Group #26132847 — subgroups

Subgroups — #26132847

Order 12032.

408 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 135 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	C₂×#15689172	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688946	C₂	1	2	yes	maximal, complemented
3	#20243421	C₂	1	1	yes	maximal, characteristic
4	#20241497	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₇×#349	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10625329	—	2	1	no	—
7	#15689172	—	2	4	no	—
8	C₂×#13093960	—	2	1	no	—
9	C₂×#13093960	C₂²	1	2	yes	—
10	C₂×#13093958	C₂²	1	1	yes	characteristic
11	C₂×#13093956	C₂²	1	1	yes	characteristic
12	#15688983	—	2	1	no	—
13	#15688946	—	2	4	no	—
14	#15688886	—	2	1	no	—
15	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×M₃₂×C₄₇	C₂²	1	2	yes	—
17	C₄₇×#349	C₄	1	4	yes	complemented
18	C₂×#10625329	—	2	4	no	—
19	C₂×#10625329	—	2	2	no	—
20	C₂×#10625329	—	4	1	no	—
21	C₂×#10625329	—	4	2	no	—
22	C₂²×C₄₇⋊C₈	—	4	1	no	—
23	C₂×C₄⋊Dic₄₇	—	2	1	no	—
24	C₂×C₄⋊Dic₄₇	—	2	1	no	—
25	C₂×C₂²⋊Dic₄₇	—	4	1	no	—
26	#13093960	—	2	4	no	—
27	#13093960	—	2	2	no	—
28	#13093960	D₄	1	4	yes	—
29	#13093958	—	2	2	no	—
30	#13093956	—	2	2	no	—
31	C₄₇⋊#95	—	4	1	no	—
32	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
33	C₂×M₁₆×C₄₇	—	2	2	no	—
34	C₂×M₁₆×C₄₇	—	2	2	no	—
35	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
36	C₂×M₁₆×C₄₇	Q₈	1	2	yes	—
37	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
38	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
39	M₃₂×C₄₇	—	2	2	no	—
40	M₃₂×C₄₇	C₂×C₄	1	4	yes	—
41	C₂×C₁₆×C₄₇	—	2	2	no	—
42	C₂⁴×C₄₇	SD₁₆	1	1	yes	characteristic
43	C₂²×C₄×C₄₇	—	2	1	no	—
44	C₂²×C₄×C₄₇	—	2	1	no	—
45	C₂²×C₄×C₄₇	—	2	1	no	—
46	C₂²×C₄×C₄₇	—	2	1	no	—
47	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
48	C₂²×C₄×C₄₇	SD₁₆	1	1	yes	characteristic
49	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
50	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
51	C₂²×Dic₄₇	—	4	1	no	—
52	C₂²×Dic₄₇	—	4	1	no	—
53	M₁₆×C₄₇	—	2	4	no	—
54	M₁₆×C₄₇	—	2	4	no	—
55	C₂×C₈×C₄₇	—	2	1	no	—
56	C₂×C₈×C₄₇	—	2	1	no	—
57	C₂×C₈×C₄₇	C₄⋊C₄	1	2	yes	—
58	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
59	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
60	C₂×C₈×C₄₇	C₂×Q₈	1	1	yes	characteristic
61	C₂×C₈×C₄₇	#41	1	2	yes	—
62	C₂²⋊Dic₄₇	—	8	2	no	—
63	C₄⋊Dic₄₇	—	4	1	no	—
64	C₄⋊Dic₄₇	—	4	1	no	—
65	C₄⋊Dic₄₇	—	4	1	no	—
66	C₄⋊Dic₄₇	—	4	1	no	—
67	#10625329	—	2	4	no	—
68	#10625329	—	4	4	no	—
69	#10625329	—	4	2	no	—
70	C₂×C₄₇⋊C₈	—	4	4	no	—
71	C₂×C₄₇⋊C₈	—	4	2	no	—
72	C₁₆×C₄₇	—	2	4	no	—
73	C₂³×C₄₇	—	2	1	no	—
74	C₂³×C₄₇	—	2	1	no	—
