Finite Group Databasebeta

← #482×D197 #38752592

Subgroups — #482×D197 #38752592

Order 25216.

468 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#121×D197C211yesmaximal, characteristic
2#117×D197C211yesmaximal, characteristic, complemented
3#27161406C211yesmaximal, characteristic, complemented
4#27161405C211yesmaximal, characteristic, complemented
5#27161404C211yesmaximal, characteristic, complemented
6#27161403C211yesmaximal, characteristic, complemented
7#27161402C211yesmaximal, characteristic, complemented
8#27161401C211yesmaximal, characteristic, complemented
9#27161400C211yesmaximal, characteristic, complemented
10#107×D197C211yesmaximal, characteristic, complemented
11#106×D197C211yesmaximal, characteristic, complemented
12#102×D197C211yesmaximal, characteristic, complemented
13#102×D197C211yesmaximal, characteristic, complemented
14C22⋊C8×D197C211yesmaximal, characteristic, complemented
15#482×C197C211yesmaximal, characteristic, complemented
16C2×D4×D197—21no—
17C2×D4×D197C2211yescharacteristic
18C22×C4×D197C2211yescharacteristic
19C2×C8×D197C2211yescharacteristic
20C2×C8×D197C2211yescharacteristic
21#20263301C2211yescharacteristic
22#20263300C2211yescharacteristic
23#20263299—21no—
24#20263298—21no—
25#20263297C2211yescharacteristic
26#20263285C2211yescharacteristic, complemented
27#20263284C2211yescharacteristic, complemented
28#20263284C2211yescharacteristic, complemented
29#20263283—21no—
30#20263282—21no—
31C4⋊C4×D197C2211yescharacteristic
32C4⋊C4×D197C2211yescharacteristic
33C4⋊C4×D197C2211yescharacteristic
34C22⋊C4×D197—21no—
35C22⋊C4×D197—21no—
36C42×D197—21no—
37#20263260C2211yescharacteristic, complemented
38#20263259C2211yescharacteristic, complemented
39#20263259C2211yescharacteristic, complemented
40#20263258C2211yescharacteristic, complemented
41#20263257C2211yescharacteristic, complemented
42#20263257C2211yescharacteristic, complemented
43#20263248C2211yescharacteristic, complemented
44#20263248C2211yescharacteristic, complemented
45#20263247C2211yescharacteristic, complemented
46#20263247C2211yescharacteristic, complemented
47#20263246C2211yescharacteristic, complemented
48#20263246C2211yescharacteristic, complemented
49C22⋊#13096802C2211yescharacteristic, complemented
50#20263238C2211yescharacteristic, complemented
51#20263238C2211yescharacteristic, complemented
52#121×C197C2211yescharacteristic
53#117×C197C2211yescharacteristic, complemented
54#107×C197C2211yescharacteristic, complemented
55#106×C197C2211yescharacteristic, complemented
56#102×C197C2211yescharacteristic, complemented
57#102×C197C2211yescharacteristic, complemented
58C22⋊C8×C197C2211yescharacteristic, complemented
59C23×D197—21no—
60C23×D197D411yescharacteristic
61C2×D788—21no—
62C2×D788C2311yescharacteristic
63C2×C22⋊D197—21no—
64C2×C22⋊D197—21no—
65C2×C22⋊D197—21no—
66D4×D197—22no—
67D4×D197—22no—
68D4×D197—44no—
69C22×Dic197D411yescharacteristic
70C2×C4×D197—22no—
71C2×C4×D197—22no—
72C2×C4×D197—21no—
73C2×C4×D197—21no—
74C2×C4×D197—21no—
75C2×C4×D197D411yescharacteristic
76C2×C4×D197D411yescharacteristic
77C2×C4×D197C2311yescharacteristic
78C2×C4×D197C2311yescharacteristic
79C2×#13096802C2311yescharacteristic
80C2×#13096802C2311yescharacteristic
81C8×D197—22no—
82C8×D197—22no—
83C4⋊Dic197C2311yescharacteristic
84C4⋊Dic197C2311yescharacteristic
85C4⋊Dic197C2311yescharacteristic
86#15691337—21no—
87#15691337—21no—
88#15691337—21no—
89C22⋊Dic197—21no—
90C22⋊Dic197—21no—
91#15691335—21no—
92#15691335—21no—
93#15691335—21no—
94#15691335—21no—
95C4×Dic197—21no—
96C4×Dic197—21no—
97C4×Dic197—21no—
98C2×D4×C197—21no—
99C2×D4×C197C2311yescharacteristic
100C22×C4×C197C2311yescharacteristic
101C2×C8×C197C2311yescharacteristic
