Finite Group Databasebeta

← #34110273

Subgroups — #34110273

Order 20096.

450 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757802C211yesmaximal, characteristic, complemented
2C4×D4×D157C211yesmaximal, characteristic, complemented
3#23757602C211yesmaximal, characteristic, complemented
4#23757585C211yesmaximal, characteristic, complemented
5#23757574C211yesmaximal, characteristic, complemented
6#23757573C211yesmaximal, characteristic, complemented
7#23757485C211yesmaximal, characteristic, complemented
8#23757422C211yesmaximal, characteristic, complemented
9#23757405C211yesmaximal, characteristic
10#23757385C211yesmaximal, characteristic, complemented
11#23757382C211yesmaximal, characteristic, complemented
12#23757376C211yesmaximal, characteristic, complemented
13#23757374C211yesmaximal, characteristic, complemented
14#23757329C211yesmaximal, characteristic, complemented
15#463×C157C211yesmaximal, characteristic, complemented
16C2×D4×D157C2211yescharacteristic
17C22×C4×D157—21no—
18C2×#14578941C2211yescharacteristic
19C2×#14578939C2211yescharacteristic
20#19097764—21no—
21#19097763C2211yescharacteristic, complemented
22#19097753—21no—
23#19097747C2211yescharacteristic
24#19097742C2211yescharacteristic
25Q8×Dic157C2211yescharacteristic, complemented
26C4×D628C2211yescharacteristic
27D4×Dic157C2211yescharacteristic
28D4×Dic157C2211yescharacteristic, complemented
29#19097733C2211yescharacteristic
30C4×C22⋊D157—21no—
31#19097731—21no—
32#19097731—21no—
33#19097727—21no—
34C4⋊C4×D157C2211yescharacteristic
35C22⋊C4×D157—21no—
36C42×D157C2211yescharacteristic
37#19097705C2211yescharacteristic, complemented
38#19097704C2211yescharacteristic, complemented
39#19097703C2211yescharacteristic, complemented
40#19097702C2211yescharacteristic, complemented
41C4⋊#11929434C2211yescharacteristic, complemented
42#19097695C2211yescharacteristic, complemented
43#19097693C2211yescharacteristic
44#19097693C2211yescharacteristic
45#19097692C2211yescharacteristic
46#19097692C2211yescharacteristic
47#19097692C2211yescharacteristic, complemented
48#19097683C2211yescharacteristic
49#19097683C2211yescharacteristic
50#19097681C2211yescharacteristic, complemented
51#19097681C2211yescharacteristic, complemented
52C2×SD16×C157C2211yescharacteristic
53C2×D8×C157C2211yescharacteristic
54#124×C157C2211yescharacteristic, complemented
55C4×D4×C157C2211yescharacteristic
56C4⋊C8×C157C2211yescharacteristic, complemented
57#103×C157C2211yescharacteristic, complemented
58#102×C157C2211yescharacteristic, complemented
59C23×D157—21no—
60C2×D628C2311yescharacteristic
61C2×C22⋊D157—21no—
62C2×C22⋊D157—21no—
63D4×D157—22no—
64D4×D157—22no—
65C22×Dic157—21no—
66C22×Dic157—21no—
67C2×C4×D157—21no—
68C2×C4×D157—21no—
69C2×C4×D157—21no—
70C2×C4×D157—44no—
71C2×C4×D157D411yescharacteristic
72C2×C4×D157D411yescharacteristic
73C2×C4×D157C2311yescharacteristic
74#14578941—22no—
75#14578939—22no—
76C2×#11929434C2311yescharacteristic
77C2×#11929434C2311yescharacteristic
78C4⋊Dic157—21no—
79C4⋊Dic157C2311yescharacteristic
80C4⋊Dic157C2311yescharacteristic
81C4⋊Dic157C2311yescharacteristic
82#14578933—21no—
83#14578933—21no—
84#14578933—21no—
85#14578933—21no—
86C22⋊Dic157—21no—
87C22⋊Dic157—21no—
88C22⋊Dic157—21no—
89#14578931—21no—
90#14578931—21no—
91#14578931—21no—
