Finite Group Databasebeta

← #35227149

Subgroups — #35227149

Order 20864.

342 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23782383C211yesmaximal, characteristic
2#23782373C211yesmaximal, characteristic
3#23782062C211yesmaximal, characteristic, complemented
4#23782004C211yesmaximal, characteristic, complemented
5#23781997C211yesmaximal, characteristic, complemented
6#23781996C211yesmaximal, characteristic, complemented
7#23781959C211yesmaximal, characteristic, complemented
8#23781948C211yesmaximal, characteristic, complemented
9#23781922C211yesmaximal, characteristic, complemented
10#23781921C211yesmaximal, characteristic, complemented
11#23781757C211yesmaximal, characteristic, complemented
12#23781740C211yesmaximal, characteristic
13#23781708C211yesmaximal, characteristic, complemented
14#23781706C211yesmaximal, characteristic, complemented
15#485×C163C211yesmaximal, characteristic, complemented
16C2×#14579689C2211yescharacteristic
17C2×#14579683C2211yescharacteristic
18C2×#14579682C2211yescharacteristic
19#19104734C2211yescharacteristic
20#19104734C2211yescharacteristic
21#19104729—21no—
22#19104728—21no—
23#19104725—21no—
24#19104721—21no—
25#19104715—21no—
26#19104715C2211yescharacteristic
27#19104714C2211yescharacteristic
28#19104712—21no—
29#19104711C2211yescharacteristic
30Q8×Dic163C2211yescharacteristic
31C4×Dic326—21no—
32#19104700C2211yescharacteristic
33C4×C22⋊D163C2211yescharacteristic
34(C22⋊D163)⋊C4—21no—
35#19104693C2211yescharacteristic
36C2×C4⋊Dic163C2211yescharacteristic
37C4⋊C4×D163C2211yescharacteristic
38#19104668C2211yescharacteristic
39#19104668C2211yescharacteristic
40#19104667C2211yescharacteristic
41#19104667C2211yescharacteristic
42#19104666C2211yescharacteristic
43#19104666C2211yescharacteristic
44#19104666C2211yescharacteristic
45Dic163⋊C8C2211yescharacteristic
46#19104660C2211yescharacteristic
47#19104660C2211yescharacteristic
48#19104659C2211yescharacteristic
49#19104658C2211yescharacteristic
50(C2×D163)⋊C8C2211yescharacteristic
51C8×Dic163C2211yescharacteristic
52C22⋊Q8×C163C2211yescharacteristic
53#117×C163C2211yescharacteristic
54#107×C163C2211yescharacteristic
55#106×C163C2211yescharacteristic
56#103×C163C2211yescharacteristic
57#103×C163C2211yescharacteristic
58C22⋊C8×C163C2211yescharacteristic
59C2×Dic326—21no—
60C2×Dic326—21no—
61C2×Dic326C2311yescharacteristic
62C2×C22⋊D163D411yescharacteristic
63C22×Dic163—21no—
64C2×C4×D163—21no—
65C2×C4×D163C2311yescharacteristic
66#14579689—22no—
67#14579683—22no—
68#14579682—22no—
69C2×C163⋊C8C2311yescharacteristic
70C2×C163⋊C8C2311yescharacteristic
71C4⋊Dic163—21no—
72C4⋊Dic163—21no—
73C4⋊Dic163—21no—
74C4⋊Dic163C2311yescharacteristic
75C4⋊Dic163C2311yescharacteristic
76C4⋊Dic163C2311yescharacteristic
77Dic163⋊C4—21no—
78Dic163⋊C4—21no—
79Dic163⋊C4—21no—
80Dic163⋊C4—21no—
81Dic163⋊C4—21no—
82Dic163⋊C4—21no—
83Dic163⋊C4D411yescharacteristic
