Finite Group Databasebeta

← #478×D163 #35224289

Subgroups — #478×D163 #35224289

Order 20864.

448 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#125×D163C211yesmaximal, characteristic, complemented
2C4×D4×D163C211yesmaximal, characteristic
3#23781968C211yesmaximal, characteristic, complemented
4#23781967C211yesmaximal, characteristic, complemented
5#23781966C211yesmaximal, characteristic, complemented
6#23781965C211yesmaximal, characteristic, complemented
7#23781964C211yesmaximal, characteristic, complemented
8#23781963C211yesmaximal, characteristic, complemented
9#23781962C211yesmaximal, characteristic, complemented
10#107×D163C211yesmaximal, characteristic, complemented
11#106×D163C211yesmaximal, characteristic, complemented
12C4⋊C8×D163C211yesmaximal, characteristic, complemented
13#102×D163C211yesmaximal, characteristic
14#102×D163C211yesmaximal, characteristic
15#478×C163C211yesmaximal, characteristic, complemented
16C2×D4×D163C2211yescharacteristic
17C22×C4×D163—21no—
18C2×C8×D163C2211yescharacteristic
19C2×C8×D163C2211yescharacteristic
20#19104727C2211yescharacteristic, complemented
21#19104726C2211yescharacteristic, complemented
22#19104726C2211yescharacteristic, complemented
23#19104725—21no—
24#19104725—21no—
25C4×D652C2211yescharacteristic
26D4×Dic163C2211yescharacteristic
27#19104697C2211yescharacteristic
28C4×C22⋊D163—21no—
29(C22⋊D163)⋊C4—21no—
30C4⋊C4×D163—21no—
31C4⋊C4×D163—21no—
32C4⋊C4×D163C2211yescharacteristic
33C4⋊C4×D163C2211yescharacteristic
34C4⋊C4×D163C2211yescharacteristic
35C22⋊C4×D163—21no—
36C42×D163C2211yescharacteristic
37#19104669C2211yescharacteristic, complemented
38#19104668C2211yescharacteristic, complemented
39#19104668C2211yescharacteristic, complemented
40#19104667C2211yescharacteristic, complemented
41#19104666C2211yescharacteristic, complemented
42#19104666C2211yescharacteristic, complemented
43C4⋊(C163⋊C8)C2211yescharacteristic, complemented
44Dic163⋊C8C2211yescharacteristic, complemented
45Dic163⋊C8C2211yescharacteristic, complemented
46#19104657C2211yescharacteristic
47#19104657C2211yescharacteristic
48#19104656C2211yescharacteristic
49#19104656C2211yescharacteristic
50#19104655C2211yescharacteristic
51#19104655C2211yescharacteristic
52#125×C163C2211yescharacteristic, complemented
53C4×D4×C163C2211yescharacteristic
54#107×C163C2211yescharacteristic, complemented
55#106×C163C2211yescharacteristic, complemented
56C4⋊C8×C163C2211yescharacteristic, complemented
57#102×C163C2211yescharacteristic
58#102×C163C2211yescharacteristic
59C23×D163—21no—
60C2×D652C2311yescharacteristic
61C2×C22⋊D163—21no—
62D4×D163—22no—
63D4×D163Q814yes—
64C22×Dic163—21no—
65C2×C4×D163—21no—
66C2×C4×D163—21no—
67C2×C4×D163—21no—
68C2×C4×D163—21no—
69C2×C4×D163—21no—
70C2×C4×D163—44no—
71C2×C4×D163D411yescharacteristic
72C2×C4×D163D411yescharacteristic
73C2×C4×D163C2311yescharacteristic
74C2×C163⋊C8C2311yescharacteristic
75C2×C163⋊C8C2311yescharacteristic
76C8×D163—22no—
77C8×D163—22no—
78C4⋊Dic163—21no—
79C4⋊Dic163—21no—
80C4⋊Dic163C2311yescharacteristic
81C4⋊Dic163C2311yescharacteristic
82C4⋊Dic163C2311yescharacteristic
83Dic163⋊C4—21no—
84Dic163⋊C4—21no—
85Dic163⋊C4—21no—
86Dic163⋊C4—21no—
87Dic163⋊C4—21no—
88Dic163⋊C4—21no—
89Dic163⋊C4—21no—
90C22⋊Dic163—21no—
91(C2×D163)⋊C4—21no—
92(C2×D163)⋊C4—21no—
93C4×Dic163D411yescharacteristic
94C4×Dic163D411yescharacteristic
