Finite Group Databasebeta

← #14960609

Subgroups — #14960609

Order 2816.

2910 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66947C211yesmaximal, characteristic, complemented
2#13076895C212yesmaximal, complemented
3#13075160C218yesmaximal, complemented
4#13074877C218yesmaximal, complemented
5#13074352C212yesmaximal, complemented
6#13074097C212yesmaximal, complemented
7#13072254C212yesmaximal, complemented
8#13071931C212yesmaximal, complemented
9#13071931C212yesmaximal, complemented
10#13071219C211yesmaximal, characteristic, complemented
11C2×C11×#537C211yesmaximal, characteristic, complemented
12C22×C11×#41C2212yes—
13C23×D44C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C11×#537—28no—
16C2×C11×C22⋊Q8C2214yescomplemented
17C2×C11×#121C2212yes—
18C2×C11×#121C2212yes—
19C2×C11×#121C2214yescomplemented
20C22×C11×C4⋊C4C2211yescharacteristic
21C2×#66993C2214yes—
22C2×#66991C2214yescomplemented
23C2×#66990C2214yes—
24C2×#66990C2214yes—
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C2×#66947—28no—
30C2×#66947C2218yes—
31#10622844C2214yescomplemented
32#10622844C2214yescomplemented
33#10622836C2214yescomplemented
34#10622836C2214yescomplemented
35#10622836C2214yescomplemented
36#10622835C2214yescomplemented
37#10622833C2214yes—
38#10622833C2214yes—
39#10622826C2218yescomplemented
40#10622826C2218yescomplemented
41#10622825C2212yes—
42#10622824C2212yes—
43C4×C22⋊Dic11C2212yes—
44#10622606C2214yescomplemented
45#10622601C2214yes—
46#10622600C2214yescomplemented
47#10622595C2214yescomplemented
48#10622594C2218yescomplemented
49#10622574C2218yescomplemented
50#10622573C2218yes—
51#10622569C2218yescomplemented
52#10622558C2218yescomplemented
53C24×D11C2311yescharacteristic
54C24×D11C2311yescharacteristic
55C2×C11×#41—28no—
56C2×C11×#41—48no—
57C22×Q8×C11C2312yes—
58C22×D4×C11C2314yes—
59C22×D4×C11C2312yes—
60C22×D4×C11C2312yes—
61C22×D4×C11C2312yes—
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2314yes—
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11C2318yes—
67C22×C22⋊D11C2318yes—
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C22×D44—24no—
71C22×D44—44no—
72C22×D44C2314yes—
73C22×C4×D11—24no—
74C22×C4×D11—44no—
75C22×C4×D11C2314yes—
76C11×C22⋊Q8—216no—
77C11×#121—28no—
78C11×#121—28no—
79C11×#121—216no—
80C2×C11×C4⋊C4D418yescomplemented
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2314yes—
84C2×C11×C22⋊C4C2314yes—
85C2×C11×C22⋊C4C2314yes—
86C2×C22⋊Dic11C2314yes—
87C2×C22⋊Dic11C2318yes—
88C2×C22⋊Dic11C2318yes—
89#66993—48no—
90#66991—48no—
91#66990—48no—
92#66990—48no—
93C2×(C2×D11)⋊C4—24no—
94C2×(C2×D11)⋊C4—24no—
95C2×(C2×D11)⋊C4—24no—
96C2×(C2×D11)⋊C4C2314yes—
97C2×(C2×D11)⋊C4C2314yes—
98C2×(C2×D11)⋊C4C2314yes—
99C2×(C2×D11)⋊C4C2318yes—
100C2×(C2×D11)⋊C4C2318yes—
101C2×C4⋊Dic11C2314yes—
102C2×Dic11⋊C4—24no—
103C2×Dic11⋊C4C2314yes—
104C2×C4×Dic11C2314yes—
105#66947—232no—
106C11⋊#95C2318yes—
107C11⋊#95C2318yes—
108C11⋊#95C2314yes—
109C11⋊#95C2314yes—
110C11⋊#95C2314yes—
111C11⋊#95C2314yes—
112#36710—111nomaximal, Sylow
113C24×C11C2414yes—
114C24×C11C2411yescharacteristic
115C23×D11—22no—
116C23×D11—24no—
117C23×D11—22no—
