Finite Group Databasebeta

← #34112095

Subgroups — #34112095

Order 20096.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757924C211yesmaximal, characteristic, complemented
2#23757914C211yesmaximal, characteristic, complemented
3#23757634C211yesmaximal, characteristic, complemented
4#23757593C211yesmaximal, characteristic, complemented
5#23757562C211yesmaximal, characteristic, complemented
6#23757527C211yesmaximal, characteristic, complemented
7#23757504C211yesmaximal, characteristic, complemented
8#23757491C211yesmaximal, characteristic, complemented
9#23757421C211yesmaximal, characteristic, complemented
10#23757409C211yesmaximal, characteristic, complemented
11#23757384C211yesmaximal, characteristic, complemented
12#23757341C211yesmaximal, characteristic, complemented
13#23757273C211yesmaximal, characteristic, complemented
14C2×#19097691C211yesmaximal, characteristic, complemented
15#483×C157C211yesmaximal, characteristic, complemented
16C2×#14578955C2211yescharacteristic
17C2×#14578954—21no—
18C22×D628C2211yescharacteristic
19C2×#14578941C2211yescharacteristic, complemented
20C2×D1256C2211yescharacteristic
21C2×D1256C2211yescharacteristic
22C2×#14578937C2211yescharacteristic, complemented
23C22×#11929434C2211yescharacteristic
24#19097770C2211yescharacteristic, complemented
25#19097760C2211yescharacteristic
26#19097756—21no—
27#19097756—21no—
28#19097754—21no—
29#19097749—21no—
30#19097746—21no—
31#19097746C2211yescharacteristic
32#19097746C2211yescharacteristic, complemented
33#19097745C2211yescharacteristic
34#19097741—21no—
35#19097733C2211yescharacteristic
36#19097733C2211yescharacteristic, complemented
37C4×C22⋊D157C2211yescharacteristic
38C4⋊C4×D157C2211yescharacteristic, complemented
39C22⋊C4×D157—21no—
40#19097702C2211yescharacteristic, complemented
41#19097700C2211yescharacteristic, complemented
42#19097695C2211yescharacteristic, complemented
43#19097693C2211yescharacteristic
44#19097693C2211yescharacteristic
45#19097691C2211yescharacteristic
46#19097691C2211yescharacteristic
47#19097691C2211yescharacteristic
48#19097691C2211yescharacteristic
49#19097691C2211yescharacteristic, complemented
50#19097683C2211yescharacteristic, complemented
51#19097681C2211yescharacteristic, complemented
52C22⋊Q8×C157C2211yescharacteristic
53C2×C4⋊C4×C157C2211yescharacteristic
54#106×C157C2211yescharacteristic, complemented
55#106×C157C2211yescharacteristic, complemented
56#103×C157C2211yescharacteristic, complemented
57#103×C157C2211yescharacteristic, complemented
58C22⋊C8×C157C2211yescharacteristic
59C23×D157—21no—
60#14578955—22no—
61#14578955—41no—
62#14578954—44no—
63C2×Dic314—21no—
64C2×D628—22no—
65C2×D628—21no—
66C2×D628—21no—
67C2×D628—21no—
68C2×D628—21no—
69C2×D628—41no—
70C2×D628C2311yescharacteristic
71C2×D628C2311yescharacteristic
72C2×D628C2311yescharacteristic
73C2×C22⋊D157—21no—
74C2×C22⋊D157D411yescharacteristic
75C2×C4×D157—21no—
76C2×C4×D157—21no—
77C2×C4×D157—21no—
78C2×C4×D157—21no—
79C2×C4×D157C2311yescharacteristic
80#14578941—41no—
81D1256—22no—
82D1256—41no—
83#14578937—41no—
84C2×#11929434—41no—
85C2×#11929434C2311yescharacteristic
86C2×#11929434C2311yescharacteristic
87C4⋊Dic157C2311yescharacteristic
88#14578933—21no—
89#14578933—21no—
90#14578933D411yescharacteristic
91C22⋊Dic157D411yescharacteristic
92#14578931—21no—
93#14578931—21no—
94#14578931—21no—
95#14578931—21no—
96#14578931—21no—
97#14578931—21no—
98#14578931—21no—
99#14578931D411yescharacteristic
