Finite Group Databasebeta

← #20255622

Subgroups — #20255622

Order 6016.

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

normal subgroups only

This group has 448 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#15689846C211yesmaximal, characteristic, complemented
2#15689758C211yesmaximal, characteristic
3#15689469C211yesmaximal, characteristic, complemented
4#15689445C212yesmaximal, complemented
5#15689404C211yesmaximal, characteristic, complemented
6#15689366C212yesmaximal, complemented
7#15689272C212yesmaximal, complemented
8C4×#10625336C211yesmaximal, characteristic, complemented
9#15689200C211yesmaximal, characteristic, complemented
10#15689126C212yesmaximal, complemented
11C47×#460C211yesmaximal, characteristic, complemented
12C2×D4×D47—21no—
13C2×D4×D47C2212yes—
14C2×#10625336C2211yescharacteristic
15C2×#10625324C2212yescomplemented
16#13094024C2211yescharacteristic, complemented
17#13094019—22no—
18#13094012—21no—
19#13094000C2212yescomplemented
20#13093995—21no—
21#13093995C2212yes—
22#13093992—22no—
23C4×Dic94—21no—
24C4×D188C2211yescharacteristic
25C4×D188C2211yescharacteristic
26#13093982C2212yescomplemented
27#13093958C2212yescomplemented
28#13093955C2211yescharacteristic, complemented
29#13093948C2211yescharacteristic, complemented
30#13093946C2212yes—
31#13093945C2212yescomplemented
32#13093945C2212yescomplemented
33#13093944C2211yescharacteristic
34(C2×D47)⋊C8C2212yescomplemented
35C4×C47⋊C8C2211yescharacteristic, complemented
36C2×SD16×C47C2212yescomplemented
37#127×C47C2211yescharacteristic
38C4×Q8×C47C2211yescharacteristic, complemented
39C4⋊C8×C47C2211yescharacteristic, complemented
40#102×C47C2212yescomplemented
41C23×D47—22no—
42C2×Q8×C47C2311yescharacteristic
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×D47C2312yes—
55C2×Dic94—21no—
56SD16×C47—42no—
57C2×C8×C47C2312yes—
58C4⋊C4×C47—21no—
59C4⋊C4×C47C2311yescharacteristic
60C42×C47—21no—
61C42×C47C2311yescharacteristic
62C22⋊Dic47—22no—
63#10625336—22no—
64(C2×D47)⋊C4—22no—
65(C2×D47)⋊C4—22no—
66(C2×D47)⋊C4—21no—
67(C2×D47)⋊C4D412yes—
68C4⋊Dic47—21no—
69C4⋊Dic47D411yescharacteristic
70C4⋊Dic47C2312yes—
71C4⋊Dic47C2311yescharacteristic
72Dic47⋊C4—22no—
73C4×Dic47—22no—
74C2×C47⋊C8C2311yescharacteristic
75C2×C47⋊C8C2311yescharacteristic
76#10625324—42no—
77C23×C47—22no—
78C22×D47—21no—
79C22×D47—44no—
80C22×D47—44no—
81C22×D47—82no—
82C22×D47C2×D412yes—
83Q8×C47—21no—
84Q8×C47—21no—
85D4×C47—22no—
86D4×C47—22no—
87D4×C47—42no—
88D4×C47—81no—
89C2×C4×C47—21no—
90C2×C4×C47—21no—
91C2×C4×C47C2×D411yescharacteristic
92C2×C4×C47C2×D411yescharacteristic
93C2×C4×C47C2411yescharacteristic
94C22⋊D47—44no—
95C22⋊D47—44no—
96C2×Dic47—22no—
97C2×Dic47—21no—
98C2×Dic47C2×D412yes—
99D188—22no—
100D188—21no—
101D188#4112yes—
102C4×D47—22no—
103C4×D47—22no—
104C4×D47—42no—
105Dic94—42no—
106C8×C47—22no—
107C47⋊C8—21no—
108C47⋊C8—21no—
109C22×C47—42no—
110C22×C47—42no—
111C22×C47—42no—
112C22×C47C22×D411yescharacteristic
113C2×D47—22no—
114C2×D47—22no—
115C2×D47—22no—
116C2×D47—22no—
117C2×D47—41no—
118C2×D47—41no—
119C2×D47—88no—
120C4×C47—21no—
121C4×C47—41no—
122C4×C47—41no—
123C4×C47AGL(1,ℤ/8)12yes—
124C4×C47C2×#4111yescharacteristic
125C4×C47H(5,𝔽2)11yescharacteristic
126Dic47—22no—
127Dic47—42no—
128Dic47—41no—
129#3324—471nomaximal, Sylow
130C2×C47—82no—
131C2×C47#54611yescharacteristic
132C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
