Group #26110745 — subgroups

Subgroups — #26110745

Order 12032.

476 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 155 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	#20246478	C₂	1	1	yes	maximal, characteristic
2	#20244191	C₂	1	1	yes	maximal, characteristic
3	#20244152	C₂	1	2	yes	maximal
4	#20241227	C₂	1	2	yes	maximal
5	C₂×C₄₇×#333	C₂	1	1	yes	maximal, characteristic
6	C₂×#13093956	—	2	2	no	—
7	C₂×#13093948	—	2	2	no	—
8	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
9	#15689030	—	2	2	no	—
10	#15689022	—	2	2	no	—
11	#15688993	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×Dic₄₇	—	2	2	no	—
13	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
14	#15688886	—	2	2	no	—
15	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
17	C₄₇×#333	C₄	1	4	yes	complemented
18	C₂²×C₄₇⋊C₈	—	2	1	no	—
19	C₂×C₄⋊Dic₄₇	—	2	1	no	—
20	C₂×C₄⋊Dic₄₇	—	2	2	no	—
21	C₂×C₄⋊Dic₄₇	—	2	2	no	—
22	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
23	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
24	C₂×C₄×Dic₄₇	—	2	2	no	—
25	C₂×C₄×Dic₄₇	—	2	2	no	—
26	#13093956	—	4	4	no	—
27	#13093948	—	4	4	no	—
28	C₄×C₄₇⋊C₈	—	2	2	no	—
29	C₄₇⋊#95	—	2	4	no	—
30	C₄₇⋊#95	—	2	2	no	—
31	C₂²×Q₈×C₄₇	D₄	1	2	yes	—
32	C₂²×C₈×C₄₇	—	2	2	no	—
33	C₄⋊Q₈×C₄₇	—	2	2	no	—
34	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
35	C₄⋊Q₈×C₄₇	Q₈	1	2	yes	—
36	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
37	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
38	C₄⋊C₈×C₄₇	—	2	2	no	—
39	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
40	C₂×Q₈×C₄₇	—	2	2	no	—
41	C₂×Q₈×C₄₇	—	4	2	no	—
42	C₂×Q₈×C₄₇	—	4	2	no	—
43	C₂×Q₈×C₄₇	C₄⋊C₄	1	4	yes	—
44	C₂²×C₄×C₄₇	—	2	2	no	—
45	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
47	C₂²×Dic₄₇	—	2	2	no	—
48	C₂²×Dic₄₇	—	2	2	no	—
49	C₂²×Dic₄₇	—	4	1	no	—
50	C₂×C₈×C₄₇	—	2	4	no	—
51	C₂×C₈×C₄₇	—	4	2	no	—
52	C₂×C₈×C₄₇	—	4	2	no	—
53	C₄⋊C₄×C₄₇	—	2	4	no	—
54	C₄⋊C₄×C₄₇	—	2	4	no	—
55	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
56	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
57	C₄²×C₄₇	#41	1	2	yes	—
58	C₄⋊Dic₄₇	—	2	2	no	—
59	C₄⋊Dic₄₇	—	2	2	no	—
60	C₄⋊Dic₄₇	—	2	2	no	—
61	C₄⋊Dic₄₇	—	4	2	no	—
62	C₄⋊Dic₄₇	—	4	2	no	—
63	C₄⋊Dic₄₇	—	4	2	no	—
64	C₄⋊Dic₄₇	—	8	2	no	—
65	C₄⋊Dic₄₇	SD₁₆	1	4	yes	—
66	C₄×Dic₄₇	—	4	2	no	—
67	C₄×Dic₄₇	—	4	2	no	—
68	C₄×Dic₄₇	—	8	2	no	—
69	C₂×C₄₇⋊C₈	—	2	2	no	—
70	C₂×C₄₇⋊C₈	—	4	1	no	—
