Finite Group Databasebeta

← #35224542

Subgroups — #35224542

Order 20864.

448 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23782219C211yesmaximal, characteristic, complemented
2C4×D4×D163C211yesmaximal, characteristic
3#23781997C211yesmaximal, characteristic, complemented
4#23781994C211yesmaximal, characteristic, complemented
5#23781954C211yesmaximal, characteristic, complemented
6#23781953C211yesmaximal, characteristic, complemented
7#23781869C211yesmaximal, characteristic, complemented
8#23781868C211yesmaximal, characteristic, complemented
9#23781817C211yesmaximal, characteristic
10#23781814C211yesmaximal, characteristic
11C4×#14579688C211yesmaximal, characteristic, complemented
12C4×#14579686C211yesmaximal, characteristic, complemented
13C4×#14579687C211yesmaximal, characteristic, complemented
14#23781716C211yesmaximal, characteristic, complemented
15C4×SD16×C163C211yesmaximal, characteristic, complemented
16C2×D4×D163C2211yescharacteristic
17C22×C4×D163—21no—
18C2×#14579688C2211yescharacteristic
19C2×#14579687C2211yescharacteristic
20C2×#14579686C2211yescharacteristic
21#19104734C2211yescharacteristic, complemented
22#19104733C2211yescharacteristic, complemented
23#19104725—21no—
24#19104715C2211yescharacteristic
25#19104713—21no—
26#19104711C2211yescharacteristic
27C4×Dic326—21no—
28C4×Dic326C2211yescharacteristic, complemented
29C4×D652C2211yescharacteristic
30D4×Dic163C2211yescharacteristic
31#19104697C2211yescharacteristic
32C4×C22⋊D163—21no—
33(C22⋊D163)⋊C4—21no—
34#19104692—21no—
35C4⋊C4×D163C2211yescharacteristic
36C22⋊C4×D163—21no—
37C42×D163C2211yescharacteristic
38#19104667C2211yescharacteristic, complemented
39#19104666C2211yescharacteristic, complemented
40#19104666C2211yescharacteristic, complemented
41Dic163⋊C8C2211yescharacteristic, complemented
42Dic163⋊C8C2211yescharacteristic, complemented
43#19104660C2211yescharacteristic, complemented
44#19104659C2211yescharacteristic, complemented
45#19104658C2211yescharacteristic, complemented
46#19104657C2211yescharacteristic
47#19104656C2211yescharacteristic
48#19104655C2211yescharacteristic
49(C2×D163)⋊C8C2211yescharacteristic
50(C2×D163)⋊C8C2211yescharacteristic
51C4×C163⋊C8C2211yescharacteristic, complemented
52C2×SD16×C163C2211yescharacteristic
53C4×Q8×C163C2211yescharacteristic, complemented
54C4×D4×C163C2211yescharacteristic
55#106×C163C2211yescharacteristic, complemented
56#103×C163C2211yescharacteristic, complemented
57#102×C163C2211yescharacteristic
58C4×C8×C163C2211yescharacteristic, complemented
59C23×D163—21no—
60C2×Dic326—21no—
61C2×Dic326C2311yescharacteristic
62C2×D652C2311yescharacteristic
63C2×C22⋊D163—21no—
64D4×D163—22no—
65D4×D163—22no—
66C22×Dic163—21no—
67C2×C4×D163—21no—
68C2×C4×D163—21no—
69C2×C4×D163—21no—
70C2×C4×D163—44no—
71C2×C4×D163D411yescharacteristic
72C2×C4×D163D411yescharacteristic
73C2×C4×D163C2311yescharacteristic
74#14579688—22no—
75#14579687—22no—
76#14579686—22no—
77C2×C163⋊C8C2311yescharacteristic
78C2×C163⋊C8C2311yescharacteristic
79C4⋊Dic163—21no—
80C4⋊Dic163C2311yescharacteristic
81C4⋊Dic163C2311yescharacteristic
82Dic163⋊C4—21no—
83Dic163⋊C4—21no—
84Dic163⋊C4—21no—
85Dic163⋊C4—21no—
86Dic163⋊C4—21no—
87Dic163⋊C4—21no—
88C22⋊Dic163—21no—
89(C2×D163)⋊C4—21no—
90(C2×D163)⋊C4—21no—
91(C2×D163)⋊C4—21no—
92(C2×D163)⋊C4—21no—
93C4×Dic163—21no—
94C4×Dic163D411yescharacteristic
95C4×Dic163D411yescharacteristic
96C4×Dic163C2311yescharacteristic
