Finite Group Databasebeta

← #35226514

Subgroups — #35226514

Order 20864.

394 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23782361C211yesmaximal, characteristic, complemented
2#23782320C211yesmaximal, characteristic, complemented
3#23782034C211yesmaximal, characteristic, complemented
4#23782007C211yesmaximal, characteristic, complemented
5#23781996C211yesmaximal, characteristic, complemented
6#23781966C211yesmaximal, characteristic, complemented
7#23781911C211yesmaximal, characteristic, complemented
8#23781894C211yesmaximal, characteristic, complemented
9#23781871C211yesmaximal, characteristic, complemented
10#23781812C211yesmaximal, characteristic, complemented
11#23781812C211yesmaximal, characteristic, complemented
12#23781778C211yesmaximal, characteristic, complemented
13#23781667C211yesmaximal, characteristic, complemented
14#23781662C211yesmaximal, characteristic, complemented
15#435×C163C211yesmaximal, characteristic, complemented
16C2×#14579699C2211yescharacteristic
17C2×#14579699C2211yescharacteristic
18C2×#14579688C2211yescharacteristic
19C2×#14579688C2211yescharacteristic
20C2×D1304C2211yescharacteristic
21#19104735C2211yescharacteristic
22#19104730—21no—
23#19104727C2211yescharacteristic
24#19104717—21no—
25#19104717—21no—
26#19104717—21no—
27#19104714C2211yescharacteristic
28#19104714C2211yescharacteristic
29#19104709C2211yescharacteristic
30#19104709C2211yescharacteristic
31#19104707—21no—
32#19104706—21no—
33C4×D652C2211yescharacteristic
34C4×D652C2211yescharacteristic
35(C22⋊D163)⋊C4—21no—
36#19104694C2211yescharacteristic
37C2×C4⋊Dic163C2211yescharacteristic
38C4⋊C4×D163—21no—
39#19104669C2211yescharacteristic
40#19104667C2211yescharacteristic
41#19104667C2211yescharacteristic
42#19104660C2211yescharacteristic
43#19104660C2211yescharacteristic
44#19104660C2211yescharacteristic
45#19104660C2211yescharacteristic
46#19104660C2211yescharacteristic
47#19104660C2211yescharacteristic
48#19104657C2211yescharacteristic
49#19104657C2211yescharacteristic
50#19104657C2211yescharacteristic
51#19104657C2211yescharacteristic
52C2×M16×C163C2211yescharacteristic
53C22×C8×C163C2211yescharacteristic
54C4×D4×C163C2211yescharacteristic
55C4⋊C8×C163C2211yescharacteristic
56C22⋊C8×C163C2211yescharacteristic
57C22⋊C8×C163C2211yescharacteristic
58#97×C163C2211yescharacteristic
59#14579699—22no—
60#14579699—22no—
61#14579699—41no—
62#14579699—41no—
63C2×Dic326C2311yescharacteristic
64C2×Dic326C2311yescharacteristic
65C2×D652C2311yescharacteristic
66C2×D652C2311yescharacteristic
67C2×C22⋊D163—21no—
68C2×C22⋊D163—21no—
69C2×C22⋊D163—21no—
70C2×C22⋊D163—21no—
71C22×Dic163—21no—
72C2×C4×D163—21no—
73C2×C4×D163—21no—
74C2×C4×D163—21no—
75C2×C4×D163—21no—
76#14579688—41no—
77#14579688—41no—
78D1304—22no—
79C4⋊Dic163—21no—
80C4⋊Dic163—21no—
81C4⋊Dic163—21no—
82C4⋊Dic163C2311yescharacteristic
83C4⋊Dic163C2311yescharacteristic
84C4⋊Dic163C2311yescharacteristic
85C4⋊Dic163C2311yescharacteristic
86Dic163⋊C4—21no—
87Dic163⋊C4—21no—
88Dic163⋊C4—21no—
89Dic163⋊C4—21no—
90C22⋊Dic163—21no—
91C22⋊Dic163—21no—
92C22⋊Dic163—21no—
93(C2×D163)⋊C4—21no—
94(C2×D163)⋊C4—21no—
95(C2×D163)⋊C4—21no—
96(C2×D163)⋊C4—21no—
97C4×Dic163—21no—
