Finite Group Databasebeta

← #34110376

Subgroups — #34110376

Order 20096.

418 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757874C211yesmaximal, characteristic, complemented
2#23757745C211yesmaximal, characteristic, complemented
3#23757600C211yesmaximal, characteristic, complemented
4#23757595C211yesmaximal, characteristic, complemented
5#23757576C211yesmaximal, characteristic, complemented
6#23757571C211yesmaximal, characteristic, complemented
7#23757467C211yesmaximal, characteristic, complemented
8#23757466C211yesmaximal, characteristic, complemented
9#23757408C211yesmaximal, characteristic, complemented
10#23757405C211yesmaximal, characteristic, complemented
11#23757383C211yesmaximal, characteristic, complemented
12#23757383C211yesmaximal, characteristic, complemented
13C4×D1256C211yesmaximal, characteristic, complemented
14#23757332C211yesmaximal, characteristic, complemented
15C4×D8×C157C211yesmaximal, characteristic, complemented
16C2×D4×D157C2211yescharacteristic
17C2×D1256C2211yescharacteristic
18C2×#14578939C2211yescharacteristic
19C2×#14578939C2211yescharacteristic
20#19097767C2211yescharacteristic, complemented
21#19097762C2211yescharacteristic, complemented
22#19097754—21no—
23#19097753—21no—
24#19097746C2211yescharacteristic
25#19097745—21no—
26#19097744—21no—
27#19097742C2211yescharacteristic
28C4×D628C2211yescharacteristic
29C4×D628C2211yescharacteristic, complemented
30D4×Dic157C2211yescharacteristic
31#19097733C2211yescharacteristic
32C4×C22⋊D157—21no—
33#19097731—21no—
34#19097729C2211yescharacteristic
35#19097728C2211yescharacteristic
36C2×#14578931—21no—
37C22⋊C4×D157—21no—
38#19097705C2211yescharacteristic, complemented
39#19097702C2211yescharacteristic, complemented
40#19097702C2211yescharacteristic, complemented
41#19097700C2211yescharacteristic, complemented
42#19097700C2211yescharacteristic, complemented
43#19097693C2211yescharacteristic
44#19097693C2211yescharacteristic, complemented
45#19097692C2211yescharacteristic
46#19097692C2211yescharacteristic, complemented
47#19097691C2211yescharacteristic
48#19097691C2211yescharacteristic, complemented
49#19097683C2211yescharacteristic
50#19097683C2211yescharacteristic
51#19097682C2211yescharacteristic, complemented
52C2×D8×C157C2211yescharacteristic
53C4×D4×C157C2211yescharacteristic
54C4×D4×C157C2211yescharacteristic, complemented
55#107×C157C2211yescharacteristic, complemented
56#102×C157C2211yescharacteristic
57#102×C157C2211yescharacteristic, complemented
58C4×C8×C157C2211yescharacteristic, complemented
59C23×D157—21no—
60C2×D628—21no—
61C2×D628C2311yescharacteristic
62C2×D628C2311yescharacteristic
63C2×C22⋊D157—21no—
64C2×C22⋊D157—21no—
65C2×C22⋊D157—21no—
66C2×C22⋊D157—21no—
67D4×D157—22no—
68D4×D157—22no—
69C22×Dic157—21no—
70C2×C4×D157—21no—
71C2×C4×D157—21no—
72C2×C4×D157—21no—
73C2×C4×D157C2311yescharacteristic
74D1256—22no—
75#14578939—22no—
76#14578939—22no—
77C2×#11929434C2311yescharacteristic
78C2×#11929434C2311yescharacteristic
79C4⋊Dic157—21no—
80C4⋊Dic157C2311yescharacteristic
81C4⋊Dic157C2311yescharacteristic
82#14578933—21no—
83#14578933D411yescharacteristic
84#14578933D411yescharacteristic
85C22⋊Dic157—21no—
86C22⋊Dic157—21no—
87#14578931—21no—
88#14578931—21no—
89#14578931—21no—
90#14578931—21no—
91#14578931—21no—
92#14578931D411yescharacteristic
93#14578931D411yescharacteristic
