Finite Group Databasebeta

← #35226493

Subgroups — #35226493

Order 20864.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23782316C211yesmaximal, characteristic, complemented
2#23782309C211yesmaximal, characteristic, complemented
3#23782023C211yesmaximal, characteristic, complemented
4#23781995C211yesmaximal, characteristic, complemented
5#23781982C211yesmaximal, characteristic, complemented
6#23781953C211yesmaximal, characteristic, complemented
7#23781917C211yesmaximal, characteristic, complemented
8#23781894C211yesmaximal, characteristic, complemented
9#23781879C211yesmaximal, characteristic, complemented
10#23781811C211yesmaximal, characteristic, complemented
11#23781799C211yesmaximal, characteristic, complemented
12#23781774C211yesmaximal, characteristic, complemented
13#23781736C211yesmaximal, characteristic, complemented
14#23781663C211yesmaximal, characteristic, complemented
15C2×#102×C163C211yesmaximal, characteristic, complemented
16C2×#14579699—21no—
17C2×#14579698C2211yescharacteristic
18C2×#14579688C2211yescharacteristic, complemented
19C2×#14579684C2211yescharacteristic
20C2×#14579684C2211yescharacteristic
21C2×#14579682C2211yescharacteristic, complemented
22#19104734C2211yescharacteristic, complemented
23#19104722C2211yescharacteristic
24#19104720—21no—
25#19104718—21no—
26#19104716—21no—
27#19104714C2211yescharacteristic
28#19104713—21no—
29#19104710C2211yescharacteristic, complemented
30#19104709C2211yescharacteristic
31#19104707—21no—
32#19104706C2211yescharacteristic
33#19104704—21no—
34D4×Dic163C2211yescharacteristic
35#19104697C2211yescharacteristic, complemented
36C4×C22⋊D163C2211yescharacteristic
37C4⋊C4×D163C2211yescharacteristic, complemented
38C2×C22⋊Dic163—21no—
39#19104667C2211yescharacteristic, complemented
40#19104666C2211yescharacteristic, complemented
41#19104666C2211yescharacteristic, complemented
42Dic163⋊C8C2211yescharacteristic, complemented
43#19104660C2211yescharacteristic, complemented
44#19104658C2211yescharacteristic, complemented
45#19104658C2211yescharacteristic, complemented
46#19104657C2211yescharacteristic, complemented
47#19104656C2211yescharacteristic
48#19104656C2211yescharacteristic
49C22⋊(C163⋊C8)C2211yescharacteristic
50(C2×D163)⋊C8C2211yescharacteristic, complemented
51#19104645C2211yescharacteristic, complemented
52C22×D4×C163C2211yescharacteristic
53C22×C8×C163C2211yescharacteristic
54C2×C4⋊C4×C163C2211yescharacteristic
55#102×C163C2211yescharacteristic
56#102×C163C2211yescharacteristic
57#102×C163C2211yescharacteristic
58#102×C163C2211yescharacteristic
59#14579699—44no—
60#14579698—22no—
61#14579698—41no—
62C2×Dic326—21no—
63C2×Dic326C2311yescharacteristic
64C2×D652—21no—
65C2×D652C2311yescharacteristic
66C2×C22⋊D163—21no—
67C2×C22⋊D163—21no—
68C2×C22⋊D163—21no—
69C2×C22⋊D163D411yescharacteristic
70C22×Dic163—21no—
71C22×Dic163—21no—
72C2×C4×D163—21no—
73C2×C4×D163—21no—
74C2×C4×D163C2311yescharacteristic
75#14579688—41no—
76#14579684—22no—
77#14579684—41no—
78#14579682—41no—
79C2×C163⋊C8C2311yescharacteristic
80C2×C163⋊C8C2311yescharacteristic
81C4⋊Dic163C2311yescharacteristic
82C4⋊Dic163C2311yescharacteristic
83Dic163⋊C4—21no—
84Dic163⋊C4—21no—
85Dic163⋊C4—21no—
86Dic163⋊C4D411yescharacteristic
87C22⋊Dic163—21no—
88C22⋊Dic163—21no—
89C22⋊Dic163—21no—
90C22⋊Dic163—21no—
91C22⋊Dic163—21no—
92C22⋊Dic163D411yescharacteristic
93(C2×D163)⋊C4—21no—
94(C2×D163)⋊C4—21no—
95(C2×D163)⋊C4—21no—
96(C2×D163)⋊C4D411yescharacteristic
97C4×Dic163C2311yescharacteristic
98C24×C163—21no—
99C2×D4×C163—22no—
