Finite Group Databasebeta

← #34110087

Subgroups — #34110087

Order 20096.

418 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757839C211yesmaximal, characteristic
2#23757754C211yesmaximal, characteristic, complemented
3#23757600C211yesmaximal, characteristic, complemented
4#23757598C211yesmaximal, characteristic, complemented
5#23757595C211yesmaximal, characteristic, complemented
6#23757594C211yesmaximal, characteristic, complemented
7#23757591C211yesmaximal, characteristic, complemented
8#23757590C211yesmaximal, characteristic, complemented
9#23757588C211yesmaximal, characteristic, complemented
10#23757314C211yesmaximal, characteristic, complemented
11#23757310C211yesmaximal, characteristic, complemented
12#23757276C211yesmaximal, characteristic, complemented
13#102×D157C211yesmaximal, characteristic, complemented
14#23757238C211yesmaximal, characteristic, complemented
15#480×C157C211yesmaximal, characteristic, complemented
16C2×#14578954C2211yescharacteristic
17C2×D4×D157C2211yescharacteristic
18C2×#14578937C2211yescharacteristic
19C2×C8×D157C2211yescharacteristic
20#19097767—21no—
21#19097757—21no—
22#19097746C2211yescharacteristic
23#19097745C2211yescharacteristic
24#19097742C2211yescharacteristic
25#19097741—21no—
26#19097739—21no—
27#19097736—21no—
28#19097733—21no—
29C4×C22⋊D157—21no—
30C4×C22⋊D157—21no—
31#19097730C2211yescharacteristic, complemented
32#19097729C2211yescharacteristic
33#19097729C2211yescharacteristic
34#19097729C2211yescharacteristic, complemented
35C4⋊C4×D157C2211yescharacteristic
36C4⋊C4×D157C2211yescharacteristic, complemented
37#19097705C2211yescharacteristic, complemented
38#19097704C2211yescharacteristic, complemented
39#19097703C2211yescharacteristic, complemented
40#19097702C2211yescharacteristic, complemented
41#19097702C2211yescharacteristic, complemented
42#19097702C2211yescharacteristic, complemented
43#19097693C2211yescharacteristic
44#19097693C2211yescharacteristic
45#19097692C2211yescharacteristic
46#19097692C2211yescharacteristic
47#19097691C2211yescharacteristic
48#19097691C2211yescharacteristic
49C22⋊#11929434C2211yescharacteristic, complemented
50#19097683C2211yescharacteristic, complemented
51#19097683C2211yescharacteristic, complemented
52#121×C157C2211yescharacteristic
53C2×C4⋊C4×C157C2211yescharacteristic, complemented
54#107×C157C2211yescharacteristic, complemented
55#107×C157C2211yescharacteristic, complemented
56#102×C157C2211yescharacteristic
57#102×C157C2211yescharacteristic
58C22⋊C8×C157C2211yescharacteristic, complemented
59C23×D157—21no—
60#14578954—22no—
61#14578954—22no—
62C2×Dic314D411yescharacteristic
63C2×D628—21no—
64C2×D628D411yescharacteristic
65C2×D628C2311yescharacteristic
66C2×C22⋊D157—21no—
67C2×C22⋊D157—21no—
68C2×C22⋊D157—21no—
69C2×C22⋊D157D411yescharacteristic
70C2×C22⋊D157D411yescharacteristic
71D4×D157—22no—
72D4×D157—22no—
73C2×C4×D157—21no—
74C2×C4×D157—21no—
75C2×C4×D157C2311yescharacteristic
76C2×C4×D157C2311yescharacteristic
77#14578937—22no—
78C2×#11929434C2311yescharacteristic
79C2×#11929434C2311yescharacteristic
80C8×D157—22no—
81C4⋊Dic157C2311yescharacteristic
82C4⋊Dic157C2311yescharacteristic
83C4⋊Dic157C2311yescharacteristic
84#14578933—21no—
85#14578933—21no—
86C22⋊Dic157—21no—
87C22⋊Dic157—21no—
88#14578931—21no—
89#14578931—21no—
90#14578931—21no—
91#14578931—21no—
92#14578931—21no—
93C4×Dic157—21no—
94C4×Dic157—21no—
95C4×Dic157—21no—
96C4×Dic157—21no—
97C2×D4×C157—21no—
