Group #25001588 — subgroups

Subgroups — #25001588

Order 11008.

320 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 95 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	#19135536	C₂	1	1	yes	maximal, characteristic
2	#19134769	C₂	1	1	yes	maximal, characteristic
3	#19133367	C₂	1	1	yes	maximal, characteristic
4	#19133366	C₂	1	1	yes	maximal, characteristic
5	#19133024	C₂	1	1	yes	maximal, characteristic
6	#19132425	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#1487	C₂	1	1	yes	maximal, characteristic
8	#14582952	C₂²	1	1	yes	characteristic
9	C₂×#13063260	—	2	2	no	—
10	#14582923	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×#13063236	C₂²	1	1	yes	characteristic
13	#14582654	—	2	2	no	—
14	#14582650	—	2	2	no	—
15	#14582649	—	2	2	no	—
16	Q₈⋊(C₄₃⋊C₈)	—	2	2	no	—
17	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
18	C₄₃×#431	C₂²	1	1	yes	characteristic
19	C₄₃×#423	C₂²	1	1	yes	characteristic
20	C₄₃×Q₈⋊C₈	—	2	2	no	—
21	C₂×#10621877	—	2	1	no	—
22	C₂²×C₄₃⋊C₈	—	2	1	no	—
23	C₂²×C₄₃⋊C₈	D₄	1	2	yes	—
24	#13063260	—	4	4	no	—
25	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
26	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
27	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
28	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
29	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
30	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
31	#13063236	—	2	1	no	—
32	#13063236	—	2	1	no	—
33	C₄×C₄₃⋊C₈	D₄	1	2	yes	—
34	C₂²×Q₈×C₄₃	Q₈	1	1	yes	characteristic
35	C₂×M₁₆×C₄₃	—	2	1	no	—
36	C₄×Q₈×C₄₃	—	2	1	no	—
37	C₄×Q₈×C₄₃	—	2	1	no	—
38	C₄×Q₈×C₄₃	—	2	1	no	—
39	C₄×Q₈×C₄₃	—	2	1	no	—
40	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
41	C₂×C₄⋊C₄×C₄₃	Q₈	1	1	yes	characteristic
42	C₂×C₄²×C₄₃	—	2	1	no	—
43	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
44	C₄⋊C₈×C₄₃	—	2	1	no	—
45	C₄⋊C₈×C₄₃	—	2	1	no	—
46	C₄⋊C₈×C₄₃	—	2	1	no	—
47	C₂²⋊C₈×C₄₃	—	2	1	no	—
48	C₄×C₈×C₄₃	D₄	1	2	yes	—
49	C₂×Q₈×C₄₃	—	2	1	no	—
50	C₂×Q₈×C₄₃	—	2	1	no	—
51	C₂×Q₈×C₄₃	—	4	2	no	—
52	C₂²×C₄×C₄₃	—	2	1	no	—
53	C₂²×C₄×C₄₃	—	2	1	no	—
54	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
56	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
57	M₁₆×C₄₃	—	4	2	no	—
58	C₂×C₈×C₄₃	—	2	2	no	—
59	C₂×C₈×C₄₃	—	4	1	no	—
60	C₄⋊C₄×C₄₃	—	2	1	no	—
61	C₄⋊C₄×C₄₃	—	2	1	no	—
62	C₄⋊C₄×C₄₃	—	4	1	no	—
63	C₄⋊C₄×C₄₃	—	4	1	no	—
64	C₄²×C₄₃	—	4	1	no	—
65	C₄²×C₄₃	—	4	1	no	—
66	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
67	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
