Finite Group Databasebeta

← #22598432

Subgroups — #22598432

Order 9088.

488 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17986549C211yesmaximal, characteristic, complemented
2C2×C4×D284C211yesmaximal, characteristic, complemented
3#17986318C212yesmaximal, complemented
4#17986290C212yesmaximal, complemented
5#17986195C212yesmaximal, complemented
6#17986135C212yesmaximal, complemented
7#17986112C214yesmaximal, complemented
8#432×C71C211yesmaximal, characteristic, complemented
9C2×#11765865—21no—
10C22×D284C2211yescharacteristic
11C22×C4×D71—21no—
12C2×D568C2214yes—
13#14556128C2211yescharacteristic, complemented
14#14556125C2211yescharacteristic, complemented
15#14556116—21no—
16#14556102—21no—
17#14556102C2212yes—
18C4×D284—21no—
19C4×D284—21no—
20C4×D284—21no—
21C4×D284C2212yes—
22C4×D284C2212yes—
23C4×D284C2212yescomplemented
24C2×C4⋊Dic71C2211yescharacteristic
25C2×(C2×D71)⋊C4—21no—
26#14556060C2214yescomplemented
27#14556050C2214yes—
28#14556050C2214yescomplemented
29C2×C42×C71C2211yescharacteristic
30C4⋊C8×C71C2212yescomplemented
31C22⋊C8×C71C2212yes—
32#97×C71C2212yescomplemented
33C23×D71—21no—
34#11765865—44no—
35C2×Dic142—21no—
36C2×D284—21no—
37C2×D284—24no—
38C2×D284—21no—
39C2×D284—21no—
40C2×D284C2312yes—
41C2×D284C2312yes—
42C2×C22⋊D71—22no—
43C22×Dic71—21no—
44C2×C4×D71—22no—
45C2×C4×D71—22no—
46C2×C4×D71—22no—
47C2×C4×D71—44no—
48D568—28no—
49C4⋊Dic71—21no—
50C4⋊Dic71—21no—
51C4⋊Dic71C2312yes—
52C4⋊Dic71C2312yes—
53(C2×D71)⋊C4—22no—
54(C2×D71)⋊C4—22no—
55(C2×D71)⋊C4—22no—
56(C2×D71)⋊C4—22no—
57C22×C4×C71D411yescharacteristic
58C22×C4×C71D411yescharacteristic
59C22×C4×C71C2311yescharacteristic
60C2×C8×C71C2314yes—
61C42×C71D411yescharacteristic
62C42×C71D411yescharacteristic
63C42×C71C2311yescharacteristic
64C42×C71C2311yescharacteristic
65C23×C71C2×D411yescharacteristic
66C22×D71—24no—
67C22×D71—22no—
68C22×D71—22no—
69C22×D71—42no—
70C22×D71—42no—
71C2×C4×C71—22no—
72C2×C4×C71—22no—
73C2×C4×C71—22no—
74C2×C4×C71C2×D411yescharacteristic
75C2×C4×C71C2×D411yescharacteristic
76C2×C4×C71C2×D411yescharacteristic
77C2×C4×C71C2×D411yescharacteristic
78C2×C4×C71C2×D411yescharacteristic
79C2×C4×C71C2411yescharacteristic
80C22⋊D71—44no—
81C2×Dic71—22no—
82C2×Dic71—22no—
83C2×Dic71—42no—
84D284—24no—
85D284—22no—
86D284—24no—
87D284—42no—
88D284—42no—
89D284#4114yescomplemented
90C4×D71—44no—
91C4×D71—44no—
92C4×D71—44no—
93Dic142—42no—
94C8×C71—24no—
95C22×C71—21no—
96C22×C71—21no—
97C22×C71AGL(1,ℤ/8)12yes—
98C22×C71C22×D411yescharacteristic
99C2×D71—24no—
100C2×D71—48no—
101C2×D71—42no—
102C2×D71—42no—
103C2×D71—42no—
104C2×D71—42no—
105C2×D71—42no—
106C4×C71—21no—
107C4×C71—21no—
108C4×C71—21no—
109C4×C71—21no—
110C4×C71AGL(1,ℤ/8)12yes—
111C4×C71C2×#4112yes—
112Dic71—42no—
113Dic71—42no—
114C2×C71—22no—
115C2×C71#52511yescharacteristic
116C2×C71C2×AGL(1,ℤ/8)11yescharacteristic
117C2×C71C2×AGL(1,ℤ/8)11yescharacteristic
118D71—44no—
119D71—82no—
120#3109—711nomaximal, Sylow
121C71#310911yescharacteristic, complemented, Sylow
