Group #26111238 — subgroups

Subgroups — #26111238

Order 12032.

502 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 103 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	#20252459	C₂	1	1	yes	maximal, characteristic, complemented
2	#20242050	C₂	1	1	yes	maximal, characteristic, complemented
3	#20241857	C₂	1	2	yes	maximal, complemented
4	#20241287	C₂	1	2	yes	maximal, complemented
5	C₄₇×#3150	C₂	1	1	yes	maximal, characteristic
6	#15689195	—	2	4	no	—
7	#15689180	C₂²	1	2	yes	—
8	#15689176	C₂²	1	2	yes	—
9	#15689090	—	2	2	no	—
10	#15688872	—	2	1	no	—
11	#15688867	—	2	1	no	—
12	D₄⋊(C₄₇⋊C₈)	—	2	4	no	—
13	C₂×#135×C₄₇	—	2	2	no	—
14	C₄₇×#532	C₂²	1	1	yes	characteristic
15	C₄₇×#532	C₂²	1	1	yes	characteristic
16	C₄₇×#497	—	2	1	no	—
17	C₄₇×#497	C₄	1	2	yes	—
18	C₄₇×#496	—	2	1	no	—
19	C₄₇×#496	C₄	1	2	yes	—
20	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×#10625329	—	2	2	no	—
22	C₂²×C₄₇⋊C₈	—	2	2	no	—
23	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
24	C₄⋊(C₄₇⋊C₈)	D₄	1	4	yes	—
25	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
26	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
27	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
28	#13093935	—	2	2	no	—
29	C₄×C₄₇⋊C₈	—	2	2	no	—
30	C₂×#41×C₄₇	—	2	1	no	—
31	C₂×#41×C₄₇	D₄	1	2	yes	—
32	#135×C₄₇	—	4	4	no	—
33	#135×C₄₇	—	4	4	no	—
34	C₂×Q₁₆×C₄₇	—	2	2	no	—
35	C₂×SD₁₆×C₄₇	—	2	2	no	—
36	C₂×SD₁₆×C₄₇	—	2	2	no	—
37	C₂×D₈×C₄₇	—	2	2	no	—
38	C₂²×C₈×C₄₇	—	2	1	no	—
39	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
40	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
41	#127×C₄₇	C₂×C₄	1	1	yes	characteristic
42	#127×C₄₇	D₄	1	1	yes	characteristic
43	#124×C₄₇	—	2	1	no	—
44	#124×C₄₇	C₂×C₄	1	2	yes	—
45	#121×C₄₇	—	2	2	no	—
46	#121×C₄₇	—	2	2	no	—
47	C₄×D₄×C₄₇	—	2	2	no	—
48	C₄×D₄×C₄₇	—	2	2	no	—
49	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
50	#97×C₄₇	—	2	1	no	—
51	#97×C₄₇	C₂×C₄	1	2	yes	—
52	#41×C₄₇	—	4	2	no	—
53	#41×C₄₇	—	4	2	no	—
54	#41×C₄₇	—	4	2	no	—
55	#41×C₄₇	—	4	2	no	—
56	C₂×Q₈×C₄₇	—	2	1	no	—
57	C₂×Q₈×C₄₇	C₂²⋊C₄	1	2	yes	—
58	C₂×D₄×C₄₇	—	2	2	no	—
59	C₂×D₄×C₄₇	—	2	1	no	—
60	C₂×D₄×C₄₇	—	2	2	no	—
61	C₂×D₄×C₄₇	—	2	2	no	—
62	C₂×D₄×C₄₇	—	4	1	no	—
63	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
64	C₂²×C₄×C₄₇	—	2	2	no	—
65	C₂²×C₄×C₄₇	—	4	1	no	—
66	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₄₇	#41	1	2	yes	—
68	Q₁₆×C₄₇	—	4	4	no	—
69	SD₁₆×C₄₇	—	4	4	no	—
70	SD₁₆×C₄₇	—	4	4	no	—
71	D₈×C₄₇	—	4	4	no	—
72	C₂×C₈×C₄₇	—	2	4	no	—
73	C₂×C₈×C₄₇	—	2	2	no	—
