Finite Group Databasebeta

← #35224800

Subgroups — #35224800

Order 20864.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23782286C211yesmaximal, characteristic, complemented
2#23782145C211yesmaximal, characteristic, complemented
3#23782001C211yesmaximal, characteristic, complemented
4#23781979C211yesmaximal, characteristic, complemented
5#23781961C211yesmaximal, characteristic, complemented
6#23781946C211yesmaximal, characteristic, complemented
7#23781888C211yesmaximal, characteristic, complemented
8#23781881C211yesmaximal, characteristic, complemented
9#23781829C211yesmaximal, characteristic, complemented
10#23781812C211yesmaximal, characteristic
11#23781767C211yesmaximal, characteristic, complemented
12#23781767C211yesmaximal, characteristic, complemented
13C4×Dic652C211yesmaximal, characteristic, complemented
14C4×D1304C211yesmaximal, characteristic, complemented
15#433×C163C211yesmaximal, characteristic, complemented
16C2×#14579699C2211yescharacteristic
17C2×Dic652C2211yescharacteristic
18C2×#14579688C2211yescharacteristic
19C2×#14579688C2211yescharacteristic
20C2×D1304C2211yescharacteristic
21#19104735C2211yescharacteristic
22#19104730—21no—
23#19104723C2211yescharacteristic
24#19104721—21no—
25#19104717—21no—
26#19104714C2211yescharacteristic
27#19104713—21no—
28#19104709C2211yescharacteristic
29C4×Dic326C2211yescharacteristic
30C4×Dic326C2211yescharacteristic
31C4×Dic326C2211yescharacteristic
32C4×D652C2211yescharacteristic
33C4×D652C2211yescharacteristic
34C4×D652C2211yescharacteristic
35(C22⋊D163)⋊C4—21no—
36(C22⋊D163)⋊C4—21no—
37#19104693—21no—
38C2×C4⋊Dic163C2211yescharacteristic
39C4⋊C4×D163—21no—
40#19104669C2211yescharacteristic
41#19104669C2211yescharacteristic
42#19104669C2211yescharacteristic
43#19104669C2211yescharacteristic
44#19104660C2211yescharacteristic
45#19104660C2211yescharacteristic
46#19104660C2211yescharacteristic
47#19104660C2211yescharacteristic
48#19104657C2211yescharacteristic
49#19104657C2211yescharacteristic
50#19104657C2211yescharacteristic
51#19104657C2211yescharacteristic
52#117×C163C2211yescharacteristic
53C4⋊C8×C163C2211yescharacteristic
54C4⋊C8×C163C2211yescharacteristic
55C22⋊C8×C163C2211yescharacteristic
56C22⋊C8×C163C2211yescharacteristic
57#97×C163C2211yescharacteristic
58C4×C8×C163C2211yescharacteristic
59#14579699—22no—
60#14579699—22no—
61C2×Dic326—21no—
62C2×Dic326C2311yescharacteristic
63C2×Dic326C2311yescharacteristic
64C2×D652C2311yescharacteristic
65C2×D652C2311yescharacteristic
66C2×C22⋊D163—21no—
67C2×C22⋊D163—21no—
68C22×Dic163—21no—
69C2×C4×D163—21no—
70C2×C4×D163—21no—
71C2×C4×D163—21no—
72C2×C4×D163—21no—
73Dic652—22no—
74#14579688—22no—
75#14579688—22no—
76D1304—22no—
77C4⋊Dic163—21no—
78C4⋊Dic163—21no—
79C4⋊Dic163C2311yescharacteristic
80C4⋊Dic163C2311yescharacteristic
81C4⋊Dic163C2311yescharacteristic
82C4⋊Dic163C2311yescharacteristic
83Dic163⋊C4—21no—
84Dic163⋊C4—21no—
85Dic163⋊C4—21no—
86Dic163⋊C4—21no—
87C22⋊Dic163—21no—
88(C2×D163)⋊C4—21no—
89(C2×D163)⋊C4—21no—
90(C2×D163)⋊C4—21no—
91(C2×D163)⋊C4—21no—
92(C2×D163)⋊C4—21no—
