Finite Group Databasebeta

← #34110375

Subgroups — #34110375

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#23757876C211yesmaximal, characteristic, complemented
2#23757747C211yesmaximal, characteristic, complemented
3#23757597C211yesmaximal, characteristic, complemented
4#23757576C211yesmaximal, characteristic, complemented
5#23757572C211yesmaximal, characteristic, complemented
6#23757467C211yesmaximal, characteristic, complemented
7#23757467C211yesmaximal, characteristic, complemented
8#23757409C211yesmaximal, characteristic, complemented
9#23757406C211yesmaximal, characteristic, complemented
10#23757384C211yesmaximal, characteristic, complemented
11#23757382C211yesmaximal, characteristic, complemented
12#23757355C211yesmaximal, characteristic, complemented
13#23757353C211yesmaximal, characteristic, complemented
14#23757331C211yesmaximal, characteristic, complemented
15#482×C157C211yesmaximal, characteristic, complemented
16C22×D628C2211yescharacteristic
17C2×D1256C2211yescharacteristic
18C2×D1256C2211yescharacteristic
19C2×#14578939C2211yescharacteristic
20C2×#14578939C2211yescharacteristic
21#19097767C2211yescharacteristic, complemented
22#19097762C2211yescharacteristic, complemented
23#19097755—21no—
24#19097753—21no—
25#19097745C2211yescharacteristic
26#19097743—21no—
27#19097742—21no—
28C4×D628—21no—
29C4×D628—21no—
30D4×Dic157C2211yescharacteristic, complemented
31#19097733C2211yescharacteristic
32#19097733C2211yescharacteristic
33#19097733C2211yescharacteristic
34#19097733C2211yescharacteristic
35#19097733C2211yescharacteristic, complemented
36#19097730C2211yescharacteristic
37C22⋊C4×D157—21no—
38C22⋊C4×D157—21no—
39#19097704C2211yescharacteristic, complemented
40#19097702C2211yescharacteristic, complemented
41#19097700C2211yescharacteristic, complemented
42#19097700C2211yescharacteristic, complemented
43#19097693C2211yescharacteristic
44#19097693C2211yescharacteristic
45#19097691C2211yescharacteristic
46#19097691C2211yescharacteristic
47#19097691C2211yescharacteristic, complemented
48#19097691C2211yescharacteristic, complemented
49C22⋊#11929434C2211yescharacteristic
50#19097681C2211yescharacteristic, complemented
51C8×Dic157C2211yescharacteristic, complemented
52#121×C157C2211yescharacteristic
53#117×C157C2211yescharacteristic
54#107×C157C2211yescharacteristic, complemented
55#106×C157C2211yescharacteristic, complemented
56#102×C157C2211yescharacteristic, complemented
57#102×C157C2211yescharacteristic, complemented
58C22⋊C8×C157C2211yescharacteristic
59C23×D157—21no—
60C2×D628—22no—
61C2×D628—22no—
62C2×D628—21no—
63C2×D628C2311yescharacteristic
64C2×D628C2311yescharacteristic
65C2×D628C2311yescharacteristic
66C2×C22⋊D157—21no—
67C2×C22⋊D157—21no—
68C2×C22⋊D157—21no—
69C22×Dic157—21no—
70C2×C4×D157—21no—
71C2×C4×D157—21no—
72C2×C4×D157—21no—
73C2×C4×D157—21no—
74C2×C4×D157—21no—
75D1256—22no—
76D1256—22no—
77#14578939—22no—
78#14578939—22no—
79C2×#11929434C2311yescharacteristic
80C2×#11929434C2311yescharacteristic
81C4⋊Dic157—21no—
82C4⋊Dic157D411yescharacteristic
83C4⋊Dic157D411yescharacteristic
