Finite Group Databasebeta

← C4×SD16×D163 #35223289

Subgroups — C4×SD16×D163 #35223289

Order 20864.

552 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D163C211yesmaximal, characteristic
2C4×Q8×D163C211yesmaximal, characteristic, complemented
3C4×D4×D163C211yesmaximal, characteristic
4#23781756C211yesmaximal, characteristic, complemented
5C4×#14579688C211yesmaximal, characteristic, complemented
6SD16×Dic163C211yesmaximal, characteristic, complemented
7C4×#14579686C211yesmaximal, characteristic, complemented
8#23781752C211yesmaximal, characteristic, complemented
9C4×#14579687C211yesmaximal, characteristic, complemented
10#23781750C211yesmaximal, characteristic, complemented
11#106×D163C211yesmaximal, characteristic, complemented
12#103×D163C211yesmaximal, characteristic, complemented
13#102×D163C211yesmaximal, characteristic
14C4×C8×D163C211yesmaximal, characteristic, complemented
15C4×SD16×C163C211yesmaximal, characteristic, complemented
16C2×Q8×D163C2211yescharacteristic
17C2×D4×D163C2211yescharacteristic
18C22×C4×D163—21no—
19C2×#14579688C2211yescharacteristic
20C2×#14579687C2211yescharacteristic
21C2×#14579686C2211yescharacteristic
22SD16×D163C418yesdirect product factor
23C2×C8×D163C2211yescharacteristic
24C2×C8×D163C2211yescharacteristic
25Q8×Dic163C2211yescharacteristic, complemented
26C4×Dic326—21no—
27C4×Dic326C2211yescharacteristic, complemented
28#19104700—21no—
29#19104700C2211yescharacteristic, complemented
30C4×D652C2211yescharacteristic
31D4×Dic163C2211yescharacteristic
32#19104697C2211yescharacteristic
33C4×C22⋊D163—21no—
34(C22⋊D163)⋊C4—21no—
35C4⋊C4×D163—21no—
36C4⋊C4×D163C2211yescharacteristic
37C4⋊C4×D163C2211yescharacteristic
38C22⋊C4×D163—21no—
39C42×D163—21no—
40C42×D163C2211yescharacteristic
41#19104667C2211yescharacteristic, complemented
42#19104666C2211yescharacteristic, complemented
43#19104666C2211yescharacteristic, complemented
44#19104660C2211yescharacteristic, complemented
45#19104659C2211yescharacteristic, complemented
46#19104658C2211yescharacteristic, complemented
47#19104657C2211yescharacteristic
48#19104656C2211yescharacteristic
49#19104655C2211yescharacteristic
50C4×C163⋊C8C2211yescharacteristic, complemented
51C8×Dic163C2211yescharacteristic, complemented
52C8×Dic163C2211yescharacteristic, complemented
53C2×SD16×C163C2211yescharacteristic
54C4×Q8×C163C2211yescharacteristic, complemented
55C4×D4×C163C2211yescharacteristic
56#106×C163C2211yescharacteristic, complemented
57#103×C163C2211yescharacteristic, complemented
58#102×C163C2211yescharacteristic
59C4×C8×C163C2211yescharacteristic, complemented
60C23×D163—21no—
61C2×Dic326—21no—
62C2×Dic326C2311yescharacteristic
63Q8×D163—22no—
64Q8×D163C2×C414yescomplemented
65C2×D652C2311yescharacteristic
66C2×C22⋊D163—21no—
67D4×D163—22no—
68D4×D163C2×C414yes—
69C22×Dic163—21no—
70C2×C4×D163—21no—
71C2×C4×D163—21no—
72C2×C4×D163—21no—
