Group #26121012 — subgroups

Subgroups — #26121012

Order 12032.

402 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 123 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	#20243516	C₂	1	1	yes	maximal, characteristic, complemented
2	#20243388	C₂	1	2	yes	maximal
3	#20241272	C₂	1	2	yes	maximal, complemented
4	#20241223	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1954	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
7	C₂×#13093945	—	2	2	no	—
8	#15688993	C₂²	1	2	yes	—
9	#15688886	—	2	2	no	—
10	#15688885	—	2	2	no	—
11	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊C₈×C₄₇	—	2	2	no	—
14	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄₇⋊C₈	—	2	2	no	—
16	C₂×C₄⋊Dic₄₇	—	2	2	no	—
17	C₂×C₄⋊Dic₄₇	—	2	2	no	—
18	C₂×C₄⋊Dic₄₇	—	2	2	no	—
19	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
20	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
21	#13093945	—	4	4	no	—
22	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₄₇	—	2	1	no	—
24	C₂²×C₈×C₄₇	—	2	1	no	—
25	C₂²×C₈×C₄₇	D₄	1	2	yes	—
26	C₄×D₄×C₄₇	—	2	2	no	—
27	C₄×D₄×C₄₇	—	2	2	no	—
28	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
29	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
30	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
31	C₄⋊C₈×C₄₇	—	2	2	no	—
32	C₂²⋊C₈×C₄₇	—	4	4	no	—
33	C₄×C₈×C₄₇	—	2	2	no	—
34	C₂⁴×C₄₇	—	2	1	no	—
35	C₂×D₄×C₄₇	—	2	2	no	—
36	C₂×D₄×C₄₇	—	2	1	no	—
37	C₂×D₄×C₄₇	—	2	2	no	—
38	C₂×D₄×C₄₇	D₈	1	2	yes	—
39	C₂²×C₄×C₄₇	—	2	1	no	—
40	C₂²×C₄×C₄₇	—	4	1	no	—
41	C₂²×C₄×C₄₇	—	4	1	no	—
42	C₂²×C₄×C₄₇	—	4	2	no	—
43	C₂²×C₄×C₄₇	—	4	2	no	—
44	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
45	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
47	C₂²×Dic₄₇	—	4	2	no	—
48	C₂×C₈×C₄₇	—	2	2	no	—
49	C₂×C₈×C₄₇	—	2	2	no	—
50	C₂×C₈×C₄₇	—	2	2	no	—
51	C₂×C₈×C₄₇	—	4	1	no	—
52	C₂×C₈×C₄₇	—	4	2	no	—
53	C₄⋊C₄×C₄₇	—	2	2	no	—
54	C₂²⋊C₄×C₄₇	—	4	2	no	—
55	C₄²×C₄₇	#41	1	2	yes	—
56	C₄²×C₄₇	#41	1	2	yes	—
57	C₄⋊Dic₄₇	—	4	2	no	—
58	C₄⋊Dic₄₇	—	4	2	no	—
59	C₄⋊Dic₄₇	—	4	2	no	—
60	C₄⋊Dic₄₇	—	4	2	no	—
61	C₄⋊Dic₄₇	—	8	2	no	—
62	C₂×C₄₇⋊C₈	—	4	2	no	—
63	C₂×C₄₇⋊C₈	—	4	2	no	—
64	C₂×C₄₇⋊C₈	—	4	2	no	—
65	C₂³×C₄₇	—	2	2	no	—
66	C₂³×C₄₇	—	4	1	no	—
67	C₂³×C₄₇	—	4	2	no	—
68	C₂³×C₄₇	—	4	1	no	—
69	C₂³×C₄₇	—	4	2	no	—
70	C₂³×C₄₇	#121	1	1	yes	characteristic
71	D₄×C₄₇	—	2	4	no	—
72	D₄×C₄₇	—	4	2	no	—
73	C₂×C₄×C₄₇	—	2	2	no	—
74	C₂×C₄×C₄₇	—	4	1	no	—