100C2×D4×C163—21no—
101C2×D4×C163—41no—
102C2×D4×C163C2311yescharacteristic
103C2×D4×C163C2311yescharacteristic
104C22×C4×C163—21no—
105C22×C4×C163C2311yescharacteristic
106C2×C8×C163—41no—
107C2×C8×C163C2311yescharacteristic
108C2×C8×C163C2311yescharacteristic
109C4⋊C4×C163—21no—
110C4⋊C4×C163C2311yescharacteristic
111C4⋊C4×C163C2311yescharacteristic
112C22×D163—21no—
113C22×D163C2×D411yescharacteristic
114Dic326—21no—
115Dic326—21no—
116Dic326—42no—
117D652—21no—
118D652—21no—
119D652—42no—
120C22⋊D163—22no—
121C22⋊D163—42no—
122C22⋊D163—42no—
123C22⋊D163—81no—
124C2×Dic163—21no—
125C2×Dic163—21no—
126C2×Dic163—21no—
127C2×Dic163—42no—
128C2×Dic163—81no—
129C2×Dic163C2×D411yescharacteristic
130C2×Dic163C2×D411yescharacteristic
131C2×Dic163C2×D411yescharacteristic
132C4×D163—21no—
133C4×D163—21no—
134C4×D163—42no—
135C4×D163—42no—
136C163⋊C8—21no—
137C163⋊C8—21no—
138C23×C163—21no—
139C23×C163—21no—
140C23×C163—42no—
141C23×C163—42no—
142C23×C163—81no—
143C23×C163C2×D411yescharacteristic
144D4×C163—21no—
145D4×C163—21no—
146D4×C163—21no—
147D4×C163—42no—
148D4×C163#4112yescomplemented
149C2×C4×C163—21no—
150C2×C4×C163—21no—
151C2×C4×C163—21no—
152C2×C4×C163—21no—
153C2×C4×C163—42no—
154C2×C4×C163C2×D411yescharacteristic
155C2×C4×C163C2411yescharacteristic
156C8×C163—21no—
157C8×C163—21no—
158C22×C163—21no—
159C22×C163—21no—
160C22×C163—22no—
161C22×C163—41no—
162C22×C163—41no—
163C22×C163—41no—
164C22×C163—41no—
165C22×C163—41no—
166C22×C163—84no—
167C22×C163AGL(1,ℤ/8)12yes—
168C22×C163C22×D411yescharacteristic
169C2×D163—21no—
170C2×D163—21no—
171C2×D163—21no—
172C2×D163—41no—
173C2×D163—41no—
174C2×D163—41no—
175C4×C163—21no—
176C4×C163—41no—
177C4×C163—41no—
178C4×C163C2×#4111yescharacteristic
179C4×C163H(5,𝔽2)11yescharacteristic
180Dic163—21no—
181Dic163—21no—
182Dic163—21no—
183Dic163—41no—
184Dic163—41no—
185Dic163—41no—
186C2×C163—22no—
187C2×C163—42no—
188C2×C163—81no—
189C2×C163#54611yescharacteristic
190C2×C163C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C163#57711yescharacteristic
192D163—41no—
193D163—81no—
194C163#330611yescharacteristic, complemented, Sylow
195#3306—1631nomaximal, Sylow
196#547—1631no—
197#546—1631no—
198#489—1631no—
199#483—1631no—
200#481—1631no—
201#476—1631no—
202#469—1631no—
203#465—1631no—
204#463—1631no—
205#449—1631no—
206#447—1631no—
207#442—1631no—
208#435—1631no—
209#417—1631no—
210C2×#102D16311yescharacteristic, complemented
211C2×#41—3261no—
212C2×#41—1631no—
213C22×D4C2×D16311yescharacteristic
214C2×SD16—1631no—
215C2×D8—1631no—
216C2×D8—1631no—
217C2×M16—1631no—
218C22×C8C2×D16311yescharacteristic
219C4⋊Q8—1631no—
220#124—1631no—
221#123—3261no—
222#123—3261no—
223#123—3261no—
224C22⋊Q8—3261no—
225C22⋊Q8—1631no—
226#121—3261no—
227#121—1631no—
228#121—1631no—
229#121—1631no—
230#120—3261no—
231C4×D4—1631no—
232C4×D4—1631no—
233C4×D4—1631no—
234C2×C4⋊C4—1631no—
235C2×C4⋊C4C2×D16311yescharacteristic
236C2×C22⋊C4—3261no—
237#106—1631no—
238#106—1631no—
239#106—1631no—
240C4⋊C8—1631no—
241#103—1631no—
242#103—1631no—
243#103—1631no—
244#102—1631no—
245#102—1631no—
246#102—1631no—
247#102C2×D16311yescharacteristic
248#102C2×D16311yescharacteristic
249#102C2×D16311yescharacteristic
250#102C2×D16311yescharacteristic
251C22⋊C8—1631no—
252C22⋊C8—1631no—
253#97—1631no—
254C24—21no—
255#41—3262no—
256#41—6524no—
257#41—6521no—
258C2×Q8—3261no—
259C2×Q8—1631no—
260C2×D4—22no—
261C2×D4—21no—
262C2×D4—41no—
263C2×D4—3261no—
264C2×D4—3261no—
265C2×D4—3261no—
266C2×D4—3261no—
267C2×D4—1631no—
268C2×D4—1631no—
269C2×D4C22×D16311yescharacteristic