102C2×C8×C197C2311yescharacteristic
103C4⋊C4×C197C2311yescharacteristic
104C4⋊C4×C197C2311yescharacteristic
105C4⋊C4×C197C2311yescharacteristic
106C22⋊C4×C197—21no—
107C22⋊C4×C197—21no—
108C42×C197—21no—
109C22×D197—22no—
110C22×D197—22no—
111C22×D197—22no—
112C22×D197—21no—
113C22×D197—42no—
114C22×D197—42no—
115C22×D197—42no—
116C22×D197C2×D411yescharacteristic
117C22×D197C2×D411yescharacteristic
118D788—21no—
119D788—21no—
120D788—42no—
121C22⋊D197—42no—
122C22⋊D197—42no—
123C22⋊D197—42no—
124C2×Dic197—22no—
125C2×Dic197—21no—
126C2×Dic197—21no—
127C2×Dic197—21no—
128C2×Dic197C2×D411yescharacteristic
129C2×Dic197C2×D411yescharacteristic
130C4×D197—22no—
131C4×D197—21no—
132C4×D197—21no—
133C4×D197—22no—
134C4×D197—42no—
135C4×D197—42no—
136C4×D197—42no—
137C4×D197#4112yes—
138C4×D197#4112yes—
139#13096802—21no—
140#13096802—21no—
141C23×C197—21no—
142C23×C197C2×D411yescharacteristic
143D4×C197—21no—
144D4×C197—21no—
145D4×C197—42no—
146C2×C4×C197—21no—
147C2×C4×C197—21no—
148C2×C4×C197—21no—
149C2×C4×C197—21no—
150C2×C4×C197—21no—
151C2×C4×C197C2×D411yescharacteristic
152C2×C4×C197C2411yescharacteristic
153C8×C197—21no—
154C8×C197—21no—
155C22×C197—21no—
156C22×C197—21no—
157C22×C197—21no—
158C22×C197—41no—
159C22×C197—41no—
160C22×C197—41no—
161C22×C197C22×D411yescharacteristic
162C2×D197—21no—
163C2×D197—21no—
164C2×D197—21no—
165C2×D197—44no—
166C2×D197—41no—
167C2×D197—41no—
168C2×D197—41no—
169C2×D197—84no—
170C2×D197#12312yes—
171C2×D197#13512yes—
172C2×D197AGL(1,ℤ/8)12yes—
173C4×C197—21no—
174C4×C197—41no—
175C4×C197—41no—
176C4×C197—41no—
177C4×C197C2×#4111yescharacteristic
178C4×C197C2×#4111yescharacteristic
179Dic197—21no—
180Dic197—41no—
181Dic197—41no—
182Dic197—41no—
183Dic197#12312yes—
184C2×C197—41no—
185C2×C197—81no—
186C2×C197C2×#12311yescharacteristic
187C2×C197C2×#13511yescharacteristic
188C2×C197C2×AGL(1,ℤ/8)11yescharacteristic
189D197—41no—
190D197—81no—
191D197#48214yesdirect product factor
192C197C2×#48211yescharacteristic, complemented, Sylow
193C2×#482—1971nomaximal, Sylow
194C2×#121—1971no—
195C2×#117—1971no—
196#482—1971no—
197#482—1971no—
198#482—1971no—
199#482—1971no—
200#482—1971no—
201#482—1971no—
202#482—1971no—
203#482D19711yescharacteristic, direct product factor
204C2×#107—1971no—
205C2×#106—1971no—
206C2×#102—1971no—
207C2×#102—1971no—
208C2×C22⋊C8—1971no—
209C22×D4—3941no—
210C22×D4—1971no—
211C23×C4—1971no—
212C22×C8—1971no—
213C22×C8—1971no—
214#121—3941no—
215#121—3941no—
216#121—1971no—
217#121—1971no—
218#121—1971no—
219#121C2×D19711yescharacteristic
220#117—3941no—
221#117—3941no—
222#117—1971no—
223#117—1971no—
224#117—1971no—
225#117C2×D19711yescharacteristic, complemented
226C2×C4⋊C4—1971no—
227C2×C4⋊C4—1971no—
228C2×C4⋊C4—1971no—
229C2×C22⋊C4—3941no—
230C2×C22⋊C4—3941no—
231C2×C42—3941no—
232#107—1971no—
233#107—1971no—
234#107—1971no—
235#107C2×D19711yescharacteristic, complemented
236#106—1971no—
237#106—1971no—
238#106—1971no—
239#106C2×D19711yescharacteristic, complemented
240#102—1971no—
241#102—1971no—
242#102—1971no—
243#102—1971no—
244#102—1971no—
245#102—1971no—
246#102C2×D19711yescharacteristic, complemented
247#102C2×D19711yescharacteristic, complemented
248C22⋊C8—1971no—
249C22⋊C8—1971no—
250C22⋊C8—1971no—
251C22⋊C8C2×D19711yescharacteristic, complemented
252C24—3941no—
253C24—1971no—
254C2×D4—21no—
255C2×D4—7884no—
256C2×D4—3941no—
257C2×D4—3941no—
258C2×D4—3941no—
259C2×D4—3942no—
260C2×D4—3942no—
261C2×D4—3941no—
262C2×D4—1971no—
263C2×D4C22×D19711yescharacteristic
264C22×C4—3941no—
265C22×C4—3941no—
266C22×C4—3941no—
267C22×C4—3942no—
268C22×C4—3942no—
269C22×C4—1971no—
270C22×C4—1971no—
271C22×C4—1971no—
272C22×C4—1971no—
273C22×C4—1971no—
274C22×C4C22×D19711yescharacteristic
