Group #26109108 — subgroups

Subgroups — #26109108

Order 12032.

476 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 141 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	#20245955	C₂	1	1	yes	maximal, characteristic
2	#20243504	C₂	1	2	yes	maximal
3	C₂×#15688871	C₂	1	2	yes	maximal
4	#20241271	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#1296	C₂	1	1	yes	maximal, characteristic
6	C₂×#13094024	C₂²	1	1	yes	characteristic
7	C₂×#13093989	C₄	1	2	yes	—
8	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
9	#15689028	C₄	1	2	yes	—
10	#15689019	—	2	2	no	—
11	C₄⋊C₄×Dic₄₇	—	2	2	no	—
12	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
13	#15688877	—	2	2	no	—
14	#15688877	—	2	2	no	—
15	#15688871	—	2	4	no	—
16	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
17	C₄₇×#384	C₂²	1	1	yes	characteristic
18	C₂²×Dic₉₄	C₂×C₄	1	2	yes	—
19	C₂²×C₄₇⋊C₈	—	2	2	no	—
20	#13094024	—	2	2	no	—
21	#13094024	D₄	1	2	yes	—
22	#13094024	Q₈	1	2	yes	—
23	#13093989	—	4	4	no	—
24	C₂×C₄⋊Dic₄₇	—	2	2	no	—
25	C₂×Dic₄₇⋊C₄	—	2	2	no	—
26	C₂×C₄×Dic₄₇	—	2	2	no	—
27	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
30	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
31	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
32	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
33	C₄₇⋊#95	—	2	4	no	—
34	C₂²×C₈×C₄₇	—	2	2	no	—
35	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
36	C₂×C₄⋊C₄×C₄₇	C₂×C₄	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	C₂²×C₄×C₄₇	—	2	2	no	—
41	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
42	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
43	C₂²×Dic₄₇	—	2	2	no	—
44	C₂²×Dic₄₇	C₂²⋊C₄	1	2	yes	—
45	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
46	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
47	C₂×Dic₉₄	—	2	2	no	—
48	C₂×Dic₉₄	—	4	2	no	—
49	C₂×Dic₉₄	—	4	2	no	—
50	C₂×Dic₉₄	C₄⋊C₄	1	4	yes	—
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	—	4	2	no	—
55	C₄⋊C₄×C₄₇	—	4	2	no	—
56	C₄⋊C₄×C₄₇	—	4	2	no	—
57	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
58	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
59	C₄²×C₄₇	#41	1	2	yes	—
60	C₄⋊Dic₄₇	—	2	4	no	—
61	C₄⋊Dic₄₇	—	2	4	no	—
62	Dic₄₇⋊C₄	—	4	4	no	—
63	C₄×Dic₄₇	—	2	2	no	—
64	C₄×Dic₄₇	—	2	2	no	—
65	C₄×Dic₄₇	—	2	2	no	—
66	C₄×Dic₄₇	—	2	2	no	—
67	C₄×Dic₄₇	—	2	2	no	—
68	C₄×Dic₄₇	—	4	1	no	—
69	C₄×Dic₄₇	—	4	4	no	—
70	C₂×C₄₇⋊C₈	—	4	2	no	—