84C4⋊Dic157C2311yescharacteristic
85#14578933—21no—
86C22⋊Dic157—21no—
87C22⋊Dic157D411yescharacteristic
88C22⋊Dic157D411yescharacteristic
89#14578931—21no—
90#14578931—21no—
91#14578931—21no—
92#14578931—21no—
93#14578931—21no—
94#14578931—21no—
95C4×Dic157C2311yescharacteristic
96C4×Dic157C2311yescharacteristic
97C2×D4×C157—21no—
98C2×D4×C157C2311yescharacteristic
99C22×C4×C157C2311yescharacteristic
100C2×C8×C157C2311yescharacteristic
101C2×C8×C157C2311yescharacteristic
102C4⋊C4×C157C2311yescharacteristic
103C4⋊C4×C157C2311yescharacteristic
104C4⋊C4×C157C2311yescharacteristic
105C22⋊C4×C157—21no—
106C22⋊C4×C157—21no—
107C42×C157—21no—
108C22×D157—21no—
109C22×D157—21no—
110C22×D157—24no—
111C22×D157—21no—
112C22×D157—81no—
113C22×D157—81no—
114D628—24no—
115D628—21no—
116D628—21no—
117D628—21no—
118D628—21no—
119D628#4112yes—
120D628#4112yes—
121C22⋊D157—81no—
122C22⋊D157—81no—
123C22⋊D157—81no—
124C2×Dic157—21no—
125C2×Dic157—81no—
126C2×Dic157C2×D411yescharacteristic
127C2×Dic157C2×D411yescharacteristic
128C2×Dic157C2×D411yescharacteristic
129C2×Dic157C2×D411yescharacteristic
130C4×D157—81no—
131C4×D157—81no—
132C4×D157—81no—
133C4×D157—81no—
134C4×D157—81no—
135#11929434—21no—
136#11929434—21no—
137C23×C157—21no—
138C23×C157C2×D411yescharacteristic
139D4×C157—21no—
140D4×C157—21no—
141D4×C157—81no—
142C2×C4×C157—21no—
143C2×C4×C157—21no—
144C2×C4×C157—21no—
145C2×C4×C157—21no—
146C2×C4×C157—21no—
147C2×C4×C157C2×D411yescharacteristic
148C2×C4×C157C2411yescharacteristic
149C8×C157—21no—
150C8×C157—21no—
151C22×C157—21no—
152C22×C157—21no—
153C22×C157—21no—
154C22×C157—41no—
155C22×C157—41no—
156C22×C157—41no—
157C22×C157C22×D411yescharacteristic
158C2×D157—22no—
159C2×D157—22no—
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—41no—
170C4×C157—41no—
171C4×C157—41no—
172C4×C157C2×#4111yescharacteristic
173C4×C157C2×#4111yescharacteristic
174Dic157—21no—
175Dic157—21no—
176Dic157—21no—
177Dic157—21no—
178Dic157—41no—
179C2×C157—41no—
180C2×C157—81no—
181C2×C157#52511yescharacteristic
182C2×C157#57611yescharacteristic
183C2×C157#57611yescharacteristic
184D157—42no—
185D157—42no—
186D157—81no—
187C157#312211yescharacteristic, complemented, Sylow
188#3122—1571nomaximal, Sylow
189#540—1571no—
190#518—1571no—
191#482—1571no—
192#482D15711yescharacteristic, complemented
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×D8—1571no—
203#433—1571no—
204C22×D4—1571no—
205C2×D8—1571no—
206C2×D8—1571no—
207C2×D8—1571no—
208C2×D8—1571no—
209#127—1571no—
210#125—1571no—
211#123—3141no—
212#123—3141no—
213#121—3141no—
214#121—3141no—
215#121—1571no—
216#121C2×D15711yescharacteristic
217C4×D4—3141no—
218C4×D4—3141no—
219C4×D4—1571no—
220C4×D4—1571no—
221C4×D4—1571no—
222C4×D4—1571no—
223C4×D4—1571no—
224C4×D4—1571no—
225#117—1571no—
226#117C2×D15711yescharacteristic
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⋊C8—1571no—
235#102—1571no—
236#102—1571no—
237#102—1571no—
238#102—1571no—
239#102—1571no—
240#102—1571no—
241#102C2×D15711yescharacteristic, complemented
242#102C2×D15711yescharacteristic, complemented
