Finite Group Databasebeta

← #14719954

Subgroups — #14719954

Order 2816.

1424 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623081C211yesmaximal, characteristic
2#13077062C212yesmaximal, complemented
3#13066975C212yesmaximal, complemented
4#13066963C214yesmaximal, complemented
5#13066954C211yesmaximal, characteristic, complemented
6#13066941C212yesmaximal, complemented
7D11×#323C212yesmaximal, complemented
8C11×#1459C211yesmaximal, characteristic, complemented
9C22×#4339C2211yescharacteristic
10C23×D44C411yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C2×#66990C412yes—
13C2×#66983C2211yescharacteristic
14C2×#66977C411yescharacteristic
15C2×#66954—22no—
16#10623081—22no—
17#10623081—22no—
18#10623081—24no—
19C2×#66947C2212yes—
20C2×#66937C412yes—
21C2×C22⋊C4×D11C2212yes—
22C2×#66928C411yescharacteristic
23C2×C4×D44C411yescharacteristic
24C2×C11×C22⋊C8C2212yescomplemented
25#10622820C2212yescomplemented
26#10622723—22no—
27#10622340—24no—
28#10622339C2214yescomplemented
29D11×C22⋊C8C2214yescomplemented
30C11×#324C2212yescomplemented
31C11×#323C2211yescharacteristic
32C11×#323C2211yescharacteristic
33#10622166C2212yescomplemented
34#10622163C2212yes—
35#10622106C2214yescomplemented
36#10622106C2214yescomplemented
37C24×D11C2×C412yes—
38C22×D4×C11C2×C411yescharacteristic
39C23×C4×C11C2×C411yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C22×C22⋊D11C2×C412yes—
42C22×C22⋊D11C2×C412yes—
43C2×#4339—44no—
44C2×#4339D412yes—
45C2×#4339D412yes—
46C2×#4339D414yes—
47C22×D44—21no—
48C22×D44—22no—
49C22×D44—21no—
50C22×D44—44no—
51C22×D44C2×C411yescharacteristic
52C22×D44C2×C411yescharacteristic
53C22×D44C2×C412yes—
54C22×C4×D11C2×C412yes—
55C22×C4×D11C2312yes—
56C22×Dic22C2×C411yescharacteristic
57C22×C8×C11—22no—
58C4×D4×C11—22no—
59C4×D4×C11—22no—
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C22⋊C4C2×C411yescharacteristic
62C2×C11×C22⋊C4C2311yescharacteristic
63C2×C42×C11C2×C411yescharacteristic
64C2×C22⋊Dic11C2×C412yes—
65#66990—24no—
66#66990—24no—
67#66983—22no—
68#66983—22no—
69C2×(C2×D11)⋊C4C2×C412yes—
70C2×(C2×D11)⋊C4C2×C412yes—
71C2×(C2×D11)⋊C4C2×C412yes—
72C2×(C2×D11)⋊C4C2312yes—
73C2×C4⋊Dic11C2×C411yescharacteristic
74#66977—22no—
75#66977—22no—
76C2×Dic11⋊C4C2×C412yes—
77C2×#4318—22no—
78#66954—48no—
79C2×#4313—24no—
80C2×C8×D11—24no—
81#66947—24no—
82#66947—24no—
83#66937—24no—
84#66937—24no—
85C22⋊C4×D11—24no—
86C22⋊C4×D11—24no—
87#66928—22no—
88#66928—22no—
89C4×D44—22no—
90C4×D44—21no—
91C4×D44—21no—
92C11×C22⋊C8—22no—
93C11×C22⋊C8C2312yes—
94C11×C22⋊C8C2312yes—
95C22⋊(C11⋊C8)—22no—
96C22⋊(C11⋊C8)C2314yes—
97(C2×D11)⋊C8—24no—
98(C2×D11)⋊C8—24no—
99#17411—111nomaximal, Sylow
100C24×C11C22×C411yescharacteristic
101C24×C11C22×C411yescharacteristic
102C23×D11—24no—
103C23×D11—22no—
104C23×D11—22no—
105C23×D11—42no—
106C23×D11—44no—
107C23×D11—82no—
108C23×D11C22×C412yes—
109C23×D11C22×C412yes—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—41no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11C22×C411yescharacteristic
118C22×C4×C11C22×C411yescharacteristic
119C22×C4×C11C22×C411yescharacteristic
