Finite Group Databasebeta

← #35224729

Subgroups — #35224729

Order 20864.

396 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#23782145C211yesmaximal, characteristic, complemented
2#23781981C211yesmaximal, characteristic, complemented
3#23781976C211yesmaximal, characteristic, complemented
4#23781969C211yesmaximal, characteristic, complemented
5#23781962C211yesmaximal, characteristic, complemented
6#23781862C211yesmaximal, characteristic, complemented
7#23781857C211yesmaximal, characteristic, complemented
8#23781808C211yesmaximal, characteristic, complemented
9#23781808C211yesmaximal, characteristic, complemented
10#23781775C211yesmaximal, characteristic, complemented
11#23781765C211yesmaximal, characteristic, complemented
12C4×#14579687C211yesmaximal, characteristic, complemented
13C4×#14579684C211yesmaximal, characteristic, complemented
14#23781726C211yesmaximal, characteristic, complemented
15#540×C163C211yesmaximal, characteristic, complemented
16C2×#14579699C2211yescharacteristic
17C2×#14579687C2211yescharacteristic
18C2×#14579687C2211yescharacteristic
19C2×#14579684C2211yescharacteristic
20C2×#14579684C2211yescharacteristic
21C4×Dic326C2211yescharacteristic
22C4×Dic326C2211yescharacteristic
23C4×D652C2211yescharacteristic
24C4×D652C2211yescharacteristic
25(C22⋊D163)⋊C4—21no—
26(C22⋊D163)⋊C4—21no—
27#19104693—21no—
28C2×C4⋊Dic163C2211yescharacteristic
29C4⋊C4×D163—21no—
30#19104668C2211yescharacteristic
31#19104668C2211yescharacteristic
32#19104666C2211yescharacteristic
33#19104666C2211yescharacteristic
34C4⋊(C163⋊C8)C2211yescharacteristic
35C4⋊(C163⋊C8)C2211yescharacteristic
36#19104658C2211yescharacteristic
37#19104658C2211yescharacteristic
38#19104656C2211yescharacteristic
39#19104656C2211yescharacteristic
40#19104656C2211yescharacteristic
41#19104656C2211yescharacteristic
42#19104655C2211yescharacteristic
43#19104655C2211yescharacteristic
44C22⋊(C163⋊C8)C2211yescharacteristic
45C22⋊(C163⋊C8)C2211yescharacteristic
46#19104646C2211yescharacteristic
47C4×C163⋊C8C2211yescharacteristic
48#127×C163C2211yescharacteristic
49#125×C163C2211yescharacteristic
50#123×C163—21no—
51#123×C163—21no—
52#121×C163—21no—
53#121×C163—21no—
54#121×C163C2211yescharacteristic
55#121×C163C2211yescharacteristic
56C4×D4×C163C2211yescharacteristic
57C4×D4×C163C2211yescharacteristic
58#117×C163C2211yescharacteristic
59#14579699—22no—
60#14579699—22no—
61C2×Dic326C2311yescharacteristic
62C2×D652C2311yescharacteristic
63C2×C22⋊D163—21no—
64C22×Dic163—21no—
65C2×C4×D163—21no—
66C2×C4×D163—21no—
67C2×C4×D163—21no—
68#14579687—22no—
69#14579687—22no—
70#14579684—22no—
71#14579684—22no—
72C2×C163⋊C8C2311yescharacteristic
73C2×C163⋊C8C2311yescharacteristic
74C2×C163⋊C8C2311yescharacteristic
75C2×C163⋊C8C2311yescharacteristic
76C4⋊Dic163—21no—
77C4⋊Dic163C2311yescharacteristic
78C4⋊Dic163C2311yescharacteristic
79Dic163⋊C4—21no—
80Dic163⋊C4—21no—
81(C2×D163)⋊C4—21no—
82(C2×D163)⋊C4—21no—
83C4×Dic163—21no—
84C4×Dic163—21no—
85C2×D4×C163—21no—
86C2×D4×C163—21no—
87C2×D4×C163—21no—
88C2×D4×C163—21no—
89C2×D4×C163C2311yescharacteristic
90C2×D4×C163C2311yescharacteristic
