Finite Group Databasebeta

← #479×D163 #35224309

Subgroups — #479×D163 #35224309

Order 20864.

384 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#125×D163C211yesmaximal, characteristic
2C4×Q8×D163C211yesmaximal, characteristic
3#23781975C211yesmaximal, characteristic, complemented
4#23781974C211yesmaximal, characteristic, complemented
5#23781973C211yesmaximal, characteristic, complemented
6#23781972C211yesmaximal, characteristic, complemented
7#23781971C211yesmaximal, characteristic, complemented
8#23781970C211yesmaximal, characteristic, complemented
9#23781969C211yesmaximal, characteristic, complemented
10#107×D163C211yesmaximal, characteristic
11#106×D163C211yesmaximal, characteristic
12C4⋊C8×D163C211yesmaximal, characteristic
13#103×D163C211yesmaximal, characteristic
14#103×D163C211yesmaximal, characteristic
15#479×C163C211yesmaximal, characteristic, complemented
16C2×Q8×D163C2211yescharacteristic
17C2×C8×D163C2211yescharacteristic
18C2×C8×D163C2211yescharacteristic
19#19104727C2211yescharacteristic
20#19104726C2211yescharacteristic
21#19104726C2211yescharacteristic
22#19104725—21no—
23#19104725—21no—
24Q8×Dic163C2211yescharacteristic
25C4×Dic326—21no—
26C4×Dic326C2211yescharacteristic
27#19104700—21no—
28#19104700C2211yescharacteristic
29C4⋊C4×D163—21no—
30C4⋊C4×D163—21no—
31C4⋊C4×D163—21no—
32C4⋊C4×D163C2211yescharacteristic
33C4⋊C4×D163C2211yescharacteristic
34C4⋊C4×D163C2211yescharacteristic
35C42×D163—21no—
36C42×D163C2211yescharacteristic
37#19104669C2211yescharacteristic
38#19104668C2211yescharacteristic
39#19104668C2211yescharacteristic
40#19104667C2211yescharacteristic
41#19104666C2211yescharacteristic
42#19104666C2211yescharacteristic
43C4⋊(C163⋊C8)C2211yescharacteristic
44Dic163⋊C8C2211yescharacteristic
45Dic163⋊C8C2211yescharacteristic
46#19104660C2211yescharacteristic
47#19104660C2211yescharacteristic
48#19104659C2211yescharacteristic
49#19104659C2211yescharacteristic
50#19104658C2211yescharacteristic
51#19104658C2211yescharacteristic
52#125×C163C2211yescharacteristic
53C4×Q8×C163C2211yescharacteristic
54#107×C163C2211yescharacteristic
55#106×C163C2211yescharacteristic
56C4⋊C8×C163C2211yescharacteristic
57#103×C163C2211yescharacteristic
58#103×C163C2211yescharacteristic
59C2×Dic326—21no—
60C2×Dic326C2311yescharacteristic
61Q8×D163—22no—
62Q8×D163Q814yes—
63C2×C4×D163—21no—
64C2×C4×D163—21no—
65C2×C4×D163—21no—
66C2×C4×D163—21no—
67C2×C4×D163D411yescharacteristic
68C2×C4×D163D411yescharacteristic
69C2×C4×D163C2311yescharacteristic
70C2×C163⋊C8C2311yescharacteristic
71C2×C163⋊C8C2311yescharacteristic
72C8×D163—22no—
73C8×D163—22no—
74C4⋊Dic163—21no—
75C4⋊Dic163—21no—
76C4⋊Dic163—21no—
77C4⋊Dic163C2311yescharacteristic
78C4⋊Dic163C2311yescharacteristic
79C4⋊Dic163C2311yescharacteristic
80Dic163⋊C4—21no—
81Dic163⋊C4—21no—
82Dic163⋊C4—21no—
83Dic163⋊C4—21no—
84Dic163⋊C4—21no—
85Dic163⋊C4—21no—
