Finite Group Databasebeta

← #34110071

Subgroups — #34110071

Order 20096.

462 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 121 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#121×D157C211yesmaximal, characteristic
2C2×#19097729C211yesmaximal, characteristic, complemented
3#23757600C212yesmaximal, complemented
4#23757596C212yesmaximal, complemented
5#23757592C211yesmaximal, characteristic, complemented
6#23757589C211yesmaximal, characteristic, complemented
7#23757586C211yesmaximal, characteristic, complemented
8#23757314C212yesmaximal, complemented
9#23757276C212yesmaximal, complemented
10#23757235C211yesmaximal, characteristic, complemented
11#480×C157C211yesmaximal, characteristic, complemented
12C2×D4×D157—21no—
13C2×D4×D157C2211yescharacteristic
14C22×C4×D157C2211yescharacteristic
15C2×#14578937C2212yes—
16#19097746C2211yescharacteristic
17#19097745C2211yescharacteristic
18#19097744—21no—
19#19097743—21no—
20#19097742C2211yescharacteristic
21#19097729—21no—
22#19097729—21no—
23#19097729C2212yes—
24#19097729C2212yescomplemented
25C2×C4⋊Dic157C2211yescharacteristic, complemented
26C4⋊C4×D157C2211yescharacteristic
27C2×#14578931—21no—
28C22⋊C4×D157—21no—
29C2×C4×Dic157—21no—
30#19097704C2212yescomplemented
31#19097703C2212yescomplemented
32#19097702C2212yescomplemented
33#19097693C2212yescomplemented
34#19097692C2212yescomplemented
35#19097691C2212yescomplemented
36C22⋊#11929434C2211yescharacteristic, complemented
37#19097683C2212yescomplemented
38#121×C157C2211yescharacteristic
39C2×C4⋊C4×C157C2211yescharacteristic, complemented
40#107×C157C2212yescomplemented
41#102×C157C2212yescomplemented
42C22⋊C8×C157C2211yescharacteristic, complemented
43C23×D157—21no—
44C23×D157D411yescharacteristic
45C2×D628—21no—
46C2×D628C2311yescharacteristic
47C2×C22⋊D157—21no—
48C2×C22⋊D157—21no—
49C2×C22⋊D157—21no—
50D4×D157—24no—
51D4×D157—44no—
52C22×Dic157—21no—
53C22×Dic157D411yescharacteristic
54C2×C4×D157—24no—
55C2×C4×D157—21no—
56C2×C4×D157D411yescharacteristic
57C2×C4×D157D411yescharacteristic
58C2×C4×D157C2311yescharacteristic
59C2×C4×D157C2311yescharacteristic
60#14578937—24no—
61C2×#11929434C2312yes—
62C4⋊Dic157—21no—
63C4⋊Dic157C2312yes—
64C4⋊Dic157C2311yescharacteristic
65#14578933—21no—
66C22⋊Dic157—21no—
67#14578931—22no—
68#14578931—22no—
69#14578931—21no—
70#14578931—21no—
71C4×Dic157—22no—
72C4×Dic157—22no—
73C2×D4×C157—21no—
74C2×D4×C157C2311yescharacteristic
75C22×C4×C157—21no—
76C22×C4×C157C2311yescharacteristic
77C2×C8×C157C2312yes—
78C4⋊C4×C157—21no—
79C4⋊C4×C157C2312yes—
80C4⋊C4×C157C2311yescharacteristic
81C22⋊C4×C157—21no—
82C22×D157—22no—
83C22×D157—22no—
84C22×D157—21no—
85C22×D157—41no—
86C22×D157—42no—
87C22×D157—42no—
88C22×D157—42no—
89C22×D157C2×D411yescharacteristic
90C22×D157C2×D411yescharacteristic
91D628—22no—
92D628—42no—
93C22⋊D157—42no—
94C22⋊D157—42no—
95C22⋊D157—42no—
96C2×Dic157—22no—
97C2×Dic157—21no—
98C2×Dic157—22no—
99C2×Dic157—42no—
100C2×Dic157C2×D411yescharacteristic
101C2×Dic157C2×D411yescharacteristic
102C4×D157—22no—
103C4×D157—22no—
104C4×D157—22no—
105C4×D157—42no—
106C4×D157#4114yes—
107#11929434—22no—
108C23×C157—21no—
109C23×C157C2×D411yescharacteristic
110D4×C157—22no—
111D4×C157—42no—
112C2×C4×C157—22no—
113C2×C4×C157—21no—
114C2×C4×C157—22no—
115C2×C4×C157—42no—
116C2×C4×C157C2×D411yescharacteristic
117C2×C4×C157C2411yescharacteristic
118C8×C157—22no—
119C22×C157—21no—
120C22×C157—21no—
121C22×C157—41no—
122C22×C157—41no—
123C22×C157—41no—
124C22×C157AGL(1,ℤ/8)12yes—
125C22×C157C22×D411yescharacteristic
126C2×D157—21no—
127C2×D157—21no—
128C2×D157—21no—
129C2×D157—21no—
130C2×D157—21no—
131C2×D157—44no—
132C2×D157—41no—
133C2×D157—41no—
134C2×D157—41no—
135C2×D157—84no—
136C2×D157#12312yes—
137C4×C157—21no—
138C4×C157—42no—
139C4×C157—41no—
140C4×C157C2×#4112yes—
141Dic157—21no—
142Dic157—41no—
143Dic157—42no—
144Dic157#12312yes—
145C2×C157—22no—
146C2×C157—81no—
147C2×C157C2×#12311yescharacteristic
148C2×C157C2×AGL(1,ℤ/8)11yescharacteristic
149C2×C157#57511yescharacteristic
150D157—22no—
151D157—41no—
