Finite Group Databasebeta

← #34109960

Subgroups — #34109960

Order 20096.

398 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757900C211yesmaximal, characteristic, complemented
2#23757745C211yesmaximal, characteristic
3#23757576C211yesmaximal, characteristic, complemented
4#23757574C211yesmaximal, characteristic, complemented
5#23757573C211yesmaximal, characteristic, complemented
6#23757571C211yesmaximal, characteristic, complemented
7#23757561C211yesmaximal, characteristic, complemented
8#23757560C211yesmaximal, characteristic, complemented
9#23757552C211yesmaximal, characteristic, complemented
10#23757314C211yesmaximal, characteristic, complemented
11#23757310C211yesmaximal, characteristic, complemented
12#23757298C211yesmaximal, characteristic, complemented
13#23757276C211yesmaximal, characteristic
14#102×D157C211yesmaximal, characteristic
15#474×C157C211yesmaximal, characteristic, complemented
16C2×D4×D157C2211yescharacteristic
17C2×#14578937C2211yescharacteristic
18C2×C8×D157C2211yescharacteristic
19#19097770C2211yescharacteristic, complemented
20#19097769—21no—
21#19097763C2211yescharacteristic, complemented
22#19097762C2211yescharacteristic, complemented
23#19097761—21no—
24#19097749—21no—
25#19097747—21no—
26C4×D628C2211yescharacteristic
27D4×Dic157C2211yescharacteristic
28#19097733C2211yescharacteristic
29C4×C22⋊D157—21no—
30#19097731—21no—
31#19097729C2211yescharacteristic
32#19097729C2211yescharacteristic
33#19097728C2211yescharacteristic
34C4⋊C4×D157C2211yescharacteristic
35C2×#14578931—21no—
36C22⋊C4×D157—21no—
37#19097705C2211yescharacteristic, complemented
38#19097704C2211yescharacteristic, complemented
39#19097703C2211yescharacteristic, complemented
40#19097702C2211yescharacteristic, complemented
41#19097702C2211yescharacteristic, complemented
42#19097702C2211yescharacteristic, complemented
43C4⋊#11929434C2211yescharacteristic, complemented
44#19097700C2211yescharacteristic, complemented
45#19097700C2211yescharacteristic, complemented
46#19097693C2211yescharacteristic
47#19097693C2211yescharacteristic
48#19097692C2211yescharacteristic
49#19097692C2211yescharacteristic
50#19097691C2211yescharacteristic
51#19097691C2211yescharacteristic
52C4⋊Q8×C157C2211yescharacteristic, complemented
53C4×D4×C157C2211yescharacteristic
54#107×C157C2211yescharacteristic, complemented
55#107×C157C2211yescharacteristic, complemented
56C4⋊C8×C157C2211yescharacteristic, complemented
57#102×C157C2211yescharacteristic
58#102×C157C2211yescharacteristic
59C23×D157—21no—
60C2×Dic314—21no—
61C2×D628C2311yescharacteristic
62C2×C22⋊D157—21no—
63D4×D157—22no—
64D4×D157Q814yescomplemented
65C22×Dic157—21no—
66C2×C4×D157—21no—
67C2×C4×D157—21no—
68C2×C4×D157—21no—
69C2×C4×D157C2311yescharacteristic
70#14578937—22no—
71C2×#11929434C2311yescharacteristic
72C2×#11929434C2311yescharacteristic
73C8×D157—22no—
74C4⋊Dic157—21no—
75C4⋊Dic157C2311yescharacteristic
76C4⋊Dic157C2311yescharacteristic
77C4⋊Dic157C2311yescharacteristic
78#14578933—21no—
79#14578933—21no—
80#14578933—21no—
81#14578933—21no—
82#14578933—21no—
83#14578933D411yescharacteristic
84#14578933D411yescharacteristic
85C22⋊Dic157—21no—
86#14578931—21no—
87#14578931—21no—
88#14578931—21no—
89#14578931—21no—
90#14578931D411yescharacteristic
91#14578931D411yescharacteristic
