Group #20248364 — subgroups

Subgroups — #20248364

Order 6016.

576 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 169 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×#13094022	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13094013	C₂	1	1	yes	maximal, characteristic
3	C₂×#13094012	C₂	1	1	yes	maximal, characteristic
4	#15689045	C₂	1	4	yes	maximal, complemented
5	#15689028	C₂	1	1	yes	maximal, characteristic, complemented
6	#15689024	C₂	1	1	yes	maximal, characteristic
7	#15689014	C₂	1	4	yes	maximal, complemented
8	C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×Dic₉₄	C₂²	1	1	yes	characteristic
11	C₂²×D₁₈₈	C₂²	1	1	yes	characteristic
12	#13094022	—	2	4	no	—
13	#13094013	—	2	4	no	—
14	#13094012	—	2	4	no	—
15	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
16	C₂×Dic₄₇⋊C₄	C₂²	1	4	yes	—
17	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
18	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	4	yes	—
19	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	4	yes	—
20	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
21	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
22	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
23	C₄₇⋊#95	C₂²	1	2	yes	—
24	C₄₇⋊#95	C₂²	1	4	yes	—
25	C₂²×Q₈×C₄₇	C₂²	1	1	yes	characteristic
26	C₄×Q₈×C₄₇	—	2	4	no	—
27	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
29	C₂×C₄²×C₄₇	C₂²	1	2	yes	—
30	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
31	C₂³×D₄₇	C₂³	1	2	yes	—
32	C₂×Q₈×C₄₇	—	2	2	no	—
33	C₂×Q₈×C₄₇	—	2	2	no	—
34	C₂×Q₈×C₄₇	D₄	1	4	yes	—
35	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
36	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
37	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
38	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
39	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
40	C₂²×Dic₄₇	C₂³	1	2	yes	—
41	C₂²×Dic₄₇	C₂³	1	2	yes	—
42	C₂²×Dic₄₇	C₂³	1	2	yes	—
43	C₂×D₁₈₈	—	2	2	no	—
44	C₂×D₁₈₈	—	2	2	no	—
45	C₂×D₁₈₈	—	2	2	no	—
46	C₂×Dic₉₄	—	2	2	no	—
47	C₂×Dic₉₄	—	2	2	no	—
48	C₂×Dic₉₄	—	2	2	no	—
49	C₄⋊C₄×C₄₇	—	2	4	no	—
50	C₄⋊C₄×C₄₇	—	2	2	no	—
51	C₄²×C₄₇	—	2	4	no	—
52	C₄²×C₄₇	D₄	1	4	yes	—
53	(C₂×D₄₇)⋊C₄	—	2	4	no	—
54	(C₂×D₄₇)⋊C₄	—	2	4	no	—
55	(C₂×D₄₇)⋊C₄	—	2	8	no	—
56	(C₂×D₄₇)⋊C₄	—	2	8	no	—
57	C₄⋊Dic₄₇	—	2	4	no	—
58	Dic₄₇⋊C₄	—	2	8	no	—
59	C₄×Dic₄₇	—	2	2	no	—
60	C₄×Dic₄₇	—	2	2	no	—
61	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
62	C₂²×D₄₇	—	2	2	no	—
63	C₂²×D₄₇	—	2	2	no	—
64	C₂²×D₄₇	—	2	4	no	—
65	C₂²×D₄₇	—	2	2	no	—
66	C₂²×D₄₇	—	2	4	no	—
67	Q₈×C₄₇	—	2	8	no	—
68	C₂×C₄×C₄₇	—	2	2	no	—
69	C₂×C₄×C₄₇	—	2	2	no	—
70	C₂×C₄×C₄₇	—	2	2	no	—
71	C₂×C₄×C₄₇	—	2	2	no	—
72	C₂×C₄×C₄₇	—	2	2	no	—
73	C₂×C₄×C₄₇	—	2	4	no	—
74	C₂×C₄×C₄₇	C₂×D₄	1	4	yes	—
75	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
76	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
77	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
78	C₂×C₄×C₄₇	C₂×D₄	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	2	no	—
86	C₂×Dic₄₇	—	2	2	no	—
87	C₂×Dic₄₇	—	2	2	no	—
88	C₂×Dic₄₇	#41	1	4	yes	—
89	D₁₈₈	—	4	4	no	—
90	Dic₉₄	—	4	4	no	—
91	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
92	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
93	C₂²×C₄₇	C₂×#41	1	2	yes	—
94	C₂²×C₄₇	C₂×#41	1	1	yes	characteristic
95	C₂²×C₄₇	2₋¹⁺⁴	1	2	yes	—
96	C₂×D₄₇	—	4	2	no	—
97	C₂×D₄₇	—	4	2	no	—
98	C₂×D₄₇	—	4	2	no	—
99	C₂×D₄₇	—	4	4	no	—
100	C₂×D₄₇	—	4	4	no	—
101	C₄×C₄₇	—	2	4	no	—
102	C₄×C₄₇	—	2	2	no	—
103	C₄×C₄₇	—	2	2	no	—
104	C₄×C₄₇	—	4	2	no	—
105	C₄×C₄₇	#121	1	4	yes	—