75	C₂³×C₄₇	—	4	1	no	—
76	C₂³×C₄₇	—	4	1	no	—
77	C₂³×C₄₇	#106	1	2	yes	—
78	C₂³×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
79	C₂×C₄×C₄₇	—	2	1	no	—
80	C₂×C₄×C₄₇	—	2	1	no	—
81	C₂×C₄×C₄₇	—	2	2	no	—
82	C₂×C₄×C₄₇	—	2	2	no	—
83	C₂×C₄×C₄₇	—	2	2	no	—
84	C₂×C₄×C₄₇	—	2	2	no	—
85	C₂×C₄×C₄₇	#106	1	2	yes	—
86	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
87	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
88	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
89	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
90	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
91	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
92	C₂×Dic₄₇	—	8	1	no	—
93	C₂×Dic₄₇	—	8	1	no	—
94	C₂×Dic₄₇	—	8	1	no	—
95	C₂×Dic₄₇	—	8	1	no	—
96	C₂×Dic₄₇	—	8	1	no	—
97	C₂×Dic₄₇	—	8	1	no	—
98	C₈×C₄₇	—	2	2	no	—
99	C₈×C₄₇	C₄×D₄	1	2	yes	—
100	C₈×C₄₇	C₂²⋊Q₈	1	2	yes	—
101	C₄₇⋊C₈	—	4	4	no	—
102	#12931	—	47	1	no	maximal, Sylow
103	C₂²×C₄₇	—	2	1	no	—
104	C₂²×C₄₇	—	2	1	no	—
105	C₂²×C₄₇	—	2	2	no	—
106	C₂²×C₄₇	—	4	2	no	—
107	C₂²×C₄₇	—	4	1	no	—
108	C₂²×C₄₇	—	4	1	no	—
109	C₂²×C₄₇	—	8	1	no	—
110	C₂²×C₄₇	C₂×#106	1	1	yes	characteristic
111	C₂²×C₄₇	#448	1	1	yes	characteristic
112	C₂²×C₄₇	#481	1	1	yes	characteristic
113	C₄×C₄₇	—	2	2	no	—
114	C₄×C₄₇	#385	1	1	yes	characteristic
115	C₄×C₄₇	#428	1	1	yes	characteristic
116	C₄×C₄₇	#450	1	1	yes	characteristic
117	C₄×C₄₇	#483	1	1	yes	characteristic
118	Dic₄₇	—	16	1	no	—
119	Dic₄₇	—	16	1	no	—
120	C₂×#430	—	47	1	no	—
121	C₂×#365	—	47	2	no	—
122	C₂×#349	D₄₇	1	1	yes	characteristic
123	#1809	—	47	1	no	—
124	#1387	—	47	2	no	—
125	C₂×C₄₇	—	2	1	no	—
126	C₂×C₄₇	—	2	1	no	—
127	C₂×C₄₇	—	4	2	no	—
128	C₂×C₄₇	#1853	1	1	yes	characteristic
129	C₂×C₄₇	#2238	1	1	yes	characteristic
130	C₂×C₄₇	#2239	1	1	yes	characteristic
131	C₂²×M₁₆	—	94	1	no	—
132	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
133	C₂×M₃₂	C₂×D₄₇	1	2	yes	—
134	#430	—	94	4	no	—
135	C₂×#108	—	47	2	no	—
136	C₂×#108	—	94	1	no	—
137	C₂×#107	—	47	1	no	—
138	C₂×#106	—	47	1	no	—
139	#380	—	94	1	no	—
140	#365	—	94	4	no	—
141	#349	Dic₄₇	1	4	yes	complemented
142	#340	—	94	1	no	—
143	C₄₇	#12931	1	1	yes	characteristic, complemented, Sylow
144	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
145	C₂×M₁₆	—	2	2	no	—
146	C₂×M₁₆	—	2	2	no	—
147	C₂×M₁₆	—	94	4	no	—
148	C₂×M₁₆	—	94	2	no	—
149	C₂×M₁₆	—	188	1	no	—
150	C₂×M₁₆	—	188	2	no	—
151	C₂×M₁₆	Dic₉₄	1	2	yes	—
152	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	—
153	C₂²×C₈	—	188	1	no	—
154	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
155	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
