Group #26109434 — subgroups

Subgroups — #26109434

Order 12032.

358 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 119 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×#15689253	C₂	1	1	yes	maximal, characteristic
2	#20242136	C₂	1	1	yes	maximal, characteristic
3	#20241816	C₂	1	2	yes	maximal
4	#20241283	C₂	1	2	yes	maximal
5	C₄₇×#1837	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
7	#15689253	—	2	1	no	—
8	#15689253	—	2	1	no	—
9	#15689253	C₄	1	2	yes	—
10	#15689253	C₄	1	2	yes	—
11	#15689176	C₂²	1	2	yes	—
12	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×Dic₄₇⋊C₈	—	2	1	no	—
14	C₂×#13093934	—	2	1	no	—
15	#15688876	—	2	1	no	—
16	#15688874	—	2	1	no	—
17	#15688853	—	2	4	no	—
18	C₄₇×#423	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
20	C₄₇×#341	—	2	1	no	—
21	C₄₇×#341	—	2	1	no	—
22	C₂²×Dic₉₄	Q₈	1	1	yes	characteristic
23	C₂²×C₄₇⋊C₈	—	2	1	no	—
24	C₄×Dic₉₄	—	2	1	no	—
25	C₄×Dic₉₄	—	2	1	no	—
26	C₄×Dic₉₄	C₂×C₄	1	2	yes	—
27	C₄×Dic₉₄	D₄	1	2	yes	—
28	C₂×C₄⋊Dic₄₇	Q₈	1	1	yes	characteristic
29	C₂×Dic₄₇⋊C₄	—	2	1	no	—
30	C₂×C₄×Dic₄₇	—	2	1	no	—
31	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
32	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
33	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
34	Dic₄₇⋊C₈	—	2	2	no	—
35	Dic₄₇⋊C₈	—	2	2	no	—
36	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
37	#13093934	—	2	2	no	—
38	#13093934	—	2	2	no	—
39	C₄×C₄₇⋊C₈	—	2	2	no	—
40	C₂×M₁₆×C₄₇	—	2	2	no	—
41	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
44	C₄⋊C₈×C₄₇	—	2	2	no	—
45	C₄⋊C₈×C₄₇	—	2	2	no	—
46	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
47	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
48	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
49	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
50	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
52	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
53	C₂²×Dic₄₇	—	2	1	no	—
54	C₂²×Dic₄₇	—	2	1	no	—
55	C₂×Dic₉₄	—	2	1	no	—
56	C₂×Dic₉₄	—	4	2	no	—
57	C₂×Dic₉₄	C₄⋊C₄	1	2	yes	—
58	M₁₆×C₄₇	—	4	2	no	—
59	M₁₆×C₄₇	—	4	2	no	—
60	C₂×C₈×C₄₇	—	2	2	no	—
61	C₂×C₈×C₄₇	—	2	2	no	—
62	C₂×C₈×C₄₇	—	4	2	no	—
63	C₂×C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
64	C₂×C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
65	C₂×C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
66	C₂×C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
67	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
68	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
69	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
70	C₄²×C₄₇	#41	1	1	yes	characteristic
71	C₄⋊Dic₄₇	—	2	1	no	—
72	C₄⋊Dic₄₇	C₄⋊C₄	1	2	yes	—
73	Dic₄₇⋊C₄	—	2	2	no	—
74	Dic₄₇⋊C₄	—	2	2	no	—
75	C₄×Dic₄₇	—	2	2	no	—
76	C₄×Dic₄₇	—	2	2	no	—
77	C₂×C₄₇⋊C₈	—	2	2	no	—
78	C₂×C₄₇⋊C₈	—	4	2	no	—
79	C₂×C₄₇⋊C₈	—	4	2	no	—
80	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
81	C₂×C₄×C₄₇	—	2	2	no	—
82	C₂×C₄×C₄₇	—	4	1	no	—
83	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
85	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
86	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
87	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
88	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
89	C₂×C₄×C₄₇	#135	1	2	yes	—
90	C₂×C₄×C₄₇	#137	1	2	yes	—
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	Dic₉₄	—	2	4	no	—
96	Dic₉₄	—	4	2	no	—
97	C₈×C₄₇	—	2	1	no	—
98	C₈×C₄₇	—	2	1	no	—
99	C₈×C₄₇	—	2	1	no	—
100	C₈×C₄₇	—	2	1	no	—
101	C₈×C₄₇	—	8	2	no	—
102	C₄₇⋊C₈	—	4	2	no	—
103	C₄₇⋊C₈	—	8	2	no	—
104	#8665	—	47	1	no	maximal, Sylow
105	C₂²×C₄₇	—	2	1	no	—
106	C₂²×C₄₇	—	2	1	no	—
107	C₂²×C₄₇	#380	1	1	yes	characteristic
108	C₂²×C₄₇	#479	1	2	yes	—
109	C₄×C₄₇	—	2	1	no	—
110	C₄×C₄₇	—	2	1	no	—
111	C₄×C₄₇	—	2	1	no	—
112	C₄×C₄₇	#416	1	1	yes	characteristic
113	C₄×C₄₇	#419	1	1	yes	characteristic
114	C₄×C₄₇	#430	1	2	yes	—
