Finite Group Databasebeta

← #35224737

Subgroups — #35224737

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#23782270C211yesmaximal, characteristic, complemented
2#23782145C211yesmaximal, characteristic, complemented
3#23781984C211yesmaximal, characteristic, complemented
4#23781979C211yesmaximal, characteristic, complemented
5#23781973C211yesmaximal, characteristic, complemented
6#23781966C211yesmaximal, characteristic, complemented
7#23781866C211yesmaximal, characteristic, complemented
8#23781861C211yesmaximal, characteristic, complemented
9#23781812C211yesmaximal, characteristic, complemented
10#23781812C211yesmaximal, characteristic, complemented
11#23781778C211yesmaximal, characteristic, complemented
12#23781767C211yesmaximal, characteristic, complemented
13C4×#14579688C211yesmaximal, characteristic, complemented
14C4×D1304C211yesmaximal, characteristic, complemented
15#433×C163C211yesmaximal, characteristic, complemented
16C2×#14579699C2211yescharacteristic
17C2×#14579688C2211yescharacteristic
18C2×#14579688C2211yescharacteristic
19C2×D1304C2211yescharacteristic
20C2×D1304C2211yescharacteristic
21#19104732C2211yescharacteristic
22#19104727C2211yescharacteristic
23#19104720—21no—
24#19104720—21no—
25#19104709C2211yescharacteristic
26#19104709C2211yescharacteristic
27#19104708—21no—
28#19104708—21no—
29C4×Dic326C2211yescharacteristic
30C4×Dic326C2211yescharacteristic
31C4×D652C2211yescharacteristic
32C4×D652C2211yescharacteristic
33C4×D652C2211yescharacteristic
34C4×D652C2211yescharacteristic
35(C22⋊D163)⋊C4—21no—
36(C22⋊D163)⋊C4—21no—
37#19104693—21no—
38C2×C4⋊Dic163C2211yescharacteristic
39C4⋊C4×D163—21no—
40#19104669C2211yescharacteristic
41#19104669C2211yescharacteristic
42#19104667C2211yescharacteristic
43#19104667C2211yescharacteristic
44#19104660C2211yescharacteristic
45#19104660C2211yescharacteristic
46#19104657C2211yescharacteristic
47#19104657C2211yescharacteristic
48#19104657C2211yescharacteristic
49#19104657C2211yescharacteristic
50#19104657C2211yescharacteristic
51#19104657C2211yescharacteristic
52#117×C163C2211yescharacteristic
53C4⋊C8×C163C2211yescharacteristic
54C4⋊C8×C163C2211yescharacteristic
55C22⋊C8×C163C2211yescharacteristic
56C22⋊C8×C163C2211yescharacteristic
57#97×C163C2211yescharacteristic
58C4×C8×C163C2211yescharacteristic
59#14579699—22no—
60#14579699—22no—
61C2×Dic326C2311yescharacteristic
62C2×D652—21no—
63C2×D652—21no—
64C2×D652C2311yescharacteristic
65C2×D652C2311yescharacteristic
66C2×D652C2311yescharacteristic
67C2×C22⋊D163—21no—
68C2×C22⋊D163—21no—
69C2×C22⋊D163—21no—
70C22×Dic163—21no—
71C2×C4×D163—21no—
72C2×C4×D163—21no—
73C2×C4×D163—21no—
74C2×C4×D163—21no—
75C2×C4×D163—21no—
76#14579688—22no—
77#14579688—22no—
78D1304—22no—
79D1304—22no—
80C4⋊Dic163—21no—
81C4⋊Dic163C2311yescharacteristic
82C4⋊Dic163C2311yescharacteristic
83C4⋊Dic163C2311yescharacteristic
84C4⋊Dic163C2311yescharacteristic
85Dic163⋊C4—21no—
86Dic163⋊C4—21no—
87Dic163⋊C4—21no—
88Dic163⋊C4—21no—
89(C2×D163)⋊C4—21no—
90(C2×D163)⋊C4—21no—
91(C2×D163)⋊C4—21no—
