Group #20244472 — subgroups

Subgroups — #20244472

Order 6016.

406 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 93 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	C₂²×#10625325	C₂	1	1	yes	maximal, characteristic
2	C₂²×#10625336	C₂	1	1	yes	maximal, characteristic
3	C₂×#13094022	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#13093947	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689024	C₂	1	1	yes	maximal, characteristic
6	#15688877	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#103×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×Dic₉₄	C₂²	1	1	yes	characteristic
9	C₂²×D₁₈₈	C₂²	1	1	yes	characteristic
10	C₂×#10625325	—	2	2	no	—
11	C₂×#10625325	—	2	2	no	—
12	C₂×#10625325	—	2	2	no	—
13	C₂×#10625336	—	2	2	no	—
14	C₂×#10625336	—	2	2	no	—
15	C₂×#10625336	—	2	2	no	—
16	C₂²×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
17	#13094022	—	2	2	no	—
18	#13094022	—	2	2	no	—
19	C₂×Dic₄₇⋊C₄	—	2	2	no	—
20	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
21	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
22	#13093947	—	2	2	no	—
23	C₂²×Q₈×C₄₇	C₂²	1	1	yes	characteristic
24	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
26	#103×C₄₇	—	2	2	no	—
27	C₂³×D₄₇	—	2	1	no	—
28	C₂×Q₈×C₄₇	—	2	1	no	—
29	C₂×Q₈×C₄₇	—	2	1	no	—
30	C₂×Q₈×C₄₇	—	2	1	no	—
31	C₂×Q₈×C₄₇	—	2	1	no	—
32	C₂×Q₈×C₄₇	—	2	1	no	—
33	C₂×Q₈×C₄₇	D₄	1	2	yes	—
34	C₂²×C₄×C₄₇	—	2	1	no	—
35	C₂²×C₄×C₄₇	—	2	1	no	—
36	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
37	C₂²×Dic₄₇	—	2	1	no	—
38	C₂²×Dic₄₇	D₄	1	2	yes	—
39	C₂×D₁₈₈	—	2	1	no	—
40	C₂×D₁₈₈	—	2	1	no	—
41	C₂×D₁₈₈	—	2	1	no	—
42	C₂×D₁₈₈	—	2	1	no	—
43	C₂×D₁₈₈	—	2	1	no	—
44	C₂×D₁₈₈	D₄	1	2	yes	—
45	C₂×Dic₉₄	—	2	1	no	—
46	C₂×Dic₉₄	—	2	1	no	—
47	C₂×Dic₉₄	—	2	1	no	—
48	C₂×Dic₉₄	—	2	1	no	—
49	C₂×Dic₉₄	—	2	1	no	—
50	C₂×Dic₉₄	D₄	1	2	yes	—
51	C₂×C₈×C₄₇	—	2	1	no	—
52	C₂×C₈×C₄₇	—	2	1	no	—
53	C₂×C₈×C₄₇	D₄	1	2	yes	—
54	C₄⋊C₄×C₄₇	—	2	1	no	—
55	C₄⋊C₄×C₄₇	—	2	1	no	—
56	#10625336	—	2	8	no	—
57	(C₂×D₄₇)⋊C₄	—	4	4	no	—
58	Dic₄₇⋊C₄	—	2	8	no	—
59	C₄×Dic₄₇	—	2	1	no	—
60	C₄×Dic₄₇	—	2	1	no	—
61	C₂×C₄₇⋊C₈	—	2	1	no	—
62	C₂×C₄₇⋊C₈	—	2	1	no	—
63	C₂×C₄₇⋊C₈	D₄	1	2	yes	—
64	#10625325	—	2	8	no	—
65	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
66	C₂²×D₄₇	—	2	2	no	—
67	C₂²×D₄₇	—	4	1	no	—
68	C₂²×D₄₇	—	4	1	no	—
69	C₂²×D₄₇	—	4	2	no	—
70	C₂²×D₄₇	—	4	2	no	—
71	Q₈×C₄₇	—	2	2	no	—
72	Q₈×C₄₇	—	2	2	no	—
73	Q₈×C₄₇	—	4	1	no	—
74	Q₈×C₄₇	—	4	1	no	—
75	C₂×C₄×C₄₇	—	2	2	no	—
76	C₂×C₄×C₄₇	—	4	1	no	—
