Finite Group Databasebeta

← #35223693

Subgroups — #35223693

Order 20864.

364 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23782195C211yesmaximal, characteristic
2#23781794C211yesmaximal, characteristic, complemented
3C8×Dic326C211yesmaximal, characteristic, complemented
4#23781740C211yesmaximal, characteristic, complemented
5#23781737C211yesmaximal, characteristic, complemented
6#23781736C211yesmaximal, characteristic, complemented
7C8×C22⋊D163C211yesmaximal, characteristic, complemented
8(C22⋊D163)⋊C8C211yesmaximal, characteristic, complemented
9#23781724C211yesmaximal, characteristic, complemented
10#23781723C211yesmaximal, characteristic, complemented
11#23781715C211yesmaximal, characteristic, complemented
12#23781691C211yesmaximal, characteristic, complemented
13#23781690C211yesmaximal, characteristic, complemented
14C2×Dic163⋊C8C211yesmaximal, characteristic, complemented
15C8×D4×C163C211yesmaximal, characteristic, complemented
16C2×#14579683C2211yescharacteristic
17C2×#14579682C2211yescharacteristic
18C22×C163⋊C8C2211yescharacteristic
19C2×C8×D163C2211yescharacteristic
20#19104730C411yescharacteristic
21#19104728C411yescharacteristic
22#19104725C411yescharacteristic
23#19104721C411yescharacteristic
24#19104719C411yescharacteristic
25#19104716C411yescharacteristic
26#19104712C411yescharacteristic
27#19104707C411yescharacteristic
28C4×Dic326C2211yescharacteristic
29C4×C22⋊D163C2211yescharacteristic
30C4×C22⋊D163C2211yescharacteristic
31#19104694C2211yescharacteristic
32#19104692C2211yescharacteristic
33C2×C4×Dic163C2211yescharacteristic
34C4⋊(C163⋊C8)C2211yescharacteristic
35Dic163⋊C8C2211yescharacteristic
36Dic163⋊C8C2211yescharacteristic
37Dic163⋊C8C2211yescharacteristic
38Dic163⋊C8C2211yescharacteristic
39Dic163⋊C8C2211yescharacteristic
40Dic163⋊C8C2211yescharacteristic
41Dic163⋊C8C2211yescharacteristic
42Dic163⋊C8C2211yescharacteristic
43C22⋊(C163⋊C8)C2211yescharacteristic
44C22⋊(C163⋊C8)C2211yescharacteristic
45(C2×D163)⋊C8C2211yescharacteristic
46(C2×D163)⋊C8C2211yescharacteristic
47#19104646C2211yescharacteristic
48#19104645C2211yescharacteristic
49C8×Dic163C2211yescharacteristic
50C8×Dic163C2211yescharacteristic
51C8×Dic163C2211yescharacteristic
52C22×C8×C163C2211yescharacteristic
53C22×C8×C163C2211yescharacteristic
54C4×D4×C163C2211yescharacteristic
55C4⋊C8×C163C2211yescharacteristic
56C22⋊C8×C163C2211yescharacteristic
57C22⋊C8×C163C2211yescharacteristic
58C4×C8×C163C2211yescharacteristic
59C2×Dic326C2×C411yescharacteristic
60C2×C22⋊D163C2×C411yescharacteristic
61C2×C22⋊D163C2×C411yescharacteristic
62C22×Dic163C2×C411yescharacteristic
63C22×Dic163C2×C411yescharacteristic
64C2×C4×D163C2311yescharacteristic
65#14579683—41no—
66#14579682—41no—
67C2×C163⋊C8—41no—
68C2×C163⋊C8C2311yescharacteristic
69C2×C163⋊C8C2311yescharacteristic
70C2×C163⋊C8C2311yescharacteristic
71C2×C163⋊C8C2311yescharacteristic
72C8×D163—41no—
73C4⋊Dic163C2×C411yescharacteristic
74C4⋊Dic163C2×C411yescharacteristic
75C4⋊Dic163C2×C411yescharacteristic
76Dic163⋊C4C2×C411yescharacteristic
77Dic163⋊C4C2×C411yescharacteristic
78Dic163⋊C4C2×C411yescharacteristic
79Dic163⋊C4C2×C411yescharacteristic
80Dic163⋊C4C2×C411yescharacteristic
81Dic163⋊C4C2×C411yescharacteristic
82C22⋊Dic163C2×C411yescharacteristic
83C22⋊Dic163C2×C411yescharacteristic
84C22⋊Dic163C2×C411yescharacteristic
85C22⋊Dic163C2×C411yescharacteristic
