Finite Group Databasebeta

← #14741656

Subgroups — #14741656

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#13079767C211yesmaximal, characteristic, complemented
2#13079534C211yesmaximal, characteristic
3#13079175C211yesmaximal, characteristic, complemented
4#13079012C211yesmaximal, characteristic, complemented
5#13078990C211yesmaximal, characteristic, complemented
6#13068267C212yesmaximal, complemented
7#13068253C212yesmaximal, complemented
8#13068215C212yesmaximal, complemented
9#13068206C212yesmaximal, complemented
10C8×#4318C211yesmaximal, characteristic, complemented
11C2×C11×#492C211yesmaximal, characteristic, complemented
12C22×C11×SD16—22no—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×#127C2211yescharacteristic
15#10623008C2211yescharacteristic
16#10623001C2211yescharacteristic
17C11×#492—22no—
18C11×#492C2212yes—
19C11×#492C2212yes—
20C2×C4×C8×C11C2211yescharacteristic
21#10622830—22no—
22#10622828—22no—
23#10622727—22no—
24#10622706C2212yescomplemented
25#10622706C2212yescomplemented
26#10622704—22no—
27#10622702—22no—
28#10622701C2212yescomplemented
29#10622691C2212yescomplemented
30#10622686C2212yes—
31#10622685—22no—
32#10622684—22no—
33#10622683C2212yes—
34#10622683C2212yes—
35#10622683C2212yes—
36#10622583—22no—
37#10622579—22no—
38#10622538C2211yescharacteristic
39C4×#4318C2211yescharacteristic
40#10622307C2211yescharacteristic, complemented
41#10622306C2211yescharacteristic, complemented
42C4×#4314—22no—
43#10622294C2211yescharacteristic, complemented
44#10622293C2211yescharacteristic, complemented
45#10622092C2212yescomplemented
46C8×C11⋊C8C2212yescomplemented
47C22×Q8×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11—21no—
50C22×D4×C11—21no—
51C2×#4339—21no—
52C2×C11×SD16—24no—
53C2×C11×SD16—24no—
54C2×C11×SD16—48no—
55C22×C8×C11D412yes—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8—21no—
58C11×C4⋊Q8—21no—
59C11×C4⋊Q8C2312yes—
60C11×#127—21no—
61C11×#127—21no—
62C11×#127—21no—
63C11×#127C2312yes—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C42×C11C2311yescharacteristic
67C2×#4323—24no—
68#66983—21no—
69#66983—21no—
70#66979—21no—
71#66977—21no—
72#66977—21no—
73C2×#4318D412yes—
74C2×#4314—22no—
75#66928—21no—
76#66927C2311yescharacteristic
77C4×D44—21no—
78C4×D44—21no—
79#66923—21no—
80#66922C2311yescharacteristic
81#66922C2311yescharacteristic
82#66922C2311yescharacteristic
83C4×Dic22—21no—
84C4×Dic22—21no—
85C4×C8×C11D412yes—
86C4×C8×C11C2311yescharacteristic
87C4×C8×C11C2311yescharacteristic
88#66896—24no—
89#66896—24no—
90#66896—24no—
91C22⋊(C11⋊C8)D412yes—
92#66885—22no—
93#66881—22no—
94#66880—22no—
95#66874—24no—
96#66874—24no—
97#66873—24no—
98#66871—24no—
99C4⋊(C11⋊C8)D412yes—
100#66867D412yes—
101C4×C11⋊C8C2312yes—
102C4×C11⋊C8C2312yes—
103#19625—111nomaximal, Sylow
104C24×C11—41no—
105C2×Q8×C11—22no—
106C2×Q8×C11—44no—
107C2×Q8×C11—41no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—44no—
112C2×D4×C11—41no—
113C2×D4×C11—41no—
114C2×D4×C11—41no—
115C2×D4×C11—44no—
116C2×D4×C11—82no—
117C22×C4×C11—41no—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C2×C22⋊D11—41no—
122#4339—44no—
123C2×D44—21no—
124C2×D44—21no—
125C2×D44—21no—
126C2×C4×D11—41no—
127C2×Dic22—21no—
128C2×Dic22—21no—
129C2×Dic22—21no—
130C11×SD16—48no—
131C11×SD16—48no—
132C2×C8×C11—24no—
133C2×C8×C11C2×D412yes—
134C2×C8×C11C2×D412yes—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—41no—
138C11×C4⋊C4—41no—