98C2×D4×C157C2311yescharacteristic
99C22×C4×C157—21no—
100C22×C4×C157C2311yescharacteristic
101C2×C8×C157C2311yescharacteristic
102C2×C8×C157C2311yescharacteristic
103C4⋊C4×C157—21no—
104C4⋊C4×C157C2311yescharacteristic
105C4⋊C4×C157C2311yescharacteristic
106C4⋊C4×C157C2311yescharacteristic
107C22⋊C4×C157—21no—
108C22×D157—21no—
109C22×D157—42no—
110C22×D157—81no—
111C22×D157—81no—
112C22×D157C2×D411yescharacteristic
113C22×D157C2×D411yescharacteristic
114Dic314—22no—
115D628—22no—
116D628—21no—
117D628—21no—
118D628—81no—
119C22⋊D157—22no—
120C22⋊D157—22no—
121C22⋊D157—42no—
122C22⋊D157—81no—
123C22⋊D157—81no—
124C2×Dic157—21no—
125C2×Dic157—21no—
126C2×Dic157—21no—
127C2×Dic157C2×D411yescharacteristic
128C2×Dic157C2×D411yescharacteristic
129C4×D157—21no—
130C4×D157—21no—
131C4×D157—81no—
132C4×D157—81no—
133C4×D157#4112yes—
134C4×D157#4112yes—
135#11929434—21no—
136#11929434—21no—
137C23×C157—21no—
138C23×C157C2×D411yescharacteristic
139D4×C157—21no—
140D4×C157—21no—
141D4×C157—81no—
142C2×C4×C157—21no—
143C2×C4×C157—21no—
144C2×C4×C157—21no—
145C2×C4×C157—21no—
146C2×C4×C157—21no—
147C2×C4×C157—81no—
148C2×C4×C157C2×D411yescharacteristic
149C2×C4×C157C2411yescharacteristic
150C8×C157—21no—
151C8×C157—21no—
152C22×C157—21no—
153C22×C157—21no—
154C22×C157—21no—
155C22×C157—41no—
156C22×C157—41no—
157C22×C157—41no—
158C22×C157C22×D411yescharacteristic
159C2×D157—21no—
160C2×D157—21no—
161C2×D157—21no—
162C2×D157—21no—
163C2×D157—21no—
164C2×D157—41no—
165C2×D157—41no—
166C2×D157—41no—
167C2×D157—84no—
168C2×D157#12312yes—
169C4×C157—21no—
170C4×C157—41no—
171C4×C157—41no—
172C4×C157—41no—
173C4×C157C2×#4111yescharacteristic
174C4×C157C2×#4111yescharacteristic
175Dic157—21no—
176Dic157—41no—
177Dic157—41no—
178Dic157—41no—
179Dic157#12312yes—
180C2×C157—41no—
181C2×C157—81no—
182C2×C157C2×#12311yescharacteristic
183C2×C157#57611yescharacteristic
184C2×C157#57711yescharacteristic
185D157—22no—
186D157—41no—
187D157—81no—
188C157#309611yescharacteristic, complemented, Sylow
189#3096—1571nomaximal, Sylow
190#535—1571no—
191#520—1571no—
192#482—1571no—
193#482—1571no—
194#482—1571no—
195#482—1571no—
196#481—1571no—
197#481—1571no—
198#480—1571no—
199#480D15711yescharacteristic, complemented
200#428—1571no—
201#427—1571no—
202#418—1571no—
203C2×#102—1571no—
204#408—1571no—
205C2×#41—1571no—
206C22×D4—1571no—
207C2×M16—1571no—
208C22×C8—1571no—
209#127—3141no—
210#124—3141no—
211#121—1571no—
212#121—1571no—
213#121—1571no—
214#121C2×D15711yescharacteristic
215#120—3141no—
216#120—3141no—
217C4×Q8—3141no—
218C4×D4—3141no—
219C4×D4—3141no—
220C4×D4—3141no—
221#117—1571no—
222#117—1571no—
223#117—1571no—
224#117—1571no—
225C2×C4⋊C4—1571no—
226C2×C4⋊C4—1571no—
227C2×C4⋊C4C2×D15711yescharacteristic, complemented
228#107—1571no—
229#107—1571no—
230#107C2×D15711yescharacteristic, complemented
231#107C2×D15711yescharacteristic, complemented
232#106—1571no—
233#106—1571no—
234#106—1571no—
235#106—1571no—
236#102—1571no—
237#102—1571no—
238#102—1571no—
239#102—1571no—
240#102—1571no—
241#102—1571no—
242#102C2×D15711yescharacteristic
243#102C2×D15711yescharacteristic
244C22⋊C8—1571no—
245C22⋊C8—1571no—
246C22⋊C8—1571no—
247C22⋊C8C2×D15711yescharacteristic, complemented
248C24—3141no—
249#41—3142no—
250#41—3142no—
251C2×Q8—1571no—
252C2×D4—21no—
253C2×D4—3141no—
254C2×D4—3141no—
255C2×D4—3141no—
256C2×D4—3142no—
257C2×D4—3142no—
258C2×D4—3141no—
259C2×D4—1571no—
260C2×D4—1571no—
261C2×D4—1571no—