275C2×C8—3942no—
276C2×C8—3942no—
277C2×C8—1971no—
278C2×C8—1971no—
279C2×C8C22×D19711yescharacteristic
280C2×C8C22×D19711yescharacteristic
281C4⋊C4—3941no—
282C4⋊C4—3941no—
283C4⋊C4—3941no—
284C4⋊C4—1971no—
285C4⋊C4—1971no—
286C4⋊C4—1971no—
287C4⋊C4C22×D19711yescharacteristic
288C4⋊C4C22×D19711yescharacteristic
289C4⋊C4C22×D19711yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—3941no—
293C22⋊C4—3941no—
294C22⋊C4—3941no—
295C22⋊C4—3941no—
296C22⋊C4—3941no—
297C22⋊C4—3941no—
298C42—21no—
299C42—3941no—
300C42—3941no—
301C42—3941no—
302C23—21no—
303C23—7882no—
304C23—7882no—
305C23—7882no—
306C23—3942no—
307C23—3942no—
308C23—3942no—
309C23—3941no—
310C23—1971no—
311C23—1971no—
312C23D4×D19711yescharacteristic
313D4—21no—
314D4—21no—
315D4—42no—
316D4—7882no—
317D4—7882no—
318D4—7882no—
319D4—7882no—
320D4—3941no—
321D4—3941no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—7882no—
328C2×C4—7882no—
329C2×C4—7882no—
330C2×C4—3942no—
331C2×C4—3942no—
332C2×C4—3941no—
333C2×C4—3941no—
334C2×C4—3941no—
335C2×C4—3942no—
336C2×C4—3941no—
337C2×C4—3941no—
338C2×C4—1971no—
339C2×C4—1971no—
340C2×C4—1972no—
341C2×C4—1972no—
342C2×C4D4×D19711yescharacteristic
343C2×C4C23×D19711yescharacteristic
344C8—21no—
345C8—21no—
346C8—3941no—
347C8—3941no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—7884no—
355C22—7881no—
356C22—7881no—
357C22—7881no—
358C22—15764no—
359C22—3941no—
360C22—3941no—
361C22—3941no—
362C22—1972no—
363C22—1972no—
364C22—1972no—
365C22C2×D4×D19711yescharacteristic
366C4—21no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—7881no—
371C4—7881no—
372C4—7881no—
373C4—3941no—
374C4—1972no—
375C4#41×D19711yescharacteristic
376C4#41×D19711yescharacteristic
377C2—41no—
378C2—81no—
379C2—7881no—
380C2—15761no—
381C2—1974no—
382C2#123×D19711yescharacteristic
383C2#135×D19711yescharacteristic
384C2AGL(1,ℤ/8)×D19711yescharacteristic
subgroupG/H
centerC22C2×D4×D197
commutator, cosocleC2×C4×C197C24
FrattiniC2×C4C23×D197
Fitting#482×C197C2
socleC22×C197C22×D4
prime radical#121×D197C2
hypercenter#482D197
hypocenterC197C2×#482
LCSG ▷ C2×C4×C197 ▷ C2×C197 ▷ C197
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #117×D197C2semidirect
3. #27161406C2semidirect
4. #27161405C2semidirect
5. #27161404C2semidirect
6. #27161403C2semidirect
7. #27161402C2semidirect
8. #27161401C2semidirect
9. #27161400C2semidirect
10. #107×D197C2semidirect
11. #106×D197C2semidirect
12. #102×D197C2semidirect
13. #102×D197C2semidirect
14. C22⋊C8×D197C2semidirect
15. #482×C197C2semidirect
26. #20263285C22semidirect
27. #20263284C22semidirect
28. #20263284C22semidirect
37. #20263260C22semidirect
38. #20263259C22semidirect
39. #20263259C22semidirect
40. #20263258C22semidirect
41. #20263257C22semidirect
42. #20263257C22semidirect
43. #20263248C22semidirect
44. #20263248C22semidirect
45. #20263247C22semidirect
46. #20263247C22semidirect
47. #20263246C22semidirect
48. #20263246C22semidirect
49. C22⋊#13096802C22semidirect
50. #20263238C22semidirect
51. #20263238C22semidirect
53. #117×C197C22semidirect
54. #107×C197C22semidirect
55. #106×C197C22semidirect
56. #102×C197C22semidirect
57. #102×C197C22semidirect
58. C22⋊C8×C197C22semidirect
191. D197#482direct (N × H)
192. C197C2×#482semidirect
203. #482D197direct (N × H)
225. #117C2×D197semidirect
235. #107C2×D197semidirect
239. #106C2×D197semidirect
246. #102C2×D197semidirect
247. #102C2×D197semidirect
251. C22⋊C8C2×D197semidirect

Maximal subgroups

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

subgroupindex
#121×D1972
#117×D1972
#271614062
#271614052
#271614042
#271614032
#271614022
#271614012
#271614002
#107×D1972
#106×D1972
#102×D1972
C22⋊C8×D1972
#482×C1972
C2×#482197