120C22×C4×C11C22×C411yescharacteristic
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2411yescharacteristic
124C2×C22⋊D11—24no—
125C2×C22⋊D11—44no—
126C2×C22⋊D11—82no—
127C2×C22⋊D11C22⋊C414yes—
128C2×C22⋊D11C22⋊C414yes—
129C22×Dic11C22×C412yes—
130C22×Dic11C22×C412yes—
131#4339—28no—
132#4339—44no—
133#4339—48no—
134C2×D44—24no—
135C2×D44—22no—
136C2×D44—22no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44—42no—
140C2×D44—44no—
141C2×D44—48no—
142C2×D44—44no—
143C2×D44—44no—
144C2×D44C22⋊C412yes—
145C2×D44C22⋊C411yescharacteristic
146C2×D44C22⋊C411yescharacteristic
147C2×C4×D11—22no—
148C2×C4×D11—22no—
149C2×C4×D11—44no—
150C2×C4×D11—82no—
151C2×C4×D11C2×D414yes—
152C2×C4×D11C2×D414yes—
153C2×Dic22—42no—
154C2×Dic22C22⋊C412yes—
155C2×Dic22C22⋊C412yes—
156C2×C8×C11—22no—
157C2×C8×C11—22no—
158C2×C8×C11—44no—
159C11×C4⋊C4—22no—
160C11×C22⋊C4—22no—
161C11×C22⋊C4—22no—
162C42×C11—21no—
163C42×C11—21no—
164C22⋊Dic11—24no—
165(C2×D11)⋊C4—24no—
166(C2×D11)⋊C4—24no—
167(C2×D11)⋊C4—22no—
168(C2×D11)⋊C4—22no—
169(C2×D11)⋊C4—24no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172Dic11⋊C4—24no—
173#4318—44no—
174C2×C11⋊C8—24no—
175#4313—48no—
176C8×D11—48no—
177C2×#546—111no—
178#2880—112no—
179#1471—112no—
180#1468—114no—
181#1465—111no—
182#1462—112no—
183#1459D1111yescharacteristic, complemented
184C2×#323—112no—
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11C2×C22⋊C412yes—
194C23×C11#13112yescomplemented
195C23×C11C23×C411yescharacteristic
196C22×D11—22no—
197C22×D11—22no—
198C22×D11—24no—
199C22×D11—22no—
200C22×D11—22no—
201C22×D11—22no—
202C22×D11—42no—
203C22×D11—44no—
204C22×D11—44no—
205C22×D11—44no—
206C22×D11—44no—
207C22×D11—42no—
208C22×D11—42no—
209C22×D11—82no—
210C22×D11—82no—
211C22×D11—88no—
212C22×D11—88no—
213C22×D11C2×C22⋊C412yes—
214C22×D11C2×C22⋊C412yes—
215D4×C11—44no—
216C2×C4×C11—24no—
217C2×C4×C11—22no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—41no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11C2×C22⋊C411yescharacteristic
230C2×C4×C11C2×C22⋊C411yescharacteristic
231C2×C4×C11C22×D412yes—
232C22⋊D11—28no—
233C22⋊D11—44no—
234C22⋊D11—84no—
235C2×Dic11—22no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11C2×C22⋊C414yes—
239D44—24no—
240D44—22no—
241D44—42no—
242D44—44no—
243D44—44no—
244D44—42no—
245D44#9914yes—
246C4×D11—28no—
247C4×D11—44no—
248C4×D11—82no—
249C4×D11—82no—
250Dic22—24no—
251Dic22—42no—
252C8×C11—42no—
253C8×C11—42no—
254C11⋊C8—44no—
255C22×#41—111no—
256C23×D4—111no—
257C2×#131—222no—
258#546—222no—
259#546—224no—
260#546—222no—
261C2×#124—111no—
262C2×#123—112no—
263C2×C22⋊Q8—111no—
264C2×#121—111no—
265C2×#121—112no—
266C2×#120—112no—
267C2×C4×D4—111no—
268C2×C4×D4C2×D1111yescharacteristic
269C22×C22⋊C4—112no—
270#408—224no—
271#408—222no—
272#407—112no—
273#407—114no—
274C2×C22⋊C8—114no—
275C2×C22⋊C8C2×D1112yescomplemented
276#324—112no—
277#324C2×D1112yescomplemented
278#323—112no—
279#323—114no—
280#323—114no—
281#323C2×D1111yescharacteristic
282#323C2×D1111yescharacteristic
283C22×C11—21no—
284C22×C11—21no—
285C22×C11—22no—
286C22×C11—22no—
287C22×C11—22no—
