Finite Group Databasebeta

← #463×D97 #27151156

Subgroups — #463×D97 #27151156

Order 12416.

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×D97C211yesmaximal, characteristic, complemented
2C2×D8×D97C211yesmaximal, characteristic
3#124×D97C211yesmaximal, characteristic, complemented
4C4×D4×D97C211yesmaximal, characteristic, complemented
5#20260953C211yesmaximal, characteristic, complemented
6#20260952C211yesmaximal, characteristic, complemented
7#20260951C211yesmaximal, characteristic, complemented
8#20260950C211yesmaximal, characteristic, complemented
9#20260949C211yesmaximal, characteristic, complemented
10#20260948C211yesmaximal, characteristic, complemented
11#20260947C211yesmaximal, characteristic, complemented
12C4⋊C8×D97C211yesmaximal, characteristic, complemented
13#103×D97C211yesmaximal, characteristic, complemented
14#102×D97C211yesmaximal, characteristic, complemented
15#463×C97C211yesmaximal, characteristic, complemented
16C2×Q8×D97C2211yescharacteristic
17C2×D4×D97C2211yescharacteristic
18C2×D4×D97C2211yescharacteristic
19C22×C4×D97—21no—
20C2×#13095500C2211yescharacteristic, complemented
21C2×#13095499C2211yescharacteristic, complemented
22C2×#13095498C2211yescharacteristic, complemented
23SD16×D97—24no—
24C2×D776C2211yescharacteristic
25C2×#13095496C2211yescharacteristic
26C2×#13095496C2211yescharacteristic
27D8×D97—24no—
28C2×C8×D97C2211yescharacteristic
29C2×C8×D97C2211yescharacteristic
30#15690799C2211yescharacteristic, complemented
31#15690798C2211yescharacteristic, complemented
32#15690797C2211yescharacteristic, complemented
33#15690796—21no—
34#15690796—21no—
35C4×D388C2211yescharacteristic, complemented
36D4×Dic97C2211yescharacteristic, complemented
37#15690772C2211yescharacteristic, complemented
38C4×C22⋊D97—21no—
39#15690770—21no—
40C4⋊C4×D97C2211yescharacteristic
41C22⋊C4×D97—21no—
42C22⋊C4×D97—21no—
43C22⋊C4×D97—21no—
44C42×D97C2211yescharacteristic
45C4⋊#11715895C2211yescharacteristic, complemented
46#15690739C2211yescharacteristic, complemented
47#15690739C2211yescharacteristic, complemented
48#15690735C2211yescharacteristic, complemented
49#15690734C2211yescharacteristic, complemented
50#15690733C2211yescharacteristic, complemented
51#15690732C2211yescharacteristic, complemented
52#15690731C2211yescharacteristic, complemented
53#15690730C2211yescharacteristic, complemented
54C2×SD16×C97C2211yescharacteristic, complemented
55C2×D8×C97C2211yescharacteristic
56#124×C97C2211yescharacteristic, complemented
57C4×D4×C97C2211yescharacteristic, complemented
58C4⋊C8×C97C2211yescharacteristic, complemented
59#103×C97C2211yescharacteristic, complemented
60#102×C97C2211yescharacteristic, complemented
61C23×D97—21no—
62C23×D97—21no—
63C2×Dic194—21no—
64C2×Dic194C2311yescharacteristic
65Q8×D97—22no—
66Q8×D97—22no—
67C2×D388C2311yescharacteristic
