Group #28491702 — subgroups

Subgroups — #28491702

Order 15104.

504 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 131 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	#21429125	C₂	1	1	yes	maximal, characteristic
2	#21425045	C₂	1	2	yes	maximal
3	#21421979	C₂	1	1	yes	maximal, characteristic
4	#21421936	C₂	1	2	yes	maximal
5	C₅₉×#1956	C₂	1	1	yes	maximal, characteristic
6	C₂×#14273726	—	2	2	no	—
7	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
8	#16837322	—	2	2	no	—
9	#16837298	—	2	2	no	—
10	C₄×C₄⋊Dic₅₉	C₂²	1	2	yes	—
11	#16837164	—	2	2	no	—
12	#16837164	—	2	2	no	—
13	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
14	C₂×#103×C₅₉	—	2	2	no	—
15	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
16	C₅₉×#384	C₂²	1	1	yes	characteristic
17	C₂²×Dic₁₁₈	—	2	2	no	—
18	C₂²×C₅₉⋊C₈	—	2	2	no	—
19	#14273726	—	4	4	no	—
20	#14273726	—	4	4	no	—
21	C₂×C₄⋊Dic₅₉	D₄	1	2	yes	—
22	C₂×C₄⋊Dic₅₉	D₄	1	2	yes	—
23	C₂×Dic₅₉⋊C₄	—	2	4	no	—
24	C₂×C₄×Dic₅₉	—	2	2	no	—
25	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
26	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
27	C₅₉⋊#95	—	2	2	no	—
28	C₅₉⋊#95	—	2	2	no	—
29	C₂²×Q₈×C₅₉	—	2	1	no	—
30	C₂²×C₈×C₅₉	—	2	1	no	—
31	C₄⋊Q₈×C₅₉	—	2	2	no	—
32	C₄⋊Q₈×C₅₉	—	2	1	no	—
33	C₄⋊Q₈×C₅₉	Q₈	1	2	yes	complemented
34	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
35	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
36	C₂×C₄⋊C₄×C₅₉	D₄	1	2	yes	—
37	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
38	#103×C₅₉	—	4	4	no	—
39	C₄×C₈×C₅₉	—	2	2	no	—
40	C₂×Q₈×C₅₉	—	2	2	no	—
41	C₂×Q₈×C₅₉	—	4	2	no	—
42	C₂×Q₈×C₅₉	—	4	2	no	—
43	C₂×Q₈×C₅₉	—	4	1	no	—
44	C₂²×C₄×C₅₉	—	2	2	no	—
45	C₂²×C₄×C₅₉	—	4	1	no	—
46	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
47	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
48	C₂²×Dic₅₉	—	2	2	no	—
49	C₂²×Dic₅₉	—	2	2	no	—
50	C₂×Dic₁₁₈	—	4	8	no	—
51	C₂×Dic₁₁₈	—	8	2	no	—
52	C₂×C₈×C₅₉	—	2	2	no	—
53	C₂×C₈×C₅₉	—	4	1	no	—
54	C₂×C₈×C₅₉	—	4	1	no	—
55	C₄⋊C₄×C₅₉	—	2	4	no	—
56	C₄⋊C₄×C₅₉	—	4	2	no	—
57	C₄⋊C₄×C₅₉	—	4	2	no	—
58	C₄⋊C₄×C₅₉	—	4	2	no	—
59	C₄⋊C₄×C₅₉	—	4	2	no	—
60	C₄²×C₅₉	C₂×Q₈	1	1	yes	characteristic
61	C₄²×C₅₉	#41	1	1	yes	characteristic
62	C₄²×C₅₉	#41	1	2	yes	—
63	C₄⋊Dic₅₉	—	2	2	no	—
64	C₄⋊Dic₅₉	—	2	2	no	—
65	C₄⋊Dic₅₉	SD₁₆	1	4	yes	—
66	C₄⋊Dic₅₉	Q₁₆	1	4	yes	—
67	Dic₅₉⋊C₄	—	4	8	no	—
68	C₄×Dic₅₉	—	4	2	no	—
69	C₄×Dic₅₉	—	4	2	no	—
