Finite Group Databasebeta

← #35225129

Subgroups — #35225129

Order 20864.

408 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23782212C211yesmaximal, characteristic, complemented
2#23782197C211yesmaximal, characteristic, complemented
3#23782073C211yesmaximal, characteristic, complemented
4#23782053C211yesmaximal, characteristic, complemented
5#23782028C211yesmaximal, characteristic, complemented
6#23782023C211yesmaximal, characteristic, complemented
7#23781917C211yesmaximal, characteristic, complemented
8#23781915C211yesmaximal, characteristic, complemented
9#23781912C211yesmaximal, characteristic, complemented
10#23781910C211yesmaximal, characteristic, complemented
11C4×#14579688C211yesmaximal, characteristic, complemented
12C4×#14579687C211yesmaximal, characteristic, complemented
13C4×#14579684C211yesmaximal, characteristic, complemented
14C4×#14579682C211yesmaximal, characteristic, complemented
15C4×D8×C163C211yesmaximal, characteristic, complemented
16C2×#14579699—21no—
17C2×#14579688C2211yescharacteristic
18C2×#14579687C2211yescharacteristic
19C2×#14579684C2211yescharacteristic
20C2×#14579682C2211yescharacteristic
21C2×#14579682C2211yescharacteristic
22#19104734C2211yescharacteristic
23#19104731C2211yescharacteristic
24#19104728—21no—
25#19104726C2211yescharacteristic
26#19104722C2211yescharacteristic
27#19104721—21no—
28#19104717—21no—
29#19104715C2211yescharacteristic
30#19104710C2211yescharacteristic
31#19104708—21no—
32#19104706C2211yescharacteristic
33#19104706C2211yescharacteristic
34C4×Dic326C2211yescharacteristic
35C4×D652C2211yescharacteristic
36C4×C22⋊D163—21no—
37C4×C22⋊D163—21no—
38#19104694—21no—
39C42×D163C2211yescharacteristic
40#19104668C2211yescharacteristic
41#19104667C2211yescharacteristic
42#19104666C2211yescharacteristic
43#19104660C2211yescharacteristic
44#19104658C2211yescharacteristic
45#19104657C2211yescharacteristic
46#19104656C2211yescharacteristic
47#19104656C2211yescharacteristic
48#19104655C2211yescharacteristic
49#19104645C2211yescharacteristic
50#19104645C2211yescharacteristic
51C4×C163⋊C8C2211yescharacteristic
52C2×D8×C163C2211yescharacteristic
53C4×D4×C163C2211yescharacteristic
54C4×D4×C163C2211yescharacteristic
55#107×C163C2211yescharacteristic
56#102×C163C2211yescharacteristic
57#102×C163C2211yescharacteristic
58C4×C8×C163C2211yescharacteristic
59#14579699—44no—
60C2×Dic326—21no—
61C2×Dic326C2311yescharacteristic
62C2×D652—21no—
63C2×D652C2311yescharacteristic
64C2×C22⋊D163—21no—
65C2×C22⋊D163—21no—
66C2×C22⋊D163—21no—
67C2×C22⋊D163—21no—
68C2×C4×D163—21no—
69C2×C4×D163D411yescharacteristic
70C2×C4×D163D411yescharacteristic
71C2×C4×D163C2311yescharacteristic
72#14579688—22no—
73#14579687—22no—
74#14579684—22no—
75#14579682—22no—
76#14579682—22no—
77C2×C163⋊C8C2311yescharacteristic
78C2×C163⋊C8C2311yescharacteristic
79C4⋊Dic163—21no—
80C4⋊Dic163—21no—
81C4⋊Dic163C2311yescharacteristic
82C4⋊Dic163C2311yescharacteristic
83Dic163⋊C4—21no—
84Dic163⋊C4—21no—
85Dic163⋊C4—21no—
86C22⋊Dic163—21no—
87C22⋊Dic163—21no—
88C22⋊Dic163—21no—
89C22⋊Dic163—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×D4×C163C2311yescharacteristic
