Finite Group Databasebeta

← #34111958

Subgroups — #34111958

Order 20096.

462 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757978C211yesmaximal, characteristic, complemented
2#23757907C211yesmaximal, characteristic
3#23757618C211yesmaximal, characteristic, complemented
4#23757593C211yesmaximal, characteristic, complemented
5#23757562C211yesmaximal, characteristic, complemented
6#23757503C211yesmaximal, characteristic, complemented
7#23757500C211yesmaximal, characteristic, complemented
8#23757472C211yesmaximal, characteristic, complemented
9#23757426C211yesmaximal, characteristic, complemented
10#23757425C211yesmaximal, characteristic, complemented
11#23757360C211yesmaximal, characteristic, complemented
12#23757336C211yesmaximal, characteristic, complemented
13C2×#19097691C211yesmaximal, characteristic, complemented
14#102×D157C211yesmaximal, characteristic, complemented
15#481×C157C211yesmaximal, characteristic, complemented
16C22×D628C2211yescharacteristic
17C2×D4×D157—21no—
18C2×D4×D157C2211yescharacteristic
19C2×#14578943C2211yescharacteristic
20C2×#14578943C2211yescharacteristic, complemented
21C2×#14578942C2211yescharacteristic, complemented
22C22×#11929434C2211yescharacteristic, complemented
23C2×C8×D157C2211yescharacteristic, complemented
24#19097770C2211yescharacteristic, complemented
25#19097767C2211yescharacteristic
26#19097761—21no—
27#19097751C2211yescharacteristic, complemented
28#19097750—21no—
29#19097750C2211yescharacteristic, complemented
30#19097749—21no—
31#19097746C2211yescharacteristic
32#19097744—21no—
33#19097741—21no—
34#19097739—21no—
35#19097736C2211yescharacteristic, complemented
36#19097733C2211yescharacteristic
37C4×C22⋊D157—21no—
38C4×C22⋊D157C2211yescharacteristic
39C4⋊C4×D157C2211yescharacteristic, complemented
40#19097702C2211yescharacteristic, complemented
41#19097700C2211yescharacteristic, complemented
42#19097694C2211yescharacteristic, complemented
43#19097693C2211yescharacteristic
44#19097693C2211yescharacteristic, complemented
45#19097692C2211yescharacteristic, complemented
46#19097691C2211yescharacteristic
47#19097691C2211yescharacteristic
48#19097691C2211yescharacteristic, complemented
49#19097691C2211yescharacteristic, complemented
50#19097683C2211yescharacteristic, complemented
51C8×Dic157C2211yescharacteristic, complemented
52#121×C157C2211yescharacteristic
53C2×C4⋊C4×C157C2211yescharacteristic, complemented
54#106×C157C2211yescharacteristic, complemented
55#106×C157C2211yescharacteristic, complemented
56#102×C157C2211yescharacteristic, complemented
57#102×C157C2211yescharacteristic, complemented
58C22⋊C8×C157C2211yescharacteristic, complemented
59C23×D157—21no—
60C23×D157—21no—
61C2×Dic314—21no—
62C2×Dic314C2311yescharacteristic
63C2×D628—22no—
64C2×D628—21no—
65C2×D628—21no—
66C2×D628—41no—
67C2×D628C2311yescharacteristic
68C2×D628C2311yescharacteristic
69C2×C22⋊D157—21no—
70C2×C22⋊D157—21no—
71C2×C22⋊D157—21no—
72C2×C22⋊D157D411yescharacteristic
73D4×D157—22no—
74D4×D157—41no—
75D4×D157—44no—
76C2×C4×D157—21no—
77C2×C4×D157—21no—
78C2×C4×D157C2311yescharacteristic
79#14578943—22no—
80#14578943—41no—
81#14578942—41no—
82C2×#11929434—41no—
83C2×#11929434C2311yescharacteristic
84C2×#11929434C2311yescharacteristic
85C8×D157—41no—
86C4⋊Dic157—21no—
87C4⋊Dic157C2311yescharacteristic
88#14578933—21no—
89#14578933—21no—
90#14578933—21no—
91#14578933—21no—
92#14578933D411yescharacteristic
93C22⋊Dic157—21no—
94C22⋊Dic157D411yescharacteristic
95#14578931—21no—
96#14578931—21no—
97#14578931—21no—
98#14578931D411yescharacteristic
99C4×Dic157—21no—
100C4×Dic157C2311yescharacteristic
101C2×D4×C157—21no—
102C2×D4×C157C2311yescharacteristic
103C22×C4×C157—21no—
104C22×C4×C157C2311yescharacteristic