139C42×C11C2×D411yescharacteristic
140C42×C11C2×D411yescharacteristic
141C42×C11C2×D411yescharacteristic
142C42×C11C2411yescharacteristic
143C22⋊Dic11—41no—
144#4323—84no—
145(C2×D11)⋊C4—41no—
146(C2×D11)⋊C4—41no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155C4×Dic11—41no—
156#4318—24no—
157C2×C11⋊C8C2×D414yes—
158C2×C11⋊C8C2×D414yes—
159#4314—44no—
160#3230—111no—
161#3205—111no—
162#3167—111no—
163C2×#492D1111yescharacteristic, complemented
164#3141—111no—
165#3138—111no—
166#1719—112no—
167#1717—112no—
168#1708—112no—
169#1706—112no—
170C8×M16—111no—
171C23×C11—42no—
172C23×C11—82no—
173C23×C11—82no—
174C23×C11—82no—
175C23×C11#12711yescharacteristic
176C22×D11—41no—
177Q8×C11—44no—
178Q8×C11—82no—
179D4×C11—44no—
180D4×C11—44no—
181D4×C11—44no—
182D4×C11—82no—
183D4×C11—82no—
184D4×C11—82no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—42no—
188C2×C4×C11—82no—
189C2×C4×C11#12711yescharacteristic
190C2×C4×C11#12711yescharacteristic
191C2×C4×C11#12711yescharacteristic
192C2×C4×C11#13514yes—
193C2×C4×C11C22×D411yescharacteristic
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C22×D411yescharacteristic
196C22⋊D11—82no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200D44—42no—
201D44—42no—
202D44—42no—
203C4×D11—82no—
204Dic22—42no—
205Dic22—42no—
206Dic22—42no—
207C8×C11—22no—
208C8×C11AGL(1,ℤ/8)14yes—
209C11⋊C8—24no—
210C11⋊C8—24no—
211C22×SD16—22no—
212#533—111no—
213#532—111no—
214C2×C4⋊Q8C2×D1111yescharacteristic
215C2×#127C2×D1111yescharacteristic
216#500—112no—
217#498—111no—
218#493—112no—
219#492—22no—
220#492—111no—
221#492C2×D1112yes—
222#492C2×D1112yes—
223#490—222no—
224#489—222no—
225#487—112no—
226#487—112no—
227#487—111no—
228#486—112no—
229#486—112no—
230#486—112no—
231#486—112no—
232#486—111no—
233#484—222no—
234#477—222no—
235#465—222no—
236#459—222no—
237#447—222no—
238C4×SD16—222no—
239#431—111no—
240#418—222no—
241#417—222no—
242C4×M16—111no—
243C2×C4×C8C2×D1111yescharacteristic
244#322—112no—
245C82—112no—
246C22×C11—21no—
247C22×C11—21no—
248C22×C11—82no—
249C22×C11—82no—
250C22×C11—82no—
251C22×C11—164no—
252C22×C11#49512yes—
253C22×C11C2×#12711yescharacteristic
254C2×D11—81no—
255C2×D11—81no—
256C2×D11—81no—
257C4×C11—21no—
258C4×C11—21no—
259C4×C11—82no—
260C4×C11#49512yes—
261C4×C11C2×#13512yes—
262C4×C11C2×AGL(1,ℤ/8)12yes—
263C4×C11#57712yes—
264Dic11—81no—
265Dic11—81no—
266Dic11—81no—
267C2×#41—221no—
268C22×Q8—21no—
269C22×D4—21no—
270C22×D4—21no—
271C22×D4—21no—
272C2×SD16—24no—
273C2×SD16—24no—
274C2×SD16—48no—
275C2×SD16—222no—
276C2×D8—224no—
277C2×M16—112no—
278C22×C8C22⋊D1112yes—
279C4⋊Q8—21no—
280C4⋊Q8—21no—
281C4⋊Q8—21no—
282C4⋊Q8—111no—
283C4⋊Q8—111no—
284C4⋊Q8—111no—
285C4⋊Q8C22×D1112yes—
286#127—21no—
287#127—21no—
288#127—21no—
289#127—111no—
290#127C22×D1112yes—
291#125—221no—
292#124—221no—
293C22⋊Q8—221no—
294C22⋊Q8—221no—
295#121—221no—
296#121—221no—
297C4×Q8—221no—
298C4×Q8—221no—
299C4×D4—221no—
300C4×D4—221no—
301#117—221no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C42C22×D1111yescharacteristic
305#107—224no—
306#106—222no—
307C4⋊C8—112no—
308#103—224no—
309#103—224no—
310#103—222no—
311#102—224no—
312#102—224no—
313#102—224no—
314#102—224no—
315#102—222no—
316C22⋊C8—112no—
317#97—112no—
318C4×C8—112no—
319C4×C8—112no—
320C4×C8C22⋊D1112yes—
321C4×C8C22×D1111yescharacteristic
322C4×C8C22×D1111yescharacteristic
323C2×C11—22no—
324C2×C11—162no—
325C2×C11C2×#49511yescharacteristic