95C4×Dic163C2311yescharacteristic
96C2×D4×C163C2311yescharacteristic
97C22×C4×C163—21no—
98C2×C8×C163C2311yescharacteristic
99C2×C8×C163C2311yescharacteristic
100C4⋊C4×C163—21no—
101C4⋊C4×C163—21no—
102C4⋊C4×C163C2311yescharacteristic
103C4⋊C4×C163C2311yescharacteristic
104C4⋊C4×C163C2311yescharacteristic
105C22⋊C4×C163—21no—
106C42×C163C2311yescharacteristic
107C22×D163—21no—
108C22×D163—24no—
109C22×D163—42no—
110C22×D163—42no—
111C22×D163C2×D411yescharacteristic
112D652—21no—
113D652C2×Q812yes—
114C22⋊D163—24no—
115C2×Dic163—21no—
116C2×Dic163—21no—
117C2×Dic163—21no—
118C2×Dic163—42no—
119C2×Dic163C2×D411yescharacteristic
120C2×Dic163C2×D411yescharacteristic
121C2×Dic163C2×D411yescharacteristic
122C4×D163—22no—
123C4×D163—22no—
124C4×D163—42no—
125C4×D163—42no—
126C4×D163—42no—
127C4×D163—42no—
128C4×D163—42no—
129C4×D163C2×Q812yes—
130C4×D163#4112yes—
131C163⋊C8—21no—
132C163⋊C8—21no—
133C23×C163—21no—
134D4×C163—21no—
135D4×C163C2×Q812yes—
136C2×C4×C163—21no—
137C2×C4×C163—21no—
138C2×C4×C163—21no—
139C2×C4×C163—42no—
140C2×C4×C163C2×D411yescharacteristic
141C2×C4×C163C2×D411yescharacteristic
142C2×C4×C163C2411yescharacteristic
143C8×C163—21no—
144C8×C163—21no—
145C22×C163—22no—
146C22×C163—41no—
147C22×C163—41no—
148C22×C163C22×D411yescharacteristic
149C2×D163—22no—
150C2×D163—41no—
151C2×D163—41no—
152C2×D163—48no—
153C2×D163C22⋊Q812yes—
154C2×D163#13512yes—
155C2×D163AGL(1,ℤ/8)12yes—
156C4×C163—21no—
157C4×C163—21no—
158C4×C163—41no—
159C4×C163—41no—
160C4×C163—41no—
161C4×C163C22×Q811yescharacteristic
162C4×C163C2×#4111yescharacteristic
163Dic163—21no—
164Dic163—21no—
165Dic163—41no—
166Dic163—41no—
167Dic163—41no—
168Dic163C22⋊Q812yes—
169C2×C163—42no—
170C2×C163C2×C22⋊Q811yescharacteristic
171C2×C163C2×#13511yescharacteristic
172C2×C163C2×AGL(1,ℤ/8)11yescharacteristic
173D163—42no—
174D163#47814yesdirect product factor
175C163C2×#47811yescharacteristic, complemented, Sylow
176C2×#478—1631nomaximal, Sylow
177C2×#125—1631no—
178C2×C4×D4—1631no—
179#478—1631no—
180#478—1631no—
181#478—1631no—
182#478—1631no—
183#478—1631no—
184#478—1631no—
185#478—1631no—
186#478D16311yescharacteristic, direct product factor
187C2×#107—1631no—
188C2×#106—1631no—
189C2×C4⋊C8—1631no—
190C2×#102—1631no—
191C2×#102—1631no—
192C22×D4—1631no—
193C23×C4—3261no—
194C22×C8—1631no—
195C22×C8—1631no—
196#125—3261no—
197#125—3261no—
198#125—1631no—
199#125—1631no—
200#125—1631no—
201#125C2×D16311yescharacteristic, complemented
202C4×D4—3261no—
203C4×D4—3261no—
204C4×D4—1631no—
205C4×D4—1631no—
206C4×D4—1631no—
207C4×D4C2×D16311yescharacteristic
208C2×C4⋊C4—3261no—
209C2×C4⋊C4—3261no—
210C2×C4⋊C4—1631no—
211C2×C4⋊C4—1631no—
212C2×C4⋊C4—1631no—
213C2×C22⋊C4—3261no—
214C2×C42—1631no—
215#107—1631no—
216#107—1631no—
217#107—1631no—
218#107C2×D16311yescharacteristic, complemented
219#106—1631no—
220#106—1631no—
221#106—1631no—
222#106C2×D16311yescharacteristic, complemented
223C4⋊C8—1631no—
224C4⋊C8—1631no—
225C4⋊C8—1631no—
226C4⋊C8C2×D16311yescharacteristic, complemented
227#102—1631no—
228#102—1631no—
229#102—1631no—
230#102—1631no—
231#102—1631no—
232#102—1631no—
233#102C2×D16311yescharacteristic
234#102C2×D16311yescharacteristic
235C24—3261no—
236C2×D4—3262no—
237C2×D4—3261no—
238C2×D4—1634no—
239C2×D4—1631no—
240C2×D4C22×D16311yescharacteristic
241C22×C4—21no—
242C22×C4—3261no—
243C22×C4—3261no—
244C22×C4—3261no—
245C22×C4—3261no—