98C2×D4×C163D411yescharacteristic
99C22×C4×C163C2311yescharacteristic
100C22×C4×C163C2311yescharacteristic
101M16×C163—41no—
102C2×C8×C163—41no—
103C2×C8×C163C2311yescharacteristic
104C2×C8×C163C2311yescharacteristic
105C2×C8×C163C2311yescharacteristic
106C2×C8×C163C2311yescharacteristic
107C4⋊C4×C163D411yescharacteristic
108C22⋊C4×C163D411yescharacteristic
109C22⋊C4×C163D411yescharacteristic
110C42×C163C2311yescharacteristic
111C22×D163—21no—
112C22×D163—21no—
113Dic326—21no—
114Dic326—21no—
115Dic326—21no—
116Dic326—21no—
117D652—21no—
118D652—21no—
119D652—21no—
120D652#4112yes—
121C22⋊D163—42no—
122C22⋊D163—42no—
123C22⋊D163—42no—
124C22⋊D163—81no—
125C2×Dic163—21no—
126C2×Dic163—21no—
127C2×Dic163—21no—
128C2×Dic163—21no—
129C2×Dic163—21no—
130C2×Dic163—21no—
131C2×Dic163—81no—
132C4×D163—42no—
133C4×D163—42no—
134C4×D163—42no—
135C4×D163—81no—
136C23×C163C2×D411yescharacteristic
137C23×C163C2×D411yescharacteristic
138D4×C163—41no—
139C2×C4×C163—21no—
140C2×C4×C163—21no—
141C2×C4×C163—21no—
142C2×C4×C163—21no—
143C2×C4×C163C2×D411yescharacteristic
144C2×C4×C163C2×D411yescharacteristic
145C2×C4×C163C2×D411yescharacteristic
146C2×C4×C163C2×D411yescharacteristic
147C2×C4×C163C2411yescharacteristic
148C8×C163—21no—
149C8×C163—21no—
150C8×C163—21no—
151C8×C163—21no—
152C22×C163—21no—
153C22×C163—21no—
154C22×C163—21no—
155C22×C163—21no—
156C22×C163—21no—
157C22×C163—21no—
158C22×C163C22×D411yescharacteristic
159C2×D163—22no—
160C2×D163—41no—
161C2×D163—41no—
162C2×D163—41no—
163C2×D163—41no—
164C2×D163—41no—
165C4×C163—21no—
166C4×C163—21no—
167C4×C163—21no—
168C4×C163—21no—
169C4×C163C2×#4111yescharacteristic
170C4×C163H(5,𝔽2)11yescharacteristic
171Dic163—41no—
172Dic163—41no—
173Dic163—41no—
174Dic163—41no—
175Dic163—41no—
176Dic163—41no—
177C2×C163—41no—
178C2×C163—41no—
179C2×C163#54611yescharacteristic
180C2×C163#57511yescharacteristic
181C2×C163#57711yescharacteristic
182D163—42no—
183D163—81no—
184C163#330711yescharacteristic, complemented, Sylow
185#3307—1631nomaximal, Sylow
186#553—1631no—
187#547—1631no—
188#491—1631no—
189#485—1631no—
190#483—1631no—
191#478—1631no—
192#468—1631no—
193#465—1631no—
194#461—1631no—
195#449—1631no—
196#449—1631no—
197#442—1631no—
198#435D16311yescharacteristic, complemented
199#417—1631no—
200#416—1631no—
201C2×#41—1631no—
202C2×#41—1631no—
203C2×SD16—1631no—
204C2×SD16—1631no—
205C2×D8—1631no—
206C2×M16C2×D16311yescharacteristic
207C22×C8C2×D16311yescharacteristic
208C4⋊Q8—1631no—
209#126—3261no—
210#125—1631no—
211#123—3261no—
212#123—3261no—
213#123—3261no—
214C22⋊Q8—1631no—
215C22⋊Q8—1631no—
216#121—3261no—
217#121—3261no—
218#121—1631no—
219#121—1631no—
220C4×D4—3261no—
221C4×D4—1631no—
222C4×D4—1631no—
223C4×D4C2×D16311yescharacteristic
224#117—1631no—
225C2×C4⋊C4—3261no—
226C2×C4⋊C4—1631no—
227#107—1631no—
228#106—1631no—
229#106—1631no—
230C4⋊C8C2×D16311yescharacteristic
231#103—1631no—
232#103—1631no—
233#103—1631no—
234#103—1631no—
235#103—1631no—
236#103—1631no—
237#102—1631no—
238#102—1631no—
239#102—1631no—
240#102—1631no—
241C22⋊C8C2×D16311yescharacteristic
242C22⋊C8C2×D16311yescharacteristic
243#97C2×D16311yescharacteristic
244#41—3262no—
245#41—3262no—
