Finite Group Databasebeta

← #14741663

Subgroups — #14741663

Order 2816.

836 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079536C211yesmaximal, characteristic
2#13079176C211yesmaximal, characteristic, complemented
3C2×#10622698C211yesmaximal, characteristic, complemented
4#13079012C211yesmaximal, characteristic, complemented
5#13078992C211yesmaximal, characteristic, complemented
6#13068272C212yesmaximal, complemented
7#13068258C212yesmaximal, complemented
8#13068219C212yesmaximal, complemented
9#13068209C212yesmaximal, complemented
10#13066897C211yesmaximal, characteristic, complemented
11C11×#3230C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C22×#4325—22no—
15#10623008C2211yescharacteristic
16C2×#66927C2211yescharacteristic
17C11×#500C2212yescomplemented
18C11×#487C2212yescomplemented
19C11×#484—22no—
20C11×#477—22no—
21C11×#431C2211yescharacteristic
22#10622706C2212yescomplemented
23#10622702—22no—
24#10622701C2212yes—
25#10622701C2212yes—
26#10622701C2211yescharacteristic, complemented
27#10622701C2212yescomplemented
28#10622698—22no—
29#10622698C2212yes—
30#10622698C2212yes—
31#10622698C2211yescharacteristic, complemented
32#10622694C2211yescharacteristic, complemented
33#10622692C2211yescharacteristic, complemented
34#10622680—22no—
35#10622661—22no—
36C4×#4325—22no—
37#10622614—22no—
38#10622579—22no—
39C4×#4318C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622456—22no—
42#10622345—22no—
43#10622308C2212yes—
44#10622307C2212yes—
45#10622092C2212yescomplemented
46C8×C11⋊C8C2212yescomplemented
47C22×Q8×C11—21no—
48C2×#4339—21no—
49C22×D44—21no—
50C22×D44—21no—
51C22×D44—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8C2311yescharacteristic
56C11×C4⋊Q8C2312yes—
57C11×C4⋊Q8C2311yescharacteristic
58C11×#125—21no—
59C11×C22⋊Q8—21no—
60C11×C22⋊Q8—21no—
61C4×Q8×C11—21no—
62C4×Q8×C11—21no—
63C11×#117—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C42×C11C2311yescharacteristic
67C2×#4325—24no—
68C2×#4325—24no—
69C2×#4325—22no—
70C2×#4325—48no—
71#66983—21no—
72#66983—21no—
73C2×#4318D412yes—
74C22×C11⋊C8D412yes—
75C2×D88—24no—
76#66928—21no—
77#66927—21no—
78#66927—21no—
79#66927—21no—
80#66927C2312yes—
81#66927C2311yescharacteristic
82C4×D44—21no—
83C4×D44—21no—
84#66922C2311yescharacteristic
85C11×#107—24no—
86C11×C4⋊C8D412yes—
87C11×#103—24no—
88C11×C22⋊C8D412yes—
89C4×C8×C11C2312yes—
90#66899—22no—
91#66885—24no—
92#66874—24no—
93#66873—24no—
94#66873—24no—
95#66873—24no—
96#66873—22no—
97#66872—22no—
98#66867D412yes—
99C4×C11⋊C8D412yes—
100C4×C11⋊C8C2311yescharacteristic
101C4×C11⋊C8C2311yescharacteristic
102C4×C11⋊C8C2312yes—
103#19625—111nomaximal, Sylow
104C23×D11—41no—
105C2×Q8×C11—21no—
106C2×Q8×C11—21no—
107C2×Q8×C11—22no—
108C2×Q8×C11—44no—
109C2×Q8×C11—41no—
110C22×C4×C11—41no—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C2×C22⋊D11—41no—
115#4339—44no—
116C2×D44—22no—
117C2×D44—21no—
118C2×D44—21no—
119C2×D44—22no—
120C2×D44—21no—
121C2×D44—22no—
122C2×D44—44no—
123C2×D44—41no—
124C2×D44—41no—
125C2×D44—41no—
126C2×D44—44no—
127C2×D44—82no—
128C2×C4×D11—41no—
129C2×Dic22—21no—
130C2×C8×C11C2×D414yes—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—41no—
138C11×C4⋊C4—41no—
139C11×C4⋊C4—41no—
140C11×C4⋊C4—41no—
141C11×C22⋊C4—41no—
142C42×C11—41no—
143C42×C11C2×D411yescharacteristic
144C42×C11C2×D411yescharacteristic
145C42×C11C2×D411yescharacteristic