98C2×D4×C163C2311yescharacteristic
99C22×C4×C163—21no—
100C22×C4×C163—21no—
101D8×C163—22no—
102C2×C8×C163C2311yescharacteristic
103C2×C8×C163C2311yescharacteristic
104C4⋊C4×C163C2311yescharacteristic
105C4⋊C4×C163C2311yescharacteristic
106C22⋊C4×C163—21no—
107C22⋊C4×C163—21no—
108C42×C163C2311yescharacteristic
109C22×D163—21no—
110C22×D163C2×D411yescharacteristic
111Dic326—21no—
112Dic326—21no—
113Dic326—42no—
114D652—21no—
115D652—21no—
116D652—42no—
117C22⋊D163—42no—
118C22⋊D163—42no—
119C22⋊D163—42no—
120C22⋊D163—42no—
121C2×Dic163—21no—
122C2×Dic163—21no—
123C2×Dic163—21no—
124C2×Dic163C2×D411yescharacteristic
125C2×Dic163C2×D411yescharacteristic
126C2×Dic163C2×D411yescharacteristic
127C4×D163—22no—
128C4×D163—21no—
129C4×D163—21no—
130C4×D163—41no—
131C4×D163—42no—
132C163⋊C8—21no—
133C163⋊C8#4112yescomplemented
134C23×C163—21no—
135C23×C163—21no—
136D4×C163—21no—
137D4×C163—21no—
138D4×C163—21no—
139D4×C163—21no—
140C2×C4×C163—21no—
141C2×C4×C163—21no—
142C2×C4×C163—42no—
143C2×C4×C163—42no—
144C2×C4×C163C2×D411yescharacteristic
145C2×C4×C163C2×D411yescharacteristic
146C2×C4×C163C2411yescharacteristic
147C8×C163—21no—
148C8×C163#4112yescomplemented
149C22×C163—41no—
150C22×C163—41no—
151C22×C163—41no—
152C22×C163—41no—
153C22×C163—41no—
154C22×C163—41no—
155C22×C163C22×D411yescharacteristic
156C2×D163—21no—
157C2×D163—21no—
158C2×D163—21no—
159C2×D163—41no—
160C2×D163—41no—
161C2×D163—41no—
162C4×C163—21no—
163C4×C163—41no—
164C4×C163—41no—
165C4×C163AGL(1,ℤ/8)12yes—
166C4×C163C2×#4111yescharacteristic
167C4×C163C2×#4111yescharacteristic
168Dic163—21no—
169Dic163—21no—
170Dic163—21no—
171Dic163—41no—
172Dic163—41no—
173Dic163—41no—
174C2×C163—81no—
175C2×C163—81no—
176C2×C163#53211yescharacteristic
177C2×C163C2×AGL(1,ℤ/8)11yescharacteristic
178C2×C163#57511yescharacteristic
179D163—41no—
180D163—81no—
181C163#317111yescharacteristic, complemented, Sylow
182#3171—1631nomaximal, Sylow
183#532—1631no—
184#529—1631no—
185#501—1631no—
186#496—1631no—
187#490—1631no—
188#489—1631no—
189#469—1631no—
190#469—1631no—
191#468—1631no—
192#468—1631no—
193C4×SD16—1631no—
194C4×SD16—1631no—
195C4×D8—1631no—
196C4×D8D16311yescharacteristic, complemented
197C4×M16—1631no—
198C2×#41—3261no—
199C2×SD16—1631no—
200C2×SD16—1631no—
201C2×D8—1631no—
202C2×D8C2×D16311yescharacteristic
203C2×M16—1631no—
204C2×M16—1631no—
205C4⋊Q8—1631no—
206#127—1631no—
207#126—3261no—
208#125—1631no—
209#124—3261no—
210#124—1631no—
211#123—3261no—
212C22⋊Q8—1631no—
213#121—3261no—
214#121—1631no—
215#121—1631no—
216#121—1631no—
217C4×Q8—1631no—
218C4×D4—3261no—
219C4×D4—3261no—
220C4×D4—1631no—
221C4×D4C2×D16311yescharacteristic
222C4×D4C2×D16311yescharacteristic
223#117—3261no—
224C2×C42—1631no—
225#107—1631no—
226#107C2×D16311yescharacteristic
227#106—1631no—
228#106—1631no—
229#103—1631no—
230#103—1631no—
231#102—1631no—
232#102—1631no—
233#102—1631no—
234#102—1631no—
235#102C2×D16311yescharacteristic
236#102C2×D16311yescharacteristic
237#97—1631no—
238#97—1631no—
239C4×C8—1631no—
240C4×C8C2×D16311yescharacteristic
241#41—6524no—
242C2×Q8—3261no—
243C2×Q8—1631no—
