Group #26109604 — subgroups

Subgroups — #26109604

Order 12032.

598 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 171 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	#20243456	C₂	1	2	yes	maximal
2	#20241231	C₂	1	4	yes	maximal
3	C₂×C₄₇×#376	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	4	yes	—
5	#15688878	—	2	4	no	—
6	C₂²×C₄²×C₄₇	C₄	1	1	yes	characteristic
7	C₂²×C₄²×C₄₇	C₄	1	1	yes	characteristic
8	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
9	C₄₇×#376	—	2	4	no	—
10	C₂×#95×C₄₇	C₄	1	2	yes	—
11	C₂×#95×C₄₇	C₂²	1	2	yes	—
12	C₂²×C₄₇⋊C₈	—	2	4	no	—
13	C₂²⋊(C₄₇⋊C₈)	—	2	8	no	—
14	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
15	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
16	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
17	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
18	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
19	C₂×C₄²×C₄₇	—	2	2	no	—
20	C₂×C₄²×C₄₇	—	2	2	no	—
21	C₂×C₄²×C₄₇	—	2	4	no	—
22	C₂×C₄²×C₄₇	—	2	2	no	—
23	C₂×C₄²×C₄₇	—	2	4	no	—
24	C₂×C₄²×C₄₇	C₈	1	4	yes	complemented
25	C₂×C₄²×C₄₇	D₄	1	4	yes	—
26	#95×C₄₇	—	2	4	no	—
27	#95×C₄₇	—	2	4	no	—
28	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
29	C₂²×C₄×C₄₇	—	2	2	no	—
30	C₂²×C₄×C₄₇	—	2	2	no	—
31	C₂²×C₄×C₄₇	—	2	2	no	—
32	C₂²×C₄×C₄₇	—	2	2	no	—
33	C₂²×C₄×C₄₇	—	2	2	no	—
34	C₂²×C₄×C₄₇	—	2	2	no	—
35	C₂²×C₄×C₄₇	—	2	2	no	—
36	C₂²×C₄×C₄₇	—	4	2	no	—
37	C₂²×C₄×C₄₇	—	4	2	no	—
38	C₂²×C₄×C₄₇	—	4	2	no	—
39	C₂²×C₄×C₄₇	—	4	2	no	—
40	C₂²×C₄×C₄₇	—	4	2	no	—
41	C₂²×C₄×C₄₇	—	4	2	no	—
42	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
43	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
44	C₂²×C₄×C₄₇	C₂×C₈	1	2	yes	—
45	C₂²×C₄×C₄₇	C₂×C₈	1	4	yes	—
46	C₂²×C₄×C₄₇	M₁₆	1	2	yes	—
47	C₂²×C₄×C₄₇	M₁₆	1	4	yes	—
48	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
49	C₂²×C₄×C₄₇	#41	1	4	yes	—
50	C₄²×C₄₇	—	2	8	no	—
51	C₄²×C₄₇	—	2	8	no	—
52	C₄²×C₄₇	—	2	8	no	—
53	C₂×C₄₇⋊C₈	—	4	8	no	—
54	C₂×C₄₇⋊C₈	—	4	4	no	—
55	C₂³×C₄₇	—	2	2	no	—
56	C₂³×C₄₇	—	2	2	no	—
57	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
58	C₂³×C₄₇	#117	1	2	yes	—
59	C₂³×C₄₇	C₂²×C₈	1	1	yes	characteristic
60	C₂³×C₄₇	C₂×M₁₆	1	1	yes	characteristic
61	C₂³×C₄₇	C₂×M₁₆	1	2	yes	—
62	C₂×C₄×C₄₇	—	2	2	no	—