146C42×C11C2411yescharacteristic
147#4325—48no—
148#4325—44no—
149#4325—48no—
150(C2×D11)⋊C4—41no—
151(C2×D11)⋊C4—41no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154#4318—24no—
155C2×C11⋊C8—24no—
156C2×C11⋊C8C2×D412yes—
157C2×C11⋊C8C2×D414yes—
158C2×C11⋊C8C2×D412yes—
159D88—84no—
160#3230D1111yescharacteristic, complemented
161#3205—111no—
162#3167—111no—
163C2×#492—111no—
164#3141—111no—
165#3138—111no—
166#1719—112no—
167#1717—112no—
168#1708—112no—
169#1706—112no—
170C8×M16—111no—
171C23×C11#12711yescharacteristic
172C22×D11—41no—
173C22×D11—42no—
174C22×D11—82no—
175C22×D11—82no—
176C22×D11—82no—
177Q8×C11—44no—
178Q8×C11—42no—
179Q8×C11—42no—
180Q8×C11—82no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—42no—
186C2×C4×C11—82no—
187C2×C4×C11#12711yescharacteristic
188C2×C4×C11#12711yescharacteristic
189C2×C4×C11#12711yescharacteristic
190C2×C4×C11#13514yes—
191C2×C4×C11C22×D411yescharacteristic
192C2×C4×C11C22×D411yescharacteristic
193C2×C4×C11C22×D411yescharacteristic
194C22⋊D11—82no—
195C2×Dic11—41no—
196D44—44no—
197D44—42no—
198D44—44no—
199D44—42no—
200D44—42no—
201D44—44no—
202D44—82no—
203D44—82no—
204D44—82no—
205C4×D11—82no—
206Dic22—42no—
207C8×C11—24no—
208C11⋊C8—24no—
209C11⋊C8—22no—
210C11⋊C8AGL(1,ℤ/8)14yes—
211C22×SD16—222no—
212#533C2×D1111yescharacteristic
213#532—111no—
214C2×C4⋊Q8C2×D1111yescharacteristic
215C2×#127—111no—
216#500C2×D1112yescomplemented
217#498—111no—
218#493—112no—
219#492—112no—
220#492—112no—
221#492—111no—
222#492—222no—
223#490—222no—
224#489—222no—
225#487—112no—
226#487—111no—
227#487C2×D1112yescomplemented
228#486—112no—
229#486—112no—
230#486—112no—
231#486—111no—
232#486—112no—
233#484—22no—
234#477—22no—
235#465—222no—
236#459—222no—
237#447—222no—
238C4×SD16—222no—
239#431C2×D1111yescharacteristic
240#418—222no—
241#417—222no—
242C4×M16—111no—
243C2×C4×C8—111no—
244#322—112no—
245C82—112no—
246C22×C11—21no—
247C22×C11—21no—
248C22×C11#49512yes—
249C22×C11C2×#12711yescharacteristic
250C2×D11—82no—
251C2×D11—81no—
252C2×D11—82no—
253C2×D11—81no—
254C2×D11—82no—
255C2×D11—81no—
256C2×D11—164no—
257C4×C11—21no—
258C4×C11—21no—
259C4×C11—82no—
260C4×C11—81no—
261C4×C11—81no—
262C4×C11#49512yes—
263C4×C11C2×#13512yes—
264C4×C11C2×AGL(1,ℤ/8)12yes—
265C4×C11#57712yes—
266Dic11—81no—
267C2×#41—221no—
268C22×Q8—21no—
269C22×D4—221no—
270C22×D4—221no—
271C22×D4—221no—
272C2×SD16—224no—
273C2×SD16—224no—
274C2×SD16—222no—
275C2×SD16—448no—
276C2×D8—224no—
277C2×M16—112no—
278C22×C8—112no—
279C4⋊Q8—21no—
280C4⋊Q8—21no—
281C4⋊Q8—21no—
282C4⋊Q8—111no—
283C4⋊Q8C22×D1112yes—
284C4⋊Q8C22×D1111yescharacteristic
285C4⋊Q8C22×D1111yescharacteristic
286#127—112no—
287#127—111no—
288#127—221no—
289#127—221no—
290#127—221no—
291#125—21no—
292#124—221no—
293C22⋊Q8—21no—
294C22⋊Q8—21no—
295#121—221no—
296#121—221no—
297C4×Q8—21no—
298C4×Q8—21no—
299C4×D4—221no—
300C4×D4—221no—
301#117—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C42C22×D1111yescharacteristic
305#107—24no—
306#106—222no—
307C4⋊C8C22⋊D1112yes—
308#103—24no—
309#103—224no—
310#103—222no—
311#102—224no—
312#102—224no—
313#102—224no—
314#102—222no—
315#102—224no—
316C22⋊C8C22⋊D1112yes—
317#97—112no—
318C4×C8—112no—
319C4×C8—111no—
320C4×C8—112no—
321C4×C8—111no—
322C4×C8C22×D1112yes—
323C2×C11—22no—
324C2×C11C2×#49511yescharacteristic
325C2×C11#315111yescharacteristic
326C2×C11#315411yescharacteristic
327D11—161no—
328D11—162no—
