Finite Group Databasebeta

← #20254135

Subgroups — #20254135

Order 6016.

520 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 121 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#121×D47C212yesmaximal, complemented
2#15689438C212yesmaximal, complemented
3#15689435C212yesmaximal, complemented
4#15689359C211yesmaximal, characteristic, complemented
5#15689357C212yesmaximal, complemented
6#15689258C212yesmaximal, complemented
7#15689255C212yesmaximal, complemented
8C2×(C2×D47)⋊C8C211yesmaximal, characteristic, complemented
9C47×#466C211yesmaximal, characteristic, complemented
10C2×D4×D47—22no—
11C2×D4×D47C2212yescomplemented
12C22×C4×D47C2211yescharacteristic
13C2×D376C2211yescharacteristic, complemented
14C2×#10625334C2212yescomplemented
15C22×C47⋊C8C2211yescharacteristic, complemented
16#13093999C2212yes—
17#13093998C2212yescomplemented
18#13093997—22no—
19#13093996—22no—
20#13093995C2212yes—
21C4⋊C4×D47C2212yescomplemented
22C22⋊C4×D47—22no—
23#13093958C2211yescharacteristic, complemented
24#13093957C2212yescomplemented
25#13093946C2212yescomplemented
26#13093945C2212yescomplemented
27#13093944C2212yescomplemented
28(C2×D47)⋊C8C2212yescomplemented
29(C2×D47)⋊C8C2212yescomplemented
30C2×D8×C47C2211yescharacteristic, complemented
31C22×C8×C47C2211yescharacteristic, complemented
32#121×C47C2212yescomplemented
33#107×C47C2211yescharacteristic, complemented
34#102×C47C2212yescomplemented
35C23×D47—22no—
36C23×D47D411yescharacteristic
37C2×D4×C47—22no—
38C2×D4×C47C2312yes—
39C22×C4×C47C2311yescharacteristic
40C2×C22⋊D47—22no—
41C2×C22⋊D47—22no—
42C2×C22⋊D47—22no—
43C22×Dic47D411yescharacteristic
44D4×D47—42no—
45D4×D47—42no—
46D4×D47—48no—
47C2×D188—22no—
48C2×D188C2312yes—
49C2×C4×D47—22no—
50C2×C4×D47—41no—
51C2×C4×D47—41no—
52C2×C4×D47D412yes—
53C2×C4×D47C2312yes—
54D8×C47—41no—
55C2×C8×C47—41no—
56C2×C8×C47C2311yescharacteristic
57C2×C8×C47C2311yescharacteristic
58C4⋊C4×C47C2312yes—
59C22⋊C4×C47—22no—
60C22⋊Dic47—22no—
61#10625334—42no—
62(C2×D47)⋊C4—22no—
63(C2×D47)⋊C4—22no—
64C4⋊Dic47C2312yes—
65Dic47⋊C4—22no—
66C2×C47⋊C8—41no—
67C2×C47⋊C8C2312yes—
68D376—41no—
69C23×C47—22no—
70C23×C47C2×D411yescharacteristic
71C22×D47—22no—
72C22×D47—41no—
73C22×D47—41no—
74C22×D47—44no—
75C22×D47—44no—
76C22×D47—44no—
77C22×D47D814yescomplemented
78C22×D47C2×D412yes—
79D4×C47—22no—
80D4×C47—22no—
81D4×C47—44no—
82C2×C4×C47—21no—
83C2×C4×C47—21no—
84C2×C4×C47—22no—
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47C2411yescharacteristic
87C22⋊D47—44no—
88C22⋊D47—44no—
89C22⋊D47—44no—
90C2×Dic47—22no—
91C2×Dic47—41no—
92C2×Dic47C2×D412yes—
93D188—22no—
94D188—22no—
95D188—44no—
96C4×D47—22no—
97C4×D47—22no—
98C4×D47—42no—
99C4×D47—44no—
100C8×C47—21no—
101C8×C47—21no—
102C47⋊C8—22no—
103C22×C47—21no—
104C22×C47—21no—
105C22×C47—42no—
106C22×C47—42no—
107C22×C47—42no—
108C22×C47C2×D812yes—
109C22×C47C22×D411yescharacteristic
110C2×D47—22no—
111C2×D47—22no—
112C2×D47—44no—
113C2×D47—42no—
114C2×D47—42no—
115C2×D47—42no—
116C2×D47—88no—
117C2×D47C2×D814yes—
118C4×C47—21no—
119C4×C47—42no—
120C4×C47H(5,𝔽2)11yescharacteristic
121C4×C47H(5,𝔽2)11yescharacteristic
122Dic47—22no—
123Dic47—42no—
124#3186—471nomaximal, Sylow
125C2×C47—22no—
126C2×C47—82no—
127C2×C47#53411yescharacteristic
128C2×C47C22×D811yescharacteristic
129C2×C47#57511yescharacteristic
130D47—24no—
131D47—82no—
132C2×#121—472no—
133#480—472no—
134#480—472no—
135#466—471no—
136#466—472no—