270C2×D4C22×D16311yescharacteristic
271C22×C4—21no—
272C22×C4—3261no—
273C22×C4—3261no—
274C22×C4—3261no—
275C22×C4—3261no—
276C22×C4—1631no—
277C22×C4C22×D16311yescharacteristic
278SD16—6521no—
279D8—3262no—
280D8—6521no—
281M16—6521no—
282C2×C8—41no—
283C2×C8—1631no—
284C2×C8—1631no—
285C2×C8C22×D16311yescharacteristic
286C2×C8C22×D16311yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—3261no—
289C4⋊C4—3261no—
290C4⋊C4—3261no—
291C4⋊C4—1631no—
292C4⋊C4—1631no—
293C4⋊C4—1631no—
294C4⋊C4C22×D16311yescharacteristic
295C4⋊C4C22×D16311yescharacteristic
296C22⋊C4—3261no—
297C22⋊C4—3261no—
298C22⋊C4—3261no—
299C22⋊C4—3261no—
300C22⋊C4—3261no—
301C22⋊C4—3261no—
302C22⋊C4—3261no—
303C22⋊C4—3261no—
304C22⋊C4—1631no—
305C22⋊C4—1631no—
306C42—1631no—
307C23—21no—
308C23—21no—
309C23—42no—
310C23—42no—
311C23—81no—
312C23—3261no—
313C23—1631no—
314C23D4×D16311yescharacteristic
315Q8—3261no—
316Q8—3261no—
317Q8—6522no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—42no—
322D4—13041no—
323D4—3262no—
324D4—3261no—
325D4—3261no—
326D4—6522no—
327D4—6522no—
328D4—6522no—
329D4#1457969912yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—42no—
335C2×C4—13041no—
336C2×C4—3261no—
337C2×C4—3261no—
338C2×C4—3261no—
339C2×C4—3261no—
340C2×C4—3261no—
341C2×C4—6522no—
342C2×C4—6522no—
343C2×C4—6522no—
344C2×C4—1631no—
345C2×C4—1631no—
346C2×C4—1631no—
347C2×C4D4×D16311yescharacteristic
348C2×C4C23×D16311yescharacteristic
349C8—21no—
350C8—21no—
351C8—3261no—
352C8—3261no—
353C22—21no—
354C22—21no—
355C22—22no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—84no—
362C22—3261no—
363C22—3261no—
364C22—3261no—
365C22—6521no—
366C22—6521no—
367C22—6521no—
368C22#1910475912yes—
369C22C2×D4×D16311yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—3261no—
374C4—3261no—
375C4—3261no—
376C4—6521no—
377C4—6521no—
378C4—6521no—
379C4C2×#1457969911yescharacteristic
380C4#1910478011yescharacteristic
381C2—22no—
382C2—42no—
383C2—81no—
384C2—13041no—
385C2—6521no—
386C2#2378230511yescharacteristic
387C2C2×#1910475911yescharacteristic
388C2#2378247111yescharacteristic
subgroupG/H
centerC22C2×D4×D163
commutator, cosocleC2×C4×C163C24
FrattiniC2×C4C23×D163
FittingC2×#102×C163C2
socleC22×C163C22×D4
hypercenterC2×#102D163
hypocenterC163#3306
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #23782316C2semidirect
2. #23782309C2semidirect
3. #23782023C2semidirect
4. #23781995C2semidirect
5. #23781982C2semidirect
6. #23781953C2semidirect
7. #23781917C2semidirect
8. #23781894C2semidirect
9. #23781879C2semidirect
10. #23781811C2semidirect
11. #23781799C2semidirect
12. #23781774C2semidirect
13. #23781736C2semidirect
14. #23781663C2semidirect
15. C2×#102×C163C2semidirect
18. C2×#14579688C22semidirect
21. C2×#14579682C22semidirect
22. #19104734C22semidirect
29. #19104710C22semidirect
35. #19104697C22semidirect
37. C4⋊C4×D163C22semidirect
39. #19104667C22semidirect
40. #19104666C22semidirect
41. #19104666C22semidirect
42. Dic163⋊C8C22semidirect
43. #19104660C22semidirect
44. #19104658C22semidirect
45. #19104658C22semidirect
46. #19104657C22semidirect
50. (C2×D163)⋊C8C22semidirect
51. #19104645C22semidirect
148. D4×C163#41semidirect
194. C163#3306semidirect
210. C2×#102D163semidirect
329. D4#14579699semidirect

Maximal subgroups

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

subgroupindex
#237823162
#237823092
#237820232
#237819952
#237819822
#237819532
#237819172
#237818942
#237818792
#237818112
#237817992
#237817742
#237817362
#237816632
C2×#102×C1632
#3306163