Finite Group Databasebeta

← #14827025

Subgroups — #14827025

Order 2816.

740 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073222C211yesmaximal, characteristic, complemented
2#13071691C211yesmaximal, characteristic
3#13070135C211yesmaximal, characteristic
4#13069929C211yesmaximal, characteristic
5#13069852C211yesmaximal, characteristic
6#13069478C211yesmaximal, characteristic, complemented
7#13069253C211yesmaximal, characteristic, complemented
8#13069247C211yesmaximal, characteristic, complemented
9#13069209C211yesmaximal, characteristic, complemented
10#13069172C211yesmaximal, characteristic, complemented
11#13068959C211yesmaximal, characteristic, complemented
12#13068952C211yesmaximal, characteristic
13#13068629C211yesmaximal, 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#10622590C2211yescharacteristic
38C4⋊C4×Dic11C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40#10622564—21no—
41#10622564—21no—
42#10622563—21no—
43C22⋊C4×Dic11—21no—
44C4×C4⋊Dic11C2211yescharacteristic
45C4×C4⋊Dic11C2211yescharacteristic
46#10622541C2211yescharacteristic
47C11⋊#401—21no—
48#10622272—21no—
49#10622268—21no—
50#10622264—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×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11C2311yescharacteristic
96C2×C4×Dic11C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C11×#103—41no—
100C11×#102—22no—
101C11×#95—21no—
102C11×#95—21no—
103#66899—22no—
104#66899—22no—
105#66899—41no—
106#66899—41no—
107#66896—22no—
108#66896—41no—
109C11⋊#95—21no—
110C11⋊#95—21no—
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#66872—41no—
126#27070—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—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—41no—
189C4⋊Dic11—42no—
190C4⋊Dic11#4112yes—
191Dic11⋊C4—42no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—42no—
197C4×Dic11—42no—
198C4×Dic11—81no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205#2514—111no—
206#2367—111no—
207#2092—111no—
208#2055—111no—
209#2042—111no—
210#2015D1111yescharacteristic
211#1969—111no—
212#1927—111no—
213#1927—111no—
214#1921—111no—
215#1916—111no—
216#1878—111no—
217#1877—111no—
218#1805—111no—
219C4×#102—111no—
220C23×C11—22no—
221C23×C11—41no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11C22×D411yescharacteristic
228Q8×C11—22no—
229Q8×C11—22no—
230Q8×C11—41no—
231Q8×C11—41no—
232Q8×C11—41no—
233Q8×C11—41no—
234Q8×C11—41no—
235Q8×C11—41no—
236D4×C11—22no—
237D4×C11—22no—
238D4×C11—41no—
239D4×C11—41no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—22no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
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×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11H(5,𝔽2)11yescharacteristic
260C2×C4×C11H(5,𝔽2)11yescharacteristic
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—22no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—41no—
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—84no—
285C2×Dic11#13512yes—
286C8×C11—22no—
287C8×C11—41no—
288C11⋊C8—41no—
289C11⋊C8—41no—
290C22×Q16C2×D1111yescharacteristic
291C22×SD16C2×D1111yescharacteristic
292C2×#124C2×D1111yescharacteristic
293C2×C4×Q8—111no—
294C2×C4×D4—111no—
295C2×#107—111no—
296C2×#106—111no—
297C2×C4⋊C8—111no—
298C2×#103—111no—
299C2×#103—111no—
300C2×#103—111no—
301C2×#103—111no—
302C2×#103C2×D1111yescharacteristic
303C2×#102—111no—
304C2×#102—111no—
305C2×#102C2×D1111yescharacteristic
306C2×C4×C8—111no—
307#401—221no—
308#400—221no—
309#391—111no—
310#391—111no—
311#391—111no—
312#391C2×D1111yescharacteristic
313#390—111no—
314#389—111no—
315#388—221no—
316#388—221no—
317#387—221no—
318#385—221no—
319#383—221no—
320#382—111no—
321C4×C4⋊C4—111no—
322C4×C4⋊C4—111no—
323C4×C4⋊C4—111no—
324C4×C22⋊C4—221no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340—111no—
329#336—111no—
330#336—111no—
331#336—111no—
332#336C2×D1111yescharacteristic
333C22×C11—42no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11—81no—
337C22×C11—81no—
338C22×C11—81no—
339C22×C11—81no—
340C22×C11#52511yescharacteristic
341C22×C11#54611yescharacteristic
342C22×C11#55011yescharacteristic
