Finite Group Databasebeta

← #35225092

Subgroups — #35225092

Order 20864.

412 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23782219C211yesmaximal, characteristic, complemented
2#23782212C211yesmaximal, characteristic
3#23782062C211yesmaximal, characteristic, complemented
4#23782036C211yesmaximal, characteristic, complemented
5#23782014C211yesmaximal, characteristic, complemented
6#23782010C211yesmaximal, characteristic, complemented
7#23781897C211yesmaximal, characteristic, complemented
8#23781895C211yesmaximal, characteristic, complemented
9#23781893C211yesmaximal, characteristic, complemented
10#23781891C211yesmaximal, characteristic, complemented
11C4×#14579688C211yesmaximal, characteristic, complemented
12C4×#14579686C211yesmaximal, characteristic, complemented
13C4×#14579687C211yesmaximal, characteristic, complemented
14C4×C8×D163C211yesmaximal, characteristic, complemented
15C4×SD16×C163C211yesmaximal, characteristic, complemented
16C2×#14579699—21no—
17C2×#14579688C2211yescharacteristic
18C2×#14579687C2211yescharacteristic
19C2×#14579686C2211yescharacteristic
20C2×C8×D163C2211yescharacteristic
21C2×C8×D163C2211yescharacteristic
22#19104734C2211yescharacteristic
23#19104734C2211yescharacteristic
24#19104733C2211yescharacteristic
25#19104731C2211yescharacteristic
26#19104725—21no—
27#19104721—21no—
28#19104715C2211yescharacteristic
29#19104713—21no—
30#19104711C2211yescharacteristic
31#19104710C2211yescharacteristic
32#19104708—21no—
33#19104706C2211yescharacteristic
34C4×Dic326—21no—
35C4×Dic326C2211yescharacteristic
36C4×D652C2211yescharacteristic
37C4×C22⋊D163—21no—
38#19104692—21no—
39C42×D163C2211yescharacteristic
40#19104667C2211yescharacteristic
41#19104666C2211yescharacteristic
42#19104666C2211yescharacteristic
43#19104660C2211yescharacteristic
44#19104659C2211yescharacteristic
45#19104658C2211yescharacteristic
46#19104657C2211yescharacteristic
47#19104656C2211yescharacteristic
48#19104655C2211yescharacteristic
49C4×C163⋊C8C2211yescharacteristic
50C8×Dic163C2211yescharacteristic
51C8×Dic163C2211yescharacteristic
52C2×SD16×C163C2211yescharacteristic
53C4×Q8×C163C2211yescharacteristic
54C4×D4×C163C2211yescharacteristic
55#106×C163C2211yescharacteristic
56#103×C163C2211yescharacteristic
57#102×C163C2211yescharacteristic
58C4×C8×C163C2211yescharacteristic
59#14579699—44no—
60C2×Dic326—21no—
61C2×Dic326—21no—
62C2×Dic326C2311yescharacteristic
63C2×D652—21no—
64C2×D652C2311yescharacteristic
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#14579686—22no—
75C2×C163⋊C8C2311yescharacteristic
76C2×C163⋊C8C2311yescharacteristic
77C8×D163—22no—
78C8×D163—22no—
79C4⋊Dic163—21no—
80C4⋊Dic163C2311yescharacteristic
81C4⋊Dic163C2311yescharacteristic
82Dic163⋊C4—21no—
83Dic163⋊C4—21no—
84Dic163⋊C4—21no—
85Dic163⋊C4—21no—
86Dic163⋊C4—21no—
87Dic163⋊C4—21no—
88C22⋊Dic163—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×Dic163D411yescharacteristic
95C4×Dic163D411yescharacteristic
96C4×Dic163C2311yescharacteristic
97C2×Q8×C163C2311yescharacteristic
