Finite Group Databasebeta

← #35227279

Subgroups — #35227279

Order 20864.

338 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23782395C211yesmaximal, characteristic, complemented
2#23782387C211yesmaximal, characteristic
3#23782027C211yesmaximal, characteristic
4#23782026C211yesmaximal, characteristic
5#23782014C211yesmaximal, characteristic, complemented
6#23781954C211yesmaximal, characteristic
7#23781949C211yesmaximal, characteristic, complemented
8#23781890C211yesmaximal, characteristic
9#23781888C211yesmaximal, characteristic
10#23781874C211yesmaximal, characteristic, complemented
11#23781794C211yesmaximal, characteristic, complemented
12#23781771C211yesmaximal, characteristic, complemented
13#23781770C211yesmaximal, characteristic, complemented
14#23781752C211yesmaximal, characteristic
15#475×C163C211yesmaximal, characteristic, complemented
16C2×Dic652C2211yescharacteristic
17C2×#14579689C2211yescharacteristic
18C2×#14579688C2211yescharacteristic
19#19104734—21no—
20#19104734C2211yescharacteristic
21#19104734C2211yescharacteristic
22#19104733—21no—
23#19104733—21no—
24#19104733C2211yescharacteristic
25#19104730—21no—
26#19104729—21no—
27#19104724C2211yescharacteristic
28#19104723C2211yescharacteristic
29#19104713—21no—
30C4×Dic326C2211yescharacteristic
31C4×Dic326C2211yescharacteristic
32#19104700—21no—
33#19104700C2211yescharacteristic
34#19104700C2211yescharacteristic
35#19104700C2211yescharacteristic
36#19104697C2211yescharacteristic
37#19104692—21no—
38#19104666C2211yescharacteristic
39Dic163⋊C8C2211yescharacteristic
40Dic163⋊C8C2211yescharacteristic
41#19104660C2211yescharacteristic
42#19104659C2211yescharacteristic
43#19104658C2211yescharacteristic
44#19104658C2211yescharacteristic
45#19104658C2211yescharacteristic
46#19104657C2211yescharacteristic
47#19104655C2211yescharacteristic
48#19104655C2211yescharacteristic
49#19104646C2211yescharacteristic
50#19104645C2211yescharacteristic
51C8×Dic163C2211yescharacteristic
52C4⋊Q8×C163C2211yescharacteristic
53C4×Q8×C163C2211yescharacteristic
54#106×C163C2211yescharacteristic
55#106×C163C2211yescharacteristic
56C4⋊C8×C163C2211yescharacteristic
57#103×C163C2211yescharacteristic
58#103×C163C2211yescharacteristic
59C2×Dic326—21no—
60C2×Dic326—21no—
61C2×Dic326D411yescharacteristic
62C2×Dic326C2311yescharacteristic
63C2×Dic326C2311yescharacteristic
64C2×D652C2311yescharacteristic
65C2×C4×D163—21no—
66Dic652—22no—
67#14579689—22no—
68#14579688—22no—
69C2×C163⋊C8C2311yescharacteristic
70C2×C163⋊C8C2311yescharacteristic
71C4⋊Dic163D411yescharacteristic
72C4⋊Dic163C2311yescharacteristic
73Dic163⋊C4—21no—
74Dic163⋊C4—21no—
75Dic163⋊C4—21no—
76Dic163⋊C4—21no—
77Dic163⋊C4—21no—
78Dic163⋊C4—21no—
79Dic163⋊C4—21no—
80Dic163⋊C4—21no—
81Dic163⋊C4D411yescharacteristic
82Dic163⋊C4D411yescharacteristic
