Finite Group Databasebeta

← #435×D97 #27150411

Subgroups — #435×D97 #27150411

Order 12416.

564 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M16×D97C211yesmaximal, characteristic, complemented
2C22×C8×D97C211yesmaximal, characteristic, complemented
3C4×D4×D97C211yesmaximal, characteristic
4#20260809C211yesmaximal, characteristic, complemented
5#20260808C211yesmaximal, characteristic, complemented
6#20260807C211yesmaximal, characteristic, complemented
7#20260806C211yesmaximal, characteristic, complemented
8#20260805C211yesmaximal, characteristic, complemented
9#20260804C211yesmaximal, characteristic, complemented
10#20260803C211yesmaximal, characteristic, complemented
11C4⋊C8×D97C211yesmaximal, characteristic, complemented
12C22⋊C8×D97C211yesmaximal, characteristic, complemented
13C22⋊C8×D97C211yesmaximal, characteristic, complemented
14#97×D97C211yesmaximal, characteristic, complemented
15#435×C97C211yesmaximal, characteristic, complemented
16C2×D4×D97C411yescharacteristic
17C22×C4×D97C2211yescharacteristic
18C22×C4×D97C2211yescharacteristic
19C2×#13095495C2211yescharacteristic, complemented
20C2×#13095494C2211yescharacteristic, complemented
21C2×#13095494C2211yescharacteristic, complemented
22M16×D97—24no—
23C22×#11715895C2211yescharacteristic, complemented
24C2×C8×D97—24no—
25C2×C8×D97C2211yescharacteristic
26C2×C8×D97C2211yescharacteristic
27C2×C8×D97C2211yescharacteristic
28C2×C8×D97C2211yescharacteristic
29C2×C8×D97C2211yescharacteristic, complemented
30C2×C8×D97C2211yescharacteristic, complemented
31C4×D388C2211yescharacteristic
32D4×Dic97C411yescharacteristic
33#15690772C411yescharacteristic
34C4×C22⋊D97C2211yescharacteristic
35C4×C22⋊D97C2211yescharacteristic
36#15690770C411yescharacteristic
37#15690770C411yescharacteristic
38C4⋊C4×D97C411yescharacteristic
39C22⋊C4×D97C411yescharacteristic
40C22⋊C4×D97C411yescharacteristic
41C42×D97C2211yescharacteristic
42C4⋊#11715895C2211yescharacteristic, complemented
43#15690739C2211yescharacteristic, complemented
44#15690739C2211yescharacteristic, complemented
45C22⋊#11715895C2211yescharacteristic, complemented
46C22⋊#11715895C2211yescharacteristic, complemented
47#15690722C2211yescharacteristic, complemented
48#15690722C2211yescharacteristic, complemented
49#15690722C2211yescharacteristic, complemented
50#15690722C2211yescharacteristic, complemented
51#15690721C2211yescharacteristic, complemented
52#15690720C2211yescharacteristic, complemented
53#15690720C2211yescharacteristic, complemented
54C2×M16×C97C2211yescharacteristic, complemented
55C22×C8×C97C2211yescharacteristic, complemented
56C4×D4×C97C2211yescharacteristic
57C4⋊C8×C97C2211yescharacteristic, complemented
58C22⋊C8×C97C2211yescharacteristic, complemented
59C22⋊C8×C97C2211yescharacteristic, complemented
60#97×C97C2211yescharacteristic, complemented
61C23×D97C2×C411yescharacteristic
62C23×D97C2×C411yescharacteristic
63C2×D388C2×C411yescharacteristic
64C2×C22⋊D97C2×C411yescharacteristic
65C2×C22⋊D97C2×C411yescharacteristic
66D4×D97—24no—
67C22×Dic97C2×C411yescharacteristic
68C22×Dic97C2×C411yescharacteristic
69C2×C4×D97—22no—
70C2×C4×D97—22no—
71C2×C4×D97—22no—
72C2×C4×D97—22no—
73C2×C4×D97C2×C411yescharacteristic
