Finite Group Databasebeta

← #20255616

Subgroups — #20255616

Order 6016.

448 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 448 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#15689847C211yesmaximal, characteristic, complemented
2D4×D188C211yesmaximal, characteristic
3#15689471C211yesmaximal, characteristic, complemented
4#15689450C212yesmaximal, complemented
5#15689370C212yesmaximal, complemented
6#15689324C211yesmaximal, characteristic, complemented
7#15689275C212yesmaximal, complemented
8C4×#10625335C211yesmaximal, characteristic, complemented
9#15689200C211yesmaximal, characteristic, complemented
10#15689126C212yesmaximal, complemented
11C47×#474C211yesmaximal, characteristic, complemented
12C22×D188—21no—
13C2×D4×D47C2212yes—
14C2×#10625325C2212yescomplemented
15C2×#10625335C2211yescharacteristic
16C2×#10625324C2212yescomplemented
17#13094021C2211yescharacteristic
18#13094019—22no—
19#13094013—21no—
20#13094004C2212yescomplemented
21#13093999C2212yes—
22#13093998—21no—
23#13093994—22no—
24Q8×Dic47—21no—
25C4×Dic94C2211yescharacteristic, complemented
26C4×D188C2211yescharacteristic
27#13093982C2212yescomplemented
28#13093955C2211yescharacteristic, complemented
29#13093947C2211yescharacteristic, complemented
30#13093946C2212yescomplemented
31#13093945C2211yescharacteristic
32#13093944C2212yescomplemented
33#13093944C2212yescomplemented
34(C2×D47)⋊C8C2212yescomplemented
35C4×C47⋊C8C2211yescharacteristic, complemented
36C4⋊Q8×C47C2211yescharacteristic, complemented
37C4×D4×C47C2211yescharacteristic
38#107×C47C2212yescomplemented
39C4⋊C8×C47C2211yescharacteristic, complemented
40#102×C47C2212yes—
41C23×D47—22no—
42C2×Q8×C47—21no—
43C2×D4×C47C2311yescharacteristic
44C22×C4×C47—21no—
45C2×C22⋊D47—22no—
46D4×D47—24no—
47D4×D47—42no—
48C2×D188—22no—
49C2×D188—21no—
50C2×D188—21no—
51C2×D188—44no—
52C2×D188D411yescharacteristic
53C2×D188C2312yes—
54C2×C4×D47C2312yes—
55C2×Dic94C2311yescharacteristic
56C2×C8×C47C2312yes—
57C4⋊C4×C47—21no—
58C4⋊C4×C47C2311yescharacteristic
59C4⋊C4×C47C2312yes—
60C22⋊C4×C47—21no—
61C42×C47C2311yescharacteristic
62#10625335—22no—
63(C2×D47)⋊C4—22no—
64(C2×D47)⋊C4—22no—
65(C2×D47)⋊C4—22no—
66(C2×D47)⋊C4D412yes—
67C4⋊Dic47—22no—
68C4⋊Dic47D411yescharacteristic
69C4⋊Dic47C2311yescharacteristic
70Dic47⋊C4—21no—
71C4×Dic47—21no—
72C4×Dic47—22no—
73C2×C47⋊C8C2311yescharacteristic
74C2×C47⋊C8C2311yescharacteristic
75#10625325—42no—
76#10625324—42no—
77C23×C47—21no—
78C22×D47—22no—
79C22×D47—44no—
80C22×D47—44no—
81C22×D47—82no—
82C22×D47C2×D412yes—
83Q8×C47—42no—
84D4×C47—21no—
85D4×C47#4112yes—
86C2×C4×C47—22no—
87C2×C4×C47—21no—
88C2×C4×C47—42no—
89C2×C4×C47C2×D411yescharacteristic
90C2×C4×C47C2×D411yescharacteristic
91C2×C4×C47C2411yescharacteristic
92C22⋊D47—44no—
93C2×Dic47—21no—
94C2×Dic47—21no—
95C2×Dic47C2×D412yes—
96D188—22no—
97D188—22no—
98D188—22no—
99D188—44no—
100D188—42no—
101D188—81no—
102C4×D47—22no—
103C4×D47—22no—
104Dic94—21no—
105Dic94—21no—
106C8×C47—22no—
107C47⋊C8—21no—
108C47⋊C8—21no—
109C22×C47—22no—
110C22×C47—41no—
111C22×C47—41no—
112C22×C47C22×D411yescharacteristic
113C2×D47—22no—
114C2×D47—22no—
115C2×D47—22no—
116C2×D47—42no—
117C2×D47—42no—
118C2×D47—42no—
119C2×D47—88no—
120C4×C47—21no—
121C4×C47—41no—
122C4×C47—42no—
123C4×C47AGL(1,ℤ/8)12yes—
124C4×C47C2×#4111yescharacteristic
125C4×C47H(5,𝔽2)11yescharacteristic
126Dic47—22no—
127Dic47—41no—
128Dic47—41no—
129#3324—471nomaximal, Sylow
130C2×C47—42no—
131C2×C47#54611yescharacteristic
