Finite Group Databasebeta

← #14741640

Subgroups — #14741640

Order 2816.

848 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079554C211yesmaximal, characteristic, complemented
2#13079538C211yesmaximal, characteristic, complemented
3#13079163C211yesmaximal, characteristic, complemented
4#13079069C211yesmaximal, characteristic
5C2×#10622307C211yesmaximal, characteristic, complemented
6#13068243C212yesmaximal, complemented
7#13068241C212yesmaximal, complemented
8#13068219C212yesmaximal, complemented
9#13068207C212yesmaximal, complemented
10C8×#4318C211yesmaximal, characteristic, complemented
11C11×#3167C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C11×#532C2211yescharacteristic
14C2×#67002—22no—
15C2×#66927C2211yescharacteristic
16C2×#66922C2211yescharacteristic
17C11×#498C2211yescharacteristic, complemented
18C11×#492C2211yescharacteristic, complemented
19C11×#487C2211yescharacteristic, complemented
20C11×#486C2211yescharacteristic, complemented
21C11×#465—22no—
22C4×C11×SD16—22no—
23C2×C4×C8×C11C2211yescharacteristic
24C2×#66885—22no—
25#10622706C2212yescomplemented
26#10622701C2212yes—
27#10622698C2212yes—
28#10622698C2212yes—
29#10622692C2212yescomplemented
30#10622691C2212yescomplemented
31#10622689C2212yescomplemented
32#10622686C2212yes—
33#10622678—22no—
34#10622671—22no—
35#10622659—22no—
36#10622653—22no—
37#10622640—22no—
38#10622632—22no—
39#10622608—22no—
40#10622538C2211yescharacteristic
41C4×#4318C2211yescharacteristic
42#10622307—22no—
43#10622307C2212yes—
44#10622307C2212yes—
45#10622092C2212yescomplemented
46C8×C11⋊C8C2212yescomplemented
47C2×C11×#41—21no—
48C22×D44—21no—
49C22×D44—21no—
50C22×D44—21no—
51C22×Dic22—21no—
52C2×C11×SD16—22no—
53C22×C8×C11D412yes—
54C11×C4⋊Q8C2311yescharacteristic
55C11×C4⋊Q8C2311yescharacteristic
56C11×C4⋊Q8C2311yescharacteristic
57C11×#127C2311yescharacteristic
58C11×#125—21no—
59C11×#124—21no—
60C11×C22⋊Q8—21no—
61C11×C22⋊Q8—21no—
62C11×#121—21no—
63C11×#121—21no—
64C4×Q8×C11—21no—
65C4×Q8×C11—21no—
66C4×D4×C11—21no—
67C4×D4×C11—21no—
68C11×#117—21no—
69C2×C42×C11C2311yescharacteristic
70#67002—48no—
71C2×#4325—24no—
72C2×#4325—24no—
73C2×#4324—24no—
74C2×#4323—24no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—21no—
77C2×#4318D412yes—
78#66927—21no—
79#66927—21no—
80#66927—21no—
81#66927C2312yes—
82#66922—21no—
83#66922—21no—
84#66922—21no—
85#66922C2312yes—
86C11×#106—22no—
87C11×#103—22no—
88C11×#102—22no—
89C4×C8×C11D412yes—
90C4×C8×C11C2311yescharacteristic
91C4×C8×C11C2311yescharacteristic
92C22⋊(C11⋊C8)D412yes—
93#66885—24no—
94#66885—24no—
95#66874—24no—
96#66873—24no—
97#66872—24no—
98#66871—24no—
99C4⋊(C11⋊C8)D412yes—
100#66867D412yes—
101C4×C11⋊C8C2312yes—
102C4×C11⋊C8C2312yes—
103#19623—111nomaximal, Sylow
104C23×D11—41no—
105C11×#41—44no—
106C2×Q8×C11—21no—
107C2×Q8×C11—21no—
108C2×Q8×C11—21no—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—41no—
113C22×C4×C11—41no—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×Dic11—41no—
118C2×D44—22no—
119C2×D44—22no—
120C2×D44—22no—
121C2×D44—44no—
122C2×D44—41no—
123C2×D44—41no—
124C2×D44—41no—
125C2×D44—44no—
126C2×D44—82no—
127C2×Dic22—22no—
128C2×Dic22—41no—
129C2×Dic22—82no—
130C11×SD16—44no—
131C2×C8×C11—42no—
132C2×C8×C11C2×D412yes—
133C2×C8×C11C2×D412yes—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—41no—
141C11×C4⋊C4—41no—
142C11×C22⋊C4—41no—
143C11×C22⋊C4—41no—
144C11×C22⋊C4—41no—
145C42×C11—41no—
146C42×C11C2×D411yescharacteristic
147C42×C11C2×D411yescharacteristic
