Finite Group Databasebeta

← #20254392

Subgroups — #20254392

Order 6016.

400 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 111 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#15689678C211yesmaximal, characteristic, complemented
2#124×D47C211yesmaximal, characteristic
3#15689518C211yesmaximal, characteristic, complemented
4#15689517C211yesmaximal, characteristic, complemented
5#15689485C211yesmaximal, characteristic, complemented
6#15689348C212yesmaximal, complemented
7#15689344C212yesmaximal, complemented
8#15689280C212yesmaximal, complemented
9#15689275C212yesmaximal
10#15689178C211yesmaximal, characteristic, complemented
11C47×#489C211yesmaximal, characteristic, complemented
12C2×Q8×D47C2211yescharacteristic
13C2×D4×D47C2211yescharacteristic
14C2×Dic188C2212yescomplemented
15C2×#10625337C2212yescomplemented
16C2×#10625325C2212yes—
17C2×#10625335C2212yes—
18#13094024C2211yescharacteristic, complemented
19#13094015—21no—
20#13094013C2211yescharacteristic
21#13094012C2211yescharacteristic
22#13094011C2211yescharacteristic
23#13094010—21no—
24#13094010—21no—
25#13094004C2212yes—
26#13094000—21no—
27Q8×Dic47—21no—
28#13093989C2212yescomplemented
29#13093982—21no—
30C22⋊C4×D47—21no—
31C22⋊C4×D47—21no—
32C42×D47C2211yescharacteristic
33Dic47⋊C8C2212yescomplemented
34#13093947C2212yescomplemented
35#13093944C2212yes—
36(C2×D47)⋊C8C2212yes—
37#13093935C2211yescharacteristic, complemented
38C4⋊Q8×C47C2211yescharacteristic, complemented
39#124×C47C2211yescharacteristic
40#103×C47C2212yescomplemented
41#102×C47C2212yes—
42#97×C47C2211yescharacteristic, complemented
43C23×D47—21no—
44C2×Q8×C47—21no—
45C2×Q8×C47C2311yescharacteristic
46C2×D4×C47C2311yescharacteristic
47C2×C22⋊D47—21no—
48Q8×D47—42no—
49D4×D47—42no—
50C2×D188C2311yescharacteristic
51C2×C4×D47—21no—
52C2×C4×D47D411yescharacteristic
53C2×C4×D47D411yescharacteristic
54C2×C4×D47C2311yescharacteristic
55C2×Dic94—21no—
56C2×Dic94C2311yescharacteristic
57C2×Dic94C2312yes—
58C2×C8×C47C2312yes—
59C4⋊C4×C47—21no—
60C4⋊C4×C47C2312yes—
61C22⋊C4×C47—21no—
62C22⋊C4×C47—21no—
63C42×C47C2311yescharacteristic
64C22⋊Dic47—21no—
65C22⋊Dic47—21no—
66#10625337—42no—
67#10625335—42no—
68(C2×D47)⋊C4—22no—
69(C2×D47)⋊C4—21no—
70(C2×D47)⋊C4—21no—
71(C2×D47)⋊C4—21no—
72(C2×D47)⋊C4—21no—
73C4⋊Dic47—21no—
74C4⋊Dic47—21no—
75C4⋊Dic47—22no—
76Dic47⋊C4—22no—
77C4×Dic47—22no—
78C4×Dic47D411yescharacteristic
79C4×Dic47D411yescharacteristic
80C4×Dic47C2311yescharacteristic
81C2×C47⋊C8C2312yes—
82Dic188—42no—
83#10625325—42no—
84C23×C47—21no—
85C22×D47—21no—
86C22×D47—42no—
87C22×D47—42no—
88C22×D47—42no—
89C22×D47C2×D411yescharacteristic
90Q8×C47—22no—
91Q8×C47—42no—
92D4×C47—22no—
93C2×C4×C47—22no—
94C2×C4×C47—21no—
95C2×C4×C47C2×D411yescharacteristic
96C2×C4×C47C2×D411yescharacteristic
97C2×C4×C47C2411yescharacteristic
98C22⋊D47—42no—
99C2×Dic47—22no—
100C2×Dic47—21no—
101C2×Dic47C2×D411yescharacteristic
102C2×Dic47C2×D411yescharacteristic
103C2×Dic47C2×D411yescharacteristic
104D188—22no—
105C4×D47—22no—
106C4×D47—22no—
107C4×D47—41no—
108C4×D47—42no—
109Dic94—22no—
110Dic94—22no—
111Dic94—22no—
112Dic94—42no—
113C8×C47—22no—
114C47⋊C8—22no—
115C22×C47—41no—
116C22×C47—41no—
117C22×C47—41no—
118C22×C47C22×D411yescharacteristic
119C2×D47—21no—
120C2×D47—21no—
121C2×D47—41no—
122C2×D47—41no—
123C2×D47—41no—
124C2×D47—84no—
125C2×D47#13712yes—
126C4×C47—21no—
127C4×C47—21no—
128C4×C47—41no—
129C4×C47—42no—
130C4×C47H(5,𝔽2)12yes—
131Dic47—21no—
132Dic47—21no—
133Dic47—21no—
134Dic47—41no—
135Dic47—42no—