63	C₂×C₄×C₄₇	—	2	2	no	—
64	C₂×C₄×C₄₇	—	2	4	no	—
65	C₂×C₄×C₄₇	—	2	4	no	—
66	C₂×C₄×C₄₇	—	2	4	no	—
67	C₂×C₄×C₄₇	—	2	2	no	—
68	C₂×C₄×C₄₇	—	2	4	no	—
69	C₂×C₄×C₄₇	—	2	4	no	—
70	C₂×C₄×C₄₇	—	2	4	no	—
71	C₂×C₄×C₄₇	—	4	4	no	—
72	C₂×C₄×C₄₇	—	4	4	no	—
73	C₂×C₄×C₄₇	—	4	4	no	—
74	C₂×C₄×C₄₇	—	4	4	no	—
75	C₂×C₄×C₄₇	—	4	2	no	—
76	C₂×C₄×C₄₇	—	4	2	no	—
77	C₂×C₄×C₄₇	—	4	2	no	—
78	C₂×C₄×C₄₇	—	4	2	no	—
79	C₂×C₄×C₄₇	—	4	4	no	—
80	C₂×C₄×C₄₇	—	4	4	no	—
81	C₂×C₄×C₄₇	C₂²⋊C₈	1	4	yes	—
82	C₂×C₄×C₄₇	#123	1	4	yes	—
83	C₄₇⋊C₈	—	8	4	no	—
84	#8699	—	47	1	no	maximal, Sylow
85	C₂²×C₄₇	—	2	2	no	—
86	C₂²×C₄₇	—	2	2	no	—
87	C₂²×C₄₇	—	2	2	no	—
88	C₂²×C₄₇	—	2	2	no	—
89	C₂²×C₄₇	—	2	2	no	—
90	C₂²×C₄₇	—	2	2	no	—
91	C₂²×C₄₇	#381	1	1	yes	characteristic
92	C₂²×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
93	C₂²×C₄₇	#407	1	1	yes	characteristic
94	C₂²×C₄₇	#410	1	2	yes	—
95	C₂²×C₄₇	#413	1	2	yes	—
96	C₂²×C₄₇	#431	1	2	yes	—
97	C₂²×C₄₇	#432	1	2	yes	—
98	C₄×C₄₇	—	2	4	no	—
99	C₄×C₄₇	—	2	4	no	—
100	C₄×C₄₇	—	4	2	no	—
101	C₄×C₄₇	—	4	4	no	—
102	C₄×C₄₇	—	4	4	no	—
103	C₂×#376	D₄₇	1	1	yes	characteristic
104	#1817	—	47	2	no	—
105	#1280	—	47	4	no	—
106	C₂×C₄₇	—	2	2	no	—
107	C₂×C₄₇	—	2	2	no	—
108	C₂×C₄₇	#1458	1	2	yes	—
109	C₂×C₄₇	#1464	1	2	yes	—
110	C₂×C₄₇	#1817	1	1	yes	characteristic
111	C₂×C₄₇	#1820	1	1	yes	characteristic
112	C₂×C₄₇	#1822	1	1	yes	characteristic
113	C₂²×C₄²	Dic₄₇	1	1	yes	characteristic
114	C₂²×C₄²	Dic₄₇	1	1	yes	characteristic
115	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
116	C₂×C₂²⋊C₈	—	47	4	no	—
117	#376	—	2	4	no	—
118	C₂×#95	Dic₄₇	1	2	yes	—
119	C₂×#95	C₂×D₄₇	1	2	yes	—
120	#336	—	94	4	no	—
121	C₄₇	#8699	1	1	yes	characteristic, complemented, Sylow
122	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
123	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
124	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
125	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
126	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
127	C₂²×C₈	—	94	4	no	—
128	C₂×C₄²	—	2	4	no	—
129	C₂×C₄²	—	2	2	no	—
130	C₂×C₄²	—	2	2	no	—
131	C₂×C₄²	—	2	2	no	—
132	C₂×C₄²	—	2	4	no	—
133	C₂×C₄²	C₄₇⋊C₈	1	4	yes	complemented
134	C₂×C₄²	C₂²⋊D₄₇	1	4	yes	—
135	C₂²⋊C₈	—	94	8	no	—
136	#95	—	2	4	no	—
137	#95	—	2	4	no	—
