Finite Group Databasebeta

← #20255633

Subgroups — #20255633

Order 6016.

460 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 115 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#15689838C211yesmaximal, characteristic, complemented
2#15689758C211yesmaximal, characteristic, complemented
3#15689469C211yesmaximal, characteristic, complemented
4#15689446C212yesmaximal, complemented
5#15689414C211yesmaximal, characteristic, complemented
6#15689373C212yesmaximal, complemented
7#15689255C212yesmaximal, complemented
8C4×#10625334C211yesmaximal, characteristic, complemented
9#15689200C211yesmaximal, characteristic, complemented
10#15689126C212yesmaximal, complemented
11C47×#459C211yesmaximal, characteristic, complemented
12C2×D4×D47—21no—
13C2×D4×D47C2212yes—
14C2×#10625334C2211yescharacteristic
15C2×#10625324C2212yescomplemented
16#13094024C2211yescharacteristic, complemented
17#13094010—22no—
18#13093998—21no—
19#13093995—21no—
20#13093995C2212yes—
21#13093995C2212yescomplemented
22#13093992—22no—
23C4×D188C2211yescharacteristic
24C4×D188C2211yescharacteristic
25#13093983—21no—
26#13093982C2212yescomplemented
27#13093957C2211yescharacteristic, complemented
28#13093956C2212yescomplemented
29#13093946C2212yes—
30#13093945C2212yescomplemented
31#13093945C2211yescharacteristic, complemented
32#13093945C2212yescomplemented
33#13093944C2211yescharacteristic
34(C2×D47)⋊C8C2212yescomplemented
35C4×C47⋊C8C2211yescharacteristic, complemented
36C2×D8×C47C2212yescomplemented
37#127×C47C2211yescharacteristic
38C4×D4×C47C2211yescharacteristic, complemented
39C4⋊C8×C47C2211yescharacteristic, complemented
40#102×C47C2212yescomplemented
41C23×D47—22no—
42C2×D4×C47—21no—
43C2×D4×C47—21no—
44C2×D4×C47C2311yescharacteristic
45C2×D4×C47C2312yes—
46C22×C4×C47—21no—
47C2×C22⋊D47—22no—
48C2×C22⋊D47—22no—
49C2×C22⋊D47—22no—
50D4×D47—24no—
51D4×D47—42no—
52D4×D47—44no—
53C2×D188D411yescharacteristic
54C2×D188C2311yescharacteristic
55C2×C4×D47—21no—
56C2×C4×D47C2312yes—
57C2×Dic94—21no—
58D8×C47—42no—
59C2×C8×C47C2312yes—
60C4⋊C4×C47C2311yescharacteristic
61C22⋊C4×C47—21no—
62C42×C47C2311yescharacteristic
63C22⋊Dic47—22no—
64C22⋊Dic47—22no—
65#10625334—22no—
66(C2×D47)⋊C4—22no—
67(C2×D47)⋊C4—21no—
68(C2×D47)⋊C4D412yes—
69C4⋊Dic47—21no—
70C4⋊Dic47D411yescharacteristic
71C4⋊Dic47C2312yes—
72C4⋊Dic47C2311yescharacteristic
73C4×Dic47—22no—
74C2×C47⋊C8C2311yescharacteristic
75C2×C47⋊C8C2311yescharacteristic
76#10625324—42no—
77C23×C47—21no—
78C23×C47—22no—
79C22×D47—21no—
80C22×D47—44no—
81C22×D47—44no—
82C22×D47—82no—
83C22×D47C2×D412yes—
84D4×C47—21no—
85D4×C47—22no—
86D4×C47—21no—
87D4×C47—22no—
88D4×C47—42no—
89D4×C47—81no—
90C2×C4×C47—21no—
91C2×C4×C47—42no—
92C2×C4×C47C2×D411yescharacteristic
93C2×C4×C47C2×D411yescharacteristic
94C2×C4×C47C2411yescharacteristic
95C22⋊D47—44no—
96C22⋊D47—44no—
97C22⋊D47—82no—
98C2×Dic47—22no—
99C2×Dic47—21no—
100C2×Dic47C2×D412yes—
101D188—22no—
102D188—21no—
103D188#4112yes—
104C4×D47—22no—
105C4×D47—22no—
106C4×D47—42no—
107Dic94—81no—
108C8×C47—22no—
109C47⋊C8—21no—
110C47⋊C8—21no—
111C22×C47—42no—
112C22×C47—41no—
113C22×C47—42no—
114C22×C47—41no—
115C22×C47—41no—
116C22×C47—42no—
117C22×C47C22×D411yescharacteristic
118C2×D47—22no—
119C2×D47—22no—
120C2×D47—22no—
121C2×D47—22no—
122C2×D47—41no—
123C2×D47—41no—
124C2×D47—88no—
125C4×C47—21no—
126C4×C47—41no—
127C4×C47AGL(1,ℤ/8)12yes—
128C4×C47C2×#4111yescharacteristic
129C4×C47H(5,𝔽2)11yescharacteristic
130Dic47—22no—
131Dic47—41no—
132Dic47—42no—
133#3325—471nomaximal, Sylow
134C2×C47—82no—
135C2×C47—81no—
136C2×C47#54611yescharacteristic
