Finite Group Databasebeta

← #35223472

Subgroups — #35223472

Order 20864.

348 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#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#23781690C211yesmaximal, characteristic
10#23781690C211yesmaximal, characteristic
11#23781687C211yesmaximal, characteristic
12#23781622C211yesmaximal, characteristic
13#23781619C211yesmaximal, characteristic
14#97×D163C211yesmaximal, characteristic
15#446×C163C211yesmaximal, characteristic, complemented
16C2×#14579682C2211yescharacteristic
17C2×#14579682C2211yescharacteristic
18C2×C8×D163C2211yescharacteristic
19C2×C8×D163C2211yescharacteristic
20#19104734C411yescharacteristic
21#19104733C411yescharacteristic
22#19104725C411yescharacteristic
23#19104725C411yescharacteristic
24#19104715C411yescharacteristic
25#19104713C411yescharacteristic
26#19104713C411yescharacteristic
27#19104711C411yescharacteristic
28C4×Dic326C2211yescharacteristic
29C4×Dic326C2211yescharacteristic
30C4×Dic326C2211yescharacteristic
31#19104692C2211yescharacteristic
32#19104692C2211yescharacteristic
33C42×D163C2211yescharacteristic
34C4⋊(C163⋊C8)C2211yescharacteristic
35C4⋊(C163⋊C8)C2211yescharacteristic
36C4⋊(C163⋊C8)C2211yescharacteristic
37Dic163⋊C8C2211yescharacteristic
38Dic163⋊C8C2211yescharacteristic
39Dic163⋊C8C2211yescharacteristic
40Dic163⋊C8C2211yescharacteristic
41Dic163⋊C8C2211yescharacteristic
42Dic163⋊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
65#14579682—22no—
66#14579682—22no—
67C2×C163⋊C8C2311yescharacteristic
68C2×C163⋊C8C2311yescharacteristic
69C2×C163⋊C8C2311yescharacteristic
70C2×C163⋊C8C2311yescharacteristic
71C8×D163—22no—
72C8×D163Q814yescomplemented
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
82Dic163⋊C4C2×C411yescharacteristic
83Dic163⋊C4C2×C411yescharacteristic
84Dic163⋊C4C2×C411yescharacteristic
85Dic163⋊C4C2×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×Q8×C163C2×C411yescharacteristic
96C2×C8×C163C2311yescharacteristic
97C2×C8×C163C2311yescharacteristic
98C2×C8×C163C2311yescharacteristic
99C2×C8×C163C2311yescharacteristic
100C4⋊C4×C163C2×C411yescharacteristic
101C4⋊C4×C163C2×C411yescharacteristic
102C4⋊C4×C163C2×C411yescharacteristic
103C42×C163C2311yescharacteristic
104C42×C163C2311yescharacteristic
105C42×C163C2311yescharacteristic
106C22×D163C22×C411yescharacteristic
107Dic326—41no—
108Dic326—41no—
109Dic326—41no—
110C2×Dic163C22×C411yescharacteristic
111C2×Dic163C22×C411yescharacteristic
112C2×Dic163C22×C411yescharacteristic
113C2×Dic163C22×C411yescharacteristic
114C2×Dic163C22×C411yescharacteristic
115C2×Dic163C22×C411yescharacteristic
116C2×Dic163C22×C411yescharacteristic
117C4×D163—41no—
118C4×D163—41no—
119C4×D163C2×Q812yes—
120C4×D163#4112yes—
121C163⋊C8—21no—
122C163⋊C8—21no—
123C163⋊C8—21no—
124C163⋊C8C2×Q812yes—
125Q8×C163—41no—
126C2×C4×C163C22×C411yescharacteristic
127C2×C4×C163C22×C411yescharacteristic
128C2×C4×C163C22×C411yescharacteristic
129C2×C4×C163C22×C411yescharacteristic
130C2×C4×C163C22×C411yescharacteristic
131C2×C4×C163C22×C411yescharacteristic
132C2×C4×C163C2411yescharacteristic
133C8×C163—21no—
134C8×C163—21no—
135C8×C163—21no—
136C8×C163C2×Q812yes—
137C22×C163C23×C411yescharacteristic
138C2×D163—21no—
139C2×D163—21no—
140C2×D163C4×Q812yes—
141C4×C163—21no—
142C4×C163—21no—
143C4×C163—21no—
144C4×C163—21no—
145C4×C163—21no—
146C4×C163—21no—
147C4×C163C22×Q811yescharacteristic
148C4×C163C2×#4111yescharacteristic
149Dic163—21no—
150Dic163—21no—
151Dic163—21no—
152Dic163—21no—
153Dic163—21no—
154Dic163—21no—
155Dic163C4×Q812yes—
156C2×C163C2×C4×Q811yescharacteristic
157C2×C163#56811yescharacteristic
158C2×C163#56811yescharacteristic
159D163—22no—
