Group #20247851 — subgroups

Subgroups — #20247851

Order 6016.

568 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 153 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×#13093983	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689037	C₂	1	4	yes	maximal, complemented
3	#15689026	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689026	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689011	C₂	1	4	yes	maximal, complemented
6	#15688992	C₂	1	1	yes	maximal, characteristic, complemented
7	#15688988	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₂²⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#121×C₄₇	C₂	1	1	yes	maximal, characteristic
10	#13093983	—	2	4	no	—
11	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
13	C₂×Dic₄₇⋊C₄	C₂²	1	4	yes	—
14	C₂×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
15	C₂×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
16	C₂×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
17	C₂×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
18	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
19	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
20	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
21	C₄₇⋊#95	C₂²	1	2	yes	—
22	C₄₇⋊#95	C₂²	1	4	yes	—
23	C₂²×D₄×C₄₇	C₂²	1	1	yes	characteristic
24	C₂²×D₄×C₄₇	C₂²	1	2	yes	—
25	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
26	#121×C₄₇	—	2	4	no	—
27	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
29	C₂⁴×C₄₇	C₂³	1	2	yes	—
30	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
31	C₂×D₄×C₄₇	—	2	4	no	—
32	C₂×D₄×C₄₇	—	2	2	no	—
33	C₂×D₄×C₄₇	—	2	2	no	—
34	C₂×D₄×C₄₇	—	2	2	no	—
35	C₂×D₄×C₄₇	—	4	4	no	—
36	C₂²×C₄×C₄₇	—	2	2	no	—
37	C₂²×C₄×C₄₇	—	2	2	no	—
38	C₂²×C₄×C₄₇	D₄	1	4	yes	—
39	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
40	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
41	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
42	C₂²×Dic₄₇	C₂³	1	2	yes	—
43	C₂²×Dic₄₇	C₂³	1	2	yes	—
44	C₂²×Dic₄₇	C₂³	1	2	yes	—
45	C₂²×Dic₄₇	C₂³	1	2	yes	—
46	C₄⋊C₄×C₄₇	—	2	2	no	—
47	C₂²⋊C₄×C₄₇	—	2	4	no	—
48	C₂²⋊Dic₄₇	—	2	4	no	—
49	C₂²⋊Dic₄₇	—	2	4	no	—
50	C₂²⋊Dic₄₇	—	2	8	no	—
51	C₂²⋊Dic₄₇	—	4	4	no	—
52	C₄⋊Dic₄₇	—	2	2	no	—
53	C₄⋊Dic₄₇	—	2	2	no	—
54	Dic₄₇⋊C₄	—	4	4	no	—
55	C₄×Dic₄₇	—	2	4	no	—
56	C₄×Dic₄₇	—	2	2	no	—
57	C₄×Dic₄₇	—	2	2	no	—
58	C₂³×C₄₇	—	2	2	no	—
59	C₂³×C₄₇	—	2	1	no	—
60	C₂³×C₄₇	—	2	1	no	—
61	C₂³×C₄₇	—	2	2	no	—
62	C₂³×C₄₇	—	2	2	no	—
