Finite Group Databasebeta

← #465×D157 #34109692

Subgroups — #465×D157 #34109692

Order 20096.

564 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D157C211yesmaximal, characteristic, complemented
2C22×C8×D157C211yesmaximal, characteristic, complemented
3C22⋊Q8×D157C211yesmaximal, characteristic, complemented
4#121×D157C211yesmaximal, characteristic
5#23757505C211yesmaximal, characteristic, complemented
6#23757504C211yesmaximal, characteristic, complemented
7#23757503C211yesmaximal, characteristic, complemented
8#23757502C211yesmaximal, characteristic, complemented
9#23757501C211yesmaximal, characteristic, complemented
10#23757500C211yesmaximal, characteristic, complemented
11#23757499C211yesmaximal, characteristic, complemented
12#106×D157C211yesmaximal, characteristic, complemented
13#103×D157C211yesmaximal, characteristic, complemented
14#102×D157C211yesmaximal, characteristic, complemented
15#465×C157C211yesmaximal, characteristic, complemented
16C2×Q8×D157C2211yescharacteristic
17C2×D4×D157—21no—
18C2×D4×D157C2211yescharacteristic
19C22×C4×D157C2211yescharacteristic
20C2×#14578943C2211yescharacteristic, complemented
21C2×#14578942C2211yescharacteristic, complemented
22C2×#14578941C2211yescharacteristic, complemented
23SD16×D157—24no—
24C22×#11929434C2211yescharacteristic, complemented
25C2×C8×D157—24no—
26C2×C8×D157C2211yescharacteristic
27C2×C8×D157C2211yescharacteristic
28C2×C8×D157C2211yescharacteristic, complemented
29C2×C8×D157C2211yescharacteristic, complemented
30#19097751C2211yescharacteristic, complemented
31#19097750C2211yescharacteristic, complemented
32#19097749—21no—
33#19097748—21no—
34#19097747C2211yescharacteristic, complemented
35#19097746C2211yescharacteristic
36#19097745C2211yescharacteristic
37#19097744—21no—
38#19097743—21no—
39#19097742C2211yescharacteristic
40C4⋊C4×D157—21no—
41C4⋊C4×D157C2211yescharacteristic
42C4⋊C4×D157C2211yescharacteristic
43C22⋊C4×D157—21no—
44C22⋊C4×D157—21no—
45#19097703C2211yescharacteristic, complemented
46#19097702C2211yescharacteristic, complemented
47#19097702C2211yescharacteristic, complemented
48#19097696C2211yescharacteristic, complemented
49#19097695C2211yescharacteristic, complemented
50#19097694C2211yescharacteristic, complemented
51#19097693C2211yescharacteristic, complemented
52#19097692C2211yescharacteristic, complemented
53#19097691C2211yescharacteristic, complemented
54C2×SD16×C157C2211yescharacteristic, complemented
55C22×C8×C157C2211yescharacteristic, complemented
56C22⋊Q8×C157C2211yescharacteristic, complemented
57#121×C157C2211yescharacteristic
58#106×C157C2211yescharacteristic, complemented
59#103×C157C2211yescharacteristic, complemented
60#102×C157C2211yescharacteristic, complemented
61C23×D157—21no—
62C23×D157D411yescharacteristic
63C2×Dic314—21no—
64C2×Dic314C2311yescharacteristic
65Q8×D157—22no—
66Q8×D157—22no—
67C2×D628—21no—
68C2×D628C2311yescharacteristic
69C2×C22⋊D157—21no—
70C2×C22⋊D157—21no—
71C2×C22⋊D157—21no—
72D4×D157—22no—
73D4×D157—22no—
74D4×D157—44no—