288C22×C11—22no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—41no—
292C22×C11—41no—
293C22×C11—81no—
294C22×C11—81no—
295C22×C11C22×C22⋊C411yescharacteristic
296C22×C11C2×#13111yescharacteristic
297C22×C11#56811yescharacteristic
298C2×D11—22no—
299C2×D11—22no—
300C2×D11—22no—
301C2×D11—22no—
302C2×D11—22no—
303C2×D11—44no—
304C2×D11—44no—
305C2×D11—42no—
306C2×D11—42no—
307C2×D11—42no—
308C2×D11—88no—
309C2×D11—88no—
310C2×D11—82no—
311C2×D11—82no—
312C2×D11C2×#9914yes—
313C4×C11—21no—
314C4×C11—22no—
315C4×C11—41no—
316C4×C11—41no—
317C4×C11—41no—
318C4×C11C2×#9912yes—
319Dic11—24no—
320Dic11—42no—
321C25—112no—
322C2×#41—112no—
323C2×#41—114no—
324C2×#41—112no—
325C2×#41—444no—
326C22×Q8—111no—
327C22×D4—112no—
328C22×D4—112no—
329C22×D4—111no—
330C22×D4—112no—
331C22×D4—111no—
332C22×D4—221no—
333C22×D4—222no—
334C22×D4—221no—
335C22×D4—444no—
336C22×D4C4×D1111yescharacteristic
337C23×C4—112no—
338C23×C4—112no—
339C23×C4C4×D1111yescharacteristic
340C23×C4C22×D1111yescharacteristic
341#131—448no—
342C2×M16—224no—
343C2×M16—222no—
344C22×C8—22no—
345C22×C8—224no—
346#124—222no—
347#124—222no—
348#123—224no—
349#123—224no—
350C22⋊Q8—222no—
351C22⋊Q8—222no—
352#121—224no—
353#121—224no—
354#121—222no—
355#121—222no—
356#120—224no—
357#120—224no—
358C4×D4—22no—
359C4×D4—22no—
360C4×D4—221no—
361C4×D4—222no—
362C4×D4—221no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—112no—
365C2×C4⋊C4C22×D1111yescharacteristic
366C2×C22⋊C4—112no—
367C2×C22⋊C4—112no—
368C2×C22⋊C4—112no—
369C2×C22⋊C4—112no—
370C2×C22⋊C4—112no—
371C2×C22⋊C4—224no—
372C2×C22⋊C4—224no—
373C2×C22⋊C4C4×D1111yescharacteristic
374C2×C22⋊C4C22×D1111yescharacteristic
375C2×C42C4×D1111yescharacteristic
376C22⋊C8—22no—
377C22⋊C8—114no—
378C22⋊C8—224no—
379C22⋊C8—224no—
380C22⋊C8—222no—
381C22⋊C8C22×D1112yes—
382C22⋊C8C22×D1112yes—
383C2×C11—21no—
384C2×C11—21no—
385C2×C11—42no—
386C2×C11—42no—
387C2×C11#288011yescharacteristic
388C2×C11C22×#9911yescharacteristic
389C2×C11#288811yescharacteristic
390D11—24no—
391D11—42no—
392D11—82no—
393C24—112no—
394C24—112no—
395C24—222no—
396C24—222no—
397C24—224no—
398C24—442no—
399C24—444no—
400C24—882no—
401C24C2×C4×D1111yescharacteristic
402C24C2×C4×D1111yescharacteristic
403#41—228no—
404#41—444no—
405#41—448no—
406C2×Q8—112no—
407C2×Q8—112no—
408C2×Q8—442no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—41no—
412C2×D4—114no—
413C2×D4—114no—
414C2×D4—111no—
415C2×D4—112no—
416C2×D4—111no—
417C2×D4—224no—
418C2×D4—222no—
419C2×D4—222no—
420C2×D4—224no—
421C2×D4—221no—
422C2×D4—221no—
423C2×D4—442no—
424C2×D4—444no—
425C2×D4—448no—
426C2×D4—444no—
427C2×D4—444no—
428C2×D4—444no—
429C2×D4—882no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—112no—
435C22×C4—114no—
436C22×C4—114no—
437C22×C4—112no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—444no—
441C22×C4—882no—
442C22×C4C2×C4×D1111yescharacteristic
443C22×C4C2×C4×D1111yescharacteristic
444C22×C4C2×C4×D1111yescharacteristic
445C22×C4C2×C4×D1111yescharacteristic
446C22×C4D4×D1112yes—
447C22×C4D4×D1112yes—
448C22×C4C23×D1111yescharacteristic
449M16—448no—
450M16—444no—
451C2×C8—22no—
452C2×C8—22no—
