Finite Group Databasebeta

← #15625313

Subgroups — #15625313

Order 2816.

2162 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081949C211yesmaximal, characteristic, complemented
2#13079671C218yesmaximal, complemented
3#13079660C218yesmaximal, complemented
4#13079066C212yesmaximal, complemented
5#13079019C212yesmaximal, complemented
6#13078080C214yesmaximal, complemented
7#13077866C214yesmaximal, complemented
8#13077254C211yesmaximal, characteristic, complemented
9C2×C11×#540C211yesmaximal, characteristic, complemented
10C22×#4339C2212yes—
11C11×#540—24no—
12C11×#540C2218yescomplemented
13C2×C11×#127C2211yescharacteristic, complemented
14C2×C11×#125C2211yescharacteristic, complemented
15C2×C11×#123—22no—
16C2×C11×#121—22no—
17C2×C11×#121C2212yes—
18C2×C4×D4×C11C2212yescomplemented
19C2×C11×#117C2211yescharacteristic
20C2×#66985C2218yescomplemented
21#10623057C2214yescomplemented
22#10623056C2214yescomplemented
23#10623055—24no—
24#10623041—22no—
25#10623024—22no—
26#10623008C2212yes—
27#10623008C2212yes—
28#10622820C2212yes—
29#10622689C2214yescomplemented
30#10622687C2218yescomplemented
31#10622686C2214yescomplemented
32#10622682C2214yescomplemented
33#10622681C2218yescomplemented
34#10622680C2214yescomplemented
35#10622653C2218yescomplemented
36#10622650C22116yescomplemented
37#10622649C2218yescomplemented
38#10622632C2218yescomplemented
39#10622629C22116yescomplemented
40#10622628C2218yescomplemented
41#10622613C2218yescomplemented
42#10622579C2218yescomplemented
43#10622537C2212yescomplemented
44C4×#4318C2212yescomplemented
45C22×D4×C11—22no—
46C22×D4×C11—22no—
47C22×D4×C11C2312yes—
48C23×C4×C11—22no—
49C23×C4×C11C2311yescharacteristic
50C22×C22⋊D11—22no—
51C2×#4339—22no—
52C2×#4339—22no—
53C2×#4339—48no—
54C2×#4339C2314yes—
55C2×#4339C2314yes—
56C22×D44C2312yes—
57C22×C4×D11—22no—
58C22×Dic22C2312yes—
59C11×#127—22no—
60C11×#127C2314yes—
61C11×#125—22no—
62C11×#125C2314yes—
63C11×#123—216no—
64C11×#121—24no—
65C11×#121—216no—
66C11×#121C2318yes—
67C4×D4×C11—24no—
68C4×D4×C11C2318yes—
69C11×#117D414yes—
70C11×#117C2314yes—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4D412yes—
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4D412yes—
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×#4324C23116yes—
80#66985—416no—
81C2×#4323C23116yes—
82#66983—24no—
83#66983—24no—
84C2×#4318C2314yes—
85#66950—28no—
86#66948—28no—
87#66939—28no—
88#66935—28no—
89#66928C2314yes—
90#66928C2314yes—
91#66927C2312yes—
92#66927C2312yes—
93C4×D44—24no—
94C4×D44—24no—
95#66922C2312yes—
96#66922C2312yes—
97C22⋊(C11⋊C8)C2318yes—
98#66874C23116yes—
99#66873C23116yes—
100C4⋊(C11⋊C8)C2318yes—
101#66867C2314yes—