98C2×D4×C163C2311yescharacteristic
99C22×C4×C163—21no—
100SD16×C163—22no—
101C2×C8×C163C2311yescharacteristic
102C2×C8×C163C2311yescharacteristic
103C4⋊C4×C163—21no—
104C4⋊C4×C163C2311yescharacteristic
105C4⋊C4×C163C2311yescharacteristic
106C22⋊C4×C163—21no—
107C42×C163—21no—
108C42×C163C2311yescharacteristic
109C22×D163—21no—
110C22×D163C2×D411yescharacteristic
111Dic326—21no—
112Dic326—21no—
113Dic326—42no—
114Dic326—42no—
115D652—21no—
116D652—21no—
117D652—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—21no—
128C4×D163—21no—
129C4×D163—22no—
130C4×D163—42no—
131C4×D163SD1614yescomplemented
132C163⋊C8—21no—
133C163⋊C8#4112yescomplemented
134C23×C163—21no—
135Q8×C163—21no—
136Q8×C163—21no—
137D4×C163—21no—
138D4×C163—21no—
139C2×C4×C163—21no—
140C2×C4×C163—21no—
141C2×C4×C163—21no—
142C2×C4×C163—42no—
143C2×C4×C163C2×D411yescharacteristic
144C2×C4×C163C2×D411yescharacteristic
145C2×C4×C163C2411yescharacteristic
146C8×C163—21no—
147C8×C163#4112yescomplemented
148C22×C163—41no—
149C22×C163—41no—
150C22×C163—41no—
151C22×C163C22×D411yescharacteristic
152C2×D163—21no—
153C2×D163—21no—
154C2×D163—41no—
155C2×D163—41no—
156C2×D163—41no—
157C2×D163C2×SD1612yes—
158C4×C163—21no—
159C4×C163—41no—
160C4×C163—41no—
161C4×C163—41no—
162C4×C163C2×SD1612yes—
163C4×C163C2×#4111yescharacteristic
164C4×C163C2×#4111yescharacteristic
165Dic163—21no—
166Dic163—41no—
167Dic163—41no—
168Dic163—41no—
169Dic163C2×SD1612yes—
170Dic163#13512yes—
171C2×C163—81no—
172C2×C163#53211yescharacteristic
173C2×C163C22×SD1611yescharacteristic
174C2×C163C2×#13511yescharacteristic
175D163—22no—
176D163—81no—
177C163#316711yescharacteristic, complemented, Sylow
178#3167—1631nomaximal, Sylow
179#533—1631no—
180#532—1631no—
181#498—1631no—
182#492—1631no—
183#487—1631no—
184#486—1631no—
185#465—1631no—
186#465—1631no—
187#465—1631no—
188#465—1631no—
189C4×SD16—1631no—
190C4×SD16—1631no—
191C4×SD16—1631no—
192C4×SD16D16311yescharacteristic, complemented
193C2×C4×C8—1631no—
194C2×#41—3261no—
195C2×SD16—1631no—
196C2×SD16—1631no—
197C2×SD16—1631no—
198C2×SD16C2×D16311yescharacteristic
199C22×C8—1631no—
200C22×C8—1631no—
201C4⋊Q8—1631no—
202C4⋊Q8—1631no—
203C4⋊Q8—1631no—
204#127—1631no—
205#125—3261no—
206#124—3261no—
207C22⋊Q8—3261no—
208C22⋊Q8—1631no—
209C22⋊Q8—1631no—
210#121—3261no—
211#121—1631no—
212#121—1631no—
213C4×Q8—3261no—
214C4×Q8—1631no—
215C4×Q8C2×D16311yescharacteristic
216C4×D4—3261no—
217C4×D4—1631no—
218C4×D4C2×D16311yescharacteristic
219#117—3261no—
220C2×C42—1631no—
221#106—1631no—
222#106—1631no—
223#106—1631no—
224#106C2×D16311yescharacteristic
225#103—1631no—
226#103—1631no—
227#103—1631no—
228#103C2×D16311yescharacteristic
229#102—1631no—
230#102—1631no—
231#102—1631no—
232#102C2×D16311yescharacteristic
233C4×C8—1631no—
234C4×C8—1631no—
235C4×C8—1631no—
236C4×C8C2×D16311yescharacteristic
237#41—6524no—
238C2×Q8—3261no—
239C2×Q8—3261no—
240C2×Q8—1631no—
241C2×Q8C22×D16311yescharacteristic
242C2×D4—3261no—
243C2×D4—3261no—
244C2×D4—3261no—
245C2×D4—3261no—
246C2×D4—1631no—
