Finite Group Databasebeta

← #14741701

Subgroups — #14741701

Order 2816.

1050 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079530C212yesmaximal, complemented
2#13079193C211yesmaximal, characteristic, complemented
3#13079067C212yesmaximal, complemented
4D11×#493C211yesmaximal, characteristic, complemented
5#13068283C212yesmaximal, complemented
6#13068281C212yesmaximal, complemented
7#13068230C211yesmaximal, characteristic, complemented
8#13068208C211yesmaximal, characteristic, complemented
9#13068205C211yesmaximal, characteristic, complemented
10C8×#4313C211yesmaximal, characteristic, complemented
11C11×#1712C211yesmaximal, characteristic, complemented
12C2×#66964—24no—
13C2×D8×D11—22no—
14#10623247C2212yes—
15D11×#127C2212yes—
16C11×#493C2211yescharacteristic
17C11×#493C2212yescomplemented
18C11×#493C2211yescharacteristic, complemented
19C11×#493C2212yescomplemented
20#10622770—22no—
21#10622769—24no—
22#10622767—24no—
23#10622764—22no—
24#10622763—24no—
25D8×Dic11—22no—
26#10622689C2212yescomplemented
27#10622686C2212yes—
28#10622686C2212yescomplemented
29#10622686C2212yescomplemented
30#10622683C2212yescomplemented
31#10622683C2212yescomplemented
32#10622308C2211yescharacteristic
33#10622307C2212yescomplemented
34#10622306C2212yescomplemented
35C4×#4313C2211yescharacteristic
36#10622298C2211yescharacteristic
37C4×C8×D11C2211yescharacteristic
38#10622295C2211yescharacteristic, complemented
39C82×C11C2211yescharacteristic, complemented
40#10622093C2211yescharacteristic, complemented
41#10622092C2211yescharacteristic, complemented
42C8×C11⋊C8C2211yescharacteristic, complemented
43C2×#4341—22no—
44C2×D4×D11—22no—
45C2×D4×D11—22no—
46C2×D4×D11—22no—
47C2×C11×D8—22no—
48C2×C11×D8—22no—
49C2×C11×D8—24no—
50C2×C11×D8—24no—
51C11×#127C2312yes—
52C11×#127C2312yes—
53#66993—22no—
54#66993—22no—
55#66993—22no—
56#66991—22no—
57#66991—22no—
58#66989—22no—
59D4×Dic11—22no—
60D4×Dic11—22no—
61C2×#4324—24no—
62C2×#4323—24no—
63C2×#4323—24no—
64C2×#4323—24no—
65#66964—416no—
66D8×D11—48no—
67C2×D88—22no—
68C2×#4314—24no—
69C2×#4313D412yes—
70C2×C8×D11D412yes—
71#66927C2312yes—
72C42×D11C2311yescharacteristic
73#66922C2312yes—
74C4×C8×C11C2311yescharacteristic
75C4×C8×C11C2311yescharacteristic
76C4×C8×C11C2311yescharacteristic
77#66896—24no—
78#66896—24no—
79#66885—24no—
80(C2×D11)⋊C8D412yes—
81#66882—22no—
82#66879D412yes—
83Dic11⋊C8D412yes—
84C8×Dic11D412yes—
85C4×C11⋊C8C2311yescharacteristic
86C4×C11⋊C8C2311yescharacteristic
87C4×C11⋊C8C2311yescharacteristic
88#19629—111nomaximal, Sylow
89C23×D11—42no—
90C2×D4×C11—22no—
91C2×D4×C11—22no—
92C2×D4×C11—22no—
93C2×D4×C11—22no—
94C2×D4×C11—22no—
95C2×D4×C11—22no—
96C2×C22⋊D11—42no—
97C2×C22⋊D11—42no—
98C2×C22⋊D11—42no—
99C2×C22⋊D11—42no—
100C22×Dic11—42no—
101#4341—48no—
102D4×D11—48no—
103D4×D11—48no—
104D4×D11—84no—
105C2×D44—22no—
106C2×D44—22no—
107C2×D44—22no—
108C2×C4×D11C2×D411yescharacteristic
109C2×C4×D11C2×D411yescharacteristic
110C2×C4×D11C2×D411yescharacteristic
111C2×Dic22—22no—
112C11×D8—48no—
113C11×D8—44no—
114C11×D8—44no—
115C11×D8—84no—
116C2×C8×C11C2×D412yes—
117C2×C8×C11C2×D412yes—
118C2×C8×C11C2×D412yes—
119C42×C11C2411yescharacteristic
120C22⋊Dic11—42no—
121C22⋊Dic11—42no—
122#4324—48no—
123#4323—48no—
124#4323—48no—
125#4323—84no—
126C4⋊Dic11—22no—
127C4⋊Dic11—22no—
128C4×Dic11C2×D411yescharacteristic
129C4×Dic11C2×D411yescharacteristic
130C4×Dic11C2×D411yescharacteristic
131C2×C11⋊C8C2×D412yes—
132C2×C11⋊C8C2×D412yes—
133C2×C11⋊C8C2×D412yes—
134D88—44no—
135#4314—48no—
136#4313D818yescomplemented
137C8×D11—24no—
138#3205—112no—
139#3169—111no—
140#3151—112no—
141C2×#493—111no—
142#1721—112no—
143#1721—112no—
144#1712—111no—
145#1712D1111yescharacteristic, complemented
146#1706—111no—
147#1706—111no—
148C8×M16—111no—
149C23×C11—42no—
150C23×C11—42no—
151C22×D11—42no—
152C22×D11—84no—
153C22×D11—84no—
154C22×D11—84no—
155C22×D11#12711yescharacteristic
156D4×C11—44no—
157D4×C11—44no—
158D4×C11—44no—
159D4×C11—44no—
160D4×C11—44no—
161D4×C11—44no—
162C2×C4×C11C22×D411yescharacteristic
163C2×C4×C11C22×D411yescharacteristic
164C2×C4×C11C22×D411yescharacteristic
165C22⋊D11—84no—
166C22⋊D11—84no—
167C22⋊D11—84no—
168C22⋊D11—84no—
169C2×Dic11—42no—
170C2×Dic11—84no—
171C2×Dic11#12711yescharacteristic
172C2×Dic11#12711yescharacteristic
173C2×Dic11#12711yescharacteristic
174D44—44no—