246#41—6521no—
247#41—6521no—
248C2×Q8—1631no—
249C2×Q8—1631no—
250C2×D4—3261no—
251C2×D4—3261no—
252C2×D4—3261no—
253C2×D4—3261no—
254C2×D4—1631no—
255C2×D4—1631no—
256C2×D4D65211yescharacteristic
257C22×C4—3261no—
258C22×C4—3261no—
259C22×C4—3261no—
260C22×C4—3261no—
261C22×C4—3261no—
262C22×C4C22×D16311yescharacteristic
263C22×C4C22×D16311yescharacteristic
264SD16—6521no—
265SD16—6521no—
266D8—3262no—
267M16—41no—
268C2×C8—41no—
269C2×C8C22×D16311yescharacteristic
270C2×C8C22×D16311yescharacteristic
271C2×C8C22×D16311yescharacteristic
272C2×C8C22×D16311yescharacteristic
273C4⋊C4—3261no—
274C4⋊C4—3261no—
275C4⋊C4—3261no—
276C4⋊C4—3261no—
277C4⋊C4—3261no—
278C4⋊C4—3261no—
279C4⋊C4—3261no—
280C4⋊C4—1631no—
281C4⋊C4—1631no—
282C4⋊C4—1631no—
283C4⋊C4—1631no—
284C4⋊C4D65211yescharacteristic
285C22⋊C4—3261no—
286C22⋊C4—3261no—
287C22⋊C4—3261no—
288C22⋊C4—3261no—
289C22⋊C4—3261no—
290C22⋊C4—3261no—
291C22⋊C4—3261no—
292C22⋊C4D65211yescharacteristic
293C22⋊C4D65211yescharacteristic
294C42—3261no—
295C42C22×D16311yescharacteristic
296C23—3261no—
297C23—3261no—
298C23C2×D65211yescharacteristic
299C23C2×D65211yescharacteristic
300Q8—3261no—
301Q8—3261no—
302Q8—3261no—
303Q8—3261no—
304D4—41no—
305D4—13041no—
306D4—3261no—
307D4—3261no—
308D4—3261no—
309D4—6522no—
310D4—6522no—
311D4—6522no—
312D4—1632no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—13041no—
318C2×C4—13041no—
319C2×C4—3261no—
320C2×C4—3261no—
321C2×C4—3261no—
322C2×C4—3261no—
323C2×C4—3261no—
324C2×C4—3261no—
325C2×C4—6522no—
326C2×C4—6522no—
327C2×C4—6522no—
328C2×C4C2×D65211yescharacteristic
329C2×C4C2×D65211yescharacteristic
330C2×C4C2×D65211yescharacteristic
331C2×C4C2×D65211yescharacteristic
332C2×C4C23×D16311yescharacteristic
333C8—21no—
334C8—21no—
335C8—21no—
336C8—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—3262no—
344C22—6521no—
345C22—6521no—
346C22—6521no—
347C22—6521no—
348C22—6521no—
349C22C22×D65211yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—6521no—
355C4—6521no—
356C4—6521no—
357C4—6521no—
358C4—6521no—
359C4—6521no—
360C4#41×D16311yescharacteristic
361C4#1910478011yescharacteristic
362C2—41no—
363C2—41no—
364C2—13041no—
365C2—6522no—
366C2#2378231011yescharacteristic
367C2#2378246511yescharacteristic
368C2#2378247711yescharacteristic
subgroupG/H
centerC22C22×D652
commutator, cosocleC2×C4×C163C24
FrattiniC2×C4C23×D163
Fitting#435×C163C2
socleC22×C163C22×D4
hypercenter#435D163
hypocenterC163#3307
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #23782361C2semidirect
2. #23782320C2semidirect
3. #23782034C2semidirect
4. #23782007C2semidirect
5. #23781996C2semidirect
6. #23781966C2semidirect
7. #23781911C2semidirect
8. #23781894C2semidirect
9. #23781871C2semidirect
10. #23781812C2semidirect
11. #23781812C2semidirect
12. #23781778C2semidirect
13. #23781667C2semidirect
14. #23781662C2semidirect
15. #435×C163C2semidirect
184. C163#3307semidirect
198. #435D163semidirect

Maximal subgroups

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

subgroupindex
#237823612
#237823202
#237820342
#237820072
#237819962
#237819662
#237819112
#237818942
#237818712
#237818122
#237817782
#237816672
#237816622
#435×C1632
#3307163