Group #26109859 — subgroups

Subgroups — #26109859

Order 12032.

422 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 131 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	#20243384	C₂	1	1	yes	maximal, characteristic
2	#20241712	C₂	1	1	yes	maximal, characteristic
3	#20241291	C₂	1	2	yes	maximal
4	#20241246	C₂	1	2	yes	maximal
5	C₄₇×#2351	C₂	1	1	yes	maximal, characteristic
6	#15689176	C₂²	1	2	yes	—
7	#15689147	C₂²	1	2	yes	—
8	C₂×#13093943	—	2	1	no	—
9	#15688892	—	2	1	no	—
10	#15688849	—	2	2	no	—
11	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
12	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
13	C₄₇×#389	—	2	2	no	—
14	C₄₇×#389	—	2	1	no	—
15	C₄₇×#382	C₄	1	2	yes	—
16	C₄₇×#382	C₂²	1	1	yes	characteristic
17	C₄×C₄⋊C₄×C₄₇	C₄	1	2	yes	—
18	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×#10625329	—	2	2	no	—
20	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
21	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
22	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
23	#13093943	—	4	2	no	—
24	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
25	C₄×C₄₇⋊C₈	—	2	2	no	—
26	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
27	C₄×Q₈×C₄₇	—	2	2	no	—
28	C₄×Q₈×C₄₇	—	2	2	no	—
29	C₄×Q₈×C₄₇	—	4	4	no	—
30	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
31	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
32	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
33	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
34	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
35	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
36	C₂×C₄²×C₄₇	—	2	2	no	—
37	C₂×C₄²×C₄₇	—	2	1	no	—
38	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
39	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
40	#95×C₄₇	—	2	2	no	—
41	#95×C₄₇	—	2	1	no	—
42	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
43	#95×C₄₇	C₂×C₄	1	2	yes	—
44	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂×Q₈×C₄₇	—	2	2	no	—
46	C₂×Q₈×C₄₇	—	2	2	no	—
47	C₂×Q₈×C₄₇	SD₁₆	1	2	yes	—
48	C₂×Q₈×C₄₇	Q₁₆	1	2	yes	—
49	C₂²×C₄×C₄₇	—	2	1	no	—
50	C₂²×C₄×C₄₇	—	2	2	no	—
51	C₂²×C₄×C₄₇	—	2	1	no	—
52	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
53	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
54	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
55	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
57	C₄⋊C₄×C₄₇	—	2	4	no	—
58	C₄⋊C₄×C₄₇	—	2	2	no	—
59	C₄⋊C₄×C₄₇	—	4	2	no	—
60	C₄⋊C₄×C₄₇	—	4	4	no	—
61	C₄⋊C₄×C₄₇	—	4	4	no	—
62	C₄⋊C₄×C₄₇	—	4	2	no	—
63	C₄²×C₄₇	—	2	2	no	—
64	C₄²×C₄₇	—	2	2	no	—
65	C₄²×C₄₇	—	4	4	no	—
66	C₄²×C₄₇	—	4	2	no	—
67	C₄²×C₄₇	#41	1	2	yes	—
68	C₄²×C₄₇	#41	1	2	yes	—
69	#10625329	—	4	2	no	—
70	#10625329	—	4	2	no	—
71	C₂×C₄₇⋊C₈	—	4	2	no	—
72	C₂×C₄₇⋊C₈	—	4	2	no	—
73	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
74	Q₈×C₄₇	—	2	4	no	—
75	Q₈×C₄₇	—	2	4	no	—
76	C₂×C₄×C₄₇	—	2	2	no	—
77	C₂×C₄×C₄₇	—	2	2	no	—
78	C₂×C₄×C₄₇	—	2	2	no	—
79	C₂×C₄×C₄₇	—	2	2	no	—
80	C₂×C₄×C₄₇	—	4	1	no	—
81	C₂×C₄×C₄₇	—	4	1	no	—
82	C₂×C₄×C₄₇	—	4	1	no	—
83	C₂×C₄×C₄₇	—	4	1	no	—
84	C₂×C₄×C₄₇	—	4	2	no	—
85	C₂×C₄×C₄₇	—	4	1	no	—
86	C₂×C₄×C₄₇	—	4	2	no	—
87	C₂×C₄×C₄₇	—	4	2	no	—
88	C₂×C₄×C₄₇	—	4	1	no	—
89	C₂×C₄×C₄₇	—	4	2	no	—
90	C₂×C₄×C₄₇	—	4	1	no	—
91	C₂×C₄×C₄₇	#103	1	4	yes	—
92	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
93	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
94	C₂×C₄×C₄₇	#123	1	2	yes	—
95	C₂×C₄×C₄₇	#123	1	2	yes	—
96	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
97	C₂×C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
98	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
99	C₄₇⋊C₈	—	8	2	no	—
100	C₄₇⋊C₈	—	8	2	no	—
101	#8767	—	47	1	no	maximal, Sylow
102	C₂²×C₄₇	—	2	1	no	—
103	C₂²×C₄₇	—	2	1	no	—
104	C₂²×C₄₇	#381	1	1	yes	characteristic
105	C₂²×C₄₇	C₂×#103	1	1	yes	characteristic
106	C₂²×C₄₇	#418	1	1	yes	characteristic
107	C₄×C₄₇	—	2	4	no	—
