Group #26104599 — subgroups

Subgroups — #26104599

Order 12032.

624 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 159 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	#20243505	C₂	1	2	yes	maximal, complemented
2	#20241209	C₂	1	4	yes	maximal, complemented
3	C₄×#127×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
5	#15688878	—	2	2	no	—
6	#15688878	C₂²	1	4	yes	—
7	C₂×#127×C₄₇	C₄	1	1	yes	characteristic
8	C₂×C₄×D₄×C₄₇	—	2	2	no	—
9	C₂×C₄×D₄×C₄₇	C₄	1	2	yes	—
10	C₄₇×#390	—	2	2	no	—
11	C₄₇×#390	C₂²	1	2	yes	—
12	C₄₇×#384	C₄	1	1	yes	characteristic
13	C₄³×C₄₇	C₂²	1	1	yes	characteristic
14	C₂²×C₄₇⋊C₈	—	2	4	no	—
15	C₄⋊(C₄₇⋊C₈)	—	4	4	no	—
16	C₂²×D₄×C₄₇	—	2	2	no	—
17	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
18	C₂³×C₄×C₄₇	—	2	2	no	—
19	#127×C₄₇	—	2	4	no	—
20	C₄×D₄×C₄₇	—	4	4	no	—
21	C₄×D₄×C₄₇	—	4	4	no	—
22	C₄×D₄×C₄₇	—	4	4	no	—
23	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
24	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
25	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
26	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
27	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄²×C₄₇	D₄	1	2	yes	—
30	C₂×C₄²×C₄₇	D₄	1	2	yes	—
31	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
32	C₂⁴×C₄₇	—	2	2	no	—
33	C₂×D₄×C₄₇	—	2	8	no	—
34	C₂×D₄×C₄₇	—	2	2	no	—
35	C₂×D₄×C₄₇	—	4	4	no	—
36	C₂×D₄×C₄₇	—	4	2	no	—
37	C₂×D₄×C₄₇	—	4	2	no	—
38	C₂×D₄×C₄₇	—	4	4	no	—
39	C₂×D₄×C₄₇	M₁₆	1	4	yes	—
40	C₂²×C₄×C₄₇	—	2	2	no	—
41	C₂²×C₄×C₄₇	—	4	4	no	—
42	C₂²×C₄×C₄₇	—	4	8	no	—
43	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
44	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
45	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
46	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
47	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
48	C₄⋊C₄×C₄₇	—	4	2	no	—
49	C₄⋊C₄×C₄₇	—	4	4	no	—
50	C₂²⋊C₄×C₄₇	—	4	4	no	—
51	C₂²⋊C₄×C₄₇	—	4	4	no	—
52	C₂²⋊C₄×C₄₇	—	4	4	no	—
53	C₄²×C₄₇	—	2	2	no	—
54	C₄²×C₄₇	—	2	2	no	—
55	C₄²×C₄₇	—	4	2	no	—
56	C₄²×C₄₇	—	4	1	no	—
57	C₄²×C₄₇	D₈	1	4	yes	—
58	C₄²×C₄₇	SD₁₆	1	4	yes	—
59	C₂×C₄₇⋊C₈	—	4	4	no	—
60	C₂×C₄₇⋊C₈	—	4	4	no	—
61	C₂×C₄₇⋊C₈	—	4	4	no	—
62	C₂³×C₄₇	—	2	4	no	—
63	C₂³×C₄₇	—	4	2	no	—
64	C₂³×C₄₇	—	4	2	no	—
65	C₂³×C₄₇	—	4	4	no	—
66	C₂³×C₄₇	—	4	4	no	—
67	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
68	D₄×C₄₇	—	4	4	no	—
69	D₄×C₄₇	—	4	4	no	—
70	D₄×C₄₇	—	4	16	no	—
71	C₂×C₄×C₄₇	—	2	2	no	—
72	C₂×C₄×C₄₇	—	2	2	no	—
73	C₂×C₄×C₄₇	—	2	1	no	—
74	C₂×C₄×C₄₇	—	2	1	no	—
75	C₂×C₄×C₄₇	—	2	2	no	—
76	C₂×C₄×C₄₇	—	2	2	no	—
77	C₂×C₄×C₄₇	—	2	1	no	—
78	C₂×C₄×C₄₇	—	2	2	no	—
79	C₂×C₄×C₄₇	—	4	2	no	—
80	C₂×C₄×C₄₇	—	4	4	no	—
81	C₂×C₄×C₄₇	—	8	8	no	—
82	C₂×C₄×C₄₇	#100	1	2	yes	—
83	C₂×C₄×C₄₇	#102	1	4	yes	—
84	C₂×C₄×C₄₇	#102	1	4	yes	—
85	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
86	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
87	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
88	C₄₇⋊C₈	—	8	4	no	—
89	#7651	—	47	1	no	maximal, Sylow
90	C₂²×C₄₇	—	4	4	no	—
91	C₂²×C₄₇	—	4	8	no	—
92	C₂²×C₄₇	—	8	2	no	—
93	C₂²×C₄₇	—	8	2	no	—
94	C₂²×C₄₇	—	8	4	no	—
95	C₂²×C₄₇	#407	1	1	yes	characteristic
96	C₂²×C₄₇	#410	1	1	yes	characteristic
97	C₂²×C₄₇	C₂×#100	1	1	yes	characteristic
98	C₂²×C₄₇	C₂×#102	1	2	yes	—
99	C₂²×C₄₇	#421	1	2	yes	—
100	C₄×C₄₇	—	2	2	no	—
101	C₄×C₄₇	—	2	4	no	—
102	C₄×C₄₇	—	2	2	no	—
103	C₄×C₄₇	—	2	2	no	—
104	C₄×C₄₇	—	4	1	no	—
105	C₄×C₄₇	—	8	2	no	—
106	C₄×C₄₇	#331	1	4	yes	—
107	C₄×#127	D₄₇	1	1	yes	characteristic
