Finite Group Databasebeta

← #34111956

Subgroups — #34111956

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
2D4×C22⋊D157C211yesmaximal, characteristic
3#23757618C211yesmaximal, characteristic, complemented
4#23757591C211yesmaximal, characteristic, complemented
5#23757590C211yesmaximal, characteristic, complemented
6#23757561C211yesmaximal, characteristic, complemented
7#23757502C211yesmaximal, characteristic, complemented
8#23757501C211yesmaximal, characteristic, complemented
9#23757472C211yesmaximal, characteristic, complemented
10#23757425C211yesmaximal, characteristic, complemented
11#23757424C211yesmaximal, characteristic, complemented
12#23757364C211yesmaximal, characteristic, complemented
13C8×C22⋊D157C211yesmaximal, characteristic, complemented
14#102×D157C211yesmaximal, characteristic, complemented
15C2×#102×C157C211yesmaximal, characteristic, complemented
16C22×C22⋊D157—21no—
17C2×D4×D157C2211yescharacteristic
18C2×#14578943C2211yescharacteristic, complemented
19C2×#14578942C2211yescharacteristic
20C2×#14578942C2211yescharacteristic, complemented
21C2×C8×D157C2211yescharacteristic, complemented
22#19097770C2211yescharacteristic, complemented
23#19097767C2211yescharacteristic
24#19097761—21no—
25#19097751C2211yescharacteristic, complemented
26#19097750—21no—
27#19097750C2211yescharacteristic, complemented
28#19097749—21no—
29#19097745C2211yescharacteristic
30#19097743—21no—
31#19097742C2211yescharacteristic
32#19097740—21no—
33#19097739—21no—
34#19097736C2211yescharacteristic, complemented
35D4×Dic157C2211yescharacteristic
36C4×C22⋊D157—21no—
37C4×C22⋊D157C2211yescharacteristic
38C4⋊C4×D157C2211yescharacteristic, complemented
39#19097703C2211yescharacteristic, complemented
40#19097702C2211yescharacteristic, complemented
41#19097702C2211yescharacteristic, complemented
42#19097700C2211yescharacteristic, complemented
43#19097696C2211yescharacteristic, complemented
44#19097693C2211yescharacteristic, complemented
45#19097692C2211yescharacteristic
46#19097692C2211yescharacteristic, complemented
47#19097691C2211yescharacteristic, complemented
48#19097691C2211yescharacteristic, complemented
49C22⋊#11929434C2211yescharacteristic, complemented
50#19097683C2211yescharacteristic, complemented
51C8×Dic157C2211yescharacteristic, complemented
52C22×D4×C157C2211yescharacteristic
53C22×C8×C157C2211yescharacteristic, complemented
54C2×C4⋊C4×C157C2211yescharacteristic, complemented
55#102×C157C2211yescharacteristic
56#102×C157C2211yescharacteristic
57#102×C157C2211yescharacteristic, complemented
58#102×C157C2211yescharacteristic, complemented
59C23×D157—21no—
60C2×Dic314—21no—
61C2×Dic314C2311yescharacteristic
62C2×D628C2311yescharacteristic
63C2×C22⋊D157—21no—
64C2×C22⋊D157—21no—
65C2×C22⋊D157—21no—
66C2×C22⋊D157—21no—
67C2×C22⋊D157—21no—
68C2×C22⋊D157—44no—
69C2×C22⋊D157D411yescharacteristic
70D4×D157—22no—
71D4×D157—41no—
72C22×Dic157—21no—
73C2×C4×D157—21no—
74C2×C4×D157C2311yescharacteristic
75#14578943—41no—
76#14578942—22no—
77#14578942—41no—
78C2×#11929434C2311yescharacteristic
79C2×#11929434C2311yescharacteristic
80C8×D157—41no—
81C4⋊Dic157—21no—
82C4⋊Dic157C2311yescharacteristic
83C4⋊Dic157C2311yescharacteristic
84#14578933—21no—
85#14578933—21no—
86#14578933—21no—
87#14578933—21no—