74C2×C4×D97C2×C411yescharacteristic
75C2×C4×D97C2×C411yescharacteristic
76C2×C4×D97C2×C411yescharacteristic
77C2×C4×D97C2×C411yescharacteristic
78C2×C4×D97C2×C411yescharacteristic
79C2×C4×D97C2311yescharacteristic
80C2×C4×D97C2311yescharacteristic
81C2×C4×D97C2311yescharacteristic
82#13095495—22no—
83#13095494—22no—
84#13095494—22no—
85C2×#11715895—22no—
86C2×#11715895C2311yescharacteristic
87C2×#11715895C2311yescharacteristic
88C2×#11715895C2311yescharacteristic
89C2×#11715895C2311yescharacteristic
90C8×D97—22no—
91C8×D97—22no—
92C8×D97—22no—
93C8×D97—22no—
94C8×D97—22no—
95C8×D97D414yescomplemented
96C4⋊Dic97C2×C411yescharacteristic
97#13095490C2×C411yescharacteristic
98#13095490C2×C411yescharacteristic
99C22⋊Dic97C2×C411yescharacteristic
100C22⋊Dic97C2×C411yescharacteristic
101#13095488C2×C411yescharacteristic
102#13095488C2×C411yescharacteristic
103#13095488C2×C411yescharacteristic
104#13095488C2×C411yescharacteristic
105C4×Dic97C2×C411yescharacteristic
106C4×Dic97C2×C411yescharacteristic
107C4×Dic97C2311yescharacteristic
108C2×D4×C97C2×C411yescharacteristic
109C22×C4×C97C2311yescharacteristic
110C22×C4×C97C2311yescharacteristic
111M16×C97—22no—
112C2×C8×C97—22no—
113C2×C8×C97C2311yescharacteristic
114C2×C8×C97C2311yescharacteristic
115C2×C8×C97C2311yescharacteristic
116C2×C8×C97C2311yescharacteristic
117C4⋊C4×C97C2×C411yescharacteristic
118C22⋊C4×C97C2×C411yescharacteristic
119C22⋊C4×C97C2×C411yescharacteristic
120C42×C97C2311yescharacteristic
121C23×C97C22×C411yescharacteristic
122C23×C97C22×C411yescharacteristic
123C22×D97—22no—
124C22×D97—22no—
125C22×D97—22no—
126C22×D97—22no—
127C22×D97—22no—
128C22×D97M1614yescomplemented
129C22×D97C22×C411yescharacteristic
130C22×D97C22×C411yescharacteristic
131C22×D97C22×C411yescharacteristic
132D4×C97—22no—
133C2×C4×C97—21no—
134C2×C4×C97—21no—
135C2×C4×C97—21no—
136C2×C4×C97—21no—
137C2×C4×C97C22×C411yescharacteristic
138C2×C4×C97C22×C411yescharacteristic
139C2×C4×C97C22×C411yescharacteristic
140C2×C4×C97C22×C411yescharacteristic
141C2×C4×C97C2411yescharacteristic
142C22⋊D97—22no—
143C22⋊D97—22no—
144C2×Dic97—22no—
145C2×Dic97—22no—
146C2×Dic97C22×C411yescharacteristic
147C2×Dic97C22×C411yescharacteristic
148C2×Dic97C22×C411yescharacteristic
149C2×Dic97C22×C411yescharacteristic
150C2×Dic97C22×C411yescharacteristic
151D388—22no—
152C4×D97—22no—
153C4×D97—22no—
154C4×D97—22no—
155C4×D97—22no—
156C4×D97—21no—
157C4×D97—21no—
158C4×D97—21no—
159C4×D97—21no—
160C4×D97—22no—
161C4×D97—22no—
162C4×D97C2×D412yes—
163C4×D97#4112yes—
164C8×C97—21no—
165C8×C97—21no—
166C8×C97—21no—
167C8×C97C2×D412yescomplemented
168#11715895—21no—
169#11715895—21no—
170#11715895—21no—
171#11715895C2×D412yescomplemented
172C22×C97—21no—
173C22×C97—21no—
174C22×C97—21no—
175C22×C97—21no—
176C22×C97—21no—
177C22×C97C2×M1612yescomplemented
178C22×C97C23×C411yescharacteristic
179C2×D97—21no—
180C2×D97—21no—
181C2×D97—28no—
182C2×D97—21no—
183C2×D97—21no—
184C2×D97—21no—
185C2×D97—44no—
186C2×D97C4×D412yes—
187C2×D97C2×M1612yes—
188C2×D97C2×M1612yescomplemented
189C2×D97#13112yes—
190C4×C97—21no—
191C4×C97—21no—
192C4×C97—21no—
193C4×C97—21no—
194C4×C97C22×D411yescharacteristic
195C4×C97C2×#4111yescharacteristic
