Group #26134772 — subgroups

Subgroups — #26134772

Order 12032.

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

normal subgroups only

This group has 482 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	#20245144	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15688939	C₂	1	2	yes	maximal, complemented
3	C₂×#15688936	C₂	1	2	yes	maximal
4	C₄×#13093960	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₇×#495	C₂	1	1	yes	maximal, characteristic
6	C₂×#13093964	C₂²	1	2	yes	—
7	C₂×#13093960	C₂²	1	2	yes	—
8	C₄×#10625329	—	2	1	no	—
9	C₄⋊(C₄₇⋊C₁₆)	—	2	2	no	—
10	#15688939	—	2	4	no	—
11	#15688936	—	2	4	no	—
12	#15688888	—	2	1	no	—
13	C₂²×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₄₇	—	2	1	no	—
15	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×#124×C₄₇	—	2	1	no	—
17	C₄₇×#495	—	2	2	no	—
18	C₄₇×#495	C₄	1	4	yes	—
19	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
20	C₂×#10625329	—	2	2	no	—
21	#13093964	—	2	2	no	—
22	#13093964	—	2	2	no	—
23	C₂×C₄₇⋊C₁₆	—	2	2	no	—
24	#13093960	—	2	2	no	—
25	#13093960	D₄	1	4	yes	—
26	#13093935	—	4	1	no	—
27	C₄×C₄₇⋊C₈	—	4	1	no	—
28	C₂²×Q₈×C₄₇	—	2	1	no	—
29	C₂²×D₄×C₄₇	—	2	1	no	—
30	C₂×Q₁₆×C₄₇	—	2	2	no	—
31	C₂×Q₁₆×C₄₇	—	2	1	no	—
32	C₂×Q₁₆×C₄₇	—	2	2	no	—
33	C₂×Q₁₆×C₄₇	C₂×C₄	1	2	yes	—
34	C₂×SD₁₆×C₄₇	—	2	4	no	—
35	C₂×SD₁₆×C₄₇	—	4	4	no	—
36	C₂×D₈×C₄₇	—	2	2	no	—
37	C₂×D₈×C₄₇	—	2	1	no	—
38	C₂×D₈×C₄₇	—	2	2	no	—
39	C₂×D₈×C₄₇	C₂×C₄	1	2	yes	—
40	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
42	#124×C₄₇	—	2	4	no	—
43	#124×C₄₇	—	4	1	no	—
44	#124×C₄₇	—	4	1	no	—
45	C₂×C₂²⋊C₄×C₄₇	—	4	2	no	—
46	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
47	C₄×C₈×C₄₇	C₂×C₄	1	2	yes	—
48	C₄×C₈×C₄₇	D₄	1	2	yes	—
49	C₂⁴×C₄₇	—	4	1	no	—
50	C₂×Q₈×C₄₇	—	2	2	no	—
51	C₂×Q₈×C₄₇	—	4	1	no	—
52	C₂×Q₈×C₄₇	—	4	2	no	—
53	C₂×Q₈×C₄₇	—	4	2	no	—
54	C₂×D₄×C₄₇	—	2	2	no	—
55	C₂×D₄×C₄₇	—	4	2	no	—
56	C₂×D₄×C₄₇	—	4	1	no	—
57	C₂×D₄×C₄₇	—	4	2	no	—
58	C₂²×C₄×C₄₇	—	4	1	no	—
59	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
60	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
61	Q₁₆×C₄₇	—	2	4	no	—
62	Q₁₆×C₄₇	—	4	1	no	—
63	Q₁₆×C₄₇	—	4	1	no	—
64	SD₁₆×C₄₇	—	4	8	no	—
65	D₈×C₄₇	—	2	4	no	—
66	D₈×C₄₇	—	4	1	no	—
67	D₈×C₄₇	—	4	1	no	—
68	C₂×C₈×C₄₇	—	2	2	no	—
69	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
70	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
71	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
72	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
73	C₂×C₈×C₄₇	#41	1	2	yes	—