136#3215—471nomaximal, Sylow
137C2×C47—81no—
138C2×C47#53511yescharacteristic
139C2×C47C2×#13711yescharacteristic
140C2×C47#57511yescharacteristic
141D47—22no—
142D47—81no—
143#533—471no—
144C2×#124—471no—
145#497—471no—
146#497—471no—
147#489—471no—
148#489D4711yescharacteristic, complemented
149#464—472no—
150#464—472no—
151#451—472no—
152#450—472no—
153#432—471no—
154C47#321511yescharacteristic, complemented, Sylow
155C22×Q8—471no—
156C22×D4—471no—
157C2×Q16—472no—
158C2×Q16—472no—
159C2×SD16—472no—
160C2×SD16—472no—
161C4⋊Q8—471no—
162C4⋊Q8C2×D4711yescharacteristic, complemented
163#125—941no—
164#124—471no—
165#124—471no—
166#124—471no—
167#124—941no—
168#124—941no—
169#124C2×D4711yescharacteristic
170C22⋊Q8—472no—
171C22⋊Q8—941no—
172C4×Q8—472no—
173C4×Q8—941no—
174#117—941no—
175C2×C22⋊C4—941no—
176C2×C22⋊C4—941no—
177C2×C42—471no—
178C4⋊C8—472no—
179#103—472no—
180#103C2×D4712yescomplemented
181#102—472no—
182#102C2×D4712yes—
183C22⋊C8—472no—
184#97—471no—
185#97C2×D4711yescharacteristic, complemented
186C24—941no—
187C2×Q8—21no—
188C2×Q8—471no—
189C2×Q8—472no—
190C2×Q8—941no—
191C2×Q8—1882no—
192C2×Q8C22×D4711yescharacteristic
193C2×D4—471no—
194C2×D4—941no—
195C2×D4—1882no—
196C2×D4C22×D4711yescharacteristic
197C22×C4—471no—
198C22×C4—471no—
199C22×C4—471no—
200C22×C4—941no—
201Q16—1882no—
202Q16—1882no—
203SD16—1882no—
204SD16—1882no—
205C2×C8—472no—
206C2×C8C22×D4712yes—
207C4⋊C4—21no—
208C4⋊C4—942no—
209C4⋊C4—942no—
210C4⋊C4—941no—
211C4⋊C4—941no—
212C4⋊C4C22×D4712yes—
213C22⋊C4—21no—
214C22⋊C4—21no—
215C22⋊C4—941no—
216C22⋊C4—941no—
217C22⋊C4—942no—
218C22⋊C4—941no—
219C22⋊C4—941no—
220C22⋊C4—941no—
221C22⋊C4—941no—
222C42—471no—
223C42—471no—
224C42—471no—
225C42—942no—
226C42C22×D4711yescharacteristic
227C23—21no—
228C23—471no—
229C23—941no—
230C23—1882no—
231C23—1882no—
232C23—1882no—
233Q8—22no—
234Q8—42no—
235Q8—942no—
236Q8—942no—
237Q8—942no—
238Q8—1882no—
239D4—22no—
240D4—942no—
241D4—1882no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—471no—
245C2×C4—471no—
246C2×C4—471no—
247C2×C4—942no—
248C2×C4—942no—
249C2×C4—942no—
250C2×C4—941no—
251C2×C4—1881no—
252C2×C4—1882no—
253C2×C4D4×D4711yescharacteristic
254C2×C4D4×D4711yescharacteristic
255C2×C4C23×D4711yescharacteristic
256C8—22no—
257C8—942no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—472no—
262C22—941no—
263C22—941no—
264C22—3764no—
265C22—1881no—
266C22—1881no—
267C22—1881no—
268C22C2×D4×D4711yescharacteristic
269C4—21no—
270C4—21no—
271C4—42no—
272C4—41no—
273C4—941no—
274C4—941no—
275C4—941no—
276C4—1881no—
277C4—1882no—
278C4#1309407012yes—
279C2—81no—
280C2—942no—
281C2—3761no—
282C2#1568969111yescharacteristic
283C2#137×D4711yescharacteristic
284C2#1568991911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#489C2
socleC22×C47C22×D4
hypercenter#489D47
hypocenterC47#3215
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #15689678C2semidirect
3. #15689518C2semidirect
4. #15689517C2semidirect
5. #15689485C2semidirect
6. #15689348C2semidirect
7. #15689344C2semidirect
8. #15689280C2semidirect
10. #15689178C2semidirect
11. C47×#489C2semidirect
14. C2×Dic188C22semidirect
15. C2×#10625337C22semidirect
18. #13094024C22semidirect
28. #13093989C22semidirect
33. Dic47⋊C8C22semidirect
34. #13093947C22semidirect
37. #13093935C22semidirect
38. C4⋊Q8×C47C22semidirect
40. #103×C47C22semidirect
42. #97×C47C22semidirect
148. #489D47semidirect
154. C47#3215semidirect
162. C4⋊Q8C2×D47semidirect
180. #103C2×D47semidirect
185. #97C2×D47semidirect