Finite Group Databasebeta

← #483×D163 #35224410

Subgroups — #483×D163 #35224410

Order 20864.

460 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22⋊Q8×D163C211yesmaximal, characteristic
2C2×C4⋊C4×D163C211yesmaximal, characteristic
3#23781997C212yesmaximal, complemented
4#23781996C211yesmaximal, characteristic, complemented
5#23781995C211yesmaximal, characteristic, complemented
6#23781994C212yesmaximal, complemented
7#23781993C211yesmaximal, characteristic, complemented
8#106×D163C212yesmaximal, complemented
9#103×D163C212yesmaximal, complemented
10C22⋊C8×D163C211yesmaximal, characteristic
11#483×C163C211yesmaximal, characteristic, complemented
12C2×Q8×D163C2211yescharacteristic
13C22×C4×D163—21no—
14C22×C4×D163C2211yescharacteristic
15C2×C8×D163C2212yes—
16#19104715C2211yescharacteristic
17#19104714C2211yescharacteristic
18#19104713—21no—
19#19104712—21no—
20#19104711C2211yescharacteristic
21C2×C4⋊Dic163C2211yescharacteristic
22C2×Dic163⋊C4—21no—
23C4⋊C4×D163—21no—
24C4⋊C4×D163—21no—
25C4⋊C4×D163—21no—
26C4⋊C4×D163C2211yescharacteristic
27C4⋊C4×D163C2212yes—
28C4⋊C4×D163C2212yes—
29C22⋊C4×D163—21no—
30#19104667C2212yescomplemented
31#19104666C2212yescomplemented
32#19104666C2212yescomplemented
33#19104660C2212yescomplemented
34#19104659C2212yescomplemented
35#19104658C2212yescomplemented
36C22⋊(C163⋊C8)C2211yescharacteristic
37(C2×D163)⋊C8C2212yes—
38C22⋊Q8×C163C2211yescharacteristic
39C2×C4⋊C4×C163C2211yescharacteristic
40#106×C163C2212yescomplemented
41#103×C163C2212yescomplemented
42C22⋊C8×C163C2211yescharacteristic
43C23×D163D411yescharacteristic
44C2×Dic326—21no—
45C2×Dic326C2311yescharacteristic
46Q8×D163—24no—
47C22×Dic163—21no—
48C22×Dic163D411yescharacteristic
49C2×C4×D163—24no—
50C2×C4×D163—22no—
51C2×C4×D163—22no—
52C2×C4×D163—21no—
53C2×C4×D163—21no—
54C2×C4×D163—44no—
55C2×C4×D163D411yescharacteristic
56C2×C4×D163D411yescharacteristic
57C2×C4×D163C2311yescharacteristic
58C2×C4×D163C2311yescharacteristic
59C2×C163⋊C8C2312yes—
60C8×D163—24no—
61C4⋊Dic163—21no—
62C4⋊Dic163—21no—
63C4⋊Dic163C2312yes—
64C4⋊Dic163C2311yescharacteristic
65Dic163⋊C4—22no—
66Dic163⋊C4—22no—
67Dic163⋊C4—21no—
68Dic163⋊C4—21no—
69Dic163⋊C4—21no—
70C22⋊Dic163—21no—
71(C2×D163)⋊C4—21no—
72(C2×D163)⋊C4—21no—
73C2×Q8×C163C2311yescharacteristic
74C22×C4×C163—21no—
75C22×C4×C163C2311yescharacteristic
76C2×C8×C163C2312yes—
77C4⋊C4×C163—21no—
78C4⋊C4×C163—21no—
79C4⋊C4×C163C2312yes—
80C4⋊C4×C163C2311yescharacteristic
81C22⋊C4×C163—21no—
82C22×D163—22no—
83C22×D163—22no—
84C22×D163SD1614yes—
85C22×D163C2×D411yescharacteristic
86C22×D163C2×D411yescharacteristic
87Dic326—22no—
88Dic326—42no—
89C2×Dic163—22no—
90C2×Dic163—21no—
91C2×Dic163—21no—
92C2×Dic163—22no—
93C2×Dic163—42no—
94C2×Dic163C2×D411yescharacteristic
95C2×Dic163C2×D411yescharacteristic
96C4×D163—22no—
97C4×D163—22no—
98C4×D163—22no—
99C4×D163—42no—
100C4×D163—44no—
101C4×D163—44no—
102C4×D163—42no—
103C4×D163#4114yes—
104C163⋊C8—22no—
105C23×C163C2×D411yescharacteristic
106Q8×C163—22no—
107C2×C4×C163—22no—
108C2×C4×C163—21no—
109C2×C4×C163—21no—
110C2×C4×C163—22no—
111C2×C4×C163—42no—
112C2×C4×C163C2×D411yescharacteristic
113C2×C4×C163C2411yescharacteristic
114C8×C163—22no—
115C22×C163—21no—
116C22×C163—21no—
117C22×C163C2×SD1612yes—
118C22×C163C22×D411yescharacteristic
119C2×D163—21no—
120C2×D163—21no—
121C2×D163—28no—
122C2×D163#12312yes—
123C2×D163C2×SD1612yes—
124C2×D163C2×SD1612yes—
125C2×D163#13712yes—
126C4×C163—21no—
127C4×C163—41no—
128C4×C163—42no—
129C4×C163—41no—
130C4×C163C2×#4112yes—
131Dic163—21no—
132Dic163—41no—
133Dic163—42no—
134Dic163—41no—
135Dic163#12312yes—
136C2×C163—22no—
137C2×C163C2×#12311yescharacteristic
138C2×C163C22×SD1611yescharacteristic
139C2×C163C2×#13711yescharacteristic
140D163—22no—