329C24—441no—
330#41—444no—
331C2×Q8—21no—
332C2×Q8—22no—
333C2×Q8—21no—
334C2×Q8—44no—
335C2×Q8—41no—
336C2×Q8—221no—
337C2×D4—221no—
338C2×D4—222no—
339C2×D4—221no—
340C2×D4—222no—
341C2×D4—222no—
342C2×D4—221no—
343C2×D4—444no—
344C2×D4—441no—
345C2×D4—444no—
346C2×D4—441no—
347C2×D4—441no—
348C2×D4—441no—
349C2×D4—882no—
350C22×C4—41no—
351C22×C4—441no—
352C22×C4D4×D1111yescharacteristic
353C22×C4D4×D1111yescharacteristic
354C22×C4C2×C22⋊D1111yescharacteristic
355SD16—448no—
356SD16—444no—
357SD16—448no—
358D8—884no—
359M16—224no—
360C2×C8—112no—
361C2×C8—112no—
362C2×C8—114no—
363C2×C8—224no—
364C2×C8C2×C22⋊D1114yes—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—22no—
368C4⋊C4—21no—
369C4⋊C4—22no—
370C4⋊C4—21no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—221no—
376C4⋊C4—221no—
377C22⋊C4—41no—
378C22⋊C4—441no—
379C22⋊C4—441no—
380C42—41no—
381C42D4×D1111yescharacteristic
382C42D4×D1111yescharacteristic
383C42C2×C22⋊D1111yescharacteristic
384C42C23×D1111yescharacteristic
385C11#1962511yescharacteristic, complemented, Sylow
386C23—441no—
387C23—442no—
388C23—882no—
389C23—882no—
390C23—882no—
391C23#6699311yescharacteristic
392Q8—44no—
393Q8—42no—
394Q8—42no—
395Q8—82no—
396Q8—442no—
397D4—444no—
398D4—442no—
399D4—444no—
400D4—442no—
401D4—442no—
402D4—444no—
403D4—882no—
404D4—882no—
405D4—882no—
406D4—882no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—82no—
413C2×C4—441no—
414C2×C4—882no—
415C2×C4#6697214yes—
416C2×C4#6699311yescharacteristic
417C2×C4#6699311yescharacteristic
418C2×C4#6699311yescharacteristic
419C2×C4C2×D4×D1111yescharacteristic
420C2×C4C2×D4×D1111yescharacteristic
421C2×C4C22×C22⋊D1111yescharacteristic
422C8—24no—
423C8—114no—
424C8—224no—
425C8—222no—
426C22—21no—
427C22—21no—
428C22—882no—
429C22—881no—
430C22—882no—
431C22—881no—
432C22—881no—
433C22—882no—
434C22—1764no—
435C22#1062280412yes—
436C22C2×#6699311yescharacteristic
437C4—21no—
438C4—21no—
439C4—82no—
440C4—81no—
441C4—81no—
442C4—881no—
443C4#1062280412yes—
444C4C2×#6697212yes—
445C4D11×AGL(1,ℤ/8)12yes—
446C4#1062336812yes—
447C2—22no—
448C2—1762no—
449C2—1761no—
450C2C2×#1062280411yescharacteristic
451C2#1307906411yescharacteristic
452C2#1307909411yescharacteristic
subgroupG/H
centerC22C2×#66993
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3230C2
socleC22×C11C2×#127
prime radical#13079536C2
hypercenter#3230D11
hypocenterC11#19625
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3230

Complements

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

NH ≅ G/Ntype
2. #13079176C2semidirect
3. C2×#10622698C2semidirect
4. #13079012C2semidirect
5. #13078992C2semidirect
6. #13068272C2semidirect
7. #13068258C2semidirect
8. #13068219C2semidirect
9. #13068209C2semidirect
10. #13066897C2semidirect
11. C11×#3230C2semidirect
17. C11×#500C22semidirect
18. C11×#487C22semidirect
22. #10622706C22semidirect
26. #10622701C22semidirect
27. #10622701C22semidirect
31. #10622698C22semidirect
32. #10622694C22semidirect
33. #10622692C22semidirect
45. #10622092C22semidirect
46. C8×C11⋊C8C22semidirect
160. #3230D11semidirect
216. #500C2×D11semidirect
227. #487C2×D11semidirect
385. C11#19625semidirect

Maximal subgroups

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

subgroupindex
#130795362
#130791762
C2×#106226982
#130790122
#130789922
#130682722
#130682582
#130682192
#130682092
#130668972
C11×#32302
#1962511