93(C2×D163)⋊C4—21no—
94C4×Dic163—21no—
95C4×Dic163—21no—
96C4×Dic163—21no—
97C22×C4×C163C2311yescharacteristic
98C2×C8×C163C2311yescharacteristic
99C2×C8×C163C2311yescharacteristic
100C2×C8×C163C2311yescharacteristic
101C2×C8×C163C2311yescharacteristic
102C4⋊C4×C163D411yescharacteristic
103C4⋊C4×C163D411yescharacteristic
104C22⋊C4×C163D411yescharacteristic
105C22⋊C4×C163D411yescharacteristic
106C42×C163C2311yescharacteristic
107C42×C163C2311yescharacteristic
108C22×D163—21no—
109C22×D163—21no—
110Dic326—21no—
111Dic326—21no—
112Dic326—21no—
113Dic326—81no—
114Dic326#4112yes—
115D652—21no—
116D652—21no—
117D652—21no—
118D652#4112yes—
119C22⋊D163—24no—
120C22⋊D163—81no—
121C2×Dic163—21no—
122C2×Dic163—21no—
123C2×Dic163—21no—
124C2×Dic163—21no—
125C2×Dic163—21no—
126C2×Dic163—21no—
127C2×Dic163—81no—
128C4×D163—24no—
129C4×D163—81no—
130C4×D163—81no—
131C4×D163—81no—
132C23×C163C2×D411yescharacteristic
133C2×C4×C163—21no—
134C2×C4×C163—21no—
135C2×C4×C163C2×D411yescharacteristic
136C2×C4×C163C2×D411yescharacteristic
137C2×C4×C163C2×D411yescharacteristic
138C2×C4×C163C2×D411yescharacteristic
139C2×C4×C163C2×D411yescharacteristic
140C2×C4×C163C2411yescharacteristic
141C8×C163—21no—
142C8×C163—21no—
143C8×C163—21no—
144C8×C163—21no—
145C22×C163—21no—
146C22×C163—21no—
147C22×C163—21no—
148C22×C163C22×D411yescharacteristic
149C2×D163—22no—
150C2×D163—41no—
151C2×D163—41no—
152C2×D163—41no—
153C2×D163—41no—
154C2×D163—41no—
155C4×C163—21no—
156C4×C163—21no—
157C4×C163—21no—
158C4×C163—21no—
159C4×C163—21no—
160C4×C163C2×#4111yescharacteristic
161C4×C163C2×#4111yescharacteristic
162Dic163—22no—
163Dic163—41no—
164Dic163—41no—
165Dic163—41no—
166Dic163—41no—
167Dic163—41no—
168C2×C163—41no—
169C2×C163#52511yescharacteristic
170C2×C163#57611yescharacteristic
171C2×C163#57811yescharacteristic
172D163—42no—
173D163—81no—
174C163#312411yescharacteristic, complemented, Sylow
175#3124—1631nomaximal, Sylow
176#542—1631no—
177#520—1631no—
178#484—1631no—
179#480—1631no—
180#477—1631no—
181#474—1631no—
182#464—1631no—
183#463—1631no—
184#452—1631no—
185#449—1631no—
186#440—1631no—
187#440—1631no—
188C4×Q16—1631no—
189C4×D8—1631no—
190#433D16311yescharacteristic, complemented
191C2×#41—1631no—
192C2×Q16—1631no—
193C2×SD16—1631no—
194C2×SD16—1631no—
195C2×D8—1631no—
196C4⋊Q8—1631no—
197#126—3261no—
198#124—3261no—
199#124—1631no—
200#123—3261no—
201C22⋊Q8—3261no—
202C22⋊Q8—1631no—
203#121—1631no—
204C4×Q8—1631no—
205C4×Q8—1631no—
206C4×Q8—1631no—
207C4×D4—3261no—
208C4×D4—3261no—
209C4×D4—1631no—
210C4×D4—1631no—
211C4×D4—1631no—
212#117—3261no—
213#117C2×D16311yescharacteristic
214C2×C4⋊C4—3261no—
215C2×C4⋊C4—1631no—
216#107—1631no—
217#107—1631no—
218#107—1631no—
219#107—1631no—
220C4⋊C8C2×D16311yescharacteristic
221C4⋊C8C2×D16311yescharacteristic
222#103—1631no—
223#103—1631no—
224#103—1631no—
225#103—1631no—
226#102—1631no—
227#102—1631no—
228#102—1631no—
229#102—1631no—
230C22⋊C8C2×D16311yescharacteristic
231C22⋊C8C2×D16311yescharacteristic
232#97C2×D16311yescharacteristic
233C4×C8C2×D16311yescharacteristic