86Dic163⋊C4—21no—
87Dic163⋊C4—21no—
88Dic163⋊C4—21no—
89C4×Dic163—21no—
90C4×Dic163—21no—
91C4×Dic163—21no—
92C4×Dic163D411yescharacteristic
93C4×Dic163D411yescharacteristic
94C4×Dic163C2311yescharacteristic
95C2×Q8×C163C2311yescharacteristic
96C2×C8×C163C2311yescharacteristic
97C2×C8×C163C2311yescharacteristic
98C4⋊C4×C163—21no—
99C4⋊C4×C163—21no—
100C4⋊C4×C163—21no—
101C4⋊C4×C163C2311yescharacteristic
102C4⋊C4×C163C2311yescharacteristic
103C4⋊C4×C163C2311yescharacteristic
104C42×C163—21no—
105C42×C163C2311yescharacteristic
106C22×D163C2×D411yescharacteristic
107Dic326—21no—
108Dic326—24no—
109Dic326C2×Q812yes—
110C2×Dic163—21no—
111C2×Dic163—21no—
112C2×Dic163—21no—
113C2×Dic163—21no—
114C2×Dic163C2×D411yescharacteristic
115C2×Dic163C2×D411yescharacteristic
116C2×Dic163C2×D411yescharacteristic
117C4×D163—24no—
118C4×D163—22no—
119C4×D163—22no—
120C4×D163—42no—
121C4×D163—42no—
122C4×D163—42no—
123C4×D163C2×Q812yes—
124C4×D163#4112yes—
125C163⋊C8—21no—
126C163⋊C8—21no—
127Q8×C163—21no—
128Q8×C163C2×Q812yes—
129C2×C4×C163—21no—
130C2×C4×C163—21no—
131C2×C4×C163—21no—
132C2×C4×C163—21no—
133C2×C4×C163C2×D411yescharacteristic
134C2×C4×C163C2×D411yescharacteristic
135C2×C4×C163C2411yescharacteristic
136C8×C163—21no—
137C8×C163—21no—
138C22×C163C22×D411yescharacteristic
139C2×D163C22⋊Q812yes—
140C2×D163#13512yes—
141C2×D163#13712yes—
142C4×C163—22no—
143C4×C163—21no—
144C4×C163—21no—
145C4×C163—41no—
146C4×C163—41no—
147C4×C163—41no—
148C4×C163C22×Q811yescharacteristic
149C4×C163C2×#4111yescharacteristic
150Dic163—22no—
151Dic163—21no—
152Dic163—21no—
153Dic163—41no—
154Dic163—41no—
155Dic163—41no—
156Dic163C22⋊Q812yes—
157C2×C163C2×C22⋊Q811yescharacteristic
158C2×C163C2×#13511yescharacteristic
159C2×C163C2×#13711yescharacteristic
160D163#47914yesdirect product factor
161C163C2×#47911yescharacteristic, complemented, Sylow
162C2×#479—1631nomaximal, Sylow
163C2×#125—1631no—
164C2×C4×Q8—1631no—
165#479—1631no—
166#479—1631no—
167#479—1631no—
168#479—1631no—
169#479—1631no—
170#479—1631no—
171#479—1631no—
172#479D16311yescharacteristic, direct product factor
173C2×#107—1631no—
174C2×#106—1631no—
175C2×C4⋊C8—1631no—
176C2×#103—1631no—
177C2×#103—1631no—
178C22×Q8—1631no—
179C22×C8—1631no—
180C22×C8—1631no—
181#125—3261no—
182#125—3261no—
183#125—1631no—
184#125—1631no—
185#125—1631no—
186#125C2×D16311yescharacteristic
187C4×Q8—3261no—
188C4×Q8—3261no—
189C4×Q8—1631no—
190C4×Q8—1631no—
191C4×Q8—1631no—
192C4×Q8C2×D16311yescharacteristic
193C2×C4⋊C4—3261no—
194C2×C4⋊C4—3261no—
195C2×C4⋊C4—3261no—
196C2×C4⋊C4—1631no—
197C2×C4⋊C4—1631no—
198C2×C4⋊C4—1631no—
199C2×C42—3261no—
200C2×C42—1631no—
201#107—1631no—
202#107—1631no—
203#107—1631no—
204#107C2×D16311yescharacteristic
205#106—1631no—
206#106—1631no—
207#106—1631no—
208#106C2×D16311yescharacteristic
209C4⋊C8—1631no—
210C4⋊C8—1631no—
211C4⋊C8—1631no—
