Finite Group Databasebeta

← #14960572

Subgroups — #14960572

Order 2816.

2782 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66949C211yesmaximal, characteristic, complemented
2#13076895C212yesmaximal, complemented
3#13075106C218yesmaximal, complemented
4#13074911C218yesmaximal, complemented
5#13074360C212yesmaximal, complemented
6#13073548C212yesmaximal, complemented
7#13072275C212yesmaximal, complemented
8#13071947C212yesmaximal, complemented
9#13071931C212yesmaximal, complemented
10#13071219C211yesmaximal, characteristic, complemented
11C2×C11×#537C211yesmaximal, characteristic, complemented
12C22×C11×#41C2212yes—
13C23×C4×D11C2211yescharacteristic
14C23×Dic22C2211yescharacteristic
15C11×#537—28no—
16C2×C11×C22⋊Q8C2214yescomplemented
17C2×C11×#121C2212yes—
18C2×C11×#121C2212yes—
19C2×C11×#121C2214yescomplemented
20C22×C11×C4⋊C4C2211yescharacteristic
21C2×#66991C2214yes—
22C2×#66990C2214yes—
23C2×#66989C2214yescomplemented
24C2×#66988C2214yes—
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C2×#66949—28no—
30C2×#66949C2218yes—
31#10622844C2214yes—
32#10622842C2214yescomplemented
33#10622836C2214yes—
34#10622836C2214yes—
35#10622835C2214yescomplemented
36#10622835C2214yescomplemented
37#10622833C2214yes—
38#10622833C2214yes—
39#10622826C2218yes—
40#10622825C2212yes—
41#10622824C2212yes—
42#10622823C2218yescomplemented
43C4×C22⋊Dic11C2212yes—
44#10622605C2214yes—
45#10622600C2214yes—
46#10622594C2218yescomplemented
47#10622593C2214yescomplemented
48#10622587C2214yescomplemented
49#10622570C2218yes—
50#10622569C2218yes—
51#10622561C2218yescomplemented
52#10622560C2218yescomplemented
53C24×D11C2311yescharacteristic
54C2×C11×#41—28no—
55C2×C11×#41—48no—
56C22×Q8×C11C2312yes—
57C22×D4×C11C2314yes—
58C22×D4×C11C2312yes—
59C22×D4×C11C2312yes—
60C22×D4×C11C2312yes—
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2314yes—
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C22×C22⋊D11C2318yes—
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C22×C4×D11—24no—
70C22×C4×D11—44no—
71C22×C4×D11C2314yes—
72C22×Dic22—24no—
73C22×Dic22—44no—
74C22×Dic22C2314yes—
75C11×C22⋊Q8—216no—
76C11×#121—28no—
77C11×#121—28no—
78C11×#121—216no—
79C2×C11×C4⋊C4D418yescomplemented
80C2×C11×C4⋊C4C2312yes—
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2314yes—
83C2×C11×C22⋊C4C2314yes—
84C2×C11×C22⋊C4C2314yes—
85C2×C22⋊Dic11C2314yes—
86C2×C22⋊Dic11C2318yes—
87C2×C22⋊Dic11C2318yes—
88C2×C22⋊Dic11C2318yes—
89#66991—48no—
90#66990—48no—
91#66989—48no—
92#66988—48no—
93C2×(C2×D11)⋊C4—24no—
94C2×(C2×D11)⋊C4—24no—
95C2×(C2×D11)⋊C4C2314yes—
96C2×(C2×D11)⋊C4C2314yes—
97C2×(C2×D11)⋊C4C2318yes—
98C2×C4⋊Dic11C2314yes—
99C2×Dic11⋊C4—24no—
100C2×Dic11⋊C4—24no—
101C2×Dic11⋊C4C2314yes—
102C2×Dic11⋊C4C2314yes—
103C2×Dic11⋊C4C2318yes—
104C2×C4×Dic11C2314yes—
105#66949—232no—
106C11⋊#95C2314yes—
107C11⋊#95C2318yes—
108C11⋊#95C2318yes—
109C11⋊#95C2314yes—
110C11⋊#95C2314yes—
111C11⋊#95C2314yes—
112#36707—111nomaximal, Sylow
