Finite Group Databasebeta

← #463×D197 #38752132

Subgroups — #463×D197 #38752132

Order 25216.

564 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D197C211yesmaximal, characteristic, complemented
2C2×D8×D197C211yesmaximal, characteristic
3#124×D197C211yesmaximal, characteristic, complemented
4C4×D4×D197C211yesmaximal, characteristic, complemented
5#27161297C211yesmaximal, characteristic, complemented
6#27161296C211yesmaximal, characteristic, complemented
7#27161295C211yesmaximal, characteristic, complemented
8#27161294C211yesmaximal, characteristic, complemented
9#27161293C211yesmaximal, characteristic, complemented
10#27161292C211yesmaximal, characteristic, complemented
11#27161291C211yesmaximal, characteristic, complemented
12C4⋊C8×D197C211yesmaximal, characteristic, complemented
13#103×D197C211yesmaximal, characteristic, complemented
14#102×D197C211yesmaximal, characteristic, complemented
15#463×C197C211yesmaximal, characteristic, complemented
16C2×Q8×D197C2211yescharacteristic
17C2×D4×D197C2211yescharacteristic
18C2×D4×D197C2211yescharacteristic
19C22×C4×D197—21no—
20C2×#15691347C2211yescharacteristic, complemented
21C2×#15691346C2211yescharacteristic, complemented
22C2×#15691345C2211yescharacteristic, complemented
23SD16×D197—24no—
24C2×D1576C2211yescharacteristic
25C2×#15691343C2211yescharacteristic
26C2×#15691343C2211yescharacteristic
27D8×D197—24no—
28C2×C8×D197C2211yescharacteristic
29C2×C8×D197C2211yescharacteristic
30#20263315C2211yescharacteristic, complemented
31#20263314C2211yescharacteristic, complemented
32#20263313C2211yescharacteristic, complemented
33#20263312—21no—
34#20263312—21no—
35C4×D788C2211yescharacteristic, complemented
36D4×Dic197C2211yescharacteristic, complemented
37#20263288C2211yescharacteristic, complemented
38C4×C22⋊D197—21no—
39#20263286—21no—
40C4⋊C4×D197C2211yescharacteristic
41C22⋊C4×D197—21no—
42C22⋊C4×D197—21no—
43C22⋊C4×D197—21no—
44C42×D197C2211yescharacteristic
45C4⋊#13096802C2211yescharacteristic, complemented
46#20263255C2211yescharacteristic, complemented
47#20263255C2211yescharacteristic, complemented
48#20263251C2211yescharacteristic, complemented
49#20263250C2211yescharacteristic, complemented
50#20263249C2211yescharacteristic, complemented
51#20263248C2211yescharacteristic, complemented
52#20263247C2211yescharacteristic, complemented
53#20263246C2211yescharacteristic, complemented
54C2×SD16×C197C2211yescharacteristic, complemented
55C2×D8×C197C2211yescharacteristic
56#124×C197C2211yescharacteristic, complemented
57C4×D4×C197C2211yescharacteristic, complemented
58C4⋊C8×C197C2211yescharacteristic, complemented
59#103×C197C2211yescharacteristic, complemented
60#102×C197C2211yescharacteristic, complemented
61C23×D197—21no—
62C23×D197—21no—
63C2×Dic394—21no—
64C2×Dic394C2311yescharacteristic
65Q8×D197—22no—
66Q8×D197—22no—
67C2×D788C2311yescharacteristic
68C2×D788C2311yescharacteristic
69C2×C22⋊D197—21no—