106	Dic₄₇	—	2	4	no	—
107	Dic₄₇	—	4	2	no	—
108	Dic₄₇	—	4	2	no	—
109	#2545	—	47	1	no	maximal, Sylow
110	C₂×C₄₇	C₂×#121	1	1	yes	characteristic
111	C₂×C₄₇	#532	1	1	yes	characteristic
112	C₂×C₄₇	#536	1	1	yes	characteristic
113	C₂×C₄₇	#548	1	2	yes	—
114	C₂×C₄₇	#556	1	2	yes	—
115	D₄₇	—	8	2	no	—
116	C₂×C₄⋊Q₈	—	47	1	no	—
117	C₂×#124	—	47	1	no	—
118	C₂×#124	—	47	1	no	—
119	C₂×C₄×Q₈	D₄₇	1	1	yes	characteristic, complemented
120	#396	—	47	4	no	—
121	#391	—	47	1	no	—
122	#390	—	47	1	no	—
123	#388	—	47	4	no	—
124	C₄×C₄⋊C₄	—	47	1	no	—
125	C₄₇	#2545	1	1	yes	characteristic, complemented, Sylow
126	C₂²×Q₈	—	47	1	no	—
127	C₂²×Q₈	C₂×D₄₇	1	1	yes	characteristic
128	C₂²×D₄	—	47	1	no	—
129	C₄⋊Q₈	—	94	4	no	—
130	#124	—	94	4	no	—
131	#124	—	94	4	no	—
132	C₄×Q₈	—	2	4	no	—
133	C₂×C₄⋊C₄	—	47	4	no	—
134	C₂×C₄⋊C₄	—	47	2	no	—
135	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
136	C₂×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
137	C₂×C₂²⋊C₄	—	47	2	no	—
138	C₂×C₂²⋊C₄	—	47	4	no	—
139	C₂×C₂²⋊C₄	—	47	2	no	—
140	C₂×C₂²⋊C₄	—	47	4	no	—
141	C₂×C₄²	—	47	1	no	—
142	C₂×C₄²	—	47	1	no	—
143	C₂×C₄²	C₂×D₄₇	1	2	yes	—
144	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
145	#95	—	47	2	no	—
146	#95	—	47	4	no	—
147	C₂⁴	—	47	2	no	—
148	C₂×Q₈	—	2	2	no	—
149	C₂×Q₈	—	2	2	no	—
150	C₂×Q₈	—	94	2	no	—
151	C₂×Q₈	—	94	2	no	—
152	C₂×Q₈	—	94	2	no	—
153	C₂×Q₈	D₁₈₈	1	4	yes	—
154	C₂×D₄	—	94	2	no	—
155	C₂×D₄	—	94	2	no	—
156	C₂×D₄	—	94	2	no	—
157	C₂²×C₄	—	47	2	no	—
158	C₂²×C₄	—	47	2	no	—
159	C₂²×C₄	—	47	2	no	—
160	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
161	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
162	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
163	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
164	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
165	C₄⋊C₄	—	2	4	no	—
166	C₄⋊C₄	—	2	2	no	—
167	C₄⋊C₄	—	94	4	no	—
168	C₄⋊C₄	—	94	8	no	—
169	C₂²⋊C₄	—	94	8	no	—
170	C₂²⋊C₄	—	94	8	no	—
171	C₂²⋊C₄	—	94	4	no	—
172	C₂²⋊C₄	—	94	4	no	—
173	C₄²	—	2	4	no	—
174	C₄²	—	94	2	no	—
175	C₄²	—	94	2	no	—
176	C₄²	C₂²⋊D₄₇	1	4	yes	—
177	C₂³	—	94	2	no	—
178	C₂³	—	94	2	no	—
179	C₂³	—	94	4	no	—
180	C₂³	—	94	2	no	—
181	C₂³	—	94	4	no	—
182	C₂³	C₂³×D₄₇	1	1	yes	characteristic
183	Q₈	—	2	8	no	—
184	Q₈	—	188	4	no	—
185	D₄	—	188	4	no	—
186	C₂×C₄	—	2	2	no	—
187	C₂×C₄	—	2	2	no	—
188	C₂×C₄	—	2	2	no	—
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	4	no	—
192	C₂×C₄	—	47	4	no	—
193	C₂×C₄	—	94	2	no	—
194	C₂×C₄	—	94	2	no	—
195	C₂×C₄	—	94	2	no	—
196	C₂×C₄	—	94	2	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	C₂×D₁₈₈	1	4	yes	—
202	C₂×C₄	C₂×D₁₈₈	1	2	yes	—
203	C₂×C₄	#10625350	1	2	yes	—
204	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
205	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
206	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
207	C₂²	—	188	4	no	—
208	C₂²	—	188	4	no	—
209	C₂²	—	188	2	no	—
210	C₂²	—	188	2	no	—
211	C₂²	—	188	2	no	—
212	C₂²	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
213	C₂²	C₂²×D₁₈₈	1	1	yes	characteristic
214	C₂²	#41×D₄₇	1	2	yes	—
215	C₂²	C₂×#10625350	1	1	yes	characteristic
216	C₂²	#13094072	1	2	yes	—
217	C₄	—	2	4	no	—
218	C₄	—	2	2	no	—
219	C₄	—	2	2	no	—
220	C₄	—	4	2	no	—
221	C₄	—	94	4	no	—
222	C₄	—	188	2	no	—
223	C₄	—	188	2	no	—
224	C₄	#13093998	1	4	yes	—
225	C₂	—	376	2	no	—
226	C₂	C₂×#13093998	1	1	yes	characteristic
227	C₂	#15689669	1	1	yes	characteristic
228	C₂	#15689697	1	1	yes	characteristic
229	C₂	#15689785	1	2	yes	—
230	C₂	#15689845	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13094022

