Group #26119304 — subgroups

Subgroups — #26119304

Order 12032.

500 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 121 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	#20248630	C₂	1	1	yes	maximal, characteristic, complemented
2	#20244314	C₂	1	2	yes	maximal
3	#20244193	C₂	1	1	yes	maximal, characteristic
4	#20241227	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1296	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#13094021	C₂²	1	1	yes	characteristic
7	C₂×#13093946	—	2	2	no	—
8	C₂×#13093946	—	2	2	no	—
9	C₂×#13093944	—	2	2	no	—
10	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
11	#15689062	—	2	2	no	—
12	#15689022	—	2	2	no	—
13	#15688988	—	2	2	no	—
14	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
15	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
16	C₄₇×#384	C₂²	1	1	yes	characteristic
17	C₂²×D₁₈₈	—	2	1	no	—
18	C₂²×D₁₈₈	—	2	2	no	—
19	C₂²×C₄₇⋊C₈	—	2	1	no	—
20	#13094021	—	2	2	no	—
21	#13094021	—	2	1	no	—
22	#13094021	Q₈	1	2	yes	—
23	C₂×C₄⋊Dic₄₇	—	2	2	no	—
24	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
25	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
26	C₂×C₄×Dic₄₇	—	2	2	no	—
27	#13093946	—	4	4	no	—
28	#13093946	—	4	4	no	—
29	#13093944	—	4	4	no	—
30	C₄×C₄₇⋊C₈	—	2	2	no	—
31	C₄₇⋊#95	—	2	2	no	—
32	C₄₇⋊#95	—	2	4	no	—
33	C₄₇⋊#95	—	2	2	no	—
34	C₂²×C₈×C₄₇	—	2	2	no	—
35	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
36	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
37	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
38	C₄⋊C₈×C₄₇	—	2	2	no	—
39	C₄⋊C₈×C₄₇	—	2	2	no	—
40	C₂³×D₄₇	—	4	1	no	—
41	C₂²×C₄×C₄₇	—	2	2	no	—
42	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
43	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
44	C₂²×Dic₄₇	—	2	2	no	—
45	C₂²×Dic₄₇	—	2	2	no	—
46	C₂×D₁₈₈	—	2	2	no	—
47	C₂×D₁₈₈	—	2	4	no	—
48	C₂×D₁₈₈	—	4	2	no	—
49	C₂×D₁₈₈	—	4	2	no	—
50	C₂×D₁₈₈	—	4	2	no	—
51	C₂×D₁₈₈	—	4	2	no	—
52	C₂×D₁₈₈	—	4	2	no	—
53	C₂×D₁₈₈	—	4	2	no	—
54	C₂×D₁₈₈	—	4	1	no	—
55	C₂×D₁₈₈	—	4	2	no	—
56	C₂×C₈×C₄₇	—	4	2	no	—
57	C₂×C₈×C₄₇	—	4	2	no	—
58	C₂×C₈×C₄₇	—	4	2	no	—
59	C₄⋊C₄×C₄₇	—	4	2	no	—
60	C₄⋊C₄×C₄₇	—	4	2	no	—
61	C₄⋊C₄×C₄₇	—	4	2	no	—
62	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
63	C₄²×C₄₇	#41	1	2	yes	—
64	C₄²×C₄₇	#41	1	1	yes	characteristic
65	C₄⋊Dic₄₇	—	2	2	no	—
66	C₄⋊Dic₄₇	—	2	2	no	—
67	C₄⋊Dic₄₇	—	2	2	no	—
68	C₄⋊Dic₄₇	—	2	2	no	—
69	C₄⋊Dic₄₇	—	8	2	no	—
70	C₄×Dic₄₇	—	4	2	no	—
71	C₄×Dic₄₇	—	4	2	no	—
72	C₂×C₄₇⋊C₈	—	2	2	no	—
73	C₂×C₄₇⋊C₈	—	4	1	no	—
74	C₂×C₄₇⋊C₈	—	4	1	no	—
75	C₂³×C₄₇	#120	1	1	yes	characteristic