97C2×Q8×C163C2311yescharacteristic
98C2×D4×C163C2311yescharacteristic
99C22×C4×C163—21no—
100SD16×C163—22no—
101C2×C8×C163C2311yescharacteristic
102C2×C8×C163C2311yescharacteristic
103C4⋊C4×C163—21no—
104C4⋊C4×C163C2311yescharacteristic
105C4⋊C4×C163C2311yescharacteristic
106C22⋊C4×C163—21no—
107C42×C163—21no—
108C42×C163C2311yescharacteristic
109C22×D163—24no—
110C22×D163—21no—
111C22×D163—42no—
112C22×D163—42no—
113C22×D163C2×D411yescharacteristic
114Dic326—21no—
115Dic326—21no—
116Dic326—42no—
117D652—21no—
118D652#4112yes—
119C22⋊D163—24no—
120C2×Dic163—21no—
121C2×Dic163—21no—
122C2×Dic163—21no—
123C2×Dic163—42no—
124C2×Dic163C2×D411yescharacteristic
125C2×Dic163C2×D411yescharacteristic
126C2×Dic163C2×D411yescharacteristic
127C4×D163—21no—
128C4×D163—21no—
129C4×D163—41no—
130C4×D163—42no—
131C4×D163—42no—
132C4×D163—42no—
133C4×D163SD1614yescomplemented
134C163⋊C8—21no—
135C163⋊C8—21no—
136C23×C163—21no—
137Q8×C163—21no—
138Q8×C163—21no—
139D4×C163—21no—
140D4×C163#4112yes—
141C2×C4×C163—21no—
142C2×C4×C163—21no—
143C2×C4×C163—21no—
144C2×C4×C163—42no—
145C2×C4×C163C2×D411yescharacteristic
146C2×C4×C163C2×D411yescharacteristic
147C2×C4×C163C2411yescharacteristic
148C8×C163—21no—
149C8×C163—21no—
150C22×C163—22no—
151C22×C163—41no—
152C22×C163—41no—
153C22×C163C22×D411yescharacteristic
154C2×D163—21no—
155C2×D163—21no—
156C2×D163—22no—
157C2×D163—48no—
158C2×D163—41no—
159C2×D163—41no—
160C2×D163C2×SD1612yes—
161C4×C163—21no—
162C4×C163—41no—
163C4×C163—41no—
164C4×C163—41no—
165C4×C163C2×SD1612yes—
166C4×C163C2×#4111yescharacteristic
167C4×C163C2×#4111yescharacteristic
168Dic163—21no—
169Dic163—21no—
170Dic163—41no—
171Dic163—41no—
172Dic163—41no—
173Dic163C2×SD1612yes—
174C2×C163—42no—
175C2×C163#52511yescharacteristic
176C2×C163C22×SD1611yescharacteristic
177C2×C163#57511yescharacteristic
178D163—22no—
179D163—42no—
180C163#310111yescharacteristic, complemented, Sylow
181#3101—1631nomaximal, Sylow
182#533—1631no—
183C2×C4×D4—1631no—
184#483—1631no—
185#483—1631no—
186#476—1631no—
187#476—1631no—
188#461—1631no—
189#461—1631no—
190#450—1631no—
191#450—1631no—
192C4×SD16—1631no—
193C4×SD16—1631no—
194C4×SD16—1631no—
195C4×SD16D16311yescharacteristic, complemented
196#431—1631no—
197C22×D4—1631no—
198C23×C4—3261no—
199C2×SD16—1631no—
200C2×SD16—1631no—
201C2×SD16—1631no—
202C2×SD16C2×D16311yescharacteristic
203C4⋊Q8—1631no—
204C4⋊Q8—1631no—
205#125—3261no—
206C22⋊Q8—3261no—
207C22⋊Q8—1631no—
208C22⋊Q8—1631no—
209C4×Q8—3261no—
210C4×Q8—1631no—
211C4×Q8C2×D16311yescharacteristic, complemented
212C4×D4—3261no—
213C4×D4—3261no—
214C4×D4—1631no—
215C4×D4—1631no—
216C4×D4—1631no—
217C4×D4C2×D16311yescharacteristic
218#117—3261no—
219C2×C4⋊C4—1631no—
220C2×C22⋊C4—3261no—
221C2×C42—1631no—
222#106—1631no—
223#106—1631no—
224#106—1631no—
225#106C2×D16311yescharacteristic, complemented
226C4⋊C8—1631no—
227C4⋊C8—1631no—
228#103—1631no—
229#103—1631no—
230#103—1631no—
231#103C2×D16311yescharacteristic, complemented
232#102—1631no—
233#102—1631no—
234#102—1631no—
235#102C2×D16311yescharacteristic
236C22⋊C8—1631no—
237C22⋊C8—1631no—
238C4×C8—1631no—
239C4×C8C2×D16311yescharacteristic, complemented
240C24—3261no—
241C2×Q8—3261no—
242C2×Q8—1631no—
243C2×Q8C22×D16311yescharacteristic
244C2×D4—3262no—
245C2×D4—3262no—
246C2×D4—3261no—
247C2×D4—1631no—
248C2×D4C22×D16311yescharacteristic
249C22×C4—21no—
250C22×C4—3261no—
251C22×C4—3261no—
252C22×C4—3261no—
