Group #28491822 — subgroups

Subgroups — #28491822

Order 15104.

416 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 99 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	#21427389	C₂	1	1	yes	maximal, characteristic
2	#21422595	C₂	1	2	yes	maximal
3	#21421997	C₂	1	2	yes	maximal
4	#21421925	C₂	1	1	yes	maximal, characteristic
5	C₅₉×#1995	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₁₁₈	—	2	1	no	—
7	#16837455	C₂²	1	2	yes	—
8	#16837334	—	2	2	no	—
9	#16837323	—	2	2	no	—
10	C₄×C₄⋊Dic₅₉	—	2	1	no	—
11	C₄×C₄⋊Dic₅₉	C₂²	1	2	yes	—
12	#16837139	—	2	2	no	—
13	#16837139	—	2	2	no	—
14	C₅₉×#533	C₂²	1	1	yes	characteristic
15	C₅₉×#423	C₂²	1	1	yes	characteristic
16	C₅₉×#376	C₂²	1	1	yes	characteristic
17	C₅₉×#339	—	2	1	no	—
18	C₅₉×#339	—	2	1	no	—
19	C₂²×Dic₁₁₈	—	2	1	no	—
20	C₄×Dic₁₁₈	—	4	2	no	—
21	C₄×Dic₁₁₈	—	4	2	no	—
22	C₂×C₄⋊Dic₅₉	—	2	2	no	—
23	C₂×C₄⋊Dic₅₉	—	2	1	no	—
24	C₂×C₄⋊Dic₅₉	—	2	2	no	—
25	C₂×Dic₅₉⋊C₄	—	2	2	no	—
26	C₂×C₄×Dic₅₉	—	2	2	no	—
27	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
28	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
29	C₄×C₅₉⋊C₈	—	2	2	no	—
30	C₅₉⋊#95	—	2	1	no	—
31	C₅₉⋊#95	—	2	1	no	—
32	C₅₉⋊#95	D₄	1	2	yes	—
33	C₅₉⋊#95	D₄	1	2	yes	—
34	C₂×M₁₆×C₅₉	—	2	1	no	—
35	C₄⋊Q₈×C₅₉	Q₈	1	2	yes	complemented
36	#125×C₅₉	—	2	1	no	—
37	C₂²⋊Q₈×C₅₉	—	2	2	no	—
38	C₄×Q₈×C₅₉	—	2	2	no	—
39	#117×C₅₉	—	2	1	no	—
40	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
43	C₄⋊C₈×C₅₉	—	2	2	no	—
44	#95×C₅₉	—	2	2	no	—
45	C₂×Q₈×C₅₉	—	2	2	no	—
46	C₂²×C₄×C₅₉	—	2	1	no	—
47	C₂²×C₄×C₅₉	—	2	1	no	—
48	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
49	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
50	C₂²×Dic₅₉	—	2	2	no	—
51	C₂²×Dic₅₉	—	2	2	no	—
52	C₂×Dic₁₁₈	—	4	4	no	—
53	C₂×Dic₁₁₈	—	4	2	no	—
54	M₁₆×C₅₉	—	4	1	no	—
55	M₁₆×C₅₉	—	4	1	no	—
56	C₂×C₈×C₅₉	—	4	1	no	—
57	C₄⋊C₄×C₅₉	—	2	2	no	—
58	C₄⋊C₄×C₅₉	—	2	2	no	—
59	C₄⋊C₄×C₅₉	—	4	2	no	—
60	C₂²⋊C₄×C₅₉	—	4	1	no	—
61	C₄²×C₅₉	—	2	1	no	—
62	C₄²×C₅₉	—	2	1	no	—
63	C₄²×C₅₉	—	4	1	no	—
64	C₄²×C₅₉	SD₁₆	1	2	yes	—
65	C₄²×C₅₉	Q₁₆	1	2	yes	—
66	C₄²×C₅₉	C₂×Q₈	1	1	yes	characteristic
67	C₄²×C₅₉	#41	1	1	yes	characteristic
68	C₄²×C₅₉	#41	1	2	yes	—
69	C₄⋊Dic₅₉	—	4	4	no	—
70	C₄⋊Dic₅₉	—	4	4	no	—
71	C₄⋊Dic₅₉	—	4	2	no	—
72	Dic₅₉⋊C₄	—	4	4	no	—
73	C₄×Dic₅₉	—	4	2	no	—
74	C₄×Dic₅₉	—	4	2	no	—
75	C₂×C₅₉⋊C₈	—	4	2	no	—