68	C₄²×C₄₃	#41	1	1	yes	characteristic
69	C₄²×C₄₃	#41	1	1	yes	characteristic
70	#10621877	—	4	2	no	—
71	C₂×C₄₃⋊C₈	—	2	2	no	—
72	C₂×C₄₃⋊C₈	—	2	2	no	—
73	C₂×C₄₃⋊C₈	—	2	2	no	—
74	C₂×C₄₃⋊C₈	—	4	1	no	—
75	C₂×C₄₃⋊C₈	—	4	1	no	—
76	C₂×C₄₃⋊C₈	—	4	2	no	—
77	C₂×C₄₃⋊C₈	SD₁₆	1	4	yes	—
78	C₂³×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
79	Q₈×C₄₃	—	2	2	no	—
80	Q₈×C₄₃	—	2	2	no	—
81	Q₈×C₄₃	—	4	1	no	—
82	Q₈×C₄₃	—	4	1	no	—
83	C₂×C₄×C₄₃	—	2	2	no	—
84	C₂×C₄×C₄₃	—	4	1	no	—
85	C₂×C₄×C₄₃	—	4	1	no	—
86	C₂×C₄×C₄₃	—	4	1	no	—
87	C₂×C₄×C₄₃	—	4	1	no	—
88	C₂×C₄×C₄₃	—	4	2	no	—
89	C₂×C₄×C₄₃	—	4	1	no	—
90	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
91	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
92	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
93	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
94	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
95	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
96	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
97	C₂×C₄×C₄₃	#137	1	2	yes	—
98	C₈×C₄₃	—	4	2	no	—
99	C₈×C₄₃	—	8	1	no	—
100	C₄₃⋊C₈	—	2	4	no	—
101	C₄₃⋊C₈	—	4	2	no	—
102	C₄₃⋊C₈	—	8	1	no	—
103	C₄₃⋊C₈	—	8	1	no	—
104	#10663	—	43	1	no	maximal, Sylow
105	C₂²×C₄₃	—	2	1	no	—
106	C₂²×C₄₃	—	2	1	no	—
107	C₂²×C₄₃	#399	1	1	yes	characteristic
108	C₂²×C₄₃	#475	1	2	yes	—
109	C₄×C₄₃	—	2	1	no	—
110	C₄×C₄₃	—	2	1	no	—
111	C₄×C₄₃	—	2	1	no	—
112	C₄×C₄₃	—	2	1	no	—
113	C₄×C₄₃	—	4	2	no	—
114	C₄×C₄₃	—	8	1	no	—
115	C₄×C₄₃	#483	1	2	yes	—
116	C₄×C₄₃	#492	1	1	yes	characteristic
117	C₄×C₄₃	#497	1	1	yes	characteristic
118	#1985	—	43	1	no	—
119	#1849	—	43	1	no	—
120	#1570	—	43	1	no	—
121	#1570	—	43	1	no	—
122	#1487	—	43	1	no	—
123	#1487	D₄₃	1	1	yes	characteristic
124	#1275	—	43	1	no	—
125	C₂×C₄₃	—	2	2	no	—
126	C₂×C₄₃	#2091	1	1	yes	characteristic
127	C₂×C₄₃	#2096	1	1	yes	characteristic
128	C₂×C₄₃	#2098	1	1	yes	characteristic
129	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
130	#431	—	43	1	no	—
131	#431	C₂×D₄₃	1	1	yes	characteristic
132	C₂×#108	—	86	2	no	—
133	#423	—	43	1	no	—
134	#423	C₂×D₄₃	1	1	yes	characteristic
135	C₂×C₄⋊C₈	—	43	1	no	—
136	C₂×#97	—	43	1	no	—
137	#336	—	86	2	no	—
138	#334	—	86	2	no	—
139	#334	—	86	2	no	—
140	Q₈⋊C₈	—	2	2	no	—
141	Q₈⋊C₈	—	86	2	no	—
142	C₄₃	#10663	1	1	yes	characteristic, complemented, Sylow
143	C₂²×Q₈	Dic₈₆	1	1	yes	characteristic
144	C₂×M₁₆	—	2	1	no	—
145	C₂×M₁₆	—	86	1	no	—
146	C₂²×C₈	—	43	2	no	—
147	C₂²×C₈	—	86	1	no	—
148	C₄×Q₈	—	2	1	no	—
149	C₄×Q₈	—	2	1	no	—
150	C₄×Q₈	—	2	1	no	—
