Finite Group Databasebeta

← #463×D163 #35223956

Subgroups — #463×D163 #35223956

Order 20864.

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×D163C211yesmaximal, characteristic, complemented
2C2×D8×D163C211yesmaximal, characteristic
3#124×D163C211yesmaximal, characteristic, complemented
4C4×D4×D163C211yesmaximal, characteristic, complemented
5#23781883C211yesmaximal, characteristic, complemented
6#23781882C211yesmaximal, characteristic, complemented
7#23781881C211yesmaximal, characteristic, complemented
8#23781880C211yesmaximal, characteristic, complemented
9#23781879C211yesmaximal, characteristic, complemented
10#23781878C211yesmaximal, characteristic, complemented
11#23781877C211yesmaximal, characteristic, complemented
12C4⋊C8×D163C211yesmaximal, characteristic, complemented
13#103×D163C211yesmaximal, characteristic, complemented
14#102×D163C211yesmaximal, characteristic, complemented
15#463×C163C211yesmaximal, characteristic, complemented
16C2×Q8×D163C2211yescharacteristic
17C2×D4×D163C2211yescharacteristic
18C2×D4×D163C2211yescharacteristic
19C22×C4×D163—21no—
20C2×#14579688C2211yescharacteristic, complemented
21C2×#14579687C2211yescharacteristic, complemented
22C2×#14579686C2211yescharacteristic, complemented
23SD16×D163—24no—
24C2×D1304C2211yescharacteristic
25C2×#14579684C2211yescharacteristic
26C2×#14579684C2211yescharacteristic
27D8×D163—24no—
28C2×C8×D163C2211yescharacteristic
29C2×C8×D163C2211yescharacteristic
30#19104724C2211yescharacteristic, complemented
31#19104723C2211yescharacteristic, complemented
32#19104722C2211yescharacteristic, complemented
33#19104721—21no—
34#19104721—21no—
35C4×D652C2211yescharacteristic, complemented
36D4×Dic163C2211yescharacteristic, complemented
37#19104697C2211yescharacteristic, complemented
38C4×C22⋊D163—21no—
39(C22⋊D163)⋊C4—21no—
40C4⋊C4×D163C2211yescharacteristic
41C22⋊C4×D163—21no—
42C22⋊C4×D163—21no—
43C22⋊C4×D163—21no—
44C42×D163C2211yescharacteristic
45C4⋊(C163⋊C8)C2211yescharacteristic, complemented
46Dic163⋊C8C2211yescharacteristic, complemented
47Dic163⋊C8C2211yescharacteristic, complemented
48#19104660C2211yescharacteristic, complemented
49#19104659C2211yescharacteristic, complemented
50#19104658C2211yescharacteristic, complemented
51#19104657C2211yescharacteristic, complemented
52#19104656C2211yescharacteristic, complemented
53#19104655C2211yescharacteristic, complemented
54C2×SD16×C163C2211yescharacteristic, complemented
55C2×D8×C163C2211yescharacteristic
56#124×C163C2211yescharacteristic, complemented
57C4×D4×C163C2211yescharacteristic, complemented
58C4⋊C8×C163C2211yescharacteristic, complemented
59#103×C163C2211yescharacteristic, complemented
60#102×C163C2211yescharacteristic, complemented
61C23×D163—21no—
62C23×D163—21no—
63C2×Dic326—21no—
64C2×Dic326C2311yescharacteristic
65Q8×D163—22no—
66Q8×D163—22no—
67C2×D652C2311yescharacteristic
68C2×D652C2311yescharacteristic
