Finite Group Databasebeta

← #20255631

Subgroups — #20255631

Order 6016.

460 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 123 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#15689838C211yesmaximal, characteristic, complemented
2D4×D188C211yesmaximal, characteristic, complemented
3#15689470C211yesmaximal, characteristic, complemented
4#15689448C212yesmaximal, complemented
5#15689414C211yesmaximal, characteristic, complemented
6#15689376C212yesmaximal, complemented
7#15689319C211yesmaximal, characteristic, complemented
8#15689259C212yesmaximal, complemented
9C4×D376C211yesmaximal, characteristic, complemented
10#15689129C212yesmaximal, complemented
11C47×#436C211yesmaximal, characteristic, complemented
12C22×D188C2212yes—
13C2×D4×D47—21no—
14C2×D376C2211yescharacteristic
15C2×D376C2212yescomplemented
16#13094024C2211yescharacteristic, complemented
17#13094021C2211yescharacteristic
18#13094010—22no—
19#13093999—21no—
20#13093998C2212yes—
21#13093998C2212yescomplemented
22#13093995—21no—
23#13093994—22no—
24C4×D188C2211yescharacteristic
25C4×D188C2211yescharacteristic, complemented
26#13093983C2212yescomplemented
27#13093982—21no—
28#13093958C2211yescharacteristic, complemented
29#13093956C2212yescomplemented
30#13093946C2212yes—
31#13093946C2211yescharacteristic
32#13093946C2212yescomplemented
33#13093946C2212yescomplemented
34#13093946C2211yescharacteristic, complemented
35#13093946C2212yescomplemented
36C2×M16×C47C2212yescomplemented
37C4×D4×C47C2211yescharacteristic
38C4⋊C8×C47C2211yescharacteristic, complemented
39C22⋊C8×C47C2212yescomplemented
40C4×C8×C47C2211yescharacteristic, complemented
41C23×D47—22no—
42C2×D4×C47D411yescharacteristic
43C22×C4×C47C2312yes—
44C2×C22⋊D47—22no—
45C2×C22⋊D47—22no—
46D4×D47—44no—
47C2×D188—24no—
48C2×D188—22no—
49C2×D188—21no—
50C2×D188—21no—
51C2×D188—42no—
52C2×D188C2312yes—
53C2×D188C2311yescharacteristic
54C2×D188C2311yescharacteristic
55C2×C4×D47—21no—
56C2×C4×D47—21no—
57C2×Dic94—21no—
58M16×C47—42no—
59C2×C8×C47C2312yes—
60C2×C8×C47C2311yescharacteristic
61C2×C8×C47C2311yescharacteristic
62C4⋊C4×C47D411yescharacteristic
63C22⋊C4×C47D412yes—
64C42×C47C2311yescharacteristic
65C22⋊Dic47—22no—
66(C2×D47)⋊C4—22no—
67(C2×D47)⋊C4—21no—
68(C2×D47)⋊C4—21no—
69(C2×D47)⋊C4—22no—
70C4⋊Dic47—21no—
71C4⋊Dic47C2312yes—
72C4⋊Dic47C2311yescharacteristic
73C4⋊Dic47C2311yescharacteristic
74C4×Dic47—22no—
75D376—22no—
76D376—42no—
77C23×C47C2×D412yes—
78C22×D47—21no—
79C22×D47—21no—
80C22×D47—22no—
81C22×D47—44no—
82C22×D47—44no—
83C22×D47—82no—
84D4×C47—22no—
85C2×C4×C47—22no—
86C2×C4×C47—22no—
87C2×C4×C47C2×D412yes—
88C2×C4×C47C2×D411yescharacteristic
89C2×C4×C47C2×D411yescharacteristic
90C2×C4×C47C2411yescharacteristic
91C22⋊D47—44no—
92C22⋊D47—82no—
93C2×Dic47—21no—
94C2×Dic47—22no—
95C2×Dic47—21no—
96D188—21no—
97D188—22no—
98D188—21no—
99D188—21no—
100D188—22no—
101D188—44no—
102D188—42no—
103D188—81no—
104D188#4112yes—
105C4×D47—42no—
106C4×D47—42no—
107Dic94—81no—
108C8×C47—21no—
109C8×C47—22no—
110C8×C47—21no—
111C22×C47—22no—
112C22×C47—22no—
113C22×C47—22no—
114C22×C47C22×D411yescharacteristic
115C2×D47—22no—
116C2×D47—41no—
117C2×D47—41no—
118C2×D47—42no—
119C2×D47—41no—
120C2×D47—41no—
121C2×D47—42no—
122C2×D47—42no—
123C2×D47—41no—
124C2×D47—88no—
125C4×C47—22no—
126C4×C47—21no—
127C4×C47AGL(1,ℤ/8)12yes—
128C4×C47C2×#4111yescharacteristic
129C4×C47H(5,𝔽2)11yescharacteristic
130Dic47—41no—
131Dic47—41no—
132Dic47—42no—
133#3325—471nomaximal, Sylow
134C2×C47—42no—
135C2×C47#54611yescharacteristic
136C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
137C2×C47#57611yescharacteristic
