Finite Group Databasebeta

← #38752991

Subgroups — #38752991

Order 25216.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27161700C211yesmaximal, characteristic, complemented
2#27161559C211yesmaximal, characteristic, complemented
3#27161410C211yesmaximal, characteristic, complemented
4#27161398C211yesmaximal, characteristic, complemented
5#27161370C211yesmaximal, characteristic, complemented
6#27161365C211yesmaximal, characteristic, complemented
7#27161302C211yesmaximal, characteristic, complemented
8#27161295C211yesmaximal, characteristic, complemented
9#27161243C211yesmaximal, characteristic, complemented
10#27161226C211yesmaximal, characteristic
11#27161192C211yesmaximal, characteristic, complemented
12#27161187C211yesmaximal, characteristic, complemented
13C4×#15691347C211yesmaximal, characteristic, complemented
14C4×#15691347C211yesmaximal, characteristic, complemented
15#433×C197C211yesmaximal, characteristic, complemented
16C2×#15691358C2211yescharacteristic
17C2×Dic788C2211yescharacteristic
18C2×#15691347C2211yescharacteristic
19C2×#15691347C2211yescharacteristic
20C2×D1576C2211yescharacteristic
21#20263326C2211yescharacteristic
22#20263321—21no—
23#20263314C2211yescharacteristic
24#20263312—21no—
25#20263308—21no—
26#20263305C2211yescharacteristic
27#20263304—21no—
28#20263300C2211yescharacteristic
29C4×Dic394C2211yescharacteristic
30C4×Dic394C2211yescharacteristic
31C4×Dic394C2211yescharacteristic
32C4×D788C2211yescharacteristic
33C4×D788C2211yescharacteristic
34C4×D788C2211yescharacteristic
35#20263286—21no—
36#20263286—21no—
37#20263284—21no—
38C2×C4⋊Dic197C2211yescharacteristic
39C4⋊C4×D197—21no—
40#20263258C2211yescharacteristic
41#20263258C2211yescharacteristic
42#20263258C2211yescharacteristic
43#20263258C2211yescharacteristic
44#20263251C2211yescharacteristic
45#20263251C2211yescharacteristic
46#20263251C2211yescharacteristic
47#20263251C2211yescharacteristic
48#20263248C2211yescharacteristic
49#20263248C2211yescharacteristic
50#20263248C2211yescharacteristic
51#20263248C2211yescharacteristic
52#117×C197C2211yescharacteristic
53C4⋊C8×C197C2211yescharacteristic
54C4⋊C8×C197C2211yescharacteristic
55C22⋊C8×C197C2211yescharacteristic
56C22⋊C8×C197C2211yescharacteristic
57#97×C197C2211yescharacteristic
58C4×C8×C197C2211yescharacteristic
59#15691358—22no—
60#15691358—22no—
61C2×Dic394—21no—
62C2×Dic394C2311yescharacteristic
63C2×Dic394C2311yescharacteristic
64C2×D788C2311yescharacteristic
65C2×D788C2311yescharacteristic
66C2×C22⋊D197—21no—
67C2×C22⋊D197—21no—
68C22×Dic197—21no—
69C2×C4×D197—21no—
70C2×C4×D197—21no—
71C2×C4×D197—21no—
72C2×C4×D197—21no—
73Dic788—22no—
74#15691347—22no—
75#15691347—22no—
76D1576—22no—
77C4⋊Dic197—21no—
78C4⋊Dic197—21no—
79C4⋊Dic197C2311yescharacteristic
80C4⋊Dic197C2311yescharacteristic
81C4⋊Dic197C2311yescharacteristic
82C4⋊Dic197C2311yescharacteristic
83#15691337—21no—
84#15691337—21no—
85#15691337—21no—
86#15691337—21no—
87C22⋊Dic197—21no—
88#15691335—21no—
89#15691335—21no—
90#15691335—21no—
91#15691335—21no—
92#15691335—21no—
93#15691335—21no—
