Finite Group Databasebeta

← #35224487

Subgroups — #35224487

Order 20864.

418 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23782231C211yesmaximal, characteristic
2#23782146C211yesmaximal, characteristic, complemented
3#23781992C211yesmaximal, characteristic, complemented
4#23781990C211yesmaximal, characteristic, complemented
5#23781987C211yesmaximal, characteristic, complemented
6#23781986C211yesmaximal, characteristic, complemented
7#23781983C211yesmaximal, characteristic, complemented
8#23781982C211yesmaximal, characteristic, complemented
9#23781980C211yesmaximal, characteristic, complemented
10#23781706C211yesmaximal, characteristic, complemented
11#23781702C211yesmaximal, characteristic, complemented
12#23781668C211yesmaximal, characteristic, complemented
13#102×D163C211yesmaximal, characteristic, complemented
14#23781630C211yesmaximal, characteristic, complemented
15#480×C163C211yesmaximal, characteristic, complemented
16C2×#14579699C2211yescharacteristic
17C2×D4×D163C2211yescharacteristic
18C2×#14579682C2211yescharacteristic
19C2×C8×D163C2211yescharacteristic
20#19104731—21no—
21#19104721—21no—
22#19104710C2211yescharacteristic
23#19104709C2211yescharacteristic
24#19104706C2211yescharacteristic
25#19104705—21no—
26#19104703—21no—
27#19104700—21no—
28#19104697—21no—
29C4×C22⋊D163—21no—
30C4×C22⋊D163—21no—
31#19104694C2211yescharacteristic, complemented
32#19104693C2211yescharacteristic
33#19104693C2211yescharacteristic
34#19104693C2211yescharacteristic, complemented
35C4⋊C4×D163C2211yescharacteristic
36C4⋊C4×D163C2211yescharacteristic, complemented
37#19104669C2211yescharacteristic, complemented
38#19104668C2211yescharacteristic, complemented
39#19104667C2211yescharacteristic, complemented
40#19104666C2211yescharacteristic, complemented
41#19104666C2211yescharacteristic, complemented
42#19104666C2211yescharacteristic, complemented
43#19104657C2211yescharacteristic
44#19104657C2211yescharacteristic
45#19104656C2211yescharacteristic
46#19104656C2211yescharacteristic
47#19104655C2211yescharacteristic
48#19104655C2211yescharacteristic
49C22⋊(C163⋊C8)C2211yescharacteristic, complemented
50(C2×D163)⋊C8C2211yescharacteristic, complemented
51(C2×D163)⋊C8C2211yescharacteristic, complemented
52#121×C163C2211yescharacteristic
53C2×C4⋊C4×C163C2211yescharacteristic, complemented
54#107×C163C2211yescharacteristic, complemented
55#107×C163C2211yescharacteristic, complemented
56#102×C163C2211yescharacteristic
57#102×C163C2211yescharacteristic
58C22⋊C8×C163C2211yescharacteristic, complemented
59C23×D163—21no—
60#14579699—22no—
61#14579699—22no—
62C2×Dic326D411yescharacteristic
63C2×D652—21no—
64C2×D652D411yescharacteristic
65C2×D652C2311yescharacteristic
66C2×C22⋊D163—21no—
67C2×C22⋊D163—21no—
68C2×C22⋊D163—21no—
69C2×C22⋊D163D411yescharacteristic
70C2×C22⋊D163D411yescharacteristic
71D4×D163—22no—
72D4×D163—22no—
73C2×C4×D163—21no—
74C2×C4×D163—21no—
75C2×C4×D163C2311yescharacteristic
76C2×C4×D163C2311yescharacteristic
77#14579682—22no—
78C2×C163⋊C8C2311yescharacteristic
79C2×C163⋊C8C2311yescharacteristic
80C8×D163—22no—
81C4⋊Dic163C2311yescharacteristic
82C4⋊Dic163C2311yescharacteristic
83C4⋊Dic163C2311yescharacteristic
84Dic163⋊C4—21no—
85Dic163⋊C4—21no—
86C22⋊Dic163—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—
93C4×Dic163—21no—
94C4×Dic163—21no—
95C4×Dic163—21no—
96C4×Dic163—21no—
97C2×D4×C163—21no—
98C2×D4×C163C2311yescharacteristic
99C22×C4×C163—21no—