113C24×C11C2414yes—
114C24×C11C2411yescharacteristic
115C23×D11—22no—
116C23×D11—24no—
117C23×D11—24no—
118C23×D11—42no—
119C23×D11C2412yes—
120C11×#41—432no—
121C2×Q8×C11—24no—
122C2×Q8×C11—44no—
123C2×D4×C11—28no—
124C2×D4×C11—28no—
125C2×D4×C11—28no—
126C2×D4×C11—24no—
127C2×D4×C11—24no—
128C2×D4×C11—24no—
129C2×D4×C11—44no—
130C2×D4×C11—44no—
131C2×D4×C11—44no—
132C22×C4×C11—24no—
133C22×C4×C11—28no—
134C22×C4×C11—42no—
135C22×C4×C11—42no—
136C22×C4×C11—44no—
137C22×C4×C11—44no—
138C22×C4×C11C2×D414yes—
139C22×C4×C11C2×D414yes—
140C22×C4×C11C2×D414yes—
141C22×C4×C11C2414yes—
142C22×C4×C11C2412yes—
143C22×C4×C11C2412yes—
144C22×C4×C11C2412yes—
145C2×C22⋊D11—216no—
146C2×C22⋊D11—48no—
147C2×C22⋊D11—48no—
148C22×Dic11—24no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—24no—
153C22×Dic11—42no—
154C22×Dic11C2418yes—
155C22×Dic11C2412yes—
156C22×Dic11C2412yes—
157C22×Dic11C2412yes—
158C2×C4×D11—28no—
159C2×C4×D11—28no—
160C2×C4×D11—44no—
161C2×C4×D11—416no—
162C2×Dic22—28no—
163C2×Dic22—28no—
164C2×Dic22—44no—
165C2×Dic22—416no—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—24no—
168C11×C4⋊C4C2×D4116yes—
169C11×C22⋊C4—28no—
170C11×C22⋊C4—28no—
171C22⋊Dic11—216no—
172C22⋊Dic11—28no—
173C22⋊Dic11—48no—
174C22⋊Dic11—48no—
175(C2×D11)⋊C4—28no—
176(C2×D11)⋊C4—28no—
177(C2×D11)⋊C4—48no—
178C4⋊Dic11—44no—
179Dic11⋊C4—28no—
180Dic11⋊C4—28no—
181Dic11⋊C4—48no—
182C4×Dic11—44no—
183C2×#537D1111yescharacteristic, complemented
184C22×C22⋊Q8—111no—
185#2847—112no—
186#2692—118no—
187#2676—118no—
188#2618—112no—
189#2539—112no—
190#2436—112no—
191#2406—112no—
192#2404—112no—
193#2313—111no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—24no—
197C23×C11—28no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—28no—
201C23×C11C22×D412yes—
202C23×C11H(5,𝔽2)14yes—
203C23×C11C2511yescharacteristic
204C22×D11—28no—
205C22×D11—22no—
206C22×D11—24no—
207C22×D11—24no—
208C22×D11—22no—
209C22×D11—416no—
210C22×D11—44no—
211C22×D11—44no—
212C22×D112−1+414yes—
213Q8×C11—48no—
214D4×C11—48no—
215D4×C11—416no—
216D4×C11—84no—
217D4×C11—84no—
218C2×C4×C11—28no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—44no—
226C2×C4×C11—44no—
227C2×C4×C11—416no—
228C2×C4×C11C22×D414yes—
229C2×C4×C11C22×D414yes—
230C2×C4×C11C22×D414yes—
231C22⋊D11—816no—
232C2×Dic11—28no—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—28no—
238C2×Dic11—24no—
239C2×Dic11—28no—
240C2×Dic11—24no—
241C2×Dic11—28no—
242C2×Dic11—44no—
243C2×Dic11—44no—
244C2×Dic11H(5,𝔽2)14yes—
245C4×D11—416no—
246Dic22—416no—
247C22×#41C2×D1112yes—
248C23×Q8—111no—
249C24×C4—111no—
250#537—28no—
251C2×#124—114no—
252C2×#123—114no—
253C2×C22⋊Q8—118no—
254C2×C22⋊Q8—228no—
255C2×C22⋊Q8C2×D1114yescomplemented
256C2×#121—114no—
257C2×#121C2×D1112yes—
258C2×#121C2×D1112yes—
259C2×#121C2×D1114yescomplemented
260C2×#120—114no—
261C22×C4⋊C4—111no—
262C22×C4⋊C4—111no—
263C22×C4⋊C4C2×D1111yescharacteristic
264C22×C22⋊C4—111no—
265C22×C22⋊C4—111no—
266#399—114no—
267#398—114no—