92(C2×D163)⋊C4—21no—
93(C2×D163)⋊C4—21no—
94(C2×D163)⋊C4—21no—
95C4×Dic163—21no—
96C4×Dic163—21no—
97C22×C4×C163C2311yescharacteristic
98C2×C8×C163C2311yescharacteristic
99C2×C8×C163C2311yescharacteristic
100C2×C8×C163C2311yescharacteristic
101C2×C8×C163C2311yescharacteristic
102C4⋊C4×C163D411yescharacteristic
103C4⋊C4×C163D411yescharacteristic
104C22⋊C4×C163D411yescharacteristic
105C22⋊C4×C163D411yescharacteristic
106C42×C163C2311yescharacteristic
107C42×C163C2311yescharacteristic
108C22×D163—21no—
109C22×D163—21no—
110C22×D163—21no—
111Dic326—21no—
112Dic326#4112yes—
113D652—21no—
114D652—21no—
115D652—21no—
116D652—21no—
117D652—21no—
118D652—81no—
119D652—81no—
120D652#4112yes—
121C22⋊D163—24no—
122C22⋊D163—81no—
123C22⋊D163—81no—
124C2×Dic163—21no—
125C2×Dic163—21no—
126C2×Dic163—21no—
127C2×Dic163—21no—
128C2×Dic163—21no—
129C2×Dic163—81no—
130C4×D163—24no—
131C4×D163—81no—
132C4×D163—81no—
133C4×D163—81no—
134C4×D163—81no—
135C23×C163C2×D411yescharacteristic
136C2×C4×C163—21no—
137C2×C4×C163—21no—
138C2×C4×C163C2×D411yescharacteristic
139C2×C4×C163C2×D411yescharacteristic
140C2×C4×C163C2×D411yescharacteristic
141C2×C4×C163C2×D411yescharacteristic
142C2×C4×C163C2×D411yescharacteristic
143C2×C4×C163C2411yescharacteristic
144C8×C163—21no—
145C8×C163—21no—
146C8×C163—21no—
147C8×C163—21no—
148C22×C163—21no—
149C22×C163—21no—
150C22×C163—21no—
151C22×C163C22×D411yescharacteristic
152C2×D163—22no—
153C2×D163—41no—
154C2×D163—41no—
155C2×D163—41no—
156C2×D163—41no—
157C2×D163—41no—
158C2×D163—41no—
159C2×D163—41no—
160C2×D163—41no—
161C4×C163—21no—
162C4×C163—21no—
163C4×C163—21no—
164C4×C163—21no—
165C4×C163—21no—
166C4×C163C2×#4111yescharacteristic
167C4×C163C2×#4111yescharacteristic
168Dic163—22no—
169Dic163—41no—
170Dic163—41no—
171Dic163—41no—
172Dic163—41no—
173C2×C163—41no—
174C2×C163#52511yescharacteristic
175C2×C163#57611yescharacteristic
176C2×C163#57711yescharacteristic
177D163—42no—
178D163—81no—
179D163—81no—
180C163#311911yescharacteristic, complemented, Sylow
181#3119—1631nomaximal, Sylow
182#540—1631no—
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#433D16311yescharacteristic, complemented
197C2×#41—1631no—
198C2×SD16—1631no—
199C2×SD16—1631no—
200C2×D8—1631no—
201C2×D8—1631no—
202#127—1631no—
203#125—1631no—
204#123—3261no—
205#123—3261no—
206#121—3261no—
207#121—3261no—
208#121—1631no—
209#121—1631no—
210C4×Q8—1631no—
211C4×Q8—1631no—
212C4×D4—3261no—
213C4×D4—3261no—
214C4×D4—1631no—
215C4×D4—1631no—
216C4×D4—1631no—
217C4×D4—1631no—
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⋊C8C2×D16311yescharacteristic
227C4⋊C8C2×D16311yescharacteristic
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⋊C8C2×D16311yescharacteristic
237C22⋊C8C2×D16311yescharacteristic
238#97C2×D16311yescharacteristic
239C4×C8C2×D16311yescharacteristic
240#41—3262no—
241#41—3262no—
242C2×Q8—1631no—
243C2×D4—3261no—
244C2×D4—3261no—
245C2×D4—3261no—
246C2×D4—3261no—
247C2×D4—3261no—
248C2×D4—1631no—
249C2×D4—1631no—
250C2×D4—1631no—
251C22×C4—3261no—
