Group #26118907 — subgroups

Subgroups — #26118907

Order 12032.

950 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 950 conjugacy classes of subgroups — too many to draw. Only its 113 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	#20254306	C₂	1	2	yes	maximal, complemented
2	#20244216	C₂	1	1	yes	maximal, characteristic, complemented
3	#20242056	C₂	1	2	yes	maximal, complemented
4	#20241221	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#2867	C₂	1	1	yes	maximal, characteristic, complemented
6	#15689673	C₂²	1	1	yes	characteristic
7	#15689499	—	2	2	no	—
8	#15689469	—	2	2	no	—
9	#15689315	—	2	4	no	—
10	#15689257	—	2	4	no	—
11	#15689176	C₂²	1	2	yes	—
12	#15689147	C₂²	1	1	yes	characteristic
13	C₂×#13093952	—	2	2	no	—
14	#15688867	—	2	4	no	—
15	C₂×#127×C₄₇	—	2	4	no	—
16	C₂×#127×C₄₇	—	2	2	no	—
17	C₂×#127×C₄₇	C₂²	1	2	yes	—
18	C₄³×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×#10625350	—	2	1	no	—
20	C₂×#10625334	—	2	8	no	—
21	C₂×#10625329	—	2	1	no	—
22	#13094024	D₄	1	1	yes	characteristic, complemented
23	#13094021	D₄	1	1	yes	characteristic, complemented
24	#13094012	—	2	1	no	—
25	#13093998	—	2	2	no	—
26	C₄×D₁₈₈	—	2	2	no	—
27	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
28	C₄⋊(C₄₇⋊C₈)	D₄	1	4	yes	complemented
29	#13093952	—	4	4	no	—
30	#13093945	—	2	8	no	—
31	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
32	C₄×C₄₇⋊C₈	—	2	2	no	—
33	C₂²×D₄×C₄₇	—	2	8	no	—
34	C₂²×D₄×C₄₇	—	2	2	no	—
35	C₂²×D₄×C₄₇	—	2	2	no	—
36	C₂²×D₄×C₄₇	D₄	1	4	yes	—
37	#127×C₄₇	—	2	2	no	—
38	#127×C₄₇	—	2	2	no	—
39	#127×C₄₇	—	2	2	no	—
40	#127×C₄₇	—	2	2	no	—
41	#127×C₄₇	—	4	16	no	—
42	#127×C₄₇	—	4	4	no	—
43	#127×C₄₇	—	4	4	no	—
44	C₂×C₄²×C₄₇	—	2	2	no	—
45	C₂×C₄²×C₄₇	D₄	1	2	yes	—
46	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
47	C₂⁴×C₄₇	—	2	4	no	—
48	C₂×D₄×C₄₇	—	2	4	no	—
49	C₂×D₄×C₄₇	—	2	4	no	—
50	C₂×D₄×C₄₇	—	4	8	no	—
51	C₂×D₄×C₄₇	—	4	32	no	—
52	C₂×D₄×C₄₇	—	4	16	no	—
53	C₂×D₄×C₄₇	—	4	8	no	—
54	C₂×D₄×C₄₇	—	4	2	no	—
55	C₂×D₄×C₄₇	—	4	2	no	—
56	C₂×D₄×C₄₇	—	4	2	no	—
57	C₂×D₄×C₄₇	—	4	2	no	—
58	C₂×D₄×C₄₇	—	4	4	no	—
59	C₂×D₄×C₄₇	—	4	4	no	—
60	C₂²×C₄×C₄₇	—	2	2	no	—
61	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
62	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
63	C₂×C₂²⋊D₄₇	—	4	1	no	—
64	#10625350	—	4	2	no	—
65	#10625350	—	4	2	no	—
66	C₂×D₁₈₈	—	2	2	no	—
67	C₂×D₁₈₈	—	2	1	no	—
68	C₂×C₄×D₄₇	—	4	1	no	—
69	C₂×Dic₉₄	—	2	1	no	—
70	C₄²×C₄₇	—	2	8	no	—
71	C₄²×C₄₇	—	2	2	no	—
72	C₄²×C₄₇	D₈	1	4	yes	complemented
73	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₄₇	C₂×D₄	1	2	yes	—