75C22×Dic157D411yescharacteristic
76C2×C4×D157—22no—
77C2×C4×D157—22no—
78C2×C4×D157—21no—
79C2×C4×D157—21no—
80C2×C4×D157—21no—
81C2×C4×D157D411yescharacteristic
82C2×C4×D157D411yescharacteristic
83C2×C4×D157C2311yescharacteristic
84C2×C4×D157C2311yescharacteristic
85#14578943—22no—
86#14578942—22no—
87#14578941—22no—
88C2×#11929434—22no—
89C2×#11929434C2311yescharacteristic
90C2×#11929434C2311yescharacteristic
91C8×D157—22no—
92C8×D157—22no—
93C8×D157—22no—
94C8×D157D414yescomplemented
95C4⋊Dic157—21no—
96C4⋊Dic157C2311yescharacteristic
97C4⋊Dic157C2311yescharacteristic
98#14578933—21no—
99#14578933—21no—
100#14578933—21no—
101#14578933—21no—
102C22⋊Dic157—21no—
103C22⋊Dic157—21no—
104#14578931—21no—
105#14578931—21no—
106#14578931—21no—
107#14578931—21no—
108C2×Q8×C157C2311yescharacteristic
109C2×D4×C157—21no—
110C2×D4×C157C2311yescharacteristic
111C22×C4×C157C2311yescharacteristic
112SD16×C157—22no—
113C2×C8×C157—22no—
114C2×C8×C157C2311yescharacteristic
115C2×C8×C157C2311yescharacteristic
116C4⋊C4×C157—21no—
117C4⋊C4×C157C2311yescharacteristic
118C4⋊C4×C157C2311yescharacteristic
119C22⋊C4×C157—21no—
120C22⋊C4×C157—21no—
121C22×D157—22no—
122C22×D157—22no—
123C22×D157—21no—
124C22×D157—42no—
125C22×D157—42no—
126C22×D157—42no—
127C22×D157SD1614yescomplemented
128C22×D157C2×D411yescharacteristic
129C22×D157C2×D411yescharacteristic
130Dic314—21no—
131Dic314—21no—
132Dic314—42no—
133D628—21no—
134D628—21no—
135D628—42no—
136C22⋊D157—42no—
137C22⋊D157—42no—
138C22⋊D157—42no—
139C2×Dic157—22no—
140C2×Dic157—21no—
141C2×Dic157—21no—
142C2×Dic157—21no—
143C2×Dic157C2×D411yescharacteristic
144C2×Dic157C2×D411yescharacteristic
145C4×D157—22no—
146C4×D157—21no—
147C4×D157—21no—
148C4×D157—22no—
149C4×D157—42no—
150C4×D157—42no—
151C4×D157—42no—
152C4×D157C2×D412yes—
153C4×D157#4112yes—
154#11929434—21no—
155#11929434C2×D412yescomplemented
156C23×C157—21no—
157C23×C157C2×D411yescharacteristic
158Q8×C157—21no—
159Q8×C157—21no—
160D4×C157—21no—
161D4×C157—21no—
162D4×C157—42no—
163C2×C4×C157—21no—
164C2×C4×C157—21no—
165C2×C4×C157—21no—
166C2×C4×C157—21no—
167C2×C4×C157—21no—
168C2×C4×C157C2×D411yescharacteristic
169C2×C4×C157C2411yescharacteristic
170C8×C157—21no—
171C8×C157C2×D412yescomplemented
172C22×C157—21no—
173C22×C157—21no—
174C22×C157—41no—
175C22×C157—41no—
176C22×C157—41no—
177C22×C157C2×SD1612yescomplemented
178C22×C157C22×D411yescharacteristic
179C2×D157—21no—
180C2×D157—21no—
181C2×D157—28no—
182C2×D157—41no—
183C2×D157—41no—
184C2×D157—41no—
185C2×D157—84no—
186C2×D157#12112yes—
187C2×D157C2×SD1612yes—
188C2×D157C2×SD1612yescomplemented
189C2×D157#13512yes—
190C4×C157—21no—
191C4×C157—41no—
192C4×C157—41no—
193C4×C157—41no—
194C4×C157C22×D411yescharacteristic
195C4×C157C2×#4111yescharacteristic
196Dic157—21no—
197Dic157—41no—
198Dic157—41no—
199Dic157—41no—
200Dic157#12112yes—
201C2×C157—22no—
202C2×C157—81no—
203C2×C157C2×#12111yescharacteristic
204C2×C157C22×SD1611yescharacteristic
205C2×C157C2×#13511yescharacteristic
