Finite Group Databasebeta

← #20255618

Subgroups — #20255618

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#15689847C211yesmaximal, characteristic, complemented
2#15689758C211yesmaximal, characteristic
3#15689446C212yesmaximal, complemented
4#15689400C211yesmaximal, characteristic, complemented
5#15689368C212yesmaximal, complemented
6#15689320C211yesmaximal, characteristic, complemented
7#15689275C212yesmaximal, complemented
8C4×#10625325C211yesmaximal, characteristic, complemented
9#15689202C211yesmaximal, characteristic, complemented
10#15689126C212yesmaximal, complemented
11C47×#486C211yesmaximal, characteristic, complemented
12C2×D4×D47—21no—
13C2×D4×D47C2212yes—
14C2×#10625325C2211yescharacteristic
15C2×#10625335C2212yescomplemented
16C2×#10625324C2212yescomplemented
17#13094019—22no—
18#13094013—21no—
19#13094004C2212yescomplemented
20#13093995—21no—
21#13093995C2212yes—
22#13093992—22no—
23Q8×Dic47—21no—
24C4×Dic94C2211yescharacteristic, complemented
25C4×D188C2211yescharacteristic
26C4×D188C2211yescharacteristic
27#13093982C2212yescomplemented
28#13093957C2212yescomplemented
29#13093956C2211yescharacteristic, complemented
30C4⋊(C47⋊C8)C2211yescharacteristic, complemented
31#13093949C2211yescharacteristic, complemented
32#13093946C2211yescharacteristic
33#13093945C2212yescomplemented
34#13093944C2212yes—
35(C2×D47)⋊C8C2212yescomplemented
36C4⋊Q8×C47C2211yescharacteristic, complemented
37#127×C47C2211yescharacteristic
38#102×C47C2212yescomplemented
39#102×C47C2212yescomplemented
40C4×C8×C47C2211yescharacteristic, complemented
41C23×D47—22no—
42C2×Q8×C47—21no—
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×Dic94C2311yescharacteristic
56C2×C8×C47C2311yescharacteristic
57C2×C8×C47C2311yescharacteristic
58C4⋊C4×C47—21no—
59C4⋊C4×C47C2312yes—
60C42×C47C2311yescharacteristic
61C22⋊Dic47—22no—
62#10625335—42no—
63(C2×D47)⋊C4—22no—
64(C2×D47)⋊C4—22no—
65(C2×D47)⋊C4—21no—
66(C2×D47)⋊C4D412yes—
67C4⋊Dic47—22no—
68C4⋊Dic47D411yescharacteristic
69C4⋊Dic47C2311yescharacteristic
70C4⋊Dic47C2311yescharacteristic
71Dic47⋊C4—21no—
72C4×Dic47—21no—
73C4×Dic47—22no—
74C2×C47⋊C8C2312yes—
75#10625325—22no—
76#10625324—42no—
77C23×C47—22no—
78C22×D47—21no—
79C22×D47—44no—
80C22×D47—44no—
81C22×D47—82no—
82C22×D47C2×D412yes—
83Q8×C47—42no—
84D4×C47—22no—
85D4×C47—22no—
86D4×C47—42no—
87D4×C47—81no—
88C2×C4×C47—22no—
89C2×C4×C47C2×D411yescharacteristic
90C2×C4×C47C2×D411yescharacteristic
91C2×C4×C47C2411yescharacteristic
92C22⋊D47—44no—
93C22⋊D47—44no—
94C2×Dic47—21no—
95C2×Dic47—21no—
96C2×Dic47—21no—
97C2×Dic47C2×D412yes—
98D188—22no—
99D188—21no—
100D188#4112yes—
101C4×D47—22no—
102C4×D47—22no—
103C4×D47—42no—
104Dic94—21no—
105Dic94—21no—
106C8×C47—21no—
107C8×C47—21no—
108C47⋊C8—22no—
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—42no—
122C4×C47AGL(1,ℤ/8)12yes—
123C4×C47C2×#4111yescharacteristic
124C4×C47H(5,𝔽2)11yescharacteristic
125Dic47—22no—
126Dic47—41no—