68C2×D388C2311yescharacteristic
69C2×C22⋊D97—21no—
70C2×C22⋊D97—21no—
71D4×D97—22no—
72D4×D97—22no—
73D4×D97—22no—
74D4×D97D414yes—
75C22×Dic97—21no—
76C2×C4×D97—21no—
77C2×C4×D97—21no—
78C2×C4×D97—21no—
79C2×C4×D97—21no—
80C2×C4×D97—44no—
81C2×C4×D97D411yescharacteristic
82C2×C4×D97D411yescharacteristic
83C2×C4×D97C2311yescharacteristic
84#13095500—22no—
85#13095499—22no—
86#13095498—22no—
87D776—22no—
88#13095496—22no—
89#13095496—22no—
90C2×#11715895C2311yescharacteristic
91C2×#11715895C2311yescharacteristic
92C8×D97—22no—
93C8×D97—22no—
94C4⋊Dic97C2311yescharacteristic
95#13095490—21no—
96C22⋊Dic97—21no—
97C22⋊Dic97—21no—
98C22⋊Dic97—21no—
99#13095488—21no—
100#13095488—21no—
101#13095488—21no—
102#13095488—21no—
103#13095488—21no—
104#13095488—21no—
105C4×Dic97D411yescharacteristic
106C4×Dic97D411yescharacteristic
107C4×Dic97C2311yescharacteristic
108C2×Q8×C97C2311yescharacteristic
109C2×D4×C97C2311yescharacteristic
110C2×D4×C97C2311yescharacteristic
111C22×C4×C97—21no—
112SD16×C97—22no—
113D8×C97—22no—
114C2×C8×C97C2311yescharacteristic
115C2×C8×C97C2311yescharacteristic
116C4⋊C4×C97C2311yescharacteristic
117C22⋊C4×C97—21no—
118C22⋊C4×C97—21no—
119C22⋊C4×C97—21no—
120C42×C97C2311yescharacteristic
121C23×C97—21no—
122C23×C97—21no—
123C22×D97—21no—
124C22×D97—24no—
125C22×D97—21no—
126C22×D97—42no—
127C22×D97—42no—
128C22×D97—42no—
129C22×D97—42no—
130C22×D97—42no—
131C22×D97C2×D411yescharacteristic
132Q8×C97—21no—
133Q8×C97—21no—
134D4×C97—21no—
135D4×C97—21no—
136D4×C97—21no—
137D4×C97C2×D412yes—
138C2×C4×C97—21no—
139C2×C4×C97—21no—
140C2×C4×C97—42no—
141C2×C4×C97C2×D411yescharacteristic
142C2×C4×C97C2×D411yescharacteristic
143C2×C4×C97C2411yescharacteristic
144C22⋊D97—24no—
145C22⋊D97—42no—
146C2×Dic97—21no—
147C2×Dic97—21no—
148C2×Dic97—42no—
149C2×Dic97C2×D411yescharacteristic
150C2×Dic97C2×D411yescharacteristic
151C2×Dic97C2×D411yescharacteristic
152D388—21no—
153D388—21no—
154D388—21no—
155D388C2×D412yes—
156C4×D97—22no—
157C4×D97—22no—
158C4×D97—42no—
159C4×D97—42no—
160C4×D97—42no—
161C4×D97—42no—
162C4×D97C2×D412yes—
163C4×D97#4112yes—
164Dic194—21no—
165Dic194—21no—
166Dic194—42no—
167C8×C97—21no—
168C8×C97—21no—
169#11715895—21no—
170#11715895—21no—
171C22×C97—22no—
172C22×C97—41no—
173C22×C97—41no—
174C22×C97—41no—
175C22×C97—41no—
176C22×C97—41no—
177C22×C97C22×D411yescharacteristic
178C2×D97—22no—
179C2×D97—41no—
180C2×D97—41no—
181C2×D97—48no—
182C2×D97—41no—
183C2×D97—41no—
184C2×D97—41no—
185C2×D97—84no—
186C2×D97#12112yes—
187C2×D97#13512yes—
188C2×D97AGL(1,ℤ/8)12yes—
189C4×C97—21no—
190C4×C97—21no—
191C4×C97—41no—
192C4×C97—41no—
193C4×C97C22×D411yescharacteristic
194C4×C97C2×#4111yescharacteristic
195Dic97—21no—
196Dic97—21no—
197Dic97—41no—
198Dic97—41no—
199Dic97#12112yes—
200C2×C97—42no—
201C2×C97—81no—
202C2×C97C2×#12111yescharacteristic