108	C₄×C₄₇	—	2	2	no	—
109	C₄×C₄₇	—	2	1	no	—
110	C₄×C₄₇	—	2	1	no	—
111	C₄×C₄₇	—	4	2	no	—
112	C₄×C₄₇	—	4	2	no	—
113	C₄×C₄₇	—	8	2	no	—
114	C₄×C₄₇	—	8	1	no	—
115	C₄×C₄₇	#481	1	2	yes	—
116	C₄×C₄₇	#484	1	2	yes	—
117	#2351	D₄₇	1	1	yes	characteristic
118	#1801	—	47	1	no	—
119	#1461	—	47	1	no	—
120	#1303	—	47	2	no	—
121	#1286	—	47	2	no	—
122	C₂×C₄₇	—	2	1	no	—
123	C₂×C₄₇	—	2	1	no	—
124	C₂×C₄₇	#1824	1	1	yes	characteristic
125	C₂×C₄₇	#1827	1	1	yes	characteristic
126	C₂×C₄₇	#1830	1	1	yes	characteristic
127	C₂×C₄×Q₈	—	2	1	no	—
128	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
129	#431	—	47	2	no	—
130	#423	—	47	2	no	—
131	C₂×#101	—	94	1	no	—
132	#389	—	2	1	no	—
133	#389	—	2	2	no	—
134	#382	Dic₄₇	1	2	yes	—
135	#382	C₂×D₄₇	1	1	yes	characteristic
136	C₄×C₄⋊C₄	Dic₄₇	1	2	yes	—
137	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
138	#343	—	94	1	no	—
139	#324	—	94	2	no	—
140	C₄₇	#8767	1	1	yes	characteristic, complemented, Sylow
141	C₂²×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
142	C₂×M₁₆	—	94	2	no	—
143	C₄×Q₈	—	2	2	no	—
144	C₄×Q₈	—	2	2	no	—
145	C₄×Q₈	—	4	4	no	—
146	C₂×C₄⋊C₄	—	2	2	no	—
147	C₂×C₄⋊C₄	—	2	2	no	—
148	C₂×C₄⋊C₄	—	2	1	no	—
149	C₂×C₄⋊C₄	—	2	1	no	—
150	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	2	yes	—
151	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
152	C₂×C₄²	—	2	2	no	—
153	C₂×C₄²	—	2	1	no	—
154	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
155	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
156	C₄⋊C₈	—	94	2	no	—
157	C₄⋊C₈	—	94	2	no	—
158	C₄⋊C₈	—	94	2	no	—
159	#101	—	188	2	no	—
160	C₂²⋊C₈	—	94	2	no	—
161	C₄×C₈	—	94	2	no	—
162	#95	—	2	2	no	—
163	#95	—	2	1	no	—
164	#95	C₂×Dic₄₇	1	1	yes	characteristic
165	#95	C₂×Dic₄₇	1	2	yes	—
166	#95	C₂×Dic₄₇	1	1	yes	characteristic
167	C₂×Q₈	—	2	2	no	—
168	C₂×Q₈	—	2	2	no	—
169	C₂×Q₈	#10625336	1	2	yes	—
170	C₂×Q₈	#10625337	1	2	yes	—
171	C₂²×C₄	—	2	1	no	—
172	C₂²×C₄	—	2	1	no	—
173	C₂²×C₄	—	2	2	no	—
174	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
175	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
176	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
177	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
178	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
179	M₁₆	—	188	2	no	—
180	M₁₆	—	188	2	no	—
181	C₂×C₈	—	188	2	no	—
182	C₂×C₈	—	188	2	no	—
183	C₄⋊C₄	—	2	4	no	—
184	C₄⋊C₄	—	2	2	no	—
185	C₄⋊C₄	—	4	2	no	—
186	C₄⋊C₄	—	4	4	no	—
187	C₄⋊C₄	—	4	4	no	—
188	C₄⋊C₄	—	4	2	no	—
189	C₄²	—	2	2	no	—
190	C₄²	—	2	2	no	—
191	C₄²	—	4	4	no	—
192	C₄²	—	4	2	no	—
193	C₄²	#10625350	1	2	yes	—
194	C₄²	#10625350	1	2	yes	—
195	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
196	Q₈	—	2	4	no	—
197	Q₈	—	2	4	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	4	1	no	—
203	C₂×C₄	—	4	1	no	—
204	C₂×C₄	—	4	1	no	—
205	C₂×C₄	—	4	1	no	—
206	C₂×C₄	—	4	2	no	—
207	C₂×C₄	—	4	1	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	4	1	no	—
210	C₂×C₄	—	4	2	no	—
211	C₂×C₄	—	4	2	no	—
212	C₂×C₄	—	4	1	no	—
213	C₂×C₄	#13093948	1	4	yes	—
214	C₂×C₄	#13093983	1	1	yes	characteristic
215	C₂×C₄	#13093983	1	1	yes	characteristic
216	C₂×C₄	#13094007	1	2	yes	—
217	C₂×C₄	#13094007	1	2	yes	—
218	C₂×C₄	C₂×#10625336	1	1	yes	characteristic
219	C₂×C₄	C₂×#10625337	1	1	yes	characteristic
220	C₂×C₄	#13094050	1	2	yes	—
221	C₈	—	376	2	no	—
222	C₈	—	376	2	no	—
223	C₂²	—	2	1	no	—
224	C₂²	—	2	1	no	—
225	C₂²	#15688986	1	1	yes	characteristic
226	C₂²	C₂×#13093948	1	1	yes	characteristic
227	C₂²	#15689128	1	1	yes	characteristic
228	C₄	—	2	4	no	—
229	C₄	—	2	2	no	—
230	C₄	—	2	1	no	—
231	C₄	—	2	1	no	—
232	C₄	—	4	2	no	—
233	C₄	—	4	2	no	—
234	C₄	—	8	2	no	—
235	C₄	—	8	1	no	—
236	C₄	#15689441	1	2	yes	—
237	C₄	#15689458	1	2	yes	—
238	C₂	—	2	1	no	—
239	C₂	—	2	1	no	—
240	C₂	#20243478	1	1	yes	characteristic
241	C₂	#20243492	1	1	yes	characteristic
242	C₂	#20243502	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20243384

