Finite Group Databasebeta

← #34110487

Subgroups — #34110487

Order 20096.

404 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757900C211yesmaximal, characteristic, complemented
2#23757841C211yesmaximal, characteristic
3#23757638C211yesmaximal, characteristic, complemented
4#23757636C211yesmaximal, characteristic, complemented
5#23757634C211yesmaximal, characteristic, complemented
6#23757629C211yesmaximal, characteristic, complemented
7#23757627C211yesmaximal, characteristic, complemented
8#23757621C211yesmaximal, characteristic, complemented
9#23757618C211yesmaximal, characteristic, complemented
10#23757276C211yesmaximal, characteristic, complemented
11#23757273C211yesmaximal, characteristic, complemented
12#23757268C211yesmaximal, characteristic, complemented
13#102×D157C211yesmaximal, characteristic, complemented
14#23757230C211yesmaximal, characteristic, complemented
15#489×C157C211yesmaximal, characteristic, complemented
16C2×#14578955C2211yescharacteristic
17C2×D4×D157C2211yescharacteristic
18C2×#14578937C2211yescharacteristic
19C2×C8×D157C2211yescharacteristic
20#19097770C2211yescharacteristic, complemented
21#19097769—21no—
22#19097768C2211yescharacteristic
23#19097767C2211yescharacteristic
24#19097763C2211yescharacteristic, complemented
25#19097762C2211yescharacteristic, complemented
26#19097761—21no—
27#19097760C2211yescharacteristic
28#19097749—21no—
29#19097747—21no—
30#19097744—21no—
31#19097744—21no—
32#19097741—21no—
33#19097741—21no—
34#19097729C2211yescharacteristic
35#19097728C2211yescharacteristic
36C4⋊C4×D157C2211yescharacteristic
37#19097695C2211yescharacteristic, complemented
38#19097695C2211yescharacteristic, complemented
39#19097693C2211yescharacteristic
40#19097693C2211yescharacteristic
41#19097693C2211yescharacteristic, complemented
42#19097693C2211yescharacteristic, complemented
43#19097692C2211yescharacteristic
44#19097692C2211yescharacteristic
45#19097691C2211yescharacteristic
46#19097691C2211yescharacteristic
47#19097691C2211yescharacteristic, complemented
48#19097691C2211yescharacteristic, complemented
49#19097681C2211yescharacteristic, complemented
50C4×#11929434C2211yescharacteristic, complemented
51C8×Dic157C2211yescharacteristic, complemented
52C4⋊Q8×C157C2211yescharacteristic, complemented
53#124×C157C2211yescharacteristic
54#103×C157C2211yescharacteristic, complemented
55#103×C157C2211yescharacteristic, complemented
56#102×C157C2211yescharacteristic
57#102×C157C2211yescharacteristic
58#97×C157C2211yescharacteristic, complemented
59C23×D157—21no—
60#14578955—22no—
61#14578955—22no—
62C2×Dic314—21no—
63C2×D628—21no—
64C2×D628—21no—
65C2×D628—21no—
66C2×D628C2311yescharacteristic
67C2×D628C2311yescharacteristic
68C2×C22⋊D157—21no—
69C2×C22⋊D157—21no—
70C2×C22⋊D157—21no—
71D4×D157—22no—
72D4×D157—22no—
73C2×C4×D157—21no—
74C2×C4×D157—21no—
75C2×C4×D157C2311yescharacteristic
76#14578937—22no—
77C2×#11929434C2311yescharacteristic
78C2×#11929434C2311yescharacteristic
79C8×D157—22no—
80C4⋊Dic157—21no—
81C4⋊Dic157C2311yescharacteristic
82C4⋊Dic157C2311yescharacteristic
83#14578933—21no—
84#14578933—21no—
85#14578933—21no—
86#14578933—21no—
87#14578933—21no—
88#14578933D411yescharacteristic
89#14578933D411yescharacteristic
90#14578931—21no—
91#14578931—21no—
92#14578931—21no—
93#14578931D411yescharacteristic
94#14578931D411yescharacteristic
95C4×Dic157—21no—