105C2×C8×C157C2311yescharacteristic
106C2×C8×C157C2311yescharacteristic
107C4⋊C4×C157—21no—
108C4⋊C4×C157C2311yescharacteristic
109C4⋊C4×C157C2311yescharacteristic
110C4⋊C4×C157C2311yescharacteristic
111C22⋊C4×C157—21no—
112C22×D157—21no—
113C22×D157—21no—
114C22×D157—42no—
115C22×D157—42no—
116C22×D157—42no—
117C22×D157—42no—
118C22×D157—81no—
119C22×D157—81no—
120C22×D157C2×D411yescharacteristic
121Dic314—21no—
122Dic314—21no—
123Dic314—81no—
124D628—21no—
125D628—21no—
126D628—21no—
127D628—42no—
128D628—42no—
129D628#4112yes—
130C22⋊D157—42no—
131C22⋊D157—42no—
132C22⋊D157—81no—
133C22⋊D157SD1614yescomplemented
134C2×Dic157—21no—
135C2×Dic157—21no—
136C2×Dic157C2×D411yescharacteristic
137C2×Dic157C2×D411yescharacteristic
138C2×Dic157C2×D411yescharacteristic
139C4×D157—21no—
140C4×D157—21no—
141C4×D157—42no—
142C4×D157—81no—
143#11929434—21no—
144#11929434—21no—
145C23×C157—21no—
146C23×C157C2×D411yescharacteristic
147D4×C157—21no—
148D4×C157—21no—
149D4×C157—42no—
150C2×C4×C157—21no—
151C2×C4×C157—21no—
152C2×C4×C157—21no—
153C2×C4×C157—21no—
154C2×C4×C157—21no—
155C2×C4×C157—81no—
156C2×C4×C157C2×D411yescharacteristic
157C2×C4×C157C2411yescharacteristic
158C8×C157—21no—
159C8×C157—21no—
160C22×C157—21no—
161C22×C157—21no—
162C22×C157—41no—
163C22×C157—41no—
164C22×C157—41no—
165C22×C157C2×SD1612yes—
166C22×C157C22×D411yescharacteristic
167C2×D157—21no—
168C2×D157—21no—
169C2×D157—22no—
170C2×D157—41no—
171C2×D157—41no—
172C2×D157—41no—
173C2×D157—41no—
174C2×D157—41no—
175C2×D157—84no—
176C2×D157—84no—
177C2×D157C2×SD1612yes—
178C4×C157—21no—
179C4×C157—41no—
180C4×C157—41no—
181C4×C157—41no—
182C4×C157C2×#4111yescharacteristic
183C4×C157H(5,𝔽2)11yescharacteristic
184Dic157—21no—
185Dic157—21no—
186Dic157—41no—
187Dic157—41no—
188Dic157C2×SD1612yes—
189C2×C157—22no—
190C2×C157—81no—
191C2×C157#54611yescharacteristic
192C2×C157C22×SD1611yescharacteristic
193C2×C157#57611yescharacteristic
194D157—22no—
195D157—42no—
196D157—81no—
197C157#329511yescharacteristic, complemented, Sylow
198#3295—1571nomaximal, Sylow
199#554—1571no—
200D42—1571no—
201#486—1571no—
202#481—1571no—
203#481D15711yescharacteristic, complemented
204#476—1571no—
205#465—1571no—
206#465—1571no—
207#460—1571no—
208#450—1571no—
209#450—1571no—
210C4×SD16—1571no—
211C8×D4—1571no—
212C2×#102—1571no—
213C2×#102—1571no—
214C22×D4—3141no—
215C22×D4—1571no—
216C22×D4—1571no—
217C2×SD16—1571no—
218C2×SD16—1571no—
219C2×SD16—1571no—
220C22×C8—1571no—
221C22×C8—1571no—
222C4⋊Q8—1571no—
223#127—1571no—
224#125—3141no—
225C22⋊Q8—3141no—
226C22⋊Q8—3141no—
227C22⋊Q8—1571no—
228C22⋊Q8—1571no—
229#121—3141no—
230#121—1571no—
231#121C2×D15711yescharacteristic
232#120—3141no—
233#120—3141no—
234C4×Q8—1571no—
235C4×D4—3141no—
236C4×D4—1571no—
237C4×D4—1571no—
238C2×C4⋊C4—1571no—
239C2×C4⋊C4C2×D15711yescharacteristic, complemented
240#106—1571no—
241#106C2×D15711yescharacteristic, complemented
242#106C2×D15711yescharacteristic, complemented
243C4⋊C8—1571no—
244#103—1571no—
245#102—1571no—
246#102—1571no—
247#102—1571no—
248#102—1571no—
249#102—1571no—
250#102—1571no—
251#102—1571no—
252#102C2×D15711yescharacteristic, complemented
253#102C2×D15711yescharacteristic, complemented
254C22⋊C8—1571no—
255C22⋊C8C2×D15711yescharacteristic, complemented
256C4×C8—1571no—
257C24—3141no—
258C24—3141no—
259C2×Q8—3141no—
260C2×Q8—1571no—
261C2×D4—21no—
262C2×D4—3142no—
263C2×D4—3141no—
264C2×D4—3142no—
265C2×D4—3141no—
266C2×D4—3141no—
267C2×D4—3141no—
268C2×D4—3141no—
269C2×D4—6281no—
270C2×D4—6281no—
271C2×D4—6284no—
272C2×D4—1571no—
273C2×D4—1571no—
274C2×D4—1571no—
275C2×D4C22×D15711yescharacteristic
276C22×C4—21no—
277C22×C4—3141no—
278C22×C4—3141no—
279C22×C4—1571no—
280C22×C4C22×D15711yescharacteristic