244C2×D4—3261no—
245C2×D4—3261no—
246C2×D4—3261no—
247C2×D4—3261no—
248C2×D4—3261no—
249C2×D4—1631no—
250C2×D4C22×D16311yescharacteristic
251C2×D4C22×D16311yescharacteristic
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—3261no—
255C22×C4—1631no—
256C22×C4—1631no—
257C22×C4—1631no—
258SD16—3262no—
259SD16—3262no—
260D8—22no—
261D8—3262no—
262M16—3262no—
263M16—3262no—
264C2×C8—1631no—
265C2×C8—1631no—
266C2×C8C22×D16311yescharacteristic
267C2×C8C22×D16311yescharacteristic
268C4⋊C4—3261no—
269C4⋊C4—3261no—
270C4⋊C4—3261no—
271C4⋊C4—3261no—
272C4⋊C4—3261no—
273C4⋊C4—1631no—
274C4⋊C4—1631no—
275C4⋊C4C22×D16311yescharacteristic
276C4⋊C4C22×D16311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—3261no—
280C22⋊C4—3261no—
281C22⋊C4—3261no—
282C22⋊C4—3261no—
283C22⋊C4—3261no—
284C22⋊C4—3261no—
285C22⋊C4—3261no—
286C42—3261no—
287C42—1631no—
288C42—1631no—
289C42—1631no—
290C42C22×D16311yescharacteristic
291C23—21no—
292C23—21no—
293C23—3261no—
294C23—1631no—
295Q8—3261no—
296Q8—3261no—
297Q8—6522no—
298D4—21no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—3261no—
303D4—3261no—
304D4—6522no—
305D4—6522no—
306D4—6522no—
307D4—6522no—
308D4—6522no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—3261no—
314C2×C4—3261no—
315C2×C4—3262no—
316C2×C4—3261no—
317C2×C4—3261no—
318C2×C4—3261no—
319C2×C4—6521no—
320C2×C4—6522no—
321C2×C4—1631no—
322C2×C4—1631no—
323C2×C4—1631no—
324C2×C4D4×D16311yescharacteristic
325C2×C4D4×D16311yescharacteristic
326C2×C4C23×D16311yescharacteristic
327C8—21no—
328C8—3261no—
329C8—1632no—
330C8#1457969912yescomplemented
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—3261no—
338C22—3261no—
339C22—3261no—
340C22—6521no—
341C22—6521no—
342C22—6521no—
343C22C2×D4×D16311yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—3261no—
348C4—3261no—
349C4—3261no—
350C4—6521no—
351C4—6521no—
352C4—6521no—
353C4#1910475912yes—
354C4#41×D16311yescharacteristic
355C4C2×#1457969911yescharacteristic
356C2—81no—
357C2—81no—
358C2—13041no—
359C2—6521no—
360C2#2378221211yescharacteristic
361C2C2×#1910475911yescharacteristic
362C2#2378246211yescharacteristic
subgroupG/H
centerC2×C4D4×D163
commutator, cosocleC2×C4×C163C24
FrattiniC2×C4C23×D163
FittingC4×D8×C163C2
socleC22×C163C22×D4
hypercenterC4×D8D163
hypocenterC163#3171
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. #23782197C2semidirect
3. #23782073C2semidirect
4. #23782053C2semidirect
5. #23782028C2semidirect
6. #23782023C2semidirect
7. #23781917C2semidirect
8. #23781915C2semidirect
9. #23781912C2semidirect
10. #23781910C2semidirect
11. C4×#14579688C2semidirect
12. C4×#14579687C2semidirect
13. C4×#14579684C2semidirect
14. C4×#14579682C2semidirect
15. C4×D8×C163C2semidirect
133. C163⋊C8#41semidirect
148. C8×C163#41semidirect
181. C163#3171semidirect
196. C4×D8D163semidirect
330. C8#14579699semidirect

Maximal subgroups

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

subgroupindex
#237822122
#237821972
#237820732
#237820532
#237820282
#237820232
#237819172
#237819152
#237819122
#237819102
C4×#145796882
C4×#145796872
C4×#145796842
C4×#145796822
C4×D8×C1632
#3171163