71	C₂×C₄₇⋊C₈	—	4	1	no	—
72	C₂³×C₄₇	#120	1	1	yes	characteristic
73	Q₈×C₄₇	—	4	4	no	—
74	Q₈×C₄₇	—	8	2	no	—
75	C₂×C₄×C₄₇	—	2	1	no	—
76	C₂×C₄×C₄₇	—	2	1	no	—
77	C₂×C₄×C₄₇	—	2	4	no	—
78	C₂×C₄×C₄₇	—	4	2	no	—
79	C₂×C₄×C₄₇	—	4	2	no	—
80	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
81	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
82	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
83	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
84	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
85	C₂×C₄×C₄₇	#135	1	2	yes	—
86	C₂×C₄×C₄₇	#137	1	2	yes	—
87	C₂×C₄×C₄₇	#137	1	2	yes	—
88	C₂×Dic₄₇	—	2	4	no	—
89	C₂×Dic₄₇	—	4	2	no	—
90	C₂×Dic₄₇	—	4	2	no	—
91	C₂×Dic₄₇	—	4	2	no	—
92	C₂×Dic₄₇	—	4	2	no	—
93	C₂×Dic₄₇	—	4	2	no	—
94	C₂×Dic₄₇	—	8	2	no	—
95	C₂×Dic₄₇	—	8	1	no	—
96	C₈×C₄₇	—	4	4	no	—
97	C₄₇⋊C₈	—	4	2	no	—
98	#8928	—	47	1	no	maximal, Sylow
99	C₂²×C₄₇	#385	1	1	yes	characteristic
100	C₂²×C₄₇	#448	1	2	yes	—
101	C₂²×C₄₇	#452	1	2	yes	—
102	C₂²×C₄₇	#453	1	1	yes	characteristic
103	C₂²×C₄₇	#455	1	1	yes	characteristic
104	C₄×C₄₇	—	2	1	no	—
105	C₄×C₄₇	—	2	1	no	—
106	C₄×C₄₇	—	4	4	no	—
107	C₄×C₄₇	C₄×SD₁₆	1	2	yes	—
108	C₄×C₄₇	#441	1	2	yes	—
109	C₄×C₄₇	#475	1	2	yes	—
110	C₄×C₄₇	#479	1	2	yes	—
111	Dic₄₇	—	4	4	no	—
112	Dic₄₇	—	8	2	no	—
113	Dic₄₇	—	16	1	no	—
114	#2369	—	47	1	no	—
115	#1956	—	47	1	no	—
116	#1948	—	47	2	no	—
117	C₂×#333	D₄₇	1	1	yes	characteristic
118	#1279	—	47	2	no	—
119	C₂×C₄₇	#1623	1	1	yes	characteristic
120	C₂×C₄₇	#1634	1	1	yes	characteristic
121	C₂×C₄₇	#1643	1	2	yes	—
122	C₂×C₄₇	#1856	1	1	yes	characteristic
123	C₂×C₄₇	#1865	1	2	yes	—
124	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
125	C₂×#106	—	94	2	no	—
126	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
127	C₂×#103	—	94	2	no	—
128	C₂×C₄×C₈	—	47	1	no	—
129	#391	—	94	2	no	—
130	#389	—	94	2	no	—
131	#384	—	47	1	no	—
132	C₄×C₄⋊C₄	—	47	2	no	—
133	C₄×C₄⋊C₄	—	94	2	no	—
134	#340	—	94	2	no	—
135	#333	Dic₄₇	1	4	yes	complemented
136	C₄₇	#8928	1	1	yes	characteristic, complemented, Sylow
137	C₂²×Q₈	D₁₈₈	1	2	yes	—
138	C₂²×C₈	—	2	2	no	—
139	C₂²×C₈	—	94	1	no	—
140	C₄⋊Q₈	—	2	2	no	—
141	C₄⋊Q₈	Dic₉₄	1	2	yes	—
142	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	—
143	C₂×C₄⋊C₄	—	2	2	no	—
144	C₂×C₄⋊C₄	—	47	2	no	—
145	C₂×C₄⋊C₄	—	47	2	no	—
146	C₂×C₄⋊C₄	—	94	2	no	—
147	C₂×C₄⋊C₄	—	94	1	no	—
148	C₂×C₄⋊C₄	—	94	2	no	—
149	C₂×C₄²	—	94	2	no	—
150	C₂×C₄²	—	94	2	no	—