77	C₂×C₄×C₄₇	—	4	1	no	—
78	C₂×C₄×C₄₇	—	4	1	no	—
79	C₂×C₄×C₄₇	—	4	2	no	—
80	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
81	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
82	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
83	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
84	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
85	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
86	C₂×Dic₄₇	—	2	2	no	—
87	C₂×Dic₄₇	—	2	2	no	—
88	C₂×Dic₄₇	—	2	2	no	—
89	C₂×Dic₄₇	—	4	1	no	—
90	C₂×Dic₄₇	—	4	1	no	—
91	C₂×Dic₄₇	SD₁₆	1	4	yes	complemented
92	D₁₈₈	—	2	2	no	—
93	D₁₈₈	—	2	2	no	—
94	D₁₈₈	—	4	1	no	—
95	D₁₈₈	—	4	1	no	—
96	Dic₉₄	—	2	2	no	—
97	Dic₉₄	—	2	2	no	—
98	Dic₉₄	—	4	1	no	—
99	Dic₉₄	—	4	1	no	—
100	C₈×C₄₇	—	2	2	no	—
101	C₄₇⋊C₈	—	2	2	no	—
102	C₂²×C₄₇	#120	1	1	yes	characteristic
103	C₂²×C₄₇	#121	1	1	yes	characteristic
104	C₂²×C₄₇	#127	1	1	yes	characteristic
105	C₂²×C₄₇	C₂×SD₁₆	1	2	yes	—
106	C₂²×C₄₇	#137	1	2	yes	—
107	C₂×D₄₇	—	4	2	no	—
108	C₂×D₄₇	—	4	4	no	—
109	C₂×D₄₇	—	8	2	no	—
110	C₂×D₄₇	—	8	1	no	—
111	C₂×D₄₇	—	8	1	no	—
112	C₄×C₄₇	—	4	2	no	—
113	C₄×C₄₇	—	8	1	no	—
114	C₄×C₄₇	#120	1	1	yes	characteristic
115	C₄×C₄₇	#120	1	1	yes	characteristic
116	C₄×C₄₇	#121	1	1	yes	characteristic
117	C₄×C₄₇	#121	1	1	yes	characteristic
118	Dic₄₇	—	2	4	no	—
119	Dic₄₇	—	4	2	no	—
120	#2013	—	47	1	no	maximal, Sylow
121	C₂×C₄₇	#392	1	1	yes	characteristic
122	C₂×C₄₇	#448	1	2	yes	—
123	C₂×C₄₇	#461	1	2	yes	—
124	C₂×C₄₇	#492	1	1	yes	characteristic
125	C₂×C₄₇	#497	1	1	yes	characteristic
126	D₄₇	—	8	2	no	—
127	C₂²×SD₁₆	—	47	1	no	—
128	C₂²×SD₁₆	—	47	1	no	—
129	C₂×C₄⋊Q₈	—	47	1	no	—
130	C₂×#103	—	47	1	no	—
131	C₂×#103	D₄₇	1	1	yes	characteristic, complemented
132	#390	—	47	1	no	—
133	#336	—	47	1	no	—
134	C₄₇	#2013	1	1	yes	characteristic, complemented, Sylow
135	C₂²×Q₈	—	47	1	no	—
136	C₂²×Q₈	C₂×D₄₇	1	1	yes	characteristic
137	C₂²×D₄	—	47	1	no	—
138	C₂×SD₁₆	—	94	2	no	—
139	C₂×SD₁₆	—	94	2	no	—
140	C₂×SD₁₆	—	94	2	no	—
141	C₂×SD₁₆	—	94	2	no	—
142	C₂×SD₁₆	—	94	2	no	—
143	C₂×SD₁₆	—	94	2	no	—
144	C₂²×C₈	—	47	1	no	—
145	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
146	C₄⋊Q₈	—	94	2	no	—
147	C₄⋊Q₈	—	94	2	no	—
148	C₂×C₄⋊C₄	—	94	2	no	—
149	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
150	C₂×C₂²⋊C₄	—	94	2	no	—
151	C₂×C₄²	—	47	1	no	—
152	#103	—	2	2	no	—
153	#103	—	94	2	no	—
154	C₂⁴	—	94	1	no	—
155	C₂×Q₈	—	2	1	no	—
156	C₂×Q₈	—	2	1	no	—
157	C₂×Q₈	—	2	1	no	—
158	C₂×Q₈	—	2	1	no	—
159	C₂×Q₈	—	2	1	no	—
160	C₂×Q₈	—	47	2	no	—
161	C₂×Q₈	—	94	1	no	—