196Dic97—21no—
197Dic97—21no—
198Dic97—21no—
199Dic97—21no—
200Dic97C4×D412yes—
201C2×C97—22no—
202C2×C97—41no—
203C2×C97C2×C4×D411yescharacteristic
204C2×C97C22×M1611yescharacteristic
205C2×C97C2×#13111yescharacteristic
206D97—22no—
207D97—41no—
208D97#43514yesdirect product factor
209C2×#435—971nomaximal, Sylow
210C97C2×#43511yescharacteristic, complemented, Sylow
211C22×M16—971no—
212C23×C8—971no—
213C2×C4×D4—971no—
214#435—971no—
215#435—971no—
216#435—971no—
217#435—971no—
218#435—971no—
219#435—971no—
220#435—971no—
221#435D9711yescharacteristic, direct product factor
222C2×C4⋊C8—971no—
223C2×C22⋊C8—971no—
224C2×C22⋊C8—971no—
225C2×#97—971no—
226C22×D4—971no—
227C23×C4—971no—
228C23×C4—971no—
229C2×M16—971no—
230C2×M16—971no—
231C2×M16—971no—
232C2×M16—1944no—
233C2×M16C2×D9711yescharacteristic, complemented
234C22×C8—971no—
235C22×C8—971no—
236C22×C8—971no—
237C22×C8—971no—
238C22×C8—971no—
239C22×C8—971no—
240C22×C8—971no—
241C22×C8—1944no—
242C22×C8C2×D9711yescharacteristic, complemented
243C4×D4—971no—
244C4×D4—971no—
245C4×D4—971no—
246C4×D4—971no—
247C4×D4—971no—
248C4×D4—971no—
249C4×D4—971no—
250C4×D4C2×D9711yescharacteristic
251C2×C4⋊C4—971no—
252C2×C22⋊C4—971no—
253C2×C22⋊C4—971no—
254C2×C42—971no—
255C4⋊C8—971no—
256C4⋊C8—971no—
257C4⋊C8—971no—
258C4⋊C8C2×D9711yescharacteristic, complemented
259C22⋊C8—971no—
260C22⋊C8—971no—
261C22⋊C8—971no—
262C22⋊C8—971no—
263C22⋊C8—971no—
264C22⋊C8—971no—
265C22⋊C8C2×D9711yescharacteristic, complemented
266C22⋊C8C2×D9711yescharacteristic, complemented
267#97—971no—
268#97—971no—
269#97—971no—
270#97C2×D9711yescharacteristic, complemented
271C24—971no—
272C24—971no—
273C2×D4—971no—
274C2×D4—971no—
275C2×D4—971no—
276C2×D4—1944no—
277C2×D4C4×D9711yescharacteristic
278C22×C4—971no—
279C22×C4—971no—
280C22×C4—971no—
281C22×C4—971no—
282C22×C4—971no—
283C22×C4—971no—
284C22×C4—971no—
285C22×C4—971no—
286C22×C4—971no—
287C22×C4—971no—
288C22×C4—971no—
289C22×C4—1942no—
290C22×C4—1942no—
291C22×C4—1942no—
292C22×C4—1942no—
293C22×C4C22×D9711yescharacteristic
294C22×C4C22×D9711yescharacteristic
295M16—22no—
296M16—1942no—
297M16—1942no—
298M16—1942no—
299C2×C8—22no—
300C2×C8—971no—
301C2×C8—974no—
302C2×C8—971no—
303C2×C8—971no—
304C2×C8—971no—
305C2×C8—1942no—
306C2×C8—1942no—
307C2×C8—1942no—
308C2×C8—1942no—
309C2×C8—1942no—
310C2×C8—1942no—
311C2×C8C22×D9711yescharacteristic
312C2×C8C22×D9711yescharacteristic
313C2×C8C22×D9711yescharacteristic
314C2×C8C22×D9711yescharacteristic
315C4⋊C4—971no—
316C4⋊C4—971no—
317C4⋊C4—971no—
318C4⋊C4C4×D9711yescharacteristic
319C22⋊C4—971no—
320C22⋊C4—971no—
321C22⋊C4—971no—
322C22⋊C4—971no—
323C22⋊C4—971no—
324C22⋊C4—971no—
325C22⋊C4C4×D9711yescharacteristic
326C22⋊C4C4×D9711yescharacteristic
327C42—971no—
328C42—971no—
329C42—971no—
330C42C22×D9711yescharacteristic
331C23—971no—
332C23—974no—
333C23—971no—
334C23—971no—
335C23—1942no—
336C23—1942no—
337C23—1942no—
338C23—1942no—
339C23—1942no—
340C23C2×C4×D9711yescharacteristic
341C23C2×C4×D9711yescharacteristic
342D4—22no—
343D4—1942no—
344D4—1942no—
345D4—1942no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—971no—
351C2×C4—972no—
352C2×C4—972no—
353C2×C4—971no—