74	C₂²⋊C₄×C₄₇	—	4	4	no	—
75	C₂²⋊C₄×C₄₇	—	4	4	no	—
76	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
77	C₄²×C₄₇	D₈	1	1	yes	characteristic
78	C₄²×C₄₇	D₈	1	1	yes	characteristic
79	#10625329	—	2	4	no	—
80	#10625329	—	4	2	no	—
81	C₂×C₄₇⋊C₈	—	4	2	no	—
82	C₄₇⋊C₁₆	—	4	2	no	—
83	C₂³×C₄₇	—	4	2	no	—
84	C₂³×C₄₇	—	8	4	no	—
85	C₂³×C₄₇	—	8	2	no	—
86	C₂³×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
87	Q₈×C₄₇	—	4	2	no	—
88	Q₈×C₄₇	—	4	2	no	—
89	Q₈×C₄₇	—	8	2	no	—
90	D₄×C₄₇	—	4	2	no	—
91	D₄×C₄₇	—	4	2	no	—
92	D₄×C₄₇	—	8	2	no	—
93	C₂×C₄×C₄₇	—	4	2	no	—
94	C₂×C₄×C₄₇	—	4	2	no	—
95	C₂×C₄×C₄₇	—	8	2	no	—
96	C₂×C₄×C₄₇	#102	1	2	yes	—
97	C₂×C₄×C₄₇	#102	1	2	yes	—
98	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₄×C₄₇	#121	1	2	yes	—
100	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
101	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
102	C₈×C₄₇	—	2	2	no	—
103	C₈×C₄₇	C₄×D₄	1	2	yes	—
104	C₈×C₄₇	#124	1	1	yes	characteristic
105	C₈×C₄₇	#127	1	1	yes	characteristic
106	C₄₇⋊C₈	—	4	4	no	—
107	#13258	—	47	1	no	maximal, Sylow
108	C₂²×C₄₇	—	2	2	no	—
109	C₂²×C₄₇	—	8	4	no	—
110	C₂²×C₄₇	—	8	2	no	—
111	C₂²×C₄₇	—	16	4	no	—
112	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
113	C₂²×C₄₇	#460	1	2	yes	—
114	C₄×C₄₇	—	2	2	no	—
115	C₄×C₄₇	—	2	2	no	—
116	C₄×C₄₇	—	8	2	no	—
117	C₄×C₄₇	#390	1	1	yes	characteristic
118	C₄×C₄₇	#418	1	1	yes	characteristic
119	C₄×C₄₇	#459	1	2	yes	—
120	C₂×#495	D₄₇	1	1	yes	characteristic
121	#2150	—	47	1	no	—
122	C₂×#362	—	47	2	no	—
123	C₂×#361	—	47	2	no	—
124	C₄×#108	—	47	1	no	—
125	C₂×C₄₇	—	2	2	no	—
126	C₂×C₄₇	—	16	2	no	—
127	C₂×C₄₇	#1982	1	1	yes	characteristic
128	C₂×C₄₇	#2148	1	2	yes	—
129	C₂²×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
130	C₂²×SD₁₆	—	2	1	no	—
131	C₂²×D₈	C₂×D₄₇	1	1	yes	characteristic
132	C₂×#124	—	2	1	no	—
133	C₂×M₃₂	—	47	2	no	—
134	#495	—	2	2	no	—
135	#495	Dic₄₇	1	4	yes	—
136	C₂×#108	—	47	2	no	—
137	C₄×M₁₆	—	94	1	no	—
138	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
139	C₄⋊C₁₆	—	94	2	no	—
140	#362	—	94	4	no	—
141	#361	—	94	4	no	—
142	#341	—	94	1	no	—
143	C₄₇	#13258	1	1	yes	characteristic, complemented, Sylow
144	C₂²×Q₈	—	2	1	no	—
145	C₂²×D₄	—	2	1	no	—
146	C₂×Q₁₆	—	2	2	no	—
147	C₂×Q₁₆	—	2	2	no	—
148	C₂×Q₁₆	—	2	1	no	—
149	C₂×Q₁₆	C₂×Dic₄₇	1	2	yes	—
150	C₂×SD₁₆	—	2	4	no	—
151	C₂×SD₁₆	—	4	4	no	—
152	C₂×D₈	—	2	2	no	—
153	C₂×D₈	—	2	2	no	—
154	C₂×D₈	—	2	1	no	—
155	C₂×D₈	C₂×Dic₄₇	1	2	yes	—
156	C₂×M₁₆	—	94	2	no	—
157	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