138D47—42no—
139D47—81no—
140D47—82no—
141#555—471no—
142D42—471no—
143#486—471no—
144#482—472no—
145#476—471no—
146#469—472no—
147#459—471no—
148#447—472no—
149C4×D8—471no—
150#436D4711yescharacteristic, complemented
151#418—472no—
152C47#332511yescharacteristic, complemented, Sylow
153C22×D4—472no—
154C22×D4—941no—
155C2×D8—471no—
156C2×D8—472no—
157C2×M16C2×D4712yescomplemented
158C4⋊Q8—471no—
159#127—471no—
160#124—942no—
161#121—472no—
162#121—472no—
163#121—941no—
164#121—941no—
165#120—942no—
166C4×D4—471no—
167C4×D4—471no—
168C4×D4C2×D4711yescharacteristic
169#117—472no—
170#117—941no—
171#107—471no—
172#106—472no—
173C4⋊C8C2×D4711yescharacteristic, complemented
174#102—471no—
175#102—472no—
176#102—472no—
177#102—472no—
178#102—471no—
179#102—472no—
180C22⋊C8C2×D4712yescomplemented
181C4×C8C2×D4711yescharacteristic, complemented
182C24—942no—
183C2×Q8—941no—
184C2×D4—471no—
185C2×D4—472no—
186C2×D4—471no—
187C2×D4—944no—
188C2×D4—942no—
189C2×D4—942no—
190C2×D4—941no—
191C2×D4—942no—
192C2×D4—941no—
193C2×D4—1882no—
194C2×D4—1884no—
195C2×D4D18811yescharacteristic
196C22×C4—941no—
197C22×C4—941no—
198C22×C4C22×D4712yes—
199D8—942no—
200D8—1882no—
201M16—42no—
202C2×C8C22×D4711yescharacteristic
203C2×C8C22×D4711yescharacteristic
204C2×C8C22×D4712yes—
205C4⋊C4—472no—
206C4⋊C4—471no—
207C4⋊C4—471no—
208C4⋊C4—941no—
209C4⋊C4D18811yescharacteristic
210C22⋊C4—942no—
211C22⋊C4—942no—
212C22⋊C4—941no—
213C22⋊C4—941no—
214C22⋊C4—942no—
215C22⋊C4D18812yes—
216C42—942no—
217C42C22×D4711yescharacteristic
218C23—941no—
219C23—941no—
220C23—942no—
221C23—3762no—
222C23—1884no—
223C23—1884no—
224C23C2×D18812yes—
225Q8—3761no—
226D4—22no—
227D4—472no—
228D4—941no—
229D4—942no—
230D4—941no—
231D4—941no—
232D4—942no—
233D4—3761no—
234D4—3762no—
235D4—1884no—
236D4—1884no—
237D4—1882no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—941no—
241C2×C4—942no—
242C2×C4—941no—
243C2×C4—1882no—
244C2×C4—1882no—
245C2×C4C2×D18812yes—
246C2×C4C2×D18811yescharacteristic
247C2×C4C2×D18811yescharacteristic
248C2×C4C23×D4711yescharacteristic
249C8—21no—
250C8—21no—
251C8—22no—
252C22—22no—
253C22—22no—
254C22—22no—
255C22—942no—
256C22—3768no—
257C22—1882no—
258C22—1881no—
259C22—1881no—
260C22—1882no—
261C22—1881no—
262C22—1882no—
263C22—1881no—
264C22—1881no—
265C22C22×D18811yescharacteristic
266C4—22no—
267C4—21no—
268C4—1881no—
269C4—1881no—
270C4—1882no—
271C4#1309405212yes—
272C4#41×D4711yescharacteristic
273C4#1309406911yescharacteristic
274C2—42no—
275C2—3762no—
276C2—3761no—
277C2—1882no—
278C2#1568976811yescharacteristic
279C2C2×#1309405211yescharacteristic
280C2#1568992811yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#436C2
socleC22×C47C22×D4
hypercenter#436D47
hypocenterC47#3325
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. #15689838C2semidirect
2. D4×D188C2semidirect
3. #15689470C2semidirect
4. #15689448C2semidirect
5. #15689414C2semidirect
6. #15689376C2semidirect
7. #15689319C2semidirect
8. #15689259C2semidirect
9. C4×D376C2semidirect
10. #15689129C2semidirect
11. C47×#436C2semidirect
15. C2×D376C22semidirect
16. #13094024C22semidirect
21. #13093998C22semidirect
25. C4×D188C22semidirect
26. #13093983C22semidirect
28. #13093958C22semidirect
29. #13093956C22semidirect
32. #13093946C22semidirect
33. #13093946C22semidirect
34. #13093946C22semidirect
35. #13093946C22semidirect
36. C2×M16×C47C22semidirect
38. C4⋊C8×C47C22semidirect
39. C22⋊C8×C47C22semidirect
40. C4×C8×C47C22semidirect
150. #436D47semidirect
152. C47#3325semidirect
157. C2×M16C2×D47semidirect
173. C4⋊C8C2×D47semidirect
180. C22⋊C8C2×D47semidirect
181. C4×C8C2×D47semidirect