100C4×Dic157C2311yescharacteristic
101C2×Q8×C157C2311yescharacteristic
102C22×C4×C157—21no—
103C22×C4×C157C2311yescharacteristic
104C2×C8×C157C2311yescharacteristic
105C2×C8×C157C2311yescharacteristic
106C4⋊C4×C157—21no—
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—21no—
115C22×D157—42no—
116C22×D157—42no—
117C22×D157—81no—
118C22×D157C2×D411yescharacteristic
119Dic314—42no—
120D628—21no—
121D628—21no—
122D628—21no—
123D628—21no—
124D628—21no—
125D628—42no—
126D628—42no—
127D628—42no—
128D628—81no—
129D628#4112yescomplemented
130C22⋊D157—22no—
131C22⋊D157—42no—
132C2×Dic157—21no—
133C2×Dic157C2×D411yescharacteristic
134C2×Dic157C2×D411yescharacteristic
135C2×Dic157C2×D411yescharacteristic
136C4×D157—21no—
137C4×D157—21no—
138C4×D157—42no—
139C4×D157—42no—
140C4×D157—42no—
141C4×D157—81no—
142#11929434—21no—
143#11929434—21no—
144C23×C157C2×D411yescharacteristic
145Q8×C157—21no—
146Q8×C157—21no—
147C2×C4×C157—21no—
148C2×C4×C157—21no—
149C2×C4×C157—21no—
150C2×C4×C157—21no—
151C2×C4×C157—21no—
152C2×C4×C157—21no—
153C2×C4×C157—42no—
154C2×C4×C157C2×D411yescharacteristic
155C2×C4×C157C2411yescharacteristic
156C8×C157—21no—
157C8×C157—21no—
158C22×C157—21no—
159C22×C157—21no—
160C22×C157AGL(1,ℤ/8)12yes—
161C22×C157C22×D411yescharacteristic
162C2×D157—21no—
163C2×D157—22no—
164C2×D157—21no—
165C2×D157—21no—
166C2×D157—41no—
167C2×D157—41no—
168C2×D157—41no—
169C2×D157—41no—
170C2×D157—41no—
171C2×D157—41no—
172C2×D157—41no—
173C2×D157—41no—
174C2×D157—84no—
175C4×C157—21no—
176C4×C157—41no—
177C4×C157—41no—
178C4×C157—41no—
179C4×C157—41no—
180C4×C157C2×#4111yescharacteristic
181C4×C157H(5,𝔽2)11yescharacteristic
182Dic157—21no—
183Dic157—21no—
184Dic157—21no—
185Dic157—41no—
186C2×C157—22no—
187C2×C157#54611yescharacteristic
188C2×C157C2×AGL(1,ℤ/8)11yescharacteristic
189C2×C157#57711yescharacteristic
190D157—41no—
191D157—42no—
192D157—81no—
193D157—81no—
194C157#330611yescharacteristic, complemented, Sylow
195#3306—1571nomaximal, Sylow
196#547—1571no—
197#546—1571no—
198#489—1571no—
199#483D15711yescharacteristic, complemented
200#481—1571no—
201#476—1571no—
202#469—1571no—
203#465—1571no—
204#463—1571no—
205#449—1571no—
206#447—1571no—
207#442—1571no—
208#435—1571no—
209#417—1571no—
210C2×#102—1571no—
211C2×#41—3141no—
212C2×#41—1571no—
213C22×D4—1571no—
214C2×SD16—1571no—
215C2×D8—1571no—
216C2×D8—1571no—
217C2×M16—1571no—
218C22×C8—1571no—
219C4⋊Q8—1571no—
220#124—1571no—
221#123—3141no—
222#123—3141no—
223#123—3141no—
224C22⋊Q8—3141no—
225C22⋊Q8C2×D15711yescharacteristic
226#121—3141no—
227#121—1571no—
228#121—1571no—
229#121—1571no—
230#120—3141no—
231C4×D4—1571no—
232C4×D4—1571no—
233C4×D4—1571no—
234C2×C4⋊C4—1571no—
235C2×C4⋊C4C2×D15711yescharacteristic
236C2×C22⋊C4—3141no—
237#106—1571no—
238#106C2×D15711yescharacteristic, complemented
239#106C2×D15711yescharacteristic, complemented
240C4⋊C8—1571no—
241#103—1571no—
242#103C2×D15711yescharacteristic, complemented
243#103C2×D15711yescharacteristic, complemented
244#102—1571no—
245#102—1571no—
246#102—1571no—
247#102—1571no—
248#102—1571no—
249#102—1571no—
250#102—1571no—
251C22⋊C8—1571no—
252C22⋊C8C2×D15711yescharacteristic
253#97—1571no—
254C24—3141no—
255#41—3142no—
256#41—6284no—
257#41—6281no—
258C2×Q8—3141no—
259C2×Q8C22×D15711yescharacteristic
260C2×D4—3142no—
261C2×D4—3141no—
262C2×D4—3141no—
263C2×D4—3141no—
264C2×D4—3141no—
265C2×D4—3141no—
266C2×D4—6281no—
267C2×D4—1571no—
268C2×D4—1571no—
269C2×D4—1571no—
270C2×D4—1571no—