115	C₄×C₄₇	#464	1	2	yes	—
116	Dic₄₇	—	4	2	no	—
117	Dic₄₇	—	4	2	no	—
118	C₂×#446	—	47	1	no	—
119	#1837	D₄₇	1	1	yes	characteristic
120	#1564	—	47	1	no	—
121	#1487	—	47	2	no	—
122	#1301	—	47	2	no	—
123	C₂×C₄₇	—	2	2	no	—
124	C₂×C₄₇	#1805	1	1	yes	characteristic
125	C₂×C₄₇	#1811	1	1	yes	characteristic
126	C₂×C₄₇	#1814	1	1	yes	characteristic
127	C₂×C₄×Q₈	—	47	1	no	—
128	#446	—	47	2	no	—
129	#446	—	47	2	no	—
130	#446	—	94	1	no	—
131	#446	—	94	1	no	—
132	#431	—	47	2	no	—
133	#423	C₂×D₄₇	1	2	yes	—
134	C₂×C₄⋊C₈	—	47	1	no	—
135	C₂×C₄⋊C₈	—	94	1	no	—
136	C₂×#97	—	94	1	no	—
137	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
138	#341	—	2	1	no	—
139	#341	—	2	1	no	—
140	#335	—	94	1	no	—
141	#334	—	94	1	no	—
142	Q₈⋊C₈	—	94	4	no	—
143	C₄₇	#8665	1	1	yes	characteristic, complemented, Sylow
144	C₂²×Q₈	—	47	1	no	—
145	C₂×M₁₆	—	2	2	no	—
146	C₂²×C₈	—	94	1	no	—
147	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
148	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
149	C₄×Q₈	—	47	2	no	—
150	C₄×Q₈	—	47	2	no	—
151	C₄×Q₈	—	94	1	no	—
152	C₄×Q₈	—	94	1	no	—
153	C₂×C₄⋊C₄	—	47	1	no	—
154	C₂×C₄⋊C₄	—	94	1	no	—
155	C₂×C₄²	—	94	1	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	—	47	2	no	—
160	C₄⋊C₈	—	94	2	no	—
161	C₄⋊C₈	—	94	2	no	—
162	C₄⋊C₈	—	94	1	no	—
163	C₄⋊C₈	—	94	2	no	—
164	C₂²⋊C₈	—	94	2	no	—
165	#97	—	94	2	no	—
166	#97	—	94	2	no	—
167	C₄×C₈	—	94	2	no	—
168	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
169	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
170	C₄×C₈	D₁₈₈	1	1	yes	characteristic
171	C₄×C₈	D₁₈₈	1	1	yes	characteristic
172	C₂×Q₈	—	47	2	no	—
173	C₂×Q₈	—	94	1	no	—
174	C₂×Q₈	—	188	2	no	—
175	C₂²×C₄	—	94	1	no	—
176	C₂²×C₄	—	94	1	no	—
177	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
178	C₂²×C₄	#10625354	1	1	yes	characteristic
179	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
180	M₁₆	—	4	2	no	—
181	M₁₆	—	4	2	no	—
182	C₂×C₈	—	2	2	no	—
183	C₂×C₈	—	2	2	no	—
184	C₂×C₈	—	4	2	no	—
185	C₂×C₈	—	94	2	no	—
186	C₂×C₈	—	188	2	no	—
187	C₂×C₈	—	188	2	no	—
188	C₂×C₈	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
189	C₂×C₈	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
190	C₂×C₈	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
191	C₂×C₈	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
192	C₄⋊C₄	—	47	2	no	—
193	C₄⋊C₄	—	94	2	no	—
194	C₄⋊C₄	—	94	2	no	—
195	C₄⋊C₄	—	94	1	no	—
196	C₄²	—	94	2	no	—
197	C₄²	—	94	2	no	—
198	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
199	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
200	C₄²	D₄×D₄₇	1	1	yes	characteristic
201	C₄²	#10625352	1	1	yes	characteristic
202	C₂³	#13094000	1	1	yes	characteristic
203	Q₈	—	94	4	no	—
204	Q₈	—	188	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	94	2	no	—
208	C₂×C₄	—	94	2	no	—
209	C₂×C₄	—	188	2	no	—
210	C₂×C₄	—	188	2	no	—
211	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
212	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
213	C₂×C₄	#13093982	1	1	yes	characteristic
214	C₂×C₄	#13093995	1	1	yes	characteristic
215	C₂×C₄	#13093999	1	1	yes	characteristic
216	C₂×C₄	#13094004	1	1	yes	characteristic
217	C₂×C₄	#13094044	1	2	yes	—
218	C₂×C₄	#13094054	1	2	yes	—
219	C₈	—	2	1	no	—
220	C₈	—	2	1	no	—
221	C₈	—	2	1	no	—
222	C₈	—	2	1	no	—
223	C₈	—	8	2	no	—
224	C₈	—	376	2	no	—
225	C₈	—	188	2	no	—
226	C₂²	—	2	1	no	—
227	C₂²	—	2	1	no	—
228	C₂²	#15688980	1	1	yes	characteristic
229	C₂²	#15689427	1	2	yes	—
230	C₄	—	2	1	no	—
231	C₄	—	2	1	no	—
232	C₄	—	2	1	no	—
233	C₄	—	188	2	no	—
234	C₄	—	188	2	no	—
235	C₄	#15689117	1	1	yes	characteristic
236	C₄	#15689131	1	1	yes	characteristic
237	C₄	#15689170	1	2	yes	—
238	C₄	#15689342	1	2	yes	—
239	C₂	—	2	2	no	—
240	C₂	#20243400	1	1	yes	characteristic
241	C₂	#20243427	1	1	yes	characteristic
242	C₂	#20243443	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#15689253