74	C₄⋊C₄×C₄₇	—	2	2	no	—
75	C₄⋊C₄×C₄₇	—	2	2	no	—
76	C₂²⋊C₄×C₄₇	—	2	4	no	—
77	C₂²⋊C₄×C₄₇	—	4	2	no	—
78	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
79	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
80	C₄²×C₄₇	C₂×D₄	1	2	yes	—
81	#10625329	—	8	2	no	—
82	C₂×C₄₇⋊C₈	—	2	4	no	—
83	C₂×C₄₇⋊C₈	—	4	2	no	—
84	C₂×C₄₇⋊C₈	—	8	2	no	—
85	C₂³×C₄₇	—	2	2	no	—
86	C₂³×C₄₇	—	4	1	no	—
87	C₂³×C₄₇	#123	1	1	yes	characteristic
88	Q₈×C₄₇	—	4	2	no	—
89	Q₈×C₄₇	—	4	2	no	—
90	D₄×C₄₇	—	4	2	no	—
91	D₄×C₄₇	—	4	2	no	—
92	D₄×C₄₇	—	4	4	no	—
93	D₄×C₄₇	—	8	2	no	—
94	D₄×C₄₇	—	8	2	no	—
95	D₄×C₄₇	—	8	1	no	—
96	D₄×C₄₇	—	8	1	no	—
97	C₂×C₄×C₄₇	—	2	2	no	—
98	C₂×C₄×C₄₇	—	2	2	no	—
99	C₂×C₄×C₄₇	—	4	2	no	—
100	C₂×C₄×C₄₇	—	4	2	no	—
101	C₂×C₄×C₄₇	—	4	2	no	—
102	C₂×C₄×C₄₇	—	4	1	no	—
103	C₂×C₄×C₄₇	—	8	2	no	—
104	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
105	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
106	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
107	C₂×C₄×C₄₇	#121	1	2	yes	—
108	C₈×C₄₇	—	2	4	no	—
109	C₄₇⋊C₈	—	4	4	no	—
110	C₄₇⋊C₈	—	8	2	no	—
111	#9007	—	47	1	no	maximal, Sylow
112	C₂²×C₄₇	—	2	2	no	—
113	C₂²×C₄₇	—	2	1	no	—
114	C₂²×C₄₇	—	4	4	no	—
115	C₂²×C₄₇	—	4	2	no	—
116	C₂²×C₄₇	—	8	2	no	—
117	C₂²×C₄₇	—	8	1	no	—
118	C₂²×C₄₇	#386	1	1	yes	characteristic
119	C₄×C₄₇	—	2	2	no	—
120	C₄×C₄₇	—	2	2	no	—
121	C₄×C₄₇	—	2	1	no	—
122	C₄×C₄₇	—	4	2	no	—
123	C₄×C₄₇	—	8	1	no	—
124	C₄×C₄₇	#453	1	2	yes	—
125	#3150	D₄₇	1	1	yes	characteristic
126	#2980	—	47	1	no	—
127	#1543	—	47	1	no	—
128	#1496	—	47	2	no	—
129	#1302	—	47	2	no	—
130	C₂×C₄₇	—	4	1	no	—
131	C₂×C₄₇	—	8	2	no	—
132	C₂×C₄₇	—	16	1	no	—
133	C₂×C₄₇	#1881	1	2	yes	—
134	C₂×C₄₇	#1887	1	1	yes	characteristic
135	C₂×#135	—	2	2	no	—
136	#532	C₂×D₄₇	1	1	yes	characteristic
137	#532	C₂×D₄₇	1	1	yes	characteristic
138	#497	—	2	1	no	—
139	#497	Dic₄₇	1	2	yes	—
140	#496	—	2	1	no	—
141	#496	Dic₄₇	1	2	yes	—
142	#435	—	94	4	no	—
143	#432	—	47	2	no	—
144	#431	—	47	2	no	—
145	#408	—	94	2	no	—
146	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
147	#333	—	94	1	no	—
148	#331	—	94	1	no	—
149	D₄⋊C₈	—	94	4	no	—
150	C₄₇	#9007	1	1	yes	characteristic, complemented, Sylow
151	C₂×#41	—	2	1	no	—
152	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
153	#135	—	4	4	no	—
154	#135	—	4	4	no	—
155	C₂×Q₁₆	—	2	2	no	—
156	C₂×SD₁₆	—	2	2	no	—
157	C₂×SD₁₆	—	2	2	no	—
158	C₂×D₈	—	2	2	no	—
159	C₂×M₁₆	—	94	2	no	—
160	C₂²×C₈	—	2	1	no	—
161	C₂²×C₈	—	94	2	no	—
162	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
