Finite Group Databasebeta

← #35224753

Subgroups — #35224753

Order 20864.

372 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23782275C211yesmaximal, characteristic, complemented
2#23782146C211yesmaximal, characteristic
3#23782000C211yesmaximal, characteristic, complemented
4#23781975C211yesmaximal, characteristic, complemented
5#23781964C211yesmaximal, characteristic, complemented
6#23781874C211yesmaximal, characteristic, complemented
7#23781869C211yesmaximal, characteristic, complemented
8#23781829C211yesmaximal, characteristic
9#23781825C211yesmaximal, characteristic
10#23781771C211yesmaximal, characteristic, complemented
11#23781768C211yesmaximal, characteristic, complemented
12#23781757C211yesmaximal, characteristic, complemented
13#23781752C211yesmaximal, characteristic, complemented
14#23781723C211yesmaximal, characteristic, complemented
15#483×C163C211yesmaximal, characteristic, complemented
16C2×#14579699C2211yescharacteristic
17C2×Dic652C2211yescharacteristic
18C2×#14579689C2211yescharacteristic
19C2×#14579688C2211yescharacteristic
20C2×#14579686C2211yescharacteristic
21#19104733C2211yescharacteristic
22#19104728—21no—
23#19104728—21no—
24#19104726—21no—
25#19104726C2211yescharacteristic
26#19104725—21no—
27#19104714C2211yescharacteristic
28Q8×Dic163C2211yescharacteristic
29#19104700C2211yescharacteristic
30#19104700C2211yescharacteristic
31#19104700C2211yescharacteristic
32#19104697C2211yescharacteristic
33#19104697C2211yescharacteristic
34C4×C22⋊D163—21no—
35C4×C22⋊D163—21no—
36#19104694C2211yescharacteristic
37#19104693—21no—
38C4⋊C4×D163—21no—
39#19104668C2211yescharacteristic
40#19104668C2211yescharacteristic
41Dic163⋊C8C2211yescharacteristic
42Dic163⋊C8C2211yescharacteristic
43#19104660C2211yescharacteristic
44#19104658C2211yescharacteristic
45#19104658C2211yescharacteristic
46#19104658C2211yescharacteristic
47#19104657C2211yescharacteristic
48#19104655C2211yescharacteristic
49C22⋊(C163⋊C8)C2211yescharacteristic
50#19104645C2211yescharacteristic
51C8×Dic163C2211yescharacteristic
52C22⋊Q8×C163C2211yescharacteristic
53C2×C4⋊C4×C163C2211yescharacteristic
54#106×C163C2211yescharacteristic
55#106×C163C2211yescharacteristic
56#103×C163C2211yescharacteristic
57#103×C163C2211yescharacteristic
58C22⋊C8×C163C2211yescharacteristic
59#14579699—22no—
60#14579699—22no—
61C2×Dic326C2311yescharacteristic
62C2×Dic326C2311yescharacteristic
63C2×D652C2311yescharacteristic
64C2×C22⋊D163—21no—
65C2×C4×D163—21no—
66C2×C4×D163—21no—
67C2×C4×D163—21no—
68Dic652—22no—
69#14579689—22no—
70#14579688—22no—
71#14579686—22no—
72C2×C163⋊C8C2311yescharacteristic
73C2×C163⋊C8C2311yescharacteristic
74C4⋊Dic163—21no—
75C4⋊Dic163—21no—
76C4⋊Dic163D411yescharacteristic
77C4⋊Dic163D411yescharacteristic
78C4⋊Dic163C2311yescharacteristic
79Dic163⋊C4—21no—
80Dic163⋊C4—21no—
81Dic163⋊C4—21no—
82Dic163⋊C4—21no—
83Dic163⋊C4—21no—
84Dic163⋊C4—21no—
85Dic163⋊C4—21no—
86C22⋊Dic163—21no—