158	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
159	#124	—	2	4	no	—
160	#124	—	4	1	no	—
161	#124	—	4	1	no	—
162	C₂×C₂²⋊C₄	—	4	2	no	—
163	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
164	M₃₂	—	94	2	no	—
165	M₃₂	—	94	2	no	—
166	C₂×C₁₆	—	94	2	no	—
167	#108	—	47	4	no	—
168	#108	—	94	2	no	—
169	#97	—	188	1	no	—
170	C₄×C₈	—	188	1	no	—
171	C₄×C₈	C₂×Dic₄₇	1	2	yes	—
172	C₄×C₈	C₂²⋊D₄₇	1	2	yes	—
173	C₂⁴	—	4	1	no	—
174	C₂×Q₈	—	2	2	no	—
175	C₂×Q₈	—	4	1	no	—
176	C₂×Q₈	—	4	2	no	—
177	C₂×Q₈	—	4	2	no	—
178	C₂×D₄	—	2	2	no	—
179	C₂×D₄	—	4	2	no	—
180	C₂×D₄	—	4	1	no	—
181	C₂×D₄	—	4	2	no	—
182	C₂²×C₄	—	4	1	no	—
183	C₂²×C₄	#10625335	1	2	yes	—
184	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
185	Q₁₆	—	2	4	no	—
186	Q₁₆	—	4	1	no	—
187	Q₁₆	—	4	1	no	—
188	SD₁₆	—	4	8	no	—
189	D₈	—	2	4	no	—
190	D₈	—	4	1	no	—
191	D₈	—	4	1	no	—
192	M₁₆	—	94	4	no	—
193	M₁₆	—	188	2	no	—
194	C₂×C₈	—	2	2	no	—
195	C₂×C₈	—	188	2	no	—
196	C₂×C₈	C₂²⋊Dic₄₇	1	2	yes	—
197	C₂×C₈	D₄×D₄₇	1	2	yes	—
198	C₂×C₈	#10625352	1	2	yes	—
199	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
200	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
201	C₂²⋊C₄	—	4	4	no	—
202	C₂²⋊C₄	—	4	4	no	—
203	C₄²	#10625334	1	1	yes	characteristic
204	C₄²	#10625334	1	1	yes	characteristic
205	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
206	C₁₆	—	188	2	no	—
207	C₂³	—	4	2	no	—
208	C₂³	—	8	4	no	—
209	C₂³	—	8	2	no	—
210	C₂³	C₂×#10625335	1	1	yes	characteristic
211	Q₈	—	4	2	no	—
212	Q₈	—	4	2	no	—
213	Q₈	—	8	2	no	—
214	D₄	—	4	2	no	—
215	D₄	—	4	2	no	—
216	D₄	—	8	2	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	4	2	no	—
219	C₂×C₄	—	8	2	no	—
220	C₂×C₄	#13093945	1	2	yes	—
221	C₂×C₄	#13093945	1	2	yes	—
222	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
223	C₂×C₄	#13093995	1	2	yes	—
224	C₂×C₄	C₂×#10625334	1	1	yes	characteristic
225	C₂×C₄	#13094050	1	2	yes	—
226	C₈	—	2	2	no	—
227	C₈	—	188	4	no	—
228	C₈	D₄×Dic₄₇	1	2	yes	—
229	C₈	#13094011	1	1	yes	characteristic
230	C₈	#13094020	1	1	yes	characteristic
231	C₂²	—	2	2	no	—
232	C₂²	—	8	2	no	—
233	C₂²	—	8	4	no	—
234	C₂²	—	16	4	no	—
235	C₂²	C₂×#13093945	1	1	yes	characteristic
236	C₂²	#15689320	1	2	yes	—
237	C₄	—	2	2	no	—
238	C₄	—	2	2	no	—
239	C₄	—	8	2	no	—
240	C₄	#15689026	1	1	yes	characteristic
241	C₄	#15689128	1	1	yes	characteristic
242	C₄	#15689315	1	2	yes	—
243	C₂	—	2	2	no	—
244	C₂	—	16	2	no	—
245	C₂	#20244316	1	1	yes	characteristic
246	C₂	#20245137	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#20245144

