Group #26132839 — subgroups

Subgroups — #26132839

Order 12032.

414 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 127 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×#15689161	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688947	C₂	1	2	yes	maximal, complemented
3	#20244999	C₂	1	1	yes	maximal, characteristic
4	#20241488	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1810	C₂	1	1	yes	maximal, characteristic
6	C₂×#13093983	—	2	1	no	—
7	C₂×#13093964	C₂²	1	2	yes	—
8	#15689161	—	2	4	no	—
9	C₂×#13093958	—	2	1	no	—
10	C₂×#13093956	C₂²	1	2	yes	—
11	#15688947	—	2	4	no	—
12	C₂²⋊(C₄₇⋊C₁₆)	C₄	1	4	yes	complemented
13	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
16	C₄₇×#407	—	2	1	no	—
17	C₄₇×#341	—	2	1	no	—
18	#13093983	—	2	4	no	—
19	#13093983	—	4	2	no	—
20	C₂×C₄⋊Dic₄₇	—	2	2	no	—
21	C₂×C₂²⋊Dic₄₇	—	4	1	no	—
22	C₂×C₄×Dic₄₇	—	4	1	no	—
23	#13093964	—	2	2	no	—
24	#13093964	—	2	2	no	—
25	C₂×C₄₇⋊C₁₆	C₂×C₄	1	4	yes	—
26	#13093958	—	2	4	no	—
27	#13093956	—	2	2	no	—
28	#13093956	D₄	1	4	yes	—
29	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
30	C₂×M₁₆×C₄₇	—	2	1	no	—
31	C₂×M₁₆×C₄₇	—	2	1	no	—
32	C₂²×C₈×C₄₇	—	2	2	no	—
33	C₂²×C₈×C₄₇	—	2	2	no	—
34	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
35	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
36	C₂²×C₈×C₄₇	Q₈	1	2	yes	—
37	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
38	#108×C₄₇	—	2	2	no	—
39	#108×C₄₇	—	2	2	no	—
40	C₂²⋊C₈×C₄₇	—	4	2	no	—
41	C₂⁴×C₄₇	SD₁₆	1	1	yes	characteristic
42	C₂²×C₄×C₄₇	—	2	1	no	—
43	C₂²×C₄×C₄₇	—	2	1	no	—
44	C₂²×C₄×C₄₇	—	2	1	no	—
45	C₂²×C₄×C₄₇	—	2	1	no	—
46	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
47	C₂²×C₄×C₄₇	SD₁₆	1	1	yes	characteristic
48	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
49	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
50	C₂²×Dic₄₇	—	4	2	no	—
51	M₁₆×C₄₇	—	4	1	no	—
52	M₁₆×C₄₇	—	4	1	no	—
53	M₁₆×C₄₇	—	4	1	no	—
54	M₁₆×C₄₇	—	4	1	no	—
55	C₂×C₈×C₄₇	—	2	1	no	—
56	C₂×C₈×C₄₇	—	2	1	no	—
57	C₂×C₈×C₄₇	—	2	4	no	—
58	C₂×C₈×C₄₇	—	2	4	no	—
59	C₂×C₈×C₄₇	—	4	1	no	—
60	C₂×C₈×C₄₇	—	4	1	no	—
61	C₂×C₈×C₄₇	C₄⋊C₄	1	2	yes	—
62	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
63	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
64	C₂×C₈×C₄₇	C₂×Q₈	1	1	yes	characteristic
65	C₂×C₈×C₄₇	#41	1	2	yes	—
66	C₂²⋊Dic₄₇	—	4	4	no	—
67	C₄⋊Dic₄₇	—	2	4	no	—
68	C₄⋊Dic₄₇	—	4	2	no	—
69	C₄×Dic₄₇	—	4	4	no	—