76	C₂³×C₅₉	#120	1	1	yes	characteristic
77	Q₈×C₅₉	—	8	2	no	—
78	C₂×C₄×C₅₉	—	2	2	no	—
79	C₂×C₄×C₅₉	—	2	2	no	—
80	C₂×C₄×C₅₉	—	4	2	no	—
81	C₂×C₄×C₅₉	—	4	2	no	—
82	C₂×C₄×C₅₉	—	4	2	no	—
83	C₂×C₄×C₅₉	—	4	2	no	—
84	C₂×C₄×C₅₉	C₂²⋊Q₈	1	2	yes	—
85	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
86	C₂×C₄×C₅₉	#124	1	2	yes	—
87	C₂×C₄×C₅₉	#124	1	1	yes	characteristic
88	C₂×C₄×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
89	C₂×C₄×C₅₉	C₂×Q₁₆	1	1	yes	characteristic
90	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
91	C₂×C₄×C₅₉	#137	1	1	yes	characteristic
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	C₂×Dic₅₉	—	4	2	no	—
98	Dic₁₁₈	—	4	8	no	—
99	C₈×C₅₉	—	8	1	no	—
100	C₅₉⋊C₈	—	8	2	no	—
101	#10371	—	59	1	no	maximal, Sylow
102	C₂²×C₅₉	—	2	2	no	—
103	C₂²×C₅₉	#393	1	1	yes	characteristic
104	C₂²×C₅₉	#450	1	1	yes	characteristic
105	C₂²×C₅₉	#451	1	1	yes	characteristic
106	C₄×C₅₉	—	2	2	no	—
107	C₄×C₅₉	—	2	2	no	—
108	C₄×C₅₉	—	4	2	no	—
109	C₄×C₅₉	—	4	2	no	—
110	C₄×C₅₉	—	8	2	no	—
111	C₄×C₅₉	#475	1	1	yes	characteristic
112	C₄×C₅₉	#477	1	1	yes	characteristic
113	C₄×C₅₉	#487	1	1	yes	characteristic
114	C₄×C₅₉	#489	1	1	yes	characteristic
115	Dic₅₉	—	4	4	no	—
116	Dic₅₉	—	8	2	no	—
117	#2399	—	59	1	no	—
118	#1995	D₅₉	1	1	yes	characteristic
119	#1503	—	59	2	no	—
120	#1303	—	59	2	no	—
121	#1274	—	59	1	no	—
122	C₂×C₅₉	—	2	1	no	—
123	C₂×C₅₉	—	2	1	no	—
124	C₂×C₅₉	#2024	1	1	yes	characteristic
125	C₂×C₅₉	#2031	1	2	yes	—
126	#533	C₂×D₅₉	1	1	yes	characteristic
127	C₂×C₄×Q₈	—	118	1	no	—
128	#431	—	59	2	no	—
129	#423	C₂×D₅₉	1	1	yes	characteristic
130	#398	—	118	2	no	—
131	#395	—	118	2	no	—
132	C₄×C₄⋊C₄	—	59	2	no	—
133	C₄×C₄⋊C₄	—	118	1	no	—
134	#376	C₂×D₅₉	1	1	yes	characteristic
135	#339	—	2	1	no	—
136	#339	—	2	1	no	—
137	#328	—	118	2	no	—
138	#328	—	118	2	no	—
139	C₅₉	#10371	1	1	yes	characteristic, complemented, Sylow
140	C₂²×Q₈	—	118	1	no	—
141	C₂×M₁₆	—	2	1	no	—
142	C₄⋊Q₈	Dic₁₁₈	1	2	yes	complemented
143	#125	—	2	1	no	—
144	C₂²⋊Q₈	—	2	2	no	—
145	C₄×Q₈	—	2	2	no	—
146	C₄×Q₈	—	236	2	no	—
147	C₄×Q₈	—	236	2	no	—
148	#117	—	2	1	no	—
149	C₂×C₄⋊C₄	—	118	2	no	—
150	C₂×C₄⋊C₄	—	118	1	no	—
151	C₂×C₄⋊C₄	—	118	2	no	—
152	C₂×C₄⋊C₄	—	118	2	no	—
153	C₂×C₄²	—	118	2	no	—
154	C₂×C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
155	C₂×C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