70	C₂×C₅₉⋊C₈	—	4	2	no	—
71	C₂×C₅₉⋊C₈	—	4	2	no	—
72	C₂×C₅₉⋊C₈	—	4	2	no	—
73	C₂³×C₅₉	#120	1	1	yes	characteristic
74	Q₈×C₅₉	—	4	4	no	—
75	Q₈×C₅₉	—	8	2	no	—
76	C₂×C₄×C₅₉	—	2	1	no	—
77	C₂×C₄×C₅₉	—	2	1	no	—
78	C₂×C₄×C₅₉	—	4	2	no	—
79	C₂×C₄×C₅₉	—	4	4	no	—
80	C₂×C₄×C₅₉	—	4	2	no	—
81	C₂×C₄×C₅₉	—	8	1	no	—
82	C₂×C₄×C₅₉	—	8	1	no	—
83	C₂×C₄×C₅₉	C₂²⋊Q₈	1	2	yes	—
84	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
85	C₂×C₄×C₅₉	#124	1	2	yes	—
86	C₂×C₄×C₅₉	#124	1	1	yes	characteristic
87	C₂×C₄×C₅₉	C₂×SD₁₆	1	2	yes	—
88	C₂×C₄×C₅₉	C₂×Q₁₆	1	2	yes	—
89	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
90	C₂×C₄×C₅₉	#137	1	2	yes	—
91	C₂×Dic₅₉	—	2	4	no	—
92	C₂×Dic₅₉	—	2	4	no	—
93	C₂×Dic₅₉	—	4	2	no	—
94	C₂×Dic₅₉	—	4	2	no	—
95	C₂×Dic₅₉	—	4	2	no	—
96	C₂×Dic₅₉	—	4	2	no	—
97	Dic₁₁₈	—	8	8	no	—
98	C₈×C₅₉	—	4	2	no	—
99	C₅₉⋊C₈	—	8	2	no	—
100	#10349	—	59	1	no	maximal, Sylow
101	C₂²×C₅₉	#393	1	1	yes	characteristic
102	C₂²×C₅₉	#450	1	2	yes	—
103	C₂²×C₅₉	#451	1	2	yes	—
104	C₂²×C₅₉	#453	1	1	yes	characteristic
105	C₂²×C₅₉	#454	1	1	yes	characteristic
106	C₄×C₅₉	—	2	1	no	—
107	C₄×C₅₉	—	2	1	no	—
108	C₄×C₅₉	—	8	2	no	—
109	C₄×C₅₉	—	8	2	no	—
110	C₄×C₅₉	#475	1	2	yes	—
111	C₄×C₅₉	#477	1	2	yes	—
112	C₄×C₅₉	#487	1	2	yes	—
113	C₄×C₅₉	#489	1	2	yes	—
114	Dic₅₉	—	4	4	no	—
115	Dic₅₉	—	4	4	no	—
116	#2551	—	59	1	no	—
117	#1987	—	59	2	no	—
118	#1956	D₅₉	1	1	yes	characteristic
119	#1296	—	59	1	no	—
120	#1279	—	59	2	no	—
121	C₂×C₅₉	#1629	1	1	yes	characteristic
122	C₂×C₅₉	#1633	1	1	yes	characteristic
123	C₂×C₅₉	#1637	1	2	yes	—
124	C₂×C₅₉	#2024	1	2	yes	—
125	C₂×C₅₉	#2027	1	1	yes	characteristic
126	C₂×C₄⋊Q₈	—	118	2	no	—
127	C₂×C₄⋊Q₈	C₂×D₅₉	1	1	yes	characteristic
128	C₂×C₄⋊C₈	—	59	2	no	—
129	C₂×#103	—	2	2	no	—
130	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
131	#395	—	118	2	no	—
132	#389	—	118	2	no	—
133	#384	C₂×D₅₉	1	1	yes	characteristic
134	C₄×C₄⋊C₄	—	59	2	no	—
135	#340	—	118	2	no	—
136	#340	—	118	2	no	—
137	C₅₉	#10349	1	1	yes	characteristic, complemented, Sylow
138	C₂²×Q₈	—	2	1	no	—
139	C₂²×Q₈	—	118	2	no	—
140	C₂²×C₈	—	2	1	no	—
141	C₂²×C₈	—	118	2	no	—
142	C₄⋊Q₈	—	2	1	no	—
143	C₄⋊Q₈	—	2	2	no	—
144	C₄⋊Q₈	—	236	4	no	—
145	C₄⋊Q₈	—	236	4	no	—
146	C₄⋊Q₈	Dic₁₁₈	1	2	yes	complemented
147	C₂×C₄⋊C₄	—	2	2	no	—
148	C₂×C₄⋊C₄	—	2	2	no	—
149	C₂×C₄⋊C₄	—	59	2	no	—
150	C₂×C₄⋊C₄	—	59	2	no	—
151	C₂×C₄⋊C₄	—	118	4	no	—
152	C₂×C₄⋊C₄	C₂²⋊D₅₉	1	2	yes	—
