Finite Group Databasebeta

← #20254255

Subgroups — #20254255

Order 6016.

410 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 117 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#15689687C211yesmaximal, characteristic
2#15689461C212yesmaximal, complemented
3#15689447C212yesmaximal, complemented
4#15689371C212yesmaximal, complemented
5#15689354C212yesmaximal, complemented
6#15689273C212yesmaximal, complemented
7#15689262C212yesmaximal, complemented
8#15689090C211yesmaximal, characteristic, complemented
9C47×#536C211yesmaximal, characteristic, complemented
10C22×D188C2211yescharacteristic
11C2×#10625336C2212yes—
12C2×#10625336C2212yes—
13C2×#10625329C2211yescharacteristic, complemented
14C22×C47⋊C8C2211yescharacteristic, complemented
15#13094020—21no—
16#13094013—21no—
17#13093998C2212yes—
18#13093998C2212yes—
19#13093992—21no—
20#13093992—21no—
21#13093983C2211yescharacteristic
22#13093957C2212yescomplemented
23#13093955C2212yescomplemented
24#13093948C2212yescomplemented
25#13093948C2212yescomplemented
26#13093944C2212yes—
27#13093944C2212yes—
28C22⋊(C47⋊C8)C2212yes—
29C22⋊(C47⋊C8)C2212yescomplemented
30C2×#41×C47C2211yescharacteristic
31C22×Q8×C47C2211yescharacteristic, complemented
32C4⋊Q8×C47—21no—
33#124×C47—21no—
34#123×C47—21no—
35#123×C47—21no—
36C22⋊Q8×C47C2212yes—
37C22⋊Q8×C47C2212yescomplemented
38#117×C47C2211yescharacteristic, complemented
39C23×D47—21no—
40#41×C47—41no—
41#41×C47—41no—
42C2×Q8×C47—21no—
43C2×Q8×C47—41no—
44C2×Q8×C47—41no—
45C2×Q8×C47D411yescharacteristic
46C2×Q8×C47C2312yes—
47C2×D4×C47D411yescharacteristic
48C2×D4×C47D411yescharacteristic
49C2×D4×C47D411yescharacteristic
50C22×C4×C47—21no—
51C22×C4×C47C2311yescharacteristic
52C22×C4×C47C2311yescharacteristic
53C22×C4×C47C2311yescharacteristic
54C2×C22⋊D47—22no—
55C2×C22⋊D47—22no—
56C2×D188—21no—
57C2×D188—41no—
58C2×D188—41no—
59C2×D188C2312yes—
60C4⋊C4×C47—22no—
61C4⋊C4×C47—22no—
62C4⋊C4×C47C2312yes—
63C22⋊C4×C47—21no—
64C22⋊C4×C47—22no—
65C22⋊C4×C47—22no—
66C42×C47—21no—
67C22⋊Dic47—21no—
68#10625336—42no—
69#10625336—42no—
70(C2×D47)⋊C4—22no—
71(C2×D47)⋊C4—22no—
72C4⋊Dic47C2312yes—
73C4×Dic47—21no—
74#10625329—41no—
75C2×C47⋊C8—41no—
76C2×C47⋊C8C2312yes—
77C2×C47⋊C8C2312yes—
78C23×C47C2×D411yescharacteristic
79C23×C47C2×D411yescharacteristic
80C23×C47C2×D411yescharacteristic
81C22×D47—22no—
82C22×D47—42no—
83C22×D47—82no—
84Q8×C47—22no—
85Q8×C47—22no—
86Q8×C47—41no—
87Q8×C47—42no—
88D4×C47—41no—
89D4×C47—41no—
90D4×C47—41no—
91C2×C4×C47—21no—
92C2×C4×C47—21no—
93C2×C4×C47—21no—
94C2×C4×C47—21no—
95C2×C4×C47—21no—
96C2×C4×C47—21no—
97C2×C4×C47—22no—
98C2×C4×C47—22no—
99C2×C4×C47—42no—
100C2×C4×C47C2×D411yescharacteristic
101C2×C4×C47C2×D411yescharacteristic
102C2×C4×C47C2×D411yescharacteristic
103C2×C4×C47C2411yescharacteristic
104C22⋊D47—82no—
105C22⋊D47—82no—
106C2×Dic47—22no—
107D188—22no—
108D188—22no—
109D188—42no—
110C47⋊C8—22no—
111C47⋊C8—22no—
112C22×C47—21no—
113C22×C47—21no—
114C22×C47—21no—
115C22×C47—22no—
116C22×C47—22no—
117C22×C47—22no—
118C22×C47C22×D411yescharacteristic
119C2×D47—42no—
120C2×D47—42no—
121C2×D47—42no—
122C2×D47—84no—
123C4×C47—21no—
124C4×C47—21no—
125C4×C47—21no—
126C4×C47—42no—
127C4×C47—42no—
128C4×C47H(5,𝔽2)11yescharacteristic
129C4×C47H(5,𝔽2)11yescharacteristic
130Dic47—42no—
131#3200—471nomaximal, Sylow
132C2×C47—41no—
133C2×C47—41no—
134C2×C47—41no—