94C4×Dic157—21no—
95C4×Dic157C2311yescharacteristic
96C2×D4×C157C2311yescharacteristic
97C2×D4×C157C2311yescharacteristic
98C22×C4×C157—21no—
99C22×C4×C157—21no—
100D8×C157—22no—
101C2×C8×C157C2311yescharacteristic
102C2×C8×C157C2311yescharacteristic
103C4⋊C4×C157C2311yescharacteristic
104C4⋊C4×C157C2311yescharacteristic
105C22⋊C4×C157—21no—
106C22⋊C4×C157—21no—
107C42×C157C2311yescharacteristic
108C22×D157—21no—
109C22×D157—24no—
110C22×D157—21no—
111C22×D157—81no—
112C22×D157—81no—
113C22×D157C2×D411yescharacteristic
114D628—21no—
115D628—21no—
116D628—21no—
117D628—81no—
118D628#4112yes—
119C22⋊D157—24no—
120C22⋊D157—81no—
121C22⋊D157—81no—
122C22⋊D157—81no—
123C2×Dic157—21no—
124C2×Dic157—21no—
125C2×Dic157—81no—
126C2×Dic157C2×D411yescharacteristic
127C2×Dic157C2×D411yescharacteristic
128C2×Dic157C2×D411yescharacteristic
129C4×D157—21no—
130C4×D157—21no—
131C4×D157—81no—
132C4×D157—81no—
133C4×D157—81no—
134#11929434—21no—
135#11929434—21no—
136C23×C157—21no—
137C23×C157—21no—
138D4×C157—21no—
139D4×C157—21no—
140D4×C157—21no—
141D4×C157#4112yes—
142C2×C4×C157—21no—
143C2×C4×C157—21no—
144C2×C4×C157—81no—
145C2×C4×C157—81no—
146C2×C4×C157C2×D411yescharacteristic
147C2×C4×C157C2×D411yescharacteristic
148C2×C4×C157C2411yescharacteristic
149C8×C157—21no—
150C8×C157—21no—
151C22×C157—22no—
152C22×C157—41no—
153C22×C157—41no—
154C22×C157—41no—
155C22×C157—41no—
156C22×C157—41no—
157C22×C157C22×D411yescharacteristic
158C2×D157—21no—
159C2×D157—22no—
160C2×D157—21no—
161C2×D157—21no—
162C2×D157—41no—
163C2×D157—41no—
164C2×D157—41no—
165C2×D157—41no—
166C2×D157—41no—
167C2×D157—84no—
168C4×C157—21no—
169C4×C157—21no—
170C4×C157—41no—
171C4×C157—41no—
172C4×C157C2×#4111yescharacteristic
173C4×C157C2×#4111yescharacteristic
174Dic157—21no—
175Dic157—21no—
176Dic157—21no—
177Dic157—41no—
178Dic157—41no—
179C2×C157—42no—
180C2×C157—81no—
181C2×C157#52511yescharacteristic
182C2×C157#57611yescharacteristic
183C2×C157#57611yescharacteristic
184D157—41no—
185D157—42no—
186D157—81no—
187C157#312211yescharacteristic, complemented, Sylow
188#3122—1571nomaximal, Sylow
189#540—1571no—
190#518—1571no—
191#482—1571no—
192#482—1571no—
193#478—1571no—
194#478—1571no—
195#459—1571no—
196#459—1571no—
197#447—1571no—
198#447—1571no—
199#442—1571no—
200#442—1571no—
201C4×D8—1571no—
202C4×D8D15711yescharacteristic, complemented
203#433—1571no—
204C22×D4—1571no—
205C2×D8—1571no—
206C2×D8—1571no—
207C2×D8—1571no—
208C2×D8C2×D15711yescharacteristic
209#127—1571no—
210#125—1571no—
211#123—3141no—
212#123—3141no—
213#121—3141no—
214#121—3141no—
215#121—1571no—
216#121—1571no—
217C4×D4—3141no—
218C4×D4—3141no—
219C4×D4—1571no—
220C4×D4—1571no—
221C4×D4—1571no—
222C4×D4—1571no—
223C4×D4C2×D15711yescharacteristic
224C4×D4C2×D15711yescharacteristic, complemented
225#117—1571no—
226#117—1571no—
227C2×C22⋊C4—3141no—
228C2×C22⋊C4—3141no—
229#107—1571no—
230#107C2×D15711yescharacteristic, complemented
231#106—1571no—
232#106—1571no—
233C4⋊C8—1571no—
234C4⋊C8—1571no—
235#102—1571no—
236#102—1571no—
237#102—1571no—
238#102—1571no—
239#102—1571no—
240#102—1571no—
241#102C2×D15711yescharacteristic
242#102C2×D15711yescharacteristic, complemented
243C22⋊C8—1571no—
244C22⋊C8—1571no—
245#97—1571no—
246C4×C8C2×D15711yescharacteristic, complemented
247C24—3141no—
248C2×D4—3141no—
249C2×D4—3142no—
250C2×D4—3142no—
251C2×D4—3141no—