138	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
139	C₂²×C₄	—	2	2	no	—
140	C₂²×C₄	—	2	2	no	—
141	C₂²×C₄	—	2	2	no	—
142	C₂²×C₄	—	2	2	no	—
143	C₂²×C₄	—	2	2	no	—
144	C₂²×C₄	—	2	2	no	—
145	C₂²×C₄	—	2	2	no	—
146	C₂²×C₄	—	4	2	no	—
147	C₂²×C₄	—	4	2	no	—
148	C₂²×C₄	—	4	2	no	—
149	C₂²×C₄	—	4	2	no	—
150	C₂²×C₄	—	4	2	no	—
151	C₂²×C₄	—	4	2	no	—
152	C₂²×C₄	C₂×C₄₇⋊C₈	1	2	yes	—
153	C₂²×C₄	C₂×C₄₇⋊C₈	1	4	yes	—
154	C₂²×C₄	#10625329	1	2	yes	—
155	C₂²×C₄	#10625329	1	4	yes	—
156	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
157	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
158	C₂²×C₄	#10625350	1	4	yes	—
159	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
160	C₂×C₈	—	188	8	no	—
161	C₂×C₈	—	188	4	no	—
162	C₄²	—	2	8	no	—
163	C₄²	—	2	8	no	—
164	C₄²	—	2	8	no	—
165	C₂³	—	2	2	no	—
166	C₂³	—	2	2	no	—
167	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
168	C₂³	#13093983	1	2	yes	—
169	C₂³	C₂²×C₄₇⋊C₈	1	1	yes	characteristic
170	C₂³	C₂×#10625329	1	1	yes	characteristic
171	C₂³	C₂×#10625329	1	2	yes	—
172	C₂×C₄	—	2	2	no	—
173	C₂×C₄	—	2	2	no	—
174	C₂×C₄	—	2	4	no	—
175	C₂×C₄	—	2	4	no	—
176	C₂×C₄	—	2	4	no	—
177	C₂×C₄	—	2	2	no	—
178	C₂×C₄	—	2	4	no	—
179	C₂×C₄	—	2	4	no	—
180	C₂×C₄	—	2	4	no	—
181	C₂×C₄	—	4	4	no	—
182	C₂×C₄	—	4	4	no	—
183	C₂×C₄	—	4	4	no	—
184	C₂×C₄	—	4	4	no	—
185	C₂×C₄	—	4	2	no	—
186	C₂×C₄	—	4	2	no	—
187	C₂×C₄	—	4	2	no	—
188	C₂×C₄	—	4	2	no	—
189	C₂×C₄	—	4	4	no	—
190	C₂×C₄	—	4	4	no	—
191	C₂×C₄	C₂²⋊(C₄₇⋊C₈)	1	4	yes	—
192	C₂×C₄	#13094007	1	4	yes	—
193	C₈	—	376	4	no	—
194	C₂²	—	2	2	no	—
195	C₂²	—	2	2	no	—
196	C₂²	—	2	2	no	—
197	C₂²	—	2	2	no	—
198	C₂²	—	2	2	no	—
199	C₂²	—	2	2	no	—
200	C₂²	#15688986	1	1	yes	characteristic
201	C₂²	C₂×C₂²⋊(C₄₇⋊C₈)	1	1	yes	characteristic
202	C₂²	#15689087	1	1	yes	characteristic
203	C₂²	#15689097	1	2	yes	—
204	C₂²	#15689107	1	2	yes	—
205	C₂²	#15689176	1	2	yes	—
206	C₂²	#15689180	1	2	yes	—
207	C₄	—	2	4	no	—
208	C₄	—	2	4	no	—
209	C₄	—	4	2	no	—
210	C₄	—	4	4	no	—
211	C₄	—	4	4	no	—
212	C₂	—	2	2	no	—
213	C₂	—	2	2	no	—
214	C₂	#20241702	1	2	yes	—
215	C₂	#20241722	1	2	yes	—
216	C₂	#20243456	1	1	yes	characteristic
217	C₂	#20243465	1	1	yes	characteristic
218	C₂	#20243471	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20243456

