Finite Group Databasebeta

← #14739001

Subgroups — #14739001

Order 2816.

696 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079746C211yesmaximal, characteristic, complemented
2C2×#10622455C211yesmaximal, characteristic, complemented
3#13078082C211yesmaximal, characteristic
4#13077639C211yesmaximal, characteristic, complemented
5#13068026C214yesmaximal, complemented
6#13067992C214yesmaximal, complemented
7#13067298C211yesmaximal, characteristic, complemented
8#13067266C211yesmaximal, characteristic, complemented
9C11×#1570C211yesmaximal, characteristic, complemented
10C2×#66961—21no—
11#10623008C2211yescharacteristic
12C2×C4×D44C2211yescharacteristic
13C2×#66922C2211yescharacteristic
14C11×#431C2211yescharacteristic
15C11×#423C2211yescharacteristic
16C2×C11×C4⋊C8C2211yescharacteristic
17#10622746—21no—
18C2×#66885—21no—
19C2×#66881—21no—
20#10622538C2211yescharacteristic
21#10622457—22no—
22#10622456C2212yes—
23#10622455—22no—
24#10622455—22no—
25#10622455C2214yes—
26#10622454C2212yes—
27#10622447—22no—
28#10622348—22no—
29D11×C22⋊C8—22no—
30#10622307C2212yescomplemented
31C8×D44C2214yes—
32#10622293C2212yescomplemented
33C11×#334C2214yescomplemented
34#10622123C2212yescomplemented
35#10622120C2212yescomplemented
36#10622119C2214yescomplemented
37C2×#4339—21no—
38C22×D44D411yescharacteristic
39C22×C4×D11—21no—
40C22×Dic22—21no—
41C2×C11×M16—21no—
42C22×C8×C11—21no—
43C2×C42×C11C2311yescharacteristic
44#66983—21no—
45#66983—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11D411yescharacteristic
50#66961—44no—
51C2×D88—22no—
52C2×#4314—22no—
53C2×C8×D11—24no—
54#66928—21no—
55#66927C2311yescharacteristic
56C4×D44—21no—
57C4×D44—21no—
58C4×D44—21no—
59C4×D44—21no—
60C4×D44D412yes—
61C4×D44C2312yes—
62#66922—21no—
63#66922—21no—
64#66922—21no—
65#66922C2312yes—
66#66922C2311yescharacteristic
67C11×C4⋊C8—21no—
68C11×C4⋊C8—21no—
69C11×C4⋊C8D412yes—
70C11×C4⋊C8C2312yes—
71C11×C4⋊C8C2312yes—
72C11×C22⋊C8D412yes—
73C4×C8×C11C2312yes—
74C22⋊(C11⋊C8)—21no—
75#66885—24no—
76#66885—24no—
77#66885—22no—
78(C2×D11)⋊C8—24no—
79#66881—24no—
80#66881—24no—
81#66880—22no—
82C4⋊(C11⋊C8)C2312yes—
83C4×C11⋊C8—21no—
84#19391—111nomaximal, Sylow
85C23×D11—21no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C2×C22⋊D11—41no—
90C22×Dic11—21no—
91C22×Dic11—41no—
92#4339—42no—
93#4339—42no—
94C2×D44—21no—
95C2×D44—22no—
96C2×D44—21no—
97C2×D44—21no—
98C2×D44—21no—
99C2×D44SD1614yes—
100C2×D44C2×D412yes—
101C2×C4×D11—22no—
102C2×C4×D11—22no—
103C2×C4×D11—41no—
104C2×C4×D11—82no—
105C2×Dic22—21no—
106C2×Dic22—22no—
107C2×Dic22—41no—
108C2×Dic22—82no—
109C11×M16—42no—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C2×C8×C11—42no—
113C2×C8×C11C2×D414yes—
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11#4111yescharacteristic
117C42×C11C2411yescharacteristic
118(C2×D11)⋊C4—22no—
119(C2×D11)⋊C4—22no—
120(C2×D11)⋊C4—41no—
121(C2×D11)⋊C4—41no—
122C4⋊Dic11—21no—
123C4⋊Dic11—21no—
124C4⋊Dic11—22no—
125C4⋊Dic11—22no—
126C4⋊Dic11—21no—
127C4⋊Dic11—41no—
128C4⋊Dic11—41no—