70	C₄₇⋊C₁₆	—	2	4	no	—
71	C₂³×C₄₇	—	2	1	no	—
72	C₂³×C₄₇	—	2	1	no	—
73	C₂³×C₄₇	—	4	2	no	—
74	C₂³×C₄₇	#106	1	2	yes	—
75	C₂³×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
76	C₂×C₄×C₄₇	—	2	1	no	—
77	C₂×C₄×C₄₇	—	2	1	no	—
78	C₂×C₄×C₄₇	—	2	2	no	—
79	C₂×C₄×C₄₇	—	2	2	no	—
80	C₂×C₄×C₄₇	—	2	2	no	—
81	C₂×C₄×C₄₇	—	2	2	no	—
82	C₂×C₄×C₄₇	#106	1	2	yes	—
83	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
85	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
86	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
87	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
88	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
89	C₂×Dic₄₇	—	4	4	no	—
90	C₂×Dic₄₇	—	8	4	no	—
91	C₈×C₄₇	—	2	2	no	—
92	C₈×C₄₇	—	8	1	no	—
93	C₈×C₄₇	—	8	1	no	—
94	C₈×C₄₇	C₄×D₄	1	2	yes	—
95	C₈×C₄₇	C₂²⋊Q₈	1	2	yes	—
96	#12930	—	47	1	no	maximal, Sylow
97	C₂²×C₄₇	—	2	2	no	—
98	C₂²×C₄₇	—	2	2	no	—
99	C₂²×C₄₇	—	2	4	no	—
100	C₂²×C₄₇	—	4	2	no	—
101	C₂²×C₄₇	—	4	2	no	—
102	C₂²×C₄₇	C₂×#106	1	1	yes	characteristic
103	C₂²×C₄₇	#450	1	1	yes	characteristic
104	C₂²×C₄₇	#483	1	1	yes	characteristic
105	C₄×C₄₇	—	2	2	no	—
106	C₄×C₄₇	#385	1	1	yes	characteristic
107	C₄×C₄₇	#428	1	1	yes	characteristic
108	C₄×C₄₇	#448	1	1	yes	characteristic
109	C₄×C₄₇	#481	1	1	yes	characteristic
110	Dic₄₇	—	8	4	no	—
111	C₂×#427	—	47	1	no	—
112	C₂×#365	—	47	2	no	—
113	#2112	—	47	1	no	—
114	#1810	D₄₇	1	1	yes	characteristic
115	#1383	—	47	2	no	—
116	C₂×C₄₇	—	2	1	no	—
117	C₂×C₄₇	—	2	1	no	—
118	C₂×C₄₇	—	4	2	no	—
119	C₂×C₄₇	#1853	1	1	yes	characteristic
120	C₂×C₄₇	#2155	1	2	yes	—
121	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
122	C₂×#117	—	94	1	no	—
123	C₂×M₃₂	—	47	2	no	—
124	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
125	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
126	#427	—	94	4	no	—
127	C₂×#107	—	94	1	no	—
128	C₂×#106	—	47	2	no	—
129	#407	—	2	1	no	—
130	#365	—	94	4	no	—
131	C₂²⋊C₁₆	—	47	4	no	—
132	#341	—	2	1	no	—
133	C₄₇	#12930	1	1	yes	characteristic, complemented, Sylow
134	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
135	C₂×M₁₆	—	2	1	no	—
136	C₂×M₁₆	—	2	1	no	—
137	C₂²×C₈	—	2	2	no	—
138	C₂²×C₈	—	2	2	no	—
139	C₂²×C₈	Dic₉₄	1	2	yes	—
140	C₂²×C₈	C₄×D₄₇	1	2	yes	—
141	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
142	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
143	#117	—	94	4	no	—
144	#117	—	188	2	no	—
145	C₂×C₄⋊C₄	—	94	2	no	—
146	C₂×C₂²⋊C₄	—	188	1	no	—