87C22⋊Dic163D411yescharacteristic
88C22⋊Dic163D411yescharacteristic
89(C2×D163)⋊C4—21no—
90(C2×D163)⋊C4—21no—
91C4×Dic163—21no—
92C4×Dic163—21no—
93C4×Dic163—21no—
94C4×Dic163—21no—
95C4×Dic163C2311yescharacteristic
96C4×Dic163C2311yescharacteristic
97C2×Q8×C163C2311yescharacteristic
98C22×C4×C163—21no—
99C22×C4×C163C2311yescharacteristic
100C2×C8×C163C2311yescharacteristic
101C2×C8×C163C2311yescharacteristic
102C4⋊C4×C163—21no—
103C4⋊C4×C163—21no—
104C4⋊C4×C163C2311yescharacteristic
105C4⋊C4×C163C2311yescharacteristic
106C4⋊C4×C163C2311yescharacteristic
107C22⋊C4×C163—21no—
108C22×D163—21no—
109Dic326—21no—
110Dic326—21no—
111Dic326—21no—
112Dic326#4112yes—
113D652—21no—
114D652#4112yes—
115C22⋊D163—24no—
116C2×Dic163—21no—
117C2×Dic163—21no—
118C2×Dic163—21no—
119C2×Dic163C2×D411yescharacteristic
120C2×Dic163C2×D411yescharacteristic
121C2×Dic163C2×D411yescharacteristic
122C2×Dic163C2×D411yescharacteristic
123C4×D163—24no—
124C4×D163—81no—
125C4×D163—81no—
126C163⋊C8—21no—
127C163⋊C8—21no—
128C23×C163C2×D411yescharacteristic
129Q8×C163—21no—
130Q8×C163—21no—
131C2×C4×C163—21no—
132C2×C4×C163—21no—
133C2×C4×C163—21no—
134C2×C4×C163—21no—
135C2×C4×C163—21no—
136C2×C4×C163—21no—
137C2×C4×C163—81no—
138C2×C4×C163C2×D411yescharacteristic
139C2×C4×C163C2411yescharacteristic
140C8×C163—21no—
141C8×C163—21no—
142C22×C163—21no—
143C22×C163—21no—
144C22×C163—21no—
145C22×C163C22×D411yescharacteristic
146C2×D163—22no—
147C2×D163—41no—
148C2×D163—41no—
149C4×C163—21no—
150C4×C163—41no—
151C4×C163—41no—
152C4×C163—41no—
153C4×C163—41no—
154C4×C163C2×#4111yescharacteristic
155C4×C163C2×#4111yescharacteristic
156Dic163—22no—
157Dic163—21no—
158Dic163—21no—
159Dic163—21no—
160Dic163—21no—
161Dic163—41no—
162Dic163—41no—
163C2×C163—41no—
164C2×C163#52511yescharacteristic
165C2×C163#57711yescharacteristic
166C2×C163#57811yescharacteristic
167D163—42no—
168C163#312011yescharacteristic, complemented, Sylow
169#3120—1631nomaximal, Sylow
170#541—1631no—
171#520—1631no—
172#484—1631no—
173#483D16311yescharacteristic, complemented
174#479—1631no—
175#478—1631no—
176#462—1631no—
177#461—1631no—
178#452—1631no—
179#452—1631no—
180#441—1631no—
181#440—1631no—
182C4×Q16—1631no—
183C4×SD16—1631no—
184#433—1631no—
185C2×#41—1631no—
186C2×Q16—1631no—
187C2×Q16—1631no—
188C2×SD16—1631no—
189C2×SD16—1631no—
190C4⋊Q8—1631no—
191#126—3261no—
192#126—3261no—
193#125—3261no—
194#125—3261no—
195#125—1631no—
196C22⋊Q8—1631no—
197C22⋊Q8C2×D16311yescharacteristic
198C4×Q8—1631no—
199C4×Q8—1631no—
200C4×Q8—1631no—
201C4×Q8—1631no—
202C4×D4—3261no—
203C4×D4—3261no—
204C4×D4—1631no—
205C4×D4—1631no—
206#117—3261no—
207#117—1631no—
208C2×C4⋊C4—3261no—
209C2×C4⋊C4C2×D16311yescharacteristic
210#107—1631no—
211#107—1631no—
212#106C2×D16311yescharacteristic
213#106C2×D16311yescharacteristic
214C4⋊C8—1631no—
215C4⋊C8—1631no—
216#103—1631no—
217#103—1631no—
218#103—1631no—
219#103—1631no—
220#103C2×D16311yescharacteristic
221#103C2×D16311yescharacteristic