75	C₄²×C₄₇	#41	1	1	yes	characteristic
76	#10625334	—	8	8	no	—
77	(C₂×D₄₇)⋊C₄	—	4	2	no	—
78	C₄⋊Dic₄₇	—	2	2	no	—
79	#10625329	—	4	2	no	—
80	C₂×C₄₇⋊C₈	—	2	4	no	—
81	C₂×C₄₇⋊C₈	—	4	1	no	—
82	C₂³×C₄₇	—	4	8	no	—
83	C₂³×C₄₇	—	4	8	no	—
84	C₂³×C₄₇	—	4	4	no	—
85	C₂³×C₄₇	—	4	8	no	—
86	C₂³×C₄₇	#120	1	1	yes	characteristic
87	C₂²×D₄₇	—	4	1	no	—
88	D₄×C₄₇	—	4	8	no	—
89	D₄×C₄₇	—	8	4	no	—
90	D₄×C₄₇	—	8	32	no	—
91	D₄×C₄₇	—	8	4	no	—
92	D₄×C₄₇	—	8	4	no	—
93	D₄×C₄₇	—	8	4	no	—
94	D₄×C₄₇	—	8	2	no	—
95	D₄×C₄₇	—	8	2	no	—
96	C₂×C₄×C₄₇	—	2	8	no	—
97	C₂×C₄×C₄₇	—	2	4	no	—
98	C₂×C₄×C₄₇	—	2	4	no	—
99	C₂×C₄×C₄₇	#120	1	2	yes	—
100	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
101	C₂×C₄×C₄₇	#121	1	2	yes	—
102	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
103	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
104	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
105	C₂²⋊D₄₇	—	8	2	no	—
106	C₂×Dic₄₇	—	4	1	no	—
107	D₁₈₈	—	4	4	no	—
108	D₁₈₈	—	4	2	no	—
109	C₄×D₄₇	—	8	1	no	—
110	C₄×D₄₇	—	8	1	no	—
111	Dic₉₄	—	4	2	no	—
112	C₄₇⋊C₈	—	4	4	no	—
113	C₄₇⋊C₈	—	8	1	no	—
114	#10280	—	47	1	no	maximal, Sylow
115	C₂²×C₄₇	—	2	2	no	—
116	C₂²×C₄₇	—	8	16	no	—
117	C₂²×C₄₇	—	8	4	no	—
118	C₂²×C₄₇	—	8	4	no	—
119	C₂²×C₄₇	—	8	4	no	—
120	C₂²×C₄₇	#392	1	1	yes	characteristic
121	C₂²×C₄₇	#447	1	2	yes	—
122	C₂×D₄₇	—	8	2	no	—
123	C₂×D₄₇	—	8	1	no	—
124	C₄×C₄₇	—	2	8	no	—
125	C₄×C₄₇	—	2	2	no	—
126	C₄×C₄₇	#453	1	4	yes	—
127	C₄×C₄₇	#459	1	2	yes	—
128	C₄×C₄₇	#493	1	1	yes	characteristic
129	C₄×C₄₇	#496	1	1	yes	characteristic
130	Dic₄₇	—	8	1	no	—
131	#3205	—	47	2	no	—
132	#2867	D₄₇	1	1	yes	characteristic, complemented
133	#1962	—	47	1	no	—
134	#1545	—	47	2	no	—
135	#1276	—	47	1	no	—
136	C₂×C₄₇	—	2	2	no	—
137	C₂×C₄₇	—	16	4	no	—
138	C₂×C₄₇	#2002	1	2	yes	—
139	C₂×C₄₇	#2011	1	1	yes	characteristic
140	D₄₇	—	16	1	no	—
141	#532	—	47	1	no	—
142	C₂×#127	—	2	4	no	—
143	C₂×#127	—	2	2	no	—
144	C₂×#127	C₂×D₄₇	1	2	yes	—
145	#493	—	94	2	no	—
146	#486	—	94	2	no	—
147	#459	—	94	4	no	—
148	#447	—	94	4	no	—
149	#431	—	47	2	no	—
150	#423	—	47	1	no	—
151	C₂×#104	—	94	2	no	—
152	C₄³	C₂×D₄₇	1	1	yes	characteristic
153	#331	—	94	4	no	—
154	C₄₇	#10280	1	1	yes	characteristic, complemented, Sylow
155	C₂×#41	—	94	1	no	—
156	C₂²×D₄	—	2	8	no	—
157	C₂²×D₄	—	2	2	no	—
158	C₂²×D₄	—	2	2	no	—
159	C₂²×D₄	C₂²⋊D₄₇	1	4	yes	—
160	C₂×D₈	—	94	8	no	—
161	C₂×M₁₆	—	94	1	no	—
162	C₄⋊Q₈	—	47	1	no	—
163	#127	—	2	2	no	—
164	#127	—	2	2	no	—
165	#127	—	2	2	no	—
166	#127	—	2	2	no	—
167	#127	—	4	16	no	—
168	#127	—	4	4	no	—
169	#127	—	4	4	no	—
170	#127	—	47	1	no	—