102C4×C11⋊C8C2314yes—
103#60808—111nomaximal, Sylow
104C24×C11—22no—
105C24×C11C2×D411yescharacteristic
106C23×D11—22no—
107C2×D4×C11—28no—
108C2×D4×C11—22no—
109C2×D4×C11—28no—
110C2×D4×C11—28no—
111C2×D4×C11—84no—
112C2×D4×C11—84no—
113C2×D4×C11C2414yes—
114C22×C4×C11—24no—
115C22×C4×C11—22no—
116C22×C4×C11—28no—
117C22×C4×C11—84no—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2412yes—
123C22×C4×C11C2411yescharacteristic
124C2×C22⋊D11—24no—
125C2×C22⋊D11—24no—
126C2×C22⋊D11—48no—
127C22×Dic11—22no—
128#4339—216no—
129#4339—48no—
130#4339—48no—
131#4339—48no—
132C2×D44—22no—
133C2×D44—24no—
134C2×D44—24no—
135C2×D44—44no—
136C2×D44C2414yes—
137C2×C4×D11—24no—
138C2×C4×D11—24no—
139C2×C4×D11—48no—
140C2×Dic22—22no—
141C2×Dic22—44no—
142C2×Dic22C2414yes—
143C11×C4⋊C4—28no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4C2×D418yes—
146C11×C4⋊C4C2414yes—
147C11×C22⋊C4—28no—
148C11×C22⋊C4—28no—
149C11×C22⋊C4C2×D418yes—
150C42×C11C2×D412yes—
151C42×C11C2×D412yes—
152C42×C11C2412yes—
153C42×C11C2412yes—
154#4324—416no—
155#4323—416no—
156(C2×D11)⋊C4—28no—
157(C2×D11)⋊C4—28no—
158C4⋊Dic11—24no—
159C4⋊Dic11—24no—
160#4318—28no—
161C2×C11⋊C8C2418yes—
162C2×#540D1111yescharacteristic, complemented
163#3449—111no—
164#3221—118no—
165#3220—118no—
166#3151—112no—
167#3142—112no—
168#3036—114no—
169#3006—114no—
170#2921—111no—
171C23×C11—22no—
172C23×C11—24no—
173C23×C11—42no—
174C23×C11—44no—
175C23×C11—44no—
176C23×C11—44no—
177C23×C11C22×D412yes—
178C23×C11C22×D411yescharacteristic
179C22×D11—24no—
180C22×D11—44no—
181C22×D11—84no—
182D4×C11—28no—
183D4×C11—44no—
184D4×C11—88no—
185D4×C11—88no—
186C2×C4×C11—22no—
187C2×C4×C11—24no—
188C2×C4×C11—24no—
189C2×C4×C11—24no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—44no—
193C2×C4×C11—88no—
194C2×C4×C11C22×D414yes—
195C2×C4×C11C22×D414yes—
196C2×C4×C11C22×D412yes—
197C2×C4×C11C22×D411yescharacteristic
198C2×C4×C11H(5,𝔽2)14yes—
199C2×C4×C11C2511yescharacteristic
200C22⋊D11—48no—
201C22⋊D11—48no—
202C2×Dic11—24no—
203C2×Dic11—44no—
204D44—28no—
205D44—44no—
206D44—84no—
207D44—84no—
208C4×D11—48no—
209C4×D11—48no—
210Dic22—28no—
211Dic22—44no—
212C11⋊C8—28no—
213C22×#41—112no—
214C2×AGL(1,ℤ/8)—118no—
215#540—24no—
216#540C2×D1118yescomplemented
217#537—222no—
218#536—114no—
219#535—114no—
220#534—222no—
221#532—112no—
222#532—112no—
223C2×#127C2×D1111yescharacteristic, complemented
224C2×#125C2×D1111yescharacteristic, complemented
225#525—224no—
226C2×#123—22no—
227C2×#121—22no—
228C2×#121C2×D1112yes—
229C2×C4×D4C2×D1112yescomplemented
230C2×#117C2×D1111yescharacteristic
231#496—118no—
232#493—114no—
233#492—114no—
234#491—114no—
235#490—114no—
236#488—118no—