156	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
157	C₄⋊C₈	—	2	2	no	—
158	C₄⋊C₈	—	118	2	no	—
159	C₂²⋊C₈	—	118	2	no	—
160	C₄×C₈	—	118	2	no	—
161	#95	—	2	2	no	—
162	#95	—	59	2	no	—
163	#95	—	59	2	no	—
164	#95	—	118	1	no	—
165	#95	—	118	1	no	—
166	C₂×Q₈	—	2	2	no	—
167	C₂×Q₈	—	236	2	no	—
168	C₂×Q₈	—	236	4	no	—
169	C₂²×C₄	—	2	1	no	—
170	C₂²×C₄	—	2	1	no	—
171	C₂²×C₄	—	118	2	no	—
172	C₂²×C₄	—	118	2	no	—
173	C₂²×C₄	D₄×D₅₉	1	2	yes	—
174	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
175	M₁₆	—	4	1	no	—
176	M₁₆	—	4	1	no	—
177	C₂×C₈	—	4	1	no	—
178	C₂×C₈	—	236	2	no	—
179	C₄⋊C₄	—	2	2	no	—
180	C₄⋊C₄	—	2	2	no	—
181	C₄⋊C₄	—	4	2	no	—
182	C₄⋊C₄	—	236	4	no	—
183	C₄⋊C₄	—	236	2	no	—
184	C₄⋊C₄	—	236	4	no	—
185	C₄⋊C₄	—	236	4	no	—
186	C₂²⋊C₄	—	4	1	no	—
187	C₄²	—	2	1	no	—
188	C₄²	—	2	1	no	—
189	C₄²	—	4	1	no	—
190	C₄²	—	236	2	no	—
191	C₄²	—	236	2	no	—
192	C₄²	#11745671	1	2	yes	—
193	C₄²	#11745672	1	2	yes	—
194	C₄²	C₂×Dic₁₁₈	1	1	yes	characteristic
195	C₄²	#11745685	1	1	yes	characteristic
196	C₄²	#11745687	1	2	yes	—
197	C₂³	#14273695	1	1	yes	characteristic
198	Q₈	—	8	2	no	—
199	Q₈	—	236	8	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	4	2	no	—
203	C₂×C₄	—	4	2	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	—	4	2	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	—	236	2	no	—
212	C₂×C₄	#14273704	1	2	yes	—
213	C₂×C₄	#14273706	1	1	yes	characteristic
214	C₂×C₄	#14273713	1	2	yes	—
215	C₂×C₄	#14273714	1	1	yes	characteristic
216	C₂×C₄	C₂×#11745671	1	1	yes	characteristic
217	C₂×C₄	C₂×#11745672	1	1	yes	characteristic
218	C₂×C₄	#14273752	1	1	yes	characteristic
219	C₂×C₄	#14273757	1	1	yes	characteristic
220	C₈	—	8	1	no	—
221	C₈	—	472	2	no	—
222	C₂²	—	2	2	no	—
223	C₂²	#16837314	1	1	yes	characteristic
224	C₂²	#16837552	1	1	yes	characteristic
225	C₂²	#16837557	1	1	yes	characteristic
226	C₄	—	2	2	no	—
227	C₄	—	2	2	no	—
228	C₄	—	4	2	no	—
229	C₄	—	4	2	no	—
230	C₄	—	8	2	no	—
231	C₄	—	472	2	no	—
232	C₄	—	236	4	no	—
233	C₄	#16837687	1	1	yes	characteristic
234	C₄	#16837697	1	1	yes	characteristic
235	C₄	#16837752	1	1	yes	characteristic
236	C₄	#16837761	1	1	yes	characteristic
237	C₂	—	2	1	no	—
238	C₂	—	2	1	no	—
239	C₂	#21425237	1	1	yes	characteristic
240	C₂	#21425266	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#21427389

