Finite Group Databasebeta

← #14739003

Subgroups — #14739003

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#13079741C211yesmaximal, characteristic, complemented
2C2×#10622455C211yesmaximal, characteristic, complemented
3#13078076C211yesmaximal, characteristic
4#13077639C211yesmaximal, characteristic, complemented
5#13068024C214yesmaximal, complemented
6#13067990C214yesmaximal, complemented
7#13067386C211yesmaximal, characteristic, complemented
8#13067296C211yesmaximal, characteristic, complemented
9C11×#1540C211yesmaximal, characteristic, complemented
10C11×#532C2211yescharacteristic
11C2×#67002—21no—
12C2×C4×D44C2211yescharacteristic
13C2×#66922C2211yescharacteristic
14C11×#431C2211yescharacteristic
15C2×C11×C4⋊C8C2211yescharacteristic
16#10622845—21no—
17C2×#66885—21no—
18C2×#66881—21no—
19#10622696C2212yes—
20#10622692C2212yescomplemented
21#10622685C2212yes—
22#10622683C2212yescomplemented
23#10622670—22no—
24#10622647—22no—
25#10622621—22no—
26#10622538C2211yescharacteristic
27#10622537C2211yescharacteristic
28#10622455—22no—
29#10622455C2214yes—
30#10622447C2214yes—
31D11×C22⋊C8—22no—
32C8×D44—22no—
33C11×#332C2212yescomplemented
34C11×#331C2212yescomplemented
35#10622119C2214yescomplemented
36#10622118C2214yescomplemented
37C2×C11×#41—21no—
38C22×D44D411yescharacteristic
39C22×C4×D11—21no—
40C22×Dic22—21no—
41C22×C8×C11—21no—
42C11×C4⋊Q8C2311yescharacteristic
43C11×#127C2311yescharacteristic
44C11×#124—21no—
45C11×#121—21no—
46C11×#121—21no—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C2×C42×C11C2311yescharacteristic
50#67002—44no—
51C2×#4325—22no—
52C2×#4323—22no—
53C2×(C2×D11)⋊C4—21no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11D411yescharacteristic
57C2×#4318—21no—
58C2×C8×D11—24no—
59C4×D44—21no—
60C4×D44—21no—
61C4×D44D412yes—
62C4×D44C2312yes—
63#66922—21no—
64#66922—21no—
65#66922—21no—
66#66922C2312yes—
67C11×C4⋊C8—21no—
68C11×C4⋊C8C2312yes—
69C11×C4⋊C8C2312yes—
70C11×C22⋊C8—21no—
71C4×C8×C11—21no—
72#66899—22no—
73#66896—22no—
74#66896—24no—
75C22⋊(C11⋊C8)D412yes—
76#66885—24no—
77(C2×D11)⋊C8—24no—
78#66881—24no—
79#66872—24no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)D412yes—
82C4⋊(C11⋊C8)C2312yes—
83C4×C11⋊C8C2312yes—
84#19391—111nomaximal, Sylow
85C23×D11—21no—
86C11×#41—42no—
87C11×#41—42no—
88C2×Q8×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11#4111yescharacteristic
97C22×Dic11—21no—
98C22×Dic11—41no—
99C2×D44—21no—
100C2×D44—22no—
101C2×D44SD1614yes—
102C2×D44C2×D412yes—
103C2×C4×D11—22no—
104C2×C4×D11—22no—
105C2×C4×D11—82no—
106C2×Dic22—22no—
107C2×Dic22—41no—
108C2×Dic22—82no—
109C2×C8×C11—22no—
110C2×C8×C11—22no—
111C2×C8×C11—42no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4—41no—
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11#4111yescharacteristic
119C42×C11C2411yescharacteristic
120#4325—44no—
121#4323—44no—
122(C2×D11)⋊C4—22no—
123(C2×D11)⋊C4—22no—
124C4⋊Dic11—21no—
125C4⋊Dic11—22no—
126C4⋊Dic11—22no—
127C4⋊Dic11—41no—
128C4⋊Dic11—41no—
129C4⋊Dic11C2×D412yes—
130#4318—42no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8C2×D414yes—
133C8×D11—84no—
134#3227—111no—
135C2×#476—111no—
136#3036—111no—
137#2972—111no—
138#1677—114no—
139#1671—114no—
140#1570—111no—
141#1548—111no—
142#1540D1111yescharacteristic, complemented
143C23×C11—41no—
144C23×C11#12111yescharacteristic
145C22×D11—22no—
146C22×D11—24no—
147C22×D11—81no—
148C22×D11—81no—
149Q8×C11—41no—
150Q8×C11—41no—
151D4×C11—41no—
152D4×C11—41no—
153D4×C11—42no—
154D4×C11—81no—
155D4×C11—82no—
156C2×C4×C11—22no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—82no—
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11C2×SD1612yes—
164C2×C4×C11#13512yes—
165C2×C4×C11C22×D411yescharacteristic
166C2×C4×C11C22×D411yescharacteristic
167C2×C4×C11C2×#4111yescharacteristic
168C2×Dic11—22no—
169C2×Dic11—42no—
170C2×Dic11—81no—
171C2×Dic11—82no—
172D44—22no—
173D44—24no—
174D44C2×SD1614yes—
175C4×D11—44no—
176C4×D11—82no—
177Dic22—82no—
178Dic22—82no—
179C8×C11—42no—
180C8×C11—42no—
181C11⋊C8—24no—
182C11⋊C8—42no—
183C2×AGL(1,ℤ/8)—221no—
184#532C2×D1111yescharacteristic
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#423—111no—
202C2×C4⋊C8C2×D1111yescharacteristic
203#417—221no—
204C2×#102—221no—
205C2×C22⋊C8—222no—
206#334—114no—
207#333—114no—
208#332C2×D1112yescomplemented
209#331C2×D1112yescomplemented
