Finite Group Databasebeta

← #14827070

Subgroups — #14827070

Order 2816.

748 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073189C211yesmaximal, characteristic, complemented
2#13071691C211yesmaximal, characteristic
3#13070142C211yesmaximal, characteristic
4#13069929C211yesmaximal, characteristic
5#13069852C211yesmaximal, characteristic
6#13069478C211yesmaximal, characteristic, complemented
7#13069260C211yesmaximal, characteristic, complemented
8#13069254C211yesmaximal, characteristic, complemented
9#13069188C211yesmaximal, characteristic, complemented
10#13069172C211yesmaximal, characteristic, complemented
11#13068959C211yesmaximal, characteristic, complemented
12#13068952C211yesmaximal, characteristic
13#13068619C211yesmaximal, characteristic, complemented
14#102×Dic11C211yesmaximal, characteristic
15C11×#2015C211yesmaximal, characteristic
16C22×C11×Q16C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C2×C11×#124C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C2×D4×Dic11C2211yescharacteristic
21C2×C11×#103C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C11×#391C2211yescharacteristic
24#10622843C2211yescharacteristic
25#10622843C2211yescharacteristic
26#10622843C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31#10622834C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36C2×C8×Dic11C2211yescharacteristic
37#10622589C2211yescharacteristic
38C4⋊C4×Dic11C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40#10622564—21no—
41#10622564—21no—
42#10622563—21no—
43C22⋊C4×Dic11—21no—
44C4×C4⋊Dic11C2211yescharacteristic
45C4×C4⋊Dic11C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622273—21no—
48#10622271—21no—
49#10622266—21no—
50#10622265—21no—
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C23×Dic11—21no—
63C2×C11×Q16—22no—
64C2×C11×Q16—22no—
65C2×C11×Q16—41no—
66C2×C11×SD16—22no—
67C2×C11×SD16—41no—
68C2×C11×SD16—41no—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C11×#124—22no—
72C11×#124—22no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80Q8×Dic11—22no—
81Q8×Dic11—41no—
82D4×Dic11—22no—
83D4×Dic11—41no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11D411yescharacteristic
86C2×C4⋊Dic11D411yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11C2311yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C11×#103—41no—
102C11×#102—22no—
103C11×#95—21no—
104C11×#95—21no—
105#66899—22no—
106#66899—22no—
107#66899—41no—
108#66899—41no—
109#66896—22no—
110#66896—41no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95D411yescharacteristic
121C11⋊#95D411yescharacteristic
122#66882—22no—
123Dic11⋊C8—41no—
124C8×Dic11—41no—
125#66871—41no—
126#27073—111nomaximal, Sylow
127C24×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11#4112yes—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11#4112yes—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—42no—
157C22×Dic11—42no—
158C22×Dic11—81no—
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C11×Q16—44no—
164C11×SD16—44no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11#4112yes—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—24no—
175C42×C11—21no—
176C42×C11—21no—
177C22⋊Dic11—42no—
178C22⋊Dic11—42no—
179C22⋊Dic11—81no—
180C4⋊Dic11—22no—
181C4⋊Dic11—22no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—42no—
190C4⋊Dic11#4112yes—
191Dic11⋊C4—42no—
192Dic11⋊C4—81no—
193Dic11⋊C4—81no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—42no—
199C4×Dic11—81no—
200C4×Dic11—81no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207#2511—111no—
208#2367—111no—
209#2093—111no—
