Group #26050050 — subgroups

Subgroups — C₄₇×#10352 #26050050

Order 12032.

416 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 138 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	C₄₇×#2571	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#1987	C₂	1	2	yes	maximal
3	C₄₇×#1956	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#1296	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#1279	C₂	1	2	yes	maximal
6	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
8	C₂×#103×C₄₇	—	2	2	no	—
9	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
10	C₄₇×#400	—	2	2	no	—
11	C₄₇×#389	—	2	2	no	—
12	C₄₇×#384	C₂²	1	1	yes	characteristic
13	C₄₇×#382	—	2	2	no	—
14	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
15	C₄₇×#340	—	2	2	no	—
16	C₄₇×#340	—	2	2	no	—
17	C₂²×Q₈×C₄₇	—	2	1	no	—
18	C₂²×C₈×C₄₇	—	2	1	no	—
19	C₂²×C₈×C₄₇	—	2	2	no	—
20	C₄⋊Q₈×C₄₇	—	2	2	no	—
21	C₄⋊Q₈×C₄₇	—	2	1	no	—
22	C₄⋊Q₈×C₄₇	Q₈	1	2	yes	—
23	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
24	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
25	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
26	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
27	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
28	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
29	C₂×C₄²×C₄₇	—	2	2	no	—
30	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
31	C₄⋊C₈×C₄₇	—	2	2	no	—
32	C₄⋊C₈×C₄₇	—	2	2	no	—
33	#103×C₄₇	—	4	4	no	—
34	C₄×C₈×C₄₇	—	2	2	no	—
35	#95×C₄₇	—	2	2	no	—
36	#95×C₄₇	—	2	4	no	—
37	#95×C₄₇	—	2	2	no	—
38	C₂×Q₈×C₄₇	—	2	2	no	—
39	C₂×Q₈×C₄₇	—	4	2	no	—
40	C₂×Q₈×C₄₇	—	4	2	no	—
41	C₂×Q₈×C₄₇	—	4	1	no	—
42	C₂²×C₄×C₄₇	—	2	2	no	—
43	C₂²×C₄×C₄₇	—	2	2	no	—
44	C₂²×C₄×C₄₇	—	2	2	no	—
45	C₂²×C₄×C₄₇	—	4	1	no	—
46	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
47	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
48	C₂×C₈×C₄₇	—	2	2	no	—
49	C₂×C₈×C₄₇	—	4	1	no	—
50	C₂×C₈×C₄₇	—	4	1	no	—
51	C₂×C₈×C₄₇	—	4	2	no	—
52	C₂×C₈×C₄₇	—	4	2	no	—
53	C₂×C₈×C₄₇	—	4	2	no	—
54	C₄⋊C₄×C₄₇	—	2	4	no	—
55	C₄⋊C₄×C₄₇	—	2	2	no	—
56	C₄⋊C₄×C₄₇	—	2	2	no	—
57	C₄⋊C₄×C₄₇	—	2	2	no	—
58	C₄⋊C₄×C₄₇	—	2	2	no	—
59	C₄⋊C₄×C₄₇	—	4	2	no	—
60	C₄⋊C₄×C₄₇	—	4	2	no	—
61	C₄⋊C₄×C₄₇	—	4	2	no	—
62	C₄⋊C₄×C₄₇	—	4	2	no	—
63	C₄⋊C₄×C₄₇	—	8	2	no	—
64	C₄²×C₄₇	—	4	2	no	—
65	C₄²×C₄₇	—	4	2	no	—
66	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
67	C₄²×C₄₇	#41	1	1	yes	characteristic