151	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
152	#106	—	188	4	no	—
153	C₄⋊C₈	—	2	2	no	—
154	C₄⋊C₈	C₂×Dic₄₇	1	4	yes	—
155	#103	—	188	4	no	—
156	C₄×C₈	—	94	2	no	—
157	#95	—	94	4	no	—
158	#95	—	94	2	no	—
159	C₂×Q₈	—	2	2	no	—
160	C₂×Q₈	—	4	2	no	—
161	C₂×Q₈	—	4	2	no	—
162	C₂×Q₈	C₄⋊Dic₄₇	1	4	yes	—
163	C₂²×C₄	—	2	2	no	—
164	C₂²×C₄	—	94	2	no	—
165	C₂²×C₄	—	94	2	no	—
166	C₂²×C₄	—	188	1	no	—
167	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
168	C₂²×C₄	D₄×D₄₇	1	2	yes	—
169	C₂×C₈	—	2	4	no	—
170	C₂×C₈	—	4	2	no	—
171	C₂×C₈	—	4	2	no	—
172	C₂×C₈	—	94	2	no	—
173	C₂×C₈	—	188	1	no	—
174	C₂×C₈	—	188	1	no	—
175	C₄⋊C₄	—	2	4	no	—
176	C₄⋊C₄	—	2	4	no	—
177	C₄⋊C₄	—	47	4	no	—
178	C₄⋊C₄	—	94	2	no	—
179	C₄⋊C₄	—	94	2	no	—
180	C₄⋊C₄	—	94	2	no	—
181	C₄⋊C₄	—	376	2	no	—
182	C₄⋊C₄	—	188	2	no	—
183	C₄⋊C₄	—	188	2	no	—
184	C₄⋊C₄	—	188	2	no	—
185	C₄²	—	376	2	no	—
186	C₄²	—	188	2	no	—
187	C₄²	—	188	2	no	—
188	C₄²	C₂×Dic₉₄	1	1	yes	characteristic
189	C₄²	#10625352	1	2	yes	—
190	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
191	C₂³	#13093994	1	1	yes	characteristic
192	Q₈	—	4	4	no	—
193	Q₈	—	8	2	no	—
194	C₂×C₄	—	2	1	no	—
195	C₂×C₄	—	2	1	no	—
196	C₂×C₄	—	2	4	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	—	94	4	no	—
200	C₂×C₄	—	376	2	no	—
201	C₂×C₄	—	376	1	no	—
202	C₂×C₄	—	188	2	no	—
203	C₂×C₄	—	188	2	no	—
204	C₂×C₄	—	188	2	no	—
205	C₂×C₄	—	188	2	no	—
206	C₂×C₄	—	188	2	no	—
207	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
208	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
209	C₂×C₄	#13094001	1	2	yes	—
210	C₂×C₄	#13094008	1	1	yes	characteristic
211	C₂×C₄	SD₁₆×D₄₇	1	2	yes	—
212	C₂×C₄	#13094045	1	2	yes	—
213	C₂×C₄	#13094056	1	2	yes	—
214	C₂×C₄	#13094056	1	2	yes	—
215	C₈	—	4	4	no	—
216	C₈	—	188	2	no	—
217	C₂²	#15688998	1	1	yes	characteristic
218	C₂²	#15689263	1	2	yes	—
219	C₂²	#15689288	1	2	yes	—
220	C₂²	#15689293	1	1	yes	characteristic
221	C₂²	#15689303	1	1	yes	characteristic
222	C₄	—	2	1	no	—
223	C₄	—	2	1	no	—
224	C₄	—	4	4	no	—
225	C₄	—	376	2	no	—
226	C₄	—	188	4	no	—
227	C₄	—	752	1	no	—
228	C₄	SD₁₆×Dic₄₇	1	2	yes	—
229	C₄	#15689230	1	2	yes	—
230	C₄	#15689406	1	2	yes	—
231	C₄	#15689428	1	2	yes	—
232	C₂	#20242467	1	1	yes	characteristic
233	C₂	#20242534	1	1	yes	characteristic
234	C₂	#20242596	1	2	yes	—
235	C₂	#20243600	1	1	yes	characteristic
236	C₂	#20243658	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#20246478