88#14578933D411yescharacteristic
89C22⋊Dic157—21no—
90C22⋊Dic157—21no—
91C22⋊Dic157—21no—
92C22⋊Dic157D411yescharacteristic
93#14578931—21no—
94#14578931—21no—
95#14578931D411yescharacteristic
96C4×Dic157—21no—
97C4×Dic157C2311yescharacteristic
98C24×C157—21no—
99C2×D4×C157—22no—
100C2×D4×C157—21no—
101C2×D4×C157—41no—
102C2×D4×C157C2311yescharacteristic
103C2×D4×C157C2311yescharacteristic
104C22×C4×C157—21no—
105C22×C4×C157C2311yescharacteristic
106C2×C8×C157—41no—
107C2×C8×C157C2311yescharacteristic
108C2×C8×C157C2311yescharacteristic
109C4⋊C4×C157—21no—
110C4⋊C4×C157C2311yescharacteristic
111C4⋊C4×C157C2311yescharacteristic
112C22×D157—21no—
113C22×D157—42no—
114C22×D157—42no—
115C22×D157—81no—
116C22×D157C2×D411yescharacteristic
117Dic314—21no—
118Dic314—21no—
119Dic314—81no—
120D628—21no—
121D628—21no—
122C22⋊D157—42no—
123C22⋊D157—42no—
124C22⋊D157—42no—
125C22⋊D157—42no—
126C22⋊D157—81no—
127C22⋊D157SD1614yescomplemented
128C2×Dic157—21no—
129C2×Dic157—21no—
130C2×Dic157—21no—
131C2×Dic157—42no—
132C2×Dic157C2×D411yescharacteristic
133C2×Dic157C2×D411yescharacteristic
134C2×Dic157C2×D411yescharacteristic
135C4×D157—21no—
136C4×D157—21no—
137C4×D157—81no—
138#11929434—21no—
139#11929434—21no—
140C23×C157—21no—
141C23×C157—21no—
142C23×C157—42no—
143C23×C157—42no—
144C23×C157—81no—
145C23×C157C2×D411yescharacteristic
146D4×C157—21no—
147D4×C157—21no—
148D4×C157—21no—
149D4×C157—42no—
150D4×C157#4112yes—
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—22no—
163C22×C157—41no—
164C22×C157—41no—
165C22×C157—41no—
166C22×C157—41no—
167C22×C157—41no—
168C22×C157—84no—
169C22×C157C2×SD1612yes—
170C22×C157C22×D411yescharacteristic
171C2×D157—21no—
172C2×D157—21no—
173C2×D157—41no—
174C2×D157—41no—
175C2×D157—41no—
176C2×D157—84no—
177C2×D157C2×SD1612yes—
178C4×C157—21no—
179C4×C157—41no—
180C4×C157—41no—
181C4×C157C2×#4111yescharacteristic
182C4×C157H(5,𝔽2)11yescharacteristic
183Dic157—21no—
184Dic157—21no—
185Dic157—41no—
186Dic157—41no—
187Dic157—41no—
188Dic157C2×SD1612yes—
189C2×C157—22no—
190C2×C157—42no—
191C2×C157—81no—
192C2×C157#54611yescharacteristic
193C2×C157C22×SD1611yescharacteristic
194C2×C157#57611yescharacteristic
195D157—22no—
196D157—81no—
197C157#329511yescharacteristic, complemented, Sylow
198#3295—1571nomaximal, Sylow
199#554—1571no—
200D42—1571no—
201#486—1571no—
202#481—1571no—
203#481—1571no—
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×#102D15711yescharacteristic, complemented
214C22×D4—3141no—
215C22×D4—1571no—
216C22×D4C2×D15711yescharacteristic
217C2×SD16—1571no—
218C2×SD16—1571no—
219C2×SD16—1571no—
220C22×C8—1571no—
221C22×C8C2×D15711yescharacteristic, complemented
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#121—1571no—
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#106—1571no—
242#106—1571no—
243C4⋊C8—1571no—
244#103—1571no—
245#102—1571no—
246#102—1571no—
247#102—1571no—
248#102—1571no—
249#102—1571no—
250#102C2×D15711yescharacteristic
251#102C2×D15711yescharacteristic
252#102C2×D15711yescharacteristic, complemented
253#102C2×D15711yescharacteristic, complemented
254C22⋊C8—1571no—
255C22⋊C8—1571no—
256C4×C8—1571no—
257C24—21no—
258C24—3141no—
259C2×Q8—3141no—
260C2×Q8—1571no—
261C2×D4—22no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—3142no—