68	C₄²×C₄₇	#41	1	2	yes	—
69	C₂³×C₄₇	#120	1	1	yes	characteristic
70	Q₈×C₄₇	—	4	4	no	—
71	Q₈×C₄₇	—	8	2	no	—
72	C₂×C₄×C₄₇	—	2	1	no	—
73	C₂×C₄×C₄₇	—	2	1	no	—
74	C₂×C₄×C₄₇	—	4	2	no	—
75	C₂×C₄×C₄₇	—	4	2	no	—
76	C₂×C₄×C₄₇	—	4	2	no	—
77	C₂×C₄×C₄₇	—	4	2	no	—
78	C₂×C₄×C₄₇	—	4	2	no	—
79	C₂×C₄×C₄₇	—	4	4	no	—
80	C₂×C₄×C₄₇	—	4	2	no	—
81	C₂×C₄×C₄₇	—	4	2	no	—
82	C₂×C₄×C₄₇	—	4	2	no	—
83	C₂×C₄×C₄₇	—	8	1	no	—
84	C₂×C₄×C₄₇	—	8	1	no	—
85	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
86	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
87	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
88	C₂×C₄×C₄₇	#124	1	2	yes	—
89	C₂×C₄×C₄₇	#135	1	2	yes	—
90	C₂×C₄×C₄₇	#135	1	2	yes	—
91	C₂×C₄×C₄₇	#137	1	2	yes	—
92	C₂×C₄×C₄₇	#137	1	2	yes	—
93	C₈×C₄₇	—	4	2	no	—
94	C₈×C₄₇	—	8	2	no	—
95	#10352	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂²×C₄₇	#393	1	1	yes	characteristic
97	C₂²×C₄₇	#452	1	2	yes	—
98	C₂²×C₄₇	#452	1	2	yes	—
99	C₂²×C₄₇	#453	1	1	yes	characteristic
100	C₂²×C₄₇	#454	1	1	yes	characteristic
101	C₄×C₄₇	—	2	1	no	—
102	C₄×C₄₇	—	2	1	no	—
103	C₄×C₄₇	—	8	2	no	—
104	C₄×C₄₇	—	8	2	no	—
105	C₄×C₄₇	—	8	2	no	—
106	C₄×C₄₇	—	8	2	no	—
107	C₄×C₄₇	#479	1	2	yes	—
108	C₄×C₄₇	#479	1	2	yes	—
109	C₄×C₄₇	#488	1	2	yes	—
110	C₄×C₄₇	#491	1	2	yes	—
111	#2571	C₂×C₄₇	1	1	yes	characteristic
112	#1987	C₂×C₄₇	1	2	yes	—
113	#1956	C₂×C₄₇	1	1	yes	characteristic
114	#1296	C₂×C₄₇	1	1	yes	characteristic
115	#1279	C₂×C₄₇	1	2	yes	—
116	C₂×C₄₇	#1630	1	1	yes	characteristic
117	C₂×C₄₇	#1634	1	1	yes	characteristic
118	C₂×C₄₇	#1638	1	2	yes	—
119	C₂×C₄₇	#2026	1	2	yes	—
120	C₂×C₄₇	#2027	1	1	yes	characteristic
121	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
122	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
123	C₂×#103	—	2	2	no	—
124	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
125	#400	—	2	2	no	—
126	#389	—	2	2	no	—
127	#384	C₂²×C₄₇	1	1	yes	characteristic
128	#382	—	2	2	no	—
129	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
130	#340	—	2	2	no	—
131	#340	—	2	2	no	—
132	C₄₇	#10352	1	1	yes	characteristic, direct product factor, Sylow
133	C₂²×Q₈	—	2	1	no	—
134	C₂²×C₈	—	2	1	no	—
135	C₂²×C₈	—	2	2	no	—
136	C₄⋊Q₈	—	2	2	no	—
137	C₄⋊Q₈	—	2	1	no	—
138	C₄⋊Q₈	Q₈×C₄₇	1	2	yes	—
139	C₂×C₄⋊C₄	—	2	2	no	—
140	C₂×C₄⋊C₄	—	2	2	no	—
141	C₂×C₄⋊C₄	—	2	2	no	—
142	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	—
