Group #26106951 — subgroups

Subgroups — #26106951

Order 12032.

530 conjugacy classes of subgroups; only the 195 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 195 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	C₄×#13094030	C₂	1	1	yes	maximal, characteristic
2	#20241771	C₂	1	2	yes	maximal
3	#20241671	C₂	1	1	yes	maximal, characteristic, complemented
4	#20241225	C₂	1	2	yes	maximal, complemented
5	C₂×C₈²×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#13094030	C₄	1	2	yes	—
7	C₄×#10625350	C₂²	1	1	yes	characteristic
8	#15689176	C₂²	1	2	yes	—
9	#15689078	C₄	1	2	yes	—
10	#15689077	—	2	2	no	—
11	C₄×#10625329	C₂²	1	1	yes	characteristic
12	C₄×#10625324	—	2	1	no	—
13	C₄×C₈×D₄₇	—	2	1	no	—
14	#15688855	C₄	1	4	yes	—
15	#15688852	C₄	1	4	yes	—
16	#15688844	—	2	1	no	—
17	C₈×C₄₇⋊C₈	—	2	1	no	—
18	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
20	C₈²×C₄₇	—	2	2	no	—
21	C₂×#10625350	C₂×C₄	1	1	yes	characteristic
22	#13094030	—	2	4	no	—
23	#13094030	C₈	1	8	yes	complemented
24	C₂×#10625329	C₂×C₄	1	2	yes	—
25	C₂×#10625324	—	2	2	no	—
26	C₂×C₈×D₄₇	—	2	2	no	—
27	C₄×Dic₉₄	C₂×C₄	1	2	yes	—
28	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
29	C₄×C₂²⋊D₄₇	—	2	2	no	—
30	#13093983	C₂×C₄	1	1	yes	characteristic
31	#13093981	—	2	1	no	—
32	C₄²×D₄₇	—	2	1	no	—
33	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
34	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
35	#13093935	—	2	1	no	—
36	#13093934	—	2	2	no	—
37	C₄×C₄₇⋊C₈	—	2	1	no	—
38	C₄×C₄₇⋊C₈	—	2	2	no	—
39	C₈×Dic₄₇	—	2	2	no	—
40	C₂²×C₈×C₄₇	—	2	2	no	—
41	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
42	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
43	C₄×C₈×C₄₇	—	2	2	no	—
44	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	—
45	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
46	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
47	C₄×C₈×C₄₇	D₄	1	2	yes	—
48	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
49	C₂²×C₄×C₄₇	#41	1	2	yes	—
50	C₂×C₂²⋊D₄₇	—	2	1	no	—
51	#10625350	—	2	2	no	—
52	#10625350	C₂×C₈	1	4	yes	—
53	C₂×D₁₈₈	C₄²	1	1	yes	characteristic
54	C₂×C₄×D₄₇	—	2	1	no	—
55	C₂×C₄×D₄₇	—	2	2	no	—
56	C₂×Dic₉₄	C₄²	1	1	yes	characteristic
57	C₂×C₈×C₄₇	—	2	8	no	—
58	C₂×C₈×C₄₇	—	2	4	no	—
59	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
60	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
61	C₂×C₈×C₄₇	C₂×C₈	1	4	yes	—
62	C₂×C₈×C₄₇	M₁₆	1	4	yes	—
63	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
64	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
65	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
66	C₂²⋊Dic₄₇	—	2	1	no	—
67	(C₂×D₄₇)⋊C₄	—	2	2	no	—
68	C₄⋊Dic₄₇	C₄²	1	2	yes	—
69	Dic₄₇⋊C₄	—	2	2	no	—
70	C₄×Dic₄₇	—	2	1	no	—
71	C₄×Dic₄₇	—	2	2	no	—
72	#10625329	—	2	2	no	—
73	#10625329	C₂×C₈	1	4	yes	—
74	C₂×C₄₇⋊C₈	—	2	2	no	—
75	C₂×C₄₇⋊C₈	—	2	4	no	—
76	#10625324	—	2	8	no	—
77	C₈×D₄₇	—	2	8	no	—
78	C₂³×C₄₇	#117	1	1	yes	characteristic
79	C₂²×D₄₇	—	2	1	no	—
80	C₂×C₄×C₄₇	—	2	4	no	—
81	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
82	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
84	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
85	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
86	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
87	C₂²⋊D₄₇	—	2	4	no	—
88	C₂×Dic₄₇	—	2	1	no	—
89	C₂×Dic₄₇	—	2	2	no	—
90	D₁₈₈	—	2	1	no	—
91	D₁₈₈	C₄×C₈	1	2	yes	—
92	C₄×D₄₇	—	2	4	no	—
93	C₄×D₄₇	—	4	4	no	—
94	Dic₉₄	—	2	1	no	—
95	Dic₉₄	C₄×C₈	1	2	yes	—
96	C₈×C₄₇	—	2	8	no	—
97	C₈×C₄₇	C₂²⋊C₈	1	4	yes	—
98	C₈×C₄₇	C₂²⋊C₈	1	4	yes	—
99	C₄₇⋊C₈	—	2	4	no	—
100	C₄₇⋊C₈	—	4	4	no	—
101	#8184	—	47	1	no	maximal, Sylow
102	C₂²×C₄₇	—	2	2	no	—
103	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
104	C₂²×C₄₇	#431	1	2	yes	—
105	C₂×D₄₇	—	2	2	no	—