73C2×C4×D163—21no—
74C2×C4×D163—21no—
75C2×C4×D163—44no—
76C2×C4×D163D411yescharacteristic
77C2×C4×D163D411yescharacteristic
78C2×C4×D163C2311yescharacteristic
79#14579688C2×C414yescomplemented
80#14579687C2×C414yescomplemented
81#14579686C2×C414yescomplemented
82C2×C163⋊C8C2311yescharacteristic
83C2×C163⋊C8C2311yescharacteristic
84C8×D163—22no—
85C8×D163C2×C414yescomplemented
86C4⋊Dic163—21no—
87C4⋊Dic163C2311yescharacteristic
88C4⋊Dic163C2311yescharacteristic
89Dic163⋊C4—21no—
90Dic163⋊C4—21no—
91Dic163⋊C4—21no—
92Dic163⋊C4—21no—
93C22⋊Dic163—21no—
94(C2×D163)⋊C4—21no—
95(C2×D163)⋊C4—21no—
96C4×Dic163—21no—
97C4×Dic163—21no—
98C4×Dic163—21no—
99C4×Dic163D411yescharacteristic
100C4×Dic163D411yescharacteristic
101C4×Dic163C2311yescharacteristic
102C2×Q8×C163C2311yescharacteristic
103C2×D4×C163C2311yescharacteristic
104C22×C4×C163—21no—
105SD16×C163C2×C414yescomplemented
106C2×C8×C163C2311yescharacteristic
107C2×C8×C163C2311yescharacteristic
108C4⋊C4×C163—21no—
109C4⋊C4×C163C2311yescharacteristic
110C4⋊C4×C163C2311yescharacteristic
111C22⋊C4×C163—21no—
112C42×C163—21no—
113C42×C163C2311yescharacteristic
114C22×D163—21no—
115C22×D163—24no—
116C22×D163—42no—
117C22×D163—42no—
118C22×D163C2×D411yescharacteristic
119Dic326—21no—
120Dic326—24no—
121Dic326C22×C412yescomplemented
122D652—21no—
123D652C22×C412yes—
124C22⋊D163—24no—
125C2×Dic163—21no—
126C2×Dic163—21no—
127C2×Dic163—21no—
128C2×Dic163—42no—
129C2×Dic163C2×D411yescharacteristic
130C2×Dic163C2×D411yescharacteristic
131C2×Dic163C2×D411yescharacteristic
132C4×D163—24no—
133C4×D163—22no—
134C4×D163—42no—
135C4×D163—42no—
136C4×D163—42no—
137C4×D163—42no—
138C4×D163SD1614yesdirect product factor
139C4×D163C22×C412yes—
140C4×D163#4112yes—
141C163⋊C8—21no—
142C163⋊C8C22×C412yescomplemented
143C23×C163—21no—
144Q8×C163—21no—
145Q8×C163C22×C412yescomplemented
146D4×C163—21no—
147D4×C163C22×C412yes—
148C2×C4×C163—21no—
149C2×C4×C163—21no—
150C2×C4×C163—21no—
151C2×C4×C163—42no—
152C2×C4×C163C2×D411yescharacteristic
153C2×C4×C163C2×D411yescharacteristic
154C2×C4×C163C2411yescharacteristic
155C8×C163—21no—
156C8×C163C22×C412yescomplemented
157C22×C163—22no—
158C22×C163—41no—
159C22×C163—41no—
160C22×C163C22×D411yescharacteristic
161C2×D163—22no—
162C2×D163—41no—
163C2×D163—41no—
164C2×D163—48no—
165C2×D163C4×D412yes—
166C2×D163C2×SD1612yes—
167C2×D163#13512yes—
168C4×C163—22no—
169C4×C163—21no—
170C4×C163—41no—
171C4×C163—41no—
172C4×C163C2×SD1612yescomplemented
173C4×C163C23×C411yescharacteristic
174C4×C163C2×#4111yescharacteristic
175Dic163—22no—
176Dic163—21no—
177Dic163—41no—
178Dic163—41no—
179Dic163C4×D412yes—
180Dic163C2×SD1612yescomplemented
181C2×C163—42no—
182C2×C163C2×C4×D411yescharacteristic
183C2×C163C22×SD1611yescharacteristic
184C2×C163C2×#13511yescharacteristic
185D163—42no—
186D163C4×SD1614yesdirect product factor
187C163C2×C4×SD1611yescharacteristic, complemented, Sylow