354C2×C4—971no—
355C2×C4—971no—
356C2×C4—971no—
357C2×C4—1942no—
358C2×C4—1942no—
359C2×C4—1942no—
360C2×C4—1942no—
361C2×C4—1942no—
362C2×C4—1942no—
363C2×C4—1942no—
364C2×C4—1942no—
365C2×C4—1941no—
366C2×C4—1941no—
367C2×C4—1941no—
368C2×C4—1941no—
369C2×C4C2×C4×D9711yescharacteristic
370C2×C4C2×C4×D9711yescharacteristic
371C2×C4C2×C4×D9711yescharacteristic
372C2×C4C2×C4×D9711yescharacteristic
373C2×C4C23×D9711yescharacteristic
374C8—21no—
375C8—21no—
376C8—21no—
377C8—972no—
378C8—1941no—
379C8—1941no—
380C8—1941no—
381C8D4×D9712yescomplemented
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—972no—
388C22—972no—
389C22—972no—
390C22—972no—
391C22—3884no—
392C22—1948no—
393C22—1941no—
394C22—1941no—
395C22—1941no—
396C22—1941no—
397C22—1941no—
398C22M16×D9712yescomplemented
399C22C22×C4×D9711yescharacteristic
400C4—21no—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—972no—
405C4—1941no—
406C4—1941no—
407C4—1941no—
408C4—1941no—
409C4C2×D4×D9711yescharacteristic
410C4#41×D9711yescharacteristic
411C2—22no—
412C2—41no—
413C2—974no—
414C2—3881no—
415C2—1942no—
416C2C4×D4×D9711yescharacteristic
417C2C2×M16×D9711yescharacteristic
418C2#131×D9711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D97
commutator, socleC22×C97C23×C4
Fitting#435×C97C2
prime radicalC2×D4×D97C4
cosocleC2×C4×C97C24
hypercenter#435D97
hypocenterC97C2×#435
LCSG ▷ C22×C97 ▷ C97
UCSC1 ◁ C2×C4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×M16×D97C2semidirect
2. C22×C8×D97C2semidirect
4. #20260809C2semidirect
5. #20260808C2semidirect
6. #20260807C2semidirect
7. #20260806C2semidirect
8. #20260805C2semidirect
9. #20260804C2semidirect
10. #20260803C2semidirect
11. C4⋊C8×D97C2semidirect
12. C22⋊C8×D97C2semidirect
13. C22⋊C8×D97C2semidirect
14. #97×D97C2semidirect
15. #435×C97C2semidirect
19. C2×#13095495C22semidirect
20. C2×#13095494C22semidirect
21. C2×#13095494C22semidirect
23. C22×#11715895C22semidirect
29. C2×C8×D97C22semidirect
30. C2×C8×D97C22semidirect
42. C4⋊#11715895C22semidirect
43. #15690739C22semidirect
44. #15690739C22semidirect
45. C22⋊#11715895C22semidirect
46. C22⋊#11715895C22semidirect
47. #15690722C22semidirect
48. #15690722C22semidirect
49. #15690722C22semidirect
50. #15690722C22semidirect
51. #15690721C22semidirect
52. #15690720C22semidirect
53. #15690720C22semidirect
54. C2×M16×C97C22semidirect
55. C22×C8×C97C22semidirect
57. C4⋊C8×C97C22semidirect
58. C22⋊C8×C97C22semidirect
59. C22⋊C8×C97C22semidirect
60. #97×C97C22semidirect
95. C8×D97D4semidirect
128. C22×D97M16semidirect
167. C8×C97C2×D4semidirect
171. #11715895C2×D4semidirect
177. C22×C97C2×M16semidirect
188. C2×D97C2×M16semidirect
208. D97#435direct (N × H)
210. C97C2×#435semidirect
221. #435D97direct (N × H)
233. C2×M16C2×D97semidirect
242. C22×C8C2×D97semidirect
258. C4⋊C8C2×D97semidirect
265. C22⋊C8C2×D97semidirect
266. C22⋊C8C2×D97semidirect
270. #97C2×D97semidirect
381. C8D4×D97semidirect
398. C22M16×D97semidirect

Maximal subgroups

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

subgroupindex
C2×M16×D972
C22×C8×D972
C4×D4×D972
#202608092
#202608082
#202608072
#202608062
#202608052
#202608042
#202608032
C4⋊C8×D972
C22⋊C8×D972
#97×D972
#435×C972
C2×#43597