C₂

yes

maximal, characteristic

#20244191

C₂

yes

maximal, characteristic

#20244152

C₂

yes

maximal

#20241227

C₂

yes

maximal

C₂×C₄₇×#333

C₂

yes

maximal, characteristic

C₂×#13093956

—

C₂×#13093948

—

C₂×C₄×C₄₇⋊C₈

C₂²

yes

—

—

C₂²

yes

characteristic

C₄⋊C₄×Dic₄₇

—

C₄×C₄⋊Dic₄₇

C₂²

yes

—

#15688886

—

C₂×C₄⋊Q₈×C₄₇

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₄₇

C₂²

yes

—

C₄₇×#333

C₄

yes

complemented

C₂²×C₄₇⋊C₈

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

D₄

yes

—

C₂×C₄⋊Dic₄₇

D₄

yes

—

C₂×C₄×Dic₄₇

—

C₂×C₄×Dic₄₇

—

#13093956

—

#13093948

—

C₄×C₄₇⋊C₈

—

C₄₇⋊#95

—

C₄₇⋊#95

—

C₂²×Q₈×C₄₇

D₄

yes

—

C₂²×C₈×C₄₇

—

C₄⋊Q₈×C₄₇

—

C₄⋊Q₈×C₄₇

C₂×C₄

yes

—

C₄⋊Q₈×C₄₇

Q₈

yes

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₄⋊C₈×C₄₇

C₂×C₄

yes

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

C₄⋊C₄

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

C₂²×C₄

yes

characteristic

C₄²×C₄₇

C₂×Q₈

yes

characteristic

C₄²×C₄₇

#41

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

SD₁₆

yes

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

#120

yes

characteristic

Q₈×C₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₄×D₄

yes

—

C₂×C₄×C₄₇

C₂²⋊Q₈

yes

—

C₂×C₄×C₄₇

#123

yes

characteristic

C₂×C₄×C₄₇

C₂×SD₁₆

yes

—

C₂×C₄×C₄₇

#135

yes

—

C₂×C₄×C₄₇

#137

yes

—

C₂×C₄×C₄₇

#137

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

—

C₂²×C₄₇

yes

100

C₂²×C₄₇

#448

yes

—

101

C₂²×C₄₇

#452

yes

—

102

C₂²×C₄₇

#453

yes

characteristic

103

C₂²×C₄₇

#455

yes

characteristic

104

C₄×C₄₇

—

105

C₄×C₄₇

—

106

C₄×C₄₇

—

107

C₄×C₄₇

C₄×SD₁₆

yes

—

108

C₄×C₄₇

#441

yes

—

109

C₄×C₄₇

#475

yes

—

110

C₄×C₄₇

#479

yes

—

111

Dic₄₇

—

112

Dic₄₇

—

113

Dic₄₇

—

114

#2369

—

115

#1956

—

116

#1948

—

117

C₂×#333

D₄₇

yes

characteristic

118

#1279

—

119

C₂×C₄₇

#1623

yes

characteristic

120

C₂×C₄₇

#1634

yes

characteristic

121

C₂×C₄₇

#1643

yes

—

122

C₂×C₄₇

#1856

yes

characteristic

123

C₂×C₄₇

#1865

yes

—

124

C₂×C₄⋊Q₈

C₂×D₄₇

yes

characteristic

125

C₂×#106

—

126

C₂×C₄⋊C₈

C₂×D₄₇

yes

—

127

C₂×#103

—

128

C₂×C₄×C₈

—

129

#391

—

130

#389

—

131

#384

—

132

C₄×C₄⋊C₄

—

133

C₄×C₄⋊C₄

—

134

#340

—

135

#333

Dic₄₇

yes

complemented

136

C₄₇

#8928

yes

characteristic, complemented, Sylow

137

C₂²×Q₈

D₁₈₈

yes

—

138

C₂²×C₈

—

139

C₂²×C₈

—

140

C₄⋊Q₈

—

141

C₄⋊Q₈

Dic₉₄

yes

—

142

C₄⋊Q₈

C₂×Dic₄₇

yes

—

143

C₂×C₄⋊C₄

—

144

C₂×C₄⋊C₄

—

145

C₂×C₄⋊C₄

—

146

C₂×C₄⋊C₄

—

147

C₂×C₄⋊C₄

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄²

—

150

C₂×C₄²

—

151

C₂×C₄²

C₂²×D₄₇

yes

characteristic

152

#106

—

188

—

153

C₄⋊C₈

—

154

C₄⋊C₈

