Finite Group Databasebeta

← #35227188

Subgroups — #35227188

Order 20864.

350 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23782387C211yesmaximal, characteristic, complemented
2#23782371C211yesmaximal, characteristic, complemented
3#23782022C211yesmaximal, characteristic, complemented
4#23782021C211yesmaximal, characteristic, complemented
5#23782014C211yesmaximal, characteristic, complemented
6#23781971C211yesmaximal, characteristic, complemented
7#23781954C211yesmaximal, characteristic, complemented
8#23781883C211yesmaximal, characteristic
9#23781881C211yesmaximal, characteristic
10#23781869C211yesmaximal, characteristic, complemented
11#23781789C211yesmaximal, characteristic, complemented
12C4×#14579686C211yesmaximal, characteristic, complemented
13#23781752C211yesmaximal, characteristic, complemented
14#23781747C211yesmaximal, characteristic
15#479×C163C211yesmaximal, characteristic, complemented
16C2×#14579688C2211yescharacteristic
17C2×#14579686C2211yescharacteristic
18C2×D1304C2211yescharacteristic
19#19104734C2211yescharacteristic
20#19104733C2211yescharacteristic
21#19104730—21no—
22#19104729—21no—
23#19104726C2211yescharacteristic
24#19104724C2211yescharacteristic
25#19104723C2211yescharacteristic
26#19104715—21no—
27#19104713—21no—
28#19104713—21no—
29#19104713—21no—
30C4×Dic326C2211yescharacteristic
31#19104700C2211yescharacteristic
32C4×D652C2211yescharacteristic
33#19104697C2211yescharacteristic
34#19104697C2211yescharacteristic
35#19104697C2211yescharacteristic
36#19104692—21no—
37C4⋊C4×D163—21no—
38#19104666C2211yescharacteristic
39Dic163⋊C8C2211yescharacteristic
40Dic163⋊C8C2211yescharacteristic
41#19104660C2211yescharacteristic
42#19104659C2211yescharacteristic
43#19104658C2211yescharacteristic
44#19104658C2211yescharacteristic
45#19104657C2211yescharacteristic
46#19104655C2211yescharacteristic
47#19104655C2211yescharacteristic
48#19104655C2211yescharacteristic
49C4×C163⋊C8C2211yescharacteristic
50C8×Dic163C2211yescharacteristic
51C8×Dic163C2211yescharacteristic
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×Dic326D411yescharacteristic
61C2×Dic326C2311yescharacteristic
62C2×D652C2311yescharacteristic
63C2×D652C2311yescharacteristic
64C2×C4×D163—21no—
65C2×C4×D163—21no—
66C2×C4×D163—21no—
67C2×C4×D163—21no—
68#14579688—22no—
69#14579686—22no—
70D1304—22no—
71C2×C163⋊C8C2311yescharacteristic
72C2×C163⋊C8C2311yescharacteristic
73C4⋊Dic163—21no—
74C4⋊Dic163D411yescharacteristic
75C4⋊Dic163C2311yescharacteristic
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—
88(C2×D163)⋊C4—21no—
89(C2×D163)⋊C4—21no—
90(C2×D163)⋊C4—21no—
91C4×Dic163—21no—
92C4×Dic163C2311yescharacteristic
93C4×Dic163C2311yescharacteristic
94C2×Q8×C163C2311yescharacteristic
95C2×C8×C163C2311yescharacteristic
96C2×C8×C163C2311yescharacteristic
97C4⋊C4×C163—21no—
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—
106C22×D163—21no—
107Dic326—22no—
108Dic326—21no—
109Dic326—21no—
110Dic326—81no—
111D652—21no—
112D652—21no—
113D652—21no—
114D652#4112yes—
115C2×Dic163—21no—
116C2×Dic163—21no—
117C2×Dic163C2×D411yescharacteristic
118C2×Dic163C2×D411yescharacteristic
119C2×Dic163C2×D411yescharacteristic
120C2×Dic163C2×D411yescharacteristic
121C4×D163—42no—
122C4×D163—42no—
123C4×D163—81no—
124C4×D163—81no—
125C163⋊C8—21no—
126C163⋊C8—21no—
127Q8×C163—21no—
128Q8×C163—21no—
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×D163—22no—
140C2×D163—41no—
141C2×D163—41no—
142C2×D163—41no—
143C2×D163—41no—
144C2×D163—41no—
145C4×C163—21no—
146C4×C163—21no—
147C4×C163—41no—
148C4×C163—41no—
149C4×C163—41no—
150C4×C163—41no—
151C4×C163C2×#4111yescharacteristic
152C4×C1632−1+411yescharacteristic
153Dic163—21no—
154Dic163—21no—
155Dic163—21no—
156Dic163—41no—
157Dic163—41no—
158Dic163#13512yes—
159C2×C163#54811yescharacteristic
160C2×C163C2×#13511yescharacteristic
161C2×C163#57711yescharacteristic
162D163—42no—
163D163—81no—