156	C₂×C₄⋊C₄	—	94	1	no	—
157	C₂×C₄⋊C₄	—	94	1	no	—
158	C₂×C₂²⋊C₄	—	188	1	no	—
159	M₃₂	—	2	2	no	—
160	M₃₂	C₂×Dic₄₇	1	4	yes	—
161	C₂×C₁₆	—	2	2	no	—
162	#108	—	47	4	no	—
163	#108	—	94	4	no	—
164	#108	—	94	2	no	—
165	#107	—	94	2	no	—
166	#106	—	94	2	no	—
167	#95	—	188	1	no	—
168	C₂⁴	#10625325	1	1	yes	characteristic
169	C₂²×C₄	—	2	1	no	—
170	C₂²×C₄	—	2	1	no	—
171	C₂²×C₄	—	2	1	no	—
172	C₂²×C₄	—	2	1	no	—
173	C₂²×C₄	—	188	1	no	—
174	C₂²×C₄	—	188	1	no	—
175	C₂²×C₄	#10625325	1	1	yes	characteristic
176	C₂²×C₄	#10625325	1	2	yes	—
177	C₂²×C₄	C₄⋊Dic₄₇	1	2	yes	—
178	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
179	M₁₆	—	2	4	no	—
180	M₁₆	—	2	4	no	—
181	M₁₆	—	94	4	no	—
182	M₁₆	—	188	4	no	—
183	M₁₆	—	188	2	no	—
184	C₂×C₈	—	2	1	no	—
185	C₂×C₈	—	2	1	no	—
186	C₂×C₈	—	188	4	no	—
187	C₂×C₈	—	188	2	no	—
188	C₂×C₈	C₄⋊Dic₄₇	1	2	yes	—
189	C₂×C₈	C₂×Dic₉₄	1	1	yes	characteristic
190	C₂×C₈	D₄×D₄₇	1	2	yes	—
191	C₂×C₈	#10625352	1	2	yes	—
192	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
193	C₄⋊C₄	—	188	1	no	—
194	C₄⋊C₄	—	188	1	no	—
195	C₄⋊C₄	—	188	1	no	—
196	C₄⋊C₄	—	188	1	no	—
197	C₂²⋊C₄	—	376	2	no	—
198	C₁₆	—	2	4	no	—
199	C₂³	—	2	1	no	—
200	C₂³	—	2	1	no	—
201	C₂³	—	4	1	no	—
202	C₂³	—	4	1	no	—
203	C₂³	#13093956	1	2	yes	—
204	C₂³	C₂×#10625325	1	1	yes	characteristic
205	C₂×C₄	—	2	1	no	—
206	C₂×C₄	—	2	1	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	376	1	no	—
212	C₂×C₄	—	376	1	no	—
213	C₂×C₄	—	376	1	no	—
214	C₂×C₄	—	376	1	no	—
215	C₂×C₄	—	376	1	no	—
216	C₂×C₄	—	376	1	no	—
217	C₂×C₄	#13093956	1	2	yes	—
218	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
219	C₂×C₄	#13093994	1	1	yes	characteristic
220	C₂×C₄	#13094008	1	1	yes	characteristic
221	C₂×C₄	C₂×#10625325	1	1	yes	characteristic
222	C₂×C₄	#13094052	1	1	yes	characteristic
223	C₂×C₄	#13094057	1	1	yes	characteristic
224	C₈	—	2	2	no	—
225	C₈	—	188	4	no	—
226	C₈	D₄×Dic₄₇	1	2	yes	—
227	C₈	#13094001	1	2	yes	—
228	C₂²	—	2	1	no	—
229	C₂²	—	2	1	no	—
230	C₂²	—	2	2	no	—
231	C₂²	—	4	2	no	—
232	C₂²	—	4	1	no	—
233	C₂²	—	4	1	no	—
234	C₂²	—	8	1	no	—
235	C₂²	C₂×#13093956	1	1	yes	characteristic
236	C₂²	#15689264	1	1	yes	characteristic
237	C₂²	#15689442	1	1	yes	characteristic
238	C₄	—	2	2	no	—
239	C₄	—	752	1	no	—
240	C₄	—	752	1	no	—
241	C₄	#15688998	1	1	yes	characteristic
242	C₄	#15689165	1	1	yes	characteristic
243	C₄	#15689276	1	1	yes	characteristic
244	C₄	#15689454	1	1	yes	characteristic
245	C₂	—	2	1	no	—
246	C₂	—	2	1	no	—
247	C₂	—	4	2	no	—
248	C₂	#20243583	1	1	yes	characteristic
249	C₂	#20245603	1	1	yes	characteristic
250	C₂	#20245608	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#15689172