268#396—118no—
269#395—114no—
270#394—114no—
271#394—114no—
272#393—114no—
273#393—118no—
274#392—114no—
275#392—114no—
276#391—114no—
277#390—118no—
278#387—118no—
279#386—114no—
280#386—114no—
281#386—118no—
282#386—118no—
283#385—118no—
284#381—112no—
285#380—112no—
286#380—114no—
287C4×C22⋊C4—112no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—28no—
291C22×C11—44no—
292C22×C11—44no—
293C22×C11—44no—
294C22×C11—48no—
295C22×C11—48no—
296C22×C11#53514yes—
297C22×C11C23×D411yescharacteristic
298C22×C11C2×H(5,𝔽2)12yes—
299C22×C11C2×H(5,𝔽2)12yes—
300C22×C11C2×2−1+412yes—
301C2×D11—24no—
302C2×D11—28no—
303C2×D11—416no—
304C2×D11—42no—
305C2×D11—42no—
306C2×D11—44no—
307C4×C11—24no—
308C4×C11—24no—
309C4×C11—24no—
310C4×C11—44no—
311Dic11—24no—
312Dic11—42no—
313Dic11—42no—
314Dic11—48no—
315C25—111no—
316C2×#41—28no—
317C2×#41—48no—
318C22×Q8—114no—
319C22×Q8—224no—
320C22×Q8—444no—
321C22×Q8C22×D1112yes—
322C22×D4—118no—
323C22×D4C22×D1114yes—
324C22×D4C22×D1112yes—
325C22×D4C22×D1112yes—
326C22×D4C22×D1112yes—
327C23×C4—111no—
328C23×C4—111no—
329C23×C4—111no—
330C23×C4—114no—
331C23×C4—224no—
332C23×C4—444no—
333C23×C4C22×D1111yescharacteristic
334C23×C4C22×D1114yes—
335C23×C4C22×D1111yescharacteristic
336C23×C4C22×D1111yescharacteristic
337#124—448no—
338#123—448no—
339C22⋊Q8—216no—
340C22⋊Q8—2232no—
341#121—28no—
342#121—28no—
343#121—216no—
344#121—448no—
345#120—448no—
346C2×C4⋊C4—114no—
347C2×C4⋊C4—114no—
348C2×C4⋊C4—114no—
349C2×C4⋊C4—118no—
350C2×C4⋊C4—224no—
351C2×C4⋊C4—224no—
352C2×C4⋊C4C22⋊D1118yescomplemented
353C2×C4⋊C4C22×D1112yes—
354C2×C4⋊C4C22×D1112yes—
355C2×C4⋊C4C22×D1114yes—
356C2×C22⋊C4—114no—
357C2×C22⋊C4—118no—
358C2×C22⋊C4—114no—
359C2×C22⋊C4—114no—
360C2×C22⋊C4—118no—
361C2×C22⋊C4—118no—
362C2×C22⋊C4—118no—
363C2×C22⋊C4—224no—
364C2×C22⋊C4—224no—
365C2×C22⋊C4C22×D1114yes—
366C2×C22⋊C4C22×D1114yes—
367C2×C42—114no—
368#95—114no—
369#95—118no—
370#95—114no—
371#95—114no—
372#95—114no—
373#95—118no—
374C2×C11—24no—
375C2×C11—84no—
376C2×C11C2×#53511yescharacteristic
377C2×C11#348411yescharacteristic
378C2×C11#348611yescharacteristic
379C2×C11#353614yes—
380D11—44no—
381C24—112no—
382C24—224no—
383C24—222no—
384C24—224no—
385C24—442no—
386C24C23×D1114yes—
387C24C23×D1111yescharacteristic
388#41—432no—
389C2×Q8—24no—
390C2×Q8—44no—
391C2×Q8—228no—
392C2×Q8—228no—
393C2×Q8—444no—
394C2×Q8—4416no—
395C2×D4—28no—
396C2×D4—28no—
397C2×D4—28no—
398C2×D4—24no—
399C2×D4—24no—
400C2×D4—24no—
401C2×D4—44no—
402C2×D4—44no—
403C2×D4—44no—
404C2×D4—2216no—
405C2×D4—448no—
406C2×D4—448no—
407C22×C4—24no—
408C22×C4—28no—
409C22×C4—42no—
410C22×C4—42no—
411C22×C4—44no—
412C22×C4—44no—
413C22×C4—112no—
414C22×C4—118no—
415C22×C4—112no—
416C22×C4—112no—
417C22×C4—228no—
418C22×C4—224no—
419C22×C4—222no—
420C22×C4—224no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—228no—
424C22×C4—444no—
425C22×C4—4416no—
426C22×C4—442no—
427C22×C4C2×C22⋊D1114yes—
428C22×C4C2×C22⋊D1114yes—
429C22×C4C2×C22⋊D1114yes—