153	C₂×C₄²	—	118	2	no	—
154	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
155	C₄⋊C₈	—	118	2	no	—
156	C₄⋊C₈	—	118	2	no	—
157	#103	—	4	4	no	—
158	C₄×C₈	—	2	2	no	—
159	#95	—	118	2	no	—
160	#95	—	118	2	no	—
161	C₂×Q₈	—	2	2	no	—
162	C₂×Q₈	—	4	2	no	—
163	C₂×Q₈	—	4	2	no	—
164	C₂×Q₈	—	4	1	no	—
165	C₂×Q₈	—	472	2	no	—
166	C₂×Q₈	—	236	8	no	—
167	C₂²×C₄	—	2	2	no	—
168	C₂²×C₄	—	4	1	no	—
169	C₂²×C₄	—	118	2	no	—
170	C₂²×C₄	—	118	2	no	—
171	C₂²×C₄	D₄×D₅₉	1	2	yes	—
172	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
173	C₂×C₈	—	2	2	no	—
174	C₂×C₈	—	4	1	no	—
175	C₂×C₈	—	4	1	no	—
176	C₂×C₈	—	236	2	no	—
177	C₂×C₈	—	236	2	no	—
178	C₂×C₈	—	236	2	no	—
179	C₄⋊C₄	—	2	4	no	—
180	C₄⋊C₄	—	4	2	no	—
181	C₄⋊C₄	—	4	2	no	—
182	C₄⋊C₄	—	4	2	no	—
183	C₄⋊C₄	—	4	2	no	—
184	C₄⋊C₄	—	59	4	no	—
185	C₄⋊C₄	—	59	4	no	—
186	C₄⋊C₄	—	118	2	no	—
187	C₄⋊C₄	—	118	2	no	—
188	C₄⋊C₄	—	236	8	no	—
189	C₄²	—	236	2	no	—
190	C₄²	—	236	2	no	—
191	C₄²	C₂×Dic₁₁₈	1	1	yes	characteristic
192	C₄²	#11745685	1	1	yes	characteristic
193	C₄²	#11745687	1	2	yes	—
194	C₂³	#14273695	1	1	yes	characteristic
195	Q₈	—	4	4	no	—
196	Q₈	—	8	2	no	—
197	Q₈	—	472	8	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	4	4	no	—
201	C₂×C₄	—	4	2	no	—
202	C₂×C₄	—	4	2	no	—
203	C₂×C₄	—	8	1	no	—
204	C₂×C₄	—	8	1	no	—
205	C₂×C₄	—	118	4	no	—
206	C₂×C₄	—	118	4	no	—
207	C₂×C₄	—	236	2	no	—
208	C₂×C₄	—	236	2	no	—
209	C₂×C₄	—	236	2	no	—
210	C₂×C₄	—	236	2	no	—
211	C₂×C₄	#14273704	1	2	yes	—
212	C₂×C₄	#14273706	1	1	yes	characteristic
213	C₂×C₄	#14273713	1	2	yes	—
214	C₂×C₄	#14273714	1	1	yes	characteristic
215	C₂×C₄	SD₁₆×D₅₉	1	2	yes	—
216	C₂×C₄	Q₁₆×D₅₉	1	2	yes	—
217	C₂×C₄	#14273754	1	2	yes	—
218	C₂×C₄	#14273759	1	2	yes	—
219	C₈	—	4	2	no	—
220	C₈	—	472	2	no	—
221	C₂²	#16837314	1	1	yes	characteristic
222	C₂²	#16837551	1	2	yes	—
223	C₂²	#16837556	1	2	yes	—
224	C₂²	#16837569	1	1	yes	characteristic
225	C₂²	#16837574	1	1	yes	characteristic
226	C₄	—	2	1	no	—
227	C₄	—	2	1	no	—
228	C₄	—	8	2	no	—
229	C₄	—	8	2	no	—
230	C₄	—	236	4	no	—
231	C₄	—	236	4	no	—
232	C₄	#16837685	1	2	yes	—
233	C₄	#16837695	1	2	yes	—
234	C₄	#16837751	1	2	yes	—
235	C₄	#16837763	1	2	yes	—
236	C₂	#21423210	1	1	yes	characteristic
237	C₂	#21423234	1	1	yes	characteristic
238	C₂	#21423258	1	2	yes	—
239	C₂	#21425235	1	2	yes	—
240	C₂	#21425252	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#21429125