C₂

yes

maximal, characteristic, complemented

C₂×#13094013

C₂

yes

maximal, characteristic

C₂×#13094012

C₂

yes

maximal, characteristic

#15689045

C₂

yes

maximal, complemented

#15689028

C₂

yes

maximal, characteristic, complemented

#15689024

C₂

yes

maximal, characteristic

#15689014

C₂

yes

maximal, complemented

C₄×C₄⋊Dic₄₇

C₂

yes

maximal, characteristic, complemented

C₂×C₄×Q₈×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂²×Dic₉₄

C₂²

yes

characteristic

C₂²×D₁₈₈

C₂²

yes

—

—

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₇)⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₇)⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₇)⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₇)⋊C₄

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂²×Q₈×C₄₇

C₂²

yes

characteristic

C₄×Q₈×C₄₇

—

C₂×C₄⋊C₄×C₄₇

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₂³×D₄₇

C₂³

yes

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

D₄

yes

—

(C₂×D₄₇)⋊C₄

—

(C₂×D₄₇)⋊C₄

—

(C₂×D₄₇)⋊C₄

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂³×C₄₇

C₂⁴

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

Q₈×C₄₇

—

C₂×C₄×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

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

#41

yes

—

D₁₈₈

—

Dic₉₄

—

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₂²×C₄₇

C₂×#41

yes

—

C₂²×C₄₇

C₂×#41

yes

characteristic

C₂²×C₄₇

2₋¹⁺⁴

yes

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

100

C₂×D₄₇

—

101

C₄×C₄₇

—

102

C₄×C₄₇

—

103

C₄×C₄₇

—

104

C₄×C₄₇

—

105

C₄×C₄₇

#121

yes

—

106

Dic₄₇

—

107

Dic₄₇

—

108

Dic₄₇

—

109

#2545

—

maximal, Sylow

110

C₂×C₄₇

C₂×#121

yes

characteristic

111

C₂×C₄₇

#532

yes

characteristic

112

C₂×C₄₇

#536

yes

characteristic

113

C₂×C₄₇

#548

yes

—

114

C₂×C₄₇

#556

yes

—

115

D₄₇

—

116

C₂×C₄⋊Q₈

—

117

C₂×#124

—

118

C₂×#124

—

119

C₂×C₄×Q₈

D₄₇

yes

characteristic, complemented

120

#396

—

121

#391

—

122

#390

—

123

#388

—

124

C₄×C₄⋊C₄

—

125

C₄₇

#2545

yes

characteristic, complemented, Sylow

126

C₂²×Q₈

—

127

C₂²×Q₈

C₂×D₄₇

yes

characteristic

128

C₂²×D₄

—

129

C₄⋊Q₈

—

130

#124

—

131

#124

—

132

C₄×Q₈

—

133

C₂×C₄⋊C₄

—

134

C₂×C₄⋊C₄

—

135

C₂×C₄⋊C₄

C₂×D₄₇

yes

characteristic

136

C₂×C₄⋊C₄

C₂×D₄₇

yes

—

137

C₂×C₂²⋊C₄

—

138

C₂×C₂²⋊C₄

—

139

C₂×C₂²⋊C₄

—

140

C₂×C₂²⋊C₄

—

141

C₂×C₄²

—

142

C₂×C₄²

—

143

C₂×C₄²

C₂×D₄₇

yes

—

144

C₂×C₄²

C₂×D₄₇

yes

characteristic

145

#95

—

146

#95

—

147

C₂⁴

—

148

C₂×Q₈

—

149

C₂×Q₈

—

