Finite Group Databasebeta

← #464×D197 #38752152

Subgroups — #464×D197 #38752152

Order 25216.

500 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q16×D197C211yesmaximal, characteristic, complemented
2C2×SD16×D197C211yesmaximal, characteristic
3#124×D197C211yesmaximal, characteristic
4C4×Q8×D197C211yesmaximal, characteristic, complemented
5#27161304C211yesmaximal, characteristic, complemented
6#27161303C211yesmaximal, characteristic, complemented
7#27161302C211yesmaximal, characteristic, complemented
8#27161301C211yesmaximal, characteristic, complemented
9#27161300C211yesmaximal, characteristic, complemented
10#27161299C211yesmaximal, characteristic, complemented
11#27161298C211yesmaximal, characteristic, complemented
12C4⋊C8×D197C211yesmaximal, characteristic, complemented
13#103×D197C211yesmaximal, characteristic, complemented
14#102×D197C211yesmaximal, characteristic
15#464×C197C211yesmaximal, characteristic, complemented
16C2×Q8×D197C2211yescharacteristic
17C2×Q8×D197C2211yescharacteristic
18C2×D4×D197C2211yescharacteristic
19C2×Dic788C2211yescharacteristic, complemented
20C2×#15691348C2211yescharacteristic, complemented
21C2×#15691348C2211yescharacteristic, complemented
22Q16×D197—24no—
23C2×#15691347C2211yescharacteristic
24C2×#15691346C2211yescharacteristic
25C2×#15691345C2211yescharacteristic
26SD16×D197—24no—
27C2×C8×D197C2211yescharacteristic
28C2×C8×D197C2211yescharacteristic
29#20263315C2211yescharacteristic
30#20263314C2211yescharacteristic
31#20263313C2211yescharacteristic
32#20263312—21no—
33#20263312—21no—
34Q8×Dic197C2211yescharacteristic, complemented
35C4×Dic394—21no—
36C4×Dic394C2211yescharacteristic, complemented
37#20263291—21no—
38#20263291C2211yescharacteristic, complemented
39C4⋊C4×D197—21no—
40C4⋊C4×D197C2211yescharacteristic
41C22⋊C4×D197—21no—
42C22⋊C4×D197—21no—
43C42×D197—21no—
44C42×D197C2211yescharacteristic
45C4⋊#13096802C2211yescharacteristic, complemented
46#20263255C2211yescharacteristic, complemented
47#20263255C2211yescharacteristic, complemented
48#20263251C2211yescharacteristic, complemented
49#20263250C2211yescharacteristic, complemented
50#20263249C2211yescharacteristic, complemented
51#20263248C2211yescharacteristic
52#20263247C2211yescharacteristic
53#20263246C2211yescharacteristic
54C2×Q16×C197C2211yescharacteristic, complemented
55C2×SD16×C197C2211yescharacteristic
56#124×C197C2211yescharacteristic
57C4×Q8×C197C2211yescharacteristic, complemented
58C4⋊C8×C197C2211yescharacteristic, complemented
59#103×C197C2211yescharacteristic, complemented
60#102×C197C2211yescharacteristic
61C23×D197—21no—
62C2×Dic394—21no—
63C2×Dic394—21no—
64C2×Dic394C2311yescharacteristic
65C2×Dic394C2311yescharacteristic
66Q8×D197—22no—
67Q8×D197—22no—
68Q8×D197—22no—
69Q8×D197D414yes—
70C2×D788C2311yescharacteristic
71C2×C22⋊D197—21no—
72D4×D197—22no—
73D4×D197—22no—
74C2×C4×D197—21no—
75C2×C4×D197—21no—
76C2×C4×D197—21no—
77C2×C4×D197D411yescharacteristic
78C2×C4×D197D411yescharacteristic
79C2×C4×D197C2311yescharacteristic
80Dic788—22no—
81#15691348—22no—
82#15691348—22no—
83#15691347—22no—
84#15691346—22no—
85#15691345—22no—
86C2×#13096802C2311yescharacteristic
87C2×#13096802C2311yescharacteristic
88C8×D197—22no—
89C8×D197—22no—
90C4⋊Dic197—21no—
91C4⋊Dic197C2311yescharacteristic
92#15691337—21no—
93#15691337—21no—
94#15691337—21no—
95C22⋊Dic197—21no—
96C22⋊Dic197—21no—
97#15691335—21no—
98#15691335—21no—
99#15691335—21no—
100#15691335—21no—
101C4×Dic197—21no—
102C4×Dic197—21no—
103C4×Dic197—21no—
104C4×Dic197D411yescharacteristic
105C4×Dic197D411yescharacteristic
106C4×Dic197C2311yescharacteristic