171	#124	—	94	1	no	—
172	#121	—	94	2	no	—
173	C₄×D₄	—	94	2	no	—
174	C₂×C₄²	—	2	2	no	—
175	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
176	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
177	C₄⋊C₈	—	47	4	no	—
178	C₄⋊C₈	—	94	2	no	—
179	#104	—	188	4	no	—
180	#102	—	94	8	no	—
181	C₂²⋊C₈	—	94	2	no	—
182	C₄×C₈	—	94	2	no	—
183	C₂⁴	—	2	4	no	—
184	#41	—	188	2	no	—
185	#41	—	188	2	no	—
186	C₂×Q₈	—	94	1	no	—
187	C₂×D₄	—	2	4	no	—
188	C₂×D₄	—	2	4	no	—
189	C₂×D₄	—	4	8	no	—
190	C₂×D₄	—	4	32	no	—
191	C₂×D₄	—	4	16	no	—
192	C₂×D₄	—	4	8	no	—
193	C₂×D₄	—	4	2	no	—
194	C₂×D₄	—	4	2	no	—
195	C₂×D₄	—	4	2	no	—
196	C₂×D₄	—	4	2	no	—
197	C₂×D₄	—	4	4	no	—
198	C₂×D₄	—	4	4	no	—
199	C₂×D₄	—	94	2	no	—
200	C₂×D₄	—	94	1	no	—
201	C₂×D₄	—	188	1	no	—
202	C₂²×C₄	—	2	2	no	—
203	C₂²×C₄	—	188	1	no	—
204	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
205	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
206	D₈	—	376	8	no	—
207	M₁₆	—	188	2	no	—
208	C₂×C₈	—	94	4	no	—
209	C₂×C₈	—	188	1	no	—
210	C₄⋊C₄	—	94	2	no	—
211	C₂²⋊C₄	—	188	2	no	—
212	C₄²	—	2	8	no	—
213	C₄²	—	2	2	no	—
214	C₄²	#10625334	1	4	yes	complemented
215	C₄²	D₄×D₄₇	1	1	yes	characteristic
216	C₄²	D₄×D₄₇	1	2	yes	—
217	C₄²	#10625352	1	1	yes	characteristic
218	C₂³	—	4	8	no	—
219	C₂³	—	4	8	no	—
220	C₂³	—	4	8	no	—
221	C₂³	—	4	4	no	—
222	C₂³	—	188	1	no	—
223	C₂³	#13093993	1	1	yes	characteristic
224	Q₈	—	188	2	no	—
225	D₄	—	4	8	no	—
226	D₄	—	8	4	no	—
227	D₄	—	8	32	no	—
228	D₄	—	8	4	no	—
229	D₄	—	8	2	no	—
230	D₄	—	8	2	no	—
231	D₄	—	8	4	no	—
232	D₄	—	8	4	no	—
233	D₄	—	376	2	no	—
234	D₄	—	188	4	no	—
235	D₄	—	188	2	no	—
236	C₂×C₄	—	2	8	no	—
237	C₂×C₄	—	2	4	no	—
238	C₂×C₄	—	2	4	no	—
239	C₂×C₄	—	376	1	no	—
240	C₂×C₄	—	376	1	no	—
241	C₂×C₄	—	188	1	no	—
242	C₂×C₄	#13093992	1	2	yes	—
243	C₂×C₄	#13093995	1	1	yes	characteristic
244	C₂×C₄	#13093996	1	2	yes	—
245	C₂×C₄	#13094020	1	1	yes	characteristic
246	C₂×C₄	C₂×#10625334	1	2	yes	—
247	C₂×C₄	#13094050	1	2	yes	—
248	C₈	—	376	1	no	—
249	C₈	—	188	4	no	—
250	C₂²	—	2	2	no	—
251	C₂²	—	8	16	no	—
252	C₂²	—	8	4	no	—
253	C₂²	—	8	4	no	—
254	C₂²	—	8	4	no	—
255	C₂²	—	376	2	no	—
256	C₂²	—	376	1	no	—
257	C₂²	#15689031	1	1	yes	characteristic
258	C₂²	#15689257	1	2	yes	—
259	C₄	—	2	8	no	—
260	C₄	—	2	2	no	—
261	C₄	—	376	1	no	—
262	C₄	#15689290	1	4	yes	—
263	C₄	#15689315	1	2	yes	—
264	C₄	#15689499	1	1	yes	characteristic
265	C₄	#15689510	1	1	yes	characteristic
266	C₂	—	2	2	no	—
267	C₂	—	16	4	no	—
268	C₂	—	752	1	no	—
269	C₂	#20244403	1	2	yes	—
270	C₂	#20244459	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20254306