86(C2×D163)⋊C4C2×C411yescharacteristic
87(C2×D163)⋊C4C2×C411yescharacteristic
88(C2×D163)⋊C4C2×C411yescharacteristic
89(C2×D163)⋊C4C2×C411yescharacteristic
90C4×Dic163C2×C411yescharacteristic
91C4×Dic163C2×C411yescharacteristic
92C4×Dic163C2311yescharacteristic
93C4×Dic163C2311yescharacteristic
94C4×Dic163C2311yescharacteristic
95C2×D4×C163C2×C411yescharacteristic
96C22×C4×C163C2311yescharacteristic
97C22×C4×C163C2311yescharacteristic
98C2×C8×C163—41no—
99C2×C8×C163—41no—
100C2×C8×C163C2311yescharacteristic
101C2×C8×C163C2311yescharacteristic
102C2×C8×C163C2311yescharacteristic
103C2×C8×C163C2311yescharacteristic
104C4⋊C4×C163C2×C411yescharacteristic
105C22⋊C4×C163C2×C411yescharacteristic
106C22⋊C4×C163C2×C411yescharacteristic
107C42×C163C2311yescharacteristic
108C22×D163C22×C411yescharacteristic
109Dic326—22no—
110C22⋊D163—22no—
111C22⋊D163—22no—
112C2×Dic163—22no—
113C2×Dic163—22no—
114C2×Dic163C22×C411yescharacteristic
115C2×Dic163C22×C411yescharacteristic
116C2×Dic163C22×C411yescharacteristic
117C2×Dic163C22×C411yescharacteristic
118C2×Dic163C22×C411yescharacteristic
119C2×Dic163C22×C411yescharacteristic
120C2×Dic163C22×C411yescharacteristic
121C4×D163—21no—
122C4×D163—21no—
123C163⋊C8—21no—
124C163⋊C8—21no—
125C163⋊C8—21no—
126C163⋊C8—21no—
127C23×C163C22×C411yescharacteristic
128C23×C163C22×C411yescharacteristic
129D4×C163—22no—
130C2×C4×C163—21no—
131C2×C4×C163—21no—
132C2×C4×C163—21no—
133C2×C4×C163—21no—
134C2×C4×C163C22×C411yescharacteristic
135C2×C4×C163C22×C411yescharacteristic
136C2×C4×C163C22×C411yescharacteristic
137C2×C4×C163C22×C411yescharacteristic
138C2×C4×C163C2411yescharacteristic
139C8×C163—21no—
140C8×C163—21no—
141C8×C163—21no—
142C8×C163—21no—
143C22×C163—21no—
144C22×C163—21no—
145C22×C163—21no—
146C22×C163—21no—
147C22×C163—21no—
148C22×C163#13112yes—
149C22×C163C23×C411yescharacteristic
150C2×D163—21no—
151C2×D163—21no—
152C2×D163—21no—
153C4×C163—21no—
154C4×C163—21no—
155C4×C163—21no—
156C4×C163—21no—
157C4×C163H(5,𝔽2)11yescharacteristic
158C4×C1632−1+411yescharacteristic
159Dic163—21no—
160Dic163—21no—
161Dic163—21no—
162Dic163—21no—
163Dic163—21no—
164Dic163—21no—
165Dic163#13112yes—
166C2×C163—22no—
167C2×C163—41no—
168C2×C163#52011yescharacteristic
169C2×C163C2×#13111yescharacteristic
170C2×C163C2×#13111yescharacteristic
171D163—41no—
172C163#299411yescharacteristic, complemented, Sylow
173#2994—1631nomaximal, Sylow
174#529—1631no—
175#446—1631no—
176C8×Q8—1631no—
177#436—1631no—
178#435—1631no—
179#435—1631no—
180C8×D4—1631no—
181C8×D4—1631no—
182C8×D4D16311yescharacteristic, complemented
183#433—1631no—
184#433—1631no—
185#431—1631no—
186#424—1631no—
187#424—1631no—
188C2×C4⋊C8—1631no—
189C2×M16—1631no—
190C2×M16—1631no—
191C22×C8—1631no—
192C22×C8—1631no—
193C22×C8C2×D16311yescharacteristic
194C22×C8C2×D16311yescharacteristic
195#126—1631no—
196#126—1631no—
197#125—1631no—
198#124—1631no—
199#123—1631no—
200#123—1631no—
201C22⋊Q8—1631no—
202#121—1631no—
203C4×Q8—1631no—
204C4×D4—1631no—
205C4×D4—1631no—
206C4×D4C2×D16311yescharacteristic
207#117—1631no—
208#117—1631no—
209C2×C42—1631no—
210C4⋊C8—1631no—
211C4⋊C8—1631no—
212C4⋊C8—1631no—
213C4⋊C8—1631no—
214C4⋊C8—1631no—
215C4⋊C8—1631no—
216C4⋊C8—1631no—
217C4⋊C8—1631no—
218C4⋊C8—1631no—
219C4⋊C8C2×D16311yescharacteristic
220C22⋊C8—1631no—
221C22⋊C8—1631no—
222C22⋊C8—1631no—
223C22⋊C8—1631no—