106	C₂×D₄₇	—	4	2	no	—
107	C₄×C₄₇	—	2	2	no	—
108	C₄×C₄₇	C₂×C₄×C₈	1	1	yes	characteristic
109	C₄×C₄₇	C₄×M₁₆	1	1	yes	characteristic
110	C₄×C₄₇	C₂×C₂²⋊C₈	1	2	yes	—
111	C₄×C₄₇	#443	1	4	yes	—
112	Dic₄₇	—	2	2	no	—
113	Dic₄₇	—	4	2	no	—
114	C₄×#131	—	47	1	no	—
115	#1476	—	47	2	no	—
116	#1450	—	47	1	no	—
117	C₂×C₈²	D₄₇	1	1	yes	characteristic, complemented
118	#1278	—	47	2	no	—
119	C₂×C₄₇	—	2	2	no	—
120	C₂×C₄₇	C₄×C₂²⋊C₈	1	1	yes	characteristic
121	C₂×C₄₇	#1764	1	2	yes	—
122	D₄₇	—	4	2	no	—
123	C₂×#131	—	47	2	no	—
124	C₄×#41	—	47	1	no	—
125	#431	—	47	2	no	—
126	#405	—	47	2	no	—
127	#405	—	94	2	no	—
128	C₄×M₁₆	—	47	1	no	—
129	C₄×M₁₆	—	94	1	no	—
130	C₂×C₄×C₈	—	94	1	no	—
131	C₂×C₄×C₈	C₂×D₄₇	1	2	yes	—
132	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
133	Q₈⋊C₈	—	47	4	no	—
134	D₄⋊C₈	—	47	4	no	—
135	#322	—	94	1	no	—
136	C₈²	—	2	2	no	—
137	C₈²	—	94	1	no	—
138	C₄₇	#8184	1	1	yes	characteristic, complemented, Sylow
139	C₂×#41	—	47	1	no	—
140	#131	—	47	8	no	—
141	#131	—	94	4	no	—
142	C₂×M₁₆	—	47	2	no	—
143	C₂×M₁₆	—	94	2	no	—
144	C₂²×C₈	—	2	2	no	—
145	C₂²×C₈	—	94	2	no	—
146	C₂²×C₈	C₄×D₄₇	1	2	yes	—
147	C₄×Q₈	—	47	2	no	—
148	C₄×D₄	—	47	2	no	—
149	C₄×D₄	—	94	2	no	—
150	#117	—	47	1	no	—
151	#117	—	94	1	no	—
152	C₂×C₄²	—	94	1	no	—
153	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
154	C₄⋊C₈	—	47	4	no	—
155	C₂²⋊C₈	—	94	2	no	—
156	#97	—	94	2	no	—
157	#97	—	94	1	no	—
158	C₄×C₈	—	2	2	no	—
159	C₄×C₈	—	94	2	no	—
160	C₄×C₈	—	94	2	no	—
161	C₄×C₈	—	94	1	no	—
162	C₄×C₈	C₄×D₄₇	1	4	yes	—
163	C₄×C₈	D₁₈₈	1	1	yes	characteristic
164	C₄×C₈	D₁₈₈	1	1	yes	characteristic
165	C₄×C₈	C₂²⋊D₄₇	1	2	yes	—
166	#41	—	47	4	no	—
167	#41	—	94	2	no	—
168	C₂×Q₈	—	47	1	no	—
169	C₂×D₄	—	47	1	no	—
170	C₂×D₄	—	94	1	no	—
171	C₂²×C₄	—	94	1	no	—
172	C₂²×C₄	—	94	2	no	—
173	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
174	C₂²×C₄	#10625350	1	2	yes	—
175	M₁₆	—	47	4	no	—
176	M₁₆	—	94	2	no	—
177	M₁₆	—	94	8	no	—
178	C₂×C₈	—	2	8	no	—
179	C₂×C₈	—	2	4	no	—
180	C₂×C₈	—	94	2	no	—
181	C₂×C₈	—	94	8	no	—
182	C₂×C₈	—	94	4	no	—
183	C₂×C₈	C₈×D₄₇	1	4	yes	—
184	C₂×C₈	#10625324	1	4	yes	—
185	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
186	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
187	C₄⋊C₄	—	47	2	no	—
188	C₄⋊C₄	—	94	2	no	—
189	C₂²⋊C₄	—	94	1	no	—
190	C₂²⋊C₄	—	94	2	no	—
191	C₄²	—	94	1	no	—
192	C₄²	—	94	2	no	—
193	C₄²	C₂×C₄×D₄₇	1	2	yes	—
194	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
195	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
196	C₂³	—	94	1	no	—
197	C₂³	#13093981	1	1	yes	characteristic
198	Q₈	—	47	2	no	—
199	Q₈	—	94	1	no	—
200	D₄	—	47	2	no	—
201	D₄	—	94	4	no	—
202	D₄	—	94	1	no	—
203	C₂×C₄	—	2	4	no	—
204	C₂×C₄	—	94	1	no	—
205	C₂×C₄	—	94	4	no	—
206	C₂×C₄	—	94	2	no	—
207	C₂×C₄	—	188	4	no	—
208	C₂×C₄	C₄²×D₄₇	1	1	yes	characteristic
209	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
210	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
211	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
212	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
213	C₂×C₄	C₂×#10625324	1	2	yes	—
214	C₈	—	2	8	no	—
215	C₈	—	94	4	no	—
216	C₈	—	188	4	no	—
217	C₈	(C₂×D₄₇)⋊C₈	1	4	yes	—
218	C₈	(C₂×D₄₇)⋊C₈	1	4	yes	—
219	C₂²	—	2	2	no	—
220	C₂²	—	94	2	no	—
221	C₂²	—	188	2	no	—
222	C₂²	C₄×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
223	C₂²	#15689174	1	2	yes	—
224	C₄	—	2	2	no	—
225	C₄	—	94	2	no	—
226	C₄	—	188	2	no	—
227	C₄	C₄×C₈×D₄₇	1	1	yes	characteristic
228	C₄	C₄×#10625324	1	1	yes	characteristic
229	C₄	C₂×(C₂×D₄₇)⋊C₈	1	2	yes	—
230	C₄	#15689241	1	4	yes	—
231	C₂	—	2	2	no	—
232	C₂	—	188	2	no	—
233	C₂	C₄×(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
234	C₂	#20243225	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#13094030