237#463—1116no—
238#461—118no—
239#459—118no—
240#449—1116no—
241#448—118no—
242#447—118no—
243#433—118no—
244#423—112no—
245#417—118no—
246#407—112no—
247C4×M16—112no—
248C22×C11—22no—
249C22×C11—24no—
250C22×C11—22no—
251C22×C11—44no—
252C22×C11—44no—
253C22×C11—44no—
254C22×C11—82no—
255C22×C11—88no—
256C22×C11#53512yes—
257C22×C11C23×D411yescharacteristic
258C2×D11—48no—
259C2×D11—44no—
260C2×D11—88no—
261C4×C11—24no—
262C4×C11—24no—
263C4×C11—22no—
264C4×C11—44no—
265C4×C11#53512yes—
266C4×C11C2×H(5,𝔽2)12yes—
267Dic11—44no—
268C2×#41—114no—
269C2×#41—114no—
270C2×#41—222no—
271C2×#41—222no—
272C2×#41—448no—
273C22×Q8—112no—
274C22×D4—22no—
275C22×D4—22no—
276C22×D4—112no—
277C22×D4—222no—
278C22×D4C22×D1112yes—
279C23×C4—22no—
280C23×C4—222no—
281C23×C4C22×D1111yescharacteristic
282AGL(1,ℤ/8)—4416no—
283C2×SD16—1116no—
284C2×D8—1116no—
285C2×M16—114no—
286C4⋊Q8—112no—
287C4⋊Q8—112no—
288#127—22no—
289#127—112no—
290#127—112no—
291#127C22×D1114yes—
292#125—22no—
293#125C22×D1114yes—
294#124—114no—
295#124—114no—
296#123—216no—
297#123—228no—
298C22⋊Q8—228no—
299#121—24no—
300#121—216no—
301#121—224no—
302#121—224no—
303#121—228no—
304#121C22×D1118yes—
305#120—228no—
306C4×D4—24no—
307C4×D4—224no—
308C4×D4—224no—
309C4×D4C22×D1118yes—
310#117C22⋊D1114yes—
311#117C22×D1114yes—
312C2×C4⋊C4—22no—
313C2×C4⋊C4C22⋊D1112yes—
314C2×C4⋊C4C22×D1112yes—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4C22⋊D1112yes—
318C2×C42C22×D1111yescharacteristic
319C2×C42C22×D1111yescharacteristic
320C4⋊C8—118no—
321#103—1116no—
322#102—1116no—
323C22⋊C8—118no—
324#97—114no—
325C4×C8—114no—
326C2×C11—22no—
327C2×C11—42no—
328C2×C11—84no—
329C2×C11C2×#53511yescharacteristic
330C2×C11#358512yes—
331D11—84no—
332C24—22no—
333C24—222no—
334C24C2×C22⋊D1111yescharacteristic
335#41—2216no—
336#41—448no—
337#41—448no—
338#41—448no—
339C2×Q8—114no—
340C2×Q8—222no—
341C2×Q8—444no—
342C2×D4—28no—
343C2×D4—28no—
344C2×D4—22no—
345C2×D4—28no—
346C2×D4—84no—
347C2×D4—84no—
348C2×D4—114no—
349C2×D4—224no—
350C2×D4—224no—
351C2×D4—222no—
352C2×D4—224no—
353C2×D4—224no—
354C2×D4—444no—
355C2×D4—448no—
356C2×D4C23×D1114yes—
357C22×C4—24no—
358C22×C4—22no—
359C22×C4—28no—
360C22×C4—84no—
361C22×C4—222no—
362C22×C4—224no—
363C22×C4—224no—
364C22×C4—448no—
365C22×C4C2×C22⋊D1111yescharacteristic
366C22×C4C2×C22⋊D1112yes—
367C22×C4C2×C22⋊D1112yes—
368C22×C4C2×C22⋊D1112yes—
369C22×C4C23×D1112yes—
370C22×C4C23×D1111yescharacteristic
371SD16—4416no—
372D8—4416no—
373M16—228no—
374C2×C8—118no—
375C4⋊C4—28no—
376C4⋊C4—22no—
377C4⋊C4—224no—
378C4⋊C4—224no—
379C4⋊C4C2×C22⋊D1118yes—
380C4⋊C4C23×D1114yes—
381C22⋊C4—28no—
382C22⋊C4—28no—
383C22⋊C4—228no—