163	C₄⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
164	#127	C₂×Dic₄₇	1	1	yes	characteristic
165	#127	C₂²⋊D₄₇	1	1	yes	characteristic
166	#124	—	2	1	no	—
167	#124	C₂×Dic₄₇	1	2	yes	—
168	#121	—	2	2	no	—
169	#121	—	2	2	no	—
170	C₄×D₄	—	2	2	no	—
171	C₄×D₄	—	2	2	no	—
172	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
173	C₄⋊C₈	—	47	4	no	—
174	C₄⋊C₈	—	94	2	no	—
175	C₂²⋊C₈	—	94	4	no	—
176	C₂²⋊C₈	—	94	2	no	—
177	C₂²⋊C₈	—	94	2	no	—
178	#97	—	2	1	no	—
179	#97	—	94	2	no	—
180	#97	C₂×Dic₄₇	1	2	yes	—
181	C₄×C₈	—	94	2	no	—
182	#41	—	4	2	no	—
183	#41	—	4	2	no	—
184	#41	—	4	2	no	—
185	#41	—	4	2	no	—
186	C₂×Q₈	—	2	1	no	—
187	C₂×Q₈	C₂²⋊Dic₄₇	1	2	yes	—
188	C₂×D₄	—	2	2	no	—
189	C₂×D₄	—	2	1	no	—
190	C₂×D₄	—	2	2	no	—
191	C₂×D₄	—	2	2	no	—
192	C₂×D₄	—	4	1	no	—
193	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
194	C₂²×C₄	—	2	2	no	—
195	C₂²×C₄	—	4	1	no	—
196	C₂²×C₄	#10625352	1	2	yes	—
197	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
198	Q₁₆	—	4	4	no	—
199	SD₁₆	—	4	4	no	—
200	SD₁₆	—	4	4	no	—
201	D₈	—	4	4	no	—
202	M₁₆	—	376	2	no	—
203	C₂×C₈	—	2	4	no	—
204	C₂×C₈	—	2	2	no	—
205	C₂×C₈	—	94	4	no	—
206	C₂×C₈	—	376	2	no	—
207	C₂×C₈	—	188	2	no	—
208	C₄⋊C₄	—	2	2	no	—
209	C₄⋊C₄	—	2	2	no	—
210	C₂²⋊C₄	—	2	4	no	—
211	C₂²⋊C₄	—	4	2	no	—
212	C₄²	D₄×D₄₇	1	2	yes	—
213	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
214	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
215	C₂³	—	2	2	no	—
216	C₂³	—	4	1	no	—
217	C₂³	#13094005	1	1	yes	characteristic
218	Q₈	—	4	2	no	—
219	Q₈	—	4	2	no	—
220	D₄	—	4	2	no	—
221	D₄	—	4	2	no	—
222	D₄	—	4	4	no	—
223	D₄	—	8	2	no	—
224	D₄	—	8	2	no	—
225	D₄	—	8	1	no	—
226	D₄	—	8	1	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	2	2	no	—
229	C₂×C₄	—	4	2	no	—
230	C₂×C₄	—	4	2	no	—
231	C₂×C₄	—	4	2	no	—
232	C₂×C₄	—	4	1	no	—
233	C₂×C₄	—	8	2	no	—
234	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
235	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
236	C₂×C₄	#13093992	1	1	yes	characteristic
237	C₂×C₄	#13093996	1	2	yes	—
238	C₈	—	2	4	no	—
239	C₈	—	376	2	no	—
240	C₈	—	188	4	no	—
241	C₂²	—	2	2	no	—
242	C₂²	—	2	1	no	—
243	C₂²	—	4	4	no	—
244	C₂²	—	4	2	no	—
245	C₂²	—	8	2	no	—
246	C₂²	—	8	1	no	—
247	C₂²	#15689003	1	1	yes	characteristic
248	C₄	—	2	2	no	—
249	C₄	—	2	2	no	—
250	C₄	—	2	1	no	—
251	C₄	—	4	2	no	—
252	C₄	—	8	1	no	—
253	C₄	#15689290	1	2	yes	—
254	C₂	—	4	1	no	—
255	C₂	—	8	2	no	—
256	C₂	—	16	1	no	—
257	C₂	#20243752	1	2	yes	—
258	C₂	#20243787	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20252459