246C22×C4—3261no—
247C22×C4—3261no—
248C22×C4—6524no—
249C22×C4—1631no—
250C22×C4—1631no—
251C22×C4—1631no—
252C2×C8—3262no—
253C2×C8—3262no—
254C2×C8—1631no—
255C2×C8—1631no—
256C2×C8C22×D16311yescharacteristic
257C2×C8C22×D16311yescharacteristic
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—3261no—
261C4⋊C4—3261no—
262C4⋊C4—3261no—
263C4⋊C4—3261no—
264C4⋊C4—3261no—
265C4⋊C4—3261no—
266C4⋊C4—3261no—
267C4⋊C4—3261no—
268C4⋊C4—3261no—
269C4⋊C4—1631no—
270C4⋊C4—1631no—
271C4⋊C4—1631no—
272C4⋊C4C22×D16311yescharacteristic
273C4⋊C4C22×D16311yescharacteristic
274C4⋊C4C22×D16311yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—3261no—
277C22⋊C4—3261no—
278C22⋊C4—3261no—
279C42—1631no—
280C42—1631no—
281C42—1631no—
282C42C22×D16311yescharacteristic
283C23—21no—
284C23—3264no—
285C23—3261no—
286C23—6522no—
287C23—6522no—
288C23—1631no—
289D4—21no—
290D4—3264no—
291D4—3261no—
292D4—1632no—
293D4Q8×D16312yes—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—42no—
298C2×C4—3262no—
299C2×C4—3262no—
300C2×C4—3261no—
301C2×C4—3261no—
302C2×C4—3261no—
303C2×C4—6522no—
304C2×C4—6522no—
305C2×C4—6522no—
306C2×C4—6522no—
307C2×C4—6522no—
308C2×C4—6522no—
309C2×C4—1631no—
310C2×C4—1631no—
311C2×C4—1631no—
312C2×C4—1632no—
313C2×C4—1632no—
314C2×C4D4×D16311yescharacteristic
315C2×C4D4×D16311yescharacteristic
316C2×C4C23×D16311yescharacteristic
317C8—21no—
318C8—21no—
319C8—3261no—
320C8—3261no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—3262no—
325C22—6528no—
326C22—6521no—
327C22—6521no—
328C22—1632no—
329C22—1632no—
330C22—1632no—
331C22C2×D4×D16311yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—3261no—
338C4—3261no—
339C4—6521no—
340C4—6521no—
341C4—6521no—
342C4—1632no—
343C4C2×Q8×D16311yescharacteristic
344C4#41×D16311yescharacteristic
345C2—42no—
346C2—6522no—
347C2—1634no—
348C2C22⋊Q8×D16311yescharacteristic
349C2#135×D16311yescharacteristic
350C2AGL(1,ℤ/8)×D16311yescharacteristic
subgroupG/H
centerC22C2×D4×D163
commutator, cosocleC2×C4×C163C24
FrattiniC2×C4C23×D163
Fitting#478×C163C2
socleC22×C163C22×D4
prime radicalC2×D4×D163C22
hypercenter#478D163
hypocenterC163C2×#478
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #125×D163C2semidirect
3. #23781968C2semidirect
4. #23781967C2semidirect
5. #23781966C2semidirect
6. #23781965C2semidirect
7. #23781964C2semidirect
8. #23781963C2semidirect
9. #23781962C2semidirect
10. #107×D163C2semidirect
11. #106×D163C2semidirect
12. C4⋊C8×D163C2semidirect
15. #478×C163C2semidirect
20. #19104727C22semidirect
21. #19104726C22semidirect
22. #19104726C22semidirect
37. #19104669C22semidirect
38. #19104668C22semidirect
39. #19104668C22semidirect
40. #19104667C22semidirect
41. #19104666C22semidirect
42. #19104666C22semidirect
43. C4⋊(C163⋊C8)C22semidirect
44. Dic163⋊C8C22semidirect
45. Dic163⋊C8C22semidirect
52. #125×C163C22semidirect
54. #107×C163C22semidirect
55. #106×C163C22semidirect
56. C4⋊C8×C163C22semidirect
174. D163#478direct (N × H)
175. C163C2×#478semidirect
186. #478D163direct (N × H)
201. #125C2×D163semidirect
218. #107C2×D163semidirect
222. #106C2×D163semidirect
226. C4⋊C8C2×D163semidirect

Maximal subgroups

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

subgroupindex
#125×D1632
C4×D4×D1632
#237819682
#237819672
#237819662
#237819652
#237819642
#237819632
#237819622
#107×D1632
#106×D1632
C4⋊C8×D1632
#102×D1632
#478×C1632
C2×#478163