Finite Group Databasebeta

← #489×D47 #20253714

Subgroups — #489×D47 #20253714

Order 6016.

436 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C4⋊Q8×D47C211yesmaximal, characteristic, complemented
2#124×D47C211yesmaximal, characteristic
3#15689485C211yesmaximal, characteristic, complemented
4#15689484C212yesmaximal, complemented
5#15689483C211yesmaximal, characteristic, complemented
6#15689482C211yesmaximal, characteristic, complemented
7#15689481C212yesmaximal, complemented
8#103×D47C212yesmaximal, complemented
9#102×D47C212yesmaximal
10#97×D47C211yesmaximal, characteristic, complemented
11C47×#489C211yesmaximal, characteristic, complemented
12C2×Q8×D47—21no—
13C2×Q8×D47C2211yescharacteristic
14C2×D4×D47C2211yescharacteristic
15C2×C8×D47C2212yes—
16#13094024C2211yescharacteristic, complemented
17#13094023—21no—
18#13094023C2212yescomplemented
19#13094022—21no—
20#13094013C2211yescharacteristic
21#13094012C2211yescharacteristic
22#13094011C2211yescharacteristic
23#13094010—21no—
24#13094010—21no—
25C4⋊C4×D47—21no—
26C4⋊C4×D47C2212yes—
27C22⋊C4×D47—21no—
28C22⋊C4×D47—21no—
29C42×D47C2211yescharacteristic
30#13093949C2212yescomplemented
31#13093948C2212yescomplemented
32#13093947C2212yescomplemented
33#13093946C2212yes—
34#13093945C2212yes—
35#13093944C2212yes—
36#13093935C2211yescharacteristic, complemented
37#13093934C2212yescomplemented
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—24no—
49Q8×D47—44no—
50D4×D47—24no—
51C2×D188C2311yescharacteristic
52C2×C4×D47—21no—
53C2×C4×D47—22no—
54C2×C4×D47D411yescharacteristic
55C2×C4×D47D411yescharacteristic
56C2×C4×D47C2311yescharacteristic
57C2×Dic94—21no—
58C2×Dic94—21no—
59C2×Dic94—22no—
60C2×Dic94C2311yescharacteristic
61C2×C8×C47C2312yes—
62C4⋊C4×C47—21no—
63C4⋊C4×C47C2312yes—
64C22⋊C4×C47—21no—
65C22⋊C4×C47—21no—
66C42×C47C2311yescharacteristic
67C22⋊Dic47—21no—
68C22⋊Dic47—21no—
69(C2×D47)⋊C4—21no—
70(C2×D47)⋊C4—21no—
71(C2×D47)⋊C4—21no—
72(C2×D47)⋊C4—21no—
73C4⋊Dic47—21no—
74C4⋊Dic47C2312yes—
75Dic47⋊C4—22no—
76Dic47⋊C4—22no—
77C4×Dic47D411yescharacteristic
78C4×Dic47D411yescharacteristic
79C4×Dic47C2311yescharacteristic
80C2×C47⋊C8C2312yes—
81C8×D47—24no—
82C23×C47—21no—
83C22×D47—21no—
84C22×D47—42no—
85C22×D47—42no—
86C22×D47—42no—
87C22×D47C2×D411yescharacteristic
88Q8×C47—22no—
89Q8×C47—42no—
90D4×C47—22no—
91C2×C4×C47—22no—
92C2×C4×C47—21no—
93C2×C4×C47C2×D411yescharacteristic
94C2×C4×C47C2×D411yescharacteristic
95C2×C4×C47C2411yescharacteristic
96C22⋊D47—42no—
97C2×Dic47—22no—
98C2×Dic47—21no—
99C2×Dic47C2×D411yescharacteristic
100C2×Dic47C2×D411yescharacteristic
101C2×Dic47C2×D411yescharacteristic
102D188—22no—
103C4×D47—22no—
104C4×D47—22no—
105C4×D47—42no—
106C4×D47—44no—
107C4×D47#4114yes—
108Dic94—22no—
109Dic94—44no—
110Dic94—42no—
111Dic94—42no—
112C8×C47—22no—
113C47⋊C8—22no—
114C22×C47—41no—
115C22×C47—41no—
116C22×C47—41no—
117C22×C47C22×D411yescharacteristic
118C2×D47—41no—
119C2×D47—41no—
120C2×D47—41no—
121C2×D47—84no—
122C2×D47#12412yes—
123C2×D47AGL(1,ℤ/8)12yes—
124C2×D47#13712yes—
125C4×C47—21no—
126C4×C47—21no—
127C4×C47—41no—
128C4×C47—42no—
129C4×C47C2×#4112yes—
130Dic47—21no—
131Dic47—21no—
132Dic47—41no—
133Dic47—42no—
134Dic47#12412yes—
135C2×#489—471nomaximal, Sylow
136C2×C47—81no—
137C2×C47C2×#12411yescharacteristic
138C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
139C2×C47C2×#13711yescharacteristic
140D47—81no—