206D157—22no—
207D157—81no—
208D157#46514yesdirect product factor
209C157C2×#46511yescharacteristic, complemented, Sylow
210C2×#465—1571nomaximal, Sylow
211C22×SD16—1571no—
212C23×C8—1571no—
213C2×C22⋊Q8—1571no—
214C2×#121—1571no—
215#465—1571no—
216#465—1571no—
217#465—1571no—
218#465—1571no—
219#465—1571no—
220#465—1571no—
221#465—1571no—
222#465D15711yescharacteristic, direct product factor
223C2×#106—1571no—
224C2×#103—1571no—
225C2×#102—1571no—
226C22×Q8—1571no—
227C22×D4—3141no—
228C22×D4—1571no—
229C23×C4—1571no—
230C2×SD16—3144no—
231C2×SD16—1571no—
232C2×SD16—1571no—
233C2×SD16—1571no—
234C2×SD16C2×D15711yescharacteristic, complemented
235C22×C8—3144no—
236C22×C8—1571no—
237C22×C8—1571no—
238C22×C8—1571no—
239C22×C8—1571no—
240C22×C8—1571no—
241C22×C8C2×D15711yescharacteristic, complemented
242C22⋊Q8—3141no—
243C22⋊Q8—3141no—
244C22⋊Q8—1571no—
245C22⋊Q8—1571no—
246C22⋊Q8—1571no—
247C22⋊Q8C2×D15711yescharacteristic, complemented
248#121—3141no—
249#121—3141no—
250#121—1571no—
251#121—1571no—
252#121—1571no—
253#121C2×D15711yescharacteristic
254C2×C4⋊C4—3141no—
255C2×C4⋊C4—1571no—
256C2×C4⋊C4—1571no—
257C2×C22⋊C4—3141no—
258C2×C22⋊C4—3141no—
259#106—1571no—
260#106—1571no—
261#106—1571no—
262#106C2×D15711yescharacteristic, complemented
263#103—1571no—
264#103—1571no—
265#103—1571no—
266#103C2×D15711yescharacteristic, complemented
267#102—1571no—
268#102—1571no—
269#102—1571no—
270#102C2×D15711yescharacteristic, complemented
271C24—3141no—
272C24—1571no—
273C2×Q8—3141no—
274C2×Q8—3142no—
275C2×Q8—3142no—
276C2×Q8—1571no—
277C2×Q8C22×D15711yescharacteristic
278C2×D4—21no—
279C2×D4—3141no—
280C2×D4—3141no—
281C2×D4—3141no—
282C2×D4—3142no—
283C2×D4—3142no—
284C2×D4—3141no—
285C2×D4—6284no—
286C2×D4—1571no—
287C2×D4C22×D15711yescharacteristic
288C22×C4—3142no—
289C22×C4—3142no—
290C22×C4—3141no—
291C22×C4—3141no—
292C22×C4—3141no—
293C22×C4—1571no—
294C22×C4—1571no—
295C22×C4—1571no—
296C22×C4—1571no—
297C22×C4—1571no—
298C22×C4C22×D15711yescharacteristic
299SD16—22no—
300SD16—3142no—
301SD16—3142no—
302SD16—3142no—
303C2×C8—22no—
304C2×C8—3142no—
305C2×C8—3142no—
306C2×C8—3142no—
307C2×C8—3142no—
308C2×C8—1571no—
309C2×C8—1571no—
310C2×C8—1574no—
311C2×C8C22×D15711yescharacteristic
312C2×C8C22×D15711yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—3141no—
315C4⋊C4—3141no—
316C4⋊C4—3141no—
317C4⋊C4—3141no—
318C4⋊C4—3141no—
319C4⋊C4—1571no—
320C4⋊C4—1571no—
321C4⋊C4C22×D15711yescharacteristic
322C4⋊C4C22×D15711yescharacteristic
323C22⋊C4—21no—
324C22⋊C4—21no—
325C22⋊C4—3141no—
326C22⋊C4—3141no—
327C22⋊C4—3141no—
328C22⋊C4—3141no—
329C22⋊C4—3141no—
330C22⋊C4—3141no—
331C23—21no—
332C23—3142no—
333C23—3142no—
334C23—3141no—
335C23—6282no—
336C23—6282no—
337C23—6282no—
338C23—1574no—
339C23—1571no—
340C23—1571no—
341C23D4×D15711yescharacteristic
342Q8—21no—
343Q8—21no—
344Q8—3141no—
345Q8—3141no—
346Q8—6282no—
347D4—21no—
348D4—21no—
349D4—42no—
350D4—3141no—
351D4—3141no—
352D4—6282no—
353D4—6282no—
354D4—6282no—