150

C₂×Q₈

—

151

C₂×Q₈

—

152

C₂×Q₈

—

153

C₂×Q₈

D₁₈₈

yes

—

154

C₂×D₄

—

155

C₂×D₄

—

156

C₂×D₄

—

157

C₂²×C₄

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

C₂²×D₄₇

yes

—

161

C₂²×C₄

C₂²×D₄₇

yes

—

162

C₂²×C₄

C₂²×D₄₇

yes

characteristic

163

C₂²×C₄

C₂²×D₄₇

yes

characteristic

164

C₂²×C₄

C₂²×D₄₇

yes

characteristic

165

C₄⋊C₄

—

166

C₄⋊C₄

—

167

C₄⋊C₄

—

168

C₄⋊C₄

—

169

C₂²⋊C₄

—

170

C₂²⋊C₄

—

171

C₂²⋊C₄

—

172

C₂²⋊C₄

—

173

C₄²

—

174

C₄²

—

175

C₄²

—

176

C₄²

C₂²⋊D₄₇

yes

—

177

C₂³

—

178

C₂³

—

179

C₂³

—

180

C₂³

—

181

C₂³

—

182

C₂³

C₂³×D₄₇

yes

characteristic

183

Q₈

—

184

Q₈

—

188

—

185

D₄

—

188

—

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

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

C₂×D₁₈₈

yes

—

202

C₂×C₄

C₂×D₁₈₈

yes

—

203

C₂×C₄

#10625350

yes

—

204

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

205

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

206

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

207

C₂²

—

188

—

208

C₂²

—

188

—

209

C₂²

—

188

—

210

C₂²

—

188

—

211

C₂²

—

188

—

212

C₂²

C₂²×C₂²⋊D₄₇

yes

characteristic

213

C₂²

C₂²×D₁₈₈

yes

characteristic

214

C₂²

#41×D₄₇

yes

—

215

C₂²

C₂×#10625350

yes

characteristic

216

C₂²

#13094072

yes

—

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

—

188

—

223

C₄

—

188

—

224

C₄

#13093998

yes

—

225

C₂

—

376

—

226

C₂

C₂×#13093998

yes

characteristic

227

C₂

#15689669

yes

characteristic

228

C₂

#15689697

yes

characteristic

229

C₂

#15689785

yes

—

230

C₂

#15689845

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂⁴
Fitting	C₂×C₄×Q₈×C₄₇	C₂
hypercenter	C₂×C₄×Q₈	D₄₇
hypocenter	C₄₇	#2545
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×Q₈

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator, socle

C₂³×C₄₇

C₂⁴

Fitting

C₂×C₄×Q₈×C₄₇

C₂

hypercenter

C₂×C₄×Q₈

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ C₂×C₄×Q₈

N	H ≅ G/N	type
1. C₂×#13094022	C₂	semidirect
4. #15689045	C₂	semidirect
5. #15689028	C₂	semidirect
7. #15689014	C₂	semidirect
8. C₄×C₄⋊Dic₄₇	C₂	semidirect
9. C₂×C₄×Q₈×C₄₇	C₂	semidirect
119. C₂×C₄×Q₈	D₄₇	semidirect
125. C₄₇	#2545	semidirect

H ≅ G/N

type

1. C₂×#13094022

C₂

semidirect

4. #15689045

C₂

semidirect

5. #15689028

C₂

semidirect

7. #15689014

C₂

semidirect

8. C₄×C₄⋊Dic₄₇

C₂

semidirect

9. C₂×C₄×Q₈×C₄₇

C₂

semidirect

119. C₂×C₄×Q₈

D₄₇

semidirect

125. C₄₇

#2545

semidirect

Subgroups — #20248364

Conjugacy classes of subgroups

Complements