247C2×D4C22×D16311yescharacteristic
248C22×C4—21no—
249C22×C4—3261no—
250C22×C4—1631no—
251C22×C4—1631no—
252C22×C4—1631no—
253SD16—22no—
254SD16—3262no—
255SD16—3262no—
256SD16—3262no—
257C2×C8—3262no—
258C2×C8—3262no—
259C2×C8—1631no—
260C2×C8—1631no—
261C2×C8C22×D16311yescharacteristic
262C2×C8C22×D16311yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—3261no—
265C4⋊C4—3261no—
266C4⋊C4—3261no—
267C4⋊C4—3261no—
268C4⋊C4—3261no—
269C4⋊C4—3261no—
270C4⋊C4—3261no—
271C4⋊C4—1631no—
272C4⋊C4—1631no—
273C4⋊C4C22×D16311yescharacteristic
274C4⋊C4C22×D16311yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—3261no—
277C22⋊C4—3261no—
278C22⋊C4—3261no—
279C22⋊C4—3261no—
280C22⋊C4—3261no—
281C42—21no—
282C42—3261no—
283C42—1631no—
284C42—1631no—
285C42—1631no—
286C42C22×D16311yescharacteristic
287C23—21no—
288C23—3261no—
289C23—1631no—
290Q8—21no—
291Q8—21no—
292Q8—3261no—
293Q8—3261no—
294Q8—6522no—
295Q8—6522no—
296D4—21no—
297D4—21no—
298D4—3261no—
299D4—3261no—
300D4—6522no—
301D4—6522no—
302D4—6522no—
303D4—6522no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—3262no—
309C2×C4—3261no—
310C2×C4—3261no—
311C2×C4—3261no—
312C2×C4—3261no—
313C2×C4—3261no—
314C2×C4—6522no—
315C2×C4—1631no—
316C2×C4—1631no—
317C2×C4—1631no—
318C2×C4—1634no—
319C2×C4D4×D16311yescharacteristic
320C2×C4D4×D16311yescharacteristic
321C2×C4C23×D16311yescharacteristic
322C8—21no—
323C8—3261no—
324C8—1632no—
325C8#1457969912yescomplemented
326C22—41no—
327C22—41no—
328C22—41no—
329C22—3261no—
330C22—3261no—
331C22—6521no—
332C22—6521no—
333C22—6521no—
334C22—1632no—
335C22C2×D4×D16311yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—3261no—
341C4—6521no—
342C4—6521no—
343C4—6521no—
344C4—1632no—
345C4—1632no—
346C4SD16×D16312yes—
347C4#41×D16311yescharacteristic
348C4C2×#1457969911yescharacteristic
349C2—81no—
350C2—13041no—
351C2—3262no—
352C2#2378221211yescharacteristic
353C2C2×SD16×D16311yescharacteristic
354C2#135×D16311yescharacteristic
subgroupG/H
centerC2×C4D4×D163
commutator, cosocleC2×C4×C163C24
FrattiniC2×C4C23×D163
FittingC4×SD16×C163C2
socleC22×C163C22×D4
prime radical#23782212C2
hypercenterC4×SD16D163
hypocenterC163#3167
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #23782219C2semidirect
3. #23782062C2semidirect
4. #23782036C2semidirect
5. #23782014C2semidirect
6. #23782010C2semidirect
7. #23781897C2semidirect
8. #23781895C2semidirect
9. #23781893C2semidirect
10. #23781891C2semidirect
11. C4×#14579688C2semidirect
12. C4×#14579686C2semidirect
13. C4×#14579687C2semidirect
14. C4×C8×D163C2semidirect
15. C4×SD16×C163C2semidirect
131. C4×D163SD16semidirect
133. C163⋊C8#41semidirect
147. C8×C163#41semidirect
177. C163#3167semidirect
192. C4×SD16D163semidirect
325. C8#14579699semidirect

Maximal subgroups

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

subgroupindex
#237822192
#237822122
#237820622
#237820362
#237820142
#237820102
#237818972
#237818952
#237818932
#237818912
C4×#145796882
C4×#145796862
C4×#145796872
C4×C8×D1632
C4×SD16×C1632
#3167163