175D44—44no—
176D44—44no—
177C4×D11—22no—
178C4×D11—22no—
179C4×D11C2×D814yes—
180Dic22—44no—
181C8×C11—22no—
182C8×C11C2×D814yescomplemented
183C8×C11AGL(1,ℤ/8)14yescomplemented
184C11⋊C8—22no—
185C11⋊C8—22no—
186C11⋊C8C2×D814yescomplemented
187C2×AGL(1,ℤ/8)—224no—
188C22×D8—222no—
189#532—112no—
190C2×#127—112no—
191#500—111no—
192#496—224no—
193#493—112no—
194#493—112no—
195#493—112no—
196#493—111no—
197#493—222no—
198#493C2×D1111yescharacteristic
199#493C2×D1112yescomplemented
200#493C2×D1111yescharacteristic, complemented
201#493C2×D1112yescomplemented
202#492—112no—
203#492—112no—
204#486—112no—
205#486—112no—
206#486—112no—
207#466—222no—
208#459—224no—
209#447—224no—
210C4×D8—222no—
211#431—111no—
212C4×M16—111no—
213C2×C4×C8—111no—
214#322—111no—
215#322—111no—
216C82—111no—
217C82C2×D1111yescharacteristic, complemented
218C22×C11—82no—
219C22×C11—82no—
220C22×C11—82no—
221C22×C11—82no—
222C22×C11—82no—
223C22×C11—82no—
224C22×C11C2×#12711yescharacteristic
225C2×D11—21no—
226C2×D11—21no—
227C2×D11—82no—
228C2×D11—82no—
229C2×D11—82no—
230C2×D11—168no—
231C2×D11#49312yes—
232C4×C11C22×D812yes—
233C4×C11C2×AGL(1,ℤ/8)12yes—
234C4×C11#57612yes—
235Dic11—21no—
236Dic11—21no—
237Dic11—82no—
238Dic11#49312yes—
239C2×#41—222no—
240C22×D4—222no—
241C22×D4—222no—
242C22×D4—222no—
243AGL(1,ℤ/8)—4416no—
244C2×SD16—224no—
245C2×SD16—224no—
246C2×D8—22no—
247C2×D8—24no—
248C2×D8—22no—
249C2×D8—24no—
250C2×D8—224no—
251C2×D8—224no—
252C2×D8—224no—
253C2×D8—222no—
254C2×D8—448no—
255C2×M16—112no—
256C22×C8—112no—
257C4⋊Q8—112no—
258#127—112no—
259#127—222no—
260#127—222no—
261#127—222no—
262#127C22×D1112yes—
263#127C22×D1112yes—
264#124—222no—
265#121—222no—
266#121—222no—
267C4×D4—222no—
268C4×D4—222no—
269C2×C42—111no—
270#107—222no—
271C4⋊C8—112no—
272#102—224no—
273#102—224no—
274#102—224no—
275C22⋊C8—112no—
276#97—112no—
277C4×C8—112no—
278C4×C8—111no—
279C4×C8—111no—
280C4×C8—111no—
281C4×C8C22×D1111yescharacteristic
282C4×C8C22×D1111yescharacteristic
283C4×C8C22×D1111yescharacteristic
284C2×C11—162no—
285C2×C11—162no—
286C2×C11C2×#49311yescharacteristic
287C2×C11#315111yescharacteristic
288C2×C11#315511yescharacteristic
289D11—22no—
290D11—162no—
291C24—442no—
292#41—448no—
293C2×Q8—222no—
294C2×D4—22no—
295C2×D4—22no—
296C2×D4—22no—
297C2×D4—22no—
298C2×D4—22no—
299C2×D4—22no—
300C2×D4—222no—
301C2×D4—222no—
302C2×D4—222no—
303C2×D4—448no—
304C2×D4—442no—
305C2×D4—442no—
306C2×D4—442no—
307C2×D4—448no—
308C2×D4—442no—
309C2×D4—884no—
310C22×C4—111no—
311C22×C4—111no—
312C22×C4—111no—
313C22×C4—442no—
314SD16—448no—
315SD16—448no—
316D8—48no—
317D8—44no—
318D8—44no—
319D8—84no—
320D8—448no—
321D8—448no—
322D8—444no—
323D8—884no—
324M16—118no—
325C2×C8—112no—
326C2×C8—112no—
327C2×C8—112no—
328C2×C8—224no—
329C2×C8D4×D1112yes—
330C2×C8D4×D1112yes—
331C2×C8D4×D1112yes—
332C4⋊C4—222no—
333C4⋊C4—222no—
334C22⋊C4—442no—
335C22⋊C4—442no—
336C42—111no—
337C42—111no—
338C42—111no—
339C42C23×D1111yescharacteristic
340C11#1962911yescharacteristic, complemented, Sylow
341C23—42no—
342C23—42no—
343C23—111no—
344C23—442no—
345C23—884no—
346C23—884no—
347C23—884no—
348Q8—444no—
349D4—44no—
350D4—44no—
351D4—44no—
352D4—44no—
353D4—44no—
354D4—44no—
355D4—444no—
356D4—444no—
357D4—444no—
358D4—884no—
359D4—884no—
360D4—884no—
361D4—884no—
362C2×C4—111no—
363C2×C4—114no—
364C2×C4—111no—
365C2×C4—111no—
366C2×C4—222no—
367C2×C4—222no—
368C2×C4—442no—
369C2×C4—884no—
370C2×C4C2×D4×D1111yescharacteristic
371C2×C4C2×D4×D1111yescharacteristic
372C2×C4C2×D4×D1111yescharacteristic
373C8—22no—
374C8—114no—
375C8—222no—
376C8—222no—
377C8D8×D1114yescomplemented
378C8#6696414yescomplemented
379C22—82no—
380C22—82no—
381C22—82no—
382C22—82no—
383C22—82no—
384C22—82no—
385C22—112no—
386C22—221no—
387C22—221no—
388C22—882no—
389C22—882no—
390C22—882no—
391C22—1768no—
392C22D11×#12711yescharacteristic
393C4—112no—
394C4—221no—
395C4—221no—
396C4—882no—
397C4C2×D8×D1112yes—
398C4C2×#6696412yes—
399C4#1062328812yes—
400C2—162no—
401C2—162no—
402C2—222no—
403C2—1762no—
404C2D11×#49311yescharacteristic
405C2#1307906711yescharacteristic
406C2#1307909611yescharacteristic
subgroupG/H
centerC22D11×#127
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1712C2
socleC22×C11C2×#127
hypercenter#1712D11
hypocenterC11#19629
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #1712