107C2×Q8×C197C2311yescharacteristic
108C2×Q8×C197C2311yescharacteristic
109C2×D4×C197C2311yescharacteristic
110Q16×C197—22no—
111SD16×C197—22no—
112C2×C8×C197C2311yescharacteristic
113C2×C8×C197C2311yescharacteristic
114C4⋊C4×C197—21no—
115C4⋊C4×C197C2311yescharacteristic
116C22⋊C4×C197—21no—
117C22⋊C4×C197—21no—
118C42×C197—21no—
119C42×C197C2311yescharacteristic
120C22×D197—21no—
121C22×D197—42no—
122C22×D197—42no—
123C22×D197—42no—
124C22×D197C2×D411yescharacteristic
125Dic394—21no—
126Dic394—24no—
127Dic394—21no—
128Dic394—21no—
129Dic394—42no—
130Dic394C2×D412yes—
131D788—21no—
132D788—21no—
133C22⋊D197—42no—
134C2×Dic197—21no—
135C2×Dic197—21no—
136C2×Dic197—21no—
137C2×Dic197C2×D411yescharacteristic
138C2×Dic197C2×D411yescharacteristic
139C2×Dic197C2×D411yescharacteristic
140C4×D197—24no—
141C4×D197—22no—
142C4×D197—22no—
143C4×D197—42no—
144C4×D197—42no—
145C4×D197C2×D412yes—
146C4×D197#4112yes—
147#13096802—21no—
148#13096802—21no—
149C23×C197—21no—
150Q8×C197—21no—
151Q8×C197—21no—
152Q8×C197—21no—
153Q8×C197C2×D412yes—
154D4×C197—21no—
155D4×C197—21no—
156C2×C4×C197—21no—
157C2×C4×C197—21no—
158C2×C4×C197—21no—
159C2×C4×C197C2×D411yescharacteristic
160C2×C4×C197C2×D411yescharacteristic
161C2×C4×C197C2411yescharacteristic
162C8×C197—21no—
163C8×C197—21no—
164C22×C197—41no—
165C22×C197—41no—
166C22×C197—41no—
167C22×C197C22×D411yescharacteristic
168C2×D197—41no—
169C2×D197—41no—
170C2×D197—41no—
171C2×D197—84no—
172C2×D197#12112yes—
173C2×D197#13512yes—
174C2×D197#13712yes—
175C4×C197—22no—
176C4×C197—21no—
177C4×C197—21no—
178C4×C197—41no—
179C4×C197—41no—
180C4×C197C22×D411yescharacteristic
181C4×C197C2×#4111yescharacteristic
182Dic197—22no—
183Dic197—21no—
184Dic197—21no—
185Dic197—41no—
186Dic197—41no—
187Dic197#12112yes—
188C2×C197—81no—
189C2×C197C2×#12111yescharacteristic
190C2×C197C2×#13511yescharacteristic
191C2×C197C2×#13711yescharacteristic
192D197—81no—
193D197#46414yesdirect product factor
194C197C2×#46411yescharacteristic, complemented, Sylow
195C2×#464—1971nomaximal, Sylow
196C22×Q16—1971no—
197C22×SD16—1971no—
198C2×#124—1971no—
199C2×C4×Q8—1971no—
200#464—1971no—
201#464—1971no—
202#464—1971no—
203#464—1971no—
204#464—1971no—
205#464—1971no—
206#464—1971no—
207#464D19711yescharacteristic, direct product factor
208C2×C4⋊C8—1971no—
209C2×#103—1971no—
210C2×#102—1971no—
211C22×Q8—1971no—
212C22×Q8—1971no—
213C22×D4—1971no—
214C2×Q16—3944no—
215C2×Q16—1971no—
216C2×Q16—1971no—
217C2×Q16—1971no—
218C2×Q16C2×D19711yescharacteristic, complemented
219C2×SD16—3944no—
220C2×SD16—1971no—
221C2×SD16—1971no—
222C2×SD16—1971no—
223C2×SD16C2×D19711yescharacteristic
224C22×C8—1971no—
225C22×C8—1971no—
226#124—3941no—
227#124—3941no—
228#124—1971no—
229#124—1971no—
230#124—1971no—
231#124C2×D19711yescharacteristic
232C4×Q8—3941no—
233C4×Q8—3941no—
234C4×Q8—1971no—
235C4×Q8—1971no—
236C4×Q8—1971no—
237C4×Q8C2×D19711yescharacteristic, complemented
238C2×C4⋊C4—3941no—
239C2×C4⋊C4—1971no—
240C2×C22⋊C4—3941no—
241C2×C22⋊C4—3941no—
242C2×C42—3941no—
243C2×C42—1971no—
244C4⋊C8—1971no—
245C4⋊C8—1971no—
246C4⋊C8—1971no—
247C4⋊C8C2×D19711yescharacteristic, complemented
248#103—1971no—
249#103—1971no—
250#103—1971no—
251#103C2×D19711yescharacteristic, complemented
252#102—1971no—
253#102—1971no—
254#102—1971no—
255#102C2×D19711yescharacteristic
256C24—3941no—
257C2×Q8—3941no—
258C2×Q8—3941no—
259C2×Q8—3942no—
260C2×Q8—3942no—
261C2×Q8—3942no—
262C2×Q8—1974no—
263C2×Q8—1971no—
264C2×Q8—1971no—
265C2×Q8C22×D19711yescharacteristic
266C2×Q8C22×D19711yescharacteristic
267C2×D4—3942no—
268C2×D4—3942no—