129C4⋊Dic11C2×D412yes—
130C2×C11⋊C8—22no—
131D88—44no—
132#4314—44no—
133C8×D11—84no—
134#3227—111no—
135C2×#476—111no—
136#3036—111no—
137#2972—111no—
138#1677—114no—
139#1671—114no—
140#1570D1111yescharacteristic, complemented
141#1548—111no—
142#1540—111no—
143C23×C11#12111yescharacteristic
144C22×D11—22no—
145C22×D11—24no—
146C22×D11—41no—
147C22×D11—81no—
148C22×D11—81no—
149C2×C4×C11—22no—
150C2×C4×C11—41no—
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11C2×SD1612yes—
155C2×C4×C11#13512yes—
156C2×C4×C11C22×D411yescharacteristic
157C2×C4×C11C22×D411yescharacteristic
158C2×C4×C11C2×#4111yescharacteristic
159C22⋊D11—82no—
160C2×Dic11—22no—
161C2×Dic11—42no—
162C2×Dic11—41no—
163C2×Dic11—81no—
164C2×Dic11—82no—
165D44—22no—
166D44—24no—
167D44—41no—
168D44—41no—
169D44—42no—
170D44—81no—
171D44C2×SD1614yes—
172C4×D11—44no—
173C4×D11—82no—
174C4×D11—82no—
175Dic22—41no—
176Dic22—41no—
177Dic22—82no—
178Dic22—82no—
179C8×C11—24no—
180C8×C11—42no—
181C8×C11—42no—
182C11⋊C8—42no—
183C2×AGL(1,ℤ/8)—221no—
184#532—111no—
185C2×C4⋊Q8—111no—
186C2×C4×D4—111no—
187#498—112no—
188#486—112no—
189#481—222no—
190#476—114no—
191#476—222no—
192#476—222no—
193#463—222no—
194#461—112no—
195#459—112no—
196C8×D4—114no—
197C8×D4—222no—
198#431—111no—
199#431C2×D1111yescharacteristic
200C2×#106—221no—
201#423C2×D1111yescharacteristic
202C2×C4⋊C8C2×D1111yescharacteristic
203#417—221no—
204C2×#102—221no—
205C2×C22⋊C8—222no—
206#334C2×D1114yescomplemented
207#333—114no—
208#332—112no—
209#331—112no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11#46512yes—
213C22×C11C2×#12111yescharacteristic
214C2×D11—24no—
215C2×D11—42no—
216C2×D11—42no—
217C2×D11—84no—
218C2×D11—81no—
219C2×D11—81no—
220C2×D11—81no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11#46512yes—
225C4×C11C22×SD1611yescharacteristic
226C4×C11C2×#13511yescharacteristic
227C4×C11#57712yes—
228Dic11—42no—
229Dic11—81no—
230Dic11—82no—
231C2×#41—221no—
232C22×Q8—221no—
233C22×D4—111no—
234C23×C4—221no—
235AGL(1,ℤ/8)—444no—
236C2×SD16—222no—
237C2×D8—222no—
238C2×M16—21no—
239C22×C8—21no—
240C22×C8—224no—
241C4⋊Q8—112no—
242C4⋊Q8—111no—
243C4⋊Q8—221no—
244C4⋊Q8—221no—
245C4⋊Q8—221no—
246#127—111no—
247#124—221no—
248#121—221no—
249#121—221no—
250C4×D4—112no—
251C4×D4—112no—
252C4×D4—221no—
253C4×D4—221no—
254C4×D4—221no—
255C4×D4—221no—
256C2×C4⋊C4—111no—
257C2×C4⋊C4—221no—
258C2×C4⋊C4—221no—
259C2×C22⋊C4—221no—
260C2×C42C22×D1111yescharacteristic
261#106—224no—
262#106—224no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—112no—
266C4⋊C8D4412yes—
267C4⋊C8C22×D1112yes—
268C4⋊C8C22×D1112yes—
269#103—222no—
270#102—222no—
271#102—224no—
272#102—224no—
273C22⋊C8—221no—
274C22⋊C8—224no—
275C22⋊C8D4412yes—
276C4×C8—221no—
277C4×C8C22×D1112yes—
278C2×C11—22no—
279C2×C11#304211yescharacteristic
280C2×C11C2×#46511yescharacteristic
281C2×C11#306811yescharacteristic
282D11—44no—
283D11—161no—
284C24—221no—
285#41—442no—
286#41—442no—
287C2×Q8—221no—
288C2×Q8—222no—
289C2×Q8—441no—
290C2×Q8—882no—
291C2×D4—114no—
292C2×D4—112no—
