Group #28493428 — subgroups

Subgroups — #28493428

Order 15104.

402 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 123 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	#21424224	C₂	1	1	yes	maximal, characteristic, complemented
2	#21424096	C₂	1	2	yes	maximal
3	#21421980	C₂	1	2	yes	maximal, complemented
4	#21421931	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#1954	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
7	C₂×#14273648	—	2	2	no	—
8	#16837272	C₂²	1	2	yes	—
9	#16837165	—	2	2	no	—
10	#16837164	—	2	2	no	—
11	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊C₈×C₅₉	—	2	2	no	—
14	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
15	C₂²×C₅₉⋊C₈	—	2	2	no	—
16	C₂×C₄⋊Dic₅₉	—	2	2	no	—
17	C₂×C₄⋊Dic₅₉	—	2	2	no	—
18	C₂×C₄⋊Dic₅₉	—	2	2	no	—
19	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
20	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
21	#14273648	—	4	4	no	—
22	C₂²×D₄×C₅₉	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₅₉	—	2	1	no	—
24	C₂²×C₈×C₅₉	—	2	1	no	—
25	C₂²×C₈×C₅₉	D₄	1	2	yes	—
26	C₄×D₄×C₅₉	—	2	2	no	—
27	C₄×D₄×C₅₉	—	2	2	no	—
28	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
29	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
30	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
31	C₄⋊C₈×C₅₉	—	2	2	no	—
32	C₂²⋊C₈×C₅₉	—	4	4	no	—
33	C₄×C₈×C₅₉	—	2	2	no	—
34	C₂⁴×C₅₉	—	2	1	no	—
35	C₂×D₄×C₅₉	—	2	2	no	—
36	C₂×D₄×C₅₉	—	2	1	no	—
37	C₂×D₄×C₅₉	—	2	2	no	—
38	C₂×D₄×C₅₉	Q₁₆	1	2	yes	—
39	C₂²×C₄×C₅₉	—	2	1	no	—
40	C₂²×C₄×C₅₉	—	4	1	no	—
41	C₂²×C₄×C₅₉	—	4	1	no	—
42	C₂²×C₄×C₅₉	—	4	2	no	—
43	C₂²×C₄×C₅₉	—	4	2	no	—
44	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
45	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
47	C₂²×Dic₅₉	—	4	2	no	—
48	C₂×C₈×C₅₉	—	2	2	no	—
49	C₂×C₈×C₅₉	—	2	2	no	—
50	C₂×C₈×C₅₉	—	2	2	no	—
51	C₂×C₈×C₅₉	—	4	1	no	—
52	C₂×C₈×C₅₉	—	4	2	no	—
53	C₄⋊C₄×C₅₉	—	2	2	no	—
54	C₂²⋊C₄×C₅₉	—	4	2	no	—
55	C₄²×C₅₉	#41	1	2	yes	—
56	C₄²×C₅₉	#41	1	2	yes	—
57	C₄⋊Dic₅₉	—	4	2	no	—
58	C₄⋊Dic₅₉	—	4	2	no	—
59	C₄⋊Dic₅₉	—	4	2	no	—
60	C₄⋊Dic₅₉	—	4	2	no	—
61	C₄⋊Dic₅₉	—	8	2	no	—
62	C₂×C₅₉⋊C₈	—	4	2	no	—
63	C₂×C₅₉⋊C₈	—	4	2	no	—
64	C₂×C₅₉⋊C₈	—	4	2	no	—
65	C₂³×C₅₉	—	2	2	no	—
66	C₂³×C₅₉	—	4	1	no	—
67	C₂³×C₅₉	—	4	2	no	—
68	C₂³×C₅₉	—	4	1	no	—
69	C₂³×C₅₉	—	4	2	no	—
70	C₂³×C₅₉	#121	1	1	yes	characteristic
71	D₄×C₅₉	—	2	4	no	—
72	D₄×C₅₉	—	4	2	no	—