252C22×C4—3261no—
253C22×C4—3261no—
254C22×C4—3261no—
255C22×C4—3261no—
256C22×C4—3261no—
257C22×C4C22×D16311yescharacteristic
258SD16—3262no—
259SD16—3262no—
260D8—3262no—
261D8—3262no—
262C2×C8C22×D16311yescharacteristic
263C2×C8C22×D16311yescharacteristic
264C2×C8C22×D16311yescharacteristic
265C2×C8C22×D16311yescharacteristic
266C4⋊C4—3261no—
267C4⋊C4—3261no—
268C4⋊C4—3261no—
269C4⋊C4—3261no—
270C4⋊C4—3261no—
271C4⋊C4—1631no—
272C4⋊C4—1631no—
273C4⋊C4—1631no—
274C4⋊C4—1631no—
275C4⋊C4D65211yescharacteristic
276C4⋊C4D65211yescharacteristic
277C22⋊C4—3261no—
278C22⋊C4—3261no—
279C22⋊C4—3261no—
280C22⋊C4—3261no—
281C22⋊C4—3261no—
282C22⋊C4—3261no—
283C22⋊C4D65211yescharacteristic
284C22⋊C4D65211yescharacteristic
285C42—3261no—
286C42—3261no—
287C42C22×D16311yescharacteristic
288C42C22×D16311yescharacteristic
289C23—3261no—
290C23—3261no—
291C23—3261no—
292C23C2×D65211yescharacteristic
293Q8—3261no—
294Q8—1632no—
295D4—13041no—
296D4—13041no—
297D4—13041no—
298D4—13041no—
299D4—3264no—
300D4—3261no—
301D4—3261no—
302D4—3261no—
303D4—3261no—
304D4—3261no—
305D4—1632no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—13041no—
309C2×C4—13041no—
310C2×C4—13041no—
311C2×C4—13041no—
312C2×C4—13041no—
313C2×C4—3264no—
314C2×C4—3261no—
315C2×C4—3261no—
316C2×C4—3261no—
317C2×C4—3261no—
318C2×C4—3261no—
319C2×C4C2×D65211yescharacteristic
320C2×C4C2×D65211yescharacteristic
321C2×C4C2×D65211yescharacteristic
322C2×C4C2×D65211yescharacteristic
323C2×C4C2×D65211yescharacteristic
324C2×C4C23×D16311yescharacteristic
325C8—21no—
326C8—21no—
327C8—21no—
328C8—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—3262no—
333C22—6521no—
334C22—6521no—
335C22—6521no—
336C22—6521no—
337C22—6521no—
338C22—6521no—
339C22—6521no—
340C22—6521no—
341C22C22×D65211yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—3262no—
348C4—6521no—
349C4—6521no—
350C4—6521no—
351C4—6521no—
352C4#41×D16311yescharacteristic
353C4#41×D16311yescharacteristic
354C2—41no—
355C2—13041no—
356C2—13041no—
357C2—6522no—
358C2#2378217711yescharacteristic
359C2#2378247011yescharacteristic
360C2#2378247711yescharacteristic
subgroupG/H
centerC22C22×D652
commutator, cosocleC2×C4×C163C24
FrattiniC2×C4C23×D163
Fitting#433×C163C2
socleC22×C163C22×D4
hypercenter#433D163
hypocenterC163#3119
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #23782270C2semidirect
2. #23782145C2semidirect
3. #23781984C2semidirect
4. #23781979C2semidirect
5. #23781973C2semidirect
6. #23781966C2semidirect
7. #23781866C2semidirect
8. #23781861C2semidirect
9. #23781812C2semidirect
10. #23781812C2semidirect
11. #23781778C2semidirect
12. #23781767C2semidirect
13. C4×#14579688C2semidirect
14. C4×D1304C2semidirect
15. #433×C163C2semidirect
180. C163#3119semidirect
196. #433D163semidirect

Maximal subgroups

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

subgroupindex
#237822702
#237821452
#237819842
#237819792
#237819732
#237819662
#237818662
#237818612
#237818122
#237817782
#237817672
C4×#145796882
C4×D13042
#433×C1632
#3119163