127Dic47—41no—
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#486D4711yescharacteristic, complemented
139#482—472no—
140#474—471no—
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—472no—
151C2×SD16—471no—
152C2×M16—472no—
153C4⋊Q8C2×D4711yescharacteristic, complemented
154#127C2×D4711yescharacteristic
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×D4—471no—
165#117—472no—
166#107—472no—
167#106—471no—
168C4⋊C8—471no—
169#103—471no—
170#102—472no—
171#102—471no—
172#102—472no—
173#102C2×D4712yescomplemented
174#102C2×D4712yescomplemented
175C22⋊C8—472no—
176C4×C8C2×D4711yescharacteristic, complemented
177C24—942no—
178C2×Q8—21no—
179C2×Q8—471no—
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—942no—
193SD16—1882no—
194M16—1882no—
195C2×C8—472no—
196C2×C8C22×D4711yescharacteristic
197C2×C8C22×D4711yescharacteristic
198C4⋊C4—21no—
199C4⋊C4—471no—
200C4⋊C4—471no—
201C4⋊C4—471no—
202C4⋊C4—942no—
203C4⋊C4—941no—
204C4⋊C4C22×D4712yes—
205C22⋊C4—472no—
206C22⋊C4—942no—
207C22⋊C4—942no—
208C22⋊C4—942no—
209C22⋊C4—941no—
210C42—942no—
211C42—941no—
212C42C22×D4711yescharacteristic
213C23—22no—
214C23—472no—
215C23—941no—
216C23—3762no—
217C23—1884no—
218C23—1884no—
219Q8—42no—
220Q8—941no—
221Q8—941no—
222D4—22no—
223D4—22no—
224D4—42no—
225D4—81no—
226D4—472no—
227D4—942no—
228D4—941no—
229D4—1884no—
230D4—1884no—
231C2×C4—22no—
232C2×C4—472no—
233C2×C4—942no—
234C2×C4—942no—
235C2×C4—941no—
236C2×C4—941no—
237C2×C4—941no—
238C2×C4—1882no—
239C2×C4D4×D4711yescharacteristic
240C2×C4D4×D4711yescharacteristic
241C2×C4C23×D4711yescharacteristic
242C8—21no—
243C8—21no—
244C8—942no—
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—42no—
258C4—942no—
259C4—1881no—
260C4—1881no—
261C4—1881no—
262C4#1309404812yes—
263C4#41×D4711yescharacteristic
264C4#1309407011yescharacteristic
265C2—82no—
266C2—1882no—
267C2—1882no—
268C2#1568976611yescharacteristic
269C2C2×#1309404811yescharacteristic
270C2#1568992911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#486C2
socleC22×C47C22×D4
hypercenter#486D47
hypocenterC47#3324
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #15689847C2semidirect
3. #15689446C2semidirect
4. #15689400C2semidirect
5. #15689368C2semidirect
6. #15689320C2semidirect
7. #15689275C2semidirect
8. C4×#10625325C2semidirect
9. #15689202C2semidirect
10. #15689126C2semidirect
11. C47×#486C2semidirect
15. C2×#10625335C22semidirect
16. C2×#10625324C22semidirect
19. #13094004C22semidirect
24. C4×Dic94C22semidirect
27. #13093982C22semidirect
28. #13093957C22semidirect
29. #13093956C22semidirect
30. C4⋊(C47⋊C8)C22semidirect
31. #13093949C22semidirect
33. #13093945C22semidirect
35. (C2×D47)⋊C8C22semidirect
36. C4⋊Q8×C47C22semidirect
38. #102×C47C22semidirect
39. #102×C47C22semidirect
40. C4×C8×C47C22semidirect
138. #486D47semidirect
147. C47#3324semidirect
153. C4⋊Q8C2×D47semidirect
173. #102C2×D47semidirect
174. #102C2×D47semidirect
176. C4×C8C2×D47semidirect