94C4×Dic197—21no—
95C4×Dic197—21no—
96C4×Dic197—21no—
97C22×C4×C197C2311yescharacteristic
98C2×C8×C197C2311yescharacteristic
99C2×C8×C197C2311yescharacteristic
100C2×C8×C197C2311yescharacteristic
101C2×C8×C197C2311yescharacteristic
102C4⋊C4×C197D411yescharacteristic
103C4⋊C4×C197D411yescharacteristic
104C22⋊C4×C197D411yescharacteristic
105C22⋊C4×C197D411yescharacteristic
106C42×C197C2311yescharacteristic
107C42×C197C2311yescharacteristic
108C22×D197—21no—
109C22×D197—21no—
110Dic394—21no—
111Dic394—21no—
112Dic394—21no—
113Dic394—81no—
114Dic394#4112yes—
115D788—21no—
116D788—21no—
117D788—21no—
118D788#4112yes—
119C22⋊D197—24no—
120C22⋊D197—81no—
121C2×Dic197—21no—
122C2×Dic197—21no—
123C2×Dic197—21no—
124C2×Dic197—21no—
125C2×Dic197—21no—
126C2×Dic197—21no—
127C2×Dic197—81no—
128C4×D197—24no—
129C4×D197—81no—
130C4×D197—81no—
131C4×D197—81no—
132C23×C197C2×D411yescharacteristic
133C2×C4×C197—21no—
134C2×C4×C197—21no—
135C2×C4×C197C2×D411yescharacteristic
136C2×C4×C197C2×D411yescharacteristic
137C2×C4×C197C2×D411yescharacteristic
138C2×C4×C197C2×D411yescharacteristic
139C2×C4×C197C2×D411yescharacteristic
140C2×C4×C197C2411yescharacteristic
141C8×C197—21no—
142C8×C197—21no—
143C8×C197—21no—
144C8×C197—21no—
145C22×C197—21no—
146C22×C197—21no—
147C22×C197—21no—
148C22×C197C22×D411yescharacteristic
149C2×D197—22no—
150C2×D197—41no—
151C2×D197—41no—
152C2×D197—41no—
153C2×D197—41no—
154C2×D197—41no—
155C4×C197—21no—
156C4×C197—21no—
157C4×C197—21no—
158C4×C197—21no—
159C4×C197—21no—
160C4×C197C2×#4111yescharacteristic
161C4×C197C2×#4111yescharacteristic
162Dic197—22no—
163Dic197—41no—
164Dic197—41no—
165Dic197—41no—
166Dic197—41no—
167Dic197—41no—
168C2×C197—41no—
169C2×C197#52511yescharacteristic
170C2×C197#57711yescharacteristic
171C2×C197#57711yescharacteristic
172D197—42no—
173D197—81no—
174C197#312511yescharacteristic, complemented, Sylow
175#3125—1971nomaximal, Sylow
176#542—1971no—
177#520—1971no—
178#483—1971no—
179#481—1971no—
180#476—1971no—
181#475—1971no—
182#464—1971no—
183#463—1971no—
184#452—1971no—
185#449—1971no—
186#442—1971no—
187#441—1971no—
188C4×SD16—1971no—
189C4×SD16—1971no—
190#433D19711yescharacteristic, complemented
191C2×#41—1971no—
192C2×Q16—1971no—
193C2×SD16—1971no—
194C2×SD16—1971no—
195C2×D8—1971no—
196C4⋊Q8—1971no—
197#126—3941no—
198#124—3941no—
199#124—1971no—
200#123—3941no—
201C22⋊Q8—3941no—
202C22⋊Q8—1971no—
203#121—1971no—
204C4×Q8—1971no—
205C4×Q8—1971no—
206C4×Q8—1971no—
207C4×D4—3941no—
208C4×D4—3941no—
209C4×D4—1971no—
210C4×D4—1971no—
211C4×D4—1971no—
212#117—3941no—
213#117C2×D19711yescharacteristic
214C2×C4⋊C4—3941no—
215C2×C4⋊C4—1971no—
216#106—1971no—
217#106—1971no—
218#106—1971no—
219#106—1971no—
220C4⋊C8C2×D19711yescharacteristic
221C4⋊C8C2×D19711yescharacteristic
222#103—1971no—
223#103—1971no—
224#103—1971no—
225#103—1971no—
226#102—1971no—
227#102—1971no—
228#102—1971no—
229#102—1971no—
230C22⋊C8C2×D19711yescharacteristic
231C22⋊C8C2×D19711yescharacteristic
232#97C2×D19711yescharacteristic
233C4×C8C2×D19711yescharacteristic
234#41—3942no—
235#41—3942no—
236C2×Q8—3941no—