151	C₄×Q₈	—	2	1	no	—
152	C₂×C₄⋊C₄	—	2	1	no	—
153	C₂×C₄⋊C₄	Dic₈₆	1	1	yes	characteristic
154	C₂×C₄²	—	2	1	no	—
155	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
156	#108	—	172	4	no	—
157	C₄⋊C₈	—	2	1	no	—
158	C₄⋊C₈	—	2	1	no	—
159	C₄⋊C₈	—	2	1	no	—
160	C₄⋊C₈	—	86	1	no	—
161	C₄⋊C₈	—	86	1	no	—
162	C₄⋊C₈	—	86	1	no	—
163	C₄⋊C₈	—	86	1	no	—
164	C₄⋊C₈	—	86	1	no	—
165	C₂²⋊C₈	—	2	1	no	—
166	C₂²⋊C₈	—	86	1	no	—
167	#97	—	86	1	no	—
168	#97	—	86	1	no	—
169	C₄×C₈	—	43	2	no	—
170	C₄×C₈	C₂²⋊D₄₃	1	2	yes	—
171	C₂×Q₈	—	2	1	no	—
172	C₂×Q₈	—	2	1	no	—
173	C₂×Q₈	—	4	2	no	—
174	C₂²×C₄	—	2	1	no	—
175	C₂²×C₄	—	2	1	no	—
176	C₂²×C₄	C₂×Dic₈₆	1	1	yes	characteristic
177	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
178	C₂²×C₄	#10621900	1	1	yes	characteristic
179	M₁₆	—	4	2	no	—
180	M₁₆	—	172	2	no	—
181	C₂×C₈	—	2	2	no	—
182	C₂×C₈	—	4	1	no	—
183	C₂×C₈	—	43	4	no	—
184	C₂×C₈	—	86	2	no	—
185	C₂×C₈	—	86	2	no	—
186	C₂×C₈	—	86	2	no	—
187	C₂×C₈	—	172	1	no	—
188	C₂×C₈	—	172	1	no	—
189	C₂×C₈	—	172	2	no	—
190	C₄⋊C₄	—	2	1	no	—
191	C₄⋊C₄	—	2	1	no	—
192	C₄⋊C₄	—	4	1	no	—
193	C₄⋊C₄	—	4	1	no	—
194	C₄²	—	4	1	no	—
195	C₄²	—	4	1	no	—
196	C₄²	#10621898	1	1	yes	characteristic
197	C₄²	D₄×D₄₃	1	1	yes	characteristic
198	C₄²	#10621900	1	1	yes	characteristic
199	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
200	C₂³	#13063302	1	1	yes	characteristic
201	Q₈	—	2	2	no	—
202	Q₈	—	2	2	no	—
203	Q₈	—	4	1	no	—
204	Q₈	—	4	1	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	4	1	no	—
208	C₂×C₄	—	4	1	no	—
209	C₂×C₄	—	4	1	no	—
210	C₂×C₄	—	4	2	no	—
211	C₂×C₄	—	4	1	no	—
212	C₂×C₄	#13063302	1	1	yes	characteristic
213	C₂×C₄	#13063304	1	1	yes	characteristic
214	C₂×C₄	#13063306	1	1	yes	characteristic
215	C₂×C₄	#13063307	1	1	yes	characteristic
216	C₂×C₄	#13063307	1	1	yes	characteristic
217	C₂×C₄	#13063321	1	1	yes	characteristic
218	C₂×C₄	SD₁₆×D₄₃	1	2	yes	—
219	C₂×C₄	#13063357	1	2	yes	—
220	C₈	—	4	2	no	—
221	C₈	—	8	1	no	—
222	C₈	—	86	4	no	—
223	C₈	—	344	1	no	—
224	C₈	—	344	1	no	—
225	C₈	—	172	2	no	—
226	C₂²	—	2	1	no	—
227	C₂²	—	2	1	no	—
228	C₂²	#14582835	1	1	yes	characteristic
229	C₂²	#14583182	1	2	yes	—
230	C₄	—	2	1	no	—
231	C₄	—	2	1	no	—
232	C₄	—	2	1	no	—
233	C₄	—	2	1	no	—
234	C₄	—	4	2	no	—
235	C₄	—	8	1	no	—
236	C₄	#14583228	1	2	yes	—
237	C₄	#14583270	1	1	yes	characteristic
238	C₄	#14583292	1	1	yes	characteristic
239	C₂	—	2	2	no	—
240	C₂	#19136111	1	1	yes	characteristic
241	C₂	#19136136	1	1	yes	characteristic
242	C₂	#19136150	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19135536