71	C₂×C₄₇⋊C₈	—	4	2	no	—
72	C₂×C₄₇⋊C₈	—	4	2	no	—
73	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
74	C₂×C₄×C₄₇	—	2	1	no	—
75	C₂×C₄×C₄₇	—	2	1	no	—
76	C₂×C₄×C₄₇	—	4	2	no	—
77	C₂×C₄×C₄₇	—	4	4	no	—
78	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
79	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
80	C₂×C₄×C₄₇	#121	1	2	yes	—
81	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
82	C₂×C₄×C₄₇	#135	1	2	yes	—
83	C₂×C₄×C₄₇	#135	1	2	yes	—
84	C₂×C₄×C₄₇	#137	1	2	yes	—
85	C₂×C₄×C₄₇	#137	1	2	yes	—
86	C₂×Dic₄₇	—	2	2	no	—
87	C₂×Dic₄₇	—	2	4	no	—
88	C₂×Dic₄₇	—	2	1	no	—
89	C₂×Dic₄₇	—	2	2	no	—
90	C₂×Dic₄₇	—	2	2	no	—
91	C₂×Dic₄₇	—	2	2	no	—
92	C₂×Dic₄₇	—	2	2	no	—
93	C₂×Dic₄₇	—	4	2	no	—
94	C₂×Dic₄₇	—	4	2	no	—
95	C₂×Dic₄₇	#100	1	2	yes	—
96	Dic₉₄	—	4	4	no	—
97	Dic₉₄	—	4	4	no	—
98	C₈×C₄₇	—	8	2	no	—
99	C₄₇⋊C₈	—	8	2	no	—
100	#8594	—	47	1	no	maximal, Sylow
101	C₂²×C₄₇	#380	1	1	yes	characteristic
102	C₂²×C₄₇	C₂×#100	1	1	yes	characteristic
103	C₂²×C₄₇	#413	1	1	yes	characteristic
104	C₂²×C₄₇	#416	1	2	yes	—
105	C₂²×C₄₇	#419	1	2	yes	—
106	C₄×C₄₇	—	2	1	no	—
107	C₄×C₄₇	—	2	1	no	—
108	C₄×C₄₇	—	8	2	no	—
109	C₄×C₄₇	#464	1	2	yes	—
110	C₄×C₄₇	#464	1	2	yes	—
111	C₄×C₄₇	#479	1	2	yes	—
112	C₄×C₄₇	#479	1	2	yes	—
113	Dic₄₇	—	2	2	no	—
114	Dic₄₇	—	4	1	no	—
115	Dic₄₇	—	4	4	no	—
116	Dic₄₇	—	4	2	no	—
117	C₄×C₄⋊Q₈	—	47	1	no	—
118	#1831	—	47	2	no	—
119	C₂×#333	—	47	2	no	—
120	#1296	—	47	1	no	—
121	#1296	D₄₇	1	1	yes	characteristic
122	C₂×C₄₇	#1543	1	1	yes	characteristic
123	C₂×C₄₇	#1554	1	2	yes	—
124	C₂×C₄₇	#1558	1	1	yes	characteristic
125	C₂×C₄₇	#1800	1	1	yes	characteristic
126	C₂×C₄₇	#1805	1	2	yes	—
127	C₂×C₄⋊Q₈	—	47	1	no	—
128	C₂×C₄×Q₈	—	47	2	no	—
129	C₂×C₄⋊C₈	—	47	2	no	—
130	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
131	#391	—	47	2	no	—
132	#389	—	94	2	no	—
133	#384	C₂×D₄₇	1	1	yes	characteristic
134	C₄×C₄⋊C₄	—	94	2	no	—
135	C₄³	—	47	1	no	—
136	#336	—	94	2	no	—
137	#336	—	94	2	no	—
138	#333	—	94	4	no	—
139	C₄₇	#8594	1	1	yes	characteristic, complemented, Sylow
140	C₂²×Q₈	—	47	2	no	—
141	C₂²×C₈	—	2	2	no	—
142	C₂²×C₈	—	94	2	no	—
143	C₄⋊Q₈	—	47	2	no	—
144	C₄⋊Q₈	—	47	2	no	—
145	C₄⋊Q₈	—	94	2	no	—
146	C₄×Q₈	—	188	4	no	—
147	C₂×C₄⋊C₄	—	2	2	no	—
148	C₂×C₄⋊C₄	—	94	2	no	—
149	C₂×C₄⋊C₄	—	94	2	no	—
150	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
151	C₂×C₄²	—	47	1	no	—
152	C₂×C₄²	—	47	2	no	—
153	C₂×C₄²	—	47	2	no	—
154	C₂×C₄²	—	47	1	no	—