137#466D4711yescharacteristic, complemented
138#447—472no—
139#447—472no—
140C2×C22⋊C8—471no—
141C47#318611yescharacteristic, complemented, Sylow
142C22×D4—472no—
143C22×D4—942no—
144C23×C4—471no—
145C2×D8—472no—
146C2×D8—471no—
147C2×D8C2×D4711yescharacteristic, complemented
148C22×C8—471no—
149C22×C8C2×D4711yescharacteristic, complemented
150#121—472no—
151#121—472no—
152#121—472no—
153#121—942no—
154#121—942no—
155#121C2×D4712yescomplemented
156C2×C4⋊C4—472no—
157C2×C22⋊C4—942no—
158#107—471no—
159#107—472no—
160#107C2×D4711yescharacteristic, complemented
161#102—472no—
162#102—472no—
163#102—472no—
164#102C2×D4712yescomplemented
165C22⋊C8—472no—
166C22⋊C8—472no—
167C24—471no—
168C24—942no—
169C2×D4—22no—
170C2×D4—472no—
171C2×D4—942no—
172C2×D4—942no—
173C2×D4—942no—
174C2×D4—942no—
175C2×D4—1882no—
176C2×D4—1882no—
177C2×D4—1888no—
178C2×D4C22×D4712yes—
179C22×C4—471no—
180C22×C4—472no—
181C22×C4—472no—
182C22×C4—942no—
183C22×C4—1881no—
184C22×C4—1881no—
185C22×C4C22×D4711yescharacteristic
186D8—41no—
187D8—1881no—
188D8—1882no—
189C2×C8—41no—
190C2×C8—472no—
191C2×C8—1881no—
192C2×C8C22×D4711yescharacteristic
193C2×C8C22×D4711yescharacteristic
194C4⋊C4—472no—
195C4⋊C4—942no—
196C4⋊C4C22×D4712yes—
197C22⋊C4—22no—
198C22⋊C4—942no—
199C22⋊C4—942no—
200C22⋊C4—942no—
201C23—22no—
202C23—472no—
203C23—474no—
204C23—942no—
205C23—1881no—
206C23—1881no—
207C23—1884no—
208C23—1884no—
209C23—1884no—
210C23D4×D4711yescharacteristic
211D4—22no—
212D4—22no—
213D4—44no—
214D4—942no—
215D4—942no—
216D4—1884no—
217D4—1884no—
218D4—1884no—
219D4—1884no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—472no—
224C2×C4—942no—
225C2×C4—942no—
226C2×C4—942no—
227C2×C4—1882no—
228C2×C4—1884no—
229C2×C4—1881no—
230C2×C4D4×D4711yescharacteristic
231C2×C4C23×D4711yescharacteristic
232C8—21no—
233C8—21no—
234C8—942no—
235C22—21no—
236C22—21no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—474no—
241C22—942no—
242C22—942no—
243C22—3768no—
244C22—1884no—
245C22—1882no—
246C22—1882no—
247C22—1882no—
248C22D8×D4712yes—
249C22C2×D4×D4711yescharacteristic
250C4—21no—
251C4—42no—
252C4—942no—
253C4—1882no—
254C4#1309406911yescharacteristic
255C4#1309407011yescharacteristic
256C2—22no—
257C2—82no—
258C2—944no—
259C2—3762no—
260C2#1568968111yescharacteristic
261C2C2×D8×D4711yescharacteristic
262C2#1568992011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#466C2
socleC22×C47C22×D4
hypercenter#466D47
hypocenterC47#3186
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #121×D47C2semidirect
2. #15689438C2semidirect
3. #15689435C2semidirect
4. #15689359C2semidirect
5. #15689357C2semidirect
6. #15689258C2semidirect
7. #15689255C2semidirect
8. C2×(C2×D47)⋊C8C2semidirect
9. C47×#466C2semidirect
11. C2×D4×D47C22semidirect
13. C2×D376C22semidirect
14. C2×#10625334C22semidirect
15. C22×C47⋊C8C22semidirect
17. #13093998C22semidirect
21. C4⋊C4×D47C22semidirect
23. #13093958C22semidirect
24. #13093957C22semidirect
25. #13093946C22semidirect
26. #13093945C22semidirect
27. #13093944C22semidirect
28. (C2×D47)⋊C8C22semidirect
29. (C2×D47)⋊C8C22semidirect
30. C2×D8×C47C22semidirect
31. C22×C8×C47C22semidirect
32. #121×C47C22semidirect
33. #107×C47C22semidirect
34. #102×C47C22semidirect
77. C22×D47D8semidirect
137. #466D47semidirect
141. C47#3186semidirect
147. C2×D8C2×D47semidirect
149. C22×C8C2×D47semidirect
155. #121C2×D47semidirect
160. #107C2×D47semidirect
164. #102C2×D47semidirect