122#532—711no—
123C2×C4×D4—711no—
124#481—712no—
125#476—712no—
126#459—712no—
127#447—712no—
128#442—714no—
129#432D7111yescharacteristic, complemented
130C2×#41—1421no—
131C22×D4—711no—
132C23×C4—1421no—
133C2×D8—714no—
134C4⋊Q8—711no—
135#127—711no—
136#124—1421no—
137#121—712no—
138#121—1421no—
139C4×D4—712no—
140C4×D4—712no—
141C4×D4—712no—
142C4×D4—1421no—
143C4×D4—1421no—
144C4×D4—1421no—
145C2×C4⋊C4—711no—
146C2×C22⋊C4—1421no—
147C2×C42C2×D7111yescharacteristic
148#106—714no—
149C4⋊C8C2×D7112yescomplemented
150#102—714no—
151#102—714no—
152C22⋊C8C2×D7112yes—
153#97C2×D7112yescomplemented
154C24—1421no—
155#41—2844no—
156C2×Q8—1421no—
157C2×D4—712no—
158C2×D4—712no—
159C2×D4—1424no—
160C2×D4—1422no—
161C2×D4—1421no—
162C2×D4—1421no—
163C2×D4—1421no—
164C22×C4—2844no—
165C22×C4—1421no—
166C22×C4—1422no—
167C22×C4—1422no—
168C22×C4—1422no—
169C22×C4D28411yescharacteristic
170C22×C4D28411yescharacteristic
171C22×C4C22×D7111yescharacteristic
172D8—1428no—
173C2×C8C22×D7114yes—
174C4⋊C4—712no—
175C4⋊C4—712no—
176C4⋊C4—1421no—
177C4⋊C4—1421no—
178C22⋊C4—1422no—
179C22⋊C4—1422no—
180C22⋊C4—1422no—
181C22⋊C4—1422no—
182C42D28411yescharacteristic
183C42D28411yescharacteristic
184C42C22×D7111yescharacteristic
185C42C22×D7111yescharacteristic
186C23—2842no—
187C23—2842no—
188C23—1424no—
189C23—1422no—
190C23—1422no—
191C23C2×D28411yescharacteristic
192Q8—2842no—
193D4—2842no—
194D4—2844no—
195D4—2842no—
196D4—714no—
197D4—1424no—
198D4—1424no—
199D4—1422no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—2844no—
204C2×C4—2844no—
205C2×C4—2842no—
206C2×C4—2844no—
207C2×C4—1422no—
208C2×C4—1422no—
209C2×C4C2×D28411yescharacteristic
210C2×C4C2×D28411yescharacteristic
211C2×C4C2×D28411yescharacteristic
212C2×C4C2×D28411yescharacteristic
213C2×C4C2×D28411yescharacteristic
214C2×C4C23×D7111yescharacteristic
215C8—24no—
216C22—21no—
217C22—21no—
218C22—2848no—
219C22—2842no—
220C22—2842no—
221C22—2842no—
222C22—2842no—
223C22—2842no—
224C22—1424no—
225C22#1455615612yes—
226C22C22×D28411yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—21no—
231C4—2842no—
232C4—2842no—
233C4#1455615612yes—
234C4#41×D7112yes—
235C2—22no—
236C2—2844no—
237C2—5682no—
238C2#1798651111yescharacteristic
239C2C2×#1455615611yescharacteristic
240C2C2×#1455615611yescharacteristic
subgroupG/H
centerC22C22×D284
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#432×C71C2
socleC22×C71C22×D4
hypercenter#432D71
hypocenterC71#3109
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #17986549C2semidirect
2. C2×C4×D284C2semidirect
3. #17986318C2semidirect
4. #17986290C2semidirect
5. #17986195C2semidirect
6. #17986135C2semidirect
7. #17986112C2semidirect
8. #432×C71C2semidirect
13. #14556128C22semidirect
14. #14556125C22semidirect
23. C4×D284C22semidirect
26. #14556060C22semidirect
28. #14556050C22semidirect
30. C4⋊C8×C71C22semidirect
32. #97×C71C22semidirect
89. D284#41semidirect
121. C71#3109semidirect
129. #432D71semidirect
149. C4⋊C8C2×D71semidirect
153. #97C2×D71semidirect