210#2055—111no—
211#2042—111no—
212#2015D1111yescharacteristic
213#1969—111no—
214#1928—111no—
215#1928—111no—
216#1918—111no—
217#1916—111no—
218#1878—111no—
219#1877—111no—
220#1803—111no—
221C4×#102—111no—
222C23×C11—22no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11C22×D411yescharacteristic
230Q8×C11—22no—
231Q8×C11—22no—
232Q8×C11—41no—
233Q8×C11—41no—
234Q8×C11—41no—
235Q8×C11—41no—
236Q8×C11—41no—
237Q8×C11—41no—
238D4×C11—22no—
239D4×C11—22no—
240D4×C11—41no—
241D4×C11—41no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—22no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11H(5,𝔽2)11yescharacteristic
262C2×C4×C11H(5,𝔽2)11yescharacteristic
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—22no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—84no—
286C2×Dic11#13512yes—
287C2×Dic11#13712yes—
288C8×C11—22no—
289C8×C11—41no—
290C11⋊C8—41no—
291C11⋊C8—41no—
292C22×Q16C2×D1111yescharacteristic
293C22×SD16C2×D1111yescharacteristic
294C2×#124C2×D1111yescharacteristic
295C2×C4×Q8—111no—
296C2×C4×D4—111no—
297C2×#107—111no—
298C2×#107—111no—
299C2×C4⋊C8—111no—
300C2×#103—111no—
301C2×#103—111no—
302C2×#103—111no—
303C2×#103—111no—
304C2×#103C2×D1111yescharacteristic
305C2×#102—111no—
306C2×#102—111no—
307C2×#102C2×D1111yescharacteristic
308C2×C4×C8—111no—
309#400—221no—
310#400—221no—
311#391—111no—
312#391—111no—
313#391—111no—
314#391C2×D1111yescharacteristic
315#390—111no—
316#389—111no—
317#388—221no—
318#388—221no—
319#387—221no—
320#387—221no—
321#385—221no—
322#384—111no—
323C4×C4⋊C4—111no—
324C4×C4⋊C4—111no—
325C4×C4⋊C4—111no—
326C4×C22⋊C4—221no—
327#340—111no—
328#340—111no—
329#340—111no—
330#340—111no—
331#336—111no—
332#336—111no—
333#336—111no—
334#336C2×D1111yescharacteristic
335C22×C11—42no—
336C22×C11—42no—
337C22×C11—42no—
338C22×C11—81no—
339C22×C11—81no—
340C22×C11—81no—
341C22×C11—81no—
342C22×C11#52511yescharacteristic
343C22×C11#54611yescharacteristic
344C22×C11#55011yescharacteristic
345C22×C11C2×#13511yescharacteristic
346C22×C11C2×#13711yescharacteristic
347C22×C11#57611yescharacteristic
348C22×C11#57811yescharacteristic
349C4×C11—41no—
350C4×C11—41no—
351C4×C11—42no—
352C4×C11—81no—
353C4×C11—81no—
354C4×C11#52911yescharacteristic
355C4×C11#53811yescharacteristic
356C4×C11#55111yescharacteristic
357C4×C11#55311yescharacteristic
358Dic11—22no—
359Dic11—22no—
360Dic11—41no—
361Dic11—41no—
362Dic11—42no—
363Dic11—81no—
364Dic11—81no—
365Dic11—81no—
366C22×Q8C22×D1111yescharacteristic
367C22×Q8C22×D1111yescharacteristic
368C22×D4C22×D1111yescharacteristic
369C23×C4—221no—
370C2×Q16—22no—
371C2×Q16—22no—
372C2×Q16—41no—
373C2×SD16—22no—
374C2×SD16—41no—
375C2×SD16—41no—
376C22×C8—111no—
377C22×C8—111no—
378C22×C8C22×D1111yescharacteristic
379C22×C8C22×D1111yescharacteristic
380#124—22no—
381#124—22no—
382C4×Q8—222no—
383C4×Q8—441no—
384C4×D4—222no—
385C4×D4—441no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4C22×D1111yescharacteristic
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—221no—
400C2×C22⋊C4—221no—
401C2×C22⋊C4—221no—
402C2×C42—111no—
403C2×C42—111no—
404C2×C42—221no—
405C2×C42—221no—
406C2×C42—221no—
407C2×C42C22×D1111yescharacteristic
408#107—222no—
409#107—441no—
410C4⋊C8—441no—
411#103—41no—
412#103—222no—
413#103—222no—
414#103—441no—
415#103—441no—
416#102—22no—
417#102—222no—
418#102—441no—
419C4×C8—441no—
420#95—21no—
421#95—21no—
422#95—111no—
423#95—111no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95—221no—
429#95—221no—
430#95—221no—
431#95—221no—
432#95—221no—
433C2×C11—82no—
434C2×C11#246711yescharacteristic