91C22×C4×C163—21no—
92C22×C4×C163—21no—
93C22×C4×C163C2311yescharacteristic
94C4⋊C4×C163—21no—
95C4⋊C4×C163—21no—
96C4⋊C4×C163D411yescharacteristic
97C4⋊C4×C163D411yescharacteristic
98C4⋊C4×C163C2311yescharacteristic
99C4⋊C4×C163C2311yescharacteristic
100C22⋊C4×C163—21no—
101C22⋊C4×C163—21no—
102C22⋊C4×C163—21no—
103C22⋊C4×C163—21no—
104C22⋊C4×C163D411yescharacteristic
105C22⋊C4×C163D411yescharacteristic
106C42×C163C2311yescharacteristic
107C42×C163C2311yescharacteristic
108C22×D163—21no—
109Dic326—21no—
110Dic326#4112yes—
111D652—21no—
112D652#4112yes—
113C22⋊D163—24no—
114C2×Dic163—21no—
115C2×Dic163—21no—
116C2×Dic163—21no—
117C2×Dic163—81no—
118C4×D163—24no—
119C4×D163—81no—
120C4×D163—81no—
121C163⋊C8—21no—
122C163⋊C8—21no—
123C163⋊C8—21no—
124C163⋊C8—21no—
125C23×C163—21no—
126C23×C163—21no—
127C23×C163C2×D411yescharacteristic
128D4×C163—21no—
129D4×C163—21no—
130D4×C163—21no—
131D4×C163—21no—
132D4×C163—81no—
133D4×C163—81no—
134D4×C163—81no—
135D4×C163—81no—
136C2×C4×C163—21no—
137C2×C4×C163—21no—
138C2×C4×C163—21no—
139C2×C4×C163—21no—
140C2×C4×C163—81no—
141C2×C4×C163—81no—
142C2×C4×C163C2×D411yescharacteristic
143C2×C4×C163C2×D411yescharacteristic
144C2×C4×C163C2×D411yescharacteristic
145C2×C4×C163C2×D411yescharacteristic
146C2×C4×C163C2×D411yescharacteristic
147C2×C4×C163C2411yescharacteristic
148C22×C163—21no—
149C22×C163—21no—
150C22×C163—21no—
151C22×C163—41no—
152C22×C163—41no—
153C22×C163—41no—
154C22×C163—41no—
155C22×C163—41no—
156C22×C163—41no—
157C22×C163C22×D411yescharacteristic
158C2×D163—22no—
159C2×D163—41no—
160C2×D163—41no—
161C4×C163—21no—
162C4×C163—21no—
163C4×C163—21no—
164C4×C163—21no—
165C4×C163—21no—
166C4×C163—41no—
167C4×C163—41no—
168C4×C163C2×#4111yescharacteristic
169C4×C163C2×#4111yescharacteristic
170Dic163—22no—
171Dic163—41no—
172Dic163—41no—
173C2×C163—41no—
174C2×C163—81no—
175C2×C163—81no—
176C2×C163#52511yescharacteristic
177C2×C163#57611yescharacteristic
178C2×C163#57711yescharacteristic
179D163—42no—
180C163#311911yescharacteristic, complemented, Sylow
181#3119—1631nomaximal, Sylow
182#540D16311yescharacteristic, complemented
183#520—1631no—
184#481—1631no—
185#480—1631no—
186#479—1631no—
187#478—1631no—
188#460—1631no—
189#459—1631no—
190#449—1631no—
191#449—1631no—
192#442—1631no—
193#440—1631no—
194C4×SD16—1631no—
195C4×D8—1631no—
196#433—1631no—
197C2×#41—1631no—
198C2×SD16—1631no—
199C2×SD16—1631no—
200C2×D8—1631no—
201C2×D8—1631no—
202#127C2×D16311yescharacteristic
203#125C2×D16311yescharacteristic
204#123—21no—
205#123—21no—
206#121—21no—
207#121—21no—
208#121C2×D16311yescharacteristic
209#121C2×D16311yescharacteristic
210C4×Q8—1631no—
211C4×Q8—1631no—
212C4×D4—3261no—
213C4×D4—3261no—
214C4×D4—1631no—
215C4×D4—1631no—
216C4×D4C2×D16311yescharacteristic
217C4×D4C2×D16311yescharacteristic
218#117—3261no—
219#117C2×D16311yescharacteristic
220C2×C4⋊C4—3261no—
221C2×C4⋊C4—1631no—
222#107—1631no—
223#107—1631no—
224#106—1631no—
225#106—1631no—
226C4⋊C8—1631no—
227C4⋊C8—1631no—
228#103—1631no—
229#103—1631no—
230#102—1631no—
231#102—1631no—
232#102—1631no—
233#102—1631no—