326C2×C11#315111yescharacteristic
327C2×C11#315411yescharacteristic
328D11—161no—
329C24—41no—
330#41—444no—
331C2×Q8—22no—
332C2×Q8—44no—
333C2×Q8—41no—
334C2×Q8—221no—
335C2×Q8—221no—
336C2×Q8—221no—
337C2×D4—22no—
338C2×D4—22no—
339C2×D4—22no—
340C2×D4—44no—
341C2×D4—44no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—82no—
346C2×D4—221no—
347C2×D4—221no—
348C2×D4—221no—
349C2×D4—441no—
350C22×C4—41no—
351C22×C4—441no—
352C22×C4D4×D1111yescharacteristic
353C22×C4D4×D1111yescharacteristic
354C22×C4C2×C22⋊D1111yescharacteristic
355SD16—48no—
356SD16—48no—
357SD16—444no—
358D8—884no—
359M16—224no—
360C2×C8—24no—
361C2×C8—114no—
362C2×C8—114no—
363C2×C8C2×C22⋊D1112yes—
364C2×C8C2×C22⋊D1112yes—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—221no—
370C4⋊C4—221no—
371C4⋊C4—221no—
372C4⋊C4—221no—
373C4⋊C4—221no—
374C4⋊C4—221no—
375C4⋊C4—441no—
376C4⋊C4—441no—
377C22⋊C4—441no—
378C22⋊C4—441no—
379C22⋊C4—441no—
380C42—441no—
381C42D4×D1111yescharacteristic
382C42D4×D1111yescharacteristic
383C42C2×C22⋊D1111yescharacteristic
384C42C23×D1111yescharacteristic
385C11#1962511yescharacteristic, complemented, Sylow
386C23—42no—
387C23—82no—
388C23—82no—
389C23—82no—
390C23—441no—
391C23#6699311yescharacteristic
392Q8—44no—
393Q8—82no—
394Q8—442no—
395Q8—442no—
396Q8—442no—
397D4—44no—
398D4—44no—
399D4—44no—
400D4—82no—
401D4—82no—
402D4—82no—
403D4—442no—
404D4—442no—
405D4—442no—
406D4—882no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—42no—
410C2×C4—82no—
411C2×C4—441no—
412C2×C4—441no—
413C2×C4—441no—
414C2×C4—882no—
415C2×C4#6696914yes—
416C2×C4#6699311yescharacteristic
417C2×C4#6699311yescharacteristic
418C2×C4#6699311yescharacteristic
419C2×C4C2×D4×D1111yescharacteristic
420C2×C4C2×D4×D1111yescharacteristic
421C2×C4C22×C22⋊D1111yescharacteristic
422C8—22no—
423C8—224no—
424C8—224no—
425C8#6698514yes—
426C22—21no—
427C22—21no—
428C22—82no—
429C22—82no—
430C22—82no—
431C22—164no—
432C22—881no—
433C22—881no—
434C22—881no—
435C22#1062278112yes—
436C22C2×#6699311yescharacteristic
437C4—21no—
438C4—21no—
439C4—82no—
440C4—881no—
441C4—881no—
442C4—881no—
443C4#1062278112yes—
444C4C2×#6696912yes—
445C4#1062329312yes—
446C4C2×#6698512yes—
447C2—22no—
448C2—162no—
449C2—1761no—
450C2C2×#1062278111yescharacteristic
451C2#1307906611yescharacteristic
452C2#1307908611yescharacteristic
subgroupG/H
centerC22C2×#66993
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#492C2
socleC22×C11C2×#127
prime radical#13079534C2
hypercenterC2×#492D11
hypocenterC11#19625
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#492

Complements

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

NH ≅ G/Ntype
1. #13079767C2semidirect
3. #13079175C2semidirect
4. #13079012C2semidirect
5. #13078990C2semidirect
6. #13068267C2semidirect
7. #13068253C2semidirect
8. #13068215C2semidirect
9. #13068206C2semidirect
10. C8×#4318C2semidirect
11. C2×C11×#492C2semidirect
24. #10622706C22semidirect
25. #10622706C22semidirect
28. #10622701C22semidirect
29. #10622691C22semidirect
40. #10622307C22semidirect
41. #10622306C22semidirect
43. #10622294C22semidirect
44. #10622293C22semidirect
45. #10622092C22semidirect
46. C8×C11⋊C8C22semidirect
163. C2×#492D11semidirect
385. C11#19625semidirect

Maximal subgroups

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

subgroupindex
#130797672
#130795342
#130791752
#130790122
#130789902
#130682672
#130682532
#130682152
#130682062
C8×#43182
C2×C11×#4922
#1962511