Finite Group Databasebeta

← #20255211

Subgroups — #20255211

Order 6016.

462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 123 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#15689834C211yesmaximal, characteristic, complemented
2#15689758C211yesmaximal, characteristic
3#15689440C212yesmaximal, complemented
4#15689410C211yesmaximal, characteristic, complemented
5#15689351C212yesmaximal, complemented
6#15689320C211yesmaximal, characteristic, complemented
7#15689275C212yesmaximal, complemented
8C4×#10625325C211yesmaximal, characteristic, complemented
9C8×D188C211yesmaximal, characteristic, complemented
10#102×D47C212yesmaximal, complemented
11C47×#486C211yesmaximal, characteristic, complemented
12C2×D4×D47—21no—
13C2×D4×D47C2212yes—
14C2×#10625325C2211yescharacteristic
15C2×#10625335C2212yescomplemented
16C2×C8×D47C2212yescomplemented
17#13094015—21no—
18#13094004C2212yescomplemented
19#13094000—22no—
20#13093995—21no—
21#13093995C2212yes—
22#13093992—22no—
23C4×Dic94C2211yescharacteristic, complemented
24C4×D188C2211yescharacteristic
25C4×D188C2211yescharacteristic
26#13093986—21no—
27C4⋊C4×D47C2212yescomplemented
28#13093956C2211yescharacteristic, complemented
29#13093955C2212yescomplemented
30C4⋊(C47⋊C8)C2211yescharacteristic, complemented
31#13093949C2211yescharacteristic, complemented
32#13093946C2211yescharacteristic
33#13093945C2212yescomplemented
34#13093944C2212yes—
35(C2×D47)⋊C8C2212yescomplemented
36C4⋊Q8×C47C2211yescharacteristic, complemented
37#127×C47C2211yescharacteristic
38#102×C47C2212yescomplemented
39#102×C47C2212yescomplemented
40C4×C8×C47C2211yescharacteristic, complemented
41C23×D47—22no—
42C2×Q8×C47—21no—
43C2×D4×C47—21no—
44C2×D4×C47—21no—
45C2×D4×C47C2312yes—
46C2×C22⋊D47—22no—
47C2×C22⋊D47—22no—
48D4×D47—24no—
49D4×D47—42no—
50D4×D47—44no—
51C2×D188D411yescharacteristic
52C2×D188C2311yescharacteristic
53C2×C4×D47—21no—
54C2×C4×D47—22no—
55C2×C4×D47C2312yes—
56C2×Dic94C2311yescharacteristic
57C2×C8×C47C2311yescharacteristic
58C2×C8×C47C2311yescharacteristic
59C4⋊C4×C47—21no—
60C4⋊C4×C47C2312yes—
61C42×C47C2311yescharacteristic
62C22⋊Dic47—22no—
63#10625335—42no—
64(C2×D47)⋊C4—22no—
65(C2×D47)⋊C4—21no—
66(C2×D47)⋊C4D412yes—
67C4⋊Dic47—22no—
68C4⋊Dic47D411yescharacteristic
69C4⋊Dic47C2311yescharacteristic
70C4⋊Dic47C2311yescharacteristic
71Dic47⋊C4—21no—
72Dic47⋊C4—22no—
73C4×Dic47—21no—
74C2×C47⋊C8C2312yes—
75#10625325—22no—
76C8×D47—42no—
77C23×C47—22no—
78C22×D47—21no—
79C22×D47—44no—
80C22×D47—44no—
81C22×D47—82no—
82C22×D47C2×D412yes—
83Q8×C47—81no—
84D4×C47—22no—
85D4×C47—22no—
86D4×C47—42no—
87D4×C47—81no—
88C2×C4×C47—22no—
89C2×C4×C47C2×D411yescharacteristic
90C2×C4×C47C2×D411yescharacteristic
91C2×C4×C47C2411yescharacteristic
92C22⋊D47—44no—
93C22⋊D47—44no—
94C2×Dic47—21no—
95C2×Dic47—21no—
96C2×Dic47—21no—
97C2×Dic47C2×D412yes—
98D188—21no—
99D188SD1614yescomplemented
100D188#4112yes—
101C4×D47—22no—
102C4×D47—22no—
103C4×D47—42no—
104C4×D47—82no—
105Dic94—21no—
106Dic94—21no—
107C8×C47—21no—
108C8×C47—21no—
109C47⋊C8—22no—
110C22×C47—42no—
111C22×C47—42no—
112C22×C47—42no—
113C22×C47C22×D411yescharacteristic
114C2×D47—22no—
115C2×D47—22no—
116C2×D47—22no—
117C2×D47—41no—
118C2×D47—41no—
119C2×D47—88no—
120C2×D47C2×SD1614yes—
121C4×C47—21no—
122C4×C47—42no—
123C4×C47C2×SD1612yes—
124C4×C47C2×#4111yescharacteristic
125C4×C47H(5,𝔽2)11yescharacteristic
126Dic47—22no—
127Dic47—41no—
128Dic47—41no—
129Dic47—41no—
130#3295—471nomaximal, Sylow
131C2×C47—82no—
132C2×C47#54611yescharacteristic
133C2×C47C22×SD1611yescharacteristic