69C2×C22⋊D163—21no—
70C2×C22⋊D163—21no—
71D4×D163—22no—
72D4×D163—22no—
73D4×D163—22no—
74D4×D163D414yes—
75C22×Dic163—21no—
76C2×C4×D163—21no—
77C2×C4×D163—21no—
78C2×C4×D163—21no—
79C2×C4×D163—21no—
80C2×C4×D163—44no—
81C2×C4×D163D411yescharacteristic
82C2×C4×D163D411yescharacteristic
83C2×C4×D163C2311yescharacteristic
84#14579688—22no—
85#14579687—22no—
86#14579686—22no—
87D1304—22no—
88#14579684—22no—
89#14579684—22no—
90C2×C163⋊C8C2311yescharacteristic
91C2×C163⋊C8C2311yescharacteristic
92C8×D163—22no—
93C8×D163—22no—
94C4⋊Dic163C2311yescharacteristic
95Dic163⋊C4—21no—
96C22⋊Dic163—21no—
97C22⋊Dic163—21no—
98C22⋊Dic163—21no—
99(C2×D163)⋊C4—21no—
100(C2×D163)⋊C4—21no—
101(C2×D163)⋊C4—21no—
102(C2×D163)⋊C4—21no—
103(C2×D163)⋊C4—21no—
104(C2×D163)⋊C4—21no—
105C4×Dic163D411yescharacteristic
106C4×Dic163D411yescharacteristic
107C4×Dic163C2311yescharacteristic
108C2×Q8×C163C2311yescharacteristic
109C2×D4×C163C2311yescharacteristic
110C2×D4×C163C2311yescharacteristic
111C22×C4×C163—21no—
112SD16×C163—22no—
113D8×C163—22no—
114C2×C8×C163C2311yescharacteristic
115C2×C8×C163C2311yescharacteristic
116C4⋊C4×C163C2311yescharacteristic
117C22⋊C4×C163—21no—
118C22⋊C4×C163—21no—
119C22⋊C4×C163—21no—
120C42×C163C2311yescharacteristic
121C22×D163—21no—
122C22×D163—24no—
123C22×D163—21no—
124C22×D163—42no—
125C22×D163—42no—
126C22×D163—42no—
127C22×D163—42no—
128C22×D163—42no—
129C22×D163C2×D411yescharacteristic
130Dic326—21no—
131Dic326—21no—
132Dic326—42no—
133D652—21no—
134D652—21no—
135D652—21no—
136D652C2×D412yes—
137C22⋊D163—24no—
138C22⋊D163—42no—
139C2×Dic163—21no—
140C2×Dic163—21no—
141C2×Dic163—42no—
142C2×Dic163C2×D411yescharacteristic
143C2×Dic163C2×D411yescharacteristic
144C2×Dic163C2×D411yescharacteristic
145C4×D163—22no—
146C4×D163—22no—
147C4×D163—42no—
148C4×D163—42no—
149C4×D163—42no—
150C4×D163—42no—
151C4×D163C2×D412yes—
152C4×D163#4112yes—
153C163⋊C8—21no—
154C163⋊C8—21no—
155C23×C163—21no—
156C23×C163—21no—
157Q8×C163—21no—
158Q8×C163—21no—
159D4×C163—21no—
160D4×C163—21no—
161D4×C163—21no—
162D4×C163C2×D412yes—
163C2×C4×C163—21no—
164C2×C4×C163—21no—
165C2×C4×C163—42no—
166C2×C4×C163C2×D411yescharacteristic
167C2×C4×C163C2×D411yescharacteristic
168C2×C4×C163C2411yescharacteristic
169C8×C163—21no—
170C8×C163—21no—
171C22×C163—22no—
172C22×C163—41no—
173C22×C163—41no—
174C22×C163—41no—
175C22×C163—41no—
176C22×C163—41no—
177C22×C163C22×D411yescharacteristic
178C2×D163—22no—
179C2×D163—41no—
180C2×D163—41no—
181C2×D163—48no—
182C2×D163—41no—
183C2×D163—41no—
184C2×D163—41no—
185C2×D163—84no—
186C2×D163#12112yes—
187C2×D163#13512yes—
188C2×D163AGL(1,ℤ/8)12yes—
189C4×C163—21no—
190C4×C163—21no—
191C4×C163—41no—
192C4×C163—41no—
193C4×C163C22×D411yescharacteristic
194C4×C163C2×#4111yescharacteristic
195Dic163—21no—
196Dic163—21no—
197Dic163—41no—
198Dic163—41no—
199Dic163#12112yes—
200C2×C163—42no—
201C2×C163—81no—
202C2×C163C2×#12111yescharacteristic
