C₄×Dic₁₁₈

D₄

yes

—

C₂×C₄⋊Dic₅₉

Q₈

yes

characteristic

C₂×Dic₅₉⋊C₄

—

C₂×C₄×Dic₅₉

—

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

C₂×C₄

yes

—

Dic₅₉⋊C₈

—

Dic₅₉⋊C₈

—

#14273637

—

#14273637

—

C₂²×C₈×C₅₉

D₄

yes

characteristic

C₂²×C₈×C₅₉

D₄

yes

characteristic

C₂×C₄²×C₅₉

C₂³

yes

characteristic

C₄⋊C₈×C₅₉

—

C₂²⋊C₈×C₅₉

—

C₄×C₈×C₅₉

—

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

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₅₉

C₂×Q₈

yes

characteristic

C₂²×C₄×C₅₉

#41

yes

characteristic

C₂²×Dic₅₉

—

C₂²×Dic₅₉

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

C₄⋊C₄

yes

—

C₂×C₈×C₅₉

—

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

C₄²×C₅₉

C₂²×C₄

yes

characteristic

C₄²×C₅₉

C₂×D₄

yes

characteristic

C₄²×C₅₉

C₂×D₄

yes

characteristic

C₄²×C₅₉

#41

yes

characteristic

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

C₄⋊C₄

yes

—

Dic₅₉⋊C₄

—

Dic₅₉⋊C₄

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

#11745664

—

#11745664

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂³×C₅₉

C₂²⋊Q₈

yes

characteristic

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

yes

C₂×C₄×C₅₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₅₉

#135

yes

—

C₂×C₄×C₅₉

#137

yes

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

Dic₁₁₈

—

Dic₁₁₈

—

C₈×C₅₉

—

C₈×C₅₉

—

C₈×C₅₉

—

100

C₈×C₅₉

—

101

C₈×C₅₉

—

102

C₅₉⋊C₈

—

103

C₅₉⋊C₈

—

104

#8665

—

maximal, Sylow

105

C₂²×C₅₉

—

106

C₂²×C₅₉

—

107

C₂²×C₅₉

#380

yes

characteristic

108

C₂²×C₅₉

#479

yes

—

109

C₄×C₅₉

—

110

C₄×C₅₉

—

111

C₄×C₅₉

—

112

C₄×C₅₉

#416

yes

characteristic

113

C₄×C₅₉

#419

yes

characteristic

114

C₄×C₅₉

#430

yes

—

115

C₄×C₅₉

#464

yes

—

116

Dic₅₉

—

117

Dic₅₉

—

118

C₂×#446

—

119

#1837

—

120

#1564

D₅₉

yes

characteristic

121

#1487

—

122

#1301

—

123

C₂×C₅₉

—

124

C₂×C₅₉

#1805

yes

characteristic

125

C₂×C₅₉

#1811

yes

characteristic

126

C₂×C₅₉

#1814

yes

characteristic

127

C₂×C₄×Q₈

—

128

#446

—

129

#446

—

130

#446

—

118

—

131

#446

—

118

—

132

#431

C₂×D₅₉

yes

—

133

#423

—

134

C₂×C₄⋊C₈

—

135

C₂×C₄⋊C₈

—

118

—

136

C₂×#97

—

118

—

137

C₂×C₄×C₈

C₂×D₅₉

yes

characteristic

138

#341

—

118

—

139

#341

—

118

—

140

#335

—

141

#334

—

142

Q₈⋊C₈

—

118

—

143

C₅₉

#8665

yes

characteristic, complemented, Sylow

144

C₂²×Q₈

—

145

C₂×M₁₆

—

118

—

146

C₂²×C₈

—

118

—

147

C₂²×C₈

D₂₃₆

yes

characteristic

148

C₂²×C₈

D₂₃₆

yes

characteristic

149

C₄×Q₈

—

150

C₄×Q₈

—

151

C₄×Q₈

—

118

—

152

C₄×Q₈

—

118

—

153

C₂×C₄⋊C₄

—

154

C₂×C₄⋊C₄

—

118

—

155

C₂×C₄²

—

118

—

156

C₂×C₄²

C₂²×D₅₉

yes

characteristic

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

118

—

160

C₄⋊C₈

—

118

—

161

C₄⋊C₈

—

118

—

162

C₄⋊C₈

—

118

—

163

C₄⋊C₈

—

118

—

164

C₂²⋊C₈

—

165

#97

—

118

—

166

#97

—

118

—

167

C₄×C₈

—

168

C₄×C₈

C₄×D₅₉

yes

characteristic

169