C₂

yes

maximal, characteristic, complemented

#20242050

C₂

yes

maximal, characteristic, complemented

#20241857

C₂

yes

maximal, complemented

#20241287

C₂

yes

maximal, complemented

C₄₇×#3150

C₂

yes

maximal, characteristic

#15689195

—

#15689180

C₂²

yes

—

#15689176

C₂²

yes

—

#15689090

—

#15688872

—

#15688867

—

D₄⋊(C₄₇⋊C₈)

—

C₂×#135×C₄₇

—

C₄₇×#532

C₂²

yes

characteristic

C₄₇×#532

C₂²

yes

characteristic

C₄₇×#497

—

C₄₇×#497

C₄

yes

—

C₄₇×#496

—

C₄₇×#496

C₄

yes

—

C₂×#97×C₄₇

C₂²

yes

characteristic

C₂×#10625329

—

C₂²×C₄₇⋊C₈

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

D₄

yes

—

C₂²⋊(C₄₇⋊C₈)

—

C₂²⋊(C₄₇⋊C₈)

—

C₂²⋊(C₄₇⋊C₈)

—

#13093935

—

C₄×C₄₇⋊C₈

—

C₂×#41×C₄₇

—

C₂×#41×C₄₇

D₄

yes

—

#135×C₄₇

—

#135×C₄₇

—

C₂×Q₁₆×C₄₇

—

C₂×SD₁₆×C₄₇

—

C₂×SD₁₆×C₄₇

—

C₂×D₈×C₄₇

—

C₂²×C₈×C₄₇

—

C₄⋊Q₈×C₄₇

C₂×C₄

yes

characteristic

C₄⋊Q₈×C₄₇

D₄

yes

characteristic

#127×C₄₇

C₂×C₄

yes

characteristic

#127×C₄₇

D₄

yes

characteristic

#124×C₄₇

—

#124×C₄₇

C₂×C₄

yes

—

#121×C₄₇

—

#121×C₄₇

—

C₄×D₄×C₄₇

—

C₄×D₄×C₄₇

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

#97×C₄₇

—

#97×C₄₇

C₂×C₄

yes

—

#41×C₄₇

—

#41×C₄₇

—

#41×C₄₇

—

#41×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

C₂²⋊C₄

yes

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

#41

yes

—

Q₁₆×C₄₇

—

SD₁₆×C₄₇

—

SD₁₆×C₄₇

—

D₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

C₂²×C₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

#123

yes

characteristic

Q₈×C₄₇

—

Q₈×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

100

C₂×C₄×C₄₇

—

101

C₂×C₄×C₄₇

—

102

C₂×C₄×C₄₇

—

103

C₂×C₄×C₄₇

—

104

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

105

C₂×C₄×C₄₇

C₄×D₄

yes

—

106

C₂×C₄×C₄₇

#120

yes

characteristic

107

C₂×C₄×C₄₇

#121

yes

—

108

C₈×C₄₇

—

109

C₄₇⋊C₈

—

110

C₄₇⋊C₈

—

111

#9007

—

maximal, Sylow

112

C₂²×C₄₇

—

113

C₂²×C₄₇

—

114

C₂²×C₄₇

—

115

C₂²×C₄₇

—

116

C₂²×C₄₇

—

117

C₂²×C₄₇

—

118

C₂²×C₄₇

#386

yes

characteristic

119

C₄×C₄₇

—

120

C₄×C₄₇

—

121

C₄×C₄₇

—

122

C₄×C₄₇

—

123

C₄×C₄₇

—

124

C₄×C₄₇

#453

yes

—

125

#3150

D₄₇

yes

characteristic

126

#2980

—

127

#1543

—

128

#1496

—

129

#1302

—

130

C₂×C₄₇

—

131

C₂×C₄₇

—

132

C₂×C₄₇

—

133

C₂×C₄₇

#1881

yes

—

134

C₂×C₄₇

#1887

yes

characteristic

135

C₂×#135

—

136

#532

C₂×D₄₇

yes

characteristic

137

#532

C₂×D₄₇

yes

characteristic

138

#497

—

139

#497

Dic₄₇

yes

—

140

#496

—

141

#496

Dic₄₇

yes

—

142

#435

—

143

#432

—

144

#431

—

145

#408

—

146

C₂×#97

C₂×D₄₇

yes

characteristic

147

#333

—

148

#331

—

149

D₄⋊C₈

—

150

C₄₇

#9007

yes

characteristic, complemented, Sylow

151

C₂×#41

—

152

C₂×#41

C₂²⋊D₄₇

yes

—

153

#135

—

154

#135

—

155

C₂×Q₁₆

—

156

C₂×SD₁₆

—

157

C₂×SD₁₆

—

158

C₂×D₈

—

159

C₂×M₁₆

—

160

C₂²×C₈

—

161

C₂²×C₈

—

162