96C4×Dic157C2311yescharacteristic
97C2×Q8×C157—21no—
98C2×Q8×C157C2311yescharacteristic
99C2×D4×C157C2311yescharacteristic
100C2×C8×C157C2311yescharacteristic
101C2×C8×C157C2311yescharacteristic
102C4⋊C4×C157—21no—
103C4⋊C4×C157C2311yescharacteristic
104C4⋊C4×C157C2311yescharacteristic
105C22⋊C4×C157—21no—
106C22⋊C4×C157—21no—
107C42×C157C2311yescharacteristic
108C22×D157—21no—
109C22×D157—21no—
110C22×D157—42no—
111C22×D157—81no—
112C22×D157—81no—
113C22×D157C2×D411yescharacteristic
114Dic314—81no—
115D628—21no—
116D628—21no—
117D628—21no—
118D628—21no—
119D628—42no—
120D628—81no—
121D628—81no—
122C22⋊D157—42no—
123C22⋊D157—81no—
124C22⋊D157—81no—
125C2×Dic157—21no—
126C2×Dic157—21no—
127C2×Dic157C2×D411yescharacteristic
128C2×Dic157C2×D411yescharacteristic
129C2×Dic157C2×D411yescharacteristic
130C4×D157—42no—
131C4×D157—81no—
132C4×D157#4112yes—
133C4×D157#4112yes—
134#11929434—21no—
135#11929434—21no—
136C23×C157—21no—
137Q8×C157—21no—
138Q8×C157—21no—
139Q8×C157—81no—
140D4×C157—21no—
141D4×C157—21no—
142C2×C4×C157—21no—
143C2×C4×C157—21no—
144C2×C4×C157—21no—
145C2×C4×C157C2×D411yescharacteristic
146C2×C4×C157C2×D411yescharacteristic
147C2×C4×C157C2411yescharacteristic
148C8×C157—21no—
149C8×C157—21no—
150C22×C157—41no—
151C22×C157—41no—
152C22×C157—41no—
153C22×C157C22×D411yescharacteristic
154C2×D157—21no—
155C2×D157—21no—
156C2×D157—41no—
157C2×D157—41no—
158C2×D157—41no—
159C2×D157—41no—
160C2×D157—41no—
161C2×D157—41no—
162C2×D157—84no—
163C2×D157#12412yes—
164C4×C157—21no—
165C4×C157—21no—
166C4×C157—41no—
167C4×C157—41no—
168C4×C157—41no—
169C4×C157C2×#4111yescharacteristic
170C4×C157C2×#4111yescharacteristic
171Dic157—21no—
172Dic157—21no—
173Dic157—41no—
174Dic157—41no—
175Dic157#12412yes—
176C2×C157—81no—
177C2×C157C2×#12411yescharacteristic
178C2×C157#57611yescharacteristic
179C2×C157#57711yescharacteristic
180D157—22no—
181D157—81no—
182D157—81no—
183C157#313611yescharacteristic, complemented, Sylow
184#3136—1571nomaximal, Sylow
185#544—1571no—
186#535—1571no—
187#490—1571no—
188#490—1571no—
189#489—1571no—
190#489D15711yescharacteristic, complemented
191#488—1571no—
192#488—1571no—
193#486—1571no—
194#486—1571no—
195#418—1571no—
196#417—1571no—
197#416—1571no—
198C2×#102—1571no—
199#405—1571no—
200C2×#41—1571no—
201C22×D4—1571no—
202C2×M16—1571no—
203C22×C8—1571no—
204C4⋊Q8—3141no—
205C4⋊Q8—1571no—
206C4⋊Q8C2×D15711yescharacteristic, complemented
207#127—1571no—
208#127—1571no—
209#125—3141no—
210#125—1571no—
211#125—1571no—
212#124—1571no—
213#124C2×D15711yescharacteristic
214C22⋊Q8—3141no—
215C22⋊Q8—3141no—
216#121—3141no—
217#121—3141no—
218#120—3141no—
219#120—3141no—
220#117—1571no—
221#117—1571no—
222C2×C4⋊C4—1571no—
223#103—1571no—
224#103—1571no—
225#103C2×D15711yescharacteristic, complemented
226#103C2×D15711yescharacteristic, complemented
227#102—1571no—
228#102—1571no—
229#102—1571no—
230#102—1571no—
231#102—1571no—
232#102—1571no—
233#102—1571no—
234#102—1571no—
235#102—1571no—
236#102—1571no—
237#102C2×D15711yescharacteristic
238#102C2×D15711yescharacteristic
239#97—1571no—
240#97C2×D15711yescharacteristic, complemented
241C4×C8—1571no—
242C4×C8—1571no—
243C24—3141no—
244#41—3142no—
245#41—3142no—
246C2×Q8—21no—
247C2×Q8—3141no—
248C2×Q8C22×D15711yescharacteristic
249C2×D4—3141no—
250C2×D4—3142no—
251C2×D4—3142no—
252C2×D4—3141no—
253C2×D4—3141no—
254C2×D4—3141no—
255C2×D4—3141no—