92C4×Dic157—21no—
93C4×Dic157D411yescharacteristic
94C4×Dic157D411yescharacteristic
95C4×Dic157C2311yescharacteristic
96C2×Q8×C157C2311yescharacteristic
97C2×D4×C157C2311yescharacteristic
98C2×D4×C157C2311yescharacteristic
99C22×C4×C157—21no—
100SD16×C157—22no—
101D8×C157—22no—
102C2×C8×C157C2311yescharacteristic
103C2×C8×C157C2311yescharacteristic
104C4⋊C4×C157C2311yescharacteristic
105C22⋊C4×C157—21no—
106C22⋊C4×C157—21no—
107C22⋊C4×C157—21no—
108C42×C157C2311yescharacteristic
109C22×D157—24no—
110C22×D157—21no—
111C22×D157—42no—
112C22×D157—42no—
113C22×D157C2×D411yescharacteristic
114D628—21no—
115D628#4112yes—
116C22⋊D157—24no—
117C22⋊D157—42no—
118C2×Dic157—21no—
119C2×Dic157—21no—
120C2×Dic157—21no—
121C2×Dic157—42no—
122C2×Dic157—42no—
123C2×Dic157C2×D411yescharacteristic
124C2×Dic157C2×D411yescharacteristic
125C2×Dic157C2×D411yescharacteristic
126C4×D157—22no—
127C4×D157—21no—
128C4×D157—21no—
129C4×D157—41no—
130C4×D157—42no—
131C4×D157—42no—
132C4×D157—42no—
133#11929434—21no—
134#11929434—21no—
135C23×C157—21no—
136C23×C157—21no—
137Q8×C157—21no—
138Q8×C157—21no—
139D4×C157—21no—
140D4×C157—21no—
141D4×C157—21no—
142D4×C157#4112yes—
143C2×C4×C157—21no—
144C2×C4×C157—21no—
145C2×C4×C157—42no—
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—21no—
160C2×D157—22no—
161C2×D157—48no—
162C2×D157—41no—
163C2×D157—41no—
164C2×D157AGL(1,ℤ/8)12yes—
165C4×C157—21no—
166C4×C157—21no—
167C4×C157—41no—
168C4×C157—41no—
169C4×C157C2×#4111yescharacteristic
170C4×C157C2×#4111yescharacteristic
171Dic157—21no—
172Dic157—21no—
173Dic157—21no—
174Dic157—41no—
175Dic157—41no—
176Dic157—41no—
177C2×C157—42no—
178C2×C157—81no—
179C2×C157#52511yescharacteristic
180C2×C157C2×AGL(1,ℤ/8)11yescharacteristic
181C2×C157#57511yescharacteristic
182D157—22no—
183D157—42no—
184C157#311411yescharacteristic, complemented, Sylow
185#3114—1571nomaximal, Sylow
186#529—1571no—
187C2×C4×D4—1571no—
188#483—1571no—
189#480—1571no—
190#478—1571no—
191#478—1571no—
192#463—1571no—
193#463D15711yescharacteristic, complemented
194#450—1571no—
195#447—1571no—
196#442—1571no—
197#442—1571no—
198#440—1571no—
199#440—1571no—
200#432—1571no—
201C22×D4—1571no—
202C23×C4—3141no—
203C2×SD16—1571no—
204C2×SD16C2×D15711yescharacteristic
205C2×D8—1571no—
206C2×D8C2×D15711yescharacteristic
207#126—3141no—
208#125—1571no—
209#124C2×D15711yescharacteristic, complemented
210#123—3141no—
211C22⋊Q8—1571no—
212#121—1571no—
213C4×Q8—1571no—
214C4×D4—3141no—
215C4×D4—3141no—
216C4×D4—3141no—
217C4×D4—1571no—
218C4×D4—1571no—
219C4×D4—1571no—
220C4×D4—1571no—
221C4×D4C2×D15711yescharacteristic
222#117—3141no—
223C2×C4⋊C4—1571no—
224C2×C22⋊C4—3141no—
225C2×C42—1571no—
226#107—1571no—
227#107—1571no—
228#106—1571no—
229#106—1571no—
230C4⋊C8—1571no—
231C4⋊C8C2×D15711yescharacteristic, complemented
232#103—1571no—
233#103C2×D15711yescharacteristic, complemented
234#102—1571no—
235#102—1571no—
236#102—1571no—
237#102—1571no—
238#102—1571no—
239#102C2×D15711yescharacteristic, complemented
240C22⋊C8—1571no—
241C22⋊C8—1571no—
242#97—1571no—
243#97—1571no—
244C24—3141no—
245C2×Q8C22×D15711yescharacteristic
246C2×D4—3142no—
247C2×D4—3142no—
248C2×D4—3141no—
249C2×D4—3141no—
250C2×D4—1571no—
251C2×D4C22×D15711yescharacteristic
252C2×D4C22×D15711yescharacteristic
253C22×C4—21no—