92C4×Dic157—21no—
93C4×Dic157—21no—
94C4×Dic157C2311yescharacteristic
95C2×Q8×C157—21no—
96C2×D4×C157C2311yescharacteristic
97C22×C4×C157—21no—
98C2×C8×C157C2311yescharacteristic
99C2×C8×C157C2311yescharacteristic
100C4⋊C4×C157—21no—
101C4⋊C4×C157C2311yescharacteristic
102C4⋊C4×C157C2311yescharacteristic
103C4⋊C4×C157C2311yescharacteristic
104C22⋊C4×C157—21no—
105C42×C157C2311yescharacteristic
106C22×D157—21no—
107C22×D157—24no—
108C22×D157—81no—
109C22×D157—81no—
110C22×D157C2×D411yescharacteristic
111Dic314—81no—
112D628—21no—
113D628C2×Q812yes—
114C22⋊D157—24no—
115C2×Dic157—21no—
116C2×Dic157—21no—
117C2×Dic157—21no—
118C2×Dic157—81no—
119C2×Dic157C2×D411yescharacteristic
120C2×Dic157C2×D411yescharacteristic
121C2×Dic157C2×D411yescharacteristic
122C4×D157—81no—
123C4×D157—81no—
124C4×D157—81no—
125C4×D157C2×Q812yes—
126C4×D157#4112yes—
127#11929434—21no—
128#11929434—21no—
129C23×C157—21no—
130Q8×C157—81no—
131D4×C157—21no—
132D4×C157C2×Q812yes—
133C2×C4×C157—21no—
134C2×C4×C157—21no—
135C2×C4×C157—21no—
136C2×C4×C157—81no—
137C2×C4×C157C2×D411yescharacteristic
138C2×C4×C157C2×D411yescharacteristic
139C2×C4×C157C2411yescharacteristic
140C8×C157—21no—
141C8×C157—21no—
142C22×C157—22no—
143C22×C157—41no—
144C22×C157—41no—
145C22×C157C22×D411yescharacteristic
146C2×D157—21no—
147C2×D157—21no—
148C2×D157—22no—
149C2×D157—41no—
150C2×D157—41no—
151C2×D157—84no—
152C2×D157C22⋊Q812yes—
153C4×C157—21no—
154C4×C157—21no—
155C4×C157—41no—
156C4×C157—41no—
157C4×C157—41no—
158C4×C157C22×Q811yescharacteristic
159C4×C157C2×#4111yescharacteristic
160Dic157—21no—
161Dic157—21no—
162Dic157—41no—
163Dic157—41no—
164Dic157—41no—
165Dic157C22⋊Q812yes—
166C2×C157—42no—
167C2×C157C2×C22⋊Q811yescharacteristic
168C2×C157#57611yescharacteristic
169C2×C157#57711yescharacteristic
170D157—22no—
171D157—42no—
172C157#308111yescharacteristic, complemented, Sylow
173#3081—1571nomaximal, Sylow
174#544—1571no—
175#518—1571no—
176#478—1571no—
177#478—1571no—
178#478—1571no—
179#478—1571no—
180#476—1571no—
181#476—1571no—
182#474—1571no—
183#474D15711yescharacteristic, complemented
184#428—1571no—
185#427—1571no—
186#424—1571no—
187#418—1571no—
188C2×#102—1571no—
189C22×D4—1571no—
190C2×M16—1571no—
191C22×C8—1571no—
192C4⋊Q8—3141no—
193C4⋊Q8—1571no—
194C4⋊Q8C2×D15711yescharacteristic, complemented
195#125—3141no—
196#125—1571no—
197#125—1571no—
198C22⋊Q8—3141no—
199C22⋊Q8—3141no—
200C4×D4—3141no—
201C4×D4—3141no—
202C4×D4—1571no—
203C4×D4—1571no—
204C4×D4—1571no—
205C4×D4C2×D15711yescharacteristic
206#117—1571no—
207#117—1571no—
208#117—1571no—
209C2×C4⋊C4—1571no—
210C2×C22⋊C4—3141no—
211C2×C22⋊C4—3141no—
212#107—1571no—
213#107—1571no—
214#107C2×D15711yescharacteristic, complemented
215#107C2×D15711yescharacteristic, complemented
216#106—1571no—
217#106—1571no—
218#106—1571no—
219#106—1571no—
220C4⋊C8—1571no—
221C4⋊C8—1571no—
222C4⋊C8—1571no—
223C4⋊C8C2×D15711yescharacteristic, complemented
224#102—1571no—
225#102—1571no—
226#102—1571no—
227#102—1571no—
228#102—1571no—
229#102—1571no—
230#102C2×D15711yescharacteristic
231#102C2×D15711yescharacteristic
232C24—3141no—
233C2×Q8—21no—
234C2×Q8—3141no—
235C2×D4—3142no—
236C2×D4—3141no—
237C2×D4—1574no—
238C2×D4—1571no—
239C2×D4C22×D15711yescharacteristic
240C22×C4—21no—
241C22×C4—3141no—