70C2×C22⋊D197—21no—
71D4×D197—22no—
72D4×D197—22no—
73D4×D197—22no—
74D4×D197D414yes—
75C22×Dic197—21no—
76C2×C4×D197—21no—
77C2×C4×D197—21no—
78C2×C4×D197—21no—
79C2×C4×D197—21no—
80C2×C4×D197—44no—
81C2×C4×D197D411yescharacteristic
82C2×C4×D197D411yescharacteristic
83C2×C4×D197C2311yescharacteristic
84#15691347—22no—
85#15691346—22no—
86#15691345—22no—
87D1576—22no—
88#15691343—22no—
89#15691343—22no—
90C2×#13096802C2311yescharacteristic
91C2×#13096802C2311yescharacteristic
92C8×D197—22no—
93C8×D197—22no—
94C4⋊Dic197C2311yescharacteristic
95#15691337—21no—
96C22⋊Dic197—21no—
97C22⋊Dic197—21no—
98C22⋊Dic197—21no—
99#15691335—21no—
100#15691335—21no—
101#15691335—21no—
102#15691335—21no—
103#15691335—21no—
104#15691335—21no—
105C4×Dic197D411yescharacteristic
106C4×Dic197D411yescharacteristic
107C4×Dic197C2311yescharacteristic
108C2×Q8×C197C2311yescharacteristic
109C2×D4×C197C2311yescharacteristic
110C2×D4×C197C2311yescharacteristic
111C22×C4×C197—21no—
112SD16×C197—22no—
113D8×C197—22no—
114C2×C8×C197C2311yescharacteristic
115C2×C8×C197C2311yescharacteristic
116C4⋊C4×C197C2311yescharacteristic
117C22⋊C4×C197—21no—
118C22⋊C4×C197—21no—
119C22⋊C4×C197—21no—
120C42×C197C2311yescharacteristic
121C22×D197—21no—
122C22×D197—24no—
123C22×D197—21no—
124C22×D197—42no—
125C22×D197—42no—
126C22×D197—42no—
127C22×D197—42no—
128C22×D197—42no—
129C22×D197C2×D411yescharacteristic
130Dic394—21no—
131Dic394—21no—
132Dic394—42no—
133D788—21no—
134D788—21no—
135D788—21no—
136D788C2×D412yes—
137C22⋊D197—24no—
138C22⋊D197—42no—
139C2×Dic197—21no—
140C2×Dic197—21no—
141C2×Dic197—42no—
142C2×Dic197C2×D411yescharacteristic
143C2×Dic197C2×D411yescharacteristic
144C2×Dic197C2×D411yescharacteristic
145C4×D197—22no—
146C4×D197—22no—
147C4×D197—42no—
148C4×D197—42no—
149C4×D197—42no—
150C4×D197—42no—
151C4×D197C2×D412yes—
152C4×D197#4112yes—
153#13096802—21no—
154#13096802—21no—
155C23×C197—21no—
156C23×C197—21no—
157Q8×C197—21no—
158Q8×C197—21no—
159D4×C197—21no—
160D4×C197—21no—
161D4×C197—21no—
162D4×C197C2×D412yes—
163C2×C4×C197—21no—
164C2×C4×C197—21no—
165C2×C4×C197—42no—
166C2×C4×C197C2×D411yescharacteristic
167C2×C4×C197C2×D411yescharacteristic
168C2×C4×C197C2411yescharacteristic
169C8×C197—21no—
170C8×C197—21no—
171C22×C197—22no—
172C22×C197—41no—
173C22×C197—41no—
174C22×C197—41no—
175C22×C197—41no—
176C22×C197—41no—
177C22×C197C22×D411yescharacteristic
178C2×D197—22no—
179C2×D197—41no—
180C2×D197—41no—
181C2×D197—48no—
182C2×D197—41no—
183C2×D197—41no—
184C2×D197—41no—
185C2×D197—84no—
186C2×D197#12112yes—
187C2×D197#13512yes—
188C2×D197AGL(1,ℤ/8)12yes—
189C4×C197—21no—
190C4×C197—21no—
191C4×C197—41no—
192C4×C197—41no—
193C4×C197C22×D411yescharacteristic
194C4×C197C2×#4111yescharacteristic
195Dic197—21no—
196Dic197—21no—
197Dic197—41no—
198Dic197—41no—
199Dic197#12112yes—
200C2×C197—42no—
201C2×C197—81no—
202C2×C197C2×#12111yescharacteristic