75	C₂×C₄×C₄₇	—	4	2	no	—
76	C₂×C₄×C₄₇	—	8	2	no	—
77	C₂×C₄×C₄₇	—	8	1	no	—
78	C₂×C₄×C₄₇	—	8	1	no	—
79	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
80	C₂×C₄×C₄₇	#123	1	2	yes	—
81	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
82	C₂×C₄×C₄₇	#126	1	2	yes	—
83	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
84	C₂×C₄×C₄₇	#135	1	2	yes	—
85	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
86	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
87	C₂×C₄×C₄₇	#137	1	2	yes	—
88	C₂×Dic₄₇	—	8	2	no	—
89	C₂×Dic₄₇	—	8	2	no	—
90	C₂×Dic₄₇	—	8	2	no	—
91	C₈×C₄₇	—	4	2	no	—
92	C₈×C₄₇	—	8	1	no	—
93	C₄₇⋊C₈	—	8	2	no	—
94	#10621	—	47	1	no	maximal, Sylow
95	C₂²×C₄₇	—	4	2	no	—
96	C₂²×C₄₇	—	4	4	no	—
97	C₂²×C₄₇	—	8	1	no	—
98	C₂²×C₄₇	—	8	1	no	—
99	C₂²×C₄₇	—	8	2	no	—
100	C₂²×C₄₇	#397	1	1	yes	characteristic
101	C₂²×C₄₇	#463	1	2	yes	—
102	C₂²×C₄₇	#466	1	1	yes	characteristic
103	C₂²×C₄₇	#470	1	1	yes	characteristic
104	C₂²×C₄₇	#471	1	2	yes	—
105	C₄×C₄₇	—	2	2	no	—
106	C₄×C₄₇	—	8	1	no	—
107	C₄×C₄₇	#480	1	2	yes	—
108	C₄×C₄₇	#482	1	2	yes	—
109	C₄×C₄₇	#485	1	2	yes	—
110	C₄×C₄₇	#488	1	1	yes	characteristic
111	C₄×C₄₇	#490	1	1	yes	characteristic
112	Dic₄₇	—	16	2	no	—
113	#1954	D₄₇	1	1	yes	characteristic
114	#1834	—	47	1	no	—
115	#1802	—	47	2	no	—
116	#1296	—	47	2	no	—
117	#1277	—	47	1	no	—
118	C₂×C₄₇	—	8	2	no	—
119	C₂×C₄₇	#1681	1	2	yes	—
120	C₂×C₄₇	#1703	1	2	yes	—
121	C₂×C₄₇	#2073	1	1	yes	characteristic
122	C₂×C₄₇	#2075	1	1	yes	characteristic
123	C₂×C₄₇	#2079	1	1	yes	characteristic
124	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
125	C₂×C₄⋊C₈	—	47	2	no	—
126	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
127	C₂×#102	—	94	2	no	—
128	C₂×C₂²⋊C₈	—	2	2	no	—
129	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
130	#384	—	47	2	no	—
131	#340	—	94	2	no	—
132	#340	—	94	2	no	—
133	C₄₇	#10621	1	1	yes	characteristic, complemented, Sylow
134	C₂²×D₄	D₁₈₈	1	1	yes	characteristic
135	C₂³×C₄	—	2	1	no	—
136	C₂²×C₈	—	2	1	no	—
137	C₂²×C₈	—	94	2	no	—
138	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
139	C₄×D₄	—	2	2	no	—
140	C₄×D₄	—	2	2	no	—
141	C₂×C₄⋊C₄	—	94	2	no	—
142	C₂×C₄⋊C₄	—	94	2	no	—
143	C₂×C₄⋊C₄	—	94	2	no	—
144	C₂×C₄⋊C₄	D₁₈₈	1	1	yes	characteristic
145	C₂×C₂²⋊C₄	—	2	1	no	—
146	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
147	C₄⋊C₈	—	2	2	no	—
148	C₄⋊C₈	—	94	2	no	—
149	C₄⋊C₈	—	94	2	no	—