C₂

yes

maximal, characteristic

C₂×#15688946

C₂

yes

maximal, complemented

#20243421

C₂

yes

maximal, characteristic

#20241497

C₂

yes

maximal, complemented

C₂×C₄₇×#349

C₂

yes

maximal, characteristic

—

—

—

C₂²

yes

—

C₂×#13093958

C₂²

yes

characteristic

C₂×#13093956

C₂²

yes

—

—

—

C₂²×M₁₆×C₄₇

C₂²

yes

characteristic

C₂×M₃₂×C₄₇

C₂²

yes

—

C₄₇×#349

C₄

yes

—

—

—

—

C₂²×C₄₇⋊C₈

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×C₂²⋊Dic₄₇

—

#13093960

—

#13093960

—

#13093960

D₄

yes

—

#13093958

—

#13093956

—

C₄₇⋊#95

—

C₂³×C₄×C₄₇

D₄

yes

characteristic

C₂×M₁₆×C₄₇

—

C₂×M₁₆×C₄₇

—

C₂×M₁₆×C₄₇

C₂×C₄

yes

—

C₂×M₁₆×C₄₇

Q₈

yes

—

C₂²×C₈×C₄₇

D₄

yes

characteristic

C₂²×C₈×C₄₇

C₂³

yes

characteristic

M₃₂×C₄₇

—

M₃₂×C₄₇

C₂×C₄

yes

—

C₂×C₁₆×C₄₇

—

C₂⁴×C₄₇

SD₁₆

yes

characteristic

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₄⋊C₄

yes

—

C₂²×C₄×C₄₇

SD₁₆

yes

characteristic

C₂²×C₄×C₄₇

SD₁₆

yes

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₄⋊C₄

yes

—

C₂×C₈×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂×D₄

yes

—

C₂×C₈×C₄₇

C₂×Q₈

yes

characteristic

C₂×C₈×C₄₇

#41

yes

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

#10625329

—

#10625329

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₁₆×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