152D157—81no—
153C157#309411yescharacteristic, complemented, Sylow
154#3094—1571nomaximal, Sylow
155C2×#121—1571no—
156C2×#117—1571no—
157#482—1572no—
158#482—1572no—
159#481—1571no—
160#481—1571no—
161#480—1571no—
162#480D15711yescharacteristic, complemented
163#428—1572no—
164#418—1572no—
165#407—1571no—
166C22×D4—3141no—
167C22×D4—1571no—
168C23×C4—1571no—
169C2×M16—1572no—
170#121—3141no—
171#121—3141no—
172#121—1571no—
173#121—1571no—
174#121—1571no—
175#121C2×D15711yescharacteristic
176#117—3141no—
177#117—3141no—
178#117—1572no—
179#117—1572no—
180C2×C4⋊C4—1571no—
181C2×C4⋊C4—1571no—
182C2×C4⋊C4C2×D15711yescharacteristic, complemented
183C2×C22⋊C4—3141no—
184C2×C22⋊C4—3141no—
185C2×C42—3141no—
186#107—1572no—
187#107C2×D15712yescomplemented
188#106—1572no—
189#106—1572no—
190#102—1572no—
191#102—1572no—
192#102—1572no—
193#102C2×D15712yescomplemented
194C22⋊C8—1571no—
195C22⋊C8—1572no—
196C22⋊C8C2×D15711yescharacteristic, complemented
197C24—3141no—
198C24—1571no—
199C2×D4—21no—
200C2×D4—3141no—
201C2×D4—3141no—
202C2×D4—3141no—
203C2×D4—3144no—
204C2×D4—3141no—
205C2×D4—6284no—
206C2×D4—1571no—
207C2×D4C22×D15711yescharacteristic
208C22×C4—21no—
209C22×C4—3144no—
210C22×C4—3141no—
211C22×C4—3141no—
212C22×C4—1571no—
213C22×C4—1571no—
214C22×C4—1571no—
215C22×C4—1571no—
216C22×C4—1571no—
217C22×C4C22×D15711yescharacteristic
218M16—3144no—
219C2×C8—1572no—
220C2×C8C22×D15712yes—
221C4⋊C4—21no—
222C4⋊C4—3141no—
223C4⋊C4—3141no—
224C4⋊C4—1572no—
225C4⋊C4—1571no—
226C4⋊C4C22×D15712yes—
227C4⋊C4C22×D15711yescharacteristic
228C22⋊C4—21no—
229C22⋊C4—3142no—
230C22⋊C4—3142no—
231C22⋊C4—3141no—
232C22⋊C4—3141no—
233C22⋊C4—3141no—
234C42—3142no—
235C42—3142no—
236C23—21no—
237C23—3142no—
238C23—3142no—
239C23—3141no—
240C23—6281no—
241C23—6282no—
242C23—6282no—
243C23—6282no—
244C23—1571no—
245C23—1571no—
246C23D4×D15711yescharacteristic
247D4—22no—
248D4—42no—
249D4—3142no—
250D4—6282no—
251D4—6282no—
252D4—6282no—
253D4—6282no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—42no—
258C2×C4—3142no—
259C2×C4—3142no—
260C2×C4—3142no—
261C2×C4—3142no—
262C2×C4—3142no—
263C2×C4—3141no—
264C2×C4—6282no—
265C2×C4—6282no—
266C2×C4—1571no—
267C2×C4—1571no—
268C2×C4—1574no—
269C2×C4D4×D15711yescharacteristic
270C2×C4C23×D15711yescharacteristic
271C8—22no—
272C8—3142no—
273C22—21no—
274C22—21no—
275C22—41no—
276C22—41no—
277C22—41no—
278C22—3141no—
279C22—3141no—
280C22—3141no—
281C22—3141no—
282C22—3141no—
283C22—6284no—
284C22—6281no—
285C22—6281no—
286C22—6281no—
287C22—1572no—
288C22—12564no—
289C22#1909779512yes—
290C22C2×D4×D15711yescharacteristic
291C4—21no—
292C4—42no—
293C4—41no—
294C4—3141no—
295C4—6281no—
296C4—6282no—
297C4—1572no—
298C4#41×D15712yes—
299C2—22no—
300C2—81no—
301C2—3142no—
302C2—6281no—
303C2—12561no—
304C2#123×D15711yescharacteristic
305C2C2×#1909779511yescharacteristic
306C2#2375807211yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#480×C157C2
socleC22×C157C22×D4
prime radical#121×D157C2
hypercenter#480D157
hypocenterC157#3094
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. C2×#19097729C2semidirect
3. #23757600C2semidirect
4. #23757596C2semidirect
5. #23757592C2semidirect
6. #23757589C2semidirect
7. #23757586C2semidirect
8. #23757314C2semidirect
9. #23757276C2semidirect
10. #23757235C2semidirect
11. #480×C157C2semidirect
24. #19097729C22semidirect
25. C2×C4⋊Dic157C22semidirect
30. #19097704C22semidirect
31. #19097703C22semidirect
32. #19097702C22semidirect
33. #19097693C22semidirect
34. #19097692C22semidirect
35. #19097691C22semidirect
36. C22⋊#11929434C22semidirect
37. #19097683C22semidirect
39. C2×C4⋊C4×C157C22semidirect
40. #107×C157C22semidirect
41. #102×C157C22semidirect
42. C22⋊C8×C157C22semidirect
153. C157#3094semidirect
162. #480D157semidirect
182. C2×C4⋊C4C2×D157semidirect
187. #107C2×D157semidirect
193. #102C2×D157semidirect
196. C22⋊C8C2×D157semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#121×D1572
C2×#190977292
#237576002
#237575962
#237575922
#237575892
#237575862
#237573142
#237572762
#237572352
#480×C1572
#3094157