143	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	—
144	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	—
145	C₂×C₄²	—	2	2	no	—
146	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
147	C₄⋊C₈	—	2	2	no	—
148	C₄⋊C₈	—	2	2	no	—
149	#103	—	4	4	no	—
150	C₄×C₈	—	2	2	no	—
151	#95	—	2	2	no	—
152	#95	—	2	4	no	—
153	#95	—	2	2	no	—
154	C₂×Q₈	—	2	2	no	—
155	C₂×Q₈	—	4	2	no	—
156	C₂×Q₈	—	4	2	no	—
157	C₂×Q₈	—	4	1	no	—
158	C₂²×C₄	—	2	2	no	—
159	C₂²×C₄	—	2	2	no	—
160	C₂²×C₄	—	2	2	no	—
161	C₂²×C₄	—	4	1	no	—
162	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
163	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
164	C₂×C₈	—	2	2	no	—
165	C₂×C₈	—	4	1	no	—
166	C₂×C₈	—	4	1	no	—
167	C₂×C₈	—	4	2	no	—
168	C₂×C₈	—	4	2	no	—
169	C₂×C₈	—	4	2	no	—
170	C₄⋊C₄	—	2	4	no	—
171	C₄⋊C₄	—	2	2	no	—
172	C₄⋊C₄	—	2	2	no	—
173	C₄⋊C₄	—	2	2	no	—
174	C₄⋊C₄	—	2	2	no	—
175	C₄⋊C₄	—	4	2	no	—
176	C₄⋊C₄	—	4	2	no	—
177	C₄⋊C₄	—	4	2	no	—
178	C₄⋊C₄	—	4	2	no	—
179	C₄⋊C₄	—	8	2	no	—
180	C₄²	—	4	2	no	—
181	C₄²	—	4	2	no	—
182	C₄²	C₂×Q₈×C₄₇	1	1	yes	characteristic
183	C₄²	#41×C₄₇	1	2	yes	—
184	C₄²	#41×C₄₇	1	1	yes	characteristic
185	C₂³	#120×C₄₇	1	1	yes	characteristic
186	Q₈	—	4	4	no	—
187	Q₈	—	8	2	no	—
188	C₂×C₄	—	2	1	no	—
189	C₂×C₄	—	2	1	no	—
190	C₂×C₄	—	4	2	no	—
191	C₂×C₄	—	4	2	no	—
192	C₂×C₄	—	4	2	no	—
193	C₂×C₄	—	4	2	no	—
194	C₂×C₄	—	4	4	no	—
195	C₂×C₄	—	4	2	no	—
196	C₂×C₄	—	4	2	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	—	8	1	no	—
200	C₂×C₄	—	8	1	no	—
201	C₂×C₄	C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
202	C₂×C₄	C₂²⋊Q₈×C₄₇	1	2	yes	—
203	C₂×C₄	#124×C₄₇	1	1	yes	characteristic
204	C₂×C₄	#124×C₄₇	1	2	yes	—
205	C₂×C₄	#135×C₄₇	1	2	yes	—
206	C₂×C₄	#135×C₄₇	1	2	yes	—
207	C₂×C₄	#137×C₄₇	1	2	yes	—
208	C₂×C₄	#137×C₄₇	1	2	yes	—
209	C₈	—	4	2	no	—
210	C₈	—	8	2	no	—
211	C₂²	C₄₇×#393	1	1	yes	characteristic
212	C₂²	C₄₇×#452	1	2	yes	—
213	C₂²	C₄₇×#452	1	2	yes	—
214	C₂²	C₄₇×#453	1	1	yes	characteristic
215	C₂²	C₄₇×#454	1	1	yes	characteristic
216	C₄	—	2	1	no	—
217	C₄	—	2	1	no	—
218	C₄	—	8	2	no	—
219	C₄	—	8	2	no	—
220	C₄	—	8	2	no	—
221	C₄	—	8	2	no	—
222	C₄	C₄₇×#479	1	2	yes	—
223	C₄	C₄₇×#479	1	2	yes	—
224	C₄	C₄₇×#488	1	2	yes	—
225	C₄	C₄₇×#491	1	2	yes	—
226	C₂	C₄₇×#1630	1	1	yes	characteristic
227	C₂	C₄₇×#1634	1	1	yes	characteristic
228	C₂	C₄₇×#1638	1	2	yes	—
229	C₂	C₄₇×#2026	1	2	yes	—
230	C₂	C₄₇×#2027	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄₇×#2571

