Finite Group Databasebeta

← #35224534

Subgroups — #35224534

Order 20864.

492 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23782212C211yesmaximal, characteristic, complemented
2C4×D4×D163C211yesmaximal, characteristic, complemented
3#23781980C211yesmaximal, characteristic, complemented
4#23781977C211yesmaximal, characteristic, complemented
5#23781944C211yesmaximal, characteristic, complemented
6#23781943C211yesmaximal, characteristic, complemented
7#23781859C211yesmaximal, characteristic, complemented
8#23781858C211yesmaximal, characteristic, complemented
9#23781800C211yesmaximal, characteristic, complemented
10#23781797C211yesmaximal, characteristic, complemented
11C4×D1304C211yesmaximal, characteristic, complemented
12C4×#14579684C211yesmaximal, characteristic, complemented
13C4×#14579684C211yesmaximal, characteristic, complemented
14#23781716C211yesmaximal, characteristic, complemented
15C4×D8×C163C211yesmaximal, characteristic, complemented
16C2×#14579699—21no—
17C2×D4×D163C2211yescharacteristic
18C22×C4×D163—21no—
19C2×D1304C2211yescharacteristic
20C2×#14579684C2211yescharacteristic
21C2×#14579684C2211yescharacteristic
22#19104734C2211yescharacteristic, complemented
23#19104731C2211yescharacteristic, complemented
24#19104721—21no—
25#19104710C2211yescharacteristic
26#19104708—21no—
27#19104706C2211yescharacteristic
28C4×D652C2211yescharacteristic
29C4×D652C2211yescharacteristic, complemented
30D4×Dic163C2211yescharacteristic
31#19104697C2211yescharacteristic
32C4×C22⋊D163—21no—
33C4×C22⋊D163—21no—
34(C22⋊D163)⋊C4—21no—
35C4⋊C4×D163C2211yescharacteristic
36C22⋊C4×D163—21no—
37C42×D163C2211yescharacteristic
38#19104669C2211yescharacteristic, complemented
39#19104668C2211yescharacteristic, complemented
40#19104668C2211yescharacteristic, complemented
41Dic163⋊C8C2211yescharacteristic, complemented
42Dic163⋊C8C2211yescharacteristic, complemented
43#19104657C2211yescharacteristic
44#19104657C2211yescharacteristic, complemented
45#19104656C2211yescharacteristic
46#19104656C2211yescharacteristic, complemented
47#19104655C2211yescharacteristic
48#19104655C2211yescharacteristic, complemented
49(C2×D163)⋊C8C2211yescharacteristic
50(C2×D163)⋊C8C2211yescharacteristic
51C4×C163⋊C8C2211yescharacteristic, complemented
52C2×D8×C163C2211yescharacteristic
53C4×D4×C163C2211yescharacteristic
54C4×D4×C163C2211yescharacteristic, complemented
55#107×C163C2211yescharacteristic, complemented
56#102×C163C2211yescharacteristic
57#102×C163C2211yescharacteristic, complemented
58C4×C8×C163C2211yescharacteristic, complemented
59C23×D163—21no—
60#14579699—44no—
61C2×Dic326—21no—
62C2×D652—21no—
63C2×D652C2311yescharacteristic
64C2×D652C2311yescharacteristic
65C2×C22⋊D163—21no—
66C2×C22⋊D163—21no—
67C2×C22⋊D163—21no—
68C2×C22⋊D163—21no—
69D4×D163—22no—
70D4×D163—22no—
71C22×Dic163—21no—
72C2×C4×D163—21no—
73C2×C4×D163—21no—
74C2×C4×D163—21no—
75C2×C4×D163—21no—
76C2×C4×D163—44no—
77C2×C4×D163D411yescharacteristic
78C2×C4×D163D411yescharacteristic
79C2×C4×D163C2311yescharacteristic
80D1304—22no—
81#14579684—22no—
82#14579684—22no—
83C2×C163⋊C8C2311yescharacteristic
84C2×C163⋊C8C2311yescharacteristic
85C4⋊Dic163C2311yescharacteristic
86C4⋊Dic163C2311yescharacteristic
87Dic163⋊C4—21no—
88Dic163⋊C4—21no—
89C22⋊Dic163—21no—
90C22⋊Dic163—21no—
91(C2×D163)⋊C4—21no—
92(C2×D163)⋊C4—21no—
93(C2×D163)⋊C4—21no—
94(C2×D163)⋊C4—21no—
95C4×Dic163D411yescharacteristic
96C4×Dic163D411yescharacteristic
97C4×Dic163C2311yescharacteristic
98C2×D4×C163C2311yescharacteristic
99C2×D4×C163C2311yescharacteristic
100C22×C4×C163—21no—
101C22×C4×C163—21no—