256C2×D4—3141no—
257C2×D4—1571no—
258C2×D4—1571no—
259C2×D4C22×D15711yescharacteristic
260C22×C4—3141no—
261C22×C4—3141no—
262C22×C4—1571no—
263M16—3142no—
264C2×C8—3142no—
265C2×C8—1571no—
266C2×C8—1571no—
267C2×C8C22×D15711yescharacteristic
268C2×C8C22×D15711yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—3141no—
271C4⋊C4—3141no—
272C4⋊C4—3141no—
273C4⋊C4—3141no—
274C4⋊C4—3141no—
275C4⋊C4—3141no—
276C4⋊C4—1571no—
277C4⋊C4—1571no—
278C4⋊C4—1571no—
279C4⋊C4—1571no—
280C4⋊C4C22×D15711yescharacteristic
281C4⋊C4C22×D15711yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—3141no—
285C22⋊C4—3141no—
286C22⋊C4—3141no—
287C22⋊C4—1571no—
288C22⋊C4—1571no—
289C42—3141no—
290C42—1571no—
291C42C22×D15711yescharacteristic
292C23—21no—
293C23—3141no—
294C23—3141no—
295C23—6282no—
296C23—1571no—
297C23—12561no—
298C23—12561no—
299Q8—21no—
300Q8—21no—
301Q8—81no—
302Q8—12561no—
303D4—21no—
304D4—21no—
305D4—3141no—
306D4—3141no—
307D4—3141no—
308D4—3141no—
309D4—6282no—
310D4—6282no—
311D4—12561no—
312D4—12561no—
313D4—12561no—
314D4—12561no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—3141no—
319C2×C4—3141no—
320C2×C4—6282no—
321C2×C4—1571no—
322C2×C4—1571no—
323C2×C4—1571no—
324C2×C4—1572no—
325C2×C4—1572no—
326C2×C4—12561no—
327C2×C4D4×D15711yescharacteristic
328C2×C4D4×D15711yescharacteristic
329C2×C4C23×D15711yescharacteristic
330C8—21no—
331C8—21no—
332C8—3141no—
333C8—3141no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—3141no—
338C22—3141no—
339C22—6281no—
340C22—6281no—
341C22—6281no—
342C22—6281no—
343C22—6281no—
344C22—6281no—
345C22—1572no—
346C22—12564no—
347C22C2×D4×D15711yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—3141no—
354C4—3141no—
355C4—6281no—
356C4—6281no—
357C4—1572no—
358C4#41×D15711yescharacteristic
359C4#41×D15711yescharacteristic
360C2—81no—
361C2—3142no—
362C2—12561no—
363C2—12561no—
364C2#124×D15711yescharacteristic
365C2#2375807711yescharacteristic
366C2#2375808211yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#489×C157C2
socleC22×C157C22×D4
prime radical#23757841C2
hypercenter#489D157
hypocenterC157#3136
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #23757900C2semidirect
3. #23757638C2semidirect
4. #23757636C2semidirect
5. #23757634C2semidirect
6. #23757629C2semidirect
7. #23757627C2semidirect
8. #23757621C2semidirect
9. #23757618C2semidirect
10. #23757276C2semidirect
11. #23757273C2semidirect
12. #23757268C2semidirect
13. #102×D157C2semidirect
14. #23757230C2semidirect
15. #489×C157C2semidirect
20. #19097770C22semidirect
24. #19097763C22semidirect
25. #19097762C22semidirect
37. #19097695C22semidirect
38. #19097695C22semidirect
41. #19097693C22semidirect
42. #19097693C22semidirect
47. #19097691C22semidirect
48. #19097691C22semidirect
49. #19097681C22semidirect
50. C4×#11929434C22semidirect
51. C8×Dic157C22semidirect
52. C4⋊Q8×C157C22semidirect
54. #103×C157C22semidirect
55. #103×C157C22semidirect
58. #97×C157C22semidirect
183. C157#3136semidirect
190. #489D157semidirect
206. C4⋊Q8C2×D157semidirect
225. #103C2×D157semidirect
226. #103C2×D157semidirect
240. #97C2×D157semidirect

Maximal subgroups

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

subgroupindex
#237579002
#237578412
#237576382
#237576362
#237576342
#237576292
#237576272
#237576212
#237576182
#237572762
#237572732
#237572682
#102×D1572
#237572302
#489×C1572
#3136157