Finite Group Databasebeta

← #14726309

Subgroups — #14726309

Order 2816.

1184 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078734C212yesmaximal, complemented
2#13074193C211yesmaximal, characteristic, complemented
3#13067619C212yesmaximal, complemented
4#13067602C212yesmaximal, complemented
5#13067585C212yesmaximal, complemented
6#13067568C212yesmaximal, complemented
7#13067163C212yesmaximal, complemented
8#13066950C211yesmaximal, characteristic, complemented
9C11×#3449C211yesmaximal, characteristic
10C22×C11×#41—21no—
11C11×#537—21no—
12C11×#537C2212yes—
13C11×#536—22no—
14C11×#535—22no—
15C11×#534—21no—
16C11×#534C2212yes—
17C11×#532—21no—
18C11×#532C2212yes—
19C11×#525—24no—
20C2×C11×#117C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic, complemented
22#10622823—21no—
23#10622704—22no—
24#10622688—22no—
25#10622653C2214yescomplemented
26#10622646C2214yescomplemented
27#10622631—24no—
28#10622596C2211yescharacteristic, complemented
29#10622592C2211yescharacteristic, complemented
30#10622591—21no—
31#10622566C2211yescharacteristic
32#10622560C2211yescharacteristic
33#10622557—21no—
34#10622550C2211yescharacteristic, complemented
35#10622546—21no—
36#10622539C2212yescomplemented
37#10622175C2214yescomplemented
38#10622175C2214yescomplemented
39#10622166C2212yescomplemented
40#10622163C2212yes—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41—44no—
46C2×C11×#41—44no—
47C22×Q8×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11—22no—
50C23×C4×C11—22no—
51C23×C4×C11D411yescharacteristic
52C22×Dic22C2311yescharacteristic
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8D412yes—
55C11×#127—21no—
56C11×#127D412yes—
57C11×#124—22no—
58C11×#124—22no—
59C11×#123—24no—
60C11×#123—24no—
61C11×C22⋊Q8—24no—
62C11×C22⋊Q8—24no—
63C11×#121—24no—
64C11×#121—24no—
65C11×#121—22no—
66C11×#121—22no—
67C11×#121—22no—
68C11×#121C2314yes—
69C11×#120—24no—
70C11×#120—24no—
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C4×D4×C11—22no—
74C4×D4×C11D414yes—
75C11×#117—22no—
76C11×#117—22no—
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4D411yescharacteristic
80C2×C11×C22⋊C4C2311yescharacteristic
81C2×C42×C11D411yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11—21no—
85C2×#4324—24no—
86C2×C4⋊Dic11C2311yescharacteristic
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×C4×Dic11—21no—
91C4×Dic22—22no—
92C4×Dic22—22no—
93#66896—24no—
94C11⋊#95—21no—
95C11⋊#95—21no—
96C11⋊#95—21no—
97C11⋊#95—21no—
98C11⋊#95—21no—
99C11⋊#95—21no—
100C11⋊#95C2311yescharacteristic
101C11⋊#95C2311yescharacteristic
102C22⋊(C11⋊C8)C2314yes—
103#66874—24no—
104#66871—24no—
105C4⋊(C11⋊C8)—22no—
106#66867—22no—
107#18153—111nomaximal, Sylow
108C24×C11—22no—
109C24×C11C2×D411yescharacteristic
110C11×#41—48no—
111C11×#41—48no—
112C11×#41—44no—
113C11×#41—44no—
114C11×#41—44no—
115C11×#41—44no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—44no—
119C2×D4×C11—24no—
120C2×D4×C11—22no—
121C2×D4×C11—24no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—44no—
127C2×D4×C11—44no—
128C2×D4×C11—44no—
129C2×D4×C11C2×D414yes—
130C22×C4×C11—22no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—22no—
134C22×C4×C11—24no—
135C22×C4×C11—22no—
136C22×C4×C11—24no—
137C22×C4×C11—48no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C2×Dic22—22no—
149C2×Dic22—42no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4C2×D414yes—
156C11×C22⋊C4—24no—
157C11×C22⋊C4—24no—
158C11×C22⋊C4—22no—
159C11×C22⋊C4—24no—
160C11×C22⋊C4—22no—
161C11×C22⋊C4—24no—
162C42×C11—21no—
163C42×C11—21no—
164C42×C11C2×D412yes—
165C42×C11C2×D412yes—
