Finite Group Databasebeta

← #20254261

Subgroups — #20254261

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#15689694C211yesmaximal, characteristic, complemented
2#15689687C211yesmaximal, characteristic
3#15689465C212yesmaximal, complemented
4#15689448C212yesmaximal, complemented
5#15689369C212yesmaximal, complemented
6#15689352C212yesmaximal, complemented
7#15689276C212yesmaximal, complemented
8#15689264C212yesmaximal, complemented
9C47×#408C211yesmaximal, characteristic, complemented
10C22×Dic94C2211yescharacteristic, complemented
11C22×D188C2211yescharacteristic
12C2×#10625325C2212yes—
13C2×#10625325C2212yes—
14#13094022—21no—
15#13094020—21no—
16#13094013—21no—
17#13094011—21no—
18#13094005—21no—
19#13094005—21no—
20#13094003C2212yes—
21#13094003C2212yescomplemented
22#13093998C2212yes—
23#13093998C2212yes—
24#13093992—21no—
25#13093992—21no—
26#13093983C2211yescharacteristic
27#13093983C2211yescharacteristic, complemented
28#13093958C2212yescomplemented
29#13093956C2212yescomplemented
30#13093949C2212yescomplemented
31#13093949C2212yescomplemented
32#13093946C2212yes—
33#13093946C2212yes—
34C2×#41×C47C2211yescharacteristic
35C2×M16×C47C2211yescharacteristic, complemented
36C22×C8×C47C2211yescharacteristic, complemented
37C22⋊C8×C47C2212yes—
38C22⋊C8×C47C2212yescomplemented
39C23×D47—21no—
40#41×C47—41no—
41#41×C47—41no—
42C2×Q8×C47D411yescharacteristic
43C2×D4×C47D411yescharacteristic
44C2×D4×C47D411yescharacteristic
45C2×D4×C47D411yescharacteristic
46C22×C4×C47C2311yescharacteristic
47C22×C4×C47C2311yescharacteristic
48C22×C4×C47C2311yescharacteristic
49C2×C22⋊D47—22no—
50C2×C22⋊D47—22no—
51C22×Dic47—21no—
52C2×D188—21no—
53C2×D188—41no—
54C2×D188—41no—
55C2×D188C2312yes—
56C2×Dic94—21no—
57C2×Dic94—41no—
58C2×Dic94—41no—
59C2×Dic94C2312yes—
60M16×C47—41no—
61C2×C8×C47—41no—
62C2×C8×C47C2312yes—
63C2×C8×C47C2312yes—
64C22⋊Dic47—21no—
65C22⋊Dic47—21no—
66C22⋊Dic47—22no—
67C22⋊Dic47—22no—
68(C2×D47)⋊C4—22no—
69(C2×D47)⋊C4—22no—
70C4⋊Dic47C2312yes—
71C4⋊Dic47C2312yes—
72Dic47⋊C4—22no—
73Dic47⋊C4—22no—
74C4×Dic47—21no—
75C4×Dic47—21no—
76#10625325—42no—
77#10625325—42no—
78C23×C47C2×D411yescharacteristic
79C23×C47C2×D411yescharacteristic
80C23×C47C2×D411yescharacteristic
81C22×D47—22no—
82C22×D47—42no—
83C22×D47—82no—
84Q8×C47—41no—
85D4×C47—41no—
86D4×C47—41no—
87D4×C47—41no—
88C2×C4×C47—21no—
89C2×C4×C47—21no—
90C2×C4×C47—21no—
91C2×C4×C47—21no—
92C2×C4×C47—21no—
93C2×C4×C47—21no—
94C2×C4×C47C2×D411yescharacteristic
95C2×C4×C47C2×D411yescharacteristic
96C2×C4×C47C2×D411yescharacteristic
97C2×C4×C47C2411yescharacteristic
98C22⋊D47—82no—
99C22⋊D47—82no—
100C2×Dic47—22no—
101C2×Dic47—22no—
102C2×Dic47—22no—
103C2×Dic47—42no—
104D188—22no—
105D188—22no—
106D188—42no—
107Dic94—22no—
108Dic94—22no—
109Dic94—42no—
110C8×C47—22no—
111C8×C47—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×C47H(5,𝔽2)11yescharacteristic
127C4×C47H(5,𝔽2)11yescharacteristic
128Dic47—42no—
129Dic47—42no—
130Dic47—42no—
131#3200—471nomaximal, Sylow
132C2×C47—41no—
133C2×C47—41no—
134C2×C47—41no—
135C2×C47#53411yescharacteristic
136C2×C47#57712yes—
137D47—82no—
138#536—471no—
139#535—471no—
140#485—472no—