162	C₂×Q₈	—	94	1	no	—
163	C₂×Q₈	—	94	1	no	—
164	C₂×Q₈	—	94	1	no	—
165	C₂×Q₈	—	94	1	no	—
166	C₂×Q₈	D₁₈₈	1	2	yes	—
167	C₂×D₄	—	47	2	no	—
168	C₂×D₄	—	94	1	no	—
169	C₂×D₄	—	94	1	no	—
170	C₂×D₄	—	94	1	no	—
171	C₂×D₄	—	94	1	no	—
172	C₂×D₄	—	94	1	no	—
173	C₂²×C₄	—	2	1	no	—
174	C₂²×C₄	—	2	1	no	—
175	C₂²×C₄	—	47	2	no	—
176	C₂²×C₄	—	94	1	no	—
177	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
178	SD₁₆	—	94	8	no	—
179	SD₁₆	—	94	8	no	—
180	C₂×C₈	—	2	1	no	—
181	C₂×C₈	—	2	1	no	—
182	C₂×C₈	—	47	2	no	—
183	C₂×C₈	—	94	1	no	—
184	C₂×C₈	—	94	1	no	—
185	C₂×C₈	C₂²⋊D₄₇	1	2	yes	—
186	C₄⋊C₄	—	2	1	no	—
187	C₄⋊C₄	—	2	1	no	—
188	C₄⋊C₄	—	94	8	no	—
189	C₂²⋊C₄	—	188	4	no	—
190	C₄²	—	94	1	no	—
191	C₄²	—	94	1	no	—
192	C₂³	—	94	2	no	—
193	C₂³	—	188	1	no	—
194	C₂³	—	188	1	no	—
195	C₂³	—	188	2	no	—
196	C₂³	—	188	2	no	—
197	C₂³	D₄×D₄₇	1	1	yes	characteristic
198	Q₈	—	2	2	no	—
199	Q₈	—	2	2	no	—
200	Q₈	—	4	1	no	—
201	Q₈	—	4	1	no	—
202	Q₈	—	94	2	no	—
203	Q₈	—	94	2	no	—
204	Q₈	—	188	1	no	—
205	Q₈	—	188	1	no	—
206	D₄	—	94	2	no	—
207	D₄	—	94	2	no	—
208	D₄	—	188	1	no	—
209	D₄	—	188	1	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	4	1	no	—
212	C₂×C₄	—	4	1	no	—
213	C₂×C₄	—	4	1	no	—
214	C₂×C₄	—	4	2	no	—
215	C₂×C₄	—	47	4	no	—
216	C₂×C₄	—	94	2	no	—
217	C₂×C₄	—	94	2	no	—
218	C₂×C₄	—	94	2	no	—
219	C₂×C₄	—	188	1	no	—
220	C₂×C₄	—	188	1	no	—
221	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
222	C₂×C₄	#10625350	1	1	yes	characteristic
223	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
224	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
225	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
226	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
227	C₈	—	2	2	no	—
228	C₈	—	94	2	no	—
229	C₂²	—	376	1	no	—
230	C₂²	—	376	1	no	—
231	C₂²	—	376	2	no	—
232	C₂²	—	188	2	no	—
233	C₂²	—	188	4	no	—
234	C₂²	#13093994	1	1	yes	characteristic
235	C₂²	#13093997	1	1	yes	characteristic
236	C₂²	#13094020	1	1	yes	characteristic
237	C₂²	SD₁₆×D₄₇	1	2	yes	—
238	C₂²	#13094056	1	2	yes	—
239	C₄	—	4	2	no	—
240	C₄	—	8	1	no	—
241	C₄	—	94	4	no	—
242	C₄	—	188	2	no	—
243	C₄	#13093992	1	1	yes	characteristic
244	C₄	#13093994	1	1	yes	characteristic
245	C₄	#13093997	1	1	yes	characteristic
246	C₄	#13093998	1	1	yes	characteristic
247	C₂	—	376	2	no	—
248	C₂	#15689032	1	1	yes	characteristic
249	C₂	#15689263	1	2	yes	—
250	C₂	#15689327	1	2	yes	—
251	C₂	#15689494	1	1	yes	characteristic
252	C₂	#15689516	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#10625325