155	C₂×C₄²	—	94	2	no	—
156	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
157	C₄⋊C₈	—	2	2	no	—
158	C₄⋊C₈	—	2	2	no	—
159	C₄⋊C₈	—	94	2	no	—
160	C₄⋊C₈	—	94	2	no	—
161	#95	—	94	4	no	—
162	C₂×Q₈	—	47	4	no	—
163	C₂×Q₈	—	94	2	no	—
164	C₂×Q₈	—	188	2	no	—
165	C₂×Q₈	—	188	2	no	—
166	C₂²×C₄	—	2	2	no	—
167	C₂²×C₄	—	47	1	no	—
168	C₂²×C₄	—	47	2	no	—
169	C₂²×C₄	—	47	1	no	—
170	C₂²×C₄	—	94	2	no	—
171	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
172	C₂²×C₄	D₄×D₄₇	1	2	yes	—
173	C₂×C₈	—	4	2	no	—
174	C₂×C₈	—	4	2	no	—
175	C₂×C₈	—	4	2	no	—
176	C₂×C₈	—	188	2	no	—
177	C₂×C₈	—	188	2	no	—
178	C₂×C₈	—	188	2	no	—
179	C₄⋊C₄	—	4	2	no	—
180	C₄⋊C₄	—	4	2	no	—
181	C₄⋊C₄	—	4	2	no	—
182	C₄⋊C₄	—	94	4	no	—
183	C₄⋊C₄	—	94	4	no	—
184	C₄⋊C₄	—	188	4	no	—
185	C₄²	—	94	2	no	—
186	C₄²	—	94	2	no	—
187	C₄²	—	94	2	no	—
188	C₄²	—	94	2	no	—
189	C₄²	—	94	2	no	—
190	C₄²	—	188	1	no	—
191	C₄²	—	188	4	no	—
192	C₄²	#10625350	1	2	yes	—
193	C₄²	D₄×D₄₇	1	1	yes	characteristic
194	C₄²	Q₈×D₄₇	1	1	yes	characteristic
195	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
196	Q₈	—	188	4	no	—
197	Q₈	—	188	4	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	4	2	no	—
201	C₂×C₄	—	4	4	no	—
202	C₂×C₄	—	47	2	no	—
203	C₂×C₄	—	94	2	no	—
204	C₂×C₄	—	94	4	no	—
205	C₂×C₄	—	94	1	no	—
206	C₂×C₄	—	94	2	no	—
207	C₂×C₄	—	94	2	no	—
208	C₂×C₄	—	94	2	no	—
209	C₂×C₄	—	94	2	no	—
210	C₂×C₄	—	188	2	no	—
211	C₂×C₄	—	188	2	no	—
212	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
213	C₂×C₄	#13093981	1	1	yes	characteristic
214	C₂×C₄	#13093997	1	2	yes	—
215	C₂×C₄	#13094002	1	2	yes	—
216	C₂×C₄	#13094043	1	2	yes	—
217	C₂×C₄	#13094045	1	2	yes	—
218	C₂×C₄	#13094053	1	2	yes	—
219	C₂×C₄	#13094056	1	2	yes	—
220	C₈	—	8	2	no	—
221	C₈	—	376	2	no	—
222	C₂²	#15688982	1	1	yes	characteristic
223	C₂²	#100×D₄₇	1	1	yes	characteristic
224	C₂²	#15689106	1	1	yes	characteristic
225	C₂²	#15689116	1	2	yes	—
226	C₂²	#15689130	1	2	yes	—
227	C₄	—	2	1	no	—
228	C₄	—	2	1	no	—
229	C₄	—	8	2	no	—
230	C₄	—	94	2	no	—
231	C₄	—	188	1	no	—
232	C₄	—	188	2	no	—
233	C₄	—	188	4	no	—
234	C₄	#15689344	1	2	yes	—
235	C₄	#15689348	1	2	yes	—
236	C₄	#15689429	1	2	yes	—
237	C₄	#15689433	1	2	yes	—
238	C₂	#20242047	1	1	yes	characteristic
239	C₂	#20242095	1	2	yes	—
240	C₂	#20242112	1	1	yes	characteristic
241	C₂	#20243379	1	1	yes	characteristic
242	C₂	#20243402	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#20245955