141#482—472no—
142#468—472no—
143#465—472no—
144#450—472no—
145#448—472no—
146#408D4711yescharacteristic, complemented
147C47#320011yescharacteristic, complemented, Sylow
148C2×#41C2×D4711yescharacteristic
149C22×Q8—471no—
150C22×D4—471no—
151C2×SD16—472no—
152C2×SD16—472no—
153C2×M16C2×D4711yescharacteristic, complemented
154C22×C8C2×D4711yescharacteristic, complemented
155C4⋊Q8—941no—
156#127—941no—
157#124—941no—
158#124—941no—
159#123—941no—
160#123—941no—
161C22⋊Q8—472no—
162C22⋊Q8—472no—
163#121—472no—
164#121—472no—
165#120—941no—
166#120—941no—
167#117—471no—
168#117—471no—
169#107—472no—
170#106—472no—
171#103—472no—
172#103—472no—
173#102—472no—
174#102—472no—
175C22⋊C8C2×D4712yes—
176C22⋊C8C2×D4712yescomplemented
177C24—941no—
178#41—41no—
179#41—41no—
180C2×Q8—472no—
181C2×Q8—941no—
182C2×Q8—1881no—
183C2×Q8—1881no—
184C2×Q8D18811yescharacteristic
185C2×D4—472no—
186C2×D4—942no—
187C2×D4—942no—
188C2×D4—941no—
189C2×D4—1881no—
190C2×D4—1881no—
191C2×D4D18811yescharacteristic
192C2×D4D18811yescharacteristic
193C2×D4D18811yescharacteristic
194C22×C4—941no—
195C22×C4C22×D4711yescharacteristic
196C22×C4C22×D4711yescharacteristic
197C22×C4C22×D4711yescharacteristic
198SD16—1882no—
199SD16—1882no—
200M16—41no—
201C2×C8—41no—
202C2×C8C22×D4712yes—
203C2×C8C22×D4712yes—
204C4⋊C4—472no—
205C4⋊C4—472no—
206C4⋊C4—942no—
207C4⋊C4—942no—
208C22⋊C4—941no—
209C22⋊C4—941no—
210C22⋊C4—942no—
211C22⋊C4—942no—
212C22⋊C4—942no—
213C22⋊C4—942no—
214C42—941no—
215C42—941no—
216C23—942no—
217C23—3762no—
218C23—1882no—
219C23C2×D18811yescharacteristic
220C23C2×D18811yescharacteristic
221C23C2×D18811yescharacteristic
222Q8—41no—
223Q8—942no—
224Q8—942no—
225Q8—1882no—
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—942no—
241C2×C4—942no—
242C2×C4—942no—
243C2×C4—1882no—
244C2×C4C2×D18811yescharacteristic
245C2×C4C2×D18811yescharacteristic
246C2×C4C2×D18811yescharacteristic
247C2×C4C23×D4711yescharacteristic
248C8—22no—
249C8—22no—
250C22—22no—
251C22—22no—
252C22—22no—
253C22—21no—
254C22—21no—
255C22—21no—
256C22—3764no—
257C22—1882no—
258C22—1882no—
259C22—1882no—
260C22C22×D18811yescharacteristic
261C4—21no—
262C4—21no—
263C4—21no—
264C4—1882no—
265C4—1882no—
266C4—1882no—
267C4#1309406911yescharacteristic
268C4#1309406911yescharacteristic
269C2—41no—
270C2—41no—
271C2—41no—
272C2—3762no—
273C2#1568968511yescharacteristic
274C2#1568993512yes—
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#408C2
socleC22×C47C22×D4
hypercenter#408D47
hypocenterC47#3200
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #15689694C2semidirect
3. #15689465C2semidirect
4. #15689448C2semidirect
5. #15689369C2semidirect
6. #15689352C2semidirect
7. #15689276C2semidirect
8. #15689264C2semidirect
9. C47×#408C2semidirect
10. C22×Dic94C22semidirect
21. #13094003C22semidirect
27. #13093983C22semidirect
28. #13093958C22semidirect
29. #13093956C22semidirect
30. #13093949C22semidirect
31. #13093949C22semidirect
35. C2×M16×C47C22semidirect
36. C22×C8×C47C22semidirect
38. C22⋊C8×C47C22semidirect
146. #408D47semidirect
147. C47#3200semidirect
153. C2×M16C2×D47semidirect
154. C22×C8C2×D47semidirect
176. C22⋊C8C2×D47semidirect