C₂

yes

maximal, characteristic

#20241771

C₂

yes

maximal

#20241671

C₂

yes

maximal, characteristic, complemented

#20241225

C₂

yes

maximal, complemented

C₂×C₈²×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂×#13094030

C₄

yes

—

C₄×#10625350

C₂²

yes

characteristic

#15689176

C₂²

yes

—

#15689078

C₄

yes

—

#15689077

—

C₄×#10625329

C₂²

yes

characteristic

C₄×#10625324

—

C₄×C₈×D₄₇

—

#15688855

C₄

yes

—

#15688852

C₄

yes

—

#15688844

—

C₈×C₄₇⋊C₈

—

C₂×C₄×C₈×C₄₇

C₂²

yes

—

C₂×C₄×C₈×C₄₇

C₂²

yes

characteristic

C₈²×C₄₇

—

C₂×#10625350

C₂×C₄

yes

characteristic

#13094030

—

#13094030

C₈

yes

complemented

C₂×#10625329

C₂×C₄

yes

—

C₂×#10625324

—

C₂×C₈×D₄₇

—

C₄×Dic₉₄

C₂×C₄

yes

—

C₄×D₁₈₈

C₂×C₄

yes

—

C₄×C₂²⋊D₄₇

—

#13093983

C₂×C₄

yes

characteristic

#13093981

—

C₄²×D₄₇

—

C₄⋊(C₄₇⋊C₈)

C₂×C₄

yes

—

C₂²⋊(C₄₇⋊C₈)