63	C₂³×C₄₇	—	2	4	no	—
64	C₂³×C₄₇	—	2	2	no	—
65	C₂³×C₄₇	—	2	2	no	—
66	C₂³×C₄₇	—	2	4	no	—
67	C₂³×C₄₇	C₂×D₄	1	2	yes	—
68	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
69	D₄×C₄₇	—	4	8	no	—
70	D₄×C₄₇	—	4	4	no	—
71	C₂×C₄×C₄₇	—	2	1	no	—
72	C₂×C₄×C₄₇	—	2	1	no	—
73	C₂×C₄×C₄₇	—	2	8	no	—
74	C₂×C₄×C₄₇	—	2	2	no	—
75	C₂×C₄×C₄₇	—	2	4	no	—
76	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
77	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
78	C₂×C₄×C₄₇	#41	1	2	yes	—
79	C₂×C₄×C₄₇	#41	1	2	yes	—
80	C₂×Dic₄₇	—	2	2	no	—
81	C₂×Dic₄₇	—	2	2	no	—
82	C₂×Dic₄₇	—	2	2	no	—
83	C₂×Dic₄₇	—	2	2	no	—
84	C₂×Dic₄₇	—	2	2	no	—
85	C₂×Dic₄₇	—	2	4	no	—
86	C₂×Dic₄₇	—	2	2	no	—
87	C₂×Dic₄₇	—	2	4	no	—
88	C₂×Dic₄₇	—	2	2	no	—
89	C₂×Dic₄₇	#41	1	4	yes	—
90	C₂²×C₄₇	—	2	2	no	—
91	C₂²×C₄₇	—	2	2	no	—
92	C₂²×C₄₇	—	2	2	no	—
93	C₂²×C₄₇	—	4	2	no	—
94	C₂²×C₄₇	—	4	2	no	—
95	C₂²×C₄₇	—	4	2	no	—
96	C₂²×C₄₇	—	4	2	no	—
97	C₂²×C₄₇	—	4	2	no	—
98	C₂²×C₄₇	—	4	4	no	—
99	C₂²×C₄₇	—	4	4	no	—
100	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
101	C₂²×C₄₇	C₂×#41	1	2	yes	—
102	C₂²×C₄₇	C₂×#41	1	1	yes	characteristic
103	C₂²×C₄₇	C₂×#41	1	1	yes	characteristic
104	C₂²×C₄₇	H(5,𝔽₂)	1	2	yes	—
105	C₄×C₄₇	—	2	2	no	—
106	C₄×C₄₇	—	4	2	no	—
107	C₄×C₄₇	#123	1	4	yes	—
108	Dic₄₇	—	2	4	no	—
109	Dic₄₇	—	4	2	no	—
110	Dic₄₇	—	4	2	no	—
111	Dic₄₇	—	4	2	no	—
112	#2500	—	47	1	no	maximal, Sylow
113	C₂×C₄₇	—	4	2	no	—
114	C₂×C₄₇	—	8	2	no	—
115	C₂×C₄₇	C₂×#123	1	1	yes	characteristic
116	C₂×C₄₇	#532	1	1	yes	characteristic
117	C₂×C₄₇	#535	1	1	yes	characteristic
118	C₂×C₄₇	#553	1	2	yes	—
119	C₂×C₄₇	#555	1	2	yes	—
120	C₂×#121	D₄₇	1	1	yes	characteristic
121	C₂×#117	—	47	1	no	—
122	#394	—	47	4	no	—
123	#390	—	47	1	no	—
124	#390	—	47	1	no	—
125	#388	—	47	4	no	—
126	#384	—	47	1	no	—
127	#382	—	47	1	no	—
128	C₄×C₂²⋊C₄	—	47	1	no	—
129	C₄₇	#2500	1	1	yes	characteristic, complemented, Sylow
130	C₂²×D₄	C₂×D₄₇	1	1	yes	characteristic
131	C₂²×D₄	C₂×D₄₇	1	2	yes	—
132	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
133	#121	—	2	4	no	—
134	#117	—	94	4	no	—
135	C₂×C₄⋊C₄	—	47	1	no	—
136	C₂×C₄⋊C₄	—	47	1	no	—
137	C₂×C₄⋊C₄	—	47	4	no	—
138	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
139	C₂×C₂²⋊C₄	—	47	2	no	—
140	C₂×C₂²⋊C₄	—	47	2	no	—
141	C₂×C₂²⋊C₄	—	47	4	no	—
142	C₂×C₂²⋊C₄	—	47	4	no	—
143	C₂×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
144	C₂×C₄²	—	47	2	no	—
145	C₂×C₄²	—	47	1	no	—
146	C₂×C₄²	—	47	1	no	—
147	#95	—	47	2	no	—