203C2×C197C2×#13511yescharacteristic
204C2×C197C2×AGL(1,ℤ/8)11yescharacteristic
205D197—42no—
206D197—81no—
207D197#46314yesdirect product factor
208C197C2×#46311yescharacteristic, complemented, Sylow
209C2×#463—1971nomaximal, Sylow
210C22×SD16—1971no—
211C22×D8—1971no—
212C2×#124—1971no—
213C2×C4×D4—1971no—
214#463—1971no—
215#463—1971no—
216#463—1971no—
217#463—1971no—
218#463—1971no—
219#463—1971no—
220#463—1971no—
221#463D19711yescharacteristic, direct product factor
222C2×C4⋊C8—1971no—
223C2×#103—1971no—
224C2×#102—1971no—
225C22×Q8—1971no—
226C22×D4—1971no—
227C22×D4—1971no—
228C23×C4—3941no—
229C2×SD16—3944no—
230C2×SD16—1971no—
231C2×SD16—1971no—
232C2×SD16—1971no—
233C2×SD16C2×D19711yescharacteristic, complemented
234C2×D8—3944no—
235C2×D8—1971no—
236C2×D8—1971no—
237C2×D8—1971no—
238C2×D8C2×D19711yescharacteristic
239C22×C8—1971no—
240C22×C8—1971no—
241#124—3941no—
242#124—3941no—
243#124—1971no—
244#124—1971no—
245#124—1971no—
246#124C2×D19711yescharacteristic, complemented
247C4×D4—3941no—
248C4×D4—3941no—
249C4×D4—1971no—
250C4×D4—1971no—
251C4×D4—1971no—
252C4×D4C2×D19711yescharacteristic, complemented
253C2×C4⋊C4—1971no—
254C2×C22⋊C4—3941no—
255C2×C22⋊C4—3941no—
256C2×C22⋊C4—3941no—
257C2×C42—1971no—
258C4⋊C8—1971no—
259C4⋊C8—1971no—
260C4⋊C8—1971no—
261C4⋊C8C2×D19711yescharacteristic, complemented
262#103—1971no—
263#103—1971no—
264#103—1971no—
265#103C2×D19711yescharacteristic, complemented
266#102—1971no—
267#102—1971no—
268#102—1971no—
269#102C2×D19711yescharacteristic, complemented
270C24—3941no—
271C24—3941no—
272C2×Q8—3941no—
273C2×Q8—3942no—
274C2×Q8—3942no—
275C2×Q8—1971no—
276C2×Q8C22×D19711yescharacteristic
277C2×D4—3942no—
278C2×D4—3942no—
279C2×D4—3942no—
280C2×D4—3941no—
281C2×D4—3941no—
282C2×D4—1974no—
283C2×D4—1971no—
284C2×D4—1971no—
285C2×D4C22×D19711yescharacteristic
286C2×D4C22×D19711yescharacteristic
287C22×C4—21no—
288C22×C4—7884no—
289C22×C4—3941no—
290C22×C4—3941no—
291C22×C4—3941no—
292C22×C4—3941no—
293C22×C4—3941no—
294C22×C4—1971no—
295C22×C4—1971no—
296C22×C4—1971no—
297SD16—22no—
298SD16—3942no—
299SD16—3942no—
300SD16—3942no—
301D8—22no—
302D8—3942no—
303D8—3942no—
304D8—3942no—
305C2×C8—3942no—
306C2×C8—3942no—
307C2×C8—1971no—
308C2×C8—1971no—
309C2×C8C22×D19711yescharacteristic
310C2×C8C22×D19711yescharacteristic
311C4⋊C4—3941no—
312C4⋊C4—1971no—
313C4⋊C4C22×D19711yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—3941no—
318C22⋊C4—3941no—
319C22⋊C4—3941no—
320C22⋊C4—3941no—
321C22⋊C4—3941no—
322C22⋊C4—3941no—
323C22⋊C4—3941no—
324C22⋊C4—3941no—
325C22⋊C4—3941no—
326C42—1971no—
327C42—1971no—
328C42—1971no—
329C42C22×D19711yescharacteristic
330C23—21no—
331C23—21no—
332C23—7882no—
333C23—7882no—
334C23—7882no—
335C23—7882no—
336C23—7882no—
337C23—3944no—
338C23—3941no—
339C23—3941no—
340C23—1971no—
341Q8—21no—
342Q8—21no—
343Q8—7882no—
344Q8—3941no—
345Q8—3941no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—7882no—