102D8×C163—22no—
103C2×C8×C163C2311yescharacteristic
104C2×C8×C163C2311yescharacteristic
105C4⋊C4×C163C2311yescharacteristic
106C4⋊C4×C163C2311yescharacteristic
107C22⋊C4×C163—21no—
108C22⋊C4×C163—21no—
109C42×C163C2311yescharacteristic
110C22×D163—24no—
111C22×D163—21no—
112C22×D163—21no—
113C22×D163—42no—
114C22×D163—42no—
115C22×D163C2×D411yescharacteristic
116Dic326—42no—
117D652—21no—
118D652—21no—
119D652—21no—
120D652—42no—
121D652#4112yescomplemented
122C22⋊D163—24no—
123C22⋊D163—42no—
124C22⋊D163—42no—
125C22⋊D163—42no—
126C2×Dic163—21no—
127C2×Dic163—21no—
128C2×Dic163—42no—
129C2×Dic163C2×D411yescharacteristic
130C2×Dic163C2×D411yescharacteristic
131C2×Dic163C2×D411yescharacteristic
132C4×D163—21no—
133C4×D163—21no—
134C4×D163—41no—
135C4×D163—42no—
136C4×D163—42no—
137C4×D163—42no—
138C4×D163—42no—
139C4×D163D814yescomplemented
140C163⋊C8—21no—
141C163⋊C8—21no—
142C23×C163—21no—
143C23×C163—21no—
144D4×C163—21no—
145D4×C163—21no—
146D4×C163—21no—
147D4×C163#4112yescomplemented
148C2×C4×C163—21no—
149C2×C4×C163—21no—
150C2×C4×C163—42no—
151C2×C4×C163—42no—
152C2×C4×C163C2×D411yescharacteristic
153C2×C4×C163C2×D411yescharacteristic
154C2×C4×C163C2411yescharacteristic
155C8×C163—21no—
156C8×C163—21no—
157C22×C163—22no—
158C22×C163—41no—
159C22×C163—41no—
160C22×C163—41no—
161C22×C163—41no—
162C22×C163—41no—
163C22×C163C22×D411yescharacteristic
164C2×D163—21no—
165C2×D163—21no—
166C2×D163—22no—
167C2×D163—48no—
168C2×D163—41no—
169C2×D163—41no—
170C2×D163—41no—
171C2×D163—41no—
172C2×D163—41no—
173C2×D163C2×D812yes—
174C4×C163—21no—
175C4×C163—41no—
176C4×C163—41no—
177C4×C163C2×D812yes—
178C4×C163C2×#4111yescharacteristic
179C4×C163C2×#4111yescharacteristic
180Dic163—21no—
181Dic163—21no—
182Dic163—41no—
183Dic163—41no—
184Dic163C2×D812yes—
185C2×C163—42no—
186C2×C163—81no—
187C2×C163#52511yescharacteristic
188C2×C163C22×D811yescharacteristic
189C2×C163#57511yescharacteristic
190D163—22no—
191D163—42no—
192D163—81no—
193C163#310011yescharacteristic, complemented, Sylow
194#3100—1631nomaximal, Sylow
195#532—1631no—
196C2×C4×D4—1631no—
197#480—1631no—
198#480—1631no—
199#474—1631no—
200#474—1631no—
201#459—1631no—
202#459—1631no—
203#447—1631no—
204#447—1631no—
205C4×D8—1631no—
206C4×D8—1631no—
207C4×D8—1631no—
208C4×D8D16311yescharacteristic, complemented
209#431—1631no—
210C2×#41—3261no—
211C22×D4—1631no—
212C23×C4—3261no—
213C2×D8—1631no—
214C2×D8—1631no—
215C2×D8—1631no—
216C2×D8C2×D16311yescharacteristic
217C4⋊Q8—1631no—
218#127—1631no—
219#124—3261no—
220#121—3261no—
221#121—1631no—
222#121—1631no—
223C4×D4—3261no—
224C4×D4—3261no—
225C4×D4—3261no—
226C4×D4—1631no—
227C4×D4—1631no—
228C4×D4—1631no—
229C4×D4—1631no—
230C4×D4C2×D16311yescharacteristic
231C4×D4C2×D16311yescharacteristic, complemented
232C2×C4⋊C4—1631no—
233C2×C22⋊C4—3261no—
234C2×C42—1631no—
235#107—1631no—
236#107—1631no—
237#107—1631no—
238#107C2×D16311yescharacteristic, complemented
239C4⋊C8—1631no—
240C4⋊C8—1631no—
241#102—1631no—
242#102—1631no—
243#102—1631no—
244#102—1631no—
245#102—1631no—
246#102—1631no—
247#102C2×D16311yescharacteristic
248#102C2×D16311yescharacteristic, complemented
249C22⋊C8—1631no—
250C22⋊C8—1631no—
251C4×C8—1631no—
252C4×C8C2×D16311yescharacteristic, complemented
253C24—3261no—
254#41—6524no—
255C2×Q8—3261no—
256C2×D4—3261no—
257C2×D4—3262no—
258C2×D4—3262no—
259C2×D4—3261no—
260C2×D4—3261no—
261C2×D4—3261no—
262C2×D4—3261no—
263C2×D4—1631no—
264C2×D4—1631no—
265C2×D4C22×D16311yescharacteristic
266C2×D4C22×D16311yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—3261no—
270C22×C4—3261no—