C₂

yes

maximal, characteristic

#20241712

C₂

yes

maximal, characteristic

#20241291

C₂

yes

maximal

#20241246

C₂

yes

maximal

C₄₇×#2351

C₂

yes

maximal, characteristic

#15689176

C₂²

yes

—

#15689147

C₂²

yes

—

C₂×#13093943

—

#15688892

—

#15688849

—

C₂×C₄×Q₈×C₄₇

—

C₂×C₄×Q₈×C₄₇

C₂²

yes

characteristic

C₄₇×#389

—

C₄₇×#389

—

C₄₇×#382

C₄

yes

—

C₄₇×#382

C₂²

yes

characteristic

C₄×C₄⋊C₄×C₄₇

C₄

yes

—

C₄×C₄⋊C₄×C₄₇

C₂²

yes

characteristic

C₂×#10625329

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

#13093943

—

C₂²⋊(C₄₇⋊C₈)

—

C₄×C₄₇⋊C₈

—

C₂²×Q₈×C₄₇

D₄

yes

characteristic

C₄×Q₈×C₄₇

—

C₄×Q₈×C₄₇

—

C₄×Q₈×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

D₄

yes

—

C₂×C₄⋊C₄×C₄₇

D₄

yes

characteristic

C₂×C₄²×C₄₇

—

C₂×C₄²×C₄₇

—

C₂×C₄²×C₄₇

C₂×C₄

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

#95×C₄₇

—

#95×C₄₇

—

#95×C₄₇

C₂×C₄

yes

characteristic

#95×C₄₇

C₂×C₄

yes

—

#95×C₄₇

C₂×C₄

yes

characteristic

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

SD₁₆

yes

—

C₂×Q₈×C₄₇

Q₁₆

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

#41

yes

—

C₄²×C₄₇

#41

yes

—

#10625329

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

C₂×C₂²⋊C₄

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×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