C₂

yes

maximal, characteristic

C₄₇×#1987

C₂

yes

maximal

C₄₇×#1956

C₂

yes

maximal, characteristic

C₄₇×#1296

C₂

yes

maximal, characteristic

C₄₇×#1279

C₂

yes

maximal

C₂×C₄⋊Q₈×C₄₇

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₄₇

C₂²

yes

—

C₂×#103×C₄₇

—

C₂×C₄×C₈×C₄₇

C₂²

yes

characteristic

C₄₇×#400

—

C₄₇×#389

—

C₄₇×#384

C₂²

yes

characteristic

C₄₇×#382

—

C₄×C₄⋊C₄×C₄₇

C₂²

yes

—

C₄₇×#340

—

C₄₇×#340

—

C₂²×Q₈×C₄₇

—

C₂²×C₈×C₄₇

—

C₂²×C₈×C₄₇

—

C₄⋊Q₈×C₄₇

—

C₄⋊Q₈×C₄₇

—

C₄⋊Q₈×C₄₇

Q₈

yes

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

D₄

yes

—

C₂×C₄⋊C₄×C₄₇

D₄

yes

—

C₂×C₄⋊C₄×C₄₇

D₄

yes

—

C₂×C₄²×C₄₇

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₄⋊C₈×C₄₇

—

#103×C₄₇

—

C₄×C₈×C₄₇

—

#95×C₄₇

—

#95×C₄₇

—

#95×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

C₂×Q₈

yes

C₄²×C₄₇

yes

C₄²×C₄₇

yes

—

C₂³×C₄₇

#120

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

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₄₇

C₂²⋊Q₈

yes

—

C₂×C₄×C₄₇

#124

yes

characteristic

C₂×C₄×C₄₇

#124

yes

—

C₂×C₄×C₄₇

#135

yes

—

C₂×C₄×C₄₇

#135

yes

—

C₂×C₄×C₄₇

#137

yes

—

C₂×C₄×C₄₇

#137

yes

—

C₈×C₄₇

—

C₈×C₄₇

—

#10352

C₄₇

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₄₇

#393

yes

characteristic

C₂²×C₄₇

#452

yes

—

C₂²×C₄₇

#452

yes

—

C₂²×C₄₇

#453

yes

characteristic

100

C₂²×C₄₇

#454

yes

characteristic

101

C₄×C₄₇

—

102

C₄×C₄₇

—

103

C₄×C₄₇

—

104

C₄×C₄₇

—

105

C₄×C₄₇

—

106

C₄×C₄₇

—

107

C₄×C₄₇

#479

yes

—

108

C₄×C₄₇

#479

yes

—

109

C₄×C₄₇

#488

yes

—

110

C₄×C₄₇

#491

yes

—

111

#2571

C₂×C₄₇

yes

characteristic

112

#1987

C₂×C₄₇

yes

—

113

#1956

C₂×C₄₇

yes

characteristic

114

#1296

C₂×C₄₇

yes

characteristic

115

#1279

C₂×C₄₇

yes

—

116

C₂×C₄₇

#1630

yes

characteristic

117

C₂×C₄₇

#1634

yes

characteristic

118

C₂×C₄₇

#1638

yes

—

119

C₂×C₄₇

#2026

yes

—

120

C₂×C₄₇

#2027

yes

characteristic

121

C₂×C₄⋊Q₈

C₂²×C₄₇

yes

characteristic

122

C₂×C₄⋊C₈

C₂²×C₄₇

yes

—

123

C₂×#103

—

124

C₂×C₄×C₈

C₂²×C₄₇

yes

characteristic

125

#400

—

126

#389

—

127

#384

C₂²×C₄₇

yes

characteristic

128

#382

—

129

C₄×C₄⋊C₄

C₂²×C₄₇

yes

—

130

#340

—

131

#340

—

132

C₄₇

#10352

yes

characteristic, direct product factor, Sylow

133

C₂²×Q₈

—

134

C₂²×C₈

—

135

C₂²×C₈

—

136

C₄⋊Q₈

—

137

C₄⋊Q₈

—

138

C₄⋊Q₈

Q₈×C₄₇

yes

—

139

C₂×C₄⋊C₄

—

140

C₂×C₄⋊C₄