453C2×C8—44no—
454C2×C8—224no—
455C2×C8—448no—
456C4⋊C4—22no—
457C4⋊C4—224no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C22⋊C4—22no—
461C22⋊C4—22no—
462C22⋊C4—224no—
463C22⋊C4—224no—
464C22⋊C4—222no—
465C22⋊C4—222no—
466C22⋊C4—224no—
467C22⋊C4—224no—
468C42—21no—
469C42—21no—
470C11#1741111yescharacteristic, complemented, Sylow
471C23—21no—
472C23—21no—
473C23—21no—
474C23—21no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—112no—
480C23—112no—
481C23—224no—
482C23—222no—
483C23—222no—
484C23—222no—
485C23—222no—
486C23—222no—
487C23—442no—
488C23—444no—
489C23—444no—
490C23—442no—
491C23—442no—
492C23—444no—
493C23—444no—
494C23—882no—
495C23—882no—
496C23—888no—
497C23—888no—
498C23C22⋊C4×D1112yes—
499C23#6695412yescomplemented
500C23C22×C4×D1111yescharacteristic
501Q8—224no—
502Q8—442no—
503D4—44no—
504D4—114no—
505D4—224no—
506D4—228no—
507D4—222no—
508D4—442no—
509D4—444no—
510D4—444no—
511D4—444no—
512D4—442no—
513D4—884no—
514C2×C4—24no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—114no—
528C2×C4—228no—
529C2×C4—222no—
530C2×C4—444no—
531C2×C4—442no—
532C2×C4—442no—
533C2×C4—882no—
534C2×C4—882no—
535C2×C4C22⋊C4×D1111yescharacteristic
536C2×C4C22⋊C4×D1111yescharacteristic
537C2×C4C2×D4×D1112yes—
538C8—42no—
539C8—42no—
540C8—444no—
541C22—21no—
542C22—21no—
543C22—22no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—42no—
548C22—42no—
549C22—41no—
550C22—41no—
551C22—81no—
552C22—81no—
553C22—114no—
554C22—222no—
555C22—222no—
556C22—222no—
557C22—222no—
558C22—222no—
559C22—444no—
560C22—444no—
561C22—442no—
562C22—442no—
563C22—442no—
564C22—882no—
565C22—882no—
566C22—888no—
567C22—888no—
568C22C2×C22⋊C4×D1111yescharacteristic
569C22C2×#6695411yescharacteristic
570C22#1062327611yescharacteristic
571C4—22no—
572C4—21no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—224no—
577C4—442no—
578C4D11×#9912yes—
579C2—21no—
580C2—21no—
581C2—42no—
582C2—42no—
583C2—224no—
584C2—442no—
585C2—882no—
586C2#1307706211yescharacteristic
587C2C2×D11×#9911yescharacteristic
588C2#1307709311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1459C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623081C2
cosocleC22×C4×C11C24
hypercenter#1459D11
hypocenterC11#17411
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1459

Complements

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

NH ≅ G/Ntype
2. #13077062C2semidirect
3. #13066975C2semidirect
4. #13066963C2semidirect
5. #13066954C2semidirect
6. #13066941C2semidirect
7. D11×#323C2semidirect
8. C11×#1459C2semidirect
24. C2×C11×C22⋊C8C22semidirect
25. #10622820C22semidirect
28. #10622339C22semidirect
29. D11×C22⋊C8C22semidirect
30. C11×#324C22semidirect
33. #10622166C22semidirect
35. #10622106C22semidirect
36. #10622106C22semidirect
183. #1459D11semidirect
194. C23×C11#131semidirect
275. C2×C22⋊C8C2×D11semidirect
277. #324C2×D11semidirect
470. C11#17411semidirect
499. C23#66954semidirect

Maximal subgroups

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

subgroupindex
C2×#106230812
#130770622
#130669752
#130669632
#130669542
#130669412
D11×#3232
C11×#14592
#1741111