100C22×C4×C163C2311yescharacteristic
101C2×C8×C163C2311yescharacteristic
102C2×C8×C163C2311yescharacteristic
103C4⋊C4×C163—21no—
104C4⋊C4×C163C2311yescharacteristic
105C4⋊C4×C163C2311yescharacteristic
106C4⋊C4×C163C2311yescharacteristic
107C22⋊C4×C163—21no—
108C22×D163—21no—
109C22×D163—42no—
110C22×D163—81no—
111C22×D163—81no—
112C22×D163C2×D411yescharacteristic
113C22×D163C2×D411yescharacteristic
114Dic326—22no—
115D652—22no—
116D652—21no—
117D652—21no—
118D652—81no—
119C22⋊D163—22no—
120C22⋊D163—22no—
121C22⋊D163—42no—
122C22⋊D163—81no—
123C22⋊D163—81no—
124C2×Dic163—21no—
125C2×Dic163—21no—
126C2×Dic163—21no—
127C2×Dic163C2×D411yescharacteristic
128C2×Dic163C2×D411yescharacteristic
129C4×D163—21no—
130C4×D163—21no—
131C4×D163—81no—
132C4×D163—81no—
133C4×D163#4112yes—
134C4×D163#4112yes—
135C163⋊C8—21no—
136C163⋊C8—21no—
137C23×C163—21no—
138C23×C163C2×D411yescharacteristic
139D4×C163—21no—
140D4×C163—21no—
141D4×C163—81no—
142C2×C4×C163—21no—
143C2×C4×C163—21no—
144C2×C4×C163—21no—
145C2×C4×C163—21no—
146C2×C4×C163—21no—
147C2×C4×C163—81no—
148C2×C4×C163C2×D411yescharacteristic
149C2×C4×C163C2411yescharacteristic
150C8×C163—21no—
151C8×C163—21no—
152C22×C163—21no—
153C22×C163—21no—
154C22×C163—21no—
155C22×C163—41no—
156C22×C163—41no—
157C22×C163—41no—
158C22×C163C22×D411yescharacteristic
159C2×D163—21no—
160C2×D163—21no—
161C2×D163—21no—
162C2×D163—21no—
163C2×D163—21no—
164C2×D163—41no—
165C2×D163—41no—
166C2×D163—41no—
167C2×D163—84no—
168C2×D163#12312yes—
169C4×C163—21no—
170C4×C163—41no—
171C4×C163—41no—
172C4×C163—41no—
173C4×C163C2×#4111yescharacteristic
174C4×C163C2×#4111yescharacteristic
175Dic163—21no—
176Dic163—41no—
177Dic163—41no—
178Dic163—41no—
179Dic163#12312yes—
180C2×C163—41no—
181C2×C163—81no—
182C2×C163C2×#12311yescharacteristic
183C2×C163#57611yescharacteristic
184C2×C163#57711yescharacteristic
185D163—22no—
186D163—41no—
187D163—81no—
188C163#309611yescharacteristic, complemented, Sylow
189#3096—1631nomaximal, Sylow
190#535—1631no—
191#520—1631no—
192#482—1631no—
193#482—1631no—
194#482—1631no—
195#482—1631no—
196#481—1631no—
197#481—1631no—
198#480—1631no—
199#480D16311yescharacteristic, complemented
200#428—1631no—
201#427—1631no—
202#418—1631no—
203C2×#102—1631no—
204#408—1631no—
205C2×#41—1631no—
206C22×D4—1631no—
207C2×M16—1631no—
208C22×C8—1631no—
209#127—3261no—
210#124—3261no—
211#121—1631no—
212#121—1631no—
213#121—1631no—
214#121C2×D16311yescharacteristic
215#120—3261no—
216#120—3261no—
217C4×Q8—3261no—
218C4×D4—3261no—
219C4×D4—3261no—
220C4×D4—3261no—
221#117—1631no—
222#117—1631no—
223#117—1631no—
224#117—1631no—
225C2×C4⋊C4—1631no—
226C2×C4⋊C4—1631no—
227C2×C4⋊C4C2×D16311yescharacteristic, complemented
228#107—1631no—
229#107—1631no—
230#107C2×D16311yescharacteristic, complemented
231#107C2×D16311yescharacteristic, complemented
232#106—1631no—
233#106—1631no—
234#106—1631no—
235#106—1631no—
236#102—1631no—
237#102—1631no—
238#102—1631no—
239#102—1631no—
240#102—1631no—
241#102—1631no—
242#102C2×D16311yescharacteristic
243#102C2×D16311yescharacteristic
244C22⋊C8—1631no—
245C22⋊C8—1631no—
246C22⋊C8—1631no—
247C22⋊C8C2×D16311yescharacteristic, complemented
248C24—3261no—
249#41—3262no—
250#41—3262no—
251C2×Q8—1631no—
252C2×D4—21no—
253C2×D4—3261no—
254C2×D4—3261no—
255C2×D4—3261no—
256C2×D4—3262no—
257C2×D4—3262no—
258C2×D4—3261no—
259C2×D4—1631no—
260C2×D4—1631no—
261C2×D4—1631no—
262C2×D4—1631no—
263C2×D4C22×D16311yescharacteristic
264C22×C4—21no—