203C2×C97C2×#13511yescharacteristic
204C2×C97C2×AGL(1,ℤ/8)11yescharacteristic
205D97—42no—
206D97—81no—
207D97#46314yesdirect product factor
208C2×#463—971nomaximal, Sylow
209C97C2×#46311yescharacteristic, complemented, Sylow
210C22×SD16—971no—
211C22×D8—971no—
212C2×#124—971no—
213C2×C4×D4—971no—
214#463—971no—
215#463—971no—
216#463—971no—
217#463—971no—
218#463—971no—
219#463—971no—
220#463—971no—
221#463D9711yescharacteristic, direct product factor
222C2×C4⋊C8—971no—
223C2×#103—971no—
224C2×#102—971no—
225C22×Q8—971no—
226C22×D4—971no—
227C22×D4—971no—
228C23×C4—1941no—
229C2×SD16—971no—
230C2×SD16—971no—
231C2×SD16—971no—
232C2×SD16—1944no—
233C2×SD16C2×D9711yescharacteristic, complemented
234C2×D8—971no—
235C2×D8—971no—
236C2×D8—971no—
237C2×D8—1944no—
238C2×D8C2×D9711yescharacteristic
239C22×C8—971no—
240C22×C8—971no—
241#124—971no—
242#124—971no—
243#124—971no—
244#124—1941no—
245#124—1941no—
246#124C2×D9711yescharacteristic, complemented
247C4×D4—971no—
248C4×D4—971no—
249C4×D4—971no—
250C4×D4—1941no—
251C4×D4—1941no—
252C4×D4C2×D9711yescharacteristic, complemented
253C2×C4⋊C4—971no—
254C2×C22⋊C4—1941no—
255C2×C22⋊C4—1941no—
256C2×C22⋊C4—1941no—
257C2×C42—971no—
258C4⋊C8—971no—
259C4⋊C8—971no—
260C4⋊C8—971no—
261C4⋊C8C2×D9711yescharacteristic, complemented
262#103—971no—
263#103—971no—
264#103—971no—
265#103C2×D9711yescharacteristic, complemented
266#102—971no—
267#102—971no—
268#102—971no—
269#102C2×D9711yescharacteristic, complemented
270C24—1941no—
271C24—1941no—
272C2×Q8—971no—
273C2×Q8—1941no—
274C2×Q8—1942no—
275C2×Q8—1942no—
276C2×Q8C22×D9711yescharacteristic
277C2×D4—974no—
278C2×D4—971no—
279C2×D4—971no—
280C2×D4—1942no—
281C2×D4—1942no—
282C2×D4—1942no—
283C2×D4—1941no—
284C2×D4—1941no—
285C2×D4C22×D9711yescharacteristic
286C2×D4C22×D9711yescharacteristic
287C22×C4—21no—
288C22×C4—971no—
289C22×C4—971no—
290C22×C4—971no—
291C22×C4—3884no—
292C22×C4—1941no—
293C22×C4—1941no—
294C22×C4—1941no—
295C22×C4—1941no—
296C22×C4—1941no—
297SD16—22no—
298SD16—1942no—
299SD16—1942no—
300SD16—1942no—
301D8—22no—
302D8—1942no—
303D8—1942no—
304D8—1942no—
305C2×C8—971no—
306C2×C8—971no—
307C2×C8—1942no—
308C2×C8—1942no—
309C2×C8C22×D9711yescharacteristic
310C2×C8C22×D9711yescharacteristic
311C4⋊C4—971no—
312C4⋊C4—1941no—
313C4⋊C4C22×D9711yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—1941no—
318C22⋊C4—1941no—
319C22⋊C4—1941no—
320C22⋊C4—1941no—
321C22⋊C4—1941no—
322C22⋊C4—1941no—
323C22⋊C4—1941no—
324C22⋊C4—1941no—
325C22⋊C4—1941no—
326C42—971no—
327C42—971no—
328C42—971no—
329C42C22×D9711yescharacteristic
330C23—21no—
331C23—21no—
332C23—971no—
333C23—3882no—
334C23—3882no—
335C23—3882no—
336C23—3882no—
337C23—3882no—
338C23—1944no—
339C23—1941no—
340C23—1941no—
341Q8—21no—
342Q8—21no—
343Q8—3882no—
344Q8—1941no—
345Q8—1941no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—972no—