148	#95	—	47	4	no	—
149	C₂⁴	C₂²×D₄₇	1	2	yes	—
150	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
151	C₂×D₄	—	2	4	no	—
152	C₂×D₄	—	2	2	no	—
153	C₂×D₄	—	2	2	no	—
154	C₂×D₄	—	2	2	no	—
155	C₂×D₄	—	4	4	no	—
156	C₂²×C₄	—	2	2	no	—
157	C₂²×C₄	—	2	2	no	—
158	C₂²×C₄	—	47	2	no	—
159	C₂²×C₄	—	47	2	no	—
160	C₂²×C₄	—	47	2	no	—
161	C₂²×C₄	—	47	2	no	—
162	C₂²×C₄	C₂²⋊D₄₇	1	4	yes	—
163	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
164	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
165	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
166	C₄⋊C₄	—	2	2	no	—
167	C₄⋊C₄	—	94	2	no	—
168	C₄⋊C₄	—	94	2	no	—
169	C₄⋊C₄	—	188	4	no	—
170	C₂²⋊C₄	—	2	4	no	—
171	C₂²⋊C₄	—	94	4	no	—
172	C₂²⋊C₄	—	94	8	no	—
173	C₂²⋊C₄	—	94	4	no	—
174	C₂²⋊C₄	—	188	4	no	—
175	C₄²	—	94	2	no	—
176	C₄²	—	94	2	no	—
177	C₄²	—	94	4	no	—
178	C₂³	—	2	2	no	—
179	C₂³	—	2	1	no	—
180	C₂³	—	2	1	no	—
181	C₂³	—	2	2	no	—
182	C₂³	—	2	2	no	—
183	C₂³	—	2	4	no	—
184	C₂³	—	2	2	no	—
185	C₂³	—	2	2	no	—
186	C₂³	—	2	4	no	—
187	C₂³	C₂×C₂²⋊D₄₇	1	2	yes	—
188	C₂³	C₂³×D₄₇	1	1	yes	characteristic
189	D₄	—	4	8	no	—
190	D₄	—	4	4	no	—
191	C₂×C₄	—	2	1	no	—
192	C₂×C₄	—	2	1	no	—
193	C₂×C₄	—	2	8	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	2	4	no	—
196	C₂×C₄	—	47	4	no	—
197	C₂×C₄	—	94	2	no	—
198	C₂×C₄	—	94	2	no	—
199	C₂×C₄	—	94	2	no	—
200	C₂×C₄	—	94	2	no	—
201	C₂×C₄	—	94	2	no	—
202	C₂×C₄	—	94	4	no	—
203	C₂×C₄	—	94	2	no	—
204	C₂×C₄	—	94	2	no	—
205	C₂×C₄	—	94	4	no	—
206	C₂×C₄	#10625352	1	2	yes	—
207	C₂×C₄	#10625352	1	2	yes	—
208	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
209	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
210	C₂²	—	2	2	no	—
211	C₂²	—	2	2	no	—
212	C₂²	—	2	2	no	—
213	C₂²	—	4	2	no	—
214	C₂²	—	4	2	no	—
215	C₂²	—	4	4	no	—
216	C₂²	—	4	4	no	—
217	C₂²	—	4	2	no	—
218	C₂²	—	4	2	no	—
219	C₂²	—	4	2	no	—
220	C₂²	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
221	C₂²	#41×D₄₇	1	2	yes	—
222	C₂²	C₂×#10625352	1	1	yes	characteristic
223	C₂²	C₂×#10625352	1	1	yes	characteristic
224	C₂²	#13094069	1	2	yes	—
225	C₄	—	2	2	no	—
226	C₄	—	4	2	no	—
227	C₄	—	94	4	no	—
228	C₄	—	188	2	no	—
229	C₄	—	188	2	no	—
230	C₄	—	188	2	no	—
231	C₄	#13094005	1	4	yes	—
232	C₂	—	4	2	no	—
233	C₂	—	8	2	no	—
234	C₂	C₂×#13094005	1	1	yes	characteristic
235	C₂	#15689669	1	1	yes	characteristic
236	C₂	#15689690	1	1	yes	characteristic
237	C₂	#15689820	1	2	yes	—
238	C₂	#15689837	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093983