#103

yes

—

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

—

C₂×C₄×C₄₇

#123

yes

—

C₂×C₄×C₄₇

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₄₇

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

—

C₄₇⋊C₈

—

100

C₄₇⋊C₈

—

101

#8767

—

maximal, Sylow

102

C₂²×C₄₇

—

103

C₂²×C₄₇

—

104

C₂²×C₄₇

#381

yes

characteristic

105

C₂²×C₄₇

C₂×#103

yes

characteristic

106

C₂²×C₄₇

#418

yes

characteristic

107

C₄×C₄₇

—

108

C₄×C₄₇

—

109

C₄×C₄₇

—

110

C₄×C₄₇

—

111

C₄×C₄₇

—

112

C₄×C₄₇

—

113

C₄×C₄₇

—

114

C₄×C₄₇

—

115

C₄×C₄₇

#481

yes

—

116

C₄×C₄₇

#484

yes

—

117

#2351

D₄₇

yes

characteristic

118

#1801

—

119

#1461

—

120

#1303

—

121

#1286

—

122

C₂×C₄₇

—

123

C₂×C₄₇

—

124

C₂×C₄₇

#1824

yes

characteristic

125

C₂×C₄₇

#1827

yes

characteristic

126

C₂×C₄₇

#1830

yes

characteristic

127

C₂×C₄×Q₈

—

128

C₂×C₄×Q₈

C₂×D₄₇

yes

characteristic

129

#431

—

130

#423

—

131

C₂×#101

—

132

#389

—

133

#389

—

134

#382

Dic₄₇

yes

—

135

#382

C₂×D₄₇

yes

characteristic

136

C₄×C₄⋊C₄

Dic₄₇

yes

—

137

C₄×C₄⋊C₄

C₂×D₄₇

yes

characteristic

138

#343

—

139

#324

—

140

C₄₇

#8767

yes

characteristic, complemented, Sylow

141

C₂²×Q₈

C₂²⋊D₄₇

yes

characteristic

142

C₂×M₁₆

—

143

C₄×Q₈

—

144

C₄×Q₈

—

145

C₄×Q₈

—

146

C₂×C₄⋊C₄

—

147

C₂×C₄⋊C₄

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

C₂²⋊D₄₇

yes

—

151

C₂×C₄⋊C₄

C₂²⋊D₄₇

yes

characteristic

152

C₂×C₄²

—

153

C₂×C₄²

—

154

C₂×C₄²

C₂×Dic₄₇

yes

—

155

C₂×C₄²

C₂²×D₄₇

yes

characteristic

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

#101

—

188

—

160

C₂²⋊C₈

—

161

C₄×C₈

—

162

#95

—

163

#95

—

164

#95

C₂×Dic₄₇

yes

characteristic

165

#95

C₂×Dic₄₇

yes

—

166

#95

C₂×Dic₄₇

yes

characteristic

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

#10625336

yes

—

170

C₂×Q₈

#10625337

yes

—

171

C₂²×C₄

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

C₂²⋊Dic₄₇

yes

—

175

C₂²×C₄

C₂²⋊Dic₄₇

yes

—

176

C₂²×C₄

C₂²×Dic₄₇

yes

characteristic

177

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

178

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

179

M₁₆

—

188

—

180

M₁₆

—

188

—

181

C₂×C₈

—

188

—

182

C₂×C₈

—

188

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄²

—

190

C₄²

—

191

C₄²

—

192

C₄²

—

193

C₄²

#10625350

yes

—

194

C₄²

#10625350

yes

—

195

C₂³

C₂×C₂²⋊Dic₄₇

yes

characteristic

196

Q₈

—

197

Q₈

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

#13093948

yes

—

214

C₂×C₄

#13093983

yes

characteristic

215

C₂×C₄

#13093983

yes

characteristic

216

C₂×C₄

#13094007

yes

—

217

C₂×C₄

#13094007

yes

—

218

C₂×C₄

C₂×#10625336

yes

characteristic

219

C₂×C₄

C₂×#10625337

yes

characteristic

220

C₂×C₄

#13094050

yes

—

221

C₈

—

376

—

222

C₈

—

376

—

223

C₂²

—

224

C₂²

—

225

C₂²

#15688986

yes

characteristic

226

C₂²

C₂×#13093948

yes

characteristic

227

C₂²

#15689128

yes

characteristic

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

#15689441

yes

—

237

C₄

#15689458

yes

—

238

C₂

—

239

C₂

—

240

C₂

#20243478

yes

characteristic

241

C₂

#20243492

yes

characteristic

242

C₂

#20243502

yes

characteristic

	subgroup	G/H
center	C₂²	#15688986
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#2351	C₂
socle	C₂²×C₄₇	#381
prime radical	C₂³×C₄₇	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#2351	D₄₇
hypocenter	C₄₇	#8767
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2351

subgroup

G/H

center

C₂²

#15688986

commutator

C₂²×C₄×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#2351

C₂

socle

C₂²×C₄₇

#381

prime radical

C₂³×C₄₇

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2351

N	H ≅ G/N	type
140. C₄₇	#8767	semidirect

H ≅ G/N

type

140. C₄₇

#8767

semidirect

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

subgroup	index
#20243384	2
#20241712	2
#20241291	2
#20241246	2
C₄₇×#2351	2
#8767	47

subgroup

index

C₄₇×#2351

Subgroups — #26109859

Conjugacy classes of subgroups

Complements

Maximal subgroups