203C2×C163C2×#13511yescharacteristic
204C2×C163C2×AGL(1,ℤ/8)11yescharacteristic
205D163—42no—
206D163—81no—
207D163#46314yesdirect product factor
208C163C2×#46311yescharacteristic, complemented, Sylow
209C2×#463—1631nomaximal, Sylow
210C22×SD16—1631no—
211C22×D8—1631no—
212C2×#124—1631no—
213C2×C4×D4—1631no—
214#463—1631no—
215#463—1631no—
216#463—1631no—
217#463—1631no—
218#463—1631no—
219#463—1631no—
220#463—1631no—
221#463D16311yescharacteristic, direct product factor
222C2×C4⋊C8—1631no—
223C2×#103—1631no—
224C2×#102—1631no—
225C22×Q8—1631no—
226C22×D4—1631no—
227C22×D4—1631no—
228C23×C4—3261no—
229C2×SD16—3264no—
230C2×SD16—1631no—
231C2×SD16—1631no—
232C2×SD16—1631no—
233C2×SD16C2×D16311yescharacteristic, complemented
234C2×D8—3264no—
235C2×D8—1631no—
236C2×D8—1631no—
237C2×D8—1631no—
238C2×D8C2×D16311yescharacteristic
239C22×C8—1631no—
240C22×C8—1631no—
241#124—3261no—
242#124—3261no—
243#124—1631no—
244#124—1631no—
245#124—1631no—
246#124C2×D16311yescharacteristic, complemented
247C4×D4—3261no—
248C4×D4—3261no—
249C4×D4—1631no—
250C4×D4—1631no—
251C4×D4—1631no—
252C4×D4C2×D16311yescharacteristic, complemented
253C2×C4⋊C4—1631no—
254C2×C22⋊C4—3261no—
255C2×C22⋊C4—3261no—
256C2×C22⋊C4—3261no—
257C2×C42—1631no—
258C4⋊C8—1631no—
259C4⋊C8—1631no—
260C4⋊C8—1631no—
261C4⋊C8C2×D16311yescharacteristic, complemented
262#103—1631no—
263#103—1631no—
264#103—1631no—
265#103C2×D16311yescharacteristic, complemented
266#102—1631no—
267#102—1631no—
268#102—1631no—
269#102C2×D16311yescharacteristic, complemented
270C24—3261no—
271C24—3261no—
272C2×Q8—3261no—
273C2×Q8—3262no—
274C2×Q8—3262no—
275C2×Q8—1631no—
276C2×Q8C22×D16311yescharacteristic
277C2×D4—3262no—
278C2×D4—3262no—
279C2×D4—3262no—
280C2×D4—3261no—
281C2×D4—3261no—
282C2×D4—1634no—
283C2×D4—1631no—
284C2×D4—1631no—
285C2×D4C22×D16311yescharacteristic
286C2×D4C22×D16311yescharacteristic
287C22×C4—21no—
288C22×C4—3261no—
289C22×C4—3261no—
290C22×C4—3261no—
291C22×C4—3261no—
292C22×C4—3261no—
293C22×C4—6524no—
294C22×C4—1631no—
295C22×C4—1631no—
296C22×C4—1631no—
297SD16—22no—
298SD16—3262no—
299SD16—3262no—
300SD16—3262no—
301D8—22no—
302D8—3262no—
303D8—3262no—
304D8—3262no—
305C2×C8—3262no—
306C2×C8—3262no—
307C2×C8—1631no—
308C2×C8—1631no—
309C2×C8C22×D16311yescharacteristic
310C2×C8C22×D16311yescharacteristic
311C4⋊C4—3261no—
312C4⋊C4—1631no—
313C4⋊C4C22×D16311yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—3261no—
318C22⋊C4—3261no—
319C22⋊C4—3261no—
320C22⋊C4—3261no—
321C22⋊C4—3261no—
322C22⋊C4—3261no—
323C22⋊C4—3261no—
324C22⋊C4—3261no—
325C22⋊C4—3261no—
326C42—1631no—
327C42—1631no—
328C42—1631no—
329C42C22×D16311yescharacteristic
330C23—21no—
331C23—21no—
332C23—3264no—
333C23—3261no—
334C23—3261no—
335C23—6522no—
336C23—6522no—
337C23—6522no—
338C23—6522no—
339C23—6522no—
340C23—1631no—
341Q8—21no—
342Q8—21no—
343Q8—3261no—
344Q8—3261no—
345Q8—6522no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—3264no—