253C22×C4—3261no—
254C22×C4—6524no—
255C22×C4—1631no—
256C22×C4—1631no—
257C22×C4—1631no—
258SD16—22no—
259SD16—3262no—
260SD16—3262no—
261SD16—3262no—
262C2×C8—1631no—
263C2×C8—1631no—
264C2×C8C22×D16311yescharacteristic
265C2×C8C22×D16311yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—3261no—
268C4⋊C4—3261no—
269C4⋊C4—3261no—
270C4⋊C4—3261no—
271C4⋊C4—3261no—
272C4⋊C4—3261no—
273C4⋊C4—3261no—
274C4⋊C4—1631no—
275C4⋊C4—1631no—
276C4⋊C4C22×D16311yescharacteristic
277C4⋊C4C22×D16311yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—3261no—
280C22⋊C4—3261no—
281C22⋊C4—3261no—
282C22⋊C4—3261no—
283C22⋊C4—3261no—
284C42—21no—
285C42—3261no—
286C42—1631no—
287C42—1631no—
288C42—1631no—
289C42C22×D16311yescharacteristic
290C23—21no—
291C23—3264no—
292C23—3261no—
293C23—6522no—
294C23—6522no—
295C23—1631no—
296Q8—21no—
297Q8—21no—
298Q8—3261no—
299Q8—3261no—
300Q8—6522no—
301D4—21no—
302D4—3264no—
303D4—3261no—
304D4—1632no—
305D4#1457969912yes—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—3261no—
311C2×C4—3261no—
312C2×C4—3261no—
313C2×C4—3261no—
314C2×C4—3261no—
315C2×C4—6521no—
316C2×C4—6522no—
317C2×C4—6522no—
318C2×C4—6522no—
319C2×C4—6522no—
320C2×C4—1631no—
321C2×C4—1631no—
322C2×C4—1631no—
323C2×C4—1634no—
324C2×C4D4×D16311yescharacteristic
325C2×C4D4×D16311yescharacteristic
326C2×C4C23×D16311yescharacteristic
327C8—21no—
328C8—21no—
329C8—3261no—
330C8—3261no—
331C22—22no—
332C22—41no—
333C22—41no—
334C22—3261no—
335C22—3261no—
336C22—3262no—
337C22—6528no—
338C22—6521no—
339C22—6521no—
340C22—1632no—
341C22C2×D4×D16311yescharacteristic
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—3261no—
347C4—3261no—
348C4—6521no—
349C4—6521no—
350C4—6521no—
351C4—1632no—
352C4SD16×D16312yes—
353C4#41×D16311yescharacteristic
354C4C2×#1457969911yescharacteristic
355C2—42no—
356C2—3262no—
357C2—6522no—
358C2#2378217411yescharacteristic
359C2C2×SD16×D16311yescharacteristic
360C2#2378246211yescharacteristic
subgroupG/H
centerC2×C4D4×D163
commutator, cosocleC2×C4×C163C24
FrattiniC2×C4C23×D163
FittingC4×SD16×C163C2
socleC22×C163C22×D4
prime radicalC2×D4×D163C22
hypercenterC4×SD16D163
hypocenterC163#3101
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #23782219C2semidirect
3. #23781997C2semidirect
4. #23781994C2semidirect
5. #23781954C2semidirect
6. #23781953C2semidirect
7. #23781869C2semidirect
8. #23781868C2semidirect
11. C4×#14579688C2semidirect
12. C4×#14579686C2semidirect
13. C4×#14579687C2semidirect
14. #23781716C2semidirect
15. C4×SD16×C163C2semidirect
21. #19104734C22semidirect
22. #19104733C22semidirect
28. C4×Dic326C22semidirect
38. #19104667C22semidirect
39. #19104666C22semidirect
40. #19104666C22semidirect
41. Dic163⋊C8C22semidirect
42. Dic163⋊C8C22semidirect
43. #19104660C22semidirect
44. #19104659C22semidirect
45. #19104658C22semidirect
51. C4×C163⋊C8C22semidirect
53. C4×Q8×C163C22semidirect
55. #106×C163C22semidirect
56. #103×C163C22semidirect
58. C4×C8×C163C22semidirect
133. C4×D163SD16semidirect
180. C163#3101semidirect
195. C4×SD16D163semidirect
211. C4×Q8C2×D163semidirect
225. #106C2×D163semidirect
231. #103C2×D163semidirect
239. C4×C8C2×D163semidirect

Maximal subgroups

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

subgroupindex
#237822192
C4×D4×D1632
#237819972
#237819942
#237819542
#237819532
#237818692
#237818682
#237818172
#237818142
C4×#145796882
C4×#145796862
C4×#145796872
#237817162
C4×SD16×C1632
#3101163