262C2×D4—1571no—
263C2×D4C22×D15711yescharacteristic
264C22×C4—21no—
265C22×C4—3141no—
266C22×C4—3141no—
267C22×C4—1571no—
268C22×C4—1571no—
269C22×C4C22×D15711yescharacteristic
270M16—3142no—
271C2×C8—3142no—
272C2×C8—1571no—
273C2×C8—1571no—
274C2×C8C22×D15711yescharacteristic
275C2×C8C22×D15711yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—3141no—
278C4⋊C4—3141no—
279C4⋊C4—1571no—
280C4⋊C4—1571no—
281C4⋊C4—1571no—
282C4⋊C4C22×D15711yescharacteristic
283C4⋊C4C22×D15711yescharacteristic
284C4⋊C4C22×D15711yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—3141no—
287C22⋊C4—3141no—
288C22⋊C4—3141no—
289C22⋊C4—3141no—
290C22⋊C4—3141no—
291C22⋊C4—3141no—
292C22⋊C4—3141no—
293C42—3141no—
294C42—3141no—
295C42—3141no—
296C42—3141no—
297C23—21no—
298C23—3141no—
299C23—6282no—
300C23—1571no—
301C23—1571no—
302C23—12561no—
303C23—12561no—
304C23D4×D15711yescharacteristic
305Q8—3142no—
306D4—21no—
307D4—21no—
308D4—81no—
309D4—3142no—
310D4—3142no—
311D4—3142no—
312D4—3141no—
313D4—3141no—
314D4—6282no—
315D4—12561no—
316D4—12561no—
317D4—12561no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—81no—
324C2×C4—3141no—
325C2×C4—3141no—
326C2×C4—3141no—
327C2×C4—3141no—
328C2×C4—3141no—
329C2×C4—1571no—
330C2×C4—1571no—
331C2×C4—1572no—
332C2×C4—1572no—
333C2×C4—12561no—
334C2×C4—12561no—
335C2×C4D4×D15711yescharacteristic
336C2×C4C23×D15711yescharacteristic
337C8—21no—
338C8—21no—
339C8—3141no—
340C8—3141no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—3141no—
348C22—3141no—
349C22—3141no—
350C22—3141no—
351C22—3141no—
352C22—6281no—
353C22—6281no—
354C22—6281no—
355C22—1572no—
356C22—12564no—
357C22C2×D4×D15711yescharacteristic
358C4—21no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—3141no—
363C4—6281no—
364C4—6281no—
365C4—6281no—
366C4—1572no—
367C4#41×D15711yescharacteristic
368C4#41×D15711yescharacteristic
369C2—41no—
370C2—81no—
371C2—3142no—
372C2—6281no—
373C2—12561no—
374C2#123×D15711yescharacteristic
375C2#2375807411yescharacteristic
376C2#2375808211yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#480×C157C2
socleC22×C157C22×D4
prime radical#23757839C2
hypercenter#480D157
hypocenterC157#3096
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. #23757754C2semidirect
3. #23757600C2semidirect
4. #23757598C2semidirect
5. #23757595C2semidirect
6. #23757594C2semidirect
7. #23757591C2semidirect
8. #23757590C2semidirect
9. #23757588C2semidirect
10. #23757314C2semidirect
11. #23757310C2semidirect
12. #23757276C2semidirect
13. #102×D157C2semidirect
14. #23757238C2semidirect
15. #480×C157C2semidirect
31. #19097730C22semidirect
34. #19097729C22semidirect
36. C4⋊C4×D157C22semidirect
37. #19097705C22semidirect
38. #19097704C22semidirect
39. #19097703C22semidirect
40. #19097702C22semidirect
41. #19097702C22semidirect
42. #19097702C22semidirect
49. C22⋊#11929434C22semidirect
50. #19097683C22semidirect
51. #19097683C22semidirect
53. C2×C4⋊C4×C157C22semidirect
54. #107×C157C22semidirect
55. #107×C157C22semidirect
58. C22⋊C8×C157C22semidirect
188. C157#3096semidirect
199. #480D157semidirect
227. C2×C4⋊C4C2×D157semidirect
230. #107C2×D157semidirect
231. #107C2×D157semidirect
247. C22⋊C8C2×D157semidirect

Maximal subgroups

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

subgroupindex
#237578392
#237577542
#237576002
#237575982
#237575952
#237575942
#237575912
#237575902
#237575882
#237573142
#237573102
#237572762
#102×D1572
#237572382
#480×C1572
#3096157