222#102—1631no—
223#102—1631no—
224C22⋊C8—1631no—
225C22⋊C8C2×D16311yescharacteristic
226#97—1631no—
227C4×C8—1631no—
228#41—3262no—
229#41—3262no—
230C2×Q8—1631no—
231C2×Q8—1631no—
232C2×Q8C22×D16311yescharacteristic
233C2×D4—3261no—
234C2×D4—1631no—
235C22×C4—21no—
236C22×C4—3261no—
237C22×C4—3261no—
238C22×C4—3261no—
239C22×C4C22×D16311yescharacteristic
240Q16—3262no—
241Q16—3262no—
242SD16—3262no—
243SD16—3262no—
244C2×C8—1631no—
245C2×C8—1631no—
246C2×C8C22×D16311yescharacteristic
247C2×C8C22×D16311yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—3261no—
251C4⋊C4—3261no—
252C4⋊C4—3261no—
253C4⋊C4—3261no—
254C4⋊C4—3261no—
255C4⋊C4—3261no—
256C4⋊C4—3261no—
257C4⋊C4—3261no—
258C4⋊C4—3261no—
259C4⋊C4—1631no—
260C4⋊C4—1631no—
261C4⋊C4—1631no—
262C4⋊C4C22×D16311yescharacteristic
263C4⋊C4C22×D16311yescharacteristic
264C4⋊C4C22×D16311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—3261no—
267C22⋊C4—3261no—
268C22⋊C4—3261no—
269C22⋊C4—1631no—
270C22⋊C4—1631no—
271C42—3261no—
272C42—3261no—
273C42—3261no—
274C42—3261no—
275C42—1631no—
276C42—1631no—
277C23—3261no—
278C23D4×D16311yescharacteristic
279Q8—21no—
280Q8—21no—
281Q8—3261no—
282Q8—3261no—
283Q8—3261no—
284Q8—1632no—
285D4—3264no—
286D4—3261no—
287D4—1632no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—81no—
295C2×C4—13041no—
296C2×C4—13041no—
297C2×C4—3264no—
298C2×C4—3261no—
299C2×C4—3261no—
300C2×C4—3261no—
301C2×C4—1631no—
302C2×C4—1631no—
303C2×C4—1631no—
304C2×C4—1631no—
305C2×C4D4×D16311yescharacteristic
306C2×C4C23×D16311yescharacteristic
307C8—21no—
308C8—21no—
309C8—3261no—
310C8—3261no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—3262no—
315C22—6521no—
316C22—6521no—
317C22C2×D4×D16311yescharacteristic
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—3262no—
324C4—3261no—
325C4—3261no—
326C4—3261no—
327C4—3261no—
328C4—6521no—
329C4—6521no—
330C4#41×D16311yescharacteristic
331C4#41×D16311yescharacteristic
332C2—41no—
333C2—6522no—
334C2#2378217311yescharacteristic
335C2#2378247111yescharacteristic
336C2#2378248111yescharacteristic
subgroupG/H
centerC22C2×D4×D163
commutator, cosocleC2×C4×C163C24
FrattiniC2×C4C23×D163
Fitting#483×C163C2
socleC22×C163C22×D4
prime radicalC2×#14579699C22
hypercenter#483D163
hypocenterC163#3120
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #23782275C2semidirect
3. #23782000C2semidirect
4. #23781975C2semidirect
5. #23781964C2semidirect
6. #23781874C2semidirect
7. #23781869C2semidirect
10. #23781771C2semidirect
11. #23781768C2semidirect
12. #23781757C2semidirect
13. #23781752C2semidirect
14. #23781723C2semidirect
15. #483×C163C2semidirect
168. C163#3120semidirect
173. #483D163semidirect

Maximal subgroups

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

subgroupindex
#237822752
#237821462
#237820002
#237819752
#237819642
#237818742
#237818692
#237818292
#237818252
#237817712
#237817682
#237817572
#237817522
#237817232
#483×C1632
#3120163