#106

yes

—

C₂³×C₄₇

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

#106

yes

—

C₂×C₄×C₄₇

C₂×C₄⋊C₄

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

C₂×SD₁₆

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₈×C₄₇

—

C₈×C₄₇

C₄×D₄

yes

—

100

C₈×C₄₇

C₂²⋊Q₈

yes

—

101

C₄₇⋊C₈

—

102

#12931

—

maximal, Sylow

103

C₂²×C₄₇

—

104

C₂²×C₄₇

—

105

C₂²×C₄₇

—

106

C₂²×C₄₇

—

107

C₂²×C₄₇

—

108

C₂²×C₄₇

—

109

C₂²×C₄₇

—

110

C₂²×C₄₇

C₂×#106

yes

characteristic

111

C₂²×C₄₇

#448

yes

characteristic

112

C₂²×C₄₇

#481

yes

characteristic

113

C₄×C₄₇

—

114

C₄×C₄₇

#385

yes

characteristic

115

C₄×C₄₇

#428

yes

characteristic

116

C₄×C₄₇

#450

yes

characteristic

117

C₄×C₄₇

#483

yes

characteristic

118

Dic₄₇

—

119

Dic₄₇

—

120

C₂×#430

—

121

C₂×#365

—

122

C₂×#349

D₄₇

yes

characteristic

123

#1809

—

124

#1387

—

125

C₂×C₄₇

—

126

C₂×C₄₇

—

127

C₂×C₄₇

—

128

C₂×C₄₇

#1853

yes

characteristic

129

C₂×C₄₇

#2238

yes

characteristic

130

C₂×C₄₇

#2239

yes

characteristic

131

C₂²×M₁₆

—

132

C₂²×M₁₆

C₂×D₄₇

yes

characteristic

133

C₂×M₃₂

C₂×D₄₇

yes

—

134

#430

—

135

C₂×#108

—

136

C₂×#108

—

137

C₂×#107

—

138

C₂×#106

—

139

#380

—

140

#365

—

141

#349

Dic₄₇

yes

complemented

142

#340

—

143

C₄₇

#12931

yes

characteristic, complemented, Sylow

144

C₂³×C₄

D₁₈₈

yes

characteristic

145

C₂×M₁₆

—

146

C₂×M₁₆

—

147

C₂×M₁₆

—

148

C₂×M₁₆

—

149

C₂×M₁₆

—

188

—

150

C₂×M₁₆

—

188

—

151

C₂×M₁₆

Dic₉₄

yes

—

152

C₂×M₁₆

C₂×Dic₄₇

yes

—

153

C₂²×C₈

—

188

—

154

C₂²×C₈

D₁₈₈

yes

characteristic

155

C₂²×C₈

C₂²×D₄₇

yes

characteristic

156

C₂×C₄⋊C₄

—

157

C₂×C₄⋊C₄

—

158

C₂×C₂²⋊C₄

—

188

—

159

M₃₂

—

160

M₃₂

C₂×Dic₄₇

yes

—

161

C₂×C₁₆

—

162

#108

—

163

#108

—

164

#108

—

165

#107

—

166

#106

—

167

#95

—

188

—

168

C₂⁴

#10625325

yes

characteristic

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

—

172

C₂²×C₄

—

173

C₂²×C₄

—

188

—

174

C₂²×C₄

—

188

—

175

C₂²×C₄

#10625325

yes

characteristic

176

C₂²×C₄

#10625325

yes

—

177

C₂²×C₄

C₄⋊Dic₄₇

yes

—

178

C₂²×C₄

C₂×D₁₈₈

yes

characteristic

179

M₁₆

—

180

M₁₆

—

181

M₁₆

—

182

M₁₆

—

188

—

183

M₁₆

—

188

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

188

—

187

C₂×C₈

—

188

—

188

C₂×C₈

C₄⋊Dic₄₇

yes

—

189

C₂×C₈

C₂×Dic₉₄

yes

characteristic

190

C₂×C₈

D₄×D₄₇

yes

—

191

C₂×C₈

#10625352

yes

—

192

C₂×C₈

C₂²×Dic₄₇

yes

characteristic

193

C₄⋊C₄

—

188

—

194

C₄⋊C₄

—

188

—

195

C₄⋊C₄

—

188

—

196

C₄⋊C₄

—

188

—

197

C₂²⋊C₄

—

376

—

198

C₁₆

—

199

C₂³

—

200

C₂³

—

201

C₂³

—

202

C₂³

—

203

C₂³

#13093956

yes

—

204

C₂³

C₂×#10625325

yes

characteristic

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

376

—

212

C₂×C₄

—

376

—

213

C₂×C₄

—

376

—

214

C₂×C₄

—

376

—

215

C₂×C₄

—

376

—

216

C₂×C₄

—

376

—

217

C₂×C₄

#13093956

yes

—

218

C₂×C₄

C₂×C₄⋊Dic₄₇

yes

characteristic

219

C₂×C₄

#13093994

yes

characteristic

220

C₂×C₄

#13094008

yes

characteristic

221

C₂×C₄

C₂×#10625325

yes

characteristic

222

C₂×C₄

#13094052

yes

characteristic

223

C₂×C₄

#13094057

yes

characteristic

224

C₈

—

225

C₈

—

188

—

226

C₈

D₄×Dic₄₇

yes

—

227

C₈

#13094001

yes

—

228

C₂²

—

229

C₂²

—

230

C₂²

—

231

C₂²

—

232

C₂²

—

233

C₂²

—

234

C₂²

—

235

C₂²

C₂×#13093956

yes

characteristic

236

C₂²

#15689264

yes

characteristic

237

C₂²

#15689442

yes

characteristic

238

C₄

—

239

C₄

—

752

—

240

C₄

—

752

—

241

C₄

#15688998

yes

characteristic

242

C₄

#15689165

yes

characteristic

243

C₄

#15689276

yes

characteristic

244

C₄

#15689454

yes

characteristic

245

C₂

—

246

C₂

—

247

C₂

—

248

C₂

#20243583

yes

characteristic

249

C₂

#20245603

yes

characteristic

250

C₂

#20245608

yes

characteristic

	subgroup	G/H
center	C₂²	#15689442
commutator	C₂×C₈×C₄₇	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₇
Fitting	C₂×C₄₇×#349	C₂
socle	C₂²×C₄₇	#481
prime radical	C₂⁴×C₄₇	SD₁₆
cosocle	C₂²×C₈×C₄₇	C₂³
hypercenter	C₂×#349	D₄₇
hypocenter	C₄₇	#12931
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×M₁₆ ◁ C₂×#349

subgroup

G/H

center

C₂²

#15689442

commutator

C₂×C₈×C₄₇

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₇

Fitting

C₂×C₄₇×#349

C₂

socle

C₂²×C₄₇

#481

prime radical

C₂⁴×C₄₇

SD₁₆

cosocle

C₂²×C₈×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×M₁₆ ◁ C₂×#349

N	H ≅ G/N	type
2. C₂×#15688946	C₂	semidirect
4. #20241497	C₂	semidirect
17. C₄₇×#349	C₄	semidirect
141. #349	Dic₄₇	semidirect
143. C₄₇	#12931	semidirect

H ≅ G/N

type

2. C₂×#15688946

C₂

semidirect

4. #20241497

C₂

semidirect

17. C₄₇×#349

C₄

semidirect

141. #349

Dic₄₇

semidirect

143. C₄₇

#12931

semidirect

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

subgroup	index
C₂×#15689172	2
C₂×#15688946	2
#20243421	2
#20241497	2
C₂×C₄₇×#349	2
#12931	47

subgroup

index

C₂×C₄₇×#349

Subgroups — #26132847

Conjugacy classes of subgroups

Complements

Maximal subgroups