118C23×D11—24no—
119C23×D11—24no—
120C23×D11—42no—
121C23×D11—42no—
122C23×D11—42no—
123C23×D11C2412yes—
124C23×D11C2412yes—
125C11×#41—432no—
126C2×Q8×C11—24no—
127C2×Q8×C11—44no—
128C2×D4×C11—28no—
129C2×D4×C11—28no—
130C2×D4×C11—28no—
131C2×D4×C11—24no—
132C2×D4×C11—24no—
133C2×D4×C11—24no—
134C2×D4×C11—44no—
135C2×D4×C11—44no—
136C2×D4×C11—44no—
137C22×C4×C11—24no—
138C22×C4×C11—28no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11—44no—
142C22×C4×C11—44no—
143C22×C4×C11C2×D414yes—
144C22×C4×C11C2×D414yes—
145C22×C4×C11C2×D414yes—
146C22×C4×C11C2414yes—
147C22×C4×C11C2412yes—
148C22×C4×C11C2412yes—
149C22×C4×C11C2412yes—
150C2×C22⋊D11—216no—
151C2×C22⋊D11—48no—
152C2×C22⋊D11—48no—
153C2×C22⋊D11—48no—
154C2×C22⋊D11—48no—
155C2×C22⋊D11—48no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—42no—
159C22×Dic11—42no—
160C22×Dic11C2418yes—
161C22×Dic11C2412yes—
162C22×Dic11C2412yes—
163C2×D44—28no—
164C2×D44—28no—
165C2×D44—44no—
166C2×D44—416no—
167C2×C4×D11—28no—
168C2×C4×D11—28no—
169C2×C4×D11—44no—
170C2×C4×D11—416no—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4C2×D4116yes—
174C11×C22⋊C4—28no—
175C11×C22⋊C4—28no—
176C22⋊Dic11—28no—
177C22⋊Dic11—48no—
178C22⋊Dic11—48no—
179(C2×D11)⋊C4—28no—
180(C2×D11)⋊C4—28no—
181(C2×D11)⋊C4—28no—
182(C2×D11)⋊C4—48no—
183(C2×D11)⋊C4—48no—
184C4⋊Dic11—44no—
185Dic11⋊C4—28no—
186C4×Dic11—44no—
187C2×#537D1111yescharacteristic, complemented
188C22×#123—111no—
189#2847—112no—
190#2696—118no—
191#2673—118no—
192#2617—112no—
193#2591—112no—
194#2433—112no—
195#2404—112no—
196#2404—112no—
197#2313—111no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—24no—
201C23×C11—28no—
202C23×C11—24no—
203C23×C11—24no—
204C23×C11—28no—
205C23×C11C22×D412yes—
206C23×C11H(5,𝔽2)14yes—
207C23×C11C2511yescharacteristic
208C22×D11—28no—
209C22×D11—22no—
210C22×D11—24no—
211C22×D11—22no—
212C22×D11—24no—
213C22×D11—22no—
214C22×D11—24no—
215C22×D11—24no—
216C22×D11—24no—
217C22×D11—416no—
218C22×D11—44no—
219C22×D11—44no—
220C22×D11—44no—
221C22×D11—44no—
222C22×D11—44no—
223C22×D11—88no—
224C22×D11H(5,𝔽2)14yes—
225Q8×C11—48no—
226D4×C11—48no—
227D4×C11—416no—
228D4×C11—84no—
229D4×C11—84no—
230C2×C4×C11—28no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—44no—
238C2×C4×C11—44no—
239C2×C4×C11—416no—
240C2×C4×C11C22×D414yes—
241C2×C4×C11C22×D414yes—
242C2×C4×C11C22×D414yes—
243C22⋊D11—816no—
244C22⋊D11—816no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—28no—
248C2×Dic11—28no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—28no—
252C2×Dic11—44no—
253C2×Dic11—44no—
254D44—416no—
255C4×D11—416no—
256C22×#41C2×D1112yes—
257C23×D4—111no—
258C24×C4—111no—
259#537—28no—
260C2×#127—114no—
261C2×#123—118no—
262C2×#123—228no—
263C2×C22⋊Q8C2×D1114yescomplemented
264C2×#121—114no—
265C2×#121C2×D1112yes—
266C2×#121C2×D1112yes—
267C2×#121C2×D1114yescomplemented
268C2×#120—114no—
269C2×#120—114no—
270C22×C4⋊C4—111no—
271C22×C4⋊C4C2×D1111yescharacteristic
272C22×C22⋊C4—111no—
273C22×C22⋊C4—111no—
274C22×C22⋊C4—111no—
275#400—114no—
276#397—114no—
277#394—114no—
278#394—118no—
279#393—114no—
280#393—114no—
281#392—114no—
282#392—114no—