108	#1831	—	47	2	no	—
109	#1270	—	47	4	no	—
110	C₂×C₄₇	—	8	4	no	—
111	C₂×C₄₇	#1466	1	1	yes	characteristic
112	C₂×C₄₇	#1486	1	2	yes	—
113	C₂×C₄₇	#1517	1	2	yes	—
114	C₂×C₄₇	#1536	1	1	yes	characteristic
115	C₂×C₄₇	C₂×#331	1	1	yes	characteristic
116	C₂×#127	Dic₄₇	1	1	yes	characteristic
117	C₂×C₄×D₄	—	2	2	no	—
118	C₂×C₄×D₄	Dic₄₇	1	2	yes	—
119	C₂×C₄⋊C₈	—	94	2	no	—
120	#390	—	2	2	no	—
121	#390	C₂×D₄₇	1	2	yes	—
122	#384	Dic₄₇	1	1	yes	characteristic
123	C₄³	C₂×D₄₇	1	1	yes	characteristic
124	#336	—	47	4	no	—
125	#336	—	94	2	no	—
126	C₄₇	#7651	1	1	yes	characteristic, complemented, Sylow
127	C₂²×D₄	—	2	2	no	—
128	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
129	C₂³×C₄	—	2	2	no	—
130	C₂²×C₈	—	94	4	no	—
131	#127	—	2	4	no	—
132	C₄×D₄	—	4	4	no	—
133	C₄×D₄	—	4	4	no	—
134	C₄×D₄	—	4	4	no	—
135	C₂×C₄⋊C₄	—	2	2	no	—
136	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
137	C₂×C₂²⋊C₄	—	2	2	no	—
138	C₂×C₂²⋊C₄	—	2	4	no	—
139	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
140	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
141	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
142	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
143	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
144	C₄⋊C₈	—	188	4	no	—
145	C₂⁴	—	2	2	no	—
146	C₂×D₄	—	2	8	no	—
147	C₂×D₄	—	2	2	no	—
148	C₂×D₄	—	4	2	no	—
149	C₂×D₄	—	4	2	no	—
150	C₂×D₄	—	4	4	no	—
151	C₂×D₄	—	4	4	no	—
152	C₂×D₄	#10625329	1	4	yes	—
153	C₂²×C₄	—	2	2	no	—
154	C₂²×C₄	—	4	4	no	—
155	C₂²×C₄	—	4	8	no	—
156	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
157	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
158	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
159	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
160	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
161	C₂×C₈	—	188	4	no	—
162	C₂×C₈	—	188	4	no	—
163	C₂×C₈	—	188	4	no	—
164	C₄⋊C₄	—	4	2	no	—
165	C₄⋊C₄	—	4	4	no	—
166	C₂²⋊C₄	—	4	4	no	—
167	C₂²⋊C₄	—	4	4	no	—
168	C₂²⋊C₄	—	4	4	no	—
169	C₄²	—	2	2	no	—
170	C₄²	—	2	2	no	—
171	C₄²	—	4	2	no	—
172	C₄²	—	4	1	no	—
173	C₄²	#10625334	1	4	yes	—
174	C₄²	#10625335	1	4	yes	—
175	C₂³	—	2	4	no	—
176	C₂³	—	4	2	no	—
177	C₂³	—	4	2	no	—
178	C₂³	—	4	4	no	—
179	C₂³	—	4	4	no	—
180	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
181	D₄	—	4	4	no	—
182	D₄	—	4	4	no	—
183	D₄	—	4	16	no	—
184	C₂×C₄	—	2	2	no	—
185	C₂×C₄	—	2	2	no	—
186	C₂×C₄	—	2	1	no	—
187	C₂×C₄	—	2	1	no	—
188	C₂×C₄	—	2	2	no	—
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	2	1	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	4	2	no	—
193	C₂×C₄	—	4	4	no	—
194	C₂×C₄	—	8	8	no	—
195	C₂×C₄	#13093941	1	2	yes	—
196	C₂×C₄	#13093945	1	4	yes	—
197	C₂×C₄	#13093945	1	4	yes	—
198	C₂×C₄	C₂×#10625329	1	2	yes	—
199	C₂×C₄	C₂×#10625334	1	2	yes	—
200	C₂×C₄	C₂×#10625335	1	2	yes	—
201	C₈	—	376	4	no	—
202	C₂²	—	4	4	no	—
203	C₂²	—	4	8	no	—
204	C₂²	—	8	4	no	—
205	C₂²	—	8	2	no	—
206	C₂²	—	8	2	no	—
207	C₂²	#15689087	1	1	yes	characteristic
208	C₂²	#15689097	1	1	yes	characteristic
209	C₂²	C₂×#13093941	1	1	yes	characteristic
210	C₂²	C₂×#13093945	1	2	yes	—
211	C₂²	#15689140	1	2	yes	—
212	C₄	—	2	2	no	—
213	C₄	—	2	2	no	—
214	C₄	—	2	2	no	—
215	C₄	—	2	4	no	—
216	C₄	—	4	1	no	—
217	C₄	—	8	2	no	—
218	C₄	#15688867	1	4	yes	—
219	C₂	—	8	4	no	—
220	C₂	#20241729	1	1	yes	characteristic
221	C₂	#20241813	1	2	yes	—
222	C₂	#20241948	1	2	yes	—
223	C₂	#20242023	1	1	yes	characteristic
224	C₂	C₂×#15688867	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20243505