C₂

yes

maximal, characteristic

#20242136

C₂

yes

maximal, characteristic

#20241816

C₂

yes

maximal

#20241283

C₂

yes

maximal

C₄₇×#1837

C₂

yes

maximal, characteristic

C₂×C₄×Dic₉₄

C₂²

yes

—

—

C₄

yes

—

#15689253

C₄

yes

—

#15689176

C₂²

yes

—

C₂×C₄⋊(C₄₇⋊C₈)

C₂²

yes

characteristic

C₂×Dic₄₇⋊C₈

—

—

—

—

—

C₄₇×#423

C₂²

yes

—

C₂×C₄×C₈×C₄₇

C₂²

yes

characteristic

C₄₇×#341

—

C₄₇×#341

—

C₂²×Dic₉₄

Q₈

yes

characteristic

C₂²×C₄₇⋊C₈

—

C₄×Dic₉₄

—

C₄×Dic₉₄

—

C₄×Dic₉₄

C₂×C₄

yes

—

C₄×Dic₉₄

D₄

yes

—

C₂×C₄⋊Dic₄₇

Q₈

yes

characteristic

C₂×Dic₄₇⋊C₄

—

C₂×C₄×Dic₄₇

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

C₂×C₄

yes

—

Dic₄₇⋊C₈

—

Dic₄₇⋊C₈

—

C₂²⋊(C₄₇⋊C₈)