73	C₂×C₄×C₅₉	—	2	2	no	—
74	C₂×C₄×C₅₉	—	4	1	no	—
75	C₂×C₄×C₅₉	—	4	2	no	—
76	C₂×C₄×C₅₉	—	8	2	no	—
77	C₂×C₄×C₅₉	—	8	1	no	—
78	C₂×C₄×C₅₉	—	8	1	no	—
79	C₂×C₄×C₅₉	#123	1	1	yes	characteristic
80	C₂×C₄×C₅₉	#123	1	2	yes	—
81	C₂×C₄×C₅₉	#124	1	1	yes	characteristic
82	C₂×C₄×C₅₉	#126	1	2	yes	—
83	C₂×C₄×C₅₉	C₂×Q₁₆	1	1	yes	characteristic
84	C₂×C₄×C₅₉	#135	1	2	yes	—
85	C₂×C₄×C₅₉	#135	1	1	yes	characteristic
86	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
87	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
88	C₂×Dic₅₉	—	8	2	no	—
89	C₂×Dic₅₉	—	8	2	no	—
90	C₂×Dic₅₉	—	8	2	no	—
91	C₈×C₅₉	—	4	2	no	—
92	C₈×C₅₉	—	8	1	no	—
93	C₅₉⋊C₈	—	8	2	no	—
94	#10622	—	59	1	no	maximal, Sylow
95	C₂²×C₅₉	—	4	2	no	—
96	C₂²×C₅₉	—	4	4	no	—
97	C₂²×C₅₉	—	8	1	no	—
98	C₂²×C₅₉	—	8	1	no	—
99	C₂²×C₅₉	—	8	2	no	—
100	C₂²×C₅₉	#397	1	1	yes	characteristic
101	C₂²×C₅₉	#463	1	2	yes	—
102	C₂²×C₅₉	#467	1	1	yes	characteristic
103	C₂²×C₅₉	#469	1	1	yes	characteristic
104	C₂²×C₅₉	#471	1	2	yes	—
105	C₄×C₅₉	—	2	2	no	—
106	C₄×C₅₉	—	8	1	no	—
107	C₄×C₅₉	#482	1	2	yes	—
108	C₄×C₅₉	#482	1	2	yes	—
109	C₄×C₅₉	#484	1	2	yes	—
110	C₄×C₅₉	#488	1	1	yes	characteristic
111	C₄×C₅₉	#490	1	1	yes	characteristic
112	Dic₅₉	—	16	2	no	—
113	#1954	D₅₉	1	1	yes	characteristic
114	#1834	—	59	1	no	—
115	#1802	—	59	2	no	—
116	#1296	—	59	2	no	—
117	#1277	—	59	1	no	—
118	C₂×C₅₉	—	8	2	no	—
119	C₂×C₅₉	#1683	1	2	yes	—
120	C₂×C₅₉	#1701	1	2	yes	—
121	C₂×C₅₉	#2073	1	1	yes	characteristic
122	C₂×C₅₉	#2076	1	1	yes	characteristic
123	C₂×C₅₉	#2079	1	1	yes	characteristic
124	C₂×C₄×D₄	C₂×D₅₉	1	1	yes	characteristic
125	C₂×C₄⋊C₈	—	59	2	no	—
126	C₂×C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
127	C₂×#102	—	118	2	no	—
128	C₂×C₂²⋊C₈	—	2	2	no	—
129	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
130	#384	—	59	2	no	—
131	#340	—	118	2	no	—
132	#340	—	118	2	no	—
133	C₅₉	#10622	1	1	yes	characteristic, complemented, Sylow
134	C₂²×D₄	D₂₃₆	1	1	yes	characteristic
135	C₂³×C₄	—	2	1	no	—
136	C₂²×C₈	—	2	1	no	—
137	C₂²×C₈	—	118	2	no	—
138	C₂²×C₈	C₂²⋊D₅₉	1	2	yes	—
139	C₄×D₄	—	2	2	no	—
140	C₄×D₄	—	2	2	no	—
141	C₂×C₄⋊C₄	—	118	2	no	—
142	C₂×C₄⋊C₄	—	118	2	no	—
143	C₂×C₄⋊C₄	—	118	2	no	—
144	C₂×C₄⋊C₄	D₂₃₆	1	1	yes	characteristic
145	C₂×C₂²⋊C₄	—	2	1	no	—
146	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
147	C₄⋊C₈	—	2	2	no	—
148	C₄⋊C₈	—	118	2	no	—
149	C₄⋊C₈	—	118	2	no	—