166C22⋊Dic11—42no—
167C22⋊Dic11—42no—
168#4324—48no—
169C4⋊Dic11—22no—
170Dic11⋊C4—42no—
171Dic11⋊C4—41no—
172Dic11⋊C4—41no—
173Dic11⋊C4—42no—
174C4×Dic11—42no—
175C2×C11⋊C8—24no—
176#3449D1111yescharacteristic
177#3112—112no—
178#2599—111no—
179#1610—112no—
180#1607—112no—
181#1604—112no—
182#1601—112no—
183#1514—112no—
184#1464—111no—
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—24no—
188C23×C11—41no—
189C23×C11—41no—
190C23×C11—44no—
191C23×C11—82no—
192C23×C11—82no—
193C23×C11AGL(1,ℤ/8)12yes—
194C23×C11C22×D411yescharacteristic
195Q8×C11—44no—
196Q8×C11—44no—
197D4×C11—44no—
198D4×C11—44no—
199D4×C11—44no—
200D4×C11—48no—
201D4×C11—44no—
202D4×C11—44no—
203D4×C11—82no—
204D4×C11—82no—
205D4×C11—82no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—24no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—48no—
218C2×C4×C11—48no—
219C2×C4×C11—44no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11#12012yes—
223C2×C4×C11#12011yescharacteristic
224C2×C4×C11#12011yescharacteristic
225C2×C4×C11AGL(1,ℤ/8)12yes—
226C2×C4×C11C22×D412yes—
227C2×Dic11—22no—
228C2×Dic11—41no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231C2×Dic11—41no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236C2×Dic11—41no—
237C2×Dic11—41no—
238C2×Dic11—41no—
239Dic22—24no—
240Dic22—42no—
241C11⋊C8—44no—
242C22×#41—21no—
243#537—21no—
244#537C2×D1112yes—
245#536—22no—
246#535—22no—
247#534—21no—
248#534C2×D1112yes—
249#532—21no—
250#532C2×D1112yes—
251#525—24no—
252C2×C4×Q8—111no—
253C2×#117C2×D1111yescharacteristic
254#480—114no—
255#477—222no—
256#460—222no—
257#448—114no—
258#440—224no—
259#432—112no—
260#398—111no—
261#397—111no—
262#395—111no—
263#393—111no—
264#388—221no—
265#387—221no—
266#387—221no—
267#385—221no—
268#383—111no—
269#327—114no—
270#327—114no—
271#324—112no—
272#323—112no—
273C22×C11—21no—
274C22×C11—21no—
275C22×C11—22no—
276C22×C11—42no—
277C22×C11—41no—
278C22×C11—41no—
279C22×C11—44no—
280C22×C11—44no—
281C22×C11—44no—
282C22×C11—81no—
283C22×C11—88no—
284C22×C11C2×#12011yescharacteristic
285C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
286C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
287C4×C11—21no—
288C4×C11—22no—
289C4×C11—21no—
290C4×C11—22no—
291C4×C11—22no—
292C4×C11—44no—
293C4×C11—41no—
294C4×C11—41no—
295Dic11—42no—
296Dic11—81no—
297Dic11—81no—
298Dic11—81no—
299C2×#41—22no—
300C2×#41—22no—
301C2×#41—22no—
302C2×#41—22no—
303C2×#41—44no—
304C2×#41—44no—
305C22×Q8—21no—
306C22×Q8—111no—
307C22×D4—21no—
308C22×D4—22no—
309C23×C4—22no—
310C23×C4C22⋊D1111yescharacteristic
311C2×SD16—224no—
312C4⋊Q8—21no—
313C4⋊Q8C22⋊D1112yes—
314#127—21no—
315#127C22⋊D1112yes—
316#124—22no—
317#124—22no—
318#123—24no—
319#123—24no—
320C22⋊Q8—24no—
321C22⋊Q8—24no—
322#121—24no—
323#121—24no—
324#121—22no—
325#121—22no—
326#121—22no—
327#121C22×D1114yes—
328#120—24no—
329#120—24no—
330C4×Q8—222no—
331C4×Q8—222no—
332C4×D4—22no—
333C4×D4—22no—
334C4×D4—22no—
335C4×D4C22⋊D1114yes—
336#117—22no—
337#117—22no—
338C2×C4⋊C4—111no—
339C2×C4⋊C4—221no—
340C2×C4⋊C4—221no—
341C2×C4⋊C4—221no—
342C2×C4⋊C4C22⋊D1111yescharacteristic
343C2×C4⋊C4C22×D1111yescharacteristic
344C2×C22⋊C4—221no—
345C2×C22⋊C4—221no—
346C2×C22⋊C4C22⋊D1111yescharacteristic
347C2×C22⋊C4C22×D1111yescharacteristic
348C2×C42—221no—
349C2×C42C22⋊D1111yescharacteristic
350C2×C42C22×D1111yescharacteristic
351#107—224no—
352C4⋊C8—222no—
353#103—224no—
354#102—224no—
355C22⋊C8—114no—
356#97—222no—
357#95—111no—
358#95—111no—
359#95—221no—
360#95—221no—
361#95—221no—
362#95—221no—
363#95—221no—
364#95—221no—
365C2×C11—21no—
366C2×C11—21no—
367C2×C11—42no—