C₂

yes

maximal, characteristic

C₂²×#10625336

C₂

yes

maximal, characteristic

C₂×#13094022

C₂

yes

maximal, characteristic, complemented

C₂×#13093947

C₂

yes

maximal, characteristic, complemented

#15689024

C₂

yes

maximal, characteristic

#15688877

C₂

yes

maximal, characteristic, complemented

C₂×#103×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂²×Dic₉₄

C₂²

yes

characteristic

C₂²×D₁₈₈

C₂²

yes

—

—

—

—

—

—

C₂²×C₄₇⋊C₈

C₂²

yes

characteristic

#13094022

—

#13094022

—

C₂×Dic₄₇⋊C₄

—

C₂×(C₂×D₄₇)⋊C₄

—

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

#13093947

—

C₂²×Q₈×C₄₇

C₂²

yes

characteristic

C₂²×C₈×C₄₇

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₇

C₂²

yes

characteristic

#103×C₄₇

—

C₂³×D₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

D₄

yes

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

D₄

yes

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

D₄

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

D₄

yes

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

#10625336

—

(C₂×D₄₇)⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

D₄

yes

—

#10625325

—

C₂³×C₄₇

C₂×D₄

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

#41

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

SD₁₆

yes

complemented

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

Dic₉₄

—

Dic₉₄

—

Dic₉₄

—

Dic₉₄

—

100

C₈×C₄₇

—

101

C₄₇⋊C₈

—

102

C₂²×C₄₇

#120

yes

characteristic

103

C₂²×C₄₇

#121

yes

characteristic

104

C₂²×C₄₇

#127

yes

characteristic

105

C₂²×C₄₇

C₂×SD₁₆

yes

—

106

C₂²×C₄₇

#137

yes

—

107

C₂×D₄₇

—

108

C₂×D₄₇

—

109

C₂×D₄₇

—

110

C₂×D₄₇

—

111

C₂×D₄₇

—

112

C₄×C₄₇

—

113

C₄×C₄₇

—

114

C₄×C₄₇

#120

yes

characteristic

115

C₄×C₄₇

#120

yes

characteristic

116

C₄×C₄₇

#121

yes

characteristic

117

C₄×C₄₇

#121

yes

characteristic

118

Dic₄₇

—

119

Dic₄₇

—

120

#2013

—

maximal, Sylow

121

C₂×C₄₇

#392

yes

characteristic

122

C₂×C₄₇

#448

yes

—

123

C₂×C₄₇

#461

yes

—

124

C₂×C₄₇

#492

yes

characteristic

125

C₂×C₄₇

#497

yes

characteristic

126

D₄₇

—

127

C₂²×SD₁₆

—

128

C₂²×SD₁₆

—

129

C₂×C₄⋊Q₈

—

130

C₂×#103

—

131

C₂×#103

D₄₇

yes

characteristic, complemented

132

#390

—

133

#336

—

134

C₄₇

#2013

yes

characteristic, complemented, Sylow

135

C₂²×Q₈

—

136

C₂²×Q₈

C₂×D₄₇

yes

characteristic

137

C₂²×D₄

—

138

C₂×SD₁₆

—

139

C₂×SD₁₆

—

140

C₂×SD₁₆

—

141

C₂×SD₁₆

—

142

C₂×SD₁₆

—

143

C₂×SD₁₆

—

144

C₂²×C₈

—

145

C₂²×C₈

C₂×D₄₇

yes

characteristic

146

C₄⋊Q₈

—

147

C₄⋊Q₈

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

C₂×D₄₇

yes

characteristic

150

C₂×C₂²⋊C₄

—

151

C₂×C₄²

—

152

#103

—

153

#103

—

154

C₂⁴

—

155

C₂×Q₈

—

156

C₂×Q₈

—

157