150	#102	—	236	4	no	—
151	C₂²⋊C₈	—	4	4	no	—
152	C₄×C₈	—	2	2	no	—
153	C₂⁴	—	2	1	no	—
154	C₂×D₄	—	2	2	no	—
155	C₂×D₄	—	2	1	no	—
156	C₂×D₄	—	2	2	no	—
157	C₂×D₄	Dic₂₃₆	1	2	yes	—
158	C₂²×C₄	—	2	1	no	—
159	C₂²×C₄	—	4	1	no	—
160	C₂²×C₄	—	4	1	no	—
161	C₂²×C₄	—	4	2	no	—
162	C₂²×C₄	—	4	2	no	—
163	C₂²×C₄	—	236	2	no	—
164	C₂²×C₄	C₂×D₂₃₆	1	1	yes	characteristic
165	C₂²×C₄	#11745685	1	1	yes	characteristic
166	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
167	C₂×C₈	—	2	2	no	—
168	C₂×C₈	—	2	2	no	—
169	C₂×C₈	—	2	2	no	—
170	C₂×C₈	—	4	1	no	—
171	C₂×C₈	—	4	2	no	—
172	C₂×C₈	—	236	2	no	—
173	C₂×C₈	—	236	2	no	—
174	C₂×C₈	—	236	2	no	—
175	C₄⋊C₄	—	2	2	no	—
176	C₄⋊C₄	—	472	2	no	—
177	C₄⋊C₄	—	236	2	no	—
178	C₄⋊C₄	—	236	2	no	—
179	C₄⋊C₄	—	236	2	no	—
180	C₄⋊C₄	—	236	2	no	—
181	C₂²⋊C₄	—	4	2	no	—
182	C₄²	#11745687	1	2	yes	—
183	C₄²	#11745687	1	2	yes	—
184	C₂³	—	2	2	no	—
185	C₂³	—	4	1	no	—
186	C₂³	—	4	2	no	—
187	C₂³	—	4	1	no	—
188	C₂³	—	4	2	no	—
189	C₂³	#14273701	1	1	yes	characteristic
190	D₄	—	2	4	no	—
191	D₄	—	4	2	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	4	1	no	—
194	C₂×C₄	—	4	2	no	—
195	C₂×C₄	—	8	2	no	—
196	C₂×C₄	—	8	1	no	—
197	C₂×C₄	—	8	1	no	—
198	C₂×C₄	—	472	2	no	—
199	C₂×C₄	—	472	2	no	—
200	C₂×C₄	—	472	2	no	—
201	C₂×C₄	#14273708	1	1	yes	characteristic
202	C₂×C₄	#14273711	1	2	yes	—
203	C₂×C₄	#14273714	1	1	yes	characteristic
204	C₂×C₄	#14273720	1	2	yes	—
205	C₂×C₄	C₂×Dic₂₃₆	1	1	yes	characteristic
206	C₂×C₄	#14273747	1	2	yes	—
207	C₂×C₄	#14273749	1	1	yes	characteristic
208	C₂×C₄	#14273753	1	2	yes	—
209	C₂×C₄	#14273755	1	2	yes	—
210	C₈	—	4	2	no	—
211	C₈	—	8	1	no	—
212	C₈	—	472	2	no	—
213	C₂²	—	4	2	no	—
214	C₂²	—	4	4	no	—
215	C₂²	—	8	2	no	—
216	C₂²	—	8	1	no	—
217	C₂²	—	8	1	no	—
218	C₂²	#16837327	1	1	yes	characteristic
219	C₂²	#16837617	1	2	yes	—
220	C₂²	#16837643	1	1	yes	characteristic
221	C₂²	#16837655	1	1	yes	characteristic
222	C₂²	#16837665	1	2	yes	—
223	C₄	—	2	2	no	—
224	C₄	—	8	1	no	—
225	C₄	—	944	2	no	—
226	C₄	#16837723	1	2	yes	—
227	C₄	#16837727	1	2	yes	—
228	C₄	#16837738	1	2	yes	—
229	C₄	#16837756	1	1	yes	characteristic
230	C₄	#16837766	1	1	yes	characteristic
231	C₂	—	8	2	no	—
232	C₂	#21423547	1	2	yes	—
233	C₂	#21423657	1	2	yes	—
234	C₂	#21425509	1	1	yes	characteristic
235	C₂	#21425524	1	1	yes	characteristic
236	C₂	#21425541	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#21424224