C₂

yes

maximal, characteristic

#21422595

C₂

yes

maximal

#21421997

C₂

yes

maximal

#21421925

C₂

yes

maximal, characteristic

C₅₉×#1995

C₂

yes

maximal, characteristic

C₂×C₄×Dic₁₁₈

—

#16837455

C₂²

yes

—

#16837334

—

#16837323

—

C₄×C₄⋊Dic₅₉

—

C₄×C₄⋊Dic₅₉

C₂²

yes

—

#16837139

—

#16837139

—

C₅₉×#533

C₂²

yes

characteristic

C₅₉×#423

C₂²

yes

characteristic

C₅₉×#376

C₂²

yes

characteristic

C₅₉×#339

—

C₅₉×#339

—

C₂²×Dic₁₁₈

—

C₄×Dic₁₁₈

—

C₄×Dic₁₁₈

—

C₂×C₄⋊Dic₅₉

—

C₂×C₄⋊Dic₅₉

—

C₂×C₄⋊Dic₅₉

—

C₂×Dic₅₉⋊C₄

—

C₂×C₄×Dic₅₉

—

C₄⋊(C₅₉⋊C₈)

—

C₂²⋊(C₅₉⋊C₈)

—

C₄×C₅₉⋊C₈

—

C₅₉⋊#95

—

C₅₉⋊#95

—

C₅₉⋊#95

D₄

yes

—

C₅₉⋊#95

D₄

yes

—

C₂×M₁₆×C₅₉

—

C₄⋊Q₈×C₅₉

Q₈

yes

complemented

#125×C₅₉

—

C₂²⋊Q₈×C₅₉

—

C₄×Q₈×C₅₉

—

#117×C₅₉

—

C₂×C₄²×C₅₉

D₄

yes

characteristic

C₂×C₄²×C₅₉

D₄

yes

characteristic

C₂×C₄²×C₅₉

C₂³

yes

characteristic

C₄⋊C₈×C₅₉

—

#95×C₅₉

—

C₂×Q₈×C₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

C₂×D₄

yes

—

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂²×Dic₅₉

—

C₂²×Dic₅₉

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

M₁₆×C₅₉

—

M₁₆×C₅₉

—

C₂×C₈×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₂²⋊C₄×C₅₉

—

C₄²×C₅₉

—

C₄²×C₅₉

—

C₄²×C₅₉

—

C₄²×C₅₉

SD₁₆

yes

—

C₄²×C₅₉

Q₁₆

yes

—

C₄²×C₅₉

C₂×Q₈

yes

C₄²×C₅₉

yes

C₄²×C₅₉

yes

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

Dic₅₉⋊C₄

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

C₂×C₅₉⋊C₈

—

C₂³×C₅₉

#120

yes

characteristic

Q₈×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

characteristic

C₂×C₄×C₅₉

C₂×Q₁₆

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

Dic₁₁₈

—

C₈×C₅₉

—

100

C₅₉⋊C₈

—

101

#10371

—

maximal, Sylow

102

C₂²×C₅₉

—

103

C₂²×C₅₉

#393

yes

characteristic

104

C₂²×C₅₉

#450

yes

characteristic

105

C₂²×C₅₉

#451

yes

characteristic

106

C₄×C₅₉

—

107

C₄×C₅₉

—

108

C₄×C₅₉

—

109

C₄×C₅₉

—

110

C₄×C₅₉

—

111

C₄×C₅₉

#475

yes

characteristic

112

C₄×C₅₉

#477

yes

characteristic

113

C₄×C₅₉

#487

yes

characteristic

114

C₄×C₅₉

#489

yes

characteristic

115

Dic₅₉

—

116

Dic₅₉

—

117

#2399

—

118

#1995

D₅₉

yes

characteristic

119

#1503

—

120

#1303

—

121

#1274

—

122

C₂×C₅₉

—

123

C₂×C₅₉

—

124

C₂×C₅₉

#2024

yes

characteristic

125

C₂×C₅₉

#2031

yes

—

126

#533

C₂×D₅₉

yes

characteristic

127

C₂×C₄×Q₈

—

118

—

128

#431

—

129

#423

C₂×D₅₉

yes

characteristic

130

#398

—

118

—

131

#395

—

118

—

132

C₄×C₄⋊C₄

—

133

C₄×C₄⋊C₄

—

118

—

134

#376

C₂×D₅₉

yes

characteristic

135

#339

—

136

#339

—

137

#328

—

118

—

138

#328

—

118

—

139

C₅₉

#10371

yes

characteristic, complemented, Sylow

140

C₂²×Q₈

—

118

—

141

C₂×M₁₆

—

142

C₄⋊Q₈

Dic₁₁₈

yes

complemented

143

#125

—

144

C₂²⋊Q₈

—

145

C₄×Q₈

—

146

C₄×Q₈

—

236

—

147

C₄×Q₈

—

236

—

148

#117

—

149

C₂×C₄⋊C₄

—

118

—

150

C₂×C₄⋊C₄

—

118

—

151

C₂×C₄⋊C₄

—

118

—

152

C₂×C₄⋊C₄

—

118

—

153

C₂×C₄²

—

118