—

#13093935

—

#13093934

—

C₄×C₄₇⋊C₈

—

C₄×C₄₇⋊C₈

—

C₈×Dic₄₇

—

C₂²×C₈×C₄₇

—

C₂²×C₈×C₄₇

C₂×C₄

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄×C₈×C₄₇

—

C₄×C₈×C₄₇

C₂×C₄

yes

—

C₄×C₈×C₄₇

D₄

yes

characteristic

C₄×C₈×C₄₇

D₄

yes

characteristic

C₄×C₈×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₇

#41

yes

—

C₂×C₂²⋊D₄₇

—

#10625350

—

#10625350

C₂×C₈

yes

—

C₂×D₁₈₈

C₄²

yes

characteristic

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×Dic₉₄

C₄²

yes

characteristic

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂²⋊C₄

yes

—

C₂×C₈×C₄₇

C₂²⋊C₄

yes

—

C₂×C₈×C₄₇

C₂×C₈

yes

—

C₂×C₈×C₄₇

M₁₆

yes

—

C₄²×C₄₇

C₂²×C₄

yes

—

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₂²⋊Dic₄₇

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

C₄²

yes

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

#10625329

—

#10625329

C₂×C₈

yes

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

#10625324

—

C₈×D₄₇

—

C₂³×C₄₇

#117

yes

characteristic

C₂²×D₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×C₄²

yes

characteristic

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₄×D₄

yes

—

C₂×C₄×C₄₇

C₄×D₄

yes

—

C₂×C₄×C₄₇

C₂²×C₈

yes

—

C₂×C₄×C₄₇

C₂×M₁₆

yes

—

C₂²⋊D₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

D₁₈₈

C₄×C₈

yes

—

C₄×D₄₇

—

C₄×D₄₇

—

Dic₉₄

—

Dic₉₄

C₄×C₈

yes

—

C₈×C₄₇

—

C₈×C₄₇

C₂²⋊C₈

yes

—

C₈×C₄₇

C₂²⋊C₈

yes

—

C₄₇⋊C₈

—

100

C₄₇⋊C₈

—

101

#8184

—

maximal, Sylow

102

C₂²×C₄₇

—

103

C₂²×C₄₇

C₄×C₂²⋊C₄

yes

characteristic

104

C₂²×C₄₇

#431

yes

—

105

C₂×D₄₇

—

106

C₂×D₄₇

—

107

C₄×C₄₇

—

108

C₄×C₄₇

C₂×C₄×C₈

yes

characteristic

109

C₄×C₄₇

C₄×M₁₆

yes

characteristic

110

C₄×C₄₇

C₂×C₂²⋊C₈

yes

—

111

C₄×C₄₇

#443

yes

—

112

Dic₄₇

—

113

Dic₄₇

—

114

C₄×#131

—

115

#1476

—

116

#1450

—

117

C₂×C₈²

D₄₇

yes

characteristic, complemented

118

#1278

—

119

C₂×C₄₇

—

120

C₂×C₄₇

C₄×C₂²⋊C₈

yes

characteristic

121

C₂×C₄₇

#1764

yes

—

122

D₄₇

—

123

C₂×#131

—

124

C₄×#41

—

125

#431

—

126

#405

—

127

#405

—

128

C₄×M₁₆

—

129

C₄×M₁₆

—

130

C₂×C₄×C₈

—

131

C₂×C₄×C₈

C₂×D₄₇

yes

—

132

C₂×C₄×C₈

C₂×D₄₇

yes

characteristic

133

Q₈⋊C₈

—

134

D₄⋊C₈

—

135

#322

—

136

C₈²

—

137

C₈²

—

138

C₄₇

#8184

yes

characteristic, complemented, Sylow

139

C₂×#41

—

140

#131

—

141

#131

—

142

C₂×M₁₆

—

143

C₂×M₁₆

—

144

C₂²×C₈

—

145

C₂²×C₈

—

146

C₂²×C₈

C₄×D₄₇

yes

—

147

C₄×Q₈

—

148

C₄×D₄

—

149

C₄×D₄

—

150

#117

—

151

#117

—

152

C₂×C₄²

—

153

C₂×C₄²

C₂²×D₄₇

yes

characteristic

154

C₄⋊C₈

—

155

C₂²⋊C₈

—

156

#97

—

157

#97

—

158

C₄×C₈

—

159

C₄×C₈

—

160

C₄×C₈

—

161

C₄×C₈

—

162

C₄×C₈

C₄×D₄₇

yes

—

163

C₄×C₈

D₁₈₈

yes

characteristic

164

C₄×C₈

D₁₈₈

yes

characteristic

165

C₄×C₈