C₂

yes

maximal, characteristic, complemented

#21424096

C₂

yes

maximal

#21421980

C₂

yes

maximal, complemented

#21421931

C₂

yes

maximal, characteristic, complemented

C₅₉×#1954

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₅₉⋊C₈)

C₂²

yes

—

C₂×#14273648

—

#16837272

C₂²

yes

—

#16837165

—

#16837164

—

C₂×C₄×D₄×C₅₉

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₅₉

C₂²

yes

characteristic

C₂×C₂²⋊C₈×C₅₉

—

C₂×C₄×C₈×C₅₉

C₂²

yes

characteristic

C₂²×C₅₉⋊C₈

—

C₂×C₄⋊Dic₅₉

—

C₂×C₄⋊Dic₅₉

—

C₂×C₄⋊Dic₅₉

—

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

—

#14273648

—

C₂²×D₄×C₅₉

D₄

yes

characteristic

C₂³×C₄×C₅₉

—

C₂²×C₈×C₅₉

—

C₂²×C₈×C₅₉

D₄

yes

—

C₄×D₄×C₅₉

—

C₄×D₄×C₅₉

—

C₂×C₄⋊C₄×C₅₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₅₉

—

C₂×C₄²×C₅₉

C₂³

yes

characteristic

C₄⋊C₈×C₅₉

—

C₂²⋊C₈×C₅₉

—

C₄×C₈×C₅₉

—

C₂⁴×C₅₉

—

C₂×D₄×C₅₉

—

C₂×D₄×C₅₉

—

C₂×D₄×C₅₉

—

C₂×D₄×C₅₉

Q₁₆

yes

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₅₉

#41

yes

characteristic

C₂²×Dic₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₄⋊C₄×C₅₉

—

C₂²⋊C₄×C₅₉

—

C₄²×C₅₉

#41

yes

—

C₄²×C₅₉

#41

yes

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

#121

yes

characteristic

D₄×C₅₉

—

D₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

#123

yes

characteristic

C₂×C₄×C₅₉

#123

yes

—

C₂×C₄×C₅₉

#124

yes

characteristic

C₂×C₄×C₅₉

#126

yes

—

C₂×C₄×C₅₉

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₅₉

#135

yes

—

C₂×C₄×C₅₉

#135

yes

characteristic

C₂×C₄×C₅₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₅₉

AGL(1,ℤ/8)