265C2×D4—3141no—
266C2×D4—3141no—
267C2×D4—3141no—
268C2×D4—3141no—
269C2×D4—3141no—
270C2×D4—6281no—
271C2×D4—6284no—
272C2×D4—1571no—
273C2×D4—1571no—
274C2×D4C22×D15711yescharacteristic
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—41no—
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⋊C4—1571no—
299C4⋊C4C22×D15711yescharacteristic
300C4⋊C4C22×D15711yescharacteristic
301C22⋊C4—3141no—
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—21no—
312C23—42no—
313C23—42no—
314C23—81no—
315C23—3141no—
316C23—6282no—
317C23—6282no—
318C23—1571no—
319C23—12561no—
320C23D4×D15711yescharacteristic
321Q8—3141no—
322Q8—3141no—
323Q8—12561no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—42no—
328D4—3141no—
329D4—3141no—
330D4—6282no—
331D4—6282no—
332D4—6282no—
333D4—6282no—
334D4—1574no—
335D4—12561no—
336D4#1457895412yes—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—81no—
342C2×C4—3141no—
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—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—84no—
367C22—3141no—
368C22—3141no—
369C22—6281no—
370C22—6281no—
371C22—6281no—
372C22—1572no—
373C22—12564no—
374C22SD16×D15712yes—
375C22C2×D4×D15711yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—3141no—
380C4—3141no—
381C4—6281no—
382C4—6281no—
383C4—6281no—
384C4—1572no—
385C4C2×#1457895411yescharacteristic
386C4#1909781611yescharacteristic
387C2—22no—
388C2—42no—
389C2—81no—
390C2—3142no—
391C2—12561no—
392C2#2375791311yescharacteristic
393C2C2×SD16×D15711yescharacteristic
394C2#2375807411yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
FittingC2×#102×C157C2
socleC22×C157C22×D4
prime radicalD4×C22⋊D157C2
hypercenterC2×#102D157
hypocenterC157#3295
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #23757978C2semidirect
3. #23757618C2semidirect
4. #23757591C2semidirect
5. #23757590C2semidirect
6. #23757561C2semidirect
7. #23757502C2semidirect
8. #23757501C2semidirect
9. #23757472C2semidirect
10. #23757425C2semidirect
11. #23757424C2semidirect
12. #23757364C2semidirect
13. C8×C22⋊D157C2semidirect
14. #102×D157C2semidirect
15. C2×#102×C157C2semidirect
18. C2×#14578943C22semidirect
20. C2×#14578942C22semidirect
21. C2×C8×D157C22semidirect
22. #19097770C22semidirect
25. #19097751C22semidirect
27. #19097750C22semidirect
34. #19097736C22semidirect
38. C4⋊C4×D157C22semidirect
39. #19097703C22semidirect
40. #19097702C22semidirect
41. #19097702C22semidirect
42. #19097700C22semidirect
43. #19097696C22semidirect
44. #19097693C22semidirect
46. #19097692C22semidirect
47. #19097691C22semidirect
48. #19097691C22semidirect
49. C22⋊#11929434C22semidirect
50. #19097683C22semidirect
51. C8×Dic157C22semidirect
53. C22×C8×C157C22semidirect
54. C2×C4⋊C4×C157C22semidirect
57. #102×C157C22semidirect
58. #102×C157C22semidirect
127. C22⋊D157SD16semidirect
197. C157#3295semidirect
213. C2×#102D157semidirect
221. C22×C8C2×D157semidirect
239. C2×C4⋊C4C2×D157semidirect
252. #102C2×D157semidirect
253. #102C2×D157semidirect

Maximal subgroups

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

subgroupindex
#237579782
D4×C22⋊D1572
#237576182
#237575912
#237575902
#237575612
#237575022
#237575012
#237574722
#237574252
#237574242
#237573642
C8×C22⋊D1572
#102×D1572
C2×#102×C1572
#3295157