368C2×C11—84no—
369C2×C11#300311yescharacteristic
370C2×C11#302211yescharacteristic
371C2×C11#302511yescharacteristic
372C24—22no—
373C24C2×C22⋊D1111yescharacteristic
374#41—48no—
375#41—48no—
376#41—44no—
377#41—44no—
378#41—44no—
379#41—44no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—44no—
383C2×Q8—222no—
384C2×Q8—442no—
385C2×D4—24no—
386C2×D4—22no—
387C2×D4—24no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—44no—
393C2×D4—44no—
394C2×D4—44no—
395C2×D4C2×C22⋊D1114yes—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—24no—
401C22×C4—22no—
402C22×C4—24no—
403C22×C4—48no—
404C22×C4—221no—
405C22×C4—221no—
406C22×C4—221no—
407C22×C4—221no—
408C22×C4C2×C22⋊D1111yescharacteristic
409C22×C4C2×C22⋊D1111yescharacteristic
410C22×C4C2×C22⋊D1111yescharacteristic
411C22×C4C2×C22⋊D1111yescharacteristic
412C22×C4C2×C22⋊D1111yescharacteristic
413C22×C4C23×D1111yescharacteristic
414SD16—448no—
415C2×C8—224no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—222no—
422C4⋊C4—442no—
423C4⋊C4—442no—
424C4⋊C4—441no—
425C4⋊C4—441no—
426C4⋊C4C2×C22⋊D1114yes—
427C22⋊C4—24no—
428C22⋊C4—24no—
429C22⋊C4—22no—
430C22⋊C4—24no—
431C22⋊C4—22no—
432C22⋊C4—24no—
433C22⋊C4—442no—
434C22⋊C4—442no—
435C42—21no—
436C42—21no—
437C42—442no—
438C42C2×C22⋊D1112yes—
439C42C2×C22⋊D1112yes—
440C11#1815311yescharacteristic, complemented, Sylow
441C23—21no—
442C23—21no—
443C23—24no—
444C23—41no—
445C23—41no—
446C23—44no—
447C23—82no—
448C23—82no—
449C23#6698512yes—
450C23C22×C22⋊D1111yescharacteristic
451Q8—44no—
452Q8—44no—
453Q8—224no—
454Q8—442no—
455D4—44no—
456D4—44no—
457D4—44no—
458D4—48no—
459D4—44no—
460D4—44no—
461D4—82no—
462D4—82no—
463D4—82no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—24no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—48no—
476C2×C4—48no—
477C2×C4—44no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—222no—
481C2×C4—441no—
482C2×C4—441no—
483C2×C4—441no—
484C2×C4—441no—
485C2×C4—441no—
486C2×C4—441no—
487C2×C4—441no—
488C2×C4—441no—
489C2×C4—441no—
490C2×C4—441no—
491C2×C4—441no—
492C2×C4#6698512yes—
493C2×C4#6700611yescharacteristic
494C2×C4#6700611yescharacteristic
495C2×C4#6700612yes—
496C2×C4C22×C22⋊D1112yes—
497C8—444no—
498C22—21no—
499C22—21no—
500C22—22no—
501C22—42no—
502C22—41no—
503C22—41no—
504C22—44no—
505C22—44no—
506C22—44no—
507C22—81no—
508C22—88no—
509C22C2×#6698511yescharacteristic
510C22C2×#6698511yescharacteristic
511C22C2×#6700611yescharacteristic
512C4—21no—
513C4—22no—
514C4—21no—
515C4—22no—
516C4—22no—
517C4—44no—
518C4—41no—
519C4—41no—
520C4—442no—
521C4—881no—
522C4—881no—
523C4—881no—
524C2—21no—
525C2—21no—
526C2—42no—
527C2—84no—
528C2#1307784311yescharacteristic
529C2#1307799511yescharacteristic
530C2#1307800811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3449C2
socleC22×C11C2×#120
hypercenter#3449D11
hypocenterC11#18153
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. #13078734C2semidirect
2. #13074193C2semidirect
3. #13067619C2semidirect
4. #13067602C2semidirect
5. #13067585C2semidirect
6. #13067568C2semidirect
7. #13067163C2semidirect
8. #13066950C2semidirect
21. C2×C4×Dic22C22semidirect
25. #10622653C22semidirect
26. #10622646C22semidirect
28. #10622596C22semidirect
29. #10622592C22semidirect
34. #10622550C22semidirect
36. #10622539C22semidirect
37. #10622175C22semidirect
38. #10622175C22semidirect
39. #10622166C22semidirect
440. C11#18153semidirect

Maximal subgroups

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

subgroupindex
#130787342
#130741932
#130676192
#130676022
#130675852
#130675682
#130671632
#130669502
C11×#34492
#1815311