234#102—1631no—
235#102—1631no—
236C22⋊C8—1631no—
237C22⋊C8—1631no—
238#97—1631no—
239C4×C8—1631no—
240#41—3262no—
241#41—3262no—
242C2×Q8—1631no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—3261no—
248C2×D4—1631no—
249C2×D4C22×D16311yescharacteristic
250C2×D4C22×D16311yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—3261no—
254C22×C4—3261no—
255C22×C4—3261no—
256C22×C4—3261no—
257C22×C4C22×D16311yescharacteristic
258SD16—3262no—
259SD16—3262no—
260D8—3262no—
261D8—3262no—
262C2×C8—1631no—
263C2×C8—1631no—
264C2×C8—1631no—
265C2×C8—1631no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—3261no—
269C4⋊C4—3261no—
270C4⋊C4—3261no—
271C4⋊C4—1631no—
272C4⋊C4—1631no—
273C4⋊C4C22⋊D16311yescharacteristic
274C4⋊C4C22⋊D16311yescharacteristic
275C4⋊C4C22×D16311yescharacteristic
276C4⋊C4C22×D16311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—3261no—
282C22⋊C4—3261no—
283C22⋊C4C22⋊D16311yescharacteristic
284C22⋊C4C22⋊D16311yescharacteristic
285C42—3261no—
286C42—3261no—
287C42C22×D16311yescharacteristic
288C42C22×D16311yescharacteristic
289C23—21no—
290C23—21no—
291C23—3261no—
292C23C2×C22⋊D16311yescharacteristic
293Q8—3261no—
294Q8—1632no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—81no—
301D4—81no—
302D4—81no—
303D4—3264no—
304D4—3261no—
305D4—1632no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—13041no—
313C2×C4—13041no—
314C2×C4—13041no—
315C2×C4—3264no—
316C2×C4—3261no—
317C2×C4—3261no—
318C2×C4—3261no—
319C2×C4C2×C22⋊D16311yescharacteristic
320C2×C4C2×C22⋊D16311yescharacteristic
321C2×C4C2×C22⋊D16311yescharacteristic
322C2×C4C2×C22⋊D16311yescharacteristic
323C2×C4C2×C22⋊D16311yescharacteristic
324C2×C4C23×D16311yescharacteristic
325C8—3261no—
326C8—3261no—
327C8—3261no—
328C8—3261no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—3262no—
339C22—6521no—
340C22—6521no—
341C22C22×C22⋊D16311yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—3262no—
350C4—6521no—
351C4—6521no—
352C4#41×D16311yescharacteristic
353C4#41×D16311yescharacteristic
354C2—41no—
355C2—81no—
356C2—81no—
357C2—6522no—
358C2#2378217211yescharacteristic
359C2#2378246811yescharacteristic
360C2#2378247611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D163
commutator, cosocleC2×C4×C163C24
FrattiniC2×C4C23×D163
Fitting#540×C163C2
socleC22×C163C22×D4
hypercenter#540D163
hypocenterC163#3119
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #23782145C2semidirect
2. #23781981C2semidirect
3. #23781976C2semidirect
4. #23781969C2semidirect
5. #23781962C2semidirect
6. #23781862C2semidirect
7. #23781857C2semidirect
8. #23781808C2semidirect
9. #23781808C2semidirect
10. #23781775C2semidirect
11. #23781765C2semidirect
12. C4×#14579687C2semidirect
13. C4×#14579684C2semidirect
14. #23781726C2semidirect
15. #540×C163C2semidirect
180. C163#3119semidirect
182. #540D163semidirect

Maximal subgroups

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

subgroupindex
#237821452
#237819812
#237819762
#237819692
#237819622
#237818622
#237818572
#237818082
#237817752
#237817652
C4×#145796872
C4×#145796842
#237817262
#540×C1632
#3119163