355D4—6282no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—3142no—
362C2×C4—3142no—
363C2×C4—3142no—
364C2×C4—3141no—
365C2×C4—3141no—
366C2×C4—3141no—
367C2×C4—3141no—
368C2×C4—3141no—
369C2×C4—6282no—
370C2×C4—6282no—
371C2×C4—6282no—
372C2×C4—1571no—
373C2×C4—1571no—
374C2×C4—1572no—
375C2×C4—1572no—
376C2×C4D4×D15711yescharacteristic
377C2×C4C23×D15711yescharacteristic
378C8—21no—
379C8—3141no—
380C8—1572no—
381C8D4×D15712yescomplemented
382C22—21no—
383C22—21no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—3148no—
388C22—3141no—
389C22—3141no—
390C22—6281no—
391C22—6281no—
392C22—6281no—
393C22—1572no—
394C22—1572no—
395C22—1572no—
396C22—1572no—
397C22—12564no—
398C22SD16×D15712yescomplemented
399C22C2×D4×D15711yescharacteristic
400C4—21no—
401C4—41no—
402C4—41no—
403C4—41no—
404C4—3141no—
405C4—6281no—
406C4—6281no—
407C4—6281no—
408C4—1572no—
409C4C2×D4×D15711yescharacteristic
410C4#41×D15711yescharacteristic
411C2—22no—
412C2—81no—
413C2—3142no—
414C2—1574no—
415C2—12561no—
416C2#121×D15711yescharacteristic
417C2C2×SD16×D15711yescharacteristic
418C2#135×D15711yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#465×C157C2
socleC22×C157C22×D4
prime radical#121×D157C2
hypercenter#465D157
hypocenterC157C2×#465
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D157C2semidirect
2. C22×C8×D157C2semidirect
3. C22⋊Q8×D157C2semidirect
5. #23757505C2semidirect
6. #23757504C2semidirect
7. #23757503C2semidirect
8. #23757502C2semidirect
9. #23757501C2semidirect
10. #23757500C2semidirect
11. #23757499C2semidirect
12. #106×D157C2semidirect
13. #103×D157C2semidirect
14. #102×D157C2semidirect
15. #465×C157C2semidirect
20. C2×#14578943C22semidirect
21. C2×#14578942C22semidirect
22. C2×#14578941C22semidirect
24. C22×#11929434C22semidirect
28. C2×C8×D157C22semidirect
29. C2×C8×D157C22semidirect
30. #19097751C22semidirect
31. #19097750C22semidirect
34. #19097747C22semidirect
45. #19097703C22semidirect
46. #19097702C22semidirect
47. #19097702C22semidirect
48. #19097696C22semidirect
49. #19097695C22semidirect
50. #19097694C22semidirect
51. #19097693C22semidirect
52. #19097692C22semidirect
53. #19097691C22semidirect
54. C2×SD16×C157C22semidirect
55. C22×C8×C157C22semidirect
56. C22⋊Q8×C157C22semidirect
58. #106×C157C22semidirect
59. #103×C157C22semidirect
60. #102×C157C22semidirect
94. C8×D157D4semidirect
127. C22×D157SD16semidirect
155. #11929434C2×D4semidirect
171. C8×C157C2×D4semidirect
177. C22×C157C2×SD16semidirect
188. C2×D157C2×SD16semidirect
208. D157#465direct (N × H)
209. C157C2×#465semidirect
222. #465D157direct (N × H)
234. C2×SD16C2×D157semidirect
241. C22×C8C2×D157semidirect
247. C22⋊Q8C2×D157semidirect
262. #106C2×D157semidirect
266. #103C2×D157semidirect
270. #102C2×D157semidirect
381. C8D4×D157semidirect
398. C22SD16×D157semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1572
C22×C8×D1572
C22⋊Q8×D1572
#121×D1572
#237575052
#237575042
#237575032
#237575022
#237575012
#237575002
#237574992
#106×D1572
#103×D1572
#102×D1572
#465×C1572
C2×#465157