283#392—114no—
284#392—118no—
285#390—114no—
286#388—118no—
287#387—118no—
288#386—114no—
289#386—114no—
290#386—118no—
291#386—118no—
292#386—118no—
293#381—112no—
294#380—112no—
295#380—114no—
296C4×C22⋊C4—112no—
297C22×C11—22no—
298C22×C11—22no—
299C22×C11—28no—
300C22×C11—44no—
301C22×C11—44no—
302C22×C11—44no—
303C22×C11—48no—
304C22×C11—48no—
305C22×C11#53514yes—
306C22×C11C23×D411yescharacteristic
307C22×C11C2×H(5,𝔽2)12yes—
308C22×C11C2×H(5,𝔽2)12yes—
309C22×C11#58512yes—
310C2×D11—24no—
311C2×D11—28no—
312C2×D11—416no—
313C2×D11—42no—
314C2×D11—42no—
315C2×D11—44no—
316C2×D11—42no—
317C2×D11—42no—
318C2×D11—42no—
319C2×D11—48no—
320C2×D11—88no—
321C4×C11—24no—
322C4×C11—24no—
323C4×C11—24no—
324C4×C11—44no—
325Dic11—42no—
326Dic11—42no—
327Dic11—48no—
328C25—111no—
329C25—111no—
330C2×#41—28no—
331C2×#41—48no—
332C22×Q8C22×D1112yes—
333C22×D4—118no—
334C22×D4—118no—
335C22×D4—114no—
336C22×D4—224no—
337C22×D4—444no—
338C22×D4C22×D1114yes—
339C22×D4C22×D1112yes—
340C22×D4C22×D1112yes—
341C22×D4C22×D1112yes—
342C23×C4—111no—
343C23×C4—111no—
344C23×C4—114no—
345C23×C4—224no—
346C23×C4—444no—
347C23×C4C22×D1111yescharacteristic
348C23×C4C22×D1114yes—
349C23×C4C22×D1111yescharacteristic
350C23×C4C22×D1111yescharacteristic
351#127—448no—
352#123—2232no—
353C22⋊Q8—216no—
354#121—28no—
355#121—28no—
356#121—216no—
357#121—448no—
358#120—448no—
359#120—448no—
360C2×C4⋊C4—114no—
361C2×C4⋊C4—114no—
362C2×C4⋊C4—224no—
363C2×C4⋊C4C22⋊D1118yescomplemented
364C2×C4⋊C4C22×D1112yes—
365C2×C4⋊C4C22×D1112yes—
366C2×C4⋊C4C22×D1114yes—
367C2×C22⋊C4—114no—
368C2×C22⋊C4—114no—
369C2×C22⋊C4—114no—
370C2×C22⋊C4—114no—
371C2×C22⋊C4—118no—
372C2×C22⋊C4—118no—
373C2×C22⋊C4—118no—
374C2×C22⋊C4—118no—
375C2×C22⋊C4—224no—
376C2×C22⋊C4—224no—
377C2×C22⋊C4—224no—
378C2×C22⋊C4C22×D1114yes—
379C2×C22⋊C4C22×D1114yes—
380C2×C42—114no—
381#95—114no—
382#95—118no—
383#95—114no—
384#95—114no—
385#95—114no—
386#95—118no—
387C2×C11—24no—
388C2×C11—84no—
389C2×C11C2×#53511yescharacteristic
390C2×C11#348411yescharacteristic
391C2×C11#348711yescharacteristic
392C2×C11#353414yes—
393D11—44no—
394D11—82no—
395C24—112no—
396C24—112no—
397C24—224no—
398C24—222no—
399C24—224no—
400C24—222no—
401C24—224no—
402C24—442no—
403C24—442no—
404C24—442no—
405C24C23×D1114yes—
406C24C23×D1111yescharacteristic
407#41—432no—
408C2×Q8—24no—
409C2×Q8—44no—
410C2×D4—28no—
411C2×D4—28no—
412C2×D4—28no—
413C2×D4—24no—
414C2×D4—24no—
415C2×D4—24no—
416C2×D4—44no—
417C2×D4—44no—
418C2×D4—44no—
419C2×D4—228no—
420C2×D4—2216no—
421C2×D4—228no—
422C2×D4—444no—
423C2×D4—4416no—
424C2×D4—448no—
425C2×D4—448no—
426C2×D4—448no—
427C2×D4—448no—
428C2×D4—448no—
429C22×C4—24no—
430C22×C4—28no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—44no—
434C22×C4—44no—
435C22×C4—118no—
436C22×C4—112no—
437C22×C4—112no—
438C22×C4—228no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—228no—
442C22×C4—444no—
443C22×C4—4416no—
444C22×C4—442no—
445C22×C4—442no—
446C22×C4C2×C22⋊D1114yes—
447C22×C4C2×C22⋊D1114yes—
448C22×C4C2×C22⋊D1114yes—
449C22×C4C23×D1114yes—
450C22×C4C23×D1112yes—
451C22×C4C23×D1112yes—
452C22×C4C23×D1112yes—
453C4⋊C4—24no—