83(C2×D163)⋊C4—21no—
84(C2×D163)⋊C4—21no—
85(C2×D163)⋊C4—21no—
86(C2×D163)⋊C4—21no—
87(C2×D163)⋊C4—21no—
88C4×Dic163—21no—
89C4×Dic163—21no—
90C4×Dic163—21no—
91C4×Dic163—21no—
92C4×Dic163C2311yescharacteristic
93C4×Dic163C2311yescharacteristic
94C2×Q8×C163—21no—
95C2×Q8×C163C2311yescharacteristic
96C2×C8×C163C2311yescharacteristic
97C2×C8×C163C2311yescharacteristic
98C4⋊C4×C163—21no—
99C4⋊C4×C163—21no—
100C4⋊C4×C163C2311yescharacteristic
101C4⋊C4×C163C2311yescharacteristic
102C4⋊C4×C163C2311yescharacteristic
103C42×C163—21no—
104C42×C163C2311yescharacteristic
105C22×D163—21no—
106Dic326—21no—
107Dic326—22no—
108Dic326—21no—
109Dic326—21no—
110Dic326—81no—
111Dic326—81no—
112Dic326#4112yes—
113D652—21no—
114D652—21no—
115C2×Dic163—21no—
116C2×Dic163—21no—
117C2×Dic163—21no—
118C2×Dic163C2×D411yescharacteristic
119C2×Dic163C2×D411yescharacteristic
120C2×Dic163C2×D411yescharacteristic
121C2×Dic163C2×D411yescharacteristic
122C4×D163—42no—
123C163⋊C8—21no—
124C163⋊C8—21no—
125Q8×C163—21no—
126Q8×C163—21no—
127Q8×C163—81no—
128C2×C4×C163—21no—
129C2×C4×C163—21no—
130C2×C4×C163—21no—
131C2×C4×C163—21no—
132C2×C4×C163C2×D411yescharacteristic
133C2×C4×C163C2×D411yescharacteristic
134C2×C4×C163C2411yescharacteristic
135C8×C163—21no—
136C8×C163—21no—
137C22×C163C22×D411yescharacteristic
138C2×D163—41no—
139C2×D163—41no—
140C2×D163—41no—
141C4×C163—21no—
142C4×C163—21no—
143C4×C163—41no—
144C4×C163—41no—
145C4×C163—41no—
146C4×C163—41no—
147C4×C163C2×#4111yescharacteristic
148C4×C1632−1+411yescharacteristic
149Dic163—22no—
150Dic163—21no—
151Dic163—21no—
152Dic163—21no—
153Dic163—41no—
154Dic163—41no—
155Dic163#13712yes—
156C2×C163#54811yescharacteristic
157C2×C163C2×#13711yescharacteristic
158C2×C163#57711yescharacteristic
159D163—81no—
160C163#336911yescharacteristic, complemented, Sylow
161#3369—1631nomaximal, Sylow
162Q82—1631no—
163#556—1631no—
164#489—1631no—
165#489—1631no—
166#487—1631no—
167#476—1631no—
168#475—1631no—
169#475D16311yescharacteristic, complemented
170#464—1631no—
171#464—1631no—
172#462—1631no—
173#446—1631no—
174#441—1631no—
175#441—1631no—
176C4×SD16—1631no—
177C2×Q16—1631no—
178C2×Q16—1631no—
179C2×SD16—1631no—
180C4⋊Q8—3261no—
181C4⋊Q8—3261no—
182C4⋊Q8—3261no—
183C4⋊Q8—1631no—
184C4⋊Q8—1631no—
185C4⋊Q8—1631no—
186C4⋊Q8C2×D16311yescharacteristic
187#126—3261no—
188#126—3261no—
189#124—1631no—
190#124—1631no—
191C22⋊Q8—3261no—
192C4×Q8—3261no—
193C4×Q8—1631no—
194C4×Q8—1631no—
195C4×Q8—1631no—
196C4×Q8—1631no—
197C4×Q8—1631no—
198C4×Q8C2×D16311yescharacteristic
199C4×D4—1631no—
200#117—3261no—
201#106—1631no—
202#106C2×D16311yescharacteristic
203#106C2×D16311yescharacteristic
204C4⋊C8—1631no—
205C4⋊C8—1631no—
206C4⋊C8C2×D16311yescharacteristic
207#103—1631no—
208#103—1631no—
209#103—1631no—
210#103—1631no—