76	C₂²×D₄₇	—	4	2	no	—
77	C₂²×D₄₇	—	8	2	no	—
78	C₂²×D₄₇	—	8	2	no	—
79	C₂²×D₄₇	—	8	1	no	—
80	C₂²×D₄₇	—	8	1	no	—
81	C₂×C₄×C₄₇	—	2	1	no	—
82	C₂×C₄×C₄₇	—	2	1	no	—
83	C₂×C₄×C₄₇	—	4	4	no	—
84	C₂×C₄×C₄₇	—	4	2	no	—
85	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
86	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
87	C₂×C₄×C₄₇	#124	1	2	yes	—
88	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
89	C₂×C₄×C₄₇	#135	1	2	yes	—
90	C₂×C₄×C₄₇	#135	1	2	yes	—
91	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
92	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
93	C₂×Dic₄₇	—	4	2	no	—
94	C₂×Dic₄₇	—	4	2	no	—
95	C₂×Dic₄₇	—	4	2	no	—
96	C₂×Dic₄₇	—	4	2	no	—
97	C₂×Dic₄₇	—	4	2	no	—
98	C₂×Dic₄₇	—	4	2	no	—
99	D₁₈₈	—	4	4	no	—
100	D₁₈₈	—	4	4	no	—
101	D₁₈₈	—	4	4	no	—
102	D₁₈₈	—	8	2	no	—
103	D₁₈₈	—	8	2	no	—
104	D₁₈₈	—	8	2	no	—
105	C₈×C₄₇	—	8	2	no	—
106	C₄₇⋊C₈	—	4	2	no	—
107	#10351	—	47	1	no	maximal, Sylow
108	C₂²×C₄₇	#393	1	1	yes	characteristic
109	C₂²×C₄₇	#449	1	2	yes	—
110	C₂²×C₄₇	#449	1	2	yes	—
111	C₂²×C₄₇	#453	1	1	yes	characteristic
112	C₂²×C₄₇	#454	1	1	yes	characteristic
113	C₂×D₄₇	—	8	4	no	—
114	C₂×D₄₇	—	8	2	no	—
115	C₂×D₄₇	—	16	1	no	—
116	C₂×D₄₇	—	16	1	no	—
117	C₂×D₄₇	—	16	2	no	—
118	C₄×C₄₇	—	2	1	no	—
119	C₄×C₄₇	—	2	1	no	—
120	C₄×C₄₇	—	8	2	no	—
121	C₄×C₄₇	#478	1	2	yes	—
122	C₄×C₄₇	#478	1	2	yes	—
123	C₄×C₄₇	#488	1	2	yes	—
124	C₄×C₄₇	#490	1	2	yes	—
125	Dic₄₇	—	8	2	no	—
126	Dic₄₇	—	8	2	no	—
127	#2571	—	47	1	no	—
128	#1982	—	47	2	no	—
129	#1957	—	47	1	no	—
130	#1296	D₄₇	1	1	yes	characteristic, complemented
131	#1279	—	47	2	no	—
132	C₂×C₄₇	#1620	1	1	yes	characteristic
133	C₂×C₄₇	#1624	1	1	yes	characteristic
134	C₂×C₄₇	#1628	1	2	yes	—
135	C₂×C₄₇	#2025	1	2	yes	—
136	C₂×C₄₇	#2027	1	1	yes	characteristic
137	D₄₇	—	16	2	no	—
138	C₂×#127	—	47	1	no	—
139	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
140	C₂×#102	—	94	2	no	—
141	C₂×#102	—	94	2	no	—
142	C₂×#102	—	94	2	no	—
143	C₂×C₄×C₈	—	47	1	no	—
144	#400	—	94	2	no	—
145	#389	—	94	2	no	—
146	#384	C₂×D₄₇	1	1	yes	characteristic
147	#382	—	94	2	no	—
148	C₄×C₄⋊C₄	—	47	2	no	—
149	C₄₇	#10351	1	1	yes	characteristic, complemented, Sylow
150	C₂²×D₄	—	94	1	no	—
151	C₂²×D₄	—	94	2	no	—
152	C₂²×C₈	—	2	2	no	—
153	C₂²×C₈	—	94	1	no	—
154	#127	—	47	2	no	—
155	#127	—	94	2	no	—
156	#127	—	94	1	no	—
157	C₂×C₄⋊C₄	—	2	2	no	—
158	C₂×C₄⋊C₄	—	47	2	no	—
159	C₂×C₄⋊C₄	—	47	2	no	—
160	C₂×C₄⋊C₄	—	94	2	no	—
161	C₂×C₄⋊C₄	D₁₈₈	1	2	yes	—
162	C₂×C₄²	—	94	2	no	—
163	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
164	C₄⋊C₈	—	2	2	no	—
165	C₄⋊C₈	—	2	2	no	—