C₂

yes

maximal, characteristic

#21425045

C₂

yes

maximal

#21421979

C₂

yes

maximal, characteristic

#21421936

C₂

yes

maximal

C₅₉×#1956

C₂

yes

maximal, characteristic

C₂×#14273726

—

C₂×C₄⋊(C₅₉⋊C₈)

C₂²

yes

—

#16837322

—

#16837298

—

C₄×C₄⋊Dic₅₉

C₂²

yes

—

#16837164

—

#16837164

—

C₂×C₄⋊Q₈×C₅₉

C₂²

yes

characteristic

C₂×#103×C₅₉

—

C₂×C₄×C₈×C₅₉

C₂²

yes

characteristic

C₅₉×#384

C₂²

yes

characteristic

C₂²×Dic₁₁₈

—

C₂²×C₅₉⋊C₈

—

#14273726

—

#14273726

—

C₂×C₄⋊Dic₅₉

D₄

yes

—

C₂×C₄⋊Dic₅₉

D₄

yes

—

C₂×Dic₅₉⋊C₄

—

C₂×C₄×Dic₅₉

—

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

—

C₅₉⋊#95

—

C₅₉⋊#95

—

C₂²×Q₈×C₅₉

—

C₂²×C₈×C₅₉

—

C₄⋊Q₈×C₅₉

—

C₄⋊Q₈×C₅₉

—

C₄⋊Q₈×C₅₉

Q₈

yes

complemented

C₂×C₄⋊C₄×C₅₉

—

C₂×C₄⋊C₄×C₅₉

—

C₂×C₄⋊C₄×C₅₉

D₄

yes

—

C₂×C₄²×C₅₉

C₂³

yes

characteristic

#103×C₅₉

—

C₄×C₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₅₉

C₂×D₄

yes

—

C₂²×Dic₅₉

—

C₂²×Dic₅₉

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄²×C₅₉

C₂×Q₈

yes

C₄²×C₅₉

yes

C₄²×C₅₉

yes

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

SD₁₆

yes

—

C₄⋊Dic₅₉

Q₁₆

yes

—

Dic₅₉⋊C₄

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂³×C₅₉

#120

yes

characteristic

Q₈×C₅₉

—

Q₈×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₅₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₅₉