C₂

yes

maximal, characteristic, complemented

#15689037

C₂

yes

maximal, complemented

#15689026

C₂

yes

maximal, characteristic, complemented

#15689026

C₂

yes

maximal, characteristic, complemented

#15689011

C₂

yes

maximal, complemented

#15688992

C₂

yes

maximal, characteristic, complemented

#15688988

C₂

yes

maximal, characteristic, complemented

C₄×C₂²⋊Dic₄₇

C₂

yes

maximal, characteristic, complemented

C₂×#121×C₄₇

C₂

yes

maximal, characteristic

#13093983

—

C₂×C₄⋊Dic₄₇

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₇

C₂²

yes

characteristic

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×C₂²⋊Dic₄₇

C₂²

yes

—

C₂×C₂²⋊Dic₄₇

C₂²

yes

—

C₂×C₂²⋊Dic₄₇

C₂²

yes

—

C₂×C₂²⋊Dic₄₇

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

C₂×C₄×Dic₄₇

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂²×D₄×C₄₇

C₂²

yes

characteristic

C₂²×D₄×C₄₇

C₂²

yes

—

C₂³×C₄×C₄₇

C₂²

yes

characteristic

#121×C₄₇

—

C₂×C₄⋊C₄×C₄₇

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₄₇

C₂²

yes

—

C₂⁴×C₄₇

C₂³

yes

—

C₂⁴×C₄₇

C₂³

yes

characteristic

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₂²⋊Dic₄₇

—

C₂²⋊Dic₄₇

—

C₂²⋊Dic₄₇

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂×D₄

yes

—

C₂³×C₄₇

C₂⁴

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×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

#41

yes

—

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

#41

yes

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

100

C₂²×C₄₇

C₂²×D₄

yes

characteristic

101

C₂²×C₄₇

C₂×#41

yes

—

102

C₂²×C₄₇

C₂×#41

yes

characteristic

103

C₂²×C₄₇

C₂×#41

yes

characteristic

104

C₂²×C₄₇

H(5,𝔽₂)

