Finite Group Databasebeta

← #34110381

Subgroups — #34110381

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#23757879C211yesmaximal, characteristic, complemented
2#23757745C211yesmaximal, characteristic, complemented
3#23757600C211yesmaximal, characteristic, complemented
4#23757599C211yesmaximal, characteristic, complemented
5#23757570C211yesmaximal, characteristic, complemented
6#23757469C211yesmaximal, characteristic, complemented
7#23757468C211yesmaximal, characteristic, complemented
8#23757408C211yesmaximal, characteristic, complemented
9#23757408C211yesmaximal, characteristic, complemented
10#23757384C211yesmaximal, characteristic, complemented
11#23757382C211yesmaximal, characteristic, complemented
12#23757355C211yesmaximal, characteristic, complemented
13#23757353C211yesmaximal, characteristic, complemented
14#23757333C211yesmaximal, characteristic, complemented
15#478×C157C211yesmaximal, characteristic, complemented
16C2×D4×D157C2211yescharacteristic
17C2×D1256C2211yescharacteristic
18C2×D1256C2211yescharacteristic
19C2×#14578939C2211yescharacteristic
20C2×#14578939C2211yescharacteristic
21#19097768C2211yescharacteristic, complemented
22#19097756—21no—
23#19097756—21no—
24#19097746—21no—
25#19097746—21no—
26#19097746C2211yescharacteristic
27#19097746C2211yescharacteristic
28C4×D628C2211yescharacteristic
29D4×Dic157C2211yescharacteristic
30#19097733C2211yescharacteristic
31#19097733C2211yescharacteristic, complemented
32#19097733C2211yescharacteristic, complemented
33C4×C22⋊D157—21no—
34#19097731—21no—
35#19097729C2211yescharacteristic
36#19097728C2211yescharacteristic
37C2×#14578931—21no—
38C22⋊C4×D157—21no—
39#19097704C2211yescharacteristic, complemented
40#19097702C2211yescharacteristic, complemented
41C4⋊#11929434C2211yescharacteristic, complemented
42#19097693C2211yescharacteristic, complemented
43#19097693C2211yescharacteristic, complemented
44#19097691C2211yescharacteristic
45#19097691C2211yescharacteristic
46#19097691C2211yescharacteristic, complemented
47#19097691C2211yescharacteristic, complemented
48#19097683C2211yescharacteristic
49#19097683C2211yescharacteristic
50#19097681C2211yescharacteristic, complemented
51C8×Dic157C2211yescharacteristic, complemented
52#125×C157C2211yescharacteristic, complemented
53C4×D4×C157C2211yescharacteristic
54#107×C157C2211yescharacteristic, complemented
55#106×C157C2211yescharacteristic, complemented
56C4⋊C8×C157C2211yescharacteristic, complemented
57#102×C157C2211yescharacteristic
58#102×C157C2211yescharacteristic
59C23×D157—21no—
60C2×D628—21no—
61C2×D628—21no—
62C2×D628—21no—
63C2×D628—21no—
64C2×D628C2311yescharacteristic
65C2×D628C2311yescharacteristic
66C2×D628C2311yescharacteristic
67C2×C22⋊D157—21no—
68D4×D157—22no—
69D4×D157—22no—
70C22×Dic157—21no—
71C2×C4×D157—21no—
72C2×C4×D157—21no—
73C2×C4×D157—21no—
74C2×C4×D157—21no—
75C2×C4×D157C2311yescharacteristic
76D1256—22no—
77D1256—22no—
78#14578939—22no—
79#14578939—22no—
80C2×#11929434C2311yescharacteristic
81C2×#11929434C2311yescharacteristic
82C4⋊Dic157C2311yescharacteristic
83#14578933D411yescharacteristic
84#14578933D411yescharacteristic
85C22⋊Dic157—21no—
86#14578931—21no—
87#14578931—21no—
88#14578931—21no—
89#14578931—21no—
90#14578931—21no—
91#14578931—21no—
92#14578931—21no—
93#14578931D411yescharacteristic
94#14578931D411yescharacteristic
95C4×Dic157—21no—
96C4×Dic157C2311yescharacteristic
97C2×D4×C157C2311yescharacteristic
98C22×C4×C157—21no—
99C2×C8×C157C2311yescharacteristic
100C2×C8×C157C2311yescharacteristic
101C4⋊C4×C157—21no—
102C4⋊C4×C157—21no—
103C4⋊C4×C157C2311yescharacteristic
104C4⋊C4×C157C2311yescharacteristic
105C4⋊C4×C157C2311yescharacteristic
106C22⋊C4×C157—21no—
107C42×C157C2311yescharacteristic
108C22×D157—21no—
109C22×D157—24no—
110C22×D157—21no—
111C22×D157—21no—
112C22×D157—81no—
113C22×D157—81no—
114C22×D157C2×D411yescharacteristic
115D628—21no—
116D628—21no—
117D628—21no—
118D628—21no—
119D628—21no—
120D628—81no—
121D628—81no—
122D628—81no—
123D628—81no—
124D628#4112yes—
125C22⋊D157—24no—
126C2×Dic157—21no—
127C2×Dic157—81no—
128C2×Dic157C2×D411yescharacteristic
129C2×Dic157C2×D411yescharacteristic
130C2×Dic157C2×D411yescharacteristic
131C4×D157—21no—
132C4×D157—21no—
133C4×D157—81no—
134C4×D157—81no—
135C4×D157—81no—
136C4×D157—81no—
137#11929434—21no—
138#11929434—21no—
139C23×C157—21no—
140D4×C157—21no—
141D4×C157#4112yes—
142C2×C4×C157—21no—
143C2×C4×C157—21no—
144C2×C4×C157—21no—
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×C157C22×D411yescharacteristic
155C2×D157—21no—
156C2×D157—22no—
157C2×D157—21no—
158C2×D157—21no—