147	C₂×C₄²	—	188	1	no	—
148	M₃₂	—	94	2	no	—
149	M₃₂	—	94	2	no	—
150	C₂×C₁₆	—	47	4	no	—
151	#108	—	2	2	no	—
152	#108	—	2	2	no	—
153	#107	—	94	4	no	—
154	#106	—	47	4	no	—
155	#106	—	94	2	no	—
156	C₂²⋊C₈	—	4	2	no	—
157	C₂⁴	#10625336	1	1	yes	characteristic
158	C₂²×C₄	—	2	1	no	—
159	C₂²×C₄	—	2	1	no	—
160	C₂²×C₄	—	2	1	no	—
161	C₂²×C₄	—	2	1	no	—
162	C₂²×C₄	—	188	2	no	—
163	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
164	C₂²×C₄	#10625335	1	2	yes	—
165	C₂²×C₄	#10625336	1	1	yes	characteristic
166	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
167	M₁₆	—	4	1	no	—
168	M₁₆	—	4	1	no	—
169	M₁₆	—	4	1	no	—
170	M₁₆	—	4	1	no	—
171	C₂×C₈	—	2	1	no	—
172	C₂×C₈	—	2	1	no	—
173	C₂×C₈	—	2	4	no	—
174	C₂×C₈	—	2	4	no	—
175	C₂×C₈	—	4	1	no	—
176	C₂×C₈	—	4	1	no	—
177	C₂×C₈	Dic₄₇⋊C₄	1	2	yes	—
178	C₂×C₈	C₂×Dic₉₄	1	1	yes	characteristic
179	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
180	C₂×C₈	D₄×D₄₇	1	2	yes	—
181	C₂×C₈	#10625352	1	2	yes	—
182	C₄⋊C₄	—	94	4	no	—
183	C₄⋊C₄	—	188	2	no	—
184	C₂²⋊C₄	—	188	4	no	—
185	C₄²	—	188	4	no	—
186	C₁₆	—	94	4	no	—
187	C₂³	—	2	1	no	—
188	C₂³	—	2	1	no	—
189	C₂³	—	4	2	no	—
190	C₂³	#13093955	1	2	yes	—
191	C₂³	C₂×#10625336	1	1	yes	characteristic
192	C₂×C₄	—	2	1	no	—
193	C₂×C₄	—	2	1	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	376	4	no	—
199	C₂×C₄	—	188	4	no	—
200	C₂×C₄	#13093955	1	2	yes	—
201	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
202	C₂×C₄	#13093992	1	1	yes	characteristic
203	C₂×C₄	#13094005	1	1	yes	characteristic
204	C₂×C₄	C₂×#10625335	1	1	yes	characteristic
205	C₂×C₄	#13094049	1	1	yes	characteristic
206	C₂×C₄	#13094054	1	1	yes	characteristic
207	C₈	—	2	2	no	—
208	C₈	—	8	1	no	—
209	C₈	—	8	1	no	—
210	C₈	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
211	C₈	#13094001	1	2	yes	—
212	C₂²	—	2	2	no	—
213	C₂²	—	2	2	no	—
214	C₂²	—	2	4	no	—
215	C₂²	—	4	2	no	—
216	C₂²	—	4	2	no	—
217	C₂²	C₂×#13093955	1	1	yes	characteristic
218	C₂²	#15689273	1	1	yes	characteristic
219	C₂²	#15689451	1	1	yes	characteristic
220	C₄	—	2	2	no	—
221	C₄	—	376	4	no	—
222	C₄	#15688995	1	1	yes	characteristic
223	C₄	#15689166	1	1	yes	characteristic
224	C₄	#15689261	1	1	yes	characteristic
225	C₄	#15689439	1	1	yes	characteristic
226	C₂	—	2	1	no	—
227	C₂	—	2	1	no	—
228	C₂	—	4	2	no	—
229	C₂	#20243580	1	1	yes	characteristic
230	C₂	#20245162	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#15689161