C₂

yes

maximal, characteristic, complemented

C₂×#15688939

C₂

yes

maximal, complemented

C₂×#15688936

C₂

yes

maximal

C₄×#13093960

C₂

yes

maximal, characteristic, complemented

C₂×C₄₇×#495

C₂

yes

maximal, characteristic

C₂×#13093964

C₂²

yes

—

C₂×#13093960

C₂²

yes

—

C₄×#10625329

—

C₄⋊(C₄₇⋊C₁₆)

—

#15688939

—

#15688936

—

#15688888

—

C₂²×Q₁₆×C₄₇

C₂²

yes

characteristic

C₂²×SD₁₆×C₄₇

—

C₂²×D₈×C₄₇

C₂²

yes

characteristic

C₂×#124×C₄₇

—

C₄₇×#495

—

C₄₇×#495

C₄

yes

—

C₂×C₄×C₈×C₄₇

C₂²

yes

—

—

—

C₂×C₄₇⋊C₁₆

—

#13093960

—

#13093960

D₄

yes

—

#13093935

—

C₄×C₄₇⋊C₈

—

C₂²×Q₈×C₄₇

—

C₂²×D₄×C₄₇

—

C₂×Q₁₆×C₄₇

—

C₂×Q₁₆×C₄₇

—

C₂×Q₁₆×C₄₇

—

C₂×Q₁₆×C₄₇

C₂×C₄

yes

—

C₂×SD₁₆×C₄₇

—

C₂×SD₁₆×C₄₇

—

C₂×D₈×C₄₇

—

C₂×D₈×C₄₇

—

C₂×D₈×C₄₇

—

C₂×D₈×C₄₇

C₂×C₄

yes

—

C₂²×C₈×C₄₇

D₄

yes

characteristic

C₂²×C₈×C₄₇

C₂³

yes

characteristic

#124×C₄₇

—

#124×C₄₇

—

#124×C₄₇

—

C₂×C₂²⋊C₄×C₄₇

—

C₂×C₄²×C₄₇

D₄

yes

characteristic

C₄×C₈×C₄₇

C₂×C₄

yes

—

C₄×C₈×C₄₇

D₄

yes

—

C₂⁴×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

SD₁₆

yes

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

Q₁₆×C₄₇

—

Q₁₆×C₄₇

—

Q₁₆×C₄₇

—

SD₁₆×C₄₇

—

D₈×C₄₇

—

D₈×C₄₇

—

D₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂²⋊C₄

yes

—

C₂×C₈×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂×D₄

yes

—

C₂×C₈×C₄₇

C₂×D₄

yes

characteristic

C₂×C₈×C₄₇

#41

yes

—

C₂²⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

C₂²⋊C₄

yes

—

C₄²×C₄₇

D₈

yes

characteristic

C₄²×C₄₇

D₈

yes

characteristic

#10625329

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂×SD₁₆

yes

characteristic

Q₈×C₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

#102

yes

—

C₂×C₄×C₄₇

#102

yes

—

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

#121

yes

—

100

C₂×C₄×C₄₇

C₂×D₈

yes

characteristic

101

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

—

102

C₈×C₄₇

—

103

C₈×C₄₇

C₄×D₄

yes

—

104

C₈×C₄₇

#124

yes

characteristic

105

C₈×C₄₇

#127

yes

characteristic

106

C₄₇⋊C₈

—

107

#13258

—

maximal, Sylow

108

C₂²×C₄₇

—

109

C₂²×C₄₇

—

110

C₂²×C₄₇

—

111

C₂²×C₄₇

—

112

C₂²×C₄₇

C₂×#102

yes

characteristic

113

C₂²×C₄₇

#460

yes

—

114

C₄×C₄₇

—

115

C₄×C₄₇

—

116

C₄×C₄₇

—

117

C₄×C₄₇

#390

yes

characteristic

118

C₄×C₄₇

#418

yes

characteristic

119

C₄×C₄₇

#459

yes

—

120

C₂×#495

D₄₇

yes

characteristic

121

#2150

—

122

C₂×#362

—

123

C₂×#361

—

124

C₄×#108

—

125

C₂×C₄₇

—

126

C₂×C₄₇

—

127

C₂×C₄₇

#1982

yes

characteristic

128

C₂×C₄₇

#2148

yes

—

129

C₂²×Q₁₆

C₂×D₄₇

yes

characteristic

130

C₂²×SD₁₆

—

131

C₂²×D₈

C₂×D₄₇

yes

characteristic

132

C₂×#124

—

133

C₂×M₃₂

—

134

#495

—

135

#495

Dic₄₇

yes

—

136

C₂×#108

—

137

C₄×M₁₆

—

138

C₂×C₄×C₈

C₂×D₄₇

yes

characteristic

139

C₄⋊C₁₆

—

140

#362

—

141

#361

—

142

#341

—

143

C₄₇

#13258

yes

characteristic, complemented, Sylow

144

C₂²×Q₈

—

145

C₂²×D₄

—

146

C₂×Q₁₆

—

147

C₂×Q₁₆

—

148

C₂×Q₁₆

—

149

C₂×Q₁₆

C₂×Dic₄₇

yes

—

150

C₂×SD₁₆

—

151

C₂×SD₁₆

—

152

C₂×D₈

—

153

C₂×D₈

—

154

C₂×D₈

—

155