C₂

yes

maximal, characteristic

#20243504

C₂

yes

maximal

C₂×#15688871

C₂

yes

maximal

#20241271

C₂

yes

maximal, characteristic

C₄₇×#1296

C₂

yes

maximal, characteristic

C₂×#13094024

C₂²

yes

characteristic

C₂×#13093989

C₄

yes

—

C₂×C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

#15689028

C₄

yes

—

#15689019

—

C₄⋊C₄×Dic₄₇

—

C₄²×Dic₄₇

C₂²

yes

—

—

—

C₂×C₄⋊C₈×C₄₇

C₂²

yes

—

C₄₇×#384

C₂²

yes

characteristic

C₂²×Dic₉₄

C₂×C₄

yes

—

C₂²×C₄₇⋊C₈

—

#13094024

—

#13094024

D₄

yes

—

#13094024

Q₈

yes

—

#13093989

—

C₂×C₄⋊Dic₄₇

—

C₂×Dic₄₇⋊C₄

—

C₂×C₄×Dic₄₇

—

C₂×C₄×Dic₄₇

C₂×C₄

yes

characteristic

C₂×C₄×Dic₄₇

C₂×C₄

yes

characteristic

C₂×C₄×Dic₄₇

D₄

yes

—

C₂×C₄×Dic₄₇

D₄

yes

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

C₄₇⋊#95

—

C₂²×C₈×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

C₂×C₄

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₄⋊C₈×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