C₂

yes

maximal, characteristic

C₂×#15688947

C₂

yes

maximal, complemented

#20244999

C₂

yes

maximal, characteristic

#20241488

C₂

yes

maximal, complemented

C₄₇×#1810

C₂

yes

maximal, characteristic

C₂×#13093983

—

C₂×#13093964

C₂²

yes

—

#15689161

—

C₂×#13093958

—

C₂×#13093956

C₂²

yes

—

#15688947

—

C₂²⋊(C₄₇⋊C₁₆)

C₄

yes

complemented

C₂³×C₈×C₄₇

C₂²

yes

characteristic

C₂×#108×C₄₇

C₂²

yes

characteristic

C₂×#108×C₄₇

C₂²

yes

characteristic

C₄₇×#407

—

C₄₇×#341

—

#13093983

—

#13093983

—

C₂×C₄⋊Dic₄₇

—

C₂×C₂²⋊Dic₄₇

—

C₂×C₄×Dic₄₇

—

#13093964

—

#13093964

—

C₂×C₄₇⋊C₁₆

C₂×C₄

yes

—

#13093958

—

#13093956

—

#13093956

D₄

yes

—

C₂³×C₄×C₄₇

D₄

yes

characteristic

C₂×M₁₆×C₄₇

—

C₂×M₁₆×C₄₇

—

C₂²×C₈×C₄₇

—

C₂²×C₈×C₄₇

—

C₂²×C₈×C₄₇

C₂×C₄

yes

—

C₂²×C₈×C₄₇

D₄

yes

characteristic

C₂²×C₈×C₄₇

Q₈

yes

—

C₂²×C₈×C₄₇

C₂³

yes

characteristic

#108×C₄₇

—

#108×C₄₇

—

C₂²⋊C₈×C₄₇

—

C₂⁴×C₄₇

SD₁₆

yes

characteristic

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₄⋊C₄

yes

—

C₂²×C₄×C₄₇

SD₁₆

yes

characteristic

C₂²×C₄×C₄₇

SD₁₆

yes

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×Dic₄₇

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₄⋊C₄

yes

—

C₂×C₈×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂×D₄

yes

—

C₂×C₈×C₄₇

C₂×Q₈

yes

characteristic

C₂×C₈×C₄₇

#41

yes

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄×Dic₄₇

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

#106

yes

—

C₂³×C₄₇

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

#106

yes

—

C₂×C₄×C₄₇

C₂×C₄⋊C₄

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

C₂×SD₁₆

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₈×C₄₇

—

C₈×C₄₇

—

C₈×C₄₇

—

C₈×C₄₇

C₄×D₄

yes

—

C₈×C₄₇

C₂²⋊Q₈

yes

—

#12930

—

maximal, Sylow

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

100

C₂²×C₄₇

—

101

C₂²×C₄₇

—

102

C₂²×C₄₇

C₂×#106

yes

characteristic

103

C₂²×C₄₇

#450

yes

characteristic

104

C₂²×C₄₇

#483

yes

characteristic

105

C₄×C₄₇

—

106

C₄×C₄₇

#385

yes

characteristic

107

C₄×C₄₇

#428

yes

characteristic

108

C₄×C₄₇

#448

yes

characteristic

109

C₄×C₄₇

#481

yes

characteristic

110

Dic₄₇

—

111

C₂×#427

—

112

C₂×#365

—

113

#2112

—

114

#1810

D₄₇

yes

characteristic

115

#1383

—

116

C₂×C₄₇

—

117

C₂×C₄₇

—

118

C₂×C₄₇

—

119

C₂×C₄₇

#1853

yes

characteristic

120

C₂×C₄₇

#2155

yes

—

121

C₂³×C₈

C₂×D₄₇

yes

characteristic

122

C₂×#117

—

123

C₂×M₃₂

—

124

C₂×#108

C₂×D₄₇

yes

characteristic

125

C₂×#108

C₂×D₄₇

yes

characteristic

126

#427

—

127

C₂×#107

—

128

C₂×#106

—

129

#407

—

130

#365

—

131

C₂²⋊C₁₆

—

132

#341

—

133

C₄₇

#12930

yes

characteristic, complemented, Sylow

134

C₂³×C₄

C₂²⋊D₄₇

yes

characteristic

135

C₂×M₁₆

—

136

C₂×M₁₆

—

137

C₂²×C₈

—

138

C₂²×C₈

—

139

C₂²×C₈

Dic₉₄

yes

—

140

C₂²×C₈

C₄×D₄₇

yes

—

141

C₂²×C₈

C₂²⋊D₄₇

yes

characteristic

142

C₂²×C₈

C₂²×D₄₇

yes

characteristic

143

#117

—

144