C₂

yes

maximal, complemented

#20244216

C₂

yes

maximal, characteristic, complemented

#20242056

C₂

yes

maximal, complemented

#20241221

C₂

yes

maximal, characteristic, complemented

C₄₇×#2867

C₂

yes

maximal, characteristic, complemented

#15689673

C₂²

yes

—

—

—

—

C₂²

yes

—

#15689147

C₂²

yes

characteristic

C₂×#13093952

—

#15688867

—

C₂×#127×C₄₇

—

C₂×#127×C₄₇

—

C₂×#127×C₄₇

C₂²

yes

—

C₄³×C₄₇

C₂²

yes

—

—

—

D₄

yes

characteristic, complemented

#13094021

D₄

yes

characteristic, complemented

#13094012

—

#13093998

—

C₄×D₁₈₈

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

D₄

yes

complemented

#13093952

—

#13093945

—

C₂²⋊(C₄₇⋊C₈)

—

C₄×C₄₇⋊C₈

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

D₄

yes

—

#127×C₄₇

—

#127×C₄₇

—

#127×C₄₇

—

#127×C₄₇

—

#127×C₄₇

—

#127×C₄₇

—

#127×C₄₇

—

C₂×C₄²×C₄₇

—

C₂×C₄²×C₄₇

D₄

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₂⁴×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×D₄