150	#102	—	188	4	no	—
151	C₂²⋊C₈	—	4	4	no	—
152	C₄×C₈	—	2	2	no	—
153	C₂⁴	—	2	1	no	—
154	C₂×D₄	—	2	2	no	—
155	C₂×D₄	—	2	1	no	—
156	C₂×D₄	—	2	2	no	—
157	C₂×D₄	D₃₇₆	1	2	yes	—
158	C₂²×C₄	—	2	1	no	—
159	C₂²×C₄	—	4	1	no	—
160	C₂²×C₄	—	4	1	no	—
161	C₂²×C₄	—	4	2	no	—
162	C₂²×C₄	—	4	2	no	—
163	C₂²×C₄	—	188	2	no	—
164	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
165	C₂²×C₄	#10625350	1	1	yes	characteristic
166	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
167	C₂×C₈	—	2	2	no	—
168	C₂×C₈	—	2	2	no	—
169	C₂×C₈	—	2	2	no	—
170	C₂×C₈	—	4	1	no	—
171	C₂×C₈	—	4	2	no	—
172	C₂×C₈	—	188	2	no	—
173	C₂×C₈	—	188	2	no	—
174	C₂×C₈	—	188	2	no	—
175	C₄⋊C₄	—	2	2	no	—
176	C₄⋊C₄	—	376	2	no	—
177	C₄⋊C₄	—	188	2	no	—
178	C₄⋊C₄	—	188	2	no	—
179	C₄⋊C₄	—	188	2	no	—
180	C₄⋊C₄	—	188	2	no	—
181	C₂²⋊C₄	—	4	2	no	—
182	C₄²	#10625352	1	2	yes	—
183	C₄²	#10625352	1	2	yes	—
184	C₂³	—	2	2	no	—
185	C₂³	—	4	1	no	—
186	C₂³	—	4	2	no	—
187	C₂³	—	4	1	no	—
188	C₂³	—	4	2	no	—
189	C₂³	#13093998	1	1	yes	characteristic
190	D₄	—	2	4	no	—
191	D₄	—	4	2	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	4	1	no	—
194	C₂×C₄	—	4	2	no	—
195	C₂×C₄	—	8	1	no	—
196	C₂×C₄	—	8	1	no	—
197	C₂×C₄	—	8	2	no	—
198	C₂×C₄	—	376	2	no	—
199	C₂×C₄	—	376	2	no	—
200	C₂×C₄	—	376	2	no	—
201	C₂×C₄	#13094005	1	1	yes	characteristic
202	C₂×C₄	#13094008	1	2	yes	—
203	C₂×C₄	#13094011	1	1	yes	characteristic
204	C₂×C₄	#13094017	1	2	yes	—
205	C₂×C₄	C₂×D₃₇₆	1	1	yes	characteristic
206	C₂×C₄	#13094044	1	2	yes	—
207	C₂×C₄	#13094046	1	1	yes	characteristic
208	C₂×C₄	#13094050	1	2	yes	—
209	C₂×C₄	#13094057	1	2	yes	—
210	C₈	—	4	2	no	—
211	C₈	—	8	1	no	—
212	C₈	—	376	2	no	—
213	C₂²	—	4	2	no	—
214	C₂²	—	4	4	no	—
215	C₂²	—	8	2	no	—
216	C₂²	—	8	1	no	—
217	C₂²	—	8	1	no	—
218	C₂²	#15689048	1	1	yes	characteristic
219	C₂²	#15689338	1	2	yes	—
220	C₂²	#15689359	1	1	yes	characteristic
221	C₂²	#15689381	1	1	yes	characteristic
222	C₂²	#15689386	1	2	yes	—
223	C₄	—	2	2	no	—
224	C₄	—	8	1	no	—
225	C₄	—	752	2	no	—
226	C₄	#15689437	1	2	yes	—
227	C₄	#15689444	1	2	yes	—
228	C₄	#15689465	1	2	yes	—
229	C₄	#15689477	1	1	yes	characteristic
230	C₄	#15689487	1	1	yes	characteristic
231	C₂	—	8	2	no	—
232	C₂	#20242825	1	2	yes	—
233	C₂	#20242963	1	2	yes	—
234	C₂	#20244801	1	1	yes	characteristic
235	C₂	#20244811	1	1	yes	characteristic
236	C₂	#20244833	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20243516