252C2×D4—3141no—
253C2×D4—3141no—
254C2×D4—3141no—
255C2×D4—1571no—
256C2×D4—1571no—
257C2×D4C22×D15711yescharacteristic
258C2×D4C22×D15711yescharacteristic
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—3141no—
262C22×C4—3141no—
263C22×C4—3141no—
264C22×C4—3141no—
265C22×C4—1571no—
266D8—22no—
267D8—3142no—
268D8—3142no—
269D8—3142no—
270C2×C8—1571no—
271C2×C8—1571no—
272C2×C8C22×D15711yescharacteristic
273C2×C8C22×D15711yescharacteristic
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—3141no—
288C22⋊C4—3141no—
289C22⋊C4—3141no—
290C22⋊C4—3141no—
291C22⋊C4—1571no—
292C22⋊C4—1571no—
293C42—3141no—
294C42—1571no—
295C42C22×D15711yescharacteristic
296C23—21no—
297C23—21no—
298C23—3144no—
299C23—3141no—
300C23—3141no—
301C23—1571no—
302C23—12561no—
303C23—12561no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—3144no—
308D4—3141no—
309D4—3141no—
310D4—3141no—
311D4—1572no—
312D4—12561no—
313D4—12561no—
314D4—12561no—
315D4—12561no—
316D4#1457895412yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—3141no—
322C2×C4—3141no—
323C2×C4—3141no—
324C2×C4—3141no—
325C2×C4—1571no—
326C2×C4—1571no—
327C2×C4—1571no—
328C2×C4—12561no—
329C2×C4—12561no—
330C2×C4—12561no—
331C2×C4—12561no—
332C2×C4D4×D15711yescharacteristic
333C2×C4D4×D15711yescharacteristic
334C2×C4C23×D15711yescharacteristic
335C8—21no—
336C8—21no—
337C8—3141no—
338C8—3141no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—3141no—
346C22—3142no—
347C22—3141no—
348C22—3141no—
349C22—6281no—
350C22—6281no—
351C22—6281no—
352C22—6281no—
353C22—6281no—
354C22—12564no—
355C22C2×D4×D15711yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—3141no—
361C4—3141no—
362C4—3141no—
363C4—6281no—
364C4—6281no—
365C4#41×D15711yescharacteristic
366C4C2×#1457895411yescharacteristic
367C2—42no—
368C2—81no—
369C2—6281no—
370C2—6282no—
371C2—12561no—
372C2#2375778211yescharacteristic
373C2#2375807411yescharacteristic
374C2#2375807511yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
FittingC4×D8×C157C2
socleC22×C157C22×D4
hypercenterC4×D8D157
hypocenterC157#3122
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #23757874C2semidirect
2. #23757745C2semidirect
3. #23757600C2semidirect
4. #23757595C2semidirect
5. #23757576C2semidirect
6. #23757571C2semidirect
7. #23757467C2semidirect
8. #23757466C2semidirect
9. #23757408C2semidirect
10. #23757405C2semidirect
11. #23757383C2semidirect
12. #23757383C2semidirect
13. C4×D1256C2semidirect
14. #23757332C2semidirect
15. C4×D8×C157C2semidirect
20. #19097767C22semidirect
21. #19097762C22semidirect
29. C4×D628C22semidirect
38. #19097705C22semidirect
39. #19097702C22semidirect
40. #19097702C22semidirect
41. #19097700C22semidirect
42. #19097700C22semidirect
44. #19097693C22semidirect
46. #19097692C22semidirect
48. #19097691C22semidirect
51. #19097682C22semidirect
54. C4×D4×C157C22semidirect
55. #107×C157C22semidirect
57. #102×C157C22semidirect
58. C4×C8×C157C22semidirect
187. C157#3122semidirect
202. C4×D8D157semidirect
224. C4×D4C2×D157semidirect
230. #107C2×D157semidirect
242. #102C2×D157semidirect
246. C4×C8C2×D157semidirect

Maximal subgroups

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

subgroupindex
#237578742
#237577452
#237576002
#237575952
#237575762
#237575712
#237574672
#237574662
#237574082
#237574052
#237573832
C4×D12562
#237573322
C4×D8×C1572
#3122157