—

141

C₂×C₄⋊C₄

—

142

C₂×C₄⋊C₄

D₄×C₄₇

yes

—

143

C₂×C₄⋊C₄

D₄×C₄₇

yes

—

144

C₂×C₄⋊C₄

D₄×C₄₇

yes

—

145

C₂×C₄²

—

146

C₂×C₄²

C₂³×C₄₇

yes

characteristic

147

C₄⋊C₈

—

148

C₄⋊C₈

—

149

#103

—

150

C₄×C₈

—

151

#95

—

152

#95

—

153

#95

—

154

C₂×Q₈

—

155

C₂×Q₈

—

156

C₂×Q₈

—

157

C₂×Q₈

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

C₂×D₄×C₄₇

yes

characteristic

163

C₂²×C₄

C₂×D₄×C₄₇

yes

—

164

C₂×C₈

—

165

C₂×C₈

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄²

—

181

C₄²

—

182

C₄²

C₂×Q₈×C₄₇

yes

characteristic

183

C₄²

#41×C₄₇

yes

—

184

C₄²

#41×C₄₇

yes

characteristic

185

C₂³

#120×C₄₇

yes

characteristic

186

Q₈

—

187

Q₈

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

C₂²⋊Q₈×C₄₇

yes

characteristic

202

C₂×C₄

C₂²⋊Q₈×C₄₇

yes

—

203

C₂×C₄

#124×C₄₇

yes

characteristic

204

C₂×C₄

#124×C₄₇

yes

—

205

C₂×C₄

#135×C₄₇

yes

—

206

C₂×C₄

#135×C₄₇

yes

—

207

C₂×C₄

#137×C₄₇

yes

—

208

C₂×C₄

#137×C₄₇

yes

—

209

C₈

—

210

C₈

—

211

C₂²

C₄₇×#393

yes

characteristic

212

C₂²

C₄₇×#452

yes

—

213

C₂²

C₄₇×#452

yes

—

214

C₂²

C₄₇×#453

yes

characteristic

215

C₂²

C₄₇×#454

yes

characteristic

216

C₄

—

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

C₄₇×#479

yes

—

223

C₄

C₄₇×#479

yes

—

224

C₄

C₄₇×#488

yes

—

225

C₄

C₄₇×#491

yes

—

226

C₂

C₄₇×#1630

yes

characteristic

227

C₂

C₄₇×#1634

yes

characteristic

228

C₂

C₄₇×#1638

yes

—

229

C₂

C₄₇×#2026

yes

—

230

C₂

C₄₇×#2027

yes

characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₄₇	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₄₇
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂×C₄²×C₄₇ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₄₇

#120

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₄₇

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₄₇ ◁ C₂×C₄²×C₄₇ ◁ G

N	H ≅ G/N	type
95. #10352	C₄₇	direct (N × H)
132. C₄₇	#10352	direct (N × H)

H ≅ G/N

type

95. #10352

C₄₇

direct (N × H)

132. C₄₇

#10352

direct (N × H)

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

subgroup	index
C₄₇×#2571	2
C₄₇×#1987	2
C₄₇×#1956	2
C₄₇×#1296	2
C₄₇×#1279	2
#10352	47

subgroup

index

C₄₇×#2571

C₄₇×#1987

C₄₇×#1956

C₄₇×#1296

C₄₇×#1279

#10352

Subgroups — C₄₇×#10352 #26050050

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C47×#10352 #26050050

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#10352 #26050050