C₂²⋊C₄

yes

—

C₂²×Dic₄₇

C₂²⋊C₄

yes

characteristic

C₂²×Dic₄₇

C₂²⋊C₄

yes

characteristic

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

C₄⋊C₄

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₄²×C₄₇

C₂×Q₈

yes

characteristic

C₄²×C₄₇

#41

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

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

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×C₄⋊C₄

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

—

C₂×C₄×C₄₇

C₂²⋊Q₈

yes

—

C₂×C₄×C₄₇

#135

yes

—

C₂×C₄×C₄₇

#135

yes

—

C₂×C₄×C₄₇

#137

yes

—

C₂×C₄×C₄₇

#137

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

#100

yes

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₄₇⋊C₈

—

100

#8594

—

maximal, Sylow

101

C₂²×C₄₇

#380

yes

characteristic

102

C₂²×C₄₇

C₂×#100

yes

characteristic

103

C₂²×C₄₇

#413

yes

characteristic

104

C₂²×C₄₇

#416

yes

—

105

C₂²×C₄₇

#419

yes

—

106

C₄×C₄₇

—

107

C₄×C₄₇

—

108

C₄×C₄₇

—

109

C₄×C₄₇

#464

yes

—

110

C₄×C₄₇

#464

yes

—

111

C₄×C₄₇

#479

yes

—

112

C₄×C₄₇

#479

yes

—

113

Dic₄₇

—

114

Dic₄₇

—

115

Dic₄₇

—

116

Dic₄₇

—

117

C₄×C₄⋊Q₈

—

118

#1831

—

119

C₂×#333

—

120

#1296

—

121

#1296

D₄₇

yes

characteristic

122

C₂×C₄₇

#1543

yes

characteristic

123

C₂×C₄₇

#1554

yes

—

124

C₂×C₄₇

#1558

yes

characteristic

125

C₂×C₄₇

#1800

yes

characteristic

126

C₂×C₄₇

#1805

yes

—

127

C₂×C₄⋊Q₈

—

128

C₂×C₄×Q₈

—

129

C₂×C₄⋊C₈

—

130

C₂×C₄⋊C₈

C₂×D₄₇

yes

—

131

#391

—

132

#389

—

133

#384

C₂×D₄₇

yes

characteristic

134

C₄×C₄⋊C₄

—

135

C₄³

—

136

#336

—

137

#336

—

138

#333

—

139

C₄₇

#8594

yes

characteristic, complemented, Sylow

140

C₂²×Q₈

—

141

C₂²×C₈

—

142

C₂²×C₈

—

143

C₄⋊Q₈

—

144

C₄⋊Q₈

—

145

C₄⋊Q₈

—

146

C₄×Q₈

—

188

—

147

C₂×C₄⋊C₄

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

C₄×D₄₇

yes

—

151

C₂×C₄²

—

152

C₂×C₄²

—

153

C₂×C₄²

—

154

C₂×C₄²

—

155

C₂×C₄²

—

156

C₂×C₄²

C₂²×D₄₇

yes

characteristic

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₄⋊C₈

—

161

#95

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

188

—

165

C₂×Q₈

—

188

—

166

C₂²×C₄

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

C₂×C₄×D₄₇

yes

characteristic

172

C₂²×C₄

D₄×D₄₇

yes

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

188

—

177

C₂×C₈

—

188

—

178

C₂×C₈

—

188

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

188

—

185

C₄²

—

186

C₄²

—

187

C₄²

—

188

C₄²

—

189

C₄²

—

190

C₄²

—

188

—

191

C₄²

—

188

—

192

C₄²

#10625350

yes

—

193

C₄²

D₄×D₄₇

yes

characteristic

194

C₄²

Q₈×D₄₇

yes

characteristic

195

C₂³

C₂²⋊C₄×D₄₇

yes

characteristic

196

Q₈

—

188

—

197

Q₈

—

188

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

188

—

211

C₂×C₄

—

188

—

212

C₂×C₄

C₄⋊C₄×D₄₇

yes

characteristic

213

C₂×C₄

#13093981

yes

characteristic

214

C₂×C₄

#13093997

yes

—

215

C₂×C₄

#13094002

yes

—

216

C₂×C₄

#13094043

yes

—

217

C₂×C₄

#13094045

yes

—

218

C₂×C₄

#13094053

yes

—

219

C₂×C₄

#13094056

yes

—

220

C₈

—

221

C₈

—

376

—

222

C₂²

#15688982

yes

characteristic

223

C₂²

#100×D₄₇

yes

characteristic

224

C₂²

#15689106

yes

characteristic

225

C₂²

#15689116

yes

—

226

C₂²

#15689130

yes

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

188

—

232

C₄

—

188

—

233

C₄

—

188

—

234

C₄

#15689344

yes

—

235

C₄

#15689348

yes

—

236

C₄

#15689429

yes

—

237

C₄

#15689433

yes

—

238

C₂

#20242047

yes

characteristic

239

C₂

#20242095

yes

—

240

C₂

#20242112

yes

characteristic

241

C₂

#20243379

yes

characteristic

242

C₂

#20243402

yes

—

	subgroup	G/H
center	C₂³	C₂²⋊C₄×D₄₇
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1296	C₂
socle, prime radical	C₂³×C₄₇	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1296	D₄₇
hypocenter	C₄₇	#8594
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

subgroup

G/H

center

C₂³

C₂²⋊C₄×D₄₇

commutator

C₂²×C₄×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#1296

C₂

socle, prime radical

C₂³×C₄₇

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

N	H ≅ G/N	type
139. C₄₇	#8594	semidirect

H ≅ G/N

type

139. C₄₇

#8594

semidirect

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

subgroup	index
#20245955	2
#20243504	2
C₂×#15688871	2
#20241271	2
C₄₇×#1296	2
#8594	47

subgroup

index

C₄₇×#1296

Subgroups — #26109108

Conjugacy classes of subgroups

Complements

Maximal subgroups