384C22⋊C4—228no—
385C22⋊C4C2×C22⋊D1118yes—
386C42C2×C22⋊D1112yes—
387C42C2×C22⋊D1112yes—
388C42C23×D1112yes—
389C42C23×D1112yes—
390C11#6080811yescharacteristic, complemented, Sylow
391C23—22no—
392C23—24no—
393C23—42no—
394C23—44no—
395C23—44no—
396C23—44no—
397C23—224no—
398C23—444no—
399C23—884no—
400C23C22×C22⋊D1112yes—
401C23C22×C22⋊D1111yescharacteristic
402Q8—228no—
403Q8—444no—
404D4—28no—
405D4—44no—
406D4—88no—
407D4—88no—
408D4—228no—
409D4—444no—
410D4—448no—
411D4—448no—
412D4—884no—
413D4—884no—
414C2×C4—22no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—44no—
421C2×C4—88no—
422C2×C4—224no—
423C2×C4—448no—
424C2×C4—444no—
425C2×C4—448no—
426C2×C4#6704214yes—
427C2×C4C22×C22⋊D1114yes—
428C2×C4C22×C22⋊D1114yes—
429C2×C4C22×C22⋊D1112yes—
430C2×C4C22×C22⋊D1111yescharacteristic
431C2×C4C24×D1111yescharacteristic
432C8—228no—
433C22—22no—
434C22—24no—
435C22—22no—
436C22—44no—
437C22—44no—
438C22—44no—
439C22—82no—
440C22—88no—
441C22—448no—
442C22—444no—
443C22—888no—
444C22#1062336112yes—
445C22C23×C22⋊D1111yescharacteristic
446C4—24no—
447C4—24no—
448C4—22no—
449C4—44no—
450C4—444no—
451C4#1062336112yes—
452C4C2×#6704212yes—
453C2—22no—
454C2—42no—
455C2—84no—
456C2—884no—
457C2C2×#1062336111yescharacteristic
458C2#1308339612yes—
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#540C2
socleC22×C11C23×D4
hypercenterC2×#540D11
hypocenterC11#60808
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. #13081949C2semidirect
2. #13079671C2semidirect
3. #13079660C2semidirect
4. #13079066C2semidirect
5. #13079019C2semidirect
6. #13078080C2semidirect
7. #13077866C2semidirect
8. #13077254C2semidirect
9. C2×C11×#540C2semidirect
12. C11×#540C22semidirect
13. C2×C11×#127C22semidirect
14. C2×C11×#125C22semidirect
18. C2×C4×D4×C11C22semidirect
20. C2×#66985C22semidirect
21. #10623057C22semidirect
22. #10623056C22semidirect
29. #10622689C22semidirect
30. #10622687C22semidirect
31. #10622686C22semidirect
32. #10622682C22semidirect
33. #10622681C22semidirect
34. #10622680C22semidirect
35. #10622653C22semidirect
36. #10622650C22semidirect
37. #10622649C22semidirect
38. #10622632C22semidirect
39. #10622629C22semidirect
40. #10622628C22semidirect
41. #10622613C22semidirect
42. #10622579C22semidirect
43. #10622537C22semidirect
44. C4×#4318C22semidirect
162. C2×#540D11semidirect
216. #540C2×D11semidirect
223. C2×#127C2×D11semidirect
224. C2×#125C2×D11semidirect
229. C2×C4×D4C2×D11semidirect
390. C11#60808semidirect

Maximal subgroups

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

subgroupindex
#130819492
#130796712
#130796602
#130790662
#130790192
#130780802
#130778662
#130772542
C2×C11×#5402
#6080811