C₂

yes

maximal, characteristic

#19134769

C₂

yes

maximal, characteristic

#19133367

C₂

yes

maximal, characteristic

#19133366

C₂

yes

maximal, characteristic

#19133024

C₂

yes

maximal, characteristic

#19132425

C₂

yes

maximal, characteristic

C₄₃×#1487

C₂

yes

maximal, characteristic

#14582952

C₂²

yes

characteristic

C₂×#13063260

—

#14582923

C₂²

yes

characteristic

C₂×C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

C₂×#13063236

C₂²

yes

—

—

—

Q₈⋊(C₄₃⋊C₈)

—

C₂×C₄×Q₈×C₄₃

C₂²

yes

characteristic

C₄₃×#431

C₂²

yes

characteristic

C₄₃×#423

C₂²

yes

characteristic

C₄₃×Q₈⋊C₈

—

C₂×#10621877

—

C₂²×C₄₃⋊C₈

—

C₂²×C₄₃⋊C₈

D₄

yes

—

#13063260

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

C₂²⋊(C₄₃⋊C₈)

—

#13063236

—

#13063236

—

C₄×C₄₃⋊C₈

D₄

yes

—

C₂²×Q₈×C₄₃

Q₈

yes

characteristic

C₂×M₁₆×C₄₃

—

C₄×Q₈×C₄₃

—

C₄×Q₈×C₄₃

—

C₄×Q₈×C₄₃

—

C₄×Q₈×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

Q₈

yes

characteristic

C₂×C₄²×C₄₃

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₄⋊C₈×C₄₃

—

C₄⋊C₈×C₄₃

—

C₂²⋊C₈×C₄₃

—

C₄×C₈×C₄₃

D₄

yes

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×Q₈

yes

characteristic

C₂²×C₄×C₄₃

#41

yes

characteristic

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂×D₄

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

C₄²×C₄₃

yes

C₄²×C₄₃

yes

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

SD₁₆

yes

—

C₂³×C₄₃

C₂²⋊Q₈

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₄₃

C₂²⋊Q₈

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

C₂×SD₁₆

yes

—

C₂×C₄×C₄₃

#137

yes

—

C₈×C₄₃

—

C₈×C₄₃

—

100

C₄₃⋊C₈

—

101

C₄₃⋊C₈

—

102

C₄₃⋊C₈

—

103

C₄₃⋊C₈

—

104

#10663

—

maximal, Sylow

105

C₂²×C₄₃

—

106

C₂²×C₄₃

—

107

C₂²×C₄₃

#399

yes

characteristic

108

C₂²×C₄₃

#475

yes

—

109

C₄×C₄₃

—

110

C₄×C₄₃

—

111

C₄×C₄₃

—

112

C₄×C₄₃

—

113

C₄×C₄₃

—

114

C₄×C₄₃

—

115

C₄×C₄₃

#483

yes

—

116

C₄×C₄₃

#492

yes

characteristic

117

C₄×C₄₃

#497

yes

characteristic

118

#1985

—

119

#1849

—

120

#1570

—

121

#1570

—

122

#1487

—

123

#1487

D₄₃

yes

characteristic

124

#1275

—

125

C₂×C₄₃

—

126

C₂×C₄₃

#2091

yes

characteristic

127

C₂×C₄₃

#2096

yes

characteristic

128

C₂×C₄₃

#2098

yes

characteristic

129

C₂×C₄×Q₈

C₂×D₄₃

yes

characteristic

130

#431

—

131

#431

C₂×D₄₃

yes

characteristic

132

C₂×#108

—

133

#423

—

134

#423

C₂×D₄₃

yes

characteristic

135

C₂×C₄⋊C₈

—

136

C₂×#97

—

137

#336

—

138

#334

—

139

#334

—

140

Q₈⋊C₈

—

141

Q₈⋊C₈

—

142

C₄₃

#10663

yes

characteristic, complemented, Sylow

143

C₂²×Q₈

Dic₈₆

yes

characteristic

144

C₂×M₁₆

—

145

C₂×M₁₆

—

146

C₂²×C₈

—

147

C₂²×C₈

—

148

C₄×Q₈

—

149

C₄×Q₈

—

150

C₄×Q₈

—

151

C₄×Q₈

—

152