148C42×C11C2×D411yescharacteristic
149C42×C11C2411yescharacteristic
150#4325—48no—
151#4325—84no—
152#4324—84no—
153#4323—48no—
154C4⋊Dic11—22no—
155C4⋊Dic11—22no—
156C4⋊Dic11—41no—
157C4⋊Dic11—41no—
158#4318SD1618yescomplemented
159C2×C11⋊C8C2×D414yes—
160C2×C11⋊C8C2×D414yes—
161#3208—111no—
162#3206—111no—
163#3167D1111yescharacteristic, complemented
164#3165—111no—
165#3151—111no—
166C2×#486—111no—
167#1715—112no—
168#1714—112no—
169#1708—112no—
170#1706—112no—
171C8×M16—111no—
172C23×C11—41no—
173C23×C11#12711yescharacteristic
174C22×D11—42no—
175C22×D11—82no—
176C22×D11—82no—
177C22×D11—82no—
178Q8×C11—42no—
179Q8×C11—42no—
180Q8×C11—42no—
181D4×C11—42no—
182D4×C11—42no—
183D4×C11—42no—
184D4×C11—82no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—82no—
191C2×C4×C11#12711yescharacteristic
192C2×C4×C11#12711yescharacteristic
193C2×C4×C11#12711yescharacteristic
194C2×C4×C11C2×SD1614yes—
195C2×C4×C11C22×D411yescharacteristic
196C2×C4×C11C22×D411yescharacteristic
197C2×C4×C11C22×D411yescharacteristic
198C2×Dic11—42no—
199C2×Dic11—82no—
200D44—44no—
201D44—44no—
202D44—44no—
203D44—82no—
204D44—82no—
205D44—82no—
206Dic22—44no—
207Dic22—82no—
208C8×C11—22no—
209C8×C11—22no—
210C11⋊C8—24no—
211C11⋊C8C2×SD1618yes—
212C2×AGL(1,ℤ/8)—222no—
213#533C2×D1111yescharacteristic
214#532C2×D1111yescharacteristic
215C2×C4⋊Q8—111no—
216C2×#127—111no—
217#501—222no—
218#500—112no—
219#498—112no—
220#498C2×D1111yescharacteristic, complemented
221#496—222no—
222#493—112no—
223#492—112no—
224#492—112no—
225#492—112no—
226#492C2×D1111yescharacteristic, complemented
227#487—112no—
228#487C2×D1111yescharacteristic, complemented
229#486—112no—
230#486—112no—
231#486—112no—
232#486—222no—
233#486C2×D1111yescharacteristic, complemented
234#465—22no—
235#461—222no—
236#460—222no—
237#450—222no—
238#448—222no—
239C4×SD16—22no—
240#431—111no—
241#428—222no—
242C2×#102—222no—
243C4×M16—111no—
244C2×C4×C8C2×D1111yescharacteristic
245#322—112no—
246C82—112no—
247C22×C11—21no—
248C22×C11—21no—
249C22×C11—81no—
250C22×C11—81no—
251C22×C11—81no—
252C22×C11#49212yes—
253C22×C11C2×#12711yescharacteristic
254C2×D11—82no—
255C2×D11—82no—
256C2×D11—82no—
257C2×D11—164no—
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—81no—
261C4×C11—81no—
262C4×C11—81no—
263C4×C11#49212yes—
264C4×C11C22×SD1612yes—
265C4×C11#57512yes—
266C4×C11#57612yes—
267Dic11—82no—
268C2×#41—21no—
269C22×Q8—221no—
270C22×D4—221no—
271C22×D4—221no—
272C22×D4—221no—
273AGL(1,ℤ/8)—448no—
274C2×SD16—22no—
275C2×SD16—224no—
276C2×SD16—224no—
277C2×SD16—224no—
278C2×D8—224no—
279C2×M16—112no—
280C22×C8C22⋊D1112yes—
281C4⋊Q8—112no—
282C4⋊Q8—221no—
283C4⋊Q8—221no—
284C4⋊Q8—221no—
285C4⋊Q8C22×D1111yescharacteristic
286C4⋊Q8C22×D1111yescharacteristic
287C4⋊Q8C22×D1111yescharacteristic
288#127—112no—
289#127—221no—
290#127—221no—
291#127—221no—
292#127C22×D1111yescharacteristic
293#125—21no—
294#124—21no—
295C22⋊Q8—21no—
296C22⋊Q8—21no—
297#121—21no—
298#121—21no—
299C4×Q8—21no—
300C4×Q8—21no—
301C4×D4—21no—
302C4×D4—21no—
303#117—21no—
304C2×C4⋊C4—221no—
305C2×C4⋊C4—221no—
306C2×C42C22×D1111yescharacteristic
307#107—224no—
308#106—22no—
309#106—224no—
310C4⋊C8—112no—
311#103—22no—
312#103—224no—
313#102—22no—
314#102—224no—
315#102—224no—
316#102—224no—
317C22⋊C8—112no—
318#97—112no—
319C4×C8—112no—
320C4×C8—112no—
321C4×C8C22⋊D1112yes—
322C4×C8C22×D1111yescharacteristic
323C4×C8C22×D1111yescharacteristic
324C2×C11—22no—
325C2×C11—161no—
326C2×C11C2×#49211yescharacteristic