84C22⋊Dic163—21no—
85C22⋊Dic163D411yescharacteristic
86(C2×D163)⋊C4—21no—
87(C2×D163)⋊C4—21no—
88(C2×D163)⋊C4—21no—
89(C2×D163)⋊C4D411yescharacteristic
90C4×Dic163—21no—
91C4×Dic163—21no—
92C4×Dic163—21no—
93C4×Dic163C2311yescharacteristic
94C2×Q8×C163C2311yescharacteristic
95C22×C4×C163C2311yescharacteristic
96C2×C8×C163C2311yescharacteristic
97C2×C8×C163C2311yescharacteristic
98C4⋊C4×C163—21no—
99C4⋊C4×C163C2311yescharacteristic
100C4⋊C4×C163C2311yescharacteristic
101C4⋊C4×C163C2311yescharacteristic
102C22⋊C4×C163—21no—
103C22⋊C4×C163—21no—
104C42×C163—21no—
105C22×D163C2×D411yescharacteristic
106Dic326—21no—
107Dic326—21no—
108Dic326—42no—
109Dic326—81no—
110C22⋊D163—22no—
111C2×Dic163—21no—
112C2×Dic163—21no—
113C2×Dic163—21no—
114C2×Dic163—21no—
115C2×Dic163—81no—
116C2×Dic163C2×D411yescharacteristic
117C2×Dic163C2×D411yescharacteristic
118C2×Dic163C2×D411yescharacteristic
119C4×D163—21no—
120C4×D163—21no—
121C4×D163—81no—
122C163⋊C8—21no—
123C163⋊C8#4112yes—
124C23×C163C2×D411yescharacteristic
125Q8×C163—21no—
126Q8×C163—21no—
127C2×C4×C163—21no—
128C2×C4×C163—21no—
129C2×C4×C163—21no—
130C2×C4×C163—21no—
131C2×C4×C163—21no—
132C2×C4×C163—21no—
133C2×C4×C163C2×D411yescharacteristic
134C2×C4×C163C2411yescharacteristic
135C8×C163—21no—
136C8×C163—21no—
137C22×C163—21no—
138C22×C163—21no—
139C22×C163—21no—
140C22×C163C22×D411yescharacteristic
141C2×D163—21no—
142C2×D163—21no—
143C2×D163—21no—
144C4×C163—21no—
145C4×C163—41no—
146C4×C163—41no—
147C4×C163—41no—
148C4×C163—41no—
149C4×C163C2×#4111yescharacteristic
150C4×C1632−1+411yescharacteristic
151Dic163—21no—
152Dic163—21no—
153Dic163—41no—
154Dic163—41no—
155Dic163—41no—
156Dic163—41no—
157Dic163#13712yes—
158C2×C163—41no—
159C2×C163#54711yescharacteristic
160C2×C163C2×#13711yescharacteristic
161C2×C163#57711yescharacteristic
162D163—41no—
163C163#335611yescharacteristic, complemented, Sylow
164#3356—1631nomaximal, Sylow
165#556—1631no—
166#554—1631no—
167#498—1631no—
168#485—1631no—
169#485D16311yescharacteristic, complemented
170#483—1631no—
171#483—1631no—
172#477—1631no—
173#475—1631no—
174#470—1631no—
175#470—1631no—
176C4×Q16—1631no—
177#436—1631no—
178#428—1631no—
179#428—1631no—
180C2×Q16—1631no—
181C2×M16—1631no—
182C2×M16—1631no—
183C4⋊Q8—1631no—
184C4⋊Q8—1631no—
185#126—3261no—
186#126—3261no—
187#125—3261no—
188#124—3261no—
189C22⋊Q8—3261no—
190C22⋊Q8—3261no—
191C22⋊Q8—1631no—
192C22⋊Q8—1631no—
193C22⋊Q8—1631no—
194C22⋊Q8C2×D16311yescharacteristic
195C4×Q8—3261no—
196C4×Q8—1631no—
197C4×Q8—1631no—
198C4×D4—3261no—
199C4×D4—1631no—
200#117—1631no—
201#117C2×D16311yescharacteristic
202C2×C4⋊C4—1631no—
203C2×C4⋊C4—1631no—
204#107—1631no—
205#107—1631no—
206#107C2×D16311yescharacteristic
207#106—1631no—
208#106—1631no—
209#106—1631no—
210#106—1631no—
211#106—1631no—
212#106C2×D16311yescharacteristic
213C4⋊C8—1631no—
214#103—1631no—
215#103—1631no—
216#103—1631no—
217#103—1631no—