—

154

C₂×C₄²

C₂²⋊D₅₉

yes

characteristic

155

C₂×C₄²

C₂²⋊D₅₉

yes

characteristic

156

C₂×C₄²

C₂²×D₅₉

yes

characteristic

157

C₄⋊C₈

—

158

C₄⋊C₈

—

118

—

159

C₂²⋊C₈

—

118

—

160

C₄×C₈

—

118

—

161

#95

—

162

#95

—

163

#95

—

164

#95

—

118

—

165

#95

—

118

—

166

C₂×Q₈

—

167

C₂×Q₈

—

236

—

168

C₂×Q₈

—

236

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

—

118

—

172

C₂²×C₄

—

118

—

173

C₂²×C₄

D₄×D₅₉

yes

—

174

C₂²×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

175

M₁₆

—

176

M₁₆

—

177

C₂×C₈

—

178

C₂×C₈

—

236

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

236

—

183

C₄⋊C₄

—

236

—

184

C₄⋊C₄

—

236

—

185

C₄⋊C₄

—

236

—

186

C₂²⋊C₄

—

187

C₄²

—

188

C₄²

—

189

C₄²

—

190

C₄²

—

236

—

191

C₄²

—

236

—

192

C₄²

#11745671

yes

—

193

C₄²

#11745672

yes

—

194

C₄²

C₂×Dic₁₁₈

yes

characteristic

195

C₄²

#11745685

yes

characteristic

196

C₄²

#11745687

yes

—

197

C₂³

#14273695

yes

characteristic

198

Q₈

—

199

Q₈

—

236

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

118

—

207

C₂×C₄

—

236

—

208

C₂×C₄

—

236

—

209

C₂×C₄

—

236

—

210

C₂×C₄

—

236

—

211

C₂×C₄

—

236

—

212

C₂×C₄

#14273704

yes

—

213

C₂×C₄

#14273706

yes

characteristic

214

C₂×C₄

#14273713

yes

—

215

C₂×C₄

#14273714

yes

characteristic

216

C₂×C₄

C₂×#11745671

yes

characteristic

217

C₂×C₄

C₂×#11745672

yes

characteristic

218

C₂×C₄

#14273752

yes

characteristic

219

C₂×C₄

#14273757

yes

characteristic

220

C₈

—

221

C₈

—

472

—

222

C₂²

—

223

C₂²

#16837314

yes

characteristic

224

C₂²

#16837552

yes

characteristic

225

C₂²

#16837557

yes

characteristic

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

472

—

232

C₄

—

236

—

233

C₄

#16837687

yes

characteristic

234

C₄

#16837697

yes

characteristic

235

C₄

#16837752

yes

characteristic

236

C₄

#16837761

yes

characteristic

237

C₂

—

238

C₂

—

239

C₂

#21425237

yes

characteristic

240

C₂

#21425266

yes

—

	subgroup	G/H
center	C₂×C₄	#14273714
commutator, cosocle	C₂×C₄²×C₅₉	C₂³
Frattini	C₂×C₄²	C₂²×D₅₉
Fitting	C₅₉×#1995	C₂
socle	C₂²×C₅₉	#393
prime radical	C₂³×C₅₉	#120
hypercenter	#1995	D₅₉
hypocenter	C₅₉	#10371
LCS	G ▷ C₂×C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1995

subgroup

G/H

center

C₂×C₄

#14273714

commutator, cosocle

C₂×C₄²×C₅₉

C₂³

Frattini

C₂×C₄²

C₂²×D₅₉

Fitting

C₅₉×#1995

C₂

C₂²×C₅₉

C₂³×C₅₉

D₅₉

C₅₉

G ▷ C₂×C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1995

N	H ≅ G/N	type
35. C₄⋊Q₈×C₅₉	Q₈	semidirect
139. C₅₉	#10371	semidirect
142. C₄⋊Q₈	Dic₁₁₈	semidirect

H ≅ G/N

type

35. C₄⋊Q₈×C₅₉

Q₈

semidirect

139. C₅₉

#10371

semidirect

142. C₄⋊Q₈

Dic₁₁₈

semidirect

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

subgroup	index
#21427389	2
#21422595	2
#21421997	2
#21421925	2
C₅₉×#1995	2
#10371	59

subgroup

index

C₅₉×#1995

Subgroups — #28491822

Conjugacy classes of subgroups

Complements

Maximal subgroups