188C2×C4×SD16—1631nomaximal, Sylow
189C22×SD16—1631no—
190C2×C4×Q8—1631no—
191C2×C4×D4—1631no—
192C4×SD16—1631no—
193C4×SD16—1631no—
194C4×SD16—1631no—
195C4×SD16—1631no—
196C4×SD16—1631no—
197C4×SD16—1631no—
198C4×SD16—1631no—
199C4×SD16D16311yescharacteristic, direct product factor
200C2×#106—1631no—
201C2×#103—1631no—
202C2×#102—1631no—
203C2×C4×C8—1631no—
204C22×Q8—1631no—
205C22×D4—1631no—
206C23×C4—3261no—
207C2×SD16—1631no—
208C2×SD16—1631no—
209C2×SD16—1638no—
210C2×SD16—1631no—
211C2×SD16C2×D16311yescharacteristic
212C22×C8—1631no—
213C22×C8—1631no—
214C4×Q8—3261no—
215C4×Q8—3261no—
216C4×Q8—1631no—
217C4×Q8—1631no—
218C4×Q8—1631no—
219C4×Q8C2×D16311yescharacteristic, complemented
220C4×D4—3261no—
221C4×D4—3261no—
222C4×D4—1631no—
223C4×D4—1631no—
224C4×D4—1631no—
225C4×D4C2×D16311yescharacteristic
226C2×C4⋊C4—3261no—
227C2×C4⋊C4—1631no—
228C2×C4⋊C4—1631no—
229C2×C22⋊C4—3261no—
230C2×C42—3261no—
231C2×C42—1631no—
232#106—1631no—
233#106—1631no—
234#106—1631no—
235#106C2×D16311yescharacteristic, complemented
236#103—1631no—
237#103—1631no—
238#103—1631no—
239#103C2×D16311yescharacteristic, complemented
240#102—1631no—
241#102—1631no—
242#102—1631no—
243#102C2×D16311yescharacteristic
244C4×C8—1631no—
245C4×C8—1631no—
246C4×C8—1631no—
247C4×C8C2×D16311yescharacteristic, complemented
248C24—3261no—
249C2×Q8—3261no—
250C2×Q8—3262no—
251C2×Q8—1634no—
252C2×Q8—1631no—
253C2×Q8C22×D16311yescharacteristic
254C2×D4—3262no—
255C2×D4—3261no—
256C2×D4—1634no—
257C2×D4—1631no—
258C2×D4C22×D16311yescharacteristic
259C22×C4—21no—
260C22×C4—3261no—
261C22×C4—3261no—
262C22×C4—3261no—
263C22×C4—3261no—
264C22×C4—3261no—
265C22×C4—3261no—
266C22×C4—6524no—
267C22×C4—1631no—
268C22×C4—1631no—
269C22×C4—1631no—
270SD16—1634no—
271SD16—1634no—
272SD16—1634no—
273SD16C4×D16314yesdirect product factor
274C2×C8—3262no—
275C2×C8—1631no—
276C2×C8—1631no—
277C2×C8—1634no—
278C2×C8C22×D16311yescharacteristic
279C2×C8C22×D16311yescharacteristic
280C4⋊C4—21no—
281C4⋊C4—3261no—
282C4⋊C4—3261no—
283C4⋊C4—3261no—
284C4⋊C4—3261no—
285C4⋊C4—3261no—
286C4⋊C4—1631no—
287C4⋊C4—1631no—
288C4⋊C4C22×D16311yescharacteristic
289C4⋊C4C22×D16311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—3261no—
292C22⋊C4—3261no—
293C22⋊C4—3261no—
294C42—21no—
295C42—3261no—
296C42—3261no—
297C42—3261no—
298C42—1631no—
299C42—1631no—
300C42—1631no—
301C42C22×D16311yescharacteristic
302C23—21no—
303C23—3264no—
304C23—3261no—
305C23—6522no—
306C23—6522no—
307C23—1631no—
308Q8—21no—
309Q8—3264no—
310Q8—3261no—
311Q8—1632no—
312Q8C2×C4×D16312yescomplemented
313D4—21no—
314D4—3264no—
315D4—3261no—
316D4—1632no—
317D4C2×C4×D16312yes—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—3264no—
323C2×C4—3262no—
324C2×C4—3261no—
325C2×C4—3261no—
326C2×C4—3261no—
327C2×C4—6522no—
328C2×C4—6522no—
329C2×C4—6522no—
330C2×C4—6522no—
331C2×C4—6522no—
332C2×C4—1631no—