254C22×C4—3141no—
255C22×C4—3141no—
256C22×C4—3141no—
257C22×C4—3141no—
258C22×C4—3141no—
259C22×C4—6284no—
260C22×C4—1571no—
261C22×C4—1571no—
262C22×C4—1571no—
263SD16—22no—
264SD16—3142no—
265D8—22no—
266D8—3142no—
267C2×C8—1571no—
268C2×C8—1571no—
269C2×C8C22×D15711yescharacteristic
270C2×C8C22×D15711yescharacteristic
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⋊C4C22×D15711yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—3141no—
284C22⋊C4—3141no—
285C22⋊C4—3141no—
286C22⋊C4—3141no—
287C22⋊C4—3141no—
288C22⋊C4—3141no—
289C42—3141no—
290C42—1571no—
291C42—1571no—
292C42—1571no—
293C42C22×D15711yescharacteristic
294C23—21no—
295C23—21no—
296C23—3144no—
297C23—3141no—
298C23—6282no—
299C23—6282no—
300C23—1571no—
301Q8—21no—
302Q8—21no—
303D4—21no—
304D4—21no—
305D4—21no—
306D4—3144no—
307D4—3141no—
308D4—6282no—
309D4—1572no—
310D4#1457895312yes—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—3142no—
315C2×C4—3141no—
316C2×C4—3141no—
317C2×C4—3141no—
318C2×C4—3141no—
319C2×C4—3141no—
320C2×C4—6281no—
321C2×C4—6282no—
322C2×C4—6282no—
323C2×C4—6282no—
324C2×C4—6282no—
325C2×C4—6282no—
326C2×C4—1571no—
327C2×C4—1571no—
328C2×C4—1571no—
329C2×C4D4×D15711yescharacteristic
330C2×C4D4×D15711yescharacteristic
331C2×C4C23×D15711yescharacteristic
332C8—21no—
333C8—21no—
334C8—3141no—
335C8—3141no—
336C22—22no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—3141no—
343C22—3141no—
344C22—3142no—
345C22—6288no—
346C22—6281no—
347C22—6281no—
348C22—1572no—
349C22C2×D4×D15711yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—3141no—
355C4—3141no—
356C4—3141no—
357C4—6281no—
358C4—6281no—
359C4—6281no—
360C4#41×D15711yescharacteristic
361C4C2×#1457895311yescharacteristic
362C2—42no—
363C2—81no—
364C2—3142no—
365C2—6282no—
366C2#2375778311yescharacteristic
367C2AGL(1,ℤ/8)×D15711yescharacteristic
368C2#2375807011yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#463×C157C2
socleC22×C157C22×D4
prime radical#23757405C2
hypercenter#463D157
hypocenterC157#3114
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #23757802C2semidirect
2. C4×D4×D157C2semidirect
3. #23757602C2semidirect
4. #23757585C2semidirect
5. #23757574C2semidirect
6. #23757573C2semidirect
7. #23757485C2semidirect
8. #23757422C2semidirect
10. #23757385C2semidirect
11. #23757382C2semidirect
12. #23757376C2semidirect
13. #23757374C2semidirect
14. #23757329C2semidirect
15. #463×C157C2semidirect
21. #19097763C22semidirect
25. Q8×Dic157C22semidirect
28. D4×Dic157C22semidirect
37. #19097705C22semidirect
38. #19097704C22semidirect
39. #19097703C22semidirect
40. #19097702C22semidirect
41. C4⋊#11929434C22semidirect
42. #19097695C22semidirect
47. #19097692C22semidirect
50. #19097681C22semidirect
51. #19097681C22semidirect
54. #124×C157C22semidirect
56. C4⋊C8×C157C22semidirect
57. #103×C157C22semidirect
58. #102×C157C22semidirect
184. C157#3114semidirect
193. #463D157semidirect
209. #124C2×D157semidirect
231. C4⋊C8C2×D157semidirect
233. #103C2×D157semidirect
239. #102C2×D157semidirect

Maximal subgroups

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

subgroupindex
#237578022
C4×D4×D1572
#237576022
#237575852
#237575742
#237575732
#237574852
#237574222
#237574052
#237573852
#237573822
#237573762
#237573742
#237573292
#463×C1572
#3114157