Complements

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

NH ≅ G/Ntype
1. #13079530C2semidirect
2. #13079193C2semidirect
3. #13079067C2semidirect
4. D11×#493C2semidirect
5. #13068283C2semidirect
6. #13068281C2semidirect
7. #13068230C2semidirect
8. #13068208C2semidirect
9. #13068205C2semidirect
10. C8×#4313C2semidirect
11. C11×#1712C2semidirect
17. C11×#493C22semidirect
18. C11×#493C22semidirect
19. C11×#493C22semidirect
26. #10622689C22semidirect
28. #10622686C22semidirect
29. #10622686C22semidirect
30. #10622683C22semidirect
31. #10622683C22semidirect
33. #10622307C22semidirect
34. #10622306C22semidirect
38. #10622295C22semidirect
39. C82×C11C22semidirect
40. #10622093C22semidirect
41. #10622092C22semidirect
42. C8×C11⋊C8C22semidirect
136. #4313D8semidirect
145. #1712D11semidirect
182. C8×C11C2×D8semidirect
183. C8×C11AGL(1,ℤ/8)semidirect
186. C11⋊C8C2×D8semidirect
199. #493C2×D11semidirect
200. #493C2×D11semidirect
201. #493C2×D11semidirect
217. C82C2×D11semidirect
340. C11#19629semidirect
377. C8D8×D11semidirect
378. C8#66964semidirect

Maximal subgroups

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

subgroupindex
#130795302
#130791932
#130790672
D11×#4932
#130682832
#130682812
#130682302
#130682082
#130682052
C8×#43132
C11×#17122
#1962911