C₂

yes

maximal, characteristic, complemented

#20243388

C₂

yes

maximal

#20241272

C₂

yes

maximal, complemented

#20241223

C₂

yes

maximal, characteristic, complemented

C₄₇×#1954

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

C₂×#13093945

—

#15688993

C₂²

yes

—

#15688886

—

#15688885

—

C₂×C₄×D₄×C₄₇

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₄₇

C₂²

yes

characteristic

C₂×C₂²⋊C₈×C₄₇

—

C₂×C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂²×C₄₇⋊C₈

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

#13093945

—

C₂²×D₄×C₄₇

D₄

yes

characteristic

C₂³×C₄×C₄₇

—

C₂²×C₈×C₄₇

—

C₂²×C₈×C₄₇

D₄

yes

—

C₄×D₄×C₄₇

—

C₄×D₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₄₇

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₂²⋊C₈×C₄₇

—

C₄×C₈×C₄₇

—

C₂⁴×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

D₈

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

#41

yes

characteristic

C₂²×Dic₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

#41

yes

—

C₄²×C₄₇

#41

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

#121

yes

characteristic

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

#123

yes

characteristic

C₂×C₄×C₄₇

#123

yes

—

C₂×C₄×C₄₇

#124

yes

characteristic

C₂×C₄×C₄₇

#126

yes

—

C₂×C₄×C₄₇

C₂×D₈

yes

characteristic

C₂×C₄×C₄₇

#135

yes

—

C₂×C₄×C₄₇

#135

yes

characteristic

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₄₇

#137

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₈×C₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