160C163#296111yescharacteristic, complemented, Sylow
161#2961—1631nomaximal, Sylow
162#533—1631no—
163#446—1631no—
164#446—1631no—
165#446—1631no—
166#446—1631no—
167#446—1631no—
168#446—1631no—
169#446—1631no—
170#446D16311yescharacteristic, complemented
171#424—1631no—
172#424—1631no—
173#423—1631no—
174#405—1631no—
175#405—1631no—
176C2×#97—1631no—
177C2×M16—1631no—
178C2×M16—1631no—
179C22×C8—1631no—
180C22×C8—1631no—
181C4⋊Q8—1631no—
182C4⋊Q8—1631no—
183#125—1631no—
184#125—1631no—
185C22⋊Q8—1631no—
186C22⋊Q8—1631no—
187C22⋊Q8—1631no—
188C22⋊Q8—1631no—
189C4×Q8—1631no—
190C4×Q8—1631no—
191C4×Q8—1631no—
192C4×Q8C2×D16311yescharacteristic
193#117—1631no—
194#117—1631no—
195C2×C42—1631no—
196C4⋊C8—1631no—
197C4⋊C8—1631no—
198C4⋊C8—1631no—
199C4⋊C8—1631no—
200C4⋊C8—1631no—
201C4⋊C8—1631no—
202C4⋊C8—1631no—
203C4⋊C8—1631no—
204C4⋊C8—1631no—
205C4⋊C8C2×D16311yescharacteristic
206C4⋊C8C2×D16311yescharacteristic
207C4⋊C8C2×D16311yescharacteristic
208#97—1631no—
209#97—1631no—
210#97—1631no—
211#97—1631no—
212#97—1631no—
213#97—1631no—
214#97C2×D16311yescharacteristic
215#97C2×D16311yescharacteristic
216C4×C8—1631no—
217C4×C8—1631no—
218C4×C8—1631no—
219C4×C8C2×D16311yescharacteristic
220C2×Q8—1631no—
221C2×Q8—1631no—
222C2×Q8—1631no—
223C2×Q8C4×D16311yescharacteristic
224C22×C4—1631no—
225C22×C4—1631no—
226C22×C4—1631no—
227M16—3262no—
228M16—3262no—
229C2×C8—3262no—
230C2×C8—1631no—
231C2×C8—1631no—
232C2×C8—1631no—
233C2×C8—1631no—
234C2×C8—1634no—
235C2×C8C22×D16311yescharacteristic
236C2×C8C22×D16311yescharacteristic
237C2×C8C22×D16311yescharacteristic
238C2×C8C22×D16311yescharacteristic
239C4⋊C4—1631no—
240C4⋊C4—1631no—
241C4⋊C4—1631no—
242C4⋊C4—1631no—
243C4⋊C4—1631no—
244C4⋊C4—1631no—
245C4⋊C4—1631no—
246C4⋊C4—1631no—
247C4⋊C4—1631no—
248C4⋊C4—1631no—
249C4⋊C4—1631no—
250C4⋊C4—1631no—
251C4⋊C4—1631no—
252C4⋊C4C4×D16311yescharacteristic
253C4⋊C4C4×D16311yescharacteristic
254C4⋊C4C4×D16311yescharacteristic
255C22⋊C4—1631no—
256C22⋊C4—1631no—
257C22⋊C4—1631no—
258C22⋊C4—1631no—
259C42—1631no—
260C42—1631no—
261C42—1631no—
262C42—1631no—
263C42—1631no—
264C42C22×D16311yescharacteristic
265C42C22×D16311yescharacteristic
266C42C22×D16311yescharacteristic
267C23—1631no—
268Q8—41no—
269Q8—6521no—
270Q8—6521no—
271Q8—6521no—
272C2×C4—6521no—
273C2×C4—6521no—
274C2×C4—1631no—
275C2×C4—1631no—
276C2×C4—1631no—
277C2×C4—1631no—
278C2×C4—1631no—
279C2×C4—1631no—
280C2×C4—1631no—
281C2×C4—1632no—
282C2×C4—1632no—
283C2×C4C2×C4×D16311yescharacteristic
284C2×C4C2×C4×D16311yescharacteristic
285C2×C4C2×C4×D16311yescharacteristic
286C2×C4C2×C4×D16311yescharacteristic
287C2×C4C2×C4×D16311yescharacteristic
288C2×C4C2×C4×D16311yescharacteristic
289C2×C4C23×D16311yescharacteristic
290C8—21no—
291C8—21no—
292C8—21no—
293C8—3261no—
294C8—3261no—
295C8—3261no—
296C8—1632no—
297C8Q8×D16312yes—
298C22—3261no—
299C22—3261no—
300C22—1632no—
301C22C22×C4×D16311yescharacteristic
302C4—21no—
303C4—21no—
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—3261no—
309C4—3261no—
310C4—3261no—
311C4—3261no—
312C4—3261no—
313C4—3261no—
314C4—1632no—
315C4C2×Q8×D16311yescharacteristic
316C4#41×D16311yescharacteristic
317C2—3262no—
318C2C4×Q8×D16311yescharacteristic
319C2#2378243011yescharacteristic
320C2#2378243111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D163
commutator, socleC22×C163C23×C4
Fitting#446×C163C2
prime radicalC22×D163C22×C4
cosocleC2×C4×C163C24
hypercenter#446D163
hypocenterC163#2961
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
72. C8×D163Q8semidirect
160. C163#2961semidirect
170. #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
#237816902
#237816872
#237816222
#237816192
#97×D1632
#446×C1632
#2961163