333C2×C4—1631no—
334C2×C4—1631no—
335C2×C4—1632no—
336C2×C4—1632no—
337C2×C4—1634no—
338C2×C4D4×D16311yescharacteristic
339C2×C4D4×D16311yescharacteristic
340C2×C4C23×D16311yescharacteristic
341C8—21no—
342C8—3261no—
343C8—1632no—
344C8C2×C4×D16312yescomplemented
345C22—22no—
346C22—41no—
347C22—41no—
348C22—3262no—
349C22—6528no—
350C22—6521no—
351C22—6521no—
352C22—1632no—
353C22—1632no—
354C22—1632no—
355C22C2×D4×D16311yescharacteristic
356C4—21no—
357C4—22no—
358C4—41no—
359C4—41no—
360C4—3261no—
361C4—3262no—
362C4—6521no—
363C4—6521no—
364C4—1632no—
365C4—1632no—
366C4SD16×D16312yesdirect product factor
367C4C22×C4×D16311yescharacteristic
368C4#41×D16311yescharacteristic
369C2—42no—
370C2—6522no—
371C2—1634no—
372C2C4×D4×D16311yescharacteristic
373C2C2×SD16×D16311yescharacteristic
374C2#135×D16311yescharacteristic
subgroupG/H
centerC2×C4D4×D163
commutatorC4×C163C23×C4
FrattiniC2×C4C23×D163
FittingC4×SD16×C163C2
socleC22×C163C22×D4
prime radicalC2×D4×D163C22
cosocleC2×C4×C163C24
hypercenterC4×SD16D163
hypocenterC163C2×C4×SD16
LCSG ▷ C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D163C2semidirect
4. #23781756C2semidirect
5. C4×#14579688C2semidirect
6. SD16×Dic163C2semidirect
7. C4×#14579686C2semidirect
8. #23781752C2semidirect
9. C4×#14579687C2semidirect
10. #23781750C2semidirect
11. #106×D163C2semidirect
12. #103×D163C2semidirect
14. C4×C8×D163C2semidirect
15. C4×SD16×C163C2semidirect
22. SD16×D163C4direct (N × H)
25. Q8×Dic163C22semidirect
27. C4×Dic326C22semidirect
29. #19104700C22semidirect
41. #19104667C22semidirect
42. #19104666C22semidirect
43. #19104666C22semidirect
44. #19104660C22semidirect
45. #19104659C22semidirect
46. #19104658C22semidirect
50. C4×C163⋊C8C22semidirect
51. C8×Dic163C22semidirect
52. C8×Dic163C22semidirect
54. C4×Q8×C163C22semidirect
56. #106×C163C22semidirect
57. #103×C163C22semidirect
59. C4×C8×C163C22semidirect
64. Q8×D163C2×C4semidirect
79. #14579688C2×C4semidirect
80. #14579687C2×C4semidirect
81. #14579686C2×C4semidirect
85. C8×D163C2×C4semidirect
105. SD16×C163C2×C4semidirect
121. Dic326C22×C4semidirect
138. C4×D163SD16direct (N × H)
142. C163⋊C8C22×C4semidirect
145. Q8×C163C22×C4semidirect
156. C8×C163C22×C4semidirect
172. C4×C163C2×SD16semidirect
180. Dic163C2×SD16semidirect
186. D163C4×SD16direct (N × H)
187. C163C2×C4×SD16semidirect
199. C4×SD16D163direct (N × H)
219. C4×Q8C2×D163semidirect
235. #106C2×D163semidirect
239. #103C2×D163semidirect
247. C4×C8C2×D163semidirect
273. SD16C4×D163direct (N × H)
312. Q8C2×C4×D163semidirect
344. C8C2×C4×D163semidirect
366. C4SD16×D163direct (N × H)

Maximal subgroups

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

subgroupindex
C2×SD16×D1632
C4×Q8×D1632
C4×D4×D1632
#237817562
C4×#145796882
SD16×Dic1632
C4×#145796862
#237817522
C4×#145796872
#237817502
#106×D1632
#103×D1632
#102×D1632
C4×C8×D1632
C4×SD16×C1632
C2×C4×SD16163