C₂

yes

maximal, complemented

#20241209

C₂

yes

maximal, complemented

C₄×#127×C₄₇

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₄₇⋊C₈)

—

#15688878

—

#15688878

C₂²

yes

—

C₂×#127×C₄₇

C₄

yes

characteristic

C₂×C₄×D₄×C₄₇

—

C₂×C₄×D₄×C₄₇

C₄

yes

—

C₄₇×#390

—

C₄₇×#390

C₂²

yes

—

C₄₇×#384

C₄

yes

characteristic

C₄³×C₄₇

C₂²

yes

characteristic

C₂²×C₄₇⋊C₈

—

C₄⋊(C₄₇⋊C₈)

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

C₂×C₄

yes

—

C₂³×C₄×C₄₇

—

#127×C₄₇

—

C₄×D₄×C₄₇

—

C₄×D₄×C₄₇

—

C₄×D₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

C₂×C₄

yes

—

C₂×C₂²⋊C₄×C₄₇

—

C₂×C₂²⋊C₄×C₄₇

—

C₂×C₄²×C₄₇

C₂×C₄

yes

characteristic

C₂×C₄²×C₄₇

C₂×C₄

yes

characteristic

C₂×C₄²×C₄₇

D₄

yes

—

C₂×C₄²×C₄₇

D₄

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₂⁴×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