yes

—

105

C₄×C₄₇

—

106

C₄×C₄₇

—

107

C₄×C₄₇

#123

yes

—

108

Dic₄₇

—

109

Dic₄₇

—

110

Dic₄₇

—

111

Dic₄₇

—

112

#2500

—

maximal, Sylow

113

C₂×C₄₇

—

114

C₂×C₄₇

—

115

C₂×C₄₇

C₂×#123

yes

characteristic

116

C₂×C₄₇

#532

yes

characteristic

117

C₂×C₄₇

#535

yes

characteristic

118

C₂×C₄₇

#553

yes

—

119

C₂×C₄₇

#555

yes

—

120

C₂×#121

D₄₇

yes

characteristic

121

C₂×#117

—

122

#394

—

123

#390

—

124

#390

—

125

#388

—

126

#384

—

127

#382

—

128

C₄×C₂²⋊C₄

—

129

C₄₇

#2500

yes

characteristic, complemented, Sylow

130

C₂²×D₄

C₂×D₄₇

yes

characteristic

131

C₂²×D₄

C₂×D₄₇

yes

—

132

C₂³×C₄

C₂×D₄₇

yes

characteristic

133

#121

—

134

#117

—

135

C₂×C₄⋊C₄

—

136

C₂×C₄⋊C₄

—

137

C₂×C₄⋊C₄

—

138

C₂×C₄⋊C₄

C₂×D₄₇

yes

characteristic

139

C₂×C₂²⋊C₄

—

140

C₂×C₂²⋊C₄

—

141

C₂×C₂²⋊C₄

—

142

C₂×C₂²⋊C₄

—

143

C₂×C₂²⋊C₄

C₂×D₄₇

yes

—

144

C₂×C₄²

—

145

C₂×C₄²

—

146

C₂×C₄²

—

147

#95

—

148

#95

—

149

C₂⁴

C₂²×D₄₇

yes

—

150

C₂⁴

C₂²×D₄₇

yes

characteristic

151

C₂×D₄

—

152

C₂×D₄

—

153

C₂×D₄

—

154

C₂×D₄

—

155

C₂×D₄

—

156

C₂²×C₄

—

157

C₂²×C₄

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

C₂²⋊D₄₇

yes

—

163

C₂²×C₄

C₂²×D₄₇

yes

—

164

C₂²×C₄

C₂²×D₄₇

yes

characteristic

165

C₂²×C₄

C₂²×D₄₇

yes

characteristic

166

C₄⋊C₄

—

167

C₄⋊C₄

—

168

C₄⋊C₄

—

169

C₄⋊C₄

—

188

—

170

C₂²⋊C₄

—

171

C₂²⋊C₄

—

172

C₂²⋊C₄

—

173

C₂²⋊C₄

—

174

C₂²⋊C₄

—

188

—

175

C₄²

—

176

C₄²

—

177

C₄²

—

178

C₂³

—

179

C₂³

—

180

C₂³

—

181

C₂³

—

182

C₂³

—

183

C₂³

—

184

C₂³

—

185

C₂³

—

186

C₂³

—

187

C₂³

C₂×C₂²⋊D₄₇

yes

—

188

C₂³

C₂³×D₄₇

yes

characteristic

189

D₄

—

190

D₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

#10625352

yes

—

207

C₂×C₄

#10625352

yes

—

208

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

209

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

210

C₂²

—

211

C₂²

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

—

218

C₂²

—

219

C₂²

—

220

C₂²

C₂²×C₂²⋊D₄₇

yes

characteristic

221

C₂²

#41×D₄₇

yes

—

222

C₂²

C₂×#10625352

yes

characteristic

223

C₂²

C₂×#10625352

yes

characteristic

224

C₂²

#13094069

yes

—

225

C₄

—

226

C₄

—

227

C₄

—

228

C₄

—

188

—

229

C₄

—

188

—

230

C₄

—

188

—

231

C₄

#13094005

yes

—

232

C₂

—

233

C₂

—

234

C₂

C₂×#13094005

yes

characteristic

235

C₂

#15689669

yes

characteristic

236

C₂

#15689690

yes

characteristic

237

C₂

#15689820

yes

—

238

C₂

#15689837

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂⁴
Fitting	C₂×#121×C₄₇	C₂
hypercenter	C₂×#121	D₄₇
hypocenter	C₄₇	#2500
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×#121

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator, socle

C₂³×C₄₇

C₂⁴

Fitting

C₂×#121×C₄₇

C₂

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ C₂×#121

N	H ≅ G/N	type
1. C₂×#13093983	C₂	semidirect
2. #15689037	C₂	semidirect
3. #15689026	C₂	semidirect
4. #15689026	C₂	semidirect
5. #15689011	C₂	semidirect
6. #15688992	C₂	semidirect
7. #15688988	C₂	semidirect
8. C₄×C₂²⋊Dic₄₇	C₂	semidirect
129. C₄₇	#2500	semidirect

H ≅ G/N

type

1. C₂×#13093983

C₂

semidirect

2. #15689037

C₂

semidirect

3. #15689026

C₂

semidirect

4. #15689026

C₂

semidirect

5. #15689011

C₂

semidirect

6. #15688992

C₂

semidirect

7. #15688988

C₂

semidirect

8. C₄×C₂²⋊Dic₄₇

C₂

semidirect

129. C₄₇

#2500

semidirect

Subgroups — #20247851

Conjugacy classes of subgroups

Complements