166	#102	—	188	4	no	—
167	#102	—	188	4	no	—
168	#102	—	188	4	no	—
169	C₄×C₈	—	94	2	no	—
170	#95	—	94	2	no	—
171	#95	—	94	4	no	—
172	#95	—	94	2	no	—
173	C₂⁴	—	188	1	no	—
174	C₂×D₄	—	94	4	no	—
175	C₂×D₄	—	94	2	no	—
176	C₂×D₄	—	188	2	no	—
177	C₂×D₄	—	188	2	no	—
178	C₂×D₄	—	188	2	no	—
179	C₂×D₄	—	188	1	no	—
180	C₂×D₄	—	188	2	no	—
181	C₂×D₄	—	188	2	no	—
182	C₂×D₄	—	188	2	no	—
183	C₂×D₄	—	188	2	no	—
184	C₂²×C₄	—	2	2	no	—
185	C₂²×C₄	—	94	2	no	—
186	C₂²×C₄	—	94	2	no	—
187	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
188	C₂²×C₄	D₄×D₄₇	1	2	yes	—
189	C₂×C₈	—	4	2	no	—
190	C₂×C₈	—	4	2	no	—
191	C₂×C₈	—	4	2	no	—
192	C₂×C₈	—	94	2	no	—
193	C₂×C₈	—	188	1	no	—
194	C₂×C₈	—	188	1	no	—
195	C₄⋊C₄	—	4	2	no	—
196	C₄⋊C₄	—	4	2	no	—
197	C₄⋊C₄	—	4	2	no	—
198	C₄⋊C₄	—	94	2	no	—
199	C₄⋊C₄	—	94	2	no	—
200	C₄⋊C₄	—	94	2	no	—
201	C₄⋊C₄	—	94	2	no	—
202	C₄⋊C₄	—	376	2	no	—
203	C₄²	—	188	2	no	—
204	C₄²	—	188	2	no	—
205	C₄²	#10625350	1	2	yes	—
206	C₄²	#10625352	1	1	yes	characteristic
207	C₄²	Q₈×D₄₇	1	1	yes	characteristic
208	C₂³	—	376	2	no	—
209	C₂³	—	376	2	no	—
210	C₂³	—	376	1	no	—
211	C₂³	—	376	1	no	—
212	C₂³	—	188	2	no	—
213	C₂³	#13093994	1	1	yes	characteristic
214	D₄	—	376	2	no	—
215	D₄	—	376	2	no	—
216	D₄	—	376	2	no	—
217	D₄	—	188	4	no	—
218	D₄	—	188	4	no	—
219	D₄	—	188	4	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	4	4	no	—
223	C₂×C₄	—	4	2	no	—
224	C₂×C₄	—	188	2	no	—
225	C₂×C₄	—	188	2	no	—
226	C₂×C₄	—	188	2	no	—
227	C₂×C₄	—	188	2	no	—
228	C₂×C₄	—	188	2	no	—
229	C₂×C₄	—	188	2	no	—
230	C₂×C₄	#13094002	1	2	yes	—
231	C₂×C₄	#13094004	1	1	yes	characteristic
232	C₂×C₄	#13094010	1	2	yes	—
233	C₂×C₄	#13094012	1	1	yes	characteristic
234	C₂×C₄	#13094045	1	2	yes	—
235	C₂×C₄	#13094047	1	2	yes	—
236	C₂×C₄	#13094048	1	2	yes	—
237	C₂×C₄	#13094051	1	2	yes	—
238	C₈	—	8	2	no	—
239	C₈	—	188	2	no	—
240	C₂²	—	376	4	no	—
241	C₂²	—	376	2	no	—
242	C₂²	—	752	1	no	—
243	C₂²	—	752	1	no	—
244	C₂²	—	752	2	no	—
245	C₂²	#15689036	1	1	yes	characteristic
246	C₂²	#15689269	1	2	yes	—
247	C₂²	#15689271	1	2	yes	—
248	C₂²	#15689293	1	1	yes	characteristic
249	C₂²	#15689298	1	1	yes	characteristic
250	C₄	—	2	1	no	—
251	C₄	—	2	1	no	—
252	C₄	—	8	2	no	—
253	C₄	—	376	2	no	—
254	C₄	—	376	2	no	—
255	C₄	#15689422	1	2	yes	—
256	C₄	#15689426	1	2	yes	—
257	C₄	#15689479	1	2	yes	—
258	C₄	#15689486	1	2	yes	—
259	C₂	—	752	2	no	—
260	C₂	#20242448	1	1	yes	characteristic
261	C₂	#20242472	1	1	yes	characteristic
262	C₂	#20242499	1	2	yes	—
263	C₂	#20244533	1	2	yes	—
264	C₂	#20244545	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20248630