C₂

yes

maximal

#20241231

C₂

yes

maximal

C₂×C₄₇×#376

C₂

yes

maximal, characteristic

C₂×C₂²⋊(C₄₇⋊C₈)

C₂²

yes

—

#15688878

—

C₂²×C₄²×C₄₇

C₄

yes

characteristic

C₂²×C₄²×C₄₇

C₄

yes

characteristic

C₂²×C₄²×C₄₇

C₂²

yes

characteristic

C₄₇×#376

—

C₂×#95×C₄₇

C₄

yes

—

C₂×#95×C₄₇

C₂²

yes

—

C₂²×C₄₇⋊C₈

—

C₂²⋊(C₄₇⋊C₈)

—

C₂³×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂³×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂³×C₄×C₄₇

C₂×C₄

yes

—

C₂³×C₄×C₄₇

C₂×C₄

yes

—

C₂³×C₄×C₄₇

C₂³

yes

characteristic

C₂×C₄²×C₄₇

—

C₂×C₄²×C₄₇

—

C₂×C₄²×C₄₇

—

C₂×C₄²×C₄₇

—

C₂×C₄²×C₄₇

—

C₂×C₄²×C₄₇

C₈

yes

complemented

C₂×C₄²×C₄₇

D₄

yes

—

#95×C₄₇

—

#95×C₄₇

—

C₂⁴×C₄₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

C₂×C₈

yes

—

C₂²×C₄×C₄₇

C₂×C₈

yes

—

C₂²×C₄×C₄₇

M₁₆

yes

—

C₂²×C₄×C₄₇

M₁₆

yes

—

C₂²×C₄×C₄₇

C₂×D₄

yes

—

C₂²×C₄×C₄₇

#41

yes

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂³×C₄₇

#117

yes

—

C₂³×C₄₇

C₂²×C₈

yes

characteristic

C₂³×C₄₇

C₂×M₁₆

yes

characteristic

C₂³×C₄₇

C₂×M₁₆

yes

—

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

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²⋊C₈

yes

—

C₂×C₄×C₄₇

#123

yes

—

C₄₇⋊C₈

—

#8699

—

maximal, Sylow

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#381

yes

characteristic

C₂²×C₄₇

C₂×C₂²⋊C₈

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

—

C₂²×C₄₇

#413

yes

—

C₂²×C₄₇

#431

yes

—

C₂²×C₄₇

#432

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

100

C₄×C₄₇

—

101

C₄×C₄₇

—

102

C₄×C₄₇

—

103

C₂×#376

D₄₇

yes

characteristic

104

#1817

—

105

#1280

—

106

C₂×C₄₇

—

107

C₂×C₄₇

—

108

C₂×C₄₇

#1458

yes

—

109

C₂×C₄₇

#1464

yes

—

110

C₂×C₄₇

#1817

yes

characteristic

111

C₂×C₄₇

#1820

yes

characteristic

112

C₂×C₄₇

#1822

yes

characteristic

113

C₂²×C₄²

Dic₄₇

yes

characteristic

114

C₂²×C₄²

Dic₄₇

yes

characteristic

115

C₂²×C₄²

C₂×D₄₇

yes

characteristic

116

C₂×C₂²⋊C₈

—

117

#376

—

118

C₂×#95

Dic₄₇

yes

—

119

C₂×#95

C₂×D₄₇

yes

—

120

#336

—

121

C₄₇

#8699

yes

characteristic, complemented, Sylow

122

C₂³×C₄

C₂×Dic₄₇

yes

characteristic

123

C₂³×C₄

C₂×Dic₄₇

yes

—

124

C₂³×C₄

C₂×Dic₄₇

yes

—

125

C₂³×C₄

C₂×Dic₄₇

yes

characteristic

126

C₂³×C₄

C₂²×D₄₇

yes

characteristic

127

C₂²×C₈

—

128

C₂×C₄²

—

129

C₂×C₄²

—

130

C₂×C₄²

—

131

C₂×C₄²

—

132

C₂×C₄²

—

133

C₂×C₄²

C₄₇⋊C₈

yes

complemented

134

C₂×C₄²

C₂²⋊D₄₇

yes

—

135

C₂²⋊C₈

—

136

#95

—

137

#95

—