yes

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₈×C₅₉

—

C₈×C₅₉

—

C₅₉⋊C₈

—

#10622

—

maximal, Sylow

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

100

C₂²×C₅₉

#397

yes

characteristic

101

C₂²×C₅₉

#463

yes

—

102

C₂²×C₅₉

#467

yes

characteristic

103

C₂²×C₅₉

#469

yes

characteristic

104

C₂²×C₅₉

#471

yes

—

105

C₄×C₅₉

—

106

C₄×C₅₉

—

107

C₄×C₅₉

#482

yes

—

108

C₄×C₅₉

#482

yes

—

109

C₄×C₅₉

#484

yes

—

110

C₄×C₅₉

#488

yes

characteristic

111

C₄×C₅₉

#490

yes

characteristic

112

Dic₅₉

—

113

#1954

D₅₉

yes

characteristic

114

#1834

—

115

#1802

—

116

#1296

—

117

#1277

—

118

C₂×C₅₉

—

119

C₂×C₅₉

#1683

yes

—

120

C₂×C₅₉

#1701

yes

—

121

C₂×C₅₉

#2073

yes

characteristic

122

C₂×C₅₉

#2076

yes

characteristic

123

C₂×C₅₉

#2079

yes

characteristic

124

C₂×C₄×D₄

C₂×D₅₉

yes

characteristic

125

C₂×C₄⋊C₈

—

126

C₂×C₄⋊C₈

C₂×D₅₉

yes

characteristic

127

C₂×#102

—

118

—

128

C₂×C₂²⋊C₈

—

129

C₂×C₄×C₈

C₂×D₅₉

yes

characteristic

130

#384

—

131

#340

—

118

—

132

#340

—

118

—

133

C₅₉

#10622

yes

characteristic, complemented, Sylow

134

C₂²×D₄

D₂₃₆

yes

characteristic

135

C₂³×C₄

—

136

C₂²×C₈

—

137

C₂²×C₈

—

118

—

138

C₂²×C₈

C₂²⋊D₅₉

yes

—

139

C₄×D₄

—

140

C₄×D₄

—

141

C₂×C₄⋊C₄

—

118

—

142

C₂×C₄⋊C₄

—

118

—

143

C₂×C₄⋊C₄

—

118

—

144

C₂×C₄⋊C₄

D₂₃₆

yes

characteristic

145

C₂×C₂²⋊C₄

—

146

C₂×C₄²

C₂²×D₅₉

yes

characteristic

147

C₄⋊C₈

—

148

C₄⋊C₈

—

118

—

149

C₄⋊C₈

—

118

—

150

#102

—

236

—

151

C₂²⋊C₈

—

152

C₄×C₈

—

153

C₂⁴

—

154

C₂×D₄

—

155

C₂×D₄

—

156

C₂×D₄

—

157

C₂×D₄

Dic₂₃₆

yes

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

163

C₂²×C₄

—

236

—

164

C₂²×C₄

C₂×D₂₃₆

yes

characteristic

165

C₂²×C₄

#11745685

yes

characteristic

166

C₂²×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

236

—

173

C₂×C₈

—

236

—

174

C₂×C₈

—

236

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

472

—

177

C₄⋊C₄

—

236

—

178

C₄⋊C₄

—

236

—

179

C₄⋊C₄

—

236

—

180

C₄⋊C₄

—

236

—

181

C₂²⋊C₄

—

182

C₄²

#11745687

yes

—

183

C₄²

#11745687

yes

—

184

C₂³

—

185

C₂³

—

186

C₂³

—

187

C₂³

—

188

C₂³

—

189

C₂³

#14273701

yes

characteristic

190

D₄

—

191

D₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

472

—

199

C₂×C₄

—

472

—

200

C₂×C₄

—

472

—

201

C₂×C₄

#14273708

yes

characteristic

202

C₂×C₄

#14273711

yes

—

203

C₂×C₄

#14273714

yes

characteristic

204

C₂×C₄

#14273720

yes

—

205

C₂×C₄

C₂×Dic₂₃₆

yes

characteristic

206

C₂×C₄

#14273747

yes

—

207

C₂×C₄

#14273749

yes

characteristic

208

C₂×C₄

#14273753

yes

—

209

C₂×C₄

#14273755

yes

—

210

C₈

—

211

C₈

—

212

C₈

—

472

—

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

—

218

C₂²

#16837327

yes

characteristic

219

C₂²

#16837617

yes

—

220

C₂²

#16837643

yes

characteristic

221

C₂²

#16837655

yes

characteristic

222

C₂²

#16837665

yes

—

223

C₄

—

224

C₄

—

225

C₄

—

944

—

226

C₄

#16837723

yes

—

227

C₄

#16837727

yes

—

228

C₄

#16837738

yes

—

229

C₄

#16837756

yes

characteristic

230

C₄

#16837766

yes

characteristic

231

C₂

—

232

C₂

#21423547

yes

—

233

C₂

#21423657

yes

—

234

C₂

#21425509

yes

characteristic

235

C₂

#21425524

yes

characteristic

236

C₂

#21425541

yes

characteristic

	subgroup	G/H
center	C₂³	#14273701
commutator, cosocle	C₂×C₄²×C₅₉	C₂³
Frattini	C₂×C₄²	C₂²×D₅₉
Fitting	C₅₉×#1954	C₂
socle	C₂³×C₅₉	#121
prime radical	C₂²×D₄×C₅₉	D₄
hypercenter	#1954	D₅₉
hypocenter	C₅₉	#10622
LCS	G ▷ C₂×C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1954

subgroup

G/H

center

C₂³

#14273701

commutator, cosocle

C₂×C₄²×C₅₉

C₂³

Frattini

C₂×C₄²

C₂²×D₅₉

Fitting

C₅₉×#1954

C₂

socle

C₂³×C₅₉

#121

prime radical

C₂²×D₄×C₅₉

D₄

D₅₉

C₅₉

G ▷ C₂×C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1954

N	H ≅ G/N	type
1. #21424224	C₂	semidirect
3. #21421980	C₂	semidirect
4. #21421931	C₂	semidirect
133. C₅₉	#10622	semidirect

H ≅ G/N

type

1. #21424224

C₂

semidirect

3. #21421980

C₂

semidirect

4. #21421931

C₂

semidirect

133. C₅₉

#10622

semidirect

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

subgroup	index
#21424224	2
#21424096	2
#21421980	2
#21421931	2
C₅₉×#1954	2
#10622	59

subgroup

index

C₅₉×#1954

Subgroups — #28493428

Conjugacy classes of subgroups

Complements

Maximal subgroups