141D163#48314yesdirect product factor
142C163C2×#48311yescharacteristic, complemented, Sylow
143C2×#483—1631nomaximal, Sylow
144C2×C22⋊Q8—1631no—
145C22×C4⋊C4—1631no—
146#483—1631no—
147#483—1631no—
148#483—1632no—
149#483—1632no—
150#483—1631no—
151#483D16311yescharacteristic, direct product factor
152C2×#106—1632no—
153C2×#103—1632no—
154C2×C22⋊C8—1631no—
155C22×Q8—1631no—
156C23×C4—3261no—
157C23×C4—1631no—
158C22×C8—1632no—
159C22⋊Q8—3261no—
160C22⋊Q8—3261no—
161C22⋊Q8—1631no—
162C22⋊Q8—1631no—
163C22⋊Q8—1631no—
164C22⋊Q8C2×D16311yescharacteristic
165C2×C4⋊C4—3261no—
166C2×C4⋊C4—3261no—
167C2×C4⋊C4—3261no—
168C2×C4⋊C4—3261no—
169C2×C4⋊C4—1631no—
170C2×C4⋊C4—1632no—
171C2×C4⋊C4—1632no—
172C2×C4⋊C4—1631no—
173C2×C4⋊C4C2×D16311yescharacteristic
174C2×C22⋊C4—3261no—
175#106—1632no—
176#106—1632no—
177#106—1632no—
178#106C2×D16312yescomplemented
179#103—1632no—
180#103—1632no—
181#103—1632no—
182#103C2×D16312yescomplemented
183C22⋊C8—1631no—
184C22⋊C8—1632no—
185C22⋊C8C2×D16311yescharacteristic
186C24—1631no—
187C2×Q8—3261no—
188C2×Q8—3264no—
189C2×Q8—1631no—
190C2×Q8C22×D16311yescharacteristic
191C22×C4—21no—
192C22×C4—3264no—
193C22×C4—3261no—
194C22×C4—3261no—
195C22×C4—3262no—
196C22×C4—3262no—
197C22×C4—3261no—
198C22×C4—6524no—
199C22×C4—1631no—
200C22×C4—1631no—
201C22×C4—1631no—
202C22×C4—1631no—
203C22×C4—1631no—
204C22×C4C22×D16311yescharacteristic
205C2×C8—3264no—
206C2×C8—1632no—
207C2×C8C22×D16312yes—
208C4⋊C4—21no—
209C4⋊C4—21no—
210C4⋊C4—3262no—
211C4⋊C4—3262no—
212C4⋊C4—3261no—
213C4⋊C4—3261no—
214C4⋊C4—3261no—
215C4⋊C4—3261no—
216C4⋊C4—3261no—
217C4⋊C4—1632no—
218C4⋊C4—1631no—
219C4⋊C4C22×D16312yes—
220C4⋊C4C22×D16311yescharacteristic
221C22⋊C4—21no—
222C22⋊C4—3261no—
223C22⋊C4—3261no—
224C22⋊C4—3261no—
225C23—3262no—
226C23—3262no—
227C23—1631no—
228C23—1634no—
229C23—1631no—
230C23D4×D16311yescharacteristic
231Q8—22no—
232Q8—3262no—
233Q8—6522no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—42no—
239C2×C4—3262no—
240C2×C4—3262no—
241C2×C4—3262no—
242C2×C4—3262no—
243C2×C4—3261no—
244C2×C4—3261no—
245C2×C4—3262no—
246C2×C4—6524no—
247C2×C4—6524no—
248C2×C4—6522no—
249C2×C4—6522no—
250C2×C4—6522no—
251C2×C4—1631no—
252C2×C4—1631no—
253C2×C4—1634no—
254C2×C4D4×D16311yescharacteristic
255C2×C4C23×D16311yescharacteristic
256C8—22no—
257C8—3262no—
258C22—21no—
259C22—21no—
260C22—3268no—
261C22—3261no—
262C22—3261no—
263C22—1632no—
264C22—1632no—
265C22—1632no—
266C22—1632no—
267C22SD16×D16312yes—
268C22C2×D4×D16311yescharacteristic
269C4—21no—
270C4—41no—
271C4—42no—
272C4—41no—
273C4—3261no—
274C4—6521no—
275C4—6522no—
276C4—6521no—
277C4—1632no—
278C4#41×D16312yes—
279C2—22no—
280C2—3262no—
281C2—1634no—
282C2#123×D16311yescharacteristic
283C2C2×SD16×D16311yescharacteristic
284C2#137×D16311yescharacteristic
subgroupG/H
centerC22C2×D4×D163
commutator, cosocleC2×C4×C163C24
FrattiniC2×C4C23×D163
Fitting#483×C163C2
socleC22×C163C22×D4
prime radicalC23×D163D4
hypercenter#483D163
hypocenterC163C2×#483
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
3. #23781997C2semidirect
4. #23781996C2semidirect
5. #23781995C2semidirect
6. #23781994C2semidirect
7. #23781993C2semidirect
8. #106×D163C2semidirect
9. #103×D163C2semidirect
11. #483×C163C2semidirect
30. #19104667C22semidirect
31. #19104666C22semidirect
32. #19104666C22semidirect
33. #19104660C22semidirect
34. #19104659C22semidirect
35. #19104658C22semidirect
40. #106×C163C22semidirect
41. #103×C163C22semidirect
141. D163#483direct (N × H)
142. C163C2×#483semidirect
151. #483D163direct (N × H)
178. #106C2×D163semidirect
182. #103C2×D163semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D1632
C2×C4⋊C4×D1632
#237819972
#237819962
#237819952
#237819942
#237819932
#106×D1632
#103×D1632
C22⋊C8×D1632
#483×C1632
C2×#483163