211#103—1631no—
212#103C2×D16311yescharacteristic
213#103C2×D16311yescharacteristic
214#102—1631no—
215#102—1631no—
216#102—1631no—
217#97—1631no—
218#97—1631no—
219C4×C8—1631no—
220C2×Q8—21no—
221C2×Q8—3261no—
222C2×Q8—3261no—
223C2×Q8—1631no—
224C2×Q8—1631no—
225C2×Q8—1631no—
226C2×Q8C22×D16311yescharacteristic
227C2×D4—1631no—
228C22×C4—3261no—
229Q16—3262no—
230Q16—3262no—
231SD16—3262no—
232C2×C8—1631no—
233C2×C8—1631no—
234C2×C8C22×D16311yescharacteristic
235C2×C8C22×D16311yescharacteristic
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—3261no—
239C4⋊C4—3261no—
240C4⋊C4—3261no—
241C4⋊C4—3261no—
242C4⋊C4—3261no—
243C4⋊C4—3261no—
244C4⋊C4—3261no—
245C4⋊C4—3261no—
246C4⋊C4—1631no—
247C4⋊C4—1631no—
248C4⋊C4—1631no—
249C4⋊C4—1631no—
250C4⋊C4C22×D16311yescharacteristic
251C4⋊C4C22×D16311yescharacteristic
252C4⋊C4C22×D16311yescharacteristic
253C22⋊C4—3261no—
254C22⋊C4—3261no—
255C22⋊C4—3261no—
256C22⋊C4—3261no—
257C22⋊C4—3261no—
258C42—21no—
259C42—3261no—
260C42—3261no—
261C42—3261no—
262C42—3261no—
263C42—1631no—
264C42—1631no—
265C42C22×D16311yescharacteristic
266C23—3261no—
267Q8—21no—
268Q8—21no—
269Q8—81no—
270Q8—13041no—
271Q8—13041no—
272Q8—3262no—
273Q8—3261no—
274Q8—3261no—
275Q8—3261no—
276Q8—1632no—
277D4—3261no—
278D4—3261no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—3261no—
284C2×C4—3261no—
285C2×C4—3261no—
286C2×C4—6522no—
287C2×C4—1631no—
288C2×C4—1631no—
289C2×C4—1631no—
290C2×C4—1631no—
291C2×C4D4×D16311yescharacteristic
292C2×C4D4×D16311yescharacteristic
293C2×C4C23×D16311yescharacteristic
294C8—21no—
295C8—21no—
296C8—3261no—
297C8—3261no—
298C22—6521no—
299C22—6521no—
300C22—6521no—
301C22C2×D4×D16311yescharacteristic
302C4—21no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—3261no—
309C4—3261no—
310C4—3261no—
311C4—3262no—
312C4—6521no—
313C4—6521no—
314C4—1632no—
315C4#41×D16311yescharacteristic
316C4#1910478311yescharacteristic
317C2—13041no—
318C2#2378232511yescharacteristic
319C2#137×D16311yescharacteristic
320C2#2378247111yescharacteristic
subgroupG/H
centerC22C2×D4×D163
commutator, cosocleC2×C4×C163C24
FrattiniC2×C4C23×D163
Fitting#475×C163C2
socleC22×C163C22×D4
prime radicalC2×D652C23
hypercenter#475D163
hypocenterC163#3369
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. #23782395C2semidirect
5. #23782014C2semidirect
7. #23781949C2semidirect
10. #23781874C2semidirect
11. #23781794C2semidirect
12. #23781771C2semidirect
13. #23781770C2semidirect
15. #475×C163C2semidirect
160. C163#3369semidirect
169. #475D163semidirect

Maximal subgroups

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

subgroupindex
#237823952
#237823872
#237820272
#237820262
#237820142
#237819542
#237819492
#237818902
#237818882
#237818742
#237817942
#237817712
#237817702
#237817522
#475×C1632
#3369163