#10621

—

maximal, Sylow

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

100

C₂²×C₄₇

#397

yes

characteristic

101

C₂²×C₄₇

#463

yes

—

102

C₂²×C₄₇

#466

yes

characteristic

103

C₂²×C₄₇

#470

yes

characteristic

104

C₂²×C₄₇

#471

yes

—

105

C₄×C₄₇

—

106

C₄×C₄₇

—

107

C₄×C₄₇

#480

yes

—

108

C₄×C₄₇

#482

yes

—

109

C₄×C₄₇

#485

yes

—

110

C₄×C₄₇

#488

yes

characteristic

111

C₄×C₄₇

#490

yes

characteristic

112

Dic₄₇

—

113

#1954

D₄₇

yes

characteristic

114

#1834

—

115

#1802

—

116

#1296

—

117

#1277

—

118

C₂×C₄₇

—

119

C₂×C₄₇

#1681

yes

—

120

C₂×C₄₇

#1703

yes

—

121

C₂×C₄₇

#2073

yes

characteristic

122

C₂×C₄₇

#2075

yes

characteristic

123

C₂×C₄₇

#2079

yes

characteristic

124

C₂×C₄×D₄

C₂×D₄₇

yes

characteristic

125

C₂×C₄⋊C₈

—

126

C₂×C₄⋊C₈

C₂×D₄₇

yes

characteristic

127

C₂×#102

—

128

C₂×C₂²⋊C₈

—

129

C₂×C₄×C₈

C₂×D₄₇

yes

characteristic

130

#384

—

131

#340

—

132

#340

—

133

C₄₇

#10621

yes

characteristic, complemented, Sylow

134

C₂²×D₄

D₁₈₈

yes

characteristic

135

C₂³×C₄

—

136

C₂²×C₈

—

137

C₂²×C₈

—

138

C₂²×C₈

C₂²⋊D₄₇

yes

—

139

C₄×D₄

—

140

C₄×D₄

—

141

C₂×C₄⋊C₄

—

142

C₂×C₄⋊C₄

—

143

C₂×C₄⋊C₄

—

144

C₂×C₄⋊C₄

D₁₈₈

yes

characteristic

145

C₂×C₂²⋊C₄

—

146

C₂×C₄²

C₂²×D₄₇

yes

characteristic

147

C₄⋊C₈

—

148

C₄⋊C₈

—

149

C₄⋊C₈

—

150

#102

—

188

—

151

C₂²⋊C₈

—

152

C₄×C₈

—

153

C₂⁴

—

154

C₂×D₄

—

155

C₂×D₄

—

156

C₂×D₄

—

157

C₂×D₄

D₃₇₆

yes

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

163

C₂²×C₄

—

188

—

164

C₂²×C₄

C₂×D₁₈₈

yes

characteristic

165

C₂²×C₄

#10625350

yes

characteristic

166

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

188

—

173

C₂×C₈

—

188

—

174

C₂×C₈

—

188

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

376

—

177

C₄⋊C₄

—

188

—

178

C₄⋊C₄

—

188

—

179

C₄⋊C₄

—

188

—

180

C₄⋊C₄

—

188

—

181

C₂²⋊C₄

—

182

C₄²

#10625352

yes

—

183

C₄²

#10625352

yes

—

184

C₂³

—

185

C₂³

—

186

C₂³

—

187

C₂³

—

188

C₂³

—

189

C₂³

#13093998

yes

characteristic

190

D₄

—

191

D₄

—

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

—

376

—

200

C₂×C₄

—

376

—

201

C₂×C₄

#13094005

yes

characteristic

202

C₂×C₄

#13094008

yes

—

203

C₂×C₄

#13094011

yes

characteristic

204

C₂×C₄

#13094017

yes

—

205

C₂×C₄

C₂×D₃₇₆

yes

characteristic

206

C₂×C₄

#13094044

yes

—

207

C₂×C₄

#13094046

yes

characteristic

208

C₂×C₄

#13094050

yes

—

209

C₂×C₄

#13094057

yes

—

210

C₈

—

211

C₈

—

212

C₈

—

376

—

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

—

218

C₂²

#15689048

yes

characteristic

219

C₂²

#15689338

yes

—

220

C₂²

#15689359

yes

characteristic

221

C₂²

#15689381

yes

characteristic

222

C₂²

#15689386

yes

—

223

C₄

—

224

C₄

—

225

C₄

—

752

—

226

C₄

#15689437

yes

—

227

C₄

#15689444

yes

—

228

C₄

#15689465

yes

—

229

C₄

#15689477

yes

characteristic

230

C₄

#15689487

yes

characteristic

231

C₂

—

232

C₂

#20242825

yes

—

233

C₂

#20242963

yes

—

234

C₂

#20244801

yes

characteristic

235

C₂

#20244811

yes

characteristic

236

C₂

#20244833

yes

characteristic

	subgroup	G/H
center	C₂³	#13093998
commutator, cosocle	C₂×C₄²×C₄₇	C₂³
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1954	C₂
socle	C₂³×C₄₇	#121
prime radical	C₂²×D₄×C₄₇	D₄
hypercenter	#1954	D₄₇
hypocenter	C₄₇	#10621
LCS	G ▷ C₂×C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1954

subgroup

G/H

center

C₂³

#13093998

commutator, cosocle

C₂×C₄²×C₄₇

C₂³

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#1954

C₂

socle

C₂³×C₄₇

#121

prime radical

C₂²×D₄×C₄₇

D₄

D₄₇

C₄₇

G ▷ C₂×C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1954

N	H ≅ G/N	type
1. #20243516	C₂	semidirect
3. #20241272	C₂	semidirect
4. #20241223	C₂	semidirect
133. C₄₇	#10621	semidirect

H ≅ G/N

type

1. #20243516

C₂

semidirect

3. #20241272

C₂

semidirect

4. #20241223

C₂

semidirect

133. C₄₇

#10621

semidirect

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

subgroup	index
#20243516	2
#20243388	2
#20241272	2
#20241223	2
C₄₇×#1954	2
#10621	47

subgroup

index

C₄₇×#1954

Subgroups — #26121012

Conjugacy classes of subgroups

Complements

Maximal subgroups