350D4—3944no—
351D4—3941no—
352D4—3941no—
353D4—3941no—
354D4—1972no—
355D4D4×D19712yes—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—7882no—
360C2×C4—7882no—
361C2×C4—7882no—
362C2×C4—7882no—
363C2×C4—7882no—
364C2×C4—3942no—
365C2×C4—3942no—
366C2×C4—3941no—
367C2×C4—3941no—
368C2×C4—1971no—
369C2×C4—1971no—
370C2×C4—1971no—
371C2×C4—1972no—
372C2×C4—1972no—
373C2×C4D4×D19711yescharacteristic
374C2×C4D4×D19711yescharacteristic
375C2×C4C23×D19711yescharacteristic
376C8—21no—
377C8—21no—
378C8—3941no—
379C8—3941no—
380C22—22no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—7888no—
387C22—7881no—
388C22—7881no—
389C22—7881no—
390C22—7881no—
391C22—7881no—
392C22—15764no—
393C22—3942no—
394C22—1972no—
395C22—1972no—
396C22—1972no—
397C22C2×D4×D19711yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—7881no—
403C4—7881no—
404C4—3941no—
405C4—3941no—
406C4—1972no—
407C4C2×D4×D19711yescharacteristic
408C4#41×D19711yescharacteristic
409C2—42no—
410C2—81no—
411C2—7882no—
412C2—15761no—
413C2—1974no—
414C2#121×D19711yescharacteristic
415C2#135×D19711yescharacteristic
416C2AGL(1,ℤ/8)×D19711yescharacteristic
subgroupG/H
centerC22C2×D4×D197
commutator, cosocleC2×C4×C197C24
FrattiniC2×C4C23×D197
Fitting#463×C197C2
socleC22×C197C22×D4
prime radicalC2×D8×D197C2
hypercenter#463D197
hypocenterC197C2×#463
LCSG ▷ C2×C4×C197 ▷ C2×C197 ▷ C197
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D197C2semidirect
3. #124×D197C2semidirect
4. C4×D4×D197C2semidirect
5. #27161297C2semidirect
6. #27161296C2semidirect
7. #27161295C2semidirect
8. #27161294C2semidirect
9. #27161293C2semidirect
10. #27161292C2semidirect
11. #27161291C2semidirect
12. C4⋊C8×D197C2semidirect
13. #103×D197C2semidirect
14. #102×D197C2semidirect
15. #463×C197C2semidirect
20. C2×#15691347C22semidirect
21. C2×#15691346C22semidirect
22. C2×#15691345C22semidirect
30. #20263315C22semidirect
31. #20263314C22semidirect
32. #20263313C22semidirect
35. C4×D788C22semidirect
36. D4×Dic197C22semidirect
37. #20263288C22semidirect
45. C4⋊#13096802C22semidirect
46. #20263255C22semidirect
47. #20263255C22semidirect
48. #20263251C22semidirect
49. #20263250C22semidirect
50. #20263249C22semidirect
51. #20263248C22semidirect
52. #20263247C22semidirect
53. #20263246C22semidirect
54. C2×SD16×C197C22semidirect
56. #124×C197C22semidirect
57. C4×D4×C197C22semidirect
58. C4⋊C8×C197C22semidirect
59. #103×C197C22semidirect
60. #102×C197C22semidirect
207. D197#463direct (N × H)
208. C197C2×#463semidirect
221. #463D197direct (N × H)
233. C2×SD16C2×D197semidirect
246. #124C2×D197semidirect
252. C4×D4C2×D197semidirect
261. C4⋊C8C2×D197semidirect
265. #103C2×D197semidirect
269. #102C2×D197semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1972
C2×D8×D1972
#124×D1972
C4×D4×D1972
#271612972
#271612962
#271612952
#271612942
#271612932
#271612922
#271612912
C4⋊C8×D1972
#103×D1972
#102×D1972
#463×C1972
C2×#463197