Finite Group Databasebeta

← #35223639

Subgroups — #35223639

Order 20864.

314 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23782219C211yesmaximal, characteristic
2#23781796C211yesmaximal, characteristic, complemented
3#23781795C211yesmaximal, characteristic, complemented
4#23781794C211yesmaximal, characteristic, complemented
5#23781794C211yesmaximal, characteristic, complemented
6#23781793C211yesmaximal, characteristic, complemented
7#23781793C211yesmaximal, characteristic, complemented
8#23781792C211yesmaximal, characteristic, complemented
9#23781727C211yesmaximal, characteristic
10#23781725C211yesmaximal, characteristic
11#23781725C211yesmaximal, characteristic
12#23781724C211yesmaximal, characteristic
13#23781721C211yesmaximal, characteristic
14#23781720C211yesmaximal, characteristic
15#446×C163C211yesmaximal, characteristic, complemented
16#19104734C411yescharacteristic
17#19104733C411yescharacteristic
18#19104725C411yescharacteristic
19#19104725C411yescharacteristic
20#19104715C411yescharacteristic
21#19104713C411yescharacteristic
22#19104713C411yescharacteristic
23#19104711C411yescharacteristic
24C4×Dic326C2211yescharacteristic
25C4×Dic326C2211yescharacteristic
26C4×Dic326C2211yescharacteristic
27#19104692C2211yescharacteristic
28#19104692C2211yescharacteristic
29C42×D163C2211yescharacteristic
30C4⋊(C163⋊C8)C2211yescharacteristic
31C4⋊(C163⋊C8)C2211yescharacteristic
32C4⋊(C163⋊C8)C2211yescharacteristic
33Dic163⋊C8C2211yescharacteristic
34Dic163⋊C8C2211yescharacteristic
35Dic163⋊C8C2211yescharacteristic
36Dic163⋊C8C2211yescharacteristic
37Dic163⋊C8C2211yescharacteristic
38Dic163⋊C8C2211yescharacteristic
39(C2×D163)⋊C8C2211yescharacteristic
40(C2×D163)⋊C8C2211yescharacteristic
41(C2×D163)⋊C8C2211yescharacteristic
42(C2×D163)⋊C8C2211yescharacteristic
43#19104646C2211yescharacteristic
44#19104646C2211yescharacteristic
45#19104645C2211yescharacteristic
46#19104645C2211yescharacteristic
47#19104645C2211yescharacteristic
48#19104645C2211yescharacteristic
49C4×C163⋊C8C2211yescharacteristic
50C8×Dic163C2211yescharacteristic
51C8×Dic163C2211yescharacteristic
52C4×Q8×C163C2211yescharacteristic
53C4⋊C8×C163C2211yescharacteristic
54C4⋊C8×C163C2211yescharacteristic
55C4⋊C8×C163C2211yescharacteristic
56#97×C163C2211yescharacteristic
57#97×C163C2211yescharacteristic
58C4×C8×C163C2211yescharacteristic
59C2×Dic326C2×C411yescharacteristic
60C2×Dic326C2×C411yescharacteristic
61C2×Dic326C2×C411yescharacteristic
62C2×C4×D163C2×C411yescharacteristic
63C2×C4×D163C2×C411yescharacteristic
64C2×C4×D163C2311yescharacteristic
65C2×C163⋊C8C2311yescharacteristic
66C2×C163⋊C8C2311yescharacteristic
67C2×C163⋊C8C2311yescharacteristic
68C2×C163⋊C8C2311yescharacteristic
69C4⋊Dic163C2×C411yescharacteristic
70C4⋊Dic163C2×C411yescharacteristic
71C4⋊Dic163C2×C411yescharacteristic
72Dic163⋊C4C2×C411yescharacteristic
73Dic163⋊C4C2×C411yescharacteristic
74Dic163⋊C4C2×C411yescharacteristic
75Dic163⋊C4C2×C411yescharacteristic
76Dic163⋊C4C2×C411yescharacteristic
77Dic163⋊C4C2×C411yescharacteristic
78Dic163⋊C4C2×C411yescharacteristic