C₄×C₈

C₄×D₅₉

yes

characteristic

170

C₄×C₈

C₂²⋊D₅₉

yes

characteristic

171

C₄×C₈

C₂²⋊D₅₉

yes

characteristic

172

C₂×Q₈

—

173

C₂×Q₈

—

118

—

174

C₂×Q₈

—

236

—

175

C₂²×C₄

—

118

—

176

C₂²×C₄

—

118

—

177

C₂²×C₄

C₂×D₂₃₆

yes

characteristic

178

C₂²×C₄

#11745687

yes

characteristic

179

C₂²×C₄

Q₈×D₅₉

yes

characteristic

180

M₁₆

—

236

—

181

M₁₆

—

236

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

118

—

186

C₂×C₈

—

236

—

187

C₂×C₈

—

236

—

188

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

characteristic

189

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

characteristic

190

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

characteristic

191

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

characteristic

192

C₄⋊C₄

—

193

C₄⋊C₄

—

118

—

194

C₄⋊C₄

—

118

—

195

C₄⋊C₄

—

118

—

196

C₄²

—

118

—

197

C₄²

—

118

—

198

C₄²

C₂×C₄×D₅₉

yes

characteristic

199

C₄²

D₄×D₅₉

yes

characteristic

200

C₄²

#11745689

yes

characteristic

201

C₄²

C₂×C₂²⋊D₅₉

yes

characteristic

202

C₂³

#14273707

yes

characteristic

203

Q₈

—

118

—

204

Q₈

—

236

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

118

—

208

C₂×C₄

—

118

—

209

C₂×C₄

—

236

—

210

C₂×C₄

—

236

—

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

#14273698

yes

characteristic

215

C₂×C₄

#14273702

yes

characteristic

216

C₂×C₄

#14273703

yes

characteristic

217

C₂×C₄

#14273749

yes

—

218

C₂×C₄

#14273760

yes

—

219

C₈

—

220

C₈

—

221

C₈

—

222

C₈

—

223

C₈

—

224

C₈

—

472

—

225

C₈

—

236

—

226

C₂²

—

227

C₂²

—

228

C₂²

#16837259

yes

characteristic

229

C₂²

#16837710

yes

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

236

—

234

C₄

—

236

—

235

C₄

#16837399

yes

characteristic

236

C₄

#16837412

yes

characteristic

237

C₄

#16837449

yes

—

238

C₄

#16837625

yes

—

239

C₂

—

240

C₂

#21424112

yes

characteristic

241

C₂

#21424135

yes

characteristic

242

C₂

#21424147

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14273702
commutator	C₄²×C₅₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₅₉
Fitting	C₅₉×#1564	C₂
socle	C₂²×C₅₉	#380
prime radical	C₂³×C₅₉	C₂²⋊Q₈
cosocle	C₂×C₄²×C₅₉	C₂³
hypercenter	#1564	D₅₉
hypocenter	C₅₉	#8665
LCS	G ▷ C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

subgroup

G/H

center

C₂×C₄

#14273702

commutator

C₄²×C₅₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₅₉

Fitting

C₅₉×#1564

C₂

socle

C₂²×C₅₉

#380

prime radical

C₂³×C₅₉

C₂²⋊Q₈

cosocle

C₂×C₄²×C₅₉

C₂³

D₅₉

C₅₉

G ▷ C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

N	H ≅ G/N	type
143. C₅₉	#8665	semidirect

H ≅ G/N

type

143. C₅₉

#8665

semidirect

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

subgroup	index
C₂×#16837532	2
#21424234	2
#21422526	2
#21421992	2
C₅₉×#1564	2
#8665	59

subgroup

index

C₅₉×#1564

Subgroups — #28481849

Conjugacy classes of subgroups

Complements

Maximal subgroups