135C2×C47#53411yescharacteristic
136C2×C47#57712yes—
137D47—82no—
138#536D4711yescharacteristic, complemented
139#535—471no—
140#485—472no—
141#482—472no—
142#468—472no—
143#465—472no—
144#450—472no—
145#448—472no—
146#408—471no—
147C47#320011yescharacteristic, complemented, Sylow
148C2×#41C2×D4711yescharacteristic
149C22×Q8C2×D4711yescharacteristic, complemented
150C22×D4—471no—
151C2×SD16—472no—
152C2×SD16—472no—
153C2×M16—471no—
154C22×C8—471no—
155C4⋊Q8—21no—
156#127—941no—
157#124—21no—
158#124—941no—
159#123—21no—
160#123—21no—
161C22⋊Q8C2×D4712yes—
162C22⋊Q8C2×D4712yescomplemented
163#121—472no—
164#121—472no—
165#120—941no—
166#120—941no—
167#117—471no—
168#117C2×D4711yescharacteristic, complemented
169#107—472no—
170#106—472no—
171#103—472no—
172#103—472no—
173#102—472no—
174#102—472no—
175C22⋊C8—472no—
176C22⋊C8—472no—
177C24—941no—
178#41—41no—
179#41—41no—
180C2×Q8—21no—
181C2×Q8—41no—
182C2×Q8—41no—
183C2×Q8C22⋊D4711yescharacteristic
184C2×Q8C22×D4712yes—
185C2×D4—472no—
186C2×D4—942no—
187C2×D4—942no—
188C2×D4—941no—
189C2×D4—1881no—
190C2×D4—1881no—
191C2×D4C22⋊D4711yescharacteristic
192C2×D4C22⋊D4711yescharacteristic
193C2×D4C22⋊D4711yescharacteristic
194C22×C4—21no—
195C22×C4C22×D4711yescharacteristic
196C22×C4C22×D4711yescharacteristic
197C22×C4C22×D4711yescharacteristic
198SD16—1882no—
199SD16—1882no—
200M16—1881no—
201C2×C8—472no—
202C2×C8—472no—
203C2×C8—1881no—
204C4⋊C4—22no—
205C4⋊C4—22no—
206C4⋊C4—472no—
207C4⋊C4C22×D4712yes—
208C22⋊C4—21no—
209C22⋊C4—22no—
210C22⋊C4—22no—
211C22⋊C4—941no—
212C22⋊C4—942no—
213C22⋊C4—942no—
214C42—21no—
215C42—941no—
216C23—942no—
217C23—3762no—
218C23—1882no—
219C23C2×C22⋊D4711yescharacteristic
220C23C2×C22⋊D4711yescharacteristic
221C23C2×C22⋊D4711yescharacteristic
222Q8—22no—
223Q8—22no—
224Q8—41no—
225Q8—42no—
226D4—41no—
227D4—41no—
228D4—41no—
229D4—942no—
230D4—942no—
231D4—3762no—
232D4—3762no—
233D4—1882no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—42no—
243C2×C4—942no—
244C2×C4C2×C22⋊D4711yescharacteristic
245C2×C4C2×C22⋊D4711yescharacteristic
246C2×C4C2×C22⋊D4711yescharacteristic
247C2×C4C23×D4711yescharacteristic
248C8—942no—
249C8—942no—
250C22—22no—
251C22—22no—
252C22—22no—
253C22—21no—
254C22—21no—
255C22—21no—
256C22—3764no—
257C22—1882no—
258C22—1882no—
259C22—1882no—
260C22C22×C22⋊D4711yescharacteristic
261C4—21no—
262C4—21no—
263C4—21no—
264C4—42no—
265C4—42no—
266C4—1882no—
267C4#1309406911yescharacteristic
268C4#1309406911yescharacteristic
269C2—41no—
270C2—41no—
271C2—41no—
272C2—3762no—
273C2#1568968211yescharacteristic
274C2#1568993112yes—
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#536C2
socleC22×C47C22×D4
hypercenter#536D47
hypocenterC47#3200
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
2. #15689461C2semidirect
3. #15689447C2semidirect
4. #15689371C2semidirect
5. #15689354C2semidirect
6. #15689273C2semidirect
7. #15689262C2semidirect
8. #15689090C2semidirect
9. C47×#536C2semidirect
13. C2×#10625329C22semidirect
14. C22×C47⋊C8C22semidirect
22. #13093957C22semidirect
23. #13093955C22semidirect
24. #13093948C22semidirect
25. #13093948C22semidirect
29. C22⋊(C47⋊C8)C22semidirect
31. C22×Q8×C47C22semidirect
37. C22⋊Q8×C47C22semidirect
38. #117×C47C22semidirect
138. #536D47semidirect
147. C47#3200semidirect
149. C22×Q8C2×D47semidirect
162. C22⋊Q8C2×D47semidirect
168. #117C2×D47semidirect