79Dic163⋊C4C2×C411yescharacteristic
80Dic163⋊C4C2×C411yescharacteristic
81Dic163⋊C4C2×C411yescharacteristic
82(C2×D163)⋊C4C2×C411yescharacteristic
83(C2×D163)⋊C4C2×C411yescharacteristic
84(C2×D163)⋊C4C2×C411yescharacteristic
85(C2×D163)⋊C4C2×C411yescharacteristic
86C4×Dic163C2×C411yescharacteristic
87C4×Dic163C2×C411yescharacteristic
88C4×Dic163C2311yescharacteristic
89C4×Dic163C2311yescharacteristic
90C4×Dic163C2311yescharacteristic
91C2×Q8×C163C2×C411yescharacteristic
92C2×C8×C163C2311yescharacteristic
93C2×C8×C163C2311yescharacteristic
94C2×C8×C163C2311yescharacteristic
95C2×C8×C163C2311yescharacteristic
96C4⋊C4×C163C2×C411yescharacteristic
97C4⋊C4×C163C2×C411yescharacteristic
98C4⋊C4×C163C2×C411yescharacteristic
99C42×C163C2311yescharacteristic
100C42×C163C2311yescharacteristic
101C42×C163C2311yescharacteristic
102C22×D163C22×C411yescharacteristic
103Dic326—41no—
104Dic326—41no—
105Dic326—41no—
106C2×Dic163C22×C411yescharacteristic
107C2×Dic163C22×C411yescharacteristic
108C2×Dic163C22×C411yescharacteristic
109C2×Dic163C22×C411yescharacteristic
110C2×Dic163C22×C411yescharacteristic
111C2×Dic163C22×C411yescharacteristic
112C2×Dic163C22×C411yescharacteristic
113C4×D163—21no—
114C4×D163—21no—
115C4×D163—41no—
116C4×D163—41no—
117C163⋊C8—21no—
118C163⋊C8—21no—
119C163⋊C8—21no—
120C163⋊C8—21no—
121Q8×C163—41no—
122C2×C4×C163C22×C411yescharacteristic
123C2×C4×C163C22×C411yescharacteristic
124C2×C4×C163C22×C411yescharacteristic
125C2×C4×C163C22×C411yescharacteristic
126C2×C4×C163C22×C411yescharacteristic
127C2×C4×C163C22×C411yescharacteristic
128C2×C4×C163C2411yescharacteristic
129C8×C163—21no—
130C8×C163—21no—
131C8×C163—21no—
132C8×C163—21no—
133C22×C163C23×C411yescharacteristic
134C2×D163—21no—
135C2×D163—21no—
136C2×D163—21no—
137C4×C163—21no—
138C4×C163—21no—
139C4×C163—21no—
140C4×C163—21no—
141C4×C163—21no—
142C4×C163—21no—
143C4×C1632−1+411yescharacteristic
144C4×C1632−1+411yescharacteristic
145Dic163—21no—
146Dic163—21no—
147Dic163—21no—
148Dic163—21no—
149Dic163—21no—
150Dic163—21no—
151Dic163—21no—
152C2×C163#51911yescharacteristic
153C2×C163#56811yescharacteristic
154C2×C163#56811yescharacteristic
155D163—41no—
156C163#298711yescharacteristic, complemented, Sylow
157#2987—1631nomaximal, Sylow
158#533—1631no—
159#446—1631no—
160#446—1631no—
161#446—1631no—
162#446—1631no—
163#446—1631no—
164#446—1631no—
165#446—1631no—
166#446D16311yescharacteristic, complemented
167#433—1631no—
168#433—1631no—
169#433—1631no—
170#433—1631no—
171#432—1631no—
172#432—1631no—
173C4⋊Q8—1631no—
174C4⋊Q8—1631no—
175#125—1631no—
176#125—1631no—
177C22⋊Q8—1631no—
178C22⋊Q8—1631no—
179C22⋊Q8—1631no—
180C22⋊Q8—1631no—
181C4×Q8—1631no—
182C4×Q8—1631no—
183C4×Q8—1631no—
184C4×Q8C2×D16311yescharacteristic
185#117—1631no—
186#117—1631no—
187C2×C42—1631no—
188C4⋊C8—1631no—
189C4⋊C8—1631no—
190C4⋊C8—1631no—
191C4⋊C8—1631no—
192C4⋊C8—1631no—
193C4⋊C8—1631no—
194C4⋊C8—1631no—
195C4⋊C8—1631no—
196C4⋊C8—1631no—
197C4⋊C8C2×D16311yescharacteristic
198C4⋊C8C2×D16311yescharacteristic
199C4⋊C8C2×D16311yescharacteristic
200C22⋊C8—1631no—