243C22⋊C8—1571no—
244C22⋊C8C2×D15711yescharacteristic
245#97—1571no—
246C4×C8—1571no—
247C24—3141no—
248C2×D4—21no—
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×D4—1571no—
258C2×D4C22×D15711yescharacteristic
259C22×C4—3141no—
260C22×C4—3141no—
261C22×C4—3141no—
262C22×C4—3141no—
263C22×C4—3141no—
264C22×C4—3141no—
265C22×C4C22×D15711yescharacteristic
266D8—3142no—
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⋊C4C22×D15711yescharacteristic
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—21no—
294C42—1571no—
295C42—1571no—
296C23—21no—
297C23—3144no—
298C23—3141no—
299C23—3141no—
300C23—3141no—
301C23—12561no—
302C23—12561no—
303C23D4×D15711yescharacteristic
304D4—21no—
305D4—21no—
306D4—81no—
307D4—3144no—
308D4—3141no—
309D4—3141no—
310D4—3141no—
311D4—3141no—
312D4—1572no—
313D4—1572no—
314D4—12561no—
315D4—12561no—
316D4—12561no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—3141no—
323C2×C4—1571no—
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×C4—12561no—
333C2×C4D4×D15711yescharacteristic
334C2×C4C23×D15711yescharacteristic
335C8—21no—
336C8—21no—
337C8—3141no—
338C8—3141no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—3142no—
346C22—3142no—
347C22—6281no—
348C22—6281no—
349C22—6281no—
350C22—6281no—
351C22—6281no—
352C22—6281no—
353C22—6281no—
354C22—12564no—
355C22C2×D4×D15711yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—3141no—
361C4—3141no—
362C4—3141no—
363C4—3141no—
364C4—6281no—
365C4#41×D15711yescharacteristic
366C4#41×D15711yescharacteristic
367C2—41no—
368C2—81no—
369C2—6282no—
370C2—6282no—
371C2—12561no—
372C2#2375778111yescharacteristic
373C2#2375807511yescharacteristic
374C2#2375807711yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#482×C157C2
socleC22×C157C22×D4
hypercenter#482D157
hypocenterC157#3122
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #23757876C2semidirect
2. #23757747C2semidirect
3. #23757597C2semidirect
4. #23757576C2semidirect
5. #23757572C2semidirect
6. #23757467C2semidirect
7. #23757467C2semidirect
8. #23757409C2semidirect
9. #23757406C2semidirect
10. #23757384C2semidirect
11. #23757382C2semidirect
12. #23757355C2semidirect
13. #23757353C2semidirect
14. #23757331C2semidirect
15. #482×C157C2semidirect
21. #19097767C22semidirect
22. #19097762C22semidirect
30. D4×Dic157C22semidirect
35. #19097733C22semidirect
39. #19097704C22semidirect
40. #19097702C22semidirect
41. #19097700C22semidirect
42. #19097700C22semidirect
47. #19097691C22semidirect
48. #19097691C22semidirect
50. #19097681C22semidirect
51. C8×Dic157C22semidirect
54. #107×C157C22semidirect
55. #106×C157C22semidirect
56. #102×C157C22semidirect
57. #102×C157C22semidirect
187. C157#3122semidirect
192. #482D157semidirect
230. #107C2×D157semidirect
232. #106C2×D157semidirect
241. #102C2×D157semidirect
242. #102C2×D157semidirect

Maximal subgroups

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

subgroupindex
#237578762
#237577472
#237575972
#237575762
#237575722
#237574672
#237574092
#237574062
#237573842
#237573822
#237573552
#237573532
#237573312
#482×C1572
#3122157