C₂

yes

maximal, characteristic, complemented

#20244314

C₂

yes

maximal

#20244193

C₂

yes

maximal, characteristic

#20241227

C₂

yes

maximal, complemented

C₄₇×#1296

C₂

yes

maximal, characteristic, complemented

C₂×#13094021

C₂²

yes

—

—

—

C₂×C₄×C₄₇⋊C₈

C₂²

yes

—

—

—

C₄×C₄⋊Dic₄₇

C₂²

yes

—

C₂×C₄⋊C₈×C₄₇

C₂²

yes

—

C₄₇×#384

C₂²

yes

characteristic

C₂²×D₁₈₈

—

C₂²×D₁₈₈

—

C₂²×C₄₇⋊C₈

—

#13094021

—

#13094021

—

#13094021

Q₈

yes

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

D₄

yes

—

C₂×C₄⋊Dic₄₇

D₄

yes

—

C₂×C₄×Dic₄₇

—

#13093946

—

#13093946

—

#13093944

—

C₄×C₄₇⋊C₈

—

C₄₇⋊#95

—

C₄₇⋊#95

—

C₄₇⋊#95

—

C₂²×C₈×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

D₄

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₄⋊C₈×C₄₇

—

C₂³×D₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

C₂×Q₈

yes

characteristic

C₄²×C₄₇

#41

yes

—

C₄²×C₄₇

#41

yes

characteristic

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

#120

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²⋊Q₈

yes

—

C₂×C₄×C₄₇

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₄₇

#124

yes

—

C₂×C₄×C₄₇

#124

yes

characteristic

C₂×C₄×C₄₇

#135

yes

—

C₂×C₄×C₄₇

#135

yes

—

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

100

D₁₈₈

—

101

D₁₈₈

—

102

D₁₈₈

—

103

D₁₈₈

—

104

D₁₈₈

—

105

C₈×C₄₇

—

106

C₄₇⋊C₈

—

107

#10351

—

maximal, Sylow

108

C₂²×C₄₇

#393

yes

characteristic

109

C₂²×C₄₇

#449

yes

—

110

C₂²×C₄₇

#449

yes

—

111

C₂²×C₄₇

#453

yes

characteristic

112

C₂²×C₄₇

#454

yes

characteristic

113

C₂×D₄₇

—

114

C₂×D₄₇

—

115

C₂×D₄₇

—

116

C₂×D₄₇

—

117

C₂×D₄₇

—

118

C₄×C₄₇

—

119

C₄×C₄₇

—

120

C₄×C₄₇

—

121

C₄×C₄₇

#478

yes

—

122

C₄×C₄₇

#478

yes

—

123

C₄×C₄₇

#488

yes

—

124

C₄×C₄₇

#490

yes

—

125

Dic₄₇

—

126

Dic₄₇

—

127

#2571

—

128

#1982

—

129

#1957

—

130

#1296

D₄₇

yes

characteristic, complemented

131

#1279

—

132

C₂×C₄₇

#1620

yes

characteristic

133

C₂×C₄₇

#1624

yes

characteristic

134

C₂×C₄₇

#1628

yes

—

135

C₂×C₄₇

#2025

yes

—

136

C₂×C₄₇

#2027

yes

characteristic

137

D₄₇

—

138

C₂×#127

—

139

C₂×C₄⋊C₈

C₂×D₄₇

yes

—

140

C₂×#102

—

141

C₂×#102

—

142

C₂×#102

—

143

C₂×C₄×C₈

—

144

#400

—

145

#389

—

146

#384

C₂×D₄₇

yes

characteristic

147

#382

—

148

C₄×C₄⋊C₄

—

149

C₄₇

#10351

yes

characteristic, complemented, Sylow

150

C₂²×D₄

—

151

C₂²×D₄

—

152

C₂²×C₈

—

153

C₂²×C₈

—

154

#127

—

155

#127

—

156

#127

—

157

C₂×C₄⋊C₄

—

158

C₂×C₄⋊C₄

—

159

C₂×C₄⋊C₄

—

160

C₂×C₄⋊C₄

—

161

C₂×C₄⋊C₄

D₁₈₈

yes

—

162

C₂×C₄²

—

163

C₂×C₄²

C₂²×D₄₇

yes

characteristic

164

C₄⋊C₈

—

165

C₄⋊C₈

—

166

#102

—

188

—

167

#102

—

188

—

168

#102

—

188

—

169

C₄×C₈

—

170

#95

—

171

#95

—

172

#95

—

173

C₂⁴

—

188

—

174

C₂×D₄

—

175

C₂×D₄

—

176

C₂×D₄

—

188

—

177

C₂×D₄

—

188

—

178

C₂×D₄

—

188

—

179

C₂×D₄

—

188

—

180

C₂×D₄

—

188

—