242C22×C4—3141no—
243C22×C4—3141no—
244C22×C4—3141no—
245C22×C4—1571no—
246M16—3142no—
247C2×C8—3142no—
248C2×C8—1571no—
249C2×C8—1571no—
250C2×C8C22×D15711yescharacteristic
251C2×C8C22×D15711yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—3141no—
254C4⋊C4—3141no—
255C4⋊C4—3141no—
256C4⋊C4—3141no—
257C4⋊C4—3141no—
258C4⋊C4—3141no—
259C4⋊C4—1571no—
260C4⋊C4—1571no—
261C4⋊C4—1571no—
262C4⋊C4—1571no—
263C4⋊C4—1571no—
264C4⋊C4C22×D15711yescharacteristic
265C4⋊C4C22×D15711yescharacteristic
266C4⋊C4C22×D15711yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—3141no—
269C22⋊C4—3141no—
270C22⋊C4—3141no—
271C22⋊C4—3141no—
272C22⋊C4—3141no—
273C22⋊C4—1571no—
274C22⋊C4—1571no—
275C42—3141no—
276C42—3141no—
277C42—1571no—
278C42C22×D15711yescharacteristic
279C23—21no—
280C23—3144no—
281C23—3141no—
282C23—1571no—
283C23—12561no—
284C23—12561no—
285Q8—81no—
286Q8—12561no—
287D4—21no—
288D4—3144no—
289D4—3141no—
290D4—1572no—
291D4Q8×D15712yes—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—81no—
296C2×C4—3141no—
297C2×C4—3141no—
298C2×C4—3141no—
299C2×C4—1571no—
300C2×C4—1571no—
301C2×C4—1571no—
302C2×C4—1572no—
303C2×C4—1572no—
304C2×C4—12561no—
305C2×C4—12561no—
306C2×C4—12561no—
307C2×C4—12561no—
308C2×C4D4×D15711yescharacteristic
309C2×C4D4×D15711yescharacteristic
310C2×C4C23×D15711yescharacteristic
311C8—21no—
312C8—21no—
313C8—3141no—
314C8—3141no—
315C22—22no—
316C22—41no—
317C22—41no—
318C22—3141no—
319C22—3141no—
320C22—3142no—
321C22—6281no—
322C22—6281no—
323C22—1572no—
324C22—12564no—
325C22C2×D4×D15711yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—3141no—
332C4—3141no—
333C4—6281no—
334C4—6281no—
335C4—6281no—
336C4—1572no—
337C4C2×Q8×D15711yescharacteristic
338C4#41×D15711yescharacteristic
339C2—42no—
340C2—3142no—
341C2—6282no—
342C2C22⋊Q8×D15711yescharacteristic
343C2#2375807411yescharacteristic
344C2#2375808211yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#474×C157C2
socleC22×C157C22×D4
prime radicalC2×D4×D157C22
hypercenter#474D157
hypocenterC157#3081
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #23757900C2semidirect
3. #23757576C2semidirect
4. #23757574C2semidirect
5. #23757573C2semidirect
6. #23757571C2semidirect
7. #23757561C2semidirect
8. #23757560C2semidirect
9. #23757552C2semidirect
10. #23757314C2semidirect
11. #23757310C2semidirect
12. #23757298C2semidirect
15. #474×C157C2semidirect
19. #19097770C22semidirect
21. #19097763C22semidirect
22. #19097762C22semidirect
37. #19097705C22semidirect
38. #19097704C22semidirect
39. #19097703C22semidirect
40. #19097702C22semidirect
41. #19097702C22semidirect
42. #19097702C22semidirect
43. C4⋊#11929434C22semidirect
44. #19097700C22semidirect
45. #19097700C22semidirect
52. C4⋊Q8×C157C22semidirect
54. #107×C157C22semidirect
55. #107×C157C22semidirect
56. C4⋊C8×C157C22semidirect
64. D4×D157Q8semidirect
172. C157#3081semidirect
183. #474D157semidirect
194. C4⋊Q8C2×D157semidirect
214. #107C2×D157semidirect
215. #107C2×D157semidirect
223. C4⋊C8C2×D157semidirect

Maximal subgroups

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

subgroupindex
#237579002
#237577452
#237575762
#237575742
#237575732
#237575712
#237575612
#237575602
#237575522
#237573142
#237573102
#237572982
#237572762
#102×D1572
#474×C1572
#3081157