#124

yes

—

C₂×C₄×C₅₉

#124

yes

characteristic

C₂×C₄×C₅₉

C₂×SD₁₆

yes

—

C₂×C₄×C₅₉

C₂×Q₁₆

yes

—

C₂×C₄×C₅₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₅₉

#137

yes

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

Dic₁₁₈

—

C₈×C₅₉

—

C₅₉⋊C₈

—

100

#10349

—

maximal, Sylow

101

C₂²×C₅₉

#393

yes

characteristic

102

C₂²×C₅₉

#450

yes

—

103

C₂²×C₅₉

#451

yes

—

104

C₂²×C₅₉

#453

yes

characteristic

105

C₂²×C₅₉

#454

yes

characteristic

106

C₄×C₅₉

—

107

C₄×C₅₉

—

108

C₄×C₅₉

—

109

C₄×C₅₉

—

110

C₄×C₅₉

#475

yes

—

111

C₄×C₅₉

#477

yes

—

112

C₄×C₅₉

#487

yes

—

113

C₄×C₅₉

#489

yes

—

114

Dic₅₉

—

115

Dic₅₉

—

116

#2551

—

117

#1987

—

118

#1956

D₅₉

yes

characteristic

119

#1296

—

120

#1279

—

121

C₂×C₅₉

#1629

yes

characteristic

122

C₂×C₅₉

#1633

yes

characteristic

123

C₂×C₅₉

#1637

yes

—

124

C₂×C₅₉

#2024

yes

—

125

C₂×C₅₉

#2027

yes

characteristic

126

C₂×C₄⋊Q₈

—

118

—

127

C₂×C₄⋊Q₈

C₂×D₅₉

yes

characteristic

128

C₂×C₄⋊C₈

—

129

C₂×#103

—

130

C₂×C₄×C₈

C₂×D₅₉

yes

characteristic

131

#395

—

118

—

132

#389

—

118

—

133

#384

C₂×D₅₉

yes

characteristic

134

C₄×C₄⋊C₄

—

135

#340

—

118

—

136

#340

—

118

—

137

C₅₉

#10349

yes

characteristic, complemented, Sylow

138

C₂²×Q₈

—

139

C₂²×Q₈

—

118

—

140

C₂²×C₈

—

141

C₂²×C₈

—

118

—

142

C₄⋊Q₈

—

143

C₄⋊Q₈

—

144

C₄⋊Q₈

—

236

—

145

C₄⋊Q₈

—

236

—

146

C₄⋊Q₈

Dic₁₁₈

yes

complemented

147

C₂×C₄⋊C₄

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

—

118

—

152

C₂×C₄⋊C₄

C₂²⋊D₅₉

yes

—

153

C₂×C₄²

—

118

—

154

C₂×C₄²

C₂²×D₅₉

yes

characteristic

155

C₄⋊C₈

—

118

—

156

C₄⋊C₈

—

118

—

157

#103

—

158

C₄×C₈

—

159

#95

—

118

—

160

#95

—

118

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

472

—

166

C₂×Q₈

—

236

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

—

118

—

170

C₂²×C₄

—

118

—

171

C₂²×C₄

D₄×D₅₉

yes

—

172

C₂²×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

236

—

177

C₂×C₈

—

236

—

178

C₂×C₈

—

236

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

118

—

187

C₄⋊C₄

—

118

—

188

C₄⋊C₄

—

236

—

189

C₄²

—

236

—

190

C₄²

—

236

—

191

C₄²

C₂×Dic₁₁₈

yes

characteristic

192

C₄²

#11745685

yes

characteristic

193

C₄²

#11745687

yes

—

194

C₂³

#14273695

yes

characteristic

195

Q₈

—

196

Q₈

—

197

Q₈

—

472

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

118

—

206

C₂×C₄

—

118

—

207

C₂×C₄

—

236

—

208

C₂×C₄

—

236

—

209

C₂×C₄

—

236

—

210

C₂×C₄

—

236

—

211

C₂×C₄

#14273704

yes

—

212

C₂×C₄

#14273706

yes

characteristic

213

C₂×C₄

#14273713

yes

—

214

C₂×C₄

#14273714

yes

characteristic

215

C₂×C₄

SD₁₆×D₅₉

yes

—

216

C₂×C₄

Q₁₆×D₅₉

yes

—

217

C₂×C₄

#14273754

yes

—

218

C₂×C₄

#14273759

yes

—

219

C₈

—

220

C₈

—

472

—

221

C₂²

#16837314

yes

characteristic

222

C₂²

#16837551

yes

—

223

C₂²

#16837556

yes

—

224

C₂²

#16837569

yes

characteristic

225

C₂²

#16837574

yes

characteristic

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

236

—

231

C₄

—

236

—

232

C₄

#16837685

yes

—

233

C₄

#16837695

yes

—

234

C₄

#16837751

yes

—

235

C₄

#16837763

yes

—

236

C₂

#21423210

yes

characteristic

237

C₂

#21423234

yes

characteristic

238

C₂

#21423258

yes

—

239

C₂

#21425235

yes

—

240

C₂

#21425252

yes

characteristic

	subgroup	G/H
center	C₂³	#14273695
commutator, cosocle	C₂×C₄²×C₅₉	C₂³
Frattini	C₂×C₄²	C₂²×D₅₉
Fitting	C₅₉×#1956	C₂
socle, prime radical	C₂³×C₅₉	#120
hypercenter	#1956	D₅₉
hypocenter	C₅₉	#10349
LCS	G ▷ C₂×C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1956

subgroup

G/H

center

C₂³

#14273695

commutator, cosocle

C₂×C₄²×C₅₉

C₂³

Frattini

C₂×C₄²

C₂²×D₅₉

Fitting

C₅₉×#1956

C₂

C₂³×C₅₉

D₅₉

C₅₉

G ▷ C₂×C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1956

N	H ≅ G/N	type
33. C₄⋊Q₈×C₅₉	Q₈	semidirect
137. C₅₉	#10349	semidirect
146. C₄⋊Q₈	Dic₁₁₈	semidirect

H ≅ G/N

type

33. C₄⋊Q₈×C₅₉

Q₈

semidirect

137. C₅₉

#10349

semidirect

146. C₄⋊Q₈

Dic₁₁₈

semidirect

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

subgroup	index
#21429125	2
#21425045	2
#21421979	2
#21421936	2
C₅₉×#1956	2
#10349	59

subgroup

index

C₅₉×#1956

Subgroups — #28491702

Conjugacy classes of subgroups

Complements

Maximal subgroups