271C22×C4—3261no—
272C22×C4—3261no—
273C22×C4—3261no—
274C22×C4—6524no—
275C22×C4—1631no—
276C22×C4—1631no—
277C22×C4—1631no—
278D8—22no—
279D8—3262no—
280D8—3262no—
281D8—3262no—
282C2×C8—1631no—
283C2×C8—1631no—
284C2×C8C22×D16311yescharacteristic
285C2×C8C22×D16311yescharacteristic
286C4⋊C4—3261no—
287C4⋊C4—3261no—
288C4⋊C4—1631no—
289C4⋊C4—1631no—
290C4⋊C4C22×D16311yescharacteristic
291C4⋊C4C22×D16311yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—3261no—
295C22⋊C4—3261no—
296C22⋊C4—3261no—
297C22⋊C4—3261no—
298C22⋊C4—3261no—
299C22⋊C4—3261no—
300C42—1631no—
301C42—1631no—
302C42—1631no—
303C42C22×D16311yescharacteristic
304C23—21no—
305C23—21no—
306C23—3264no—
307C23—3261no—
308C23—3261no—
309C23—6522no—
310C23—6522no—
311C23—1631no—
312Q8—6522no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—3264no—
317D4—3261no—
318D4—3261no—
319D4—3261no—
320D4—6522no—
321D4—6522no—
322D4—6522no—
323D4—6522no—
324D4—1632no—
325D4#1457969912yescomplemented
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—3261no—
331C2×C4—3261no—
332C2×C4—3261no—
333C2×C4—3261no—
334C2×C4—6521no—
335C2×C4—6522no—
336C2×C4—6522no—
337C2×C4—6522no—
338C2×C4—6522no—
339C2×C4—6522no—
340C2×C4—1631no—
341C2×C4—1631no—
342C2×C4—1631no—
343C2×C4—1634no—
344C2×C4D4×D16311yescharacteristic
345C2×C4D4×D16311yescharacteristic
346C2×C4C23×D16311yescharacteristic
347C8—21no—
348C8—21no—
349C8—3261no—
350C8—3261no—
351C22—22no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—3261no—
358C22—3261no—
359C22—3262no—
360C22—6528no—
361C22—6521no—
362C22—6521no—
363C22—6521no—
364C22—6521no—
365C22—6521no—
366C22—1632no—
367C22C2×D4×D16311yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—3261no—
372C4—3261no—
373C4—6521no—
374C4—6521no—
375C4—1632no—
376C4D8×D16312yes—
377C4#41×D16311yescharacteristic
378C4C2×#1457969911yescharacteristic
379C2—42no—
380C2—81no—
381C2—13041no—
382C2—3262no—
383C2—6522no—
384C2#2378217411yescharacteristic
385C2C2×D8×D16311yescharacteristic
386C2#2378246211yescharacteristic
subgroupG/H
centerC2×C4D4×D163
commutator, cosocleC2×C4×C163C24
FrattiniC2×C4C23×D163
FittingC4×D8×C163C2
socleC22×C163C22×D4
hypercenterC4×D8D163
hypocenterC163#3100
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #23782212C2semidirect
2. C4×D4×D163C2semidirect
3. #23781980C2semidirect
4. #23781977C2semidirect
5. #23781944C2semidirect
6. #23781943C2semidirect
7. #23781859C2semidirect
8. #23781858C2semidirect
9. #23781800C2semidirect
10. #23781797C2semidirect
11. C4×D1304C2semidirect
12. C4×#14579684C2semidirect
13. C4×#14579684C2semidirect
14. #23781716C2semidirect
15. C4×D8×C163C2semidirect
22. #19104734C22semidirect
23. #19104731C22semidirect
29. C4×D652C22semidirect
38. #19104669C22semidirect
39. #19104668C22semidirect
40. #19104668C22semidirect
41. Dic163⋊C8C22semidirect
42. Dic163⋊C8C22semidirect
44. #19104657C22semidirect
46. #19104656C22semidirect
48. #19104655C22semidirect
51. C4×C163⋊C8C22semidirect
54. C4×D4×C163C22semidirect
55. #107×C163C22semidirect
57. #102×C163C22semidirect
58. C4×C8×C163C22semidirect
121. D652#41semidirect
139. C4×D163D8semidirect
147. D4×C163#41semidirect
193. C163#3100semidirect
208. C4×D8D163semidirect
231. C4×D4C2×D163semidirect
238. #107C2×D163semidirect
248. #102C2×D163semidirect
252. C4×C8C2×D163semidirect
325. D4#14579699semidirect

Maximal subgroups

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

subgroupindex
#237822122
C4×D4×D1632
#237819802
#237819772
#237819442
#237819432
#237818592
#237818582
#237818002
#237817972
C4×D13042
C4×#145796842
#237817162
C4×D8×C1632
#3100163