265C22×C4—3261no—
266C22×C4—3261no—
267C22×C4—1631no—
268C22×C4—1631no—
269C22×C4C22×D16311yescharacteristic
270M16—3262no—
271C2×C8—3262no—
272C2×C8—1631no—
273C2×C8—1631no—
274C2×C8C22×D16311yescharacteristic
275C2×C8C22×D16311yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—3261no—
278C4⋊C4—3261no—
279C4⋊C4—1631no—
280C4⋊C4—1631no—
281C4⋊C4—1631no—
282C4⋊C4C22×D16311yescharacteristic
283C4⋊C4C22×D16311yescharacteristic
284C4⋊C4C22×D16311yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—3261no—
287C22⋊C4—3261no—
288C22⋊C4—3261no—
289C22⋊C4—3261no—
290C22⋊C4—3261no—
291C22⋊C4—3261no—
292C22⋊C4—3261no—
293C42—3261no—
294C42—3261no—
295C42—3261no—
296C42—3261no—
297C23—21no—
298C23—13041no—
299C23—13041no—
300C23—3261no—
301C23—6522no—
302C23—1631no—
303C23—1631no—
304C23D4×D16311yescharacteristic
305Q8—3262no—
306D4—21no—
307D4—21no—
308D4—81no—
309D4—13041no—
310D4—13041no—
311D4—13041no—
312D4—3262no—
313D4—3262no—
314D4—3262no—
315D4—3261no—
316D4—3261no—
317D4—6522no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—81no—
324C2×C4—13041no—
325C2×C4—13041no—
326C2×C4—3261no—
327C2×C4—3261no—
328C2×C4—3261no—
329C2×C4—3261no—
330C2×C4—3261no—
331C2×C4—1631no—
332C2×C4—1631no—
333C2×C4—1632no—
334C2×C4—1632no—
335C2×C4D4×D16311yescharacteristic
336C2×C4C23×D16311yescharacteristic
337C8—21no—
338C8—21no—
339C8—3261no—
340C8—3261no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—13044no—
348C22—3261no—
349C22—3261no—
350C22—3261no—
351C22—3261no—
352C22—3261no—
353C22—6521no—
354C22—6521no—
355C22—6521no—
356C22—1632no—
357C22C2×D4×D16311yescharacteristic
358C4—21no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—3261no—
363C4—6521no—
364C4—6521no—
365C4—6521no—
366C4—1632no—
367C4#41×D16311yescharacteristic
368C4#41×D16311yescharacteristic
369C2—41no—
370C2—81no—
371C2—13041no—
372C2—3262no—
373C2—6521no—
374C2#123×D16311yescharacteristic
375C2#2378246611yescharacteristic
376C2#2378247411yescharacteristic
subgroupG/H
centerC22C2×D4×D163
commutator, cosocleC2×C4×C163C24
FrattiniC2×C4C23×D163
Fitting#480×C163C2
socleC22×C163C22×D4
prime radical#23782231C2
hypercenter#480D163
hypocenterC163#3096
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #23782146C2semidirect
3. #23781992C2semidirect
4. #23781990C2semidirect
5. #23781987C2semidirect
6. #23781986C2semidirect
7. #23781983C2semidirect
8. #23781982C2semidirect
9. #23781980C2semidirect
10. #23781706C2semidirect
11. #23781702C2semidirect
12. #23781668C2semidirect
13. #102×D163C2semidirect
14. #23781630C2semidirect
15. #480×C163C2semidirect
31. #19104694C22semidirect
34. #19104693C22semidirect
36. C4⋊C4×D163C22semidirect
37. #19104669C22semidirect
38. #19104668C22semidirect
39. #19104667C22semidirect
40. #19104666C22semidirect
41. #19104666C22semidirect
42. #19104666C22semidirect
49. C22⋊(C163⋊C8)C22semidirect
50. (C2×D163)⋊C8C22semidirect
51. (C2×D163)⋊C8C22semidirect
53. C2×C4⋊C4×C163C22semidirect
54. #107×C163C22semidirect
55. #107×C163C22semidirect
58. C22⋊C8×C163C22semidirect
188. C163#3096semidirect
199. #480D163semidirect
227. C2×C4⋊C4C2×D163semidirect
230. #107C2×D163semidirect
231. #107C2×D163semidirect
247. C22⋊C8C2×D163semidirect

Maximal subgroups

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

subgroupindex
#237822312
#237821462
#237819922
#237819902
#237819872
#237819862
#237819832
#237819822
#237819802
#237817062
#237817022
#237816682
#102×D1632
#237816302
#480×C1632
#3096163