435C2×C11#310711yescharacteristic
436C2×C11#312411yescharacteristic
437C2×C11#330011yescharacteristic
438C2×C11#331411yescharacteristic
439C2×C11#339611yescharacteristic
440C2×C11#339811yescharacteristic
441C24—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8#434112yes—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4#434112yes—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—111no—
464C22×C4—111no—
465C22×C4—111no—
466C22×C4—111no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4—221no—
471C22×C4—442no—
472C22×C4—442no—
473C22×C4—881no—
474C22×C4D4×D1111yescharacteristic
475C22×C4D4×D1111yescharacteristic
476C22×C4C23×D1111yescharacteristic
477Q16—44no—
478SD16—44no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8#434112yes—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—112no—
494C4⋊C4—222no—
495C4⋊C4—222no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—442no—
504C4⋊C4—442no—
505C4⋊C4—881no—
506C4⋊C4—881no—
507C22⋊C4—24no—
508C22⋊C4—24no—
509C22⋊C4—442no—
510C22⋊C4—442no—
511C22⋊C4—881no—
512C42—21no—
513C42—21no—
514C42—221no—
515C42—221no—
516C42—221no—
517C42—221no—
518C42—442no—
519C42—881no—
520C42—881no—
521C11#2707311yescharacteristic, complemented, Sylow
522C23—22no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23C2×D4×D1111yescharacteristic
530Q8—22no—
531Q8—22no—
532Q8—41no—
533Q8—41no—
534Q8—41no—
535Q8—41no—
536Q8—41no—
537Q8—41no—
538D4—22no—
539D4—22no—
540D4—41no—
541D4—41no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—22no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—112no—
558C2×C4—112no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—222no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—884no—
582C2×C4C2×#434111yescharacteristic
583C2×C4C2×#434111yescharacteristic
584C2×C4C2×#434111yescharacteristic
585C2×C4#6703711yescharacteristic
586C2×C4#6703711yescharacteristic
587C2×C4#41×D1111yescharacteristic
588C8—22no—
589C8—41no—
590C8—441no—
591C8—441no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22#1062311711yescharacteristic
600C22#1062314311yescharacteristic
601C22#1062324911yescharacteristic
602C22D11×#13511yescharacteristic
603C22#1062330011yescharacteristic
604C22D11×#13711yescharacteristic
605C22#1062331011yescharacteristic
606C4—42no—
607C4—41no—
608C4—41no—
609C4—81no—
610C4—81no—
611C4—222no—
612C4—222no—
613C4—441no—
614C4—442no—
615C4—441no—
616C4—881no—
617C4—881no—
618C4—881no—
619C4#1062311811yescharacteristic
620C4#1062312411yescharacteristic
621C4#1062313111yescharacteristic
622C4#1062313211yescharacteristic
623C2—82no—
624C2#1307266211yescharacteristic
625C2#1307868011yescharacteristic
626C2#1307887911yescharacteristic
627C2#1308051011yescharacteristic
628C2#1308070411yescharacteristic
629C2#1308162511yescharacteristic
630C2#1308164411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2015C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2015D11
hypocenterC11#27073
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2015

Complements

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

NH ≅ G/Ntype
1. #13073189C2semidirect
6. #13069478C2semidirect
7. #13069260C2semidirect
8. #13069254C2semidirect
9. #13069188C2semidirect
10. #13069172C2semidirect
11. #13068959C2semidirect
13. #13068619C2semidirect
521. C11#27073semidirect

Maximal subgroups

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

subgroupindex
#130731892
#130716912
#130701422
#130699292
#130698522
#130694782
#130692602
#130692542
#130691882
#130691722
#130689592
#130689522
#130686192
#102×Dic112
C11×#20152
#2707311