350D4—3261no—
351D4—3261no—
352D4—3261no—
353D4—6522no—
354D4—1632no—
355D4D4×D16312yes—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—3262no—
360C2×C4—3262no—
361C2×C4—3261no—
362C2×C4—3261no—
363C2×C4—6522no—
364C2×C4—6522no—
365C2×C4—6522no—
366C2×C4—6522no—
367C2×C4—6522no—
368C2×C4—1631no—
369C2×C4—1631no—
370C2×C4—1631no—
371C2×C4—1632no—
372C2×C4—1632no—
373C2×C4D4×D16311yescharacteristic
374C2×C4D4×D16311yescharacteristic
375C2×C4C23×D16311yescharacteristic
376C8—21no—
377C8—21no—
378C8—3261no—
379C8—3261no—
380C22—22no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—13044no—
387C22—3262no—
388C22—6528no—
389C22—6521no—
390C22—6521no—
391C22—6521no—
392C22—6521no—
393C22—6521no—
394C22—1632no—
395C22—1632no—
396C22—1632no—
397C22C2×D4×D16311yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—3261no—
403C4—3261no—
404C4—6521no—
405C4—6521no—
406C4—1632no—
407C4C2×D4×D16311yescharacteristic
408C4#41×D16311yescharacteristic
409C2—42no—
410C2—81no—
411C2—13041no—
412C2—6522no—
413C2—1634no—
414C2#121×D16311yescharacteristic
415C2#135×D16311yescharacteristic
416C2AGL(1,ℤ/8)×D16311yescharacteristic
subgroupG/H
centerC22C2×D4×D163
commutator, cosocleC2×C4×C163C24
FrattiniC2×C4C23×D163
Fitting#463×C163C2
socleC22×C163C22×D4
prime radicalC2×D8×D163C2
hypercenter#463D163
hypocenterC163C2×#463
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D163C2semidirect
3. #124×D163C2semidirect
4. C4×D4×D163C2semidirect
5. #23781883C2semidirect
6. #23781882C2semidirect
7. #23781881C2semidirect
8. #23781880C2semidirect
9. #23781879C2semidirect
10. #23781878C2semidirect
11. #23781877C2semidirect
12. C4⋊C8×D163C2semidirect
13. #103×D163C2semidirect
14. #102×D163C2semidirect
15. #463×C163C2semidirect
20. C2×#14579688C22semidirect
21. C2×#14579687C22semidirect
22. C2×#14579686C22semidirect
30. #19104724C22semidirect
31. #19104723C22semidirect
32. #19104722C22semidirect
35. C4×D652C22semidirect
36. D4×Dic163C22semidirect
37. #19104697C22semidirect
45. C4⋊(C163⋊C8)C22semidirect
46. Dic163⋊C8C22semidirect
47. Dic163⋊C8C22semidirect
48. #19104660C22semidirect
49. #19104659C22semidirect
50. #19104658C22semidirect
51. #19104657C22semidirect
52. #19104656C22semidirect
53. #19104655C22semidirect
54. C2×SD16×C163C22semidirect
56. #124×C163C22semidirect
57. C4×D4×C163C22semidirect
58. C4⋊C8×C163C22semidirect
59. #103×C163C22semidirect
60. #102×C163C22semidirect
207. D163#463direct (N × H)
208. C163C2×#463semidirect
221. #463D163direct (N × H)
233. C2×SD16C2×D163semidirect
246. #124C2×D163semidirect
252. C4×D4C2×D163semidirect
261. C4⋊C8C2×D163semidirect
265. #103C2×D163semidirect
269. #102C2×D163semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1632
C2×D8×D1632
#124×D1632
C4×D4×D1632
#237818832
#237818822
#237818812
#237818802
#237818792
#237818782
#237818772
C4⋊C8×D1632
#103×D1632
#102×D1632
#463×C1632
C2×#463163