159C2×D157—41no—
160C2×D157—41no—
161C2×D157—41no—
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×C157—41no—
173C4×C157C2×#4111yescharacteristic
174C4×C157C2×#4111yescharacteristic
175Dic157—21no—
176Dic157—21no—
177Dic157—21no—
178Dic157—41no—
179C2×C157—42no—
180C2×C157#52511yescharacteristic
181C2×C157#57611yescharacteristic
182C2×C157#57611yescharacteristic
183D157—41no—
184D157—42no—
185D157—81no—
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#478D15711yescharacteristic, complemented
195#459—1571no—
196#459—1571no—
197#447—1571no—
198#447—1571no—
199#442—1571no—
200#442—1571no—
201C4×D8—1571no—
202C4×D8—1571no—
203#433—1571no—
204C22×D4—1571no—
205C2×D8—1571no—
206C2×D8—1571no—
207C2×D8—1571no—
208C2×D8—1571no—
209#127—1571no—
210#125C2×D15711yescharacteristic, complemented
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×D4—1571no—
224C4×D4C2×D15711yescharacteristic
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#106C2×D15711yescharacteristic, complemented
233C4⋊C8—1571no—
234C4⋊C8C2×D15711yescharacteristic, complemented
235#102—1571no—
236#102—1571no—
237#102—1571no—
238#102—1571no—
239#102—1571no—
240#102—1571no—
241#102C2×D15711yescharacteristic
242#102C2×D15711yescharacteristic
243C22⋊C8—1571no—
244C22⋊C8—1571no—
245#97—1571no—
246C4×C8—1571no—
247C24—3141no—
248C2×D4—3141no—
249C2×D4—3141no—
250C2×D4—3142no—
251C2×D4—3142no—
252C2×D4—3141no—
253C2×D4—3141no—
254C2×D4—3141no—
255C2×D4—1571no—
256C2×D4—1571no—
257C2×D4—1571no—
258C2×D4C22×D15711yescharacteristic
259C22×C4—21no—
260C22×C4—3141no—
261C22×C4—3141no—
262C22×C4—3141no—
263C22×C4—3141no—
264C22×C4—3141no—
265C22×C4—1571no—
266D8—3142no—
267D8—3142no—
268D8—3142no—
269D8—3142no—
270C2×C8—1571no—
271C2×C8—1571no—
272C2×C8C22×D15711yescharacteristic
273C2×C8C22×D15711yescharacteristic
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—1571no—
277C4⋊C4—1571no—
278C4⋊C4—1571no—
279C4⋊C4C22×D15711yescharacteristic
280C4⋊C4C22×D15711yescharacteristic
281C4⋊C4C22×D15711yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—3141no—
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—3144no—
298C23—3141no—
299C23—3141no—
300C23—3141no—
301C23—1571no—
302C23—12561no—
303C23—12561no—
304D4—21no—
305D4—3144no—
306D4—3141no—
307D4—3141no—
308D4—3141no—
309D4—3141no—
310D4—3141no—
311D4—1572no—
312D4—12561no—
313D4—12561no—
314D4—12561no—
315D4—12561no—
316D4#1457895512yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—81no—
321C2×C4—3141no—
322C2×C4—3141no—
323C2×C4—3141no—
324C2×C4—1571no—
325C2×C4—1571no—
326C2×C4—1571no—
327C2×C4—12561no—
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—3141no—
343C22—3142no—
344C22—3141no—
345C22—3141no—
346C22—6281no—
347C22—6281no—
348C22—6281no—
349C22—6281no—
350C22—6281no—
351C22—6281no—
352C22—6281no—
353C22—6281no—
354C22—12564no—
355C22C2×D4×D15711yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—3141no—
362C4—3141no—
363C4—3141no—
364C4—6281no—
365C4#41×D15711yescharacteristic
366C4C2×#1457895511yescharacteristic
367C2—42no—
368C2—6281no—
369C2—6282no—
370C2—12561no—
371C2—12561no—
372C2#2375778611yescharacteristic
373C2#2375807511yescharacteristic
374C2#2375807711yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#478×C157C2
socleC22×C157C22×D4
hypercenter#478D157
hypocenterC157#3122
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #23757879C2semidirect
2. #23757745C2semidirect
3. #23757600C2semidirect
4. #23757599C2semidirect
5. #23757570C2semidirect
6. #23757469C2semidirect
7. #23757468C2semidirect
8. #23757408C2semidirect
9. #23757408C2semidirect
10. #23757384C2semidirect
11. #23757382C2semidirect
12. #23757355C2semidirect
13. #23757353C2semidirect
14. #23757333C2semidirect
15. #478×C157C2semidirect
21. #19097768C22semidirect
31. #19097733C22semidirect
32. #19097733C22semidirect
39. #19097704C22semidirect
40. #19097702C22semidirect
41. C4⋊#11929434C22semidirect
42. #19097693C22semidirect
43. #19097693C22semidirect
46. #19097691C22semidirect
47. #19097691C22semidirect
50. #19097681C22semidirect
51. C8×Dic157C22semidirect
52. #125×C157C22semidirect
54. #107×C157C22semidirect
55. #106×C157C22semidirect
56. C4⋊C8×C157C22semidirect
187. C157#3122semidirect
194. #478D157semidirect
210. #125C2×D157semidirect
230. #107C2×D157semidirect
232. #106C2×D157semidirect
234. C4⋊C8C2×D157semidirect

Maximal subgroups

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

subgroupindex
#237578792
#237577452
#237576002
#237575992
#237575702
#237574692
#237574682
#237574082
#237573842
#237573822
#237573552
#237573532
#237573332
#478×C1572
#3122157