269C2×D4—3941no—
270C2×D4—1971no—
271C2×D4C22×D19711yescharacteristic
272C22×C4—3941no—
273C22×C4—3941no—
274C22×C4—3941no—
275C22×C4—1971no—
276C22×C4—1971no—
277C22×C4—1971no—
278Q16—22no—
279Q16—3942no—
280Q16—3942no—
281Q16—3942no—
282SD16—22no—
283SD16—3942no—
284SD16—3942no—
285SD16—3942no—
286C2×C8—3942no—
287C2×C8—3942no—
288C2×C8—1971no—
289C2×C8—1971no—
290C2×C8C22×D19711yescharacteristic
291C2×C8C22×D19711yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—3941no—
294C4⋊C4—3941no—
295C4⋊C4—3941no—
296C4⋊C4—3941no—
297C4⋊C4—1971no—
298C4⋊C4C22×D19711yescharacteristic
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—3941no—
302C22⋊C4—3941no—
303C22⋊C4—3941no—
304C22⋊C4—3941no—
305C22⋊C4—3941no—
306C22⋊C4—3941no—
307C42—21no—
308C42—3941no—
309C42—3941no—
310C42—3941no—
311C42—1971no—
312C42—1971no—
313C42—1971no—
314C42C22×D19711yescharacteristic
315C23—21no—
316C23—7882no—
317C23—7882no—
318C23—7882no—
319C23—3941no—
320C23—1971no—
321Q8—21no—
322Q8—21no—
323Q8—21no—
324Q8—7882no—
325Q8—3944no—
326Q8—3941no—
327Q8—3941no—
328Q8—3941no—
329Q8—1972no—
330Q8D4×D19712yes—
331D4—21no—
332D4—21no—
333D4—7882no—
334D4—3941no—
335D4—3941no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—7882no—
340C2×C4—7882no—
341C2×C4—3944no—
342C2×C4—3942no—
343C2×C4—3942no—
344C2×C4—3941no—
345C2×C4—3941no—
346C2×C4—3941no—
347C2×C4—1971no—
348C2×C4—1971no—
349C2×C4—1971no—
350C2×C4—1972no—
351C2×C4—1972no—
352C2×C4D4×D19711yescharacteristic
353C2×C4D4×D19711yescharacteristic
354C2×C4C23×D19711yescharacteristic
355C8—21no—
356C8—21no—
357C8—3941no—
358C8—3941no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—7881no—
363C22—7881no—
364C22—7881no—
365C22—15764no—
366C22—1972no—
367C22—1972no—
368C22—1972no—
369C22C2×D4×D19711yescharacteristic
370C4—21no—
371C4—21no—
372C4—22no—
373C4—41no—
374C4—41no—
375C4—7881no—
376C4—7881no—
377C4—3941no—
378C4—3941no—
379C4—3942no—
380C4—1972no—
381C4C2×D4×D19711yescharacteristic
382C4#41×D19711yescharacteristic
383C2—81no—
384C2—15761no—
385C2—1974no—
386C2#121×D19711yescharacteristic
387C2#135×D19711yescharacteristic
388C2#137×D19711yescharacteristic
subgroupG/H
centerC22C2×D4×D197
commutator, cosocleC2×C4×C197C24
FrattiniC2×C4C23×D197
Fitting#464×C197C2
socleC22×C197C22×D4
prime radicalC2×D4×D197C22
hypercenter#464D197
hypocenterC197C2×#464
LCSG ▷ C2×C4×C197 ▷ C2×C197 ▷ C197
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×Q16×D197C2semidirect
4. C4×Q8×D197C2semidirect
5. #27161304C2semidirect
6. #27161303C2semidirect
7. #27161302C2semidirect
8. #27161301C2semidirect
9. #27161300C2semidirect
10. #27161299C2semidirect
11. #27161298C2semidirect
12. C4⋊C8×D197C2semidirect
13. #103×D197C2semidirect
15. #464×C197C2semidirect
19. C2×Dic788C22semidirect
20. C2×#15691348C22semidirect
21. C2×#15691348C22semidirect
34. Q8×Dic197C22semidirect
36. C4×Dic394C22semidirect
38. #20263291C22semidirect
45. C4⋊#13096802C22semidirect
46. #20263255C22semidirect
47. #20263255C22semidirect
48. #20263251C22semidirect
49. #20263250C22semidirect
50. #20263249C22semidirect
54. C2×Q16×C197C22semidirect
57. C4×Q8×C197C22semidirect
58. C4⋊C8×C197C22semidirect
59. #103×C197C22semidirect
193. D197#464direct (N × H)
194. C197C2×#464semidirect
207. #464D197direct (N × H)
218. C2×Q16C2×D197semidirect
237. C4×Q8C2×D197semidirect
247. C4⋊C8C2×D197semidirect
251. #103C2×D197semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×D1972
C2×SD16×D1972
#124×D1972
C4×Q8×D1972
#271613042
#271613032
#271613022
#271613012
#271613002
#271612992
#271612982
C4⋊C8×D1972
#103×D1972
#102×D1972
#464×C1972
C2×#464197