281SD16—3142no—
282SD16—6281no—
283SD16—6281no—
284C2×C8—6281no—
285C2×C8—6281no—
286C2×C8—1571no—
287C2×C8—1571no—
288C2×C8C22×D15711yescharacteristic
289C2×C8C22×D15711yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—3141no—
292C4⋊C4—3141no—
293C4⋊C4—3141no—
294C4⋊C4—3141no—
295C4⋊C4—3141no—
296C4⋊C4—1571no—
297C4⋊C4—1571no—
298C4⋊C4C22×D15711yescharacteristic
299C4⋊C4C22×D15711yescharacteristic
300C4⋊C4C22×D15711yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—3141no—
303C22⋊C4—3141no—
304C22⋊C4—3141no—
305C22⋊C4—3141no—
306C22⋊C4—1571no—
307C22⋊C4—1571no—
308C42—3141no—
309C42—1571no—
310C23—21no—
311C23—3141no—
312C23—3141no—
313C23—6282no—
314C23—6282no—
315C23—6282no—
316C23—6282no—
317C23—1571no—
318C23—12561no—
319C23—12561no—
320C23D4×D15711yescharacteristic
321Q8—3141no—
322Q8—3141no—
323Q8—12561no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—3141no—
328D4—3141no—
329D4—3141no—
330D4—6282no—
331D4—6282no—
332D4—6282no—
333D4—6282no—
334D4—1574no—
335D4—1572no—
336D4—12561no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—81no—
343C2×C4—3141no—
344C2×C4—3141no—
345C2×C4—3141no—
346C2×C4—3141no—
347C2×C4—6282no—
348C2×C4—1571no—
349C2×C4—1571no—
350C2×C4—1571no—
351C2×C4—12561no—
352C2×C4D4×D15711yescharacteristic
353C2×C4C23×D15711yescharacteristic
354C8—21no—
355C8—21no—
356C8—3141no—
357C8—3141no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—3141no—
364C22—3141no—
365C22—3142no—
366C22—6281no—
367C22—6281no—
368C22—6281no—
369C22—6281no—
370C22—6281no—
371C22—1572no—
372C22—12564no—
373C22—12564no—
374C22SD16×D15712yes—
375C22C2×D4×D15711yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—3141no—
381C4—3141no—
382C4—6281no—
383C4—6281no—
384C4—1572no—
385C4#41×D15711yescharacteristic
386C4#1909781711yescharacteristic
387C2—22no—
388C2—81no—
389C2—3142no—
390C2—6282no—
391C2—12561no—
392C2#2375791511yescharacteristic
393C2C2×SD16×D15711yescharacteristic
394C2#2375807711yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#481×C157C2
socleC22×C157C22×D4
prime radical#23757907C2
hypercenter#481D157
hypocenterC157#3295
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. #23757978C2semidirect
3. #23757618C2semidirect
4. #23757593C2semidirect
5. #23757562C2semidirect
6. #23757503C2semidirect
7. #23757500C2semidirect
8. #23757472C2semidirect
9. #23757426C2semidirect
10. #23757425C2semidirect
11. #23757360C2semidirect
12. #23757336C2semidirect
13. C2×#19097691C2semidirect
14. #102×D157C2semidirect
15. #481×C157C2semidirect
20. C2×#14578943C22semidirect
21. C2×#14578942C22semidirect
22. C22×#11929434C22semidirect
23. C2×C8×D157C22semidirect
24. #19097770C22semidirect
27. #19097751C22semidirect
29. #19097750C22semidirect
35. #19097736C22semidirect
39. C4⋊C4×D157C22semidirect
40. #19097702C22semidirect
41. #19097700C22semidirect
42. #19097694C22semidirect
44. #19097693C22semidirect
45. #19097692C22semidirect
48. #19097691C22semidirect
49. #19097691C22semidirect
50. #19097683C22semidirect
51. C8×Dic157C22semidirect
53. C2×C4⋊C4×C157C22semidirect
54. #106×C157C22semidirect
55. #106×C157C22semidirect
56. #102×C157C22semidirect
57. #102×C157C22semidirect
58. C22⋊C8×C157C22semidirect
133. C22⋊D157SD16semidirect
197. C157#3295semidirect
203. #481D157semidirect
239. C2×C4⋊C4C2×D157semidirect
241. #106C2×D157semidirect
242. #106C2×D157semidirect
252. #102C2×D157semidirect
253. #102C2×D157semidirect
255. C22⋊C8C2×D157semidirect

Maximal subgroups

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

subgroupindex
#237579782
#237579072
#237576182
#237575932
#237575622
#237575032
#237575002
#237574722
#237574262
#237574252
#237573602
#237573362
C2×#190976912
#102×D1572
#481×C1572
#3295157