224C22⋊C8C2×D16311yescharacteristic
225C22⋊C8C2×D16311yescharacteristic
226#97—1631no—
227#97—1631no—
228C4×C8—1631no—
229C4×C8—1631no—
230C4×C8—1631no—
231C4×C8C2×D16311yescharacteristic
232C2×Q8—1631no—
233C2×D4—1631no—
234C2×D4—1631no—
235C2×D4C4×D16311yescharacteristic
236C22×C4—1631no—
237C22×C4—1631no—
238C22×C4—1631no—
239C22×C4C22×D16311yescharacteristic
240C22×C4C22×D16311yescharacteristic
241M16—6521no—
242M16—6521no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—6521no—
246C2×C8—6521no—
247C2×C8—1631no—
248C2×C8—1631no—
249C2×C8—1631no—
250C2×C8—1631no—
251C2×C8C22×D16311yescharacteristic
252C2×C8C22×D16311yescharacteristic
253C2×C8C22×D16311yescharacteristic
254C2×C8C22×D16311yescharacteristic
255C4⋊C4—1631no—
256C4⋊C4—1631no—
257C4⋊C4—1631no—
258C4⋊C4—1631no—
259C4⋊C4—1631no—
260C4⋊C4—1631no—
261C4⋊C4—1631no—
262C4⋊C4—1631no—
263C4⋊C4—1631no—
264C4⋊C4C4×D16311yescharacteristic
265C22⋊C4—1631no—
266C22⋊C4—1631no—
267C22⋊C4—1631no—
268C22⋊C4—1631no—
269C22⋊C4—1631no—
270C22⋊C4—1631no—
271C22⋊C4—1631no—
272C22⋊C4—1631no—
273C22⋊C4C4×D16311yescharacteristic
274C22⋊C4C4×D16311yescharacteristic
275C42—1631no—
276C42—1631no—
277C42—1631no—
278C42—1631no—
279C42—1631no—
280C42C22×D16311yescharacteristic
281C23—1631no—
282C23C2×C4×D16311yescharacteristic
283C23C2×C4×D16311yescharacteristic
284Q8—3262no—
285D4—22no—
286D4—3262no—
287D4—3262no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—3262no—
293C2×C4—3262no—
294C2×C4—3261no—
295C2×C4—3261no—
296C2×C4—1631no—
297C2×C4—1631no—
298C2×C4—1631no—
299C2×C4—1631no—
300C2×C4—1631no—
301C2×C4—1631no—
302C2×C4—1631no—
303C2×C4C2×C4×D16311yescharacteristic
304C2×C4C2×C4×D16311yescharacteristic
305C2×C4C2×C4×D16311yescharacteristic
306C2×C4C2×C4×D16311yescharacteristic
307C2×C4C23×D16311yescharacteristic
308C8—21no—
309C8—21no—
310C8—21no—
311C8—21no—
312C8—3261no—
313C8—3261no—
314C8—3261no—
315C8—3261no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—3261no—
322C22—3261no—
323C22—3261no—
324C22#1910474112yes—
325C22C22×C4×D16311yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—3261no—
331C4—3261no—
332C4—3261no—
333C4—3261no—
334C4—3261no—
335C4—3261no—
336C4—1632no—
337C4#1910478011yescharacteristic
338C4#1910478211yescharacteristic
339C2—22no—
340C2—41no—
341C2—6521no—
342C2#2378214411yescharacteristic
343C2#131×D16311yescharacteristic
344C2C2×#1910474111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D163
commutator, socleC22×C163C23×C4
FittingC8×D4×C163C2
prime radical#19104707C4
cosocleC2×C4×C163C24
hypercenterC8×D4D163
hypocenterC163#2994
LCSG ▷ C22×C163 ▷ C163
UCSC1 ◁ C2×C4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
2. #23781794C2semidirect
3. C8×Dic326C2semidirect
4. #23781740C2semidirect
5. #23781737C2semidirect
6. #23781736C2semidirect
7. C8×C22⋊D163C2semidirect
8. (C22⋊D163)⋊C8C2semidirect
9. #23781724C2semidirect
10. #23781723C2semidirect
11. #23781715C2semidirect
12. #23781691C2semidirect
13. #23781690C2semidirect
14. C2×Dic163⋊C8C2semidirect
15. C8×D4×C163C2semidirect
172. C163#2994semidirect
182. C8×D4D163semidirect

Maximal subgroups

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

subgroupindex
#237821952
#237817942
C8×Dic3262
#237817402
#237817372
#237817362
C8×C22⋊D1632
(C22⋊D163)⋊C82
#237817242
#237817232
#237817152
#237816912
#237816902
C2×Dic163⋊C82
C8×D4×C1632
#2994163