yes

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₂²⋊D₄₇

—

#10625350

—

#10625350

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×C₄×D₄₇

—

C₂×Dic₉₄

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

D₈

yes

complemented

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

—

C₄²×C₄₇

#41

yes

characteristic

#10625334

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

#120

yes

characteristic

C₂²×D₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

#120

yes

—

100

C₂×C₄×C₄₇

#121

yes

characteristic

101

C₂×C₄×C₄₇

#121

yes

—

102

C₂×C₄×C₄₇

#127

yes

characteristic

103

C₂×C₄×C₄₇

C₂×D₈

yes

—

104

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

—

105

C₂²⋊D₄₇

—

106

C₂×Dic₄₇

—

107

D₁₈₈

—

108

D₁₈₈

—

109

C₄×D₄₇

—

110

C₄×D₄₇

—

111

Dic₉₄

—

112

C₄₇⋊C₈

—

113

C₄₇⋊C₈

—

114

#10280

—

maximal, Sylow

115

C₂²×C₄₇

—

116

C₂²×C₄₇

—

117

C₂²×C₄₇

—

118

C₂²×C₄₇

—

119

C₂²×C₄₇

—

120

C₂²×C₄₇

#392

yes

characteristic

121

C₂²×C₄₇

#447

yes

—

122

C₂×D₄₇

—

123

C₂×D₄₇

—

124

C₄×C₄₇

—

125

C₄×C₄₇

—

126

C₄×C₄₇

#453

yes

—

127

C₄×C₄₇

#459

yes

—

128

C₄×C₄₇

#493

yes

characteristic

129

C₄×C₄₇

#496

yes

characteristic

130

Dic₄₇

—

131

#3205

—

132

#2867

D₄₇

yes

characteristic, complemented

133

#1962

—

134

#1545

—

135

#1276

—

136

C₂×C₄₇

—

137

C₂×C₄₇

—

138

C₂×C₄₇

#2002

yes

—

139

C₂×C₄₇

#2011

yes

characteristic

140

D₄₇

—

141

#532

—

142

C₂×#127

—

143

C₂×#127

—

144

C₂×#127

C₂×D₄₇

yes

—

145

#493

—

146

#486

—

147

#459

—

148

#447

—

149

#431

—

150

#423

—

151

C₂×#104

—

152

C₄³

C₂×D₄₇

yes

characteristic

153

#331

—

154

C₄₇

#10280

yes

characteristic, complemented, Sylow

155

C₂×#41

—

156

C₂²×D₄

—

157

C₂²×D₄

—

158

C₂²×D₄

—

159

C₂²×D₄

C₂²⋊D₄₇

yes

—

160

C₂×D₈

—

161

C₂×M₁₆

—

162

C₄⋊Q₈

—

163

#127

—

164

#127

—

165

#127

—

166

#127

—

167

#127

—

168

#127

—

169

#127

—

170

#127

—

171

#124

—

172

#121

—

173

C₄×D₄

—

174

C₂×C₄²

—

175

C₂×C₄²

C₂²⋊D₄₇

yes

—

176

C₂×C₄²

C₂²×D₄₇

yes

characteristic

177

C₄⋊C₈

—

178

C₄⋊C₈

—

179

#104

—

188

—

180

#102

—

181

C₂²⋊C₈

—

182

C₄×C₈

—

183

C₂⁴

—

184

#41

—

188

—

185

#41

—

188

—

186

C₂×Q₈

—

187

C₂×D₄

—

188

C₂×D₄

—

189

C₂×D₄

—

190

C₂×D₄

—

191

C₂×D₄

—

192

C₂×D₄

—

193

C₂×D₄

—

194

C₂×D₄

—

195

C₂×D₄

—

196

C₂×D₄

—

197

C₂×D₄

—

198

C₂×D₄

—

199

C₂×D₄

—

200

C₂×D₄

—

201

C₂×D₄

—

188

—

202

C₂²×C₄

—

203

C₂²×C₄

—

188

—

204

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

—

205

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

206

D₈

—

376

—

207

M₁₆

—

188

—

208

C₂×C₈

—

209

C₂×C₈

—

188

—

210