C₂×Dic₄₇

yes

—

155

#103

—

188

—

156

C₄×C₈

—

157

#95

—

158

#95

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

C₄⋊Dic₄₇

yes

—

163

C₂²×C₄

—

164

C₂²×C₄

—

165

C₂²×C₄

—

166

C₂²×C₄

—

188

—

167

C₂²×C₄

C₂×D₁₈₈

yes

characteristic

168

C₂²×C₄

D₄×D₄₇

yes

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

188

—

174

C₂×C₈

—

188

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

376

—

182

C₄⋊C₄

—

188

—

183

C₄⋊C₄

—

188

—

184

C₄⋊C₄

—

188

—

185

C₄²

—

376

—

186

C₄²

—

188

—

187

C₄²

—

188

—

188

C₄²

C₂×Dic₉₄

yes

characteristic

189

C₄²

#10625352

yes

—

190

C₄²

C₂²×Dic₄₇

yes

characteristic

191

C₂³

#13093994

yes

characteristic

192

Q₈

—

193

Q₈

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

376

—

201

C₂×C₄

—

376

—

202

C₂×C₄

—

188

—

203

C₂×C₄

—

188

—

204

C₂×C₄

—

188

—

205

C₂×C₄

—

188

—

206

C₂×C₄

—

188

—

207

C₂×C₄

C₂×C₄⋊Dic₄₇

yes

characteristic

208

C₂×C₄

D₄×Dic₄₇

yes

—

209

C₂×C₄

#13094001

yes

—

210

C₂×C₄

#13094008

yes

characteristic

211

C₂×C₄

SD₁₆×D₄₇

yes

—

212

C₂×C₄

#13094045

yes

—

213

C₂×C₄

#13094056

yes

—

214

C₂×C₄

#13094056

yes

—

215

C₈

—

216

C₈

—

188

—

217

C₂²

#15688998

yes

characteristic

218

C₂²

#15689263

yes

—

219

C₂²

#15689288

yes

—

220

C₂²

#15689293

yes

characteristic

221

C₂²

#15689303

yes

characteristic

222

C₄

—

223

C₄

—

224

C₄

—

225

C₄

—

376

—

226

C₄

—

188

—

227

C₄

—

752

—

228

C₄

SD₁₆×Dic₄₇

yes

—

229

C₄

#15689230

yes

—

230

C₄

#15689406

yes

—

231

C₄

#15689428

yes

—

232

C₂

#20242467

yes

characteristic

233

C₂

#20242534

yes

characteristic

234

C₂

#20242596

yes

—

235

C₂

#20243600

yes

characteristic

236

C₂

#20243658

yes

—

	subgroup	G/H
center	C₂³	#13093994
commutator	C₄²×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₂×C₄₇×#333	C₂
socle, prime radical	C₂³×C₄₇	#120
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₂×#333	D₄₇
hypocenter	C₄₇	#8928
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#333

subgroup

G/H

center

C₂³

#13093994

commutator

C₄²×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₂×C₄₇×#333

C₂

socle, prime radical

C₂³×C₄₇

#120

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#333

N	H ≅ G/N	type
17. C₄₇×#333	C₄	semidirect
135. #333	Dic₄₇	semidirect
136. C₄₇	#8928	semidirect

H ≅ G/N

type

17. C₄₇×#333

C₄

semidirect

135. #333

Dic₄₇

semidirect

136. C₄₇

#8928

semidirect

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

subgroup	index
#20246478	2
#20244191	2
#20244152	2
#20241227	2
C₂×C₄₇×#333	2
#8928	47

subgroup

index

C₂×C₄₇×#333

Subgroups — #26110745

Conjugacy classes of subgroups

Complements

Maximal subgroups