430C22×C4C23×D1114yes—
431C22×C4C23×D1112yes—
432C22×C4C23×D1112yes—
433C22×C4C23×D1112yes—
434C4⋊C4—24no—
435C4⋊C4—24no—
436C4⋊C4—228no—
437C4⋊C4—228no—
438C4⋊C4—444no—
439C4⋊C4—448no—
440C4⋊C4C2×C22⋊D11116yes—
441C22⋊C4—28no—
442C22⋊C4—28no—
443C22⋊C4—2216no—
444C22⋊C4—228no—
445C22⋊C4—228no—
446C22⋊C4—228no—
447C22⋊C4—448no—
448C22⋊C4—448no—
449C22⋊C4—448no—
450C42—444no—
451C11#3670711yescharacteristic, complemented, Sylow
452C23—22no—
453C23—22no—
454C23—24no—
455C23—24no—
456C23—28no—
457C23—28no—
458C23—24no—
459C23—114no—
460C23—228no—
461C23—224no—
462C23—224no—
463C23—222no—
464C23—222no—
465C23—4416no—
466C23—444no—
467C23—444no—
468C23#6703714yes—
469C23C22×C22⋊D1112yes—
470C23C24×D1111yescharacteristic
471Q8—48no—
472Q8—4416no—
473D4—48no—
474D4—416no—
475D4—84no—
476D4—84no—
477D4—8816no—
478C2×C4—28no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—44no—
486C2×C4—44no—
487C2×C4—416no—
488C2×C4—114no—
489C2×C4—228no—
490C2×C4—222no—
491C2×C4—222no—
492C2×C4—228no—
493C2×C4—224no—
494C2×C4—228no—
495C2×C4—224no—
496C2×C4—228no—
497C2×C4—222no—
498C2×C4—222no—
499C2×C4—4416no—
500C2×C4—444no—
501C2×C4—444no—
502C2×C4C22×C22⋊D1114yes—
503C2×C4C22×C22⋊D1114yes—
504C2×C4C22×C22⋊D1114yes—
505C22—22no—
506C22—22no—
507C22—28no—
508C22—44no—
509C22—44no—
510C22—44no—
511C22—48no—
512C22—48no—
513C22—224no—
514C22—228no—
515C22—4416no—
516C22—442no—
517C22—442no—
518C22—444no—
519C22#1062333614yes—
520C22C2×#6703712yes—
521C22D11×H(5,𝔽2)12yes—
522C22D11×2−1+412yes—
523C22C23×C22⋊D1111yescharacteristic
524C4—24no—
525C4—24no—
526C4—24no—
527C4—44no—
528C4—224no—
529C4—442no—
530C4—442no—
531C4—448no—
532C2—24no—
533C2—84no—
534C2—444no—
535C2C2×#1062333611yescharacteristic
536C2#1308224711yescharacteristic
537C2#1308226411yescharacteristic
538C2#1308283314yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC2×C11×#537C2
hypercenterC2×#537D11
hypocenterC11#36707
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C22×#66949C2semidirect
2. #13076895C2semidirect
3. #13075106C2semidirect
4. #13074911C2semidirect
5. #13074360C2semidirect
6. #13073548C2semidirect
7. #13072275C2semidirect
8. #13071947C2semidirect
9. #13071931C2semidirect
10. #13071219C2semidirect
11. C2×C11×#537C2semidirect
16. C2×C11×C22⋊Q8C22semidirect
19. C2×C11×#121C22semidirect
23. C2×#66989C22semidirect
32. #10622842C22semidirect
35. #10622835C22semidirect
36. #10622835C22semidirect
42. #10622823C22semidirect
46. #10622594C22semidirect
47. #10622593C22semidirect
48. #10622587C22semidirect
51. #10622561C22semidirect
52. #10622560C22semidirect
79. C2×C11×C4⋊C4D4semidirect
183. C2×#537D11semidirect
255. C2×C22⋊Q8C2×D11semidirect
259. C2×#121C2×D11semidirect
352. C2×C4⋊C4C22⋊D11semidirect
451. C11#36707semidirect

Maximal subgroups

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

subgroupindex
C22×#669492
#130768952
#130751062
#130749112
#130743602
#130735482
#130722752
#130719472
#130719312
#130712192
C2×C11×#5372
#3670711