327C2×C11#315311yescharacteristic
328C2×C11#315511yescharacteristic
329D11—162no—
330C24—441no—
331#41—44no—
332C2×Q8—21no—
333C2×Q8—21no—
334C2×Q8—21no—
335C2×Q8—222no—
336C2×Q8—441no—
337C2×Q8—882no—
338C2×D4—21no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—41no—
342C2×D4—222no—
343C2×D4—222no—
344C2×D4—222no—
345C2×D4—444no—
346C2×D4—444no—
347C2×D4—441no—
348C2×D4—441no—
349C2×D4—441no—
350C2×D4—882no—
351C22×C4—41no—
352C22×C4—441no—
353C22×C4D4×D1111yescharacteristic
354C22×C4D4×D1111yescharacteristic
355C22×C4C2×C22⋊D1111yescharacteristic
356SD16—44no—
357SD16—448no—
358SD16—884no—
359SD16—884no—
360D8—448no—
361M16—118no—
362C2×C8—42no—
363C2×C8—114no—
364C2×C8—114no—
365C2×C8C2×C22⋊D1112yes—
366C2×C8C2×C22⋊D1112yes—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—222no—
376C4⋊C4—222no—
377C4⋊C4—441no—
378C4⋊C4—441no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C42—41no—
383C42D4×D1111yescharacteristic
384C42D4×D1111yescharacteristic
385C42C2×C22⋊D1111yescharacteristic
386C42C23×D1111yescharacteristic
387C11#1962311yescharacteristic, complemented, Sylow
388C23—41no—
389C23—442no—
390C23—882no—
391C23—882no—
392C23—882no—
393C23#6699311yescharacteristic
394Q8—42no—
395Q8—42no—
396Q8—42no—
397Q8—444no—
398Q8—882no—
399D4—42no—
400D4—42no—
401D4—42no—
402D4—82no—
403D4—444no—
404D4—444no—
405D4—444no—
406D4—882no—
407D4—882no—
408D4—882no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—82no—
415C2×C4—442no—
416C2×C4—882no—
417C2×C4SD16×D1114yes—
418C2×C4#6699311yescharacteristic
419C2×C4#6699311yescharacteristic
420C2×C4#6699311yescharacteristic
421C2×C4C2×D4×D1111yescharacteristic
422C2×C4C2×D4×D1111yescharacteristic
423C2×C4C22×C22⋊D1111yescharacteristic
424C8—22no—
425C8—22no—
426C8—118no—
427C8—224no—
428C22—21no—
429C22—21no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22—882no—
434C22—882no—
435C22—882no—
436C22—1764no—
437C22#1062278812yes—
438C22C2×#6699311yescharacteristic
439C4—21no—
440C4—21no—
441C4—81no—
442C4—81no—
443C4—81no—
444C4—882no—
445C4#1062278812yes—
446C4C2×SD16×D1112yes—
447C4#1062330012yes—
448C4#1062335312yes—
449C2—22no—
450C2—161no—
451C2—1762no—
452C2C2×#1062278811yescharacteristic
453C2#1307908411yescharacteristic
454C2#1307910311yescharacteristic
subgroupG/H
centerC22C2×#66993
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3167C2
socleC22×C11C2×#127
prime radical#13079069C2
hypercenter#3167D11
hypocenterC11#19623
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3167

Complements

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

NH ≅ G/Ntype
1. #13079554C2semidirect
2. #13079538C2semidirect
3. #13079163C2semidirect
5. C2×#10622307C2semidirect
6. #13068243C2semidirect
7. #13068241C2semidirect
8. #13068219C2semidirect
9. #13068207C2semidirect
10. C8×#4318C2semidirect
11. C11×#3167C2semidirect
17. C11×#498C22semidirect
18. C11×#492C22semidirect
19. C11×#487C22semidirect
20. C11×#486C22semidirect
25. #10622706C22semidirect
29. #10622692C22semidirect
30. #10622691C22semidirect
31. #10622689C22semidirect
45. #10622092C22semidirect
46. C8×C11⋊C8C22semidirect
158. #4318SD16semidirect
163. #3167D11semidirect
220. #498C2×D11semidirect
226. #492C2×D11semidirect
228. #487C2×D11semidirect
233. #486C2×D11semidirect
387. C11#19623semidirect

Maximal subgroups

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

subgroupindex
#130795542
#130795382
#130791632
#130790692
C2×#106223072
#130682432
#130682412
#130682192
#130682072
C8×#43182
C11×#31672
#1962311