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—81no—
213C22×C11—81no—
214C22×C11—81no—
215C22×C11#46512yes—
216C22×C11C2×#12111yescharacteristic
217C2×D11—24no—
218C2×D11—42no—
219C2×D11—42no—
220C2×D11—84no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—81no—
225C4×C11#46512yes—
226C4×C11C22×SD1611yescharacteristic
227C4×C11C2×#13511yescharacteristic
228C4×C11#57712yes—
229Dic11—42no—
230Dic11—82no—
231C2×#41—21no—
232C22×Q8—221no—
233C22×D4—111no—
234C23×C4—221no—
235AGL(1,ℤ/8)—444no—
236C2×SD16—222no—
237C2×D8—222no—
238C2×M16—221no—
239C22×C8—21no—
240C22×C8—224no—
241C4⋊Q8—112no—
242C4⋊Q8—221no—
243C4⋊Q8—221no—
244C4⋊Q8—221no—
245C4⋊Q8C22×D1111yescharacteristic
246#127C22×D1111yescharacteristic
247#124—21no—
248#121—21no—
249#121—21no—
250C4×D4—21no—
251C4×D4—21no—
252C4×D4—112no—
253C4×D4—112no—
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—112no—
265C4⋊C8—112no—
266C4⋊C8—221no—
267C4⋊C8C22×D1112yes—
268C4⋊C8C22×D1112yes—
269#103—222no—
270#102—222no—
271#102—224no—
272#102—224no—
273C22⋊C8—21no—
274C22⋊C8—112no—
275C22⋊C8—224no—
276C4×C8—21no—
277C4×C8—112no—
278C2×C11—22no—
279C2×C11—161no—
280C2×C11#304211yescharacteristic
281C2×C11C2×#46511yescharacteristic
282C2×C11#306811yescharacteristic
283D11—44no—
284C24—221no—
285#41—42no—
286#41—42no—
287C2×Q8—21no—
288C2×Q8—222no—
289C2×Q8—441no—
290C2×Q8—882no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—41no—
295C2×D4—114no—
296C2×D4—112no—
297C2×D4—221no—
298C2×D4—222no—
299C22×C4—41no—
300C22×C4—221no—
301C22×C4—222no—
302C22×C4—222no—
303C22×C4—441no—
304C22×C4—882no—
305C22×C4#433911yescharacteristic
306C22×C4D4×D1111yescharacteristic
307C22×C4D4×D1111yescharacteristic
308SD16—444no—
309D8—444no—
310M16—442no—
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—42no—
314C2×C8—114no—
315C2×C8—222no—
316C2×C8—884no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—112no—
320C4⋊C4—221no—
321C4⋊C4—222no—
322C4⋊C4—222no—
323C4⋊C4—441no—
324C4⋊C4—441no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4—222no—
328C22⋊C4—222no—
329C42#433911yescharacteristic
330C42D4×D1111yescharacteristic
331C42D4×D1111yescharacteristic
332C42C23×D1111yescharacteristic
333C11#1939111yescharacteristic, complemented, Sylow
334C23—41no—
335C23—222no—
336C23—224no—
337C23—881no—
338C23—881no—
339C23#6693711yescharacteristic
340Q8—41no—
341Q8—41no—
342Q8—882no—
343Q8—882no—
344D4—41no—
345D4—41no—
346D4—42no—
347D4—81no—
348D4—82no—
349D4—114no—
350D4—222no—
351D4—224no—
352C2×C4—22no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—82no—
356C2×C4—222no—
357C2×C4—444no—
358C2×C4—442no—
359C2×C4—882no—
360C2×C4—881no—
361C2×C4—882no—
362C2×C4#6693711yescharacteristic
363C2×C4#6693711yescharacteristic
364C2×C4#6693711yescharacteristic
365C2×C4#6696512yes—
366C2×C4SD16×D1112yes—
367C2×C4C2×#433911yescharacteristic
368C2×C4C2×D4×D1111yescharacteristic
369C2×C4C2×D4×D1111yescharacteristic
370C8—42no—
371C8—42no—
372C8—224no—
373C8—442no—
374C22—21no—
375C22—21no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22—224no—
380C22—442no—
381C22—442no—
382C22—884no—
383C22#1062239112yes—
384C22C2×#6693711yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—81no—
389C4—442no—
390C4—882no—
391C4#1062239112yes—
392C4C2×#6696511yescharacteristic
393C4C2×SD16×D1111yescharacteristic
394C4#1062330112yes—
395C2—22no—
396C2—161no—
397C2—444no—
398C2#1307813111yescharacteristic
399C2C2×#1062239111yescharacteristic
400C2#1307834711yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1540C2
socleC22×C11C2×#121
prime radical#13078076C2
hypercenter#1540D11
hypocenterC11#19391
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1540

Complements

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

NH ≅ G/Ntype
1. #13079741C2semidirect
2. C2×#10622455C2semidirect
4. #13077639C2semidirect
5. #13068024C2semidirect
6. #13067990C2semidirect
7. #13067386C2semidirect
8. #13067296C2semidirect
9. C11×#1540C2semidirect
20. #10622692C22semidirect
22. #10622683C22semidirect
33. C11×#332C22semidirect
34. C11×#331C22semidirect
35. #10622119C22semidirect
36. #10622118C22semidirect
142. #1540D11semidirect
208. #332C2×D11semidirect
209. #331C2×D11semidirect
333. C11#19391semidirect

Maximal subgroups

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

subgroupindex
#130797412
C2×#106224552
#130780762
#130776392
#130680242
#130679902
#130673862
#130672962
C11×#15402
#1939111