237C2×Q8—1971no—
238C2×Q8—1971no—
239C2×D4—3941no—
240C2×D4—3941no—
241C2×D4—1971no—
242C2×D4—1971no—
243C22×C4—3941no—
244C22×C4—3941no—
245C22×C4—3941no—
246C22×C4—3941no—
247C22×C4—3941no—
248C22×C4C22×D19711yescharacteristic
249Q16—3942no—
250SD16—3942no—
251SD16—3942no—
252D8—3942no—
253C2×C8C22×D19711yescharacteristic
254C2×C8C22×D19711yescharacteristic
255C2×C8C22×D19711yescharacteristic
256C2×C8C22×D19711yescharacteristic
257C4⋊C4—3941no—
258C4⋊C4—3941no—
259C4⋊C4—3941no—
260C4⋊C4—3941no—
261C4⋊C4—3941no—
262C4⋊C4—3941no—
263C4⋊C4—1971no—
264C4⋊C4—1971no—
265C4⋊C4—1971no—
266C4⋊C4—1971no—
267C4⋊C4D78811yescharacteristic
268C4⋊C4D78811yescharacteristic
269C22⋊C4—3941no—
270C22⋊C4—3941no—
271C22⋊C4—3941no—
272C22⋊C4—3941no—
273C22⋊C4—3941no—
274C22⋊C4—3941no—
275C22⋊C4—3941no—
276C22⋊C4D78811yescharacteristic
277C22⋊C4D78811yescharacteristic
278C42—3941no—
279C42—3941no—
280C42—3941no—
281C42C22×D19711yescharacteristic
282C42C22×D19711yescharacteristic
283C23—3941no—
284C23—3941no—
285C23C2×D78811yescharacteristic
286Q8—15761no—
287Q8—3941no—
288Q8—3941no—
289Q8—3941no—
290Q8—1972no—
291D4—15761no—
292D4—3944no—
293D4—3941no—
294D4—3941no—
295D4—3941no—
296D4—1972no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—15761no—
300C2×C4—15761no—
301C2×C4—15761no—
302C2×C4—15761no—
303C2×C4—3944no—
304C2×C4—3941no—
305C2×C4—3941no—
306C2×C4—3941no—
307C2×C4—3941no—
308C2×C4—3941no—
309C2×C4—3941no—
310C2×C4C2×D78811yescharacteristic
311C2×C4C2×D78811yescharacteristic
312C2×C4C2×D78811yescharacteristic
313C2×C4C2×D78811yescharacteristic
314C2×C4C2×D78811yescharacteristic
315C2×C4C23×D19711yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—7881no—
324C22—7881no—
325C22—7881no—
326C22—7881no—
327C22—7881no—
328C22—3942no—
329C22C22×D78811yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—7881no—
336C4—7881no—
337C4—7881no—
338C4—7881no—
339C4—7881no—
340C4—3942no—
341C4#41×D19711yescharacteristic
342C4#41×D19711yescharacteristic
343C2—41no—
344C2—7882no—
345C2—15761no—
346C2#2716159111yescharacteristic
347C2#2716189111yescharacteristic
348C2#2716189111yescharacteristic
subgroupG/H
centerC22C22×D788
commutator, cosocleC2×C4×C197C24
FrattiniC2×C4C23×D197
Fitting#433×C197C2
socleC22×C197C22×D4
prime radical#27161226C2
hypercenter#433D197
hypocenterC197#3125
LCSG ▷ C2×C4×C197 ▷ C2×C197 ▷ C197
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #27161700C2semidirect
2. #27161559C2semidirect
3. #27161410C2semidirect
4. #27161398C2semidirect
5. #27161370C2semidirect
6. #27161365C2semidirect
7. #27161302C2semidirect
8. #27161295C2semidirect
9. #27161243C2semidirect
11. #27161192C2semidirect
12. #27161187C2semidirect
13. C4×#15691347C2semidirect
14. C4×#15691347C2semidirect
15. #433×C197C2semidirect
174. C197#3125semidirect
190. #433D197semidirect

Maximal subgroups

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

subgroupindex
#271617002
#271615592
#271614102
#271613982
#271613702
#271613652
#271613022
#271612952
#271612432
#271612262
#271611922
#271611872
C4×#156913472
#433×C1972
#3125197