—

#13093934

—

#13093934

—

C₄×C₄₇⋊C₈

—

C₂×M₁₆×C₄₇

—

C₂²×C₈×C₄₇

D₄

yes

characteristic

C₂²×C₈×C₄₇

D₄

yes

characteristic

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₄⋊C₈×C₄₇

—

C₄×C₈×C₄₇

C₂×C₄

yes

characteristic

C₄×C₈×C₄₇

C₂×C₄

yes

characteristic

C₄×C₈×C₄₇

D₄

yes

characteristic

C₄×C₈×C₄₇

D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×Q₈

yes

characteristic

C₂²×C₄×C₄₇

#41

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

C₄⋊C₄

yes

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₇

C₂²⋊C₄

yes

characteristic

C₄²×C₄₇

C₂²×C₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₄²×C₄₇

#41

yes

characteristic

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

C₄⋊C₄

yes

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×C₄⋊C₄

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₄₇

#135

yes

—

C₂×C₄×C₄₇

#137

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

—

C₈×C₄₇

—

100

C₈×C₄₇

—

101

C₈×C₄₇

—

102

C₄₇⋊C₈

—

103

C₄₇⋊C₈

—

104

#8665

—

maximal, Sylow

105

C₂²×C₄₇

—

106

C₂²×C₄₇

—

107

C₂²×C₄₇

#380

yes

characteristic

108

C₂²×C₄₇

#479

yes

—

109

C₄×C₄₇

—

110

C₄×C₄₇

—

111

C₄×C₄₇

—

112

C₄×C₄₇

#416

yes

characteristic

113

C₄×C₄₇

#419

yes

characteristic

114

C₄×C₄₇

#430

yes

—

115

C₄×C₄₇

#464

yes

—

116

Dic₄₇

—

117

Dic₄₇

—

118

C₂×#446

—

119

#1837

D₄₇

yes

characteristic

120

#1564

—

121

#1487

—

122

#1301

—

123

C₂×C₄₇

—

124

C₂×C₄₇

#1805

yes

characteristic

125

C₂×C₄₇

#1811

yes

characteristic

126

C₂×C₄₇

#1814

yes

characteristic

127

C₂×C₄×Q₈

—

128

#446

—

129

#446

—

130

#446

—

131

#446

—

132

#431

—

133

#423

C₂×D₄₇

yes

—

134

C₂×C₄⋊C₈

—

135

C₂×C₄⋊C₈

—

136

C₂×#97

—

137

C₂×C₄×C₈

C₂×D₄₇

yes

characteristic

138

#341

—

139

#341

—

140

#335

—

141

#334

—

142

Q₈⋊C₈

—

143

C₄₇

#8665

yes

characteristic, complemented, Sylow

144

C₂²×Q₈

—

145

C₂×M₁₆

—

146

C₂²×C₈

—

147

C₂²×C₈

C₂²⋊D₄₇

yes

characteristic

148

C₂²×C₈

C₂²⋊D₄₇

yes

characteristic

149

C₄×Q₈

—

150

C₄×Q₈

—

151

C₄×Q₈

—

152

C₄×Q₈

—

153

C₂×C₄⋊C₄

—

154

C₂×C₄⋊C₄

—

155

C₂×C₄²

—

156

C₂×C₄²

C₂²×D₄₇

yes

characteristic

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₄⋊C₈

—

161

C₄⋊C₈

—

162

C₄⋊C₈

—

163

C₄⋊C₈

—

164

C₂²⋊C₈

—

165

#97

—

166

#97

—

167

C₄×C₈

—

168

C₄×C₈

C₄×D₄₇

yes

characteristic

169

C₄×C₈

C₄×D₄₇

yes

characteristic

170

C₄×C₈

D₁₈₈

yes

characteristic

171

C₄×C₈

D₁₈₈

yes

characteristic

172

C₂×Q₈

—

173

C₂×Q₈

—

174

C₂×Q₈

—

188

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

Q₈×D₄₇

yes

characteristic

178

C₂²×C₄

#10625354

yes

characteristic

179

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

180

M₁₆

—

181

M₁₆

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

188

—

187

C₂×C₈

—

188

—

188

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

characteristic

189

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

characteristic

190

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

characteristic

191

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

characteristic

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄²

—

197

C₄²

—

198

C₄²

C₂×C₄×D₄₇

yes

characteristic

199

C₄²

C₂×D₁₈₈

yes

characteristic

200

C₄²

D₄×D₄₇

yes

characteristic

201

C₄²

#10625352

yes

characteristic

202

C₂³

#13094000

yes

characteristic

203

Q₈

—

204

Q₈

—

188

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

188

—

210

C₂×C₄

—

188

—

211

C₂×C₄

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

212

C₂×C₄

C₄⋊C₄×D₄₇

yes

characteristic

213

C₂×C₄

#13093982

yes

characteristic

214

C₂×C₄

#13093995

yes

characteristic

215

C₂×C₄

#13093999

yes

characteristic

216

C₂×C₄

#13094004

yes

characteristic

217

C₂×C₄

#13094044

yes

—

218

C₂×C₄

#13094054

yes

—

219

C₈

—

220

C₈

—

221

C₈

—

222

C₈

—

223

C₈

—

224

C₈

—

376

—

225

C₈

—

188

—

226

C₂²

—

227

C₂²

—

228

C₂²

#15688980

yes

characteristic

229

C₂²

#15689427

yes

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

188

—

234

C₄

—

188

—

235

C₄

#15689117

yes

characteristic

236

C₄

#15689131

yes

characteristic

237

C₄

#15689170

yes

—

238

C₄

#15689342

yes

—

239

C₂

—

240

C₂

#20243400

yes

characteristic

241

C₂

#20243427

yes

characteristic

242

C₂

#20243443

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#13093995
commutator	C₄²×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1837	C₂
socle	C₂²×C₄₇	#380
prime radical	C₂³×C₄₇	C₂²⋊Q₈
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1837	D₄₇
hypocenter	C₄₇	#8665
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1837

subgroup

G/H

center

C₂×C₄

#13093995

commutator

C₄²×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#1837

C₂

socle

C₂²×C₄₇

#380

prime radical

C₂³×C₄₇

C₂²⋊Q₈

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1837

N	H ≅ G/N	type
143. C₄₇	#8665	semidirect

H ≅ G/N

type

143. C₄₇

#8665

semidirect

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

subgroup	index
C₂×#15689253	2
#20242136	2
#20241816	2
#20241283	2
C₄₇×#1837	2
#8665	47

subgroup

index

C₄₇×#1837

Subgroups — #26109434

Conjugacy classes of subgroups

Complements

Maximal subgroups