138

C₂⁴

C₂²×Dic₄₇

yes

characteristic

139

C₂²×C₄

—

140

C₂²×C₄

—

141

C₂²×C₄

—

142

C₂²×C₄

—

143

C₂²×C₄

—

144

C₂²×C₄

—

145

C₂²×C₄

—

146

C₂²×C₄

—

147

C₂²×C₄

—

148

C₂²×C₄

—

149

C₂²×C₄

—

150

C₂²×C₄

—

151

C₂²×C₄

—

152

C₂²×C₄

C₂×C₄₇⋊C₈

yes

—

153

C₂²×C₄

C₂×C₄₇⋊C₈

yes

—

154

C₂²×C₄

#10625329

yes

—

155

C₂²×C₄

#10625329

yes

—

156

C₂²×C₄

C₂²⋊Dic₄₇

yes

—

157

C₂²×C₄

C₂²⋊Dic₄₇

yes

—

158

C₂²×C₄

#10625350

yes

—

159

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

—

160

C₂×C₈

—

188

—

161

C₂×C₈

—

188

—

162

C₄²

—

163

C₄²

—

164

C₄²

—

165

C₂³

—

166

C₂³

—

167

C₂³

C₂×C₂²⋊Dic₄₇

yes

characteristic

168

C₂³

#13093983

yes

—

169

C₂³

C₂²×C₄₇⋊C₈

yes

characteristic

170

C₂³

C₂×#10625329

yes

characteristic

171

C₂³

C₂×#10625329

yes

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

C₂²⋊(C₄₇⋊C₈)

yes

—

192

C₂×C₄

#13094007

yes

—

193

C₈

—

376

—

194

C₂²

—

195

C₂²

—

196

C₂²

—

197

C₂²

—

198

C₂²

—

199

C₂²

—

200

C₂²

#15688986

yes

characteristic

201

C₂²

C₂×C₂²⋊(C₄₇⋊C₈)

yes

characteristic

202

C₂²

#15689087

yes

characteristic

203

C₂²

#15689097

yes

—

204

C₂²

#15689107

yes

—

205

C₂²

#15689176

yes

—

206

C₂²

#15689180

yes

—

207

C₄

—

208

C₄

—

209

C₄

—

210

C₄

—

211

C₄

—

212

C₂

—

213

C₂

—

214

C₂

#20241702

yes

—

215

C₂

#20241722

yes

—

216

C₂

#20243456

yes

characteristic

217

C₂

#20243465

yes

characteristic

218

C₂

#20243471

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₄₇
commutator	C₂³×C₄₇	C₂²×C₈
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#376	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#376	D₄₇
hypocenter	C₄₇	#8699
LCS	G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#376

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₄₇

commutator

C₂³×C₄₇

C₂²×C₈

Frattini

C₂³×C₄

C₂²×D₄₇

Fitting

C₂×C₄₇×#376

C₂

socle

C₂³×C₄₇

C₂×C₂²⋊C₄

prime radical

C₂⁴×C₄₇

C₂²×C₄

cosocle

C₂³×C₄×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#376

N	H ≅ G/N	type
24. C₂×C₄²×C₄₇	C₈	semidirect
121. C₄₇	#8699	semidirect
133. C₂×C₄²	C₄₇⋊C₈	semidirect

H ≅ G/N

type

24. C₂×C₄²×C₄₇

C₈

semidirect

121. C₄₇

#8699

semidirect

133. C₂×C₄²

C₄₇⋊C₈

semidirect

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

subgroup	index
#20243456	2
#20241231	2
C₂×C₄₇×#376	2
#8699	47

subgroup

index

#20243456

#20241231

C₂×C₄₇×#376

#8699

Subgroups — #26109604

Conjugacy classes of subgroups

Complements

Maximal subgroups