164C163#336011yescharacteristic, complemented, Sylow
165#3360—1631nomaximal, Sylow
166#556—1631no—
167#554—1631no—
168#488—1631no—
169#488—1631no—
170#487—1631no—
171#479—1631no—
172#479D16311yescharacteristic, complemented
173#476—1631no—
174#463—1631no—
175#463—1631no—
176#461—1631no—
177C8×Q8—1631no—
178C4×SD16—1631no—
179C4×SD16—1631no—
180C4×D8—1631no—
181C2×SD16—1631no—
182C2×SD16—1631no—
183C2×D8—1631no—
184C4⋊Q8—1631no—
185C4⋊Q8—1631no—
186#126—3261no—
187#126—3261no—
188#125—1631no—
189#125C2×D16311yescharacteristic
190#124—1631no—
191#124—1631no—
192C22⋊Q8—3261no—
193C22⋊Q8—3261no—
194C22⋊Q8—3261no—
195C22⋊Q8—3261no—
196C4×Q8—1631no—
197C4×Q8—1631no—
198C4×Q8C2×D16311yescharacteristic
199C4×D4—1631no—
200C4×D4—1631no—
201C4×D4—1631no—
202C4×D4—1631no—
203#117—3261no—
204C2×C4⋊C4—3261no—
205#107C2×D16311yescharacteristic
206#106—1631no—
207#106C2×D16311yescharacteristic
208C4⋊C8—1631no—
209C4⋊C8—1631no—
210C4⋊C8C2×D16311yescharacteristic
211#103—1631no—
212#103—1631no—
213#103—1631no—
214#103—1631no—
215#103C2×D16311yescharacteristic
216#103C2×D16311yescharacteristic
217#102—1631no—
218#102—1631no—
219#102—1631no—
220#102—1631no—
221C4×C8—1631no—
222C4×C8—1631no—
223C4×C8—1631no—
224C2×Q8—3261no—
225C2×Q8—1631no—
226C2×Q8—1631no—
227C2×Q8C22×D16311yescharacteristic
228C2×D4—1631no—
229C2×D4—1631no—
230C22×C4—3261no—
231C22×C4—3261no—
232C22×C4—3261no—
233C22×C4—3261no—
234SD16—3262no—
235SD16—3262no—
236D8—3262no—
237C2×C8—1631no—
238C2×C8—1631no—
239C2×C8C22×D16311yescharacteristic
240C2×C8C22×D16311yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—3261no—
245C4⋊C4—3261no—
246C4⋊C4—3261no—
247C4⋊C4—3261no—
248C4⋊C4—3261no—
249C4⋊C4—3261no—
250C4⋊C4—1631no—
251C4⋊C4—1631no—
252C4⋊C4—1631no—
253C4⋊C4—1631no—
254C4⋊C4C22×D16311yescharacteristic
255C4⋊C4C22×D16311yescharacteristic
256C4⋊C4C22×D16311yescharacteristic
257C22⋊C4—3261no—
258C22⋊C4—3261no—
259C22⋊C4—3261no—
260C22⋊C4—3261no—
261C22⋊C4—3261no—
262C22⋊C4—3261no—
263C22⋊C4—3261no—
264C22⋊C4—3261no—
265C42—21no—
266C42—3261no—
267C42—1631no—
268C42—1631no—
269C42C22×D16311yescharacteristic
270C23—3261no—
271C23—3261no—
272Q8—21no—
273Q8—21no—
274Q8—13041no—
275Q8—3262no—
276Q8—3261no—
277Q8—3261no—
278D4—3261no—
279D4—3261no—
280D4—3261no—
281D4—1632no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—13041no—
287C2×C4—13041no—
288C2×C4—3261no—
289C2×C4—3261no—
290C2×C4—6522no—
291C2×C4—6522no—
292C2×C4—1631no—
293C2×C4—1631no—
294C2×C4—1631no—
295C2×C4—1631no—
296C2×C4D4×D16311yescharacteristic
297C2×C4D4×D16311yescharacteristic
298C2×C4C23×D16311yescharacteristic
299C8—21no—
300C8—21no—
301C8—3261no—
302C8—3261no—
303C22—3262no—
304C22—6521no—
305C22—6521no—
306C22—6521no—
307C22—6521no—
308C22—6521no—
309C22C2×D4×D16311yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—3261no—
317C4—3261no—
318C4—3261no—
319C4—6521no—
320C4—6521no—
321C4—1632no—
322C4#41×D16311yescharacteristic
323C4#1910478311yescharacteristic
324C2—13041no—
325C2—6522no—
326C2#2378232511yescharacteristic
327C2#135×D16311yescharacteristic
328C2#2378247411yescharacteristic
subgroupG/H
centerC22C2×D4×D163
commutator, cosocleC2×C4×C163C24
FrattiniC2×C4C23×D163
Fitting#479×C163C2
socleC22×C163C22×D4
prime radicalC2×D1304C22
hypercenter#479D163
hypocenterC163#3360
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
1. #23782387C2semidirect
2. #23782371C2semidirect
3. #23782022C2semidirect
4. #23782021C2semidirect
5. #23782014C2semidirect
6. #23781971C2semidirect
7. #23781954C2semidirect
10. #23781869C2semidirect
11. #23781789C2semidirect
12. C4×#14579686C2semidirect
13. #23781752C2semidirect
15. #479×C163C2semidirect
164. C163#3360semidirect
172. #479D163semidirect

Maximal subgroups

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

subgroupindex
#237823872
#237823712
#237820222
#237820212
#237820142
#237819712
#237819542
#237818832
#237818812
#237818692
#237817892
C4×#145796862
#237817522
#237817472
#479×C1632
#3360163