132C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
133C2×C47#57711yescharacteristic
134D47—42no—
135D47—82no—
136#556—471no—
137D42—471no—
138#486—471no—
139#482—472no—
140#474D4711yescharacteristic, complemented
141#468—472no—
142#460—471no—
143#450—472no—
144C4×SD16—471no—
145#436—471no—
146#418—472no—
147C47#332411yescharacteristic, complemented, Sylow
148C22×D4—472no—
149C22×D4—941no—
150C2×SD16—471no—
151C2×SD16—472no—
152C2×M16—472no—
153C4⋊Q8C2×D4711yescharacteristic, complemented
154#127—471no—
155#126—942no—
156#124—941no—
157C22⋊Q8—472no—
158#121—472no—
159#121—941no—
160#120—942no—
161C4×Q8—471no—
162C4×Q8—941no—
163C4×D4—471no—
164C4×D4C2×D4711yescharacteristic
165#117—472no—
166#107C2×D4712yescomplemented
167#106—471no—
168C4⋊C8C2×D4711yescharacteristic, complemented
169#103—471no—
170#102—471no—
171#102—472no—
172#102—472no—
173#102—472no—
174#102C2×D4712yes—
175C22⋊C8—472no—
176C4×C8—471no—
177C24—942no—
178C2×Q8—21no—
179C2×Q8—471no—
180C2×D4—471no—
181C2×D4—472no—
182C2×D4—942no—
183C2×D4—942no—
184C2×D4—944no—
185C2×D4—941no—
186C2×D4—941no—
187C2×D4—1884no—
188C2×D4—1882no—
189C2×D4C22×D4711yescharacteristic
190C22×C4—21no—
191C22×C4—472no—
192SD16—942no—
193SD16—1882no—
194M16—1882no—
195C2×C8—471no—
196C2×C8—471no—
197C2×C8C22×D4712yes—
198C4⋊C4—21no—
199C4⋊C4—471no—
200C4⋊C4—471no—
201C4⋊C4—942no—
202C4⋊C4—941no—
203C4⋊C4C22×D4712yes—
204C4⋊C4C22×D4711yescharacteristic
205C22⋊C4—21no—
206C22⋊C4—472no—
207C22⋊C4—942no—
208C22⋊C4—942no—
209C22⋊C4—942no—
210C42—942no—
211C42—941no—
212C42C22×D4711yescharacteristic
213C23—21no—
214C23—472no—
215C23—942no—
216C23—3762no—
217C23—1884no—
218C23—1884no—
219Q8—42no—
220Q8—941no—
221Q8—941no—
222D4—21no—
223D4—942no—
224D4—942no—
225D4—942no—
226D4—3761no—
227D4—1884no—
228D4—1884no—
229D4—1882no—
230D4#1062535412yes—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—42no—
234C2×C4—472no—
235C2×C4—942no—
236C2×C4—942no—
237C2×C4—941no—
238C2×C4—941no—
239C2×C4D4×D4711yescharacteristic
240C2×C4D4×D4711yescharacteristic
241C2×C4C23×D4711yescharacteristic
242C8—22no—
243C8—941no—
244C8—941no—
245C22—22no—
246C22—41no—
247C22—41no—
248C22—942no—
249C22—942no—
250C22—942no—
251C22—3768no—
252C22—1882no—
253C22—1882no—
254C22—1882no—
255C22C2×D4×D4711yescharacteristic
256C4—21no—
257C4—41no—
258C4—42no—
259C4—942no—
260C4—1881no—
261C4—1881no—
262C4#1309404812yes—
263C4C2×#1062535411yescharacteristic
264C4#1309407011yescharacteristic
265C2—42no—
266C2—3762no—
267C2—1882no—
268C2#1568976411yescharacteristic
269C2C2×#1309404811yescharacteristic
270C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#474C2
socleC22×C47C22×D4
hypercenter#474D47
hypocenterC47#3324
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #15689847C2semidirect
3. #15689471C2semidirect
4. #15689450C2semidirect
5. #15689370C2semidirect
6. #15689324C2semidirect
7. #15689275C2semidirect
8. C4×#10625335C2semidirect
9. #15689200C2semidirect
10. #15689126C2semidirect
11. C47×#474C2semidirect
14. C2×#10625325C22semidirect
16. C2×#10625324C22semidirect
20. #13094004C22semidirect
25. C4×Dic94C22semidirect
27. #13093982C22semidirect
28. #13093955C22semidirect
29. #13093947C22semidirect
30. #13093946C22semidirect
32. #13093944C22semidirect
33. #13093944C22semidirect
34. (C2×D47)⋊C8C22semidirect
35. C4×C47⋊C8C22semidirect
36. C4⋊Q8×C47C22semidirect
38. #107×C47C22semidirect
39. C4⋊C8×C47C22semidirect
140. #474D47semidirect
147. C47#3324semidirect
153. C4⋊Q8C2×D47semidirect
166. #107C2×D47semidirect
168. C4⋊C8C2×D47semidirect