C₂²⋊D₄₇

yes

—

166

#41

—

167

#41

—

168

C₂×Q₈

—

169

C₂×D₄

—

170

C₂×D₄

—

171

C₂²×C₄

—

172

C₂²×C₄

—

173

C₂²×C₄

C₂×C₄×D₄₇

yes

characteristic

174

C₂²×C₄

#10625350

yes

—

175

M₁₆

—

176

M₁₆

—

177

M₁₆

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

C₈×D₄₇

yes

—

184

C₂×C₈

#10625324

yes

—

185

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

—

186

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₂²⋊C₄

—

190

C₂²⋊C₄

—

191

C₄²

—

192

C₄²

—

193

C₄²

C₂×C₄×D₄₇

yes

—

194

C₄²

C₂×D₁₈₈

yes

characteristic

195

C₄²

C₂×C₂²⋊D₄₇

yes

characteristic

196

C₂³

—

197

C₂³

#13093981

yes

characteristic

198

Q₈

—

199

Q₈

—

200

D₄

—

201

D₄

—

202

D₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

188

—

208

C₂×C₄

C₄²×D₄₇

yes

characteristic

209

C₂×C₄

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

210

C₂×C₄

C₄×C₂²⋊D₄₇

yes

—

211

C₂×C₄

C₄×D₁₈₈

yes

—

212

C₂×C₄

C₂×C₈×D₄₇

yes

—

213

C₂×C₄

C₂×#10625324

yes

—

214

C₈

—

215

C₈

—

216

C₈

—

188

—

217

C₈

(C₂×D₄₇)⋊C₈

yes

—

218

C₈

(C₂×D₄₇)⋊C₈

yes

—

219

C₂²

—

220

C₂²

—

221

C₂²

—

188

—

222

C₂²

C₄×(C₂×D₄₇)⋊C₄

yes

characteristic

223

C₂²

#15689174

yes

—

224

C₄

—

225

C₄

—

226

C₄

—

188

—

227

C₄

C₄×C₈×D₄₇

yes

characteristic

228

C₄

C₄×#10625324

yes

characteristic

229

C₄

C₂×(C₂×D₄₇)⋊C₈

yes

—

230

C₄

#15689241

yes

—

231

C₂

—

232

C₂

—

188

—

233

C₂

C₄×(C₂×D₄₇)⋊C₈

yes

characteristic

234

C₂

#20243225

yes

—

	subgroup	G/H
center	C₄×C₈	D₁₈₈
commutator	C₄×C₄₇	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₂×C₈²×C₄₇	C₂
socle	C₂²×C₄₇	C₄×C₂²⋊C₄
prime radical	C₂×#10625350	C₂×C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₂×C₈²	D₄₇
hypocenter	C₄₇	#8184
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄×C₈ ◁ C₂×C₄×C₈ ◁ C₂×C₈²

subgroup

G/H

center

C₄×C₈

D₁₈₈

commutator

C₄×C₄₇

C₂×C₄×C₈

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₂×C₈²×C₄₇

C₂

socle

C₂²×C₄₇

C₄×C₂²⋊C₄

prime radical

C₂×#10625350

C₂×C₄

cosocle

C₂×C₄²×C₄₇

C₂³

hypercenter

C₂×C₈²

D₄₇

hypocenter

C₄₇

#8184

LCS

G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₄×C₈ ◁ C₂×C₄×C₈ ◁ C₂×C₈²

N	H ≅ G/N	type
3. #20241671	C₂	semidirect
4. #20241225	C₂	semidirect
5. C₂×C₈²×C₄₇	C₂	semidirect
23. #13094030	C₈	semidirect
117. C₂×C₈²	D₄₇	semidirect
138. C₄₇	#8184	semidirect

H ≅ G/N

type

3. #20241671

C₂

semidirect

4. #20241225

C₂

semidirect

5. C₂×C₈²×C₄₇

C₂

semidirect

23. #13094030

C₈

semidirect

117. C₂×C₈²

D₄₇

semidirect

138. C₄₇

#8184

semidirect

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

subgroup	index
C₄×#13094030	2
#20241771	2
#20241671	2
#20241225	2
C₂×C₈²×C₄₇	2
#8184	47

subgroup

index

C₂×C₈²×C₄₇

Subgroups — #26106951

Conjugacy classes of subgroups

Complements

Maximal subgroups