C₄⋊Q₈

C₂×Dic₄₇

yes

characteristic

163

C₄⋊Q₈

C₂²⋊D₄₇

yes

characteristic

164

#127

C₂×Dic₄₇

yes

characteristic

165

#127

C₂²⋊D₄₇

yes

characteristic

166

#124

—

167

#124

C₂×Dic₄₇

yes

—

168

#121

—

169

#121

—

170

C₄×D₄

—

171

C₄×D₄

—

172

C₂×C₄²

C₂²×D₄₇

yes

characteristic

173

C₄⋊C₈

—

174

C₄⋊C₈

—

175

C₂²⋊C₈

—

176

C₂²⋊C₈

—

177

C₂²⋊C₈

—

178

#97

—

179

#97

—

180

#97

C₂×Dic₄₇

yes

—

181

C₄×C₈

—

182

#41

—

183

#41

—

184

#41

—

185

#41

—

186

C₂×Q₈

—

187

C₂×Q₈

C₂²⋊Dic₄₇

yes

—

188

C₂×D₄

—

189

C₂×D₄

—

190

C₂×D₄

—

191

C₂×D₄

—

192

C₂×D₄

—

193

C₂×D₄

C₂²⋊Dic₄₇

yes

—

194

C₂²×C₄

—

195

C₂²×C₄

—

196

C₂²×C₄

#10625352

yes

—

197

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

198

Q₁₆

—

199

SD₁₆

—

200

SD₁₆

—

201

D₈

—

202

M₁₆

—

376

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

—

376

—

207

C₂×C₈

—

188

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

210

C₂²⋊C₄

—

211

C₂²⋊C₄

—

212

C₄²

D₄×D₄₇

yes

—

213

C₄²

C₂²×Dic₄₇

yes

characteristic

214

C₄²

C₂×C₂²⋊D₄₇

yes

characteristic

215

C₂³

—

216

C₂³

—

217

C₂³

#13094005

yes

characteristic

218

Q₈

—

219

Q₈

—

220

D₄

—

221

D₄

—

222

D₄

—

223

D₄

—

224

D₄

—

225

D₄

—

226

D₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

C₂×C₂²⋊Dic₄₇

yes

characteristic

235

C₂×C₄

D₄×Dic₄₇

yes

—

236

C₂×C₄

#13093992

yes

characteristic

237

C₂×C₄

#13093996

yes

—

238

C₈

—

239

C₈

—

376

—

240

C₈

—

188

—

241

C₂²

—

242

C₂²

—

243

C₂²

—

244

C₂²

—

245

C₂²

—

246

C₂²

—

247

C₂²

#15689003

yes

characteristic

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

—

252

C₄

—

253

C₄

#15689290

yes

—

254

C₂

—

255

C₂

—

256

C₂

—

257

C₂

#20243752

yes

—

258

C₂

#20243787

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#13093992
commutator	C₄²×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting, prime radical	C₄₇×#3150	C₂
socle	C₂²×C₄₇	#386
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#3150	D₄₇
hypocenter	C₄₇	#9007
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3150

subgroup

G/H

center

C₂×C₄

#13093992

commutator

C₄²×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting, prime radical

C₄₇×#3150

C₂

socle

C₂²×C₄₇

#386

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3150

N	H ≅ G/N	type
1. #20252459	C₂	semidirect
2. #20242050	C₂	semidirect
3. #20241857	C₂	semidirect
4. #20241287	C₂	semidirect
150. C₄₇	#9007	semidirect

H ≅ G/N

type

1. #20252459

C₂

semidirect

2. #20242050

C₂

semidirect

3. #20241857

C₂

semidirect

4. #20241287

C₂

semidirect

150. C₄₇

#9007

semidirect

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

subgroup	index
#20252459	2
#20242050	2
#20241857	2
#20241287	2
C₄₇×#3150	2
#9007	47

subgroup

index

C₄₇×#3150

Subgroups — #26111238

Conjugacy classes of subgroups

Complements

Maximal subgroups