212C4⋊C8C2×D16311yescharacteristic
213#103—1631no—
214#103—1631no—
215#103—1631no—
216#103—1631no—
217#103—1631no—
218#103—1631no—
219#103C2×D16311yescharacteristic
220#103C2×D16311yescharacteristic
221C2×Q8—3261no—
222C2×Q8—3262no—
223C2×Q8—1634no—
224C2×Q8—1631no—
225C2×Q8C22×D16311yescharacteristic
226C22×C4—3261no—
227C22×C4—3261no—
228C22×C4—3261no—
229C22×C4—3261no—
230C22×C4—1631no—
231C22×C4—1631no—
232C22×C4—1631no—
233C2×C8—3262no—
234C2×C8—3262no—
235C2×C8—1631no—
236C2×C8—1631no—
237C2×C8C22×D16311yescharacteristic
238C2×C8C22×D16311yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—3261no—
243C4⋊C4—3261no—
244C4⋊C4—3261no—
245C4⋊C4—3261no—
246C4⋊C4—3261no—
247C4⋊C4—3261no—
248C4⋊C4—3261no—
249C4⋊C4—3261no—
250C4⋊C4—3261no—
251C4⋊C4—3261no—
252C4⋊C4—3261no—
253C4⋊C4—3261no—
254C4⋊C4—1631no—
255C4⋊C4—1631no—
256C4⋊C4—1631no—
257C4⋊C4C22×D16311yescharacteristic
258C4⋊C4C22×D16311yescharacteristic
259C4⋊C4C22×D16311yescharacteristic
260C42—21no—
261C42—3261no—
262C42—3261no—
263C42—3261no—
264C42—1631no—
265C42—1631no—
266C42—1631no—
267C42C22×D16311yescharacteristic
268C23—1631no—
269Q8—21no—
270Q8—3264no—
271Q8—3261no—
272Q8—1632no—
273Q8Q8×D16312yes—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—3264no—
279C2×C4—3262no—
280C2×C4—3262no—
281C2×C4—3261no—
282C2×C4—3261no—
283C2×C4—3261no—
284C2×C4—3261no—
285C2×C4—6522no—
286C2×C4—6522no—
287C2×C4—6522no—
288C2×C4—1631no—
289C2×C4—1631no—
290C2×C4—1631no—
291C2×C4—1632no—
292C2×C4—1632no—
293C2×C4D4×D16311yescharacteristic
294C2×C4D4×D16311yescharacteristic
295C2×C4C23×D16311yescharacteristic
296C8—21no—
297C8—21no—
298C8—3261no—
299C8—3261no—
300C22—1632no—
301C22—1632no—
302C22—1632no—
303C22C2×D4×D16311yescharacteristic
304C4—22no—
305C4—21no—
306C4—21no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—3262no—
311C4—3261no—
312C4—3261no—
313C4—6521no—
314C4—6521no—
315C4—6521no—
316C4—1632no—
317C4C2×Q8×D16311yescharacteristic
318C4#41×D16311yescharacteristic
319C2—1634no—
320C2C22⋊Q8×D16311yescharacteristic
321C2#135×D16311yescharacteristic
322C2#137×D16311yescharacteristic
subgroupG/H
centerC22C2×D4×D163
commutator, cosocleC2×C4×C163C24
FrattiniC2×C4C23×D163
Fitting#479×C163C2
socleC22×C163C22×D4
prime radicalC22×D163C2×D4
hypercenter#479D163
hypocenterC163C2×#479
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
3. #23781975C2semidirect
4. #23781974C2semidirect
5. #23781973C2semidirect
6. #23781972C2semidirect
7. #23781971C2semidirect
8. #23781970C2semidirect
9. #23781969C2semidirect
15. #479×C163C2semidirect
160. D163#479direct (N × H)
161. C163C2×#479semidirect
172. #479D163direct (N × H)

Maximal subgroups

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

subgroupindex
#125×D1632
C4×Q8×D1632
#237819752
#237819742
#237819732
#237819722
#237819712
#237819702
#237819692
#107×D1632
#106×D1632
C4⋊C8×D1632
#103×D1632
#479×C1632
C2×#479163