271C22×C4—21no—
272C22×C4—3141no—
273C22×C4—3141no—
274C22×C4—3141no—
275C22×C4—3141no—
276C22×C4—1571no—
277C22×C4C22×D15711yescharacteristic
278SD16—6281no—
279D8—3142no—
280D8—6281no—
281M16—6281no—
282C2×C8—6281no—
283C2×C8—1571no—
284C2×C8—1571no—
285C2×C8C22×D15711yescharacteristic
286C2×C8C22×D15711yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—3141no—
290C4⋊C4—3141no—
291C4⋊C4—1571no—
292C4⋊C4—1571no—
293C4⋊C4C22×D15711yescharacteristic
294C4⋊C4C22×D15711yescharacteristic
295C4⋊C4C22×D15711yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—3141no—
298C22⋊C4—3141no—
299C22⋊C4—3141no—
300C22⋊C4—3141no—
301C22⋊C4—3141no—
302C22⋊C4—3141no—
303C22⋊C4—3141no—
304C22⋊C4—1571no—
305C22⋊C4—1571no—
306C42—1571no—
307C23—3141no—
308C23—3141no—
309C23—3141no—
310C23—6282no—
311C23—6282no—
312C23—1571no—
313C23—12561no—
314C23D4×D15711yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—6282no—
318D4—3142no—
319D4—3141no—
320D4—3141no—
321D4—3141no—
322D4—3141no—
323D4—3141no—
324D4—6282no—
325D4—6282no—
326D4—6282no—
327D4—6282no—
328D4—1572no—
329D4—12561no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—3141no—
338C2×C4—3141no—
339C2×C4—3141no—
340C2×C4—6282no—
341C2×C4—6282no—
342C2×C4—6282no—
343C2×C4—1571no—
344C2×C4—1571no—
345C2×C4—1571no—
346C2×C4—12561no—
347C2×C4D4×D15711yescharacteristic
348C2×C4C23×D15711yescharacteristic
349C8—21no—
350C8—21no—
351C8—3141no—
352C8—3141no—
353C22—21no—
354C22—21no—
355C22—3141no—
356C22—3141no—
357C22—3142no—
358C22—3141no—
359C22—6281no—
360C22—6281no—
361C22—6281no—
362C22—6281no—
363C22—6281no—
364C22—6281no—
365C22—6281no—
366C22—6281no—
367C22—12564no—
368C22#1909779812yes—
369C22C2×D4×D15711yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—3141no—
376C4—3141no—
377C4—3141no—
378C4—6281no—
379C4#41×D15711yescharacteristic
380C4#1909781711yescharacteristic
381C2—22no—
382C2—6281no—
383C2—6282no—
384C2—12561no—
385C2—12561no—
386C2#2375791511yescharacteristic
387C2C2×#1909779811yescharacteristic
388C2#2375808211yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#483×C157C2
socleC22×C157C22×D4
hypercenter#483D157
hypocenterC157#3306
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #23757924C2semidirect
2. #23757914C2semidirect
3. #23757634C2semidirect
4. #23757593C2semidirect
5. #23757562C2semidirect
6. #23757527C2semidirect
7. #23757504C2semidirect
8. #23757491C2semidirect
9. #23757421C2semidirect
10. #23757409C2semidirect
11. #23757384C2semidirect
12. #23757341C2semidirect
13. #23757273C2semidirect
14. C2×#19097691C2semidirect
15. #483×C157C2semidirect
19. C2×#14578941C22semidirect
22. C2×#14578937C22semidirect
24. #19097770C22semidirect
32. #19097746C22semidirect
36. #19097733C22semidirect
38. C4⋊C4×D157C22semidirect
40. #19097702C22semidirect
41. #19097700C22semidirect
42. #19097695C22semidirect
49. #19097691C22semidirect
50. #19097683C22semidirect
51. #19097681C22semidirect
54. #106×C157C22semidirect
55. #106×C157C22semidirect
56. #103×C157C22semidirect
57. #103×C157C22semidirect
129. D628#41semidirect
194. C157#3306semidirect
199. #483D157semidirect
238. #106C2×D157semidirect
239. #106C2×D157semidirect
242. #103C2×D157semidirect
243. #103C2×D157semidirect

Maximal subgroups

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

subgroupindex
#237579242
#237579142
#237576342
#237575932
#237575622
#237575272
#237575042
#237574912
#237574212
#237574092
#237573842
#237573412
#237572732
C2×#190976912
#483×C1572
#3306157