454C4⋊C4—24no—
455C4⋊C4—228no—
456C4⋊C4—444no—
457C4⋊C4C2×C22⋊D11116yes—
458C22⋊C4—28no—
459C22⋊C4—28no—
460C22⋊C4—228no—
461C22⋊C4—228no—
462C22⋊C4—228no—
463C22⋊C4—228no—
464C22⋊C4—448no—
465C22⋊C4—448no—
466C22⋊C4—448no—
467C22⋊C4—448no—
468C42—444no—
469C11#3671011yescharacteristic, complemented, Sylow
470C23—22no—
471C23—22no—
472C23—24no—
473C23—24no—
474C23—28no—
475C23—28no—
476C23—24no—
477C23—114no—
478C23—228no—
479C23—224no—
480C23—222no—
481C23—224no—
482C23—222no—
483C23—224no—
484C23—224no—
485C23—224no—
486C23—222no—
487C23—4416no—
488C23—444no—
489C23—444no—
490C23—444no—
491C23—444no—
492C23—444no—
493C23—888no—
494C23#6703714yes—
495C23C22×C22⋊D1112yes—
496C23C24×D1111yescharacteristic
497Q8—48no—
498D4—48no—
499D4—416no—
500D4—84no—
501D4—84no—
502D4—4416no—
503D4—8816no—
504D4—8816no—
505C2×C4—28no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—44no—
513C2×C4—44no—
514C2×C4—416no—
515C2×C4—228no—
516C2×C4—228no—
517C2×C4—224no—
518C2×C4—224no—
519C2×C4—228no—
520C2×C4—222no—
521C2×C4—222no—
522C2×C4—4416no—
523C2×C4—444no—
524C2×C4—444no—
525C2×C4C22×C22⋊D1114yes—
526C2×C4C22×C22⋊D1114yes—
527C2×C4C22×C22⋊D1114yes—
528C22—22no—
529C22—22no—
530C22—28no—
531C22—44no—
532C22—44no—
533C22—44no—
534C22—48no—
535C22—48no—
536C22—224no—
537C22—228no—
538C22—4416no—
539C22—442no—
540C22—442no—
541C22—444no—
542C22—442no—
543C22—442no—
544C22—442no—
545C22—448no—
546C22—888no—
547C22#1062333614yes—
548C22C2×#6703712yes—
549C22D11×H(5,𝔽2)12yes—
550C22#1062345712yes—
551C22C23×C22⋊D1111yescharacteristic
552C4—24no—
553C4—24no—
554C4—24no—
555C4—44no—
556C4—442no—
557C4—442no—
558C4—448no—
559C2—24no—
560C2—84no—
561C2—444no—
562C2—882no—
563C2C2×#1062333611yescharacteristic
564C2#1308224711yescharacteristic
565C2#1308227111yescharacteristic
566C2#1308279514yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC2×C11×#537C2
hypercenterC2×#537D11
hypocenterC11#36710
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C22×#66947C2semidirect
2. #13076895C2semidirect
3. #13075160C2semidirect
4. #13074877C2semidirect
5. #13074352C2semidirect
6. #13074097C2semidirect
7. #13072254C2semidirect
8. #13071931C2semidirect
9. #13071931C2semidirect
10. #13071219C2semidirect
11. C2×C11×#537C2semidirect
16. C2×C11×C22⋊Q8C22semidirect
19. C2×C11×#121C22semidirect
22. C2×#66991C22semidirect
31. #10622844C22semidirect
32. #10622844C22semidirect
33. #10622836C22semidirect
34. #10622836C22semidirect
35. #10622836C22semidirect
36. #10622835C22semidirect
39. #10622826C22semidirect
40. #10622826C22semidirect
44. #10622606C22semidirect
46. #10622600C22semidirect
47. #10622595C22semidirect
48. #10622594C22semidirect
49. #10622574C22semidirect
51. #10622569C22semidirect
52. #10622558C22semidirect
80. C2×C11×C4⋊C4D4semidirect
187. C2×#537D11semidirect
263. C2×C22⋊Q8C2×D11semidirect
267. C2×#121C2×D11semidirect
363. C2×C4⋊C4C22⋊D11semidirect
469. C11#36710semidirect

Maximal subgroups

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

subgroupindex
C22×#669472
#130768952
#130751602
#130748772
#130743522
#130740972
#130722542
#130719312
#130712192
C2×C11×#5372
#3671011