C₄⋊C₄

—

211

C₂²⋊C₄

—

188

—

212

C₄²

—

213

C₄²

—

214

C₄²

#10625334

yes

complemented

215

C₄²

D₄×D₄₇

yes

characteristic

216

C₄²

D₄×D₄₇

yes

—

217

C₄²

#10625352

yes

characteristic

218

C₂³

—

219

C₂³

—

220

C₂³

—

221

C₂³

—

222

C₂³

—

188

—

223

C₂³

#13093993

yes

characteristic

224

Q₈

—

188

—

225

D₄

—

226

D₄

—

227

D₄

—

228

D₄

—

229

D₄

—

230

D₄

—

231

D₄

—

232

D₄

—

233

D₄

—

376

—

234

D₄

—

188

—

235

D₄

—

188

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

—

376

—

240

C₂×C₄

—

376

—

241

C₂×C₄

—

188

—

242

C₂×C₄

#13093992

yes

—

243

C₂×C₄

#13093995

yes

characteristic

244

C₂×C₄

#13093996

yes

—

245

C₂×C₄

#13094020

yes

characteristic

246

C₂×C₄

C₂×#10625334

yes

—

247

C₂×C₄

#13094050

yes

—

248

C₈

—

376

—

249

C₈

—

188

—

250

C₂²

—

251

C₂²

—

252

C₂²

—

253

C₂²

—

254

C₂²

—

255

C₂²

—

376

—

256

C₂²

—

376

—

257

C₂²

#15689031

yes

characteristic

258

C₂²

#15689257

yes

—

259

C₄

—

260

C₄

—

261

C₄

—

376

—

262

C₄

#15689290

yes

—

263

C₄

#15689315

yes

—

264

C₄

#15689499

yes

characteristic

265

C₄

#15689510

yes

characteristic

266

C₂

—

267

C₂

—

268

C₂

—

752

—

269

C₂

#20244403

yes

—

270

C₂

#20244459

yes

characteristic

	subgroup	G/H
center	C₂²	#15689031
commutator, cosocle	C₂×C₄²×C₄₇	C₂³
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#2867	C₂
socle	C₂²×C₄₇	#392
hypercenter	#2867	D₄₇
hypocenter	C₄₇	#10280
LCS	G ▷ C₂×C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2867

subgroup

G/H

center

C₂²

#15689031

commutator, cosocle

C₂×C₄²×C₄₇

C₂³

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#2867

C₂

C₂²×C₄₇

D₄₇

C₄₇

G ▷ C₂×C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2867

N	H ≅ G/N	type
1. #20254306	C₂	semidirect
2. #20244216	C₂	semidirect
3. #20242056	C₂	semidirect
4. #20241221	C₂	semidirect
5. C₄₇×#2867	C₂	semidirect
22. #13094024	D₄	semidirect
23. #13094021	D₄	semidirect
28. C₄⋊(C₄₇⋊C₈)	D₄	semidirect
72. C₄²×C₄₇	D₈	semidirect
132. #2867	D₄₇	semidirect
154. C₄₇	#10280	semidirect
214. C₄²	#10625334	semidirect

H ≅ G/N

type

1. #20254306

C₂

semidirect

2. #20244216

C₂

semidirect

3. #20242056

C₂

semidirect

4. #20241221

C₂

semidirect

5. C₄₇×#2867

C₂

semidirect

22. #13094024

D₄

semidirect

23. #13094021

D₄

semidirect

28. C₄⋊(C₄₇⋊C₈)

D₄

semidirect

72. C₄²×C₄₇

D₈

semidirect

132. #2867

D₄₇

semidirect

154. C₄₇

#10280

semidirect

214. C₄²

#10625334

semidirect

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

subgroup	index
#20254306	2
#20244216	2
#20242056	2
#20241221	2
C₄₇×#2867	2
#10280	47

subgroup

index

C₄₇×#2867

Subgroups — #26118907

Conjugacy classes of subgroups

Complements

Maximal subgroups