218#103C2×D16311yescharacteristic
219#103C2×D16311yescharacteristic
220C22⋊C8—1631no—
221C22⋊C8C2×D16311yescharacteristic
222C4×C8—1631no—
223C2×Q8—3261no—
224C2×Q8—3261no—
225C2×Q8—1631no—
226C2×Q8C22×D16311yescharacteristic
227C2×D4—1631no—
228C22×C4—3261no—
229C22×C4—3261no—
230C22×C4—1631no—
231C22×C4C22×D16311yescharacteristic
232Q16—3262no—
233M16—3262no—
234M16—3262no—
235C2×C8—1631no—
236C2×C8—1631no—
237C2×C8C22×D16311yescharacteristic
238C2×C8C22×D16311yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—3261no—
241C4⋊C4—3261no—
242C4⋊C4—3261no—
243C4⋊C4—3261no—
244C4⋊C4—3261no—
245C4⋊C4—3261no—
246C4⋊C4—3261no—
247C4⋊C4—3261no—
248C4⋊C4—3261no—
249C4⋊C4—1631no—
250C4⋊C4—1631no—
251C4⋊C4—1631no—
252C4⋊C4—1631no—
253C4⋊C4C22×D16311yescharacteristic
254C4⋊C4C22×D16311yescharacteristic
255C4⋊C4C22×D16311yescharacteristic
256C22⋊C4—21no—
257C22⋊C4—21no—
258C22⋊C4—3261no—
259C22⋊C4—3261no—
260C22⋊C4—3261no—
261C22⋊C4—3261no—
262C22⋊C4—1631no—
263C22⋊C4—1631no—
264C42—21no—
265C42—3261no—
266C42—3261no—
267C42—3261no—
268C42—1631no—
269C23—1631no—
270C23D4×D16311yescharacteristic
271Q8—21no—
272Q8—21no—
273Q8—13041no—
274Q8—3261no—
275Q8—3261no—
276Q8—6522no—
277D4—3262no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—13041no—
285C2×C4—13041no—
286C2×C4—3261no—
287C2×C4—3261no—
288C2×C4—3261no—
289C2×C4—3261no—
290C2×C4—3261no—
291C2×C4—3261no—
292C2×C4—1631no—
293C2×C4—1631no—
294C2×C4—1631no—
295C2×C4D4×D16311yescharacteristic
296C2×C4C23×D16311yescharacteristic
297C8—21no—
298C8—21no—
299C8—3261no—
300C8—1632no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—3261no—
305C22—3261no—
306C22—3261no—
307C22C2×D4×D16311yescharacteristic
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—3261no—
314C4—3261no—
315C4—6521no—
316C4—6521no—
317C4—6521no—
318C4—6521no—
319C4—1632no—
320C4#41×D16311yescharacteristic
321C4#1910478211yescharacteristic
322C2—41no—
323C2—6521no—
324C2#2378231311yescharacteristic
325C2#137×D16311yescharacteristic
326C2#2378247211yescharacteristic
subgroupG/H
centerC22C2×D4×D163
commutator, cosocleC2×C4×C163C24
FrattiniC2×C4C23×D163
Fitting#485×C163C2
socleC22×C163C22×D4
prime radicalC2×C22⋊D163D4
hypercenter#485D163
hypocenterC163#3356
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. #23782062C2semidirect
4. #23782004C2semidirect
5. #23781997C2semidirect
6. #23781996C2semidirect
7. #23781959C2semidirect
8. #23781948C2semidirect
9. #23781922C2semidirect
10. #23781921C2semidirect
11. #23781757C2semidirect
13. #23781708C2semidirect
14. #23781706C2semidirect
15. #485×C163C2semidirect
163. C163#3356semidirect
169. #485D163semidirect

Maximal subgroups

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

subgroupindex
#237823832
#237823732
#237820622
#237820042
#237819972
#237819962
#237819592
#237819482
#237819222
#237819212
#237817572
#237817402
#237817082
#237817062
#485×C1632
#3356163