234#41—3262no—
235#41—3262no—
236C2×Q8—3261no—
237C2×Q8—1631no—
238C2×Q8—1631no—
239C2×D4—3261no—
240C2×D4—3261no—
241C2×D4—1631no—
242C2×D4—1631no—
243C22×C4—3261no—
244C22×C4—3261no—
245C22×C4—3261no—
246C22×C4—3261no—
247C22×C4—3261no—
248C22×C4C22×D16311yescharacteristic
249Q16—3262no—
250SD16—3262no—
251SD16—3262no—
252D8—3262no—
253C2×C8C22×D16311yescharacteristic
254C2×C8C22×D16311yescharacteristic
255C2×C8C22×D16311yescharacteristic
256C2×C8C22×D16311yescharacteristic
257C4⋊C4—3261no—
258C4⋊C4—3261no—
259C4⋊C4—3261no—
260C4⋊C4—3261no—
261C4⋊C4—3261no—
262C4⋊C4—3261no—
263C4⋊C4—1631no—
264C4⋊C4—1631no—
265C4⋊C4—1631no—
266C4⋊C4—1631no—
267C4⋊C4D65211yescharacteristic
268C4⋊C4D65211yescharacteristic
269C22⋊C4—3261no—
270C22⋊C4—3261no—
271C22⋊C4—3261no—
272C22⋊C4—3261no—
273C22⋊C4—3261no—
274C22⋊C4—3261no—
275C22⋊C4—3261no—
276C22⋊C4D65211yescharacteristic
277C22⋊C4D65211yescharacteristic
278C42—3261no—
279C42—3261no—
280C42—3261no—
281C42C22×D16311yescharacteristic
282C42C22×D16311yescharacteristic
283C23—3261no—
284C23—3261no—
285C23C2×D65211yescharacteristic
286Q8—13041no—
287Q8—3261no—
288Q8—3261no—
289Q8—3261no—
290Q8—1632no—
291D4—13041no—
292D4—3264no—
293D4—3261no—
294D4—3261no—
295D4—3261no—
296D4—1632no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—13041no—
300C2×C4—13041no—
301C2×C4—13041no—
302C2×C4—13041no—
303C2×C4—3264no—
304C2×C4—3261no—
305C2×C4—3261no—
306C2×C4—3261no—
307C2×C4—3261no—
308C2×C4—3261no—
309C2×C4—3261no—
310C2×C4C2×D65211yescharacteristic
311C2×C4C2×D65211yescharacteristic
312C2×C4C2×D65211yescharacteristic
313C2×C4C2×D65211yescharacteristic
314C2×C4C2×D65211yescharacteristic
315C2×C4C23×D16311yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—3262no—
324C22—6521no—
325C22—6521no—
326C22—6521no—
327C22—6521no—
328C22—6521no—
329C22C22×D65211yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—3262no—
336C4—6521no—
337C4—6521no—
338C4—6521no—
339C4—6521no—
340C4—6521no—
341C4#41×D16311yescharacteristic
342C4#41×D16311yescharacteristic
343C2—41no—
344C2—13041no—
345C2—6522no—
346C2#2378217711yescharacteristic
347C2#2378247011yescharacteristic
348C2#2378248211yescharacteristic
subgroupG/H
centerC22C22×D652
commutator, cosocleC2×C4×C163C24
FrattiniC2×C4C23×D163
Fitting#433×C163C2
socleC22×C163C22×D4
prime radical#23781812C2
hypercenter#433D163
hypocenterC163#3124
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #23782286C2semidirect
2. #23782145C2semidirect
3. #23782001C2semidirect
4. #23781979C2semidirect
5. #23781961C2semidirect
6. #23781946C2semidirect
7. #23781888C2semidirect
8. #23781881C2semidirect
9. #23781829C2semidirect
11. #23781767C2semidirect
12. #23781767C2semidirect
13. C4×Dic652C2semidirect
14. C4×D1304C2semidirect
15. #433×C163C2semidirect
174. C163#3124semidirect
190. #433D163semidirect

Maximal subgroups

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

subgroupindex
#237822862
#237821452
#237820012
#237819792
#237819612
#237819462
#237818882
#237818812
#237818292
#237818122
#237817672
C4×Dic6522
C4×D13042
#433×C1632
#3124163