C₂×Q₈

—

158

C₂×Q₈

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

D₁₈₈

yes

—

167

C₂×D₄

—

168

C₂×D₄

—

169

C₂×D₄

—

170

C₂×D₄

—

171

C₂×D₄

—

172

C₂×D₄

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

C₂²×D₄₇

yes

characteristic

178

SD₁₆

—

179

SD₁₆

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

C₂²⋊D₄₇

yes

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₂²⋊C₄

—

188

—

190

C₄²

—

191

C₄²

—

192

C₂³

—

193

C₂³

—

188

—

194

C₂³

—

188

—

195

C₂³

—

188

—

196

C₂³

—

188

—

197

C₂³

D₄×D₄₇

yes

characteristic

198

Q₈

—

199

Q₈

—

200

Q₈

—

201

Q₈

—

202

Q₈

—

203

Q₈

—

204

Q₈

—

188

—

205

Q₈

—

188

—

206

D₄

—

207

D₄

—

208

D₄

—

188

—

209

D₄

—

188

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

188

—

220

C₂×C₄

—

188

—

221

C₂×C₄

C₂×D₁₈₈

yes

characteristic

222

C₂×C₄

#10625350

yes

characteristic

223

C₂×C₄

D₄×D₄₇

yes

characteristic

224

C₂×C₄

D₄×D₄₇

yes

characteristic

225

C₂×C₄

D₄×D₄₇

yes

characteristic

226

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

227

C₈

—

228

C₈

—

229

C₂²

—

376

—

230

C₂²

—

376

—

231

C₂²

—

376

—

232

C₂²

—

188

—

233

C₂²

—

188

—

234

C₂²

#13093994

yes

characteristic

235

C₂²

#13093997

yes

characteristic

236

C₂²

#13094020

yes

characteristic

237

C₂²

SD₁₆×D₄₇

yes

—

238

C₂²

#13094056

yes

—

239

C₄

—

240

C₄

—

241

C₄

—

242

C₄

—

188

—

243

C₄

#13093992

yes

characteristic

244

C₄

#13093994

yes

characteristic

245

C₄

#13093997

yes

characteristic

246

C₄

#13093998

yes

characteristic

247

C₂

—

376

—

248

C₂

#15689032

yes

characteristic

249

C₂

#15689263

yes

—

250

C₂

#15689327

yes

—

251

C₂

#15689494

yes

characteristic

252

C₂

#15689516

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₄₇
commutator	C₂²×C₄×C₄₇	C₂³
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₂×#103×C₄₇	C₂
socle	C₂³×C₄₇	C₂×D₄
hypercenter	C₂×#103	D₄₇
hypocenter	C₄₇	#2013
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#103

subgroup

G/H

center

C₂³

D₄×D₄₇

commutator

C₂²×C₄×C₄₇

C₂³

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₂×#103×C₄₇

C₂

socle

C₂³×C₄₇

C₂×D₄

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#103

N	H ≅ G/N	type
3. C₂×#13094022	C₂	semidirect
4. C₂×#13093947	C₂	semidirect
6. #15688877	C₂	semidirect
7. C₂×#103×C₄₇	C₂	semidirect
91. C₂×Dic₄₇	SD₁₆	semidirect
131. C₂×#103	D₄₇	semidirect
134. C₄₇	#2013	semidirect

H ≅ G/N

type

3. C₂×#13094022

C₂

semidirect

4. C₂×#13093947

C₂

semidirect

6. #15688877

C₂

semidirect

7. C₂×#103×C₄₇

C₂

semidirect

91. C₂×Dic₄₇

SD₁₆

semidirect

131. C₂×#103

D₄₇

semidirect

134. C₄₇

#2013

semidirect

Subgroups — #20244472

Conjugacy classes of subgroups

Complements