137C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C47#57611yescharacteristic
139D47—42no—
140D47—42no—
141#555—471no—
142D42—471no—
143#486—471no—
144#482—472no—
145#476—471no—
146#469—472no—
147#459D4711yescharacteristic, complemented
148#447—472no—
149C4×D8—471no—
150#436—471no—
151#418—472no—
152C47#332511yescharacteristic, complemented, Sylow
153C22×D4—472no—
154C22×D4—941no—
155C2×D8—471no—
156C2×D8C2×D4712yescomplemented
157C2×M16—472no—
158C4⋊Q8—471no—
159#127C2×D4711yescharacteristic
160#124—942no—
161#121—472no—
162#121—472no—
163#121—941no—
164#121—941no—
165#120—942no—
166C4×D4—471no—
167C4×D4—471no—
168C4×D4C2×D4711yescharacteristic, complemented
169#117—472no—
170#117—941no—
171#107—471no—
172#106—472no—
173C4⋊C8C2×D4711yescharacteristic, complemented
174#102—472no—
175#102—471no—
176#102—472no—
177#102—472no—
178#102—471no—
179#102C2×D4712yescomplemented
180C22⋊C8—472no—
181C4×C8—471no—
182C24—942no—
183C2×Q8—941no—
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—471no—
187C2×D4—471no—
188C2×D4—942no—
189C2×D4—944no—
190C2×D4—942no—
191C2×D4—942no—
192C2×D4—1882no—
193C2×D4—1884no—
194C2×D4C22×D4712yes—
195C2×D4C22×D4711yescharacteristic
196C22×C4—21no—
197C22×C4—472no—
198C22×C4—941no—
199D8—42no—
200D8—942no—
201M16—1882no—
202C2×C8—471no—
203C2×C8—471no—
204C2×C8C22×D4712yes—
205C4⋊C4—471no—
206C4⋊C4—472no—
207C4⋊C4—471no—
208C4⋊C4—941no—
209C4⋊C4C22×D4711yescharacteristic
210C22⋊C4—21no—
211C22⋊C4—472no—
212C22⋊C4—942no—
213C22⋊C4—942no—
214C22⋊C4—942no—
215C22⋊C4—941no—
216C42—942no—
217C42C22×D4711yescharacteristic
218C23—21no—
219C23—22no—
220C23—472no—
221C23—941no—
222C23—3762no—
223C23—1884no—
224C23—1884no—
225Q8—3761no—
226D4—21no—
227D4—22no—
228D4—21no—
229D4—22no—
230D4—42no—
231D4—81no—
232D4—472no—
233D4—942no—
234D4—941no—
235D4—3762no—
236D4—1884no—
237D4—1884no—
238C2×C4—21no—
239C2×C4—42no—
240C2×C4—472no—
241C2×C4—942no—
242C2×C4—942no—
243C2×C4—942no—
244C2×C4—941no—
245C2×C4—1882no—
246C2×C4D4×D4711yescharacteristic
247C2×C4D4×D4711yescharacteristic
248C2×C4C23×D4711yescharacteristic
249C8—22no—
250C8—941no—
251C8—941no—
252C22—42no—
253C22—41no—
254C22—41no—
255C22—42no—
256C22—42no—
257C22—41no—
258C22—942no—
259C22—942no—
260C22—942no—
261C22—942no—
262C22—3768no—
263C22—1881no—
264C22—1881no—
265C22C2×D4×D4711yescharacteristic
266C4—21no—
267C4—41no—
268C4—942no—
269C4—1881no—
270C4—1882no—
271C4#1309404812yes—
272C4#41×D4711yescharacteristic
273C4#1309406911yescharacteristic
274C2—82no—
275C2—81no—
276C2—1882no—
277C2—1882no—
278C2#1568977011yescharacteristic
279C2C2×#1309404811yescharacteristic
280C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#459C2
socleC22×C47C22×D4
hypercenter#459D47
hypocenterC47#3325
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #15689838C2semidirect
2. #15689758C2semidirect
3. #15689469C2semidirect
4. #15689446C2semidirect
5. #15689414C2semidirect
6. #15689373C2semidirect
7. #15689255C2semidirect
8. C4×#10625334C2semidirect
9. #15689200C2semidirect
10. #15689126C2semidirect
11. C47×#459C2semidirect
15. C2×#10625324C22semidirect
16. #13094024C22semidirect
21. #13093995C22semidirect
26. #13093982C22semidirect
27. #13093957C22semidirect
28. #13093956C22semidirect
30. #13093945C22semidirect
31. #13093945C22semidirect
32. #13093945C22semidirect
34. (C2×D47)⋊C8C22semidirect
35. C4×C47⋊C8C22semidirect
36. C2×D8×C47C22semidirect
38. C4×D4×C47C22semidirect
39. C4⋊C8×C47C22semidirect
40. #102×C47C22semidirect
147. #459D47semidirect
152. C47#3325semidirect
156. C2×D8C2×D47semidirect
168. C4×D4C2×D47semidirect
173. C4⋊C8C2×D47semidirect
179. #102C2×D47semidirect