293C2×D4—221no—
294C2×D4—222no—
295C2×D4—221no—
296C2×D4—221no—
297C2×D4—221no—
298C2×D4—441no—
299C22×C4—221no—
300C22×C4—222no—
301C22×C4—222no—
302C22×C4—441no—
303C22×C4—441no—
304C22×C4—882no—
305C22×C4C2×D4411yescharacteristic
306C22×C4D4×D1111yescharacteristic
307C22×C4#434311yescharacteristic
308SD16—444no—
309D8—444no—
310M16—42no—
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—42no—
314C2×C8—222no—
315C2×C8—884no—
316C2×C8C2×D4414yes—
317C4⋊C4—112no—
318C4⋊C4—221no—
319C4⋊C4—222no—
320C4⋊C4—221no—
321C4⋊C4—222no—
322C4⋊C4—221no—
323C4⋊C4—441no—
324C4⋊C4—441no—
325C22⋊C4—222no—
326C22⋊C4—222no—
327C22⋊C4—441no—
328C22⋊C4—441no—
329C42C2×D4411yescharacteristic
330C42D4×D1111yescharacteristic
331C42#434311yescharacteristic
332C42C23×D1111yescharacteristic
333C11#1939111yescharacteristic, complemented, Sylow
334C23—222no—
335C23—224no—
336C23—441no—
337C23—881no—
338C23—881no—
339C23#6694811yescharacteristic
340Q8—441no—
341Q8—441no—
342Q8—882no—
343Q8—882no—
344D4—114no—
345D4—224no—
346D4—222no—
347D4—442no—
348D4—441no—
349D4—441no—
350D4—881no—
351D4—882no—
352C2×C4—22no—
353C2×C4—41no—
354C2×C4—222no—
355C2×C4—444no—
356C2×C4—441no—
357C2×C4—442no—
358C2×C4—882no—
359C2×C4—881no—
360C2×C4—882no—
361C2×C4—882no—
362C2×C4#6694811yescharacteristic
363C2×C4#6694811yescharacteristic
364C2×C4#6694811yescharacteristic
365C2×C4SD16×D1112yes—
366C2×C4#6696912yes—
367C2×C4C22×D4411yescharacteristic
368C2×C4C2×D4×D1111yescharacteristic
369C2×C4C2×#434311yescharacteristic
370C8—24no—
371C8—42no—
372C8—42no—
373C8—442no—
374C22—21no—
375C22—21no—
376C22—224no—
377C22—442no—
378C22—442no—
379C22—884no—
380C22—881no—
381C22—881no—
382C22—881no—
383C22#1062247712yes—
384C22C2×#6694811yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—442no—
389C4—882no—
390C4—881no—
391C4#1062247712yes—
392C4#1062328212yes—
393C4C2×SD16×D1111yescharacteristic
394C4C2×#6696911yescharacteristic
395C2—22no—
396C2—444no—
397C2—1761no—
398C2#1307812911yescharacteristic
399C2C2×#1062247711yescharacteristic
400C2#1307834511yescharacteristic
subgroupG/H
centerC22C2×#66948
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1570C2
socleC22×C11C2×#121
prime radical#13078082C2
hypercenter#1570D11
hypocenterC11#19391
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1570

Complements

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

NH ≅ G/Ntype
1. #13079746C2semidirect
2. C2×#10622455C2semidirect
4. #13077639C2semidirect
5. #13068026C2semidirect
6. #13067992C2semidirect
7. #13067298C2semidirect
8. #13067266C2semidirect
9. C11×#1570C2semidirect
30. #10622307C22semidirect
32. #10622293C22semidirect
33. C11×#334C22semidirect
34. #10622123C22semidirect
35. #10622120C22semidirect
36. #10622119C22semidirect
140. #1570D11semidirect
206. #334C2×D11semidirect
333. C11#19391semidirect

Maximal subgroups

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

subgroupindex
#130797462
C2×#106224552
#130780822
#130776392
#130680262
#130679922
#130672982
#130672662
C11×#15702
#1939111