201C22⋊C8—1631no—
202C22⋊C8—1631no—
203C22⋊C8—1631no—
204#97—1631no—
205#97—1631no—
206#97—1631no—
207#97—1631no—
208#97—1631no—
209#97—1631no—
210#97C2×D16311yescharacteristic
211#97C2×D16311yescharacteristic
212C4×C8—1631no—
213C4×C8—1631no—
214C4×C8—1631no—
215C4×C8C2×D16311yescharacteristic
216C2×Q8—1631no—
217C2×Q8—1631no—
218C2×Q8—1631no—
219C2×Q8C4×D16311yescharacteristic
220C22×C4—1631no—
221C22×C4—1631no—
222C22×C4—1631no—
223C2×C8—1631no—
224C2×C8—1631no—
225C2×C8—1631no—
226C2×C8—1631no—
227C2×C8C22×D16311yescharacteristic
228C2×C8C22×D16311yescharacteristic
229C2×C8C22×D16311yescharacteristic
230C2×C8C22×D16311yescharacteristic
231C4⋊C4—1631no—
232C4⋊C4—1631no—
233C4⋊C4—1631no—
234C4⋊C4—1631no—
235C4⋊C4—1631no—
236C4⋊C4—1631no—
237C4⋊C4—1631no—
238C4⋊C4—1631no—
239C4⋊C4—1631no—
240C4⋊C4—1631no—
241C4⋊C4—1631no—
242C4⋊C4—1631no—
243C4⋊C4—1631no—
244C4⋊C4C4×D16311yescharacteristic
245C4⋊C4C4×D16311yescharacteristic
246C4⋊C4C4×D16311yescharacteristic
247C22⋊C4—1631no—
248C22⋊C4—1631no—
249C22⋊C4—1631no—
250C22⋊C4—1631no—
251C42—1631no—
252C42—1631no—
253C42—1631no—
254C42—1631no—
255C42—1631no—
256C42C22×D16311yescharacteristic
257C42C22×D16311yescharacteristic
258C42C22×D16311yescharacteristic
259C23—1631no—
260Q8—41no—
261Q8—6521no—
262Q8—6521no—
263Q8—6521no—
264C2×C4—3261no—
265C2×C4—3261no—
266C2×C4—6521no—
267C2×C4—6521no—
268C2×C4—1631no—
269C2×C4—1631no—
270C2×C4—1631no—
271C2×C4—1631no—
272C2×C4—1631no—
273C2×C4—1631no—
274C2×C4—1631no—
275C2×C4C2×C4×D16311yescharacteristic
276C2×C4C2×C4×D16311yescharacteristic
277C2×C4C2×C4×D16311yescharacteristic
278C2×C4C2×C4×D16311yescharacteristic
279C2×C4C2×C4×D16311yescharacteristic
280C2×C4C2×C4×D16311yescharacteristic
281C2×C4C23×D16311yescharacteristic
282C8—21no—
283C8—21no—
284C8—21no—
285C8—21no—
286C8—3261no—
287C8—3261no—
288C8—3261no—
289C8—3261no—
290C22—3261no—
291C22—3261no—
292C22—3261no—
293C22C22×C4×D16311yescharacteristic
294C4—21no—
295C4—21no—
296C4—21no—
297C4—21no—
298C4—21no—
299C4—21no—
300C4—3261no—
301C4—3261no—
302C4—3261no—
303C4—3261no—
304C4—3261no—
305C4—3261no—
306C4—3261no—
307C4#1910478211yescharacteristic
308C4#1910478311yescharacteristic
309C2—6521no—
310C2#2378214111yescharacteristic
311C2#2378243011yescharacteristic
312C2#2378243111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D163
commutator, socleC22×C163C23×C4
Fitting#446×C163C2
prime radicalC22×D163C22×C4
cosocleC2×C4×C163C24
hypercenter#446D163
hypocenterC163#2987
LCSG ▷ C22×C163 ▷ C163
UCSC1 ◁ C2×C4 ◁ #446

Complements

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

NH ≅ G/Ntype
2. #23781796C2semidirect
3. #23781795C2semidirect
4. #23781794C2semidirect
5. #23781794C2semidirect
6. #23781793C2semidirect
7. #23781793C2semidirect
8. #23781792C2semidirect
15. #446×C163C2semidirect
156. C163#2987semidirect
166. #446D163semidirect

Maximal subgroups

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

subgroupindex
#237822192
#237817962
#237817952
#237817942
#237817932
#237817922
#237817272
#237817252
#237817242
#237817212
#237817202
#446×C1632
#2987163