#117

—

188

—

145

C₂×C₄⋊C₄

—

146

C₂×C₂²⋊C₄

—

188

—

147

C₂×C₄²

—

188

—

148

M₃₂

—

149

M₃₂

—

150

C₂×C₁₆

—

151

#108

—

152

#108

—

153

#107

—

154

#106

—

155

#106

—

156

C₂²⋊C₈

—

157

C₂⁴

#10625336

yes

characteristic

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

188

—

163

C₂²×C₄

Dic₄₇⋊C₄

yes

—

164

C₂²×C₄

#10625335

yes

—

165

C₂²×C₄

#10625336

yes

characteristic

166

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

167

M₁₆

—

168

M₁₆

—

169

M₁₆

—

170

M₁₆

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

Dic₄₇⋊C₄

yes

—

178

C₂×C₈

C₂×Dic₉₄

yes

characteristic

179

C₂×C₈

C₂×C₄×D₄₇

yes

characteristic

180

C₂×C₈

D₄×D₄₇

yes

—

181

C₂×C₈

#10625352

yes

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

188

—

184

C₂²⋊C₄

—

188

—

185

C₄²

—

188

—

186

C₁₆

—

187

C₂³

—

188

C₂³

—

189

C₂³

—

190

C₂³

#13093955

yes

—

191

C₂³

C₂×#10625336

yes

characteristic

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

376

—

199

C₂×C₄

—

188

—

200

C₂×C₄

#13093955

yes

—

201

C₂×C₄

C₂×Dic₄₇⋊C₄

yes

characteristic

202

C₂×C₄

#13093992

yes

characteristic

203

C₂×C₄

#13094005

yes

characteristic

204

C₂×C₄

C₂×#10625335

yes

characteristic

205

C₂×C₄

#13094049

yes

characteristic

206

C₂×C₄

#13094054

yes

characteristic

207

C₈

—

208

C₈

—

209

C₈

—

210

C₈

(C₂²⋊D₄₇)⋊C₄

yes

—

211

C₈

#13094001

yes

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

C₂×#13093955

yes

characteristic

218

C₂²

#15689273

yes

characteristic

219

C₂²

#15689451

yes

characteristic

220

C₄

—

221

C₄

—

376

—

222

C₄

#15688995

yes

characteristic

223

C₄

#15689166

yes

characteristic

224

C₄

#15689261

yes

characteristic

225

C₄

#15689439

yes

characteristic

226

C₂

—

227

C₂

—

228

C₂

—

229

C₂

#20243580

yes

characteristic

230

C₂

#20245162

yes

—

	subgroup	G/H
center	C₂²	C₂×#13093955
commutator	C₂×C₈×C₄₇	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₇
Fitting	C₄₇×#1810	C₂
socle	C₂²×C₄₇	C₂×#106
prime radical	C₂⁴×C₄₇	SD₁₆
cosocle	C₂²×C₈×C₄₇	C₂³
hypercenter	#1810	D₄₇
hypocenter	C₄₇	#12930
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ #1810

subgroup

G/H

center

C₂²

C₂×#13093955

commutator

C₂×C₈×C₄₇

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₇

Fitting

C₄₇×#1810

C₂

socle

C₂²×C₄₇

C₂×#106

prime radical

C₂⁴×C₄₇

SD₁₆

cosocle

C₂²×C₈×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ #1810

N	H ≅ G/N	type
2. C₂×#15688947	C₂	semidirect
4. #20241488	C₂	semidirect
12. C₂²⋊(C₄₇⋊C₁₆)	C₄	semidirect
133. C₄₇	#12930	semidirect

H ≅ G/N

type

2. C₂×#15688947

C₂

semidirect

4. #20241488

C₂

semidirect

12. C₂²⋊(C₄₇⋊C₁₆)

C₄

semidirect

133. C₄₇

#12930

semidirect

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

subgroup	index
C₂×#15689161	2
C₂×#15688947	2
#20244999	2
#20241488	2
C₄₇×#1810	2
#12930	47

subgroup

index

C₄₇×#1810

Subgroups — #26132839

Conjugacy classes of subgroups

Complements

Maximal subgroups