C₂×C₄⋊C₄

—

153

C₂×C₄⋊C₄

Dic₈₆

yes

characteristic

154

C₂×C₄²

—

155

C₂×C₄²

C₂²×D₄₃

yes

characteristic

156

#108

—

172

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₄⋊C₈

—

161

C₄⋊C₈

—

162

C₄⋊C₈

—

163

C₄⋊C₈

—

164

C₄⋊C₈

—

165

C₂²⋊C₈

—

166

C₂²⋊C₈

—

167

#97

—

168

#97

—

169

C₄×C₈

—

170

C₄×C₈

C₂²⋊D₄₃

yes

—

171

C₂×Q₈

—

172

C₂×Q₈

—

173

C₂×Q₈

—

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

C₂×Dic₈₆

yes

characteristic

177

C₂²×C₄

D₄×D₄₃

yes

characteristic

178

C₂²×C₄

#10621900

yes

characteristic

179

M₁₆

—

180

M₁₆

—

172

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

187

C₂×C₈

—

172

—

188

C₂×C₈

—

172

—

189

C₂×C₈

—

172

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄²

—

195

C₄²

—

196

C₄²

#10621898

yes

characteristic

197

C₄²

D₄×D₄₃

yes

characteristic

198

C₄²

#10621900

yes

characteristic

199

C₄²

C₂×C₂²⋊D₄₃

yes

characteristic

200

C₂³

#13063302

yes

characteristic

201

Q₈

—

202

Q₈

—

203

Q₈

—

204

Q₈

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

#13063302

yes

characteristic

213

C₂×C₄

#13063304

yes

characteristic

214

C₂×C₄

#13063306

yes

characteristic

215

C₂×C₄

#13063307

yes

characteristic

216

C₂×C₄

#13063307

yes

characteristic

217

C₂×C₄

#13063321

yes

characteristic

218

C₂×C₄

SD₁₆×D₄₃

yes

—

219

C₂×C₄

#13063357

yes

—

220

C₈

—

221

C₈

—

222

C₈

—

223

C₈

—

344

—

224

C₈

—

344

—

225

C₈

—

172

—

226

C₂²

—

227

C₂²

—

228

C₂²

#14582835

yes

characteristic

229

C₂²

#14583182

yes

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

#14583228

yes

—

237

C₄

#14583270

yes

characteristic

238

C₄

#14583292

yes

characteristic

239

C₂

—

240

C₂

#19136111

yes

characteristic

241

C₂

#19136136

yes

characteristic

242

C₂

#19136150

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#13063321
commutator, cosocle	C₂×C₄²×C₄₃	C₂³
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1487	C₂
socle	C₂²×C₄₃	#399
prime radical	C₂³×C₄₃	C₂²⋊Q₈
hypercenter	#1487	D₄₃
hypocenter	C₄₃	#10663
LCS	G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1487

subgroup

G/H

center

C₂×C₄

#13063321

commutator, cosocle

C₂×C₄²×C₄₃

C₂³

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1487

C₂

socle

C₂²×C₄₃

#399

prime radical

C₂³×C₄₃

C₂²⋊Q₈

D₄₃

C₄₃

G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1487

N	H ≅ G/N	type
142. C₄₃	#10663	semidirect

H ≅ G/N

type

142. C₄₃

#10663

semidirect

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

subgroup	index
#19135536	2
#19134769	2
#19133367	2
#19133366	2
#19133024	2
#19132425	2
C₄₃×#1487	2
#10663	43

subgroup

index

C₄₃×#1487

Subgroups — #25001588

Conjugacy classes of subgroups

Complements

Maximal subgroups