134C2×C47#57611yescharacteristic
135D47—24no—
136D47—42no—
137#554—471no—
138D42—471no—
139#486D4711yescharacteristic, complemented
140#481—472no—
141#476—471no—
142#465—472no—
143#460—471no—
144#450—472no—
145C4×SD16—471no—
146C8×D4—471no—
147C2×#102—472no—
148C47#329511yescharacteristic, complemented, Sylow
149C22×D4—472no—
150C22×D4—941no—
151C2×SD16—472no—
152C2×SD16—471no—
153C22×C8—472no—
154C4⋊Q8C2×D4711yescharacteristic, complemented
155#127C2×D4711yescharacteristic
156#125—941no—
157C22⋊Q8—472no—
158C22⋊Q8—942no—
159#121—472no—
160#121—941no—
161#120—942no—
162C4×Q8—471no—
163C4×D4—471no—
164C4×D4—471no—
165C4×D4—941no—
166C2×C4⋊C4—472no—
167#106—471no—
168#106—472no—
169C4⋊C8—471no—
170#103—471no—
171#102—472no—
172#102—471no—
173#102—472no—
174#102C2×D4712yescomplemented
175#102C2×D4712yescomplemented
176C22⋊C8—472no—
177C4×C8C2×D4711yescharacteristic, complemented
178C24—942no—
179C2×Q8—21no—
180C2×Q8—471no—
181C2×D4—21no—
182C2×D4—21no—
183C2×D4—471no—
184C2×D4—471no—
185C2×D4—942no—
186C2×D4—944no—
187C2×D4—942no—
188C2×D4—1882no—
189C2×D4—1884no—
190C2×D4C22×D4712yes—
191C22×C4—472no—
192C22×C4—942no—
193C22×C4—941no—
194SD16—942no—
195SD16—1882no—
196C2×C8—472no—
197C2×C8—1882no—
198C2×C8C22×D4711yescharacteristic
199C2×C8C22×D4711yescharacteristic
200C4⋊C4—21no—
201C4⋊C4—471no—
202C4⋊C4—471no—
203C4⋊C4—471no—
204C4⋊C4—942no—
205C4⋊C4—942no—
206C4⋊C4—941no—
207C4⋊C4C22×D4712yes—
208C22⋊C4—472no—
209C22⋊C4—942no—
210C22⋊C4—942no—
211C22⋊C4—941no—
212C42—941no—
213C42C22×D4711yescharacteristic
214C23—22no—
215C23—472no—
216C23—941no—
217C23—3762no—
218C23—1884no—
219C23—1884no—
220Q8—81no—
221Q8—941no—
222Q8—941no—
223D4—22no—
224D4—22no—
225D4—42no—
226D4—81no—
227D4—474no—
228D4—472no—
229D4—941no—
230D4—1884no—
231D4—1884no—
232C2×C4—22no—
233C2×C4—472no—
234C2×C4—942no—
235C2×C4—942no—
236C2×C4—941no—
237C2×C4—941no—
238C2×C4—941no—
239C2×C4—3762no—
240C2×C4—1882no—
241C2×C4D4×D4711yescharacteristic
242C2×C4D4×D4711yescharacteristic
243C2×C4C23×D4711yescharacteristic
244C8—21no—
245C8—21no—
246C8—942no—
247C22—42no—
248C22—42no—
249C22—42no—
250C22—474no—
251C22—942no—
252C22—942no—
253C22—942no—
254C22—3768no—
255C22—1881no—
256C22—1881no—
257C22C2×D4×D4711yescharacteristic
258C4—21no—
259C4—42no—
260C4—942no—
261C4—1881no—
262C4—1881no—
263C4—1881no—
264C4SD16×D4712yes—
265C4#41×D4711yescharacteristic
266C4#1309407011yescharacteristic
267C2—82no—
268C2—944no—
269C2—1882no—
270C2#1568976611yescharacteristic
271C2C2×SD16×D4711yescharacteristic
272C2#1568992411yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#486C2
socleC22×C47C22×D4
hypercenter#486D47
hypocenterC47#3295
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #15689834C2semidirect
3. #15689440C2semidirect
4. #15689410C2semidirect
5. #15689351C2semidirect
6. #15689320C2semidirect
7. #15689275C2semidirect
8. C4×#10625325C2semidirect
9. C8×D188C2semidirect
10. #102×D47C2semidirect
11. C47×#486C2semidirect
15. C2×#10625335C22semidirect
16. C2×C8×D47C22semidirect
18. #13094004C22semidirect
23. C4×Dic94C22semidirect
27. C4⋊C4×D47C22semidirect
28. #13093956C22semidirect
29. #13093955C22semidirect
30. C4⋊(C47⋊C8)C22semidirect
31. #13093949C22semidirect
33. #13093945C22semidirect
35. (C2×D47)⋊C8C22semidirect
36. C4⋊Q8×C47C22semidirect
38. #102×C47C22semidirect
39. #102×C47C22semidirect
40. C4×C8×C47C22semidirect
99. D188SD16semidirect
139. #486D47semidirect
148. C47#3295semidirect
154. C4⋊Q8C2×D47semidirect
174. #102C2×D47semidirect
175. #102C2×D47semidirect
177. C4×C8C2×D47semidirect