C₂×D₈

C₂×Dic₄₇

yes

—

156

C₂×M₁₆

—

157

C₂²×C₈

C₂²⋊D₄₇

yes

characteristic

158

C₂²×C₈

C₂²×D₄₇

yes

characteristic

159

#124

—

160

#124

—

161

#124

—

162

C₂×C₂²⋊C₄

—

163

C₂×C₄²

C₂²⋊D₄₇

yes

characteristic

164

M₃₂

—

165

M₃₂

—

166

C₂×C₁₆

—

167

#108

—

168

#108

—

169

#97

—

188

—

170

C₄×C₈

—

188

—

171

C₄×C₈

C₂×Dic₄₇

yes

—

172

C₄×C₈

C₂²⋊D₄₇

yes

—

173

C₂⁴

—

174

C₂×Q₈

—

175

C₂×Q₈

—

176

C₂×Q₈

—

177

C₂×Q₈

—

178

C₂×D₄

—

179

C₂×D₄

—

180

C₂×D₄

—

181

C₂×D₄

—

182

C₂²×C₄

—

183

C₂²×C₄

#10625335

yes

—

184

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

185

Q₁₆

—

186

Q₁₆

—

187

Q₁₆

—

188

SD₁₆

—

189

D₈

—

190

D₈

—

191

D₈

—

192

M₁₆

—

193

M₁₆

—

188

—

194

C₂×C₈

—

195

C₂×C₈

—

188

—

196

C₂×C₈

C₂²⋊Dic₄₇

yes

—

197

C₂×C₈

D₄×D₄₇

yes

—

198

C₂×C₈

#10625352

yes

—

199

C₂×C₈

C₂²×Dic₄₇

yes

characteristic

200

C₂×C₈

C₂×C₂²⋊D₄₇

yes

characteristic

201

C₂²⋊C₄

—

202

C₂²⋊C₄

—

203

C₄²

#10625334

yes

characteristic

204

C₄²

#10625334

yes

characteristic

205

C₄²

C₂²⋊Dic₄₇

yes

—

206

C₁₆

—

188

—

207

C₂³

—

208

C₂³

—

209

C₂³

—

210

C₂³

C₂×#10625335

yes

characteristic

211

Q₈

—

212

Q₈

—

213

Q₈

—

214

D₄

—

215

D₄

—

216

D₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

#13093945

yes

—

221

C₂×C₄

#13093945

yes

—

222

C₂×C₄

C₂×C₂²⋊Dic₄₇

yes

characteristic

223

C₂×C₄

#13093995

yes

—

224

C₂×C₄

C₂×#10625334

yes

characteristic

225

C₂×C₄

#13094050

yes

—

226

C₈

—

227

C₈

—

188

—

228

C₈

D₄×Dic₄₇

yes

—

229

C₈

#13094011

yes

characteristic

230

C₈

#13094020

yes

characteristic

231

C₂²

—

232

C₂²

—

233

C₂²

—

234

C₂²

—

235

C₂²

C₂×#13093945

yes

characteristic

236

C₂²

#15689320

yes

—

237

C₄

—

238

C₄

—

239

C₄

—

240

C₄

#15689026

yes

characteristic

241

C₄

#15689128

yes

characteristic

242

C₄

#15689315

yes

—

243

C₂

—

244

C₂

—

245

C₂

#20244316

yes

characteristic

246

C₂

#20245137

yes

—

	subgroup	G/H
center	C₂²	C₂×#13093945
commutator	C₂×C₈×C₄₇	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₇
Fitting	C₂×C₄₇×#495	C₂
socle	C₂²×C₄₇	C₂×#102
prime radical	C₂²×D₈×C₄₇	C₂²
cosocle	C₂²×C₈×C₄₇	C₂³
hypercenter	C₂×#495	D₄₇
hypocenter	C₄₇	#13258
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#495

subgroup

G/H

center

C₂²

C₂×#13093945

commutator

C₂×C₈×C₄₇

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₇

Fitting

C₂×C₄₇×#495

C₂

socle

C₂²×C₄₇

C₂×#102

prime radical

C₂²×D₈×C₄₇

C₂²

cosocle

C₂²×C₈×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#495

N	H ≅ G/N	type
1. #20245144	C₂	semidirect
2. C₂×#15688939	C₂	semidirect
4. C₄×#13093960	C₂	semidirect
143. C₄₇	#13258	semidirect

H ≅ G/N

type

1. #20245144

C₂

semidirect

2. C₂×#15688939

C₂

semidirect

4. C₄×#13093960

C₂

semidirect

143. C₄₇

#13258

semidirect

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

subgroup	index
#20245144	2
C₂×#15688939	2
C₂×#15688936	2
C₄×#13093960	2
C₂×C₄₇×#495	2
#13258	47

subgroup

index

C₂×C₄₇×#495

Subgroups — #26134772

Conjugacy classes of subgroups

Complements

Maximal subgroups