350D4—3882no—
351D4—1944no—
352D4—1941no—
353D4—1941no—
354D4—1941no—
355D4D4×D9712yes—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—971no—
360C2×C4—972no—
361C2×C4—972no—
362C2×C4—971no—
363C2×C4—971no—
364C2×C4—3882no—
365C2×C4—3882no—
366C2×C4—3882no—
367C2×C4—3882no—
368C2×C4—3882no—
369C2×C4—1942no—
370C2×C4—1942no—
371C2×C4—1941no—
372C2×C4—1941no—
373C2×C4D4×D9711yescharacteristic
374C2×C4D4×D9711yescharacteristic
375C2×C4C23×D9711yescharacteristic
376C8—21no—
377C8—21no—
378C8—1941no—
379C8—1941no—
380C22—22no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—7764no—
387C22—972no—
388C22—972no—
389C22—972no—
390C22—3888no—
391C22—3881no—
392C22—3881no—
393C22—3881no—
394C22—3881no—
395C22—3881no—
396C22—1942no—
397C22C2×D4×D9711yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—972no—
403C4—3881no—
404C4—3881no—
405C4—1941no—
406C4—1941no—
407C4C2×D4×D9711yescharacteristic
408C4#41×D9711yescharacteristic
409C2—42no—
410C2—81no—
411C2—7761no—
412C2—974no—
413C2—3882no—
414C2#121×D9711yescharacteristic
415C2#135×D9711yescharacteristic
416C2AGL(1,ℤ/8)×D9711yescharacteristic
subgroupG/H
centerC22C2×D4×D97
commutator, cosocleC2×C4×C97C24
FrattiniC2×C4C23×D97
Fitting#463×C97C2
socleC22×C97C22×D4
prime radicalC2×D8×D97C2
hypercenter#463D97
hypocenterC97C2×#463
LCSG ▷ C2×C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D97C2semidirect
3. #124×D97C2semidirect
4. C4×D4×D97C2semidirect
5. #20260953C2semidirect
6. #20260952C2semidirect
7. #20260951C2semidirect
8. #20260950C2semidirect
9. #20260949C2semidirect
10. #20260948C2semidirect
11. #20260947C2semidirect
12. C4⋊C8×D97C2semidirect
13. #103×D97C2semidirect
14. #102×D97C2semidirect
15. #463×C97C2semidirect
20. C2×#13095500C22semidirect
21. C2×#13095499C22semidirect
22. C2×#13095498C22semidirect
30. #15690799C22semidirect
31. #15690798C22semidirect
32. #15690797C22semidirect
35. C4×D388C22semidirect
36. D4×Dic97C22semidirect
37. #15690772C22semidirect
45. C4⋊#11715895C22semidirect
46. #15690739C22semidirect
47. #15690739C22semidirect
48. #15690735C22semidirect
49. #15690734C22semidirect
50. #15690733C22semidirect
51. #15690732C22semidirect
52. #15690731C22semidirect
53. #15690730C22semidirect
54. C2×SD16×C97C22semidirect
56. #124×C97C22semidirect
57. C4×D4×C97C22semidirect
58. C4⋊C8×C97C22semidirect
59. #103×C97C22semidirect
60. #102×C97C22semidirect
207. D97#463direct (N × H)
209. C97C2×#463semidirect
221. #463D97direct (N × H)
233. C2×SD16C2×D97semidirect
246. #124C2×D97semidirect
252. C4×D4C2×D97semidirect
261. C4⋊C8C2×D97semidirect
265. #103C2×D97semidirect
269. #102C2×D97semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D972
C2×D8×D972
#124×D972
C4×D4×D972
#202609532
#202609522
#202609512
#202609502
#202609492
#202609482
#202609472
C4⋊C8×D972
#103×D972
#102×D972
#463×C972
C2×#46397