M₁₆

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

D₈

yes

—

C₄²×C₄₇

SD₁₆

yes

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

#100

yes

—

C₂×C₄×C₄₇

#102

yes

—

C₂×C₄×C₄₇

#102

yes

—

C₂×C₄×C₄₇

C₂×M₁₆

yes

—

C₂×C₄×C₄₇

C₂×D₈

yes

—

C₂×C₄×C₄₇

C₂×SD₁₆

yes

—

C₄₇⋊C₈

—

#7651

—

maximal, Sylow

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

—

C₂²×C₄₇

#421

yes

—

100

C₄×C₄₇

—

101

C₄×C₄₇

—

102

C₄×C₄₇

—

103

C₄×C₄₇

—

104

C₄×C₄₇

—

105

C₄×C₄₇

—

106

C₄×C₄₇

#331

yes

—

107

C₄×#127

D₄₇

yes

characteristic

108

#1831

—

109

#1270

—

110

C₂×C₄₇

—

111

C₂×C₄₇

#1466

yes

characteristic

112

C₂×C₄₇

#1486

yes

—

113

C₂×C₄₇

#1517

yes

—

114

C₂×C₄₇

#1536

yes

characteristic

115

C₂×C₄₇

C₂×#331

yes

characteristic

116

C₂×#127

Dic₄₇

yes

characteristic

117

C₂×C₄×D₄

—

118

C₂×C₄×D₄

Dic₄₇

yes

—

119

C₂×C₄⋊C₈

—

120

#390

—

121

#390

C₂×D₄₇

yes

—

122

#384

Dic₄₇

yes

characteristic

123

C₄³

C₂×D₄₇

yes

characteristic

124

#336

—

125

#336

—

126

C₄₇

#7651

yes

characteristic, complemented, Sylow

127

C₂²×D₄

—

128

C₂²×D₄

C₂×Dic₄₇

yes

—

129

C₂³×C₄

—

130

C₂²×C₈

—

131

#127

—

132

C₄×D₄

—

133

C₄×D₄

—

134

C₄×D₄

—

135

C₂×C₄⋊C₄

—

136

C₂×C₄⋊C₄

C₂×Dic₄₇

yes

—

137

C₂×C₂²⋊C₄

—

138

C₂×C₂²⋊C₄

—

139

C₂×C₄²

C₂×Dic₄₇

yes

characteristic

140

C₂×C₄²

C₂×Dic₄₇

yes

characteristic

141

C₂×C₄²

C₂²⋊D₄₇

yes

—

142

C₂×C₄²

C₂²⋊D₄₇

yes

—

143

C₂×C₄²

C₂²×D₄₇

yes

characteristic

144

C₄⋊C₈

—

188

—

145

C₂⁴

—

146

C₂×D₄

—

147

C₂×D₄

—

148

C₂×D₄

—

149

C₂×D₄

—

150

C₂×D₄

—

151

C₂×D₄

—

152

C₂×D₄

#10625329

yes

—

153

C₂²×C₄

—

154

C₂²×C₄

—

155

C₂²×C₄

—

156

C₂²×C₄

C₂²⋊Dic₄₇

yes

characteristic

157

C₂²×C₄

C₂²⋊Dic₄₇

yes

—

158

C₂²×C₄

C₂²⋊Dic₄₇

yes

characteristic

159

C₂²×C₄

C₂²×Dic₄₇

yes

characteristic

160

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

—

161

C₂×C₈

—

188

—

162

C₂×C₈

—

188

—

163

C₂×C₈

—

188

—

164

C₄⋊C₄

—

165

C₄⋊C₄

—

166

C₂²⋊C₄

—

167

C₂²⋊C₄

—

168

C₂²⋊C₄

—

169

C₄²

—

170

C₄²

—

171

C₄²

—

172

C₄²

—

173

C₄²

#10625334

yes

—

174

C₄²

#10625335

yes

—

175

C₂³

—

176

C₂³

—

177

C₂³

—

178

C₂³

—

179

C₂³

—

180

C₂³

C₂×C₂²⋊Dic₄₇

yes

characteristic

181

D₄

—

182

D₄

—

183

D₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

#13093941

yes

—

196

C₂×C₄

#13093945

yes

—

197

C₂×C₄

#13093945

yes

—

198

C₂×C₄

C₂×#10625329

yes

—

199

C₂×C₄

C₂×#10625334

yes

—

200

C₂×C₄

C₂×#10625335

yes

—

201

C₈

—

376

—

202

C₂²

—

203

C₂²

—

204

C₂²

—

205

C₂²

—

206

C₂²

—

207

C₂²

#15689087

yes

characteristic

208

C₂²

#15689097

yes

characteristic

209

C₂²

C₂×#13093941

yes

characteristic

210

C₂²

C₂×#13093945

yes

—

211

C₂²

#15689140

yes

—

212

C₄

—

213

C₄

—

214

C₄

—

215

C₄

—

216

C₄

—

217

C₄

—

218

C₄

#15688867

yes

—

219

C₂

—

220

C₂

#20241729

yes

characteristic

221

C₂

#20241813

yes

—

222

C₂

#20241948

yes

—

223

C₂

#20242023

yes

characteristic

224

C₂

C₂×#15688867

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₄₇
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄×#127×C₄₇	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂×#127×C₄₇	C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₄×#127	D₄₇
hypocenter	C₄₇	#7651
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×#127

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₄₇

commutator

C₂²×C₄×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄×#127×C₄₇

C₂

socle

C₂³×C₄₇

C₂×C₂²⋊C₄

prime radical

C₂×#127×C₄₇

C₄

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×#127

N	H ≅ G/N	type
1. #20243505	C₂	semidirect
2. #20241209	C₂	semidirect
126. C₄₇	#7651	semidirect

H ≅ G/N

type

1. #20243505

C₂

semidirect

2. #20241209

C₂

semidirect

126. C₄₇

#7651

semidirect

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

subgroup	index
#20243505	2
#20241209	2
C₄×#127×C₄₇	2
#7651	47

subgroup

index

#20243505

#20241209

C₄×#127×C₄₇

#7651

Subgroups — #26104599

Conjugacy classes of subgroups

Complements

Maximal subgroups