141D47#48914yesdirect product factor
142C2×C4⋊Q8—471no—
143C2×#124—471no—
144#489—471no—
145#489—471no—
146#489—472no—
147#489—472no—
148#489—471no—
149#489D4711yescharacteristic, direct product factor
150C2×#103—472no—
151C2×#102—472no—
152C2×#97—471no—
153C47C2×#48911yescharacteristic, complemented, Sylow
154C22×Q8—471no—
155C22×Q8—941no—
156C22×D4—471no—
157C22×C8—472no—
158C4⋊Q8—472no—
159C4⋊Q8—471no—
160C4⋊Q8—941no—
161C4⋊Q8—941no—
162C4⋊Q8C2×D4711yescharacteristic, complemented
163#124—471no—
164#124—471no—
165#124—471no—
166#124—941no—
167#124—941no—
168#124C2×D4711yescharacteristic
169C2×C4⋊C4—472no—
170C2×C4⋊C4—941no—
171C2×C22⋊C4—941no—
172C2×C22⋊C4—941no—
173C2×C42—471no—
174#103—472no—
175#103—472no—
176#103—472no—
177#103C2×D4712yescomplemented
178#102—472no—
179#102—472no—
180#102—472no—
181#102C2×D4712yes—
182#97—472no—
183#97—471no—
184#97C2×D4711yescharacteristic, complemented
185C24—941no—
186C2×Q8—21no—
187C2×Q8—471no—
188C2×Q8—941no—
189C2×Q8—942no—
190C2×Q8—944no—
191C2×Q8—941no—
192C2×Q8—1884no—
193C2×Q8C22×D4711yescharacteristic
194C2×D4—471no—
195C2×D4—944no—
196C2×D4—941no—
197C2×D4C22×D4711yescharacteristic
198C22×C4—471no—
199C22×C4—471no—
200C22×C4—471no—
201C22×C4—941no—
202C22×C4—942no—
203C2×C8—472no—
204C2×C8—944no—
205C2×C8C22×D4712yes—
206C4⋊C4—21no—
207C4⋊C4—472no—
208C4⋊C4—942no—
209C4⋊C4—942no—
210C4⋊C4—941no—
211C4⋊C4C22×D4712yes—
212C22⋊C4—21no—
213C22⋊C4—21no—
214C22⋊C4—941no—
215C22⋊C4—941no—
216C22⋊C4—941no—
217C22⋊C4—941no—
218C22⋊C4—941no—
219C22⋊C4—941no—
220C42—471no—
221C42—471no—
222C42—471no—
223C42C22×D4711yescharacteristic
224C23—21no—
225C23—471no—
226C23—941no—
227C23—1882no—
228C23—1882no—
229C23—1882no—
230Q8—22no—
231Q8—42no—
232Q8—942no—
233Q8—1882no—
234Q8—1882no—
235Q8—1884no—
236D4—22no—
237D4—942no—
238D4—1882no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—471no—
242C2×C4—474no—
243C2×C4—471no—
244C2×C4—471no—
245C2×C4—942no—
246C2×C4—942no—
247C2×C4—941no—
248C2×C4—942no—
249C2×C4—1882no—
250C2×C4—1884no—
251C2×C4D4×D4711yescharacteristic
252C2×C4D4×D4711yescharacteristic
253C2×C4C23×D4711yescharacteristic
254C8—22no—
255C8—942no—
256C22—41no—
257C22—41no—
258C22—41no—
259C22—472no—
260C22—472no—
261C22—472no—
262C22—3764no—
263C22—1881no—
264C22—1881no—
265C22—1881no—
266C22C2×D4×D4711yescharacteristic
267C4—21no—
268C4—21no—
269C4—41no—
270C4—42no—
271C4—472no—
272C4—941no—
273C4—941no—
274C4—1881no—
275C4—1882no—
276C4#41×D4712yes—
277C2—81no—
278C2—474no—
279C2—3761no—
280C2#124×D4711yescharacteristic
281C2AGL(1,ℤ/8)×D4711yescharacteristic
282C2#137×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#489C2
socleC22×C47C22×D4
hypercenter#489D47
hypocenterC47C2×#489
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. C4⋊Q8×D47C2semidirect
3. #15689485C2semidirect
4. #15689484C2semidirect
5. #15689483C2semidirect
6. #15689482C2semidirect
7. #15689481C2semidirect
8. #103×D47C2semidirect
10. #97×D47C2semidirect
11. C47×#489C2semidirect
16. #13094024C22semidirect
18. #13094023C22semidirect
30. #13093949C22semidirect
31. #13093948C22semidirect
32. #13093947C22semidirect
36. #13093935C22semidirect
37. #13093934C22semidirect
38. C4⋊Q8×C47C22semidirect
40. #103×C47C22semidirect
42. #97×C47C22semidirect
141. D47#489direct (N × H)
149. #489D47direct (N × H)
153. C47C2×#489semidirect
162. C4⋊Q8C2×D47semidirect
177. #103C2×D47semidirect
184. #97C2×D47semidirect