133C2×C47#57711yescharacteristic
134D47—42no—
135D47—42no—
136#556—471no—
137D42—471no—
138#486—471no—
139#482—472no—
140#474—471no—
141#468—472no—
142#460D4711yescharacteristic, complemented
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×SD16C2×D4712yescomplemented
152C2×M16—472no—
153C4⋊Q8—471no—
154#127C2×D4711yescharacteristic
155#126—942no—
156#124—941no—
157C22⋊Q8—472no—
158#121—472no—
159#121—941no—
160#120—942no—
161C4×Q8—941no—
162C4×Q8C2×D4711yescharacteristic, complemented
163C4×D4—471no—
164C4×D4—471no—
165#117—472no—
166#107—472no—
167#106—471no—
168C4⋊C8C2×D4711yescharacteristic, complemented
169#103—471no—
170#102—472no—
171#102—472no—
172#102—472no—
173#102—471no—
174#102C2×D4712yescomplemented
175C22⋊C8—472no—
176C4×C8—471no—
177C24—942no—
178C2×Q8—941no—
179C2×Q8C22×D4711yescharacteristic
180C2×D4—21no—
181C2×D4—21no—
182C2×D4—471no—
183C2×D4—471no—
184C2×D4—942no—
185C2×D4—944no—
186C2×D4—942no—
187C2×D4—1882no—
188C2×D4—1884no—
189C2×D4C22×D4712yes—
190C22×C4—472no—
191C22×C4—941no—
192SD16—42no—
193SD16—942no—
194M16—1882no—
195C2×C8—471no—
196C2×C8—471no—
197C2×C8C22×D4712yes—
198C4⋊C4—21no—
199C4⋊C4—471no—
200C4⋊C4—472no—
201C4⋊C4—471no—
202C4⋊C4—942no—
203C4⋊C4—941no—
204C4⋊C4C22×D4711yescharacteristic
205C22⋊C4—472no—
206C22⋊C4—942no—
207C22⋊C4—942no—
208C22⋊C4—942no—
209C22⋊C4—941no—
210C42—21no—
211C42—942no—
212C42C22×D4711yescharacteristic
213C23—22no—
214C23—472no—
215C23—941no—
216C23—3762no—
217C23—1884no—
218C23—1884no—
219Q8—21no—
220Q8—21no—
221Q8—1882no—
222D4—22no—
223D4—22no—
224D4—42no—
225D4—81no—
226D4—472no—
227D4—942no—
228D4—941no—
229D4—1884no—
230D4—1884no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—472no—
234C2×C4—942no—
235C2×C4—942no—
236C2×C4—942no—
237C2×C4—941no—
238C2×C4—1882no—
239C2×C4D4×D4711yescharacteristic
240C2×C4D4×D4711yescharacteristic
241C2×C4C23×D4711yescharacteristic
242C8—22no—
243C8—941no—
244C8—941no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22—942no—
249C22—942no—
250C22—942no—
251C22—942no—
252C22—3768no—
253C22—1881no—
254C22—1881no—
255C22C2×D4×D4711yescharacteristic
256C4—21no—
257C4—41no—
258C4—41no—
259C4—942no—
260C4—1881no—
261C4—1882no—
262C4#1309405112yes—
263C4#41×D4711yescharacteristic
264C4#1309406911yescharacteristic
265C2—82no—
266C2—1882no—
267C2—1882no—
268C2#1568977011yescharacteristic
269C2C2×#1309405111yescharacteristic
270C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#460C2
socleC22×C47C22×D4
hypercenter#460D47
hypocenterC47#3324
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #15689846C2semidirect
3. #15689469C2semidirect
4. #15689445C2semidirect
5. #15689404C2semidirect
6. #15689366C2semidirect
7. #15689272C2semidirect
8. C4×#10625336C2semidirect
9. #15689200C2semidirect
10. #15689126C2semidirect
11. C47×#460C2semidirect
15. C2×#10625324C22semidirect
16. #13094024C22semidirect
19. #13094000C22semidirect
26. #13093982C22semidirect
27. #13093958C22semidirect
28. #13093955C22semidirect
29. #13093948C22semidirect
31. #13093945C22semidirect
32. #13093945C22semidirect
34. (C2×D47)⋊C8C22semidirect
35. C4×C47⋊C8C22semidirect
36. C2×SD16×C47C22semidirect
38. C4×Q8×C47C22semidirect
39. C4⋊C8×C47C22semidirect
40. #102×C47C22semidirect
142. #460D47semidirect
147. C47#3324semidirect
151. C2×SD16C2×D47semidirect
162. C4×Q8C2×D47semidirect
168. C4⋊C8C2×D47semidirect
174. #102C2×D47semidirect