181

C₂×D₄

—

188

—

182

C₂×D₄

—

188

—

183

C₂×D₄

—

188

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

C₂×D₁₈₈

yes

characteristic

188

C₂²×C₄

D₄×D₄₇

yes

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

188

—

194

C₂×C₈

—

188

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₄⋊C₄

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

376

—

203

C₄²

—

188

—

204

C₄²

—

188

—

205

C₄²

#10625350

yes

—

206

C₄²

#10625352

yes

characteristic

207

C₄²

Q₈×D₄₇

yes

characteristic

208

C₂³

—

376

—

209

C₂³

—

376

—

210

C₂³

—

376

—

211

C₂³

—

376

—

212

C₂³

—

188

—

213

C₂³

#13093994

yes

characteristic

214

D₄

—

376

—

215

D₄

—

376

—

216

D₄

—

376

—

217

D₄

—

188

—

218

D₄

—

188

—

219

D₄

—

188

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

188

—

225

C₂×C₄

—

188

—

226

C₂×C₄

—

188

—

227

C₂×C₄

—

188

—

228

C₂×C₄

—

188

—

229

C₂×C₄

—

188

—

230

C₂×C₄

#13094002

yes

—

231

C₂×C₄

#13094004

yes

characteristic

232

C₂×C₄

#13094010

yes

—

233

C₂×C₄

#13094012

yes

characteristic

234

C₂×C₄

#13094045

yes

—

235

C₂×C₄

#13094047

yes

—

236

C₂×C₄

#13094048

yes

—

237

C₂×C₄

#13094051

yes

—

238

C₈

—

239

C₈

—

188

—

240

C₂²

—

376

—

241

C₂²

—

376

—

242

C₂²

—

752

—

243

C₂²

—

752

—

244

C₂²

—

752

—

245

C₂²

#15689036

yes

characteristic

246

C₂²

#15689269

yes

—

247

C₂²

#15689271

yes

—

248

C₂²

#15689293

yes

characteristic

249

C₂²

#15689298

yes

characteristic

250

C₄

—

251

C₄

—

252

C₄

—

253

C₄

—

376

—

254

C₄

—

376

—

255

C₄

#15689422

yes

—

256

C₄

#15689426

yes

—

257

C₄

#15689479

yes

—

258

C₄

#15689486

yes

—

259

C₂

—

752

—

260

C₂

#20242448

yes

characteristic

261

C₂

#20242472

yes

characteristic

262

C₂

#20242499

yes

—

263

C₂

#20244533

yes

—

264

C₂

#20244545

yes

characteristic

	subgroup	G/H
center	C₂³	#13093994
commutator, cosocle	C₂×C₄²×C₄₇	C₂³
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1296	C₂
socle	C₂³×C₄₇	#120
prime radical	C₂×#13094021	C₂²
hypercenter	#1296	D₄₇
hypocenter	C₄₇	#10351
LCS	G ▷ C₂×C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

subgroup

G/H

center

C₂³

#13093994

commutator, cosocle

C₂×C₄²×C₄₇

C₂³

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#1296

C₂

C₂³×C₄₇

C₂²

D₄₇

C₄₇

G ▷ C₂×C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

N	H ≅ G/N	type
1. #20248630	C₂	semidirect
4. #20241227	C₂	semidirect
5. C₄₇×#1296	C₂	semidirect
130. #1296	D₄₇	semidirect
149. C₄₇	#10351	semidirect

H ≅ G/N

type

1. #20248630

C₂

semidirect

4. #20241227

C₂

semidirect

5. C₄₇×#1296

C₂

semidirect

130. #1296

D₄₇

semidirect

149. C₄₇

#10351

semidirect

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

subgroup	index
#20248630	2
#20244314	2
#20244193	2
#20241227	2
C₄₇×#1296	2
#10351	47

subgroup

index

C₄₇×#1296

Subgroups — #26119304

Conjugacy classes of subgroups

Complements

Maximal subgroups