343C22×C11C2×#13511yescharacteristic
344C22×C11#57511yescharacteristic
345C22×C11#57711yescharacteristic
346C22×C11#57811yescharacteristic
347C4×C11—41no—
348C4×C11—41no—
349C4×C11—42no—
350C4×C11—81no—
351C4×C11—81no—
352C4×C11#52911yescharacteristic
353C4×C11#53811yescharacteristic
354C4×C11#55111yescharacteristic
355C4×C11#55311yescharacteristic
356Dic11—22no—
357Dic11—41no—
358Dic11—42no—
359Dic11—41no—
360Dic11—41no—
361Dic11—81no—
362Dic11—81no—
363Dic11—81no—
364C22×Q8C22×D1111yescharacteristic
365C22×Q8C22×D1111yescharacteristic
366C22×D4C22×D1111yescharacteristic
367C23×C4—221no—
368C2×Q16—22no—
369C2×Q16—22no—
370C2×Q16—41no—
371C2×SD16—22no—
372C2×SD16—41no—
373C2×SD16—41no—
374C22×C8—111no—
375C22×C8—111no—
376C22×C8C22×D1111yescharacteristic
377C22×C8C22×D1111yescharacteristic
378#124—22no—
379#124—22no—
380C4×Q8—222no—
381C4×Q8—441no—
382C4×D4—222no—
383C4×D4—441no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4C22×D1111yescharacteristic
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—221no—
396C2×C22⋊C4—221no—
397C2×C22⋊C4—221no—
398C2×C42—111no—
399C2×C42—111no—
400C2×C42—221no—
401C2×C42—221no—
402C2×C42—221no—
403C2×C42C22×D1111yescharacteristic
404#107—222no—
405#106—441no—
406C4⋊C8—441no—
407#103—41no—
408#103—222no—
409#103—222no—
410#103—441no—
411#103—441no—
412#102—22no—
413#102—222no—
414#102—441no—
415C4×C8—441no—
416#95—21no—
417#95—21no—
418#95—111no—
419#95—111no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95—221no—
429#95—221no—
430#95—221no—
431C2×C11—82no—
432C2×C11#246711yescharacteristic
433C2×C11#310211yescharacteristic
434C2×C11#312011yescharacteristic
435C2×C11#329611yescharacteristic
436C2×C11#331311yescharacteristic
437C2×C11#339311yescharacteristic
438C2×C11#340111yescharacteristic
439C24—21no—
440C2×Q8—21no—
441C2×Q8—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#434112yes—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4#434112yes—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—111no—
462C22×C4—111no—
463C22×C4—111no—
464C22×C4—111no—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—442no—
470C22×C4—442no—
471C22×C4—881no—
472C22×C4D4×D1111yescharacteristic
473C22×C4D4×D1111yescharacteristic
474C22×C4C23×D1111yescharacteristic
475Q16—44no—
476SD16—44no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8#434112yes—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—112no—
492C4⋊C4—222no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—441no—
501C4⋊C4—442no—
502C4⋊C4—442no—
503C22⋊C4—24no—
504C22⋊C4—24no—
505C22⋊C4—442no—
506C22⋊C4—442no—
507C22⋊C4—881no—
508C42—21no—
509C42—21no—
510C42—221no—
511C42—221no—
512C42—221no—
513C42—221no—
514C42—442no—
515C42—442no—
516C42—881no—
517C11#2707011yescharacteristic, complemented, Sylow
518C23—22no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23C2×D4×D1111yescharacteristic
526Q8—22no—
527Q8—22no—
528Q8—41no—
529Q8—41no—
530Q8—41no—
531Q8—41no—
532Q8—41no—
533Q8—41no—
534D4—22no—
535D4—22no—
536D4—41no—
537D4—41no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—112no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—222no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—884no—
578C2×C4C2×#434111yescharacteristic
579C2×C4C2×#434111yescharacteristic
580C2×C4C2×#434111yescharacteristic
581C2×C4#6703711yescharacteristic
582C2×C4#6703711yescharacteristic
583C2×C4#41×D1111yescharacteristic
584C8—22no—
585C8—41no—
586C8—441no—
587C8—441no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22#1062311711yescharacteristic
596C22#1062314311yescharacteristic
597C22#1062324911yescharacteristic
598C22D11×#13511yescharacteristic
599C22#1062330211yescharacteristic
600C22#1062330811yescharacteristic
601C22#1062330911yescharacteristic
602C4—42no—
603C4—41no—
604C4—41no—
605C4—81no—
606C4—81no—
607C4—222no—
608C4—441no—
609C4—441no—
610C4—441no—
611C4—442no—
612C4—881no—
613C4—881no—
614C4—881no—
615C4#1062311811yescharacteristic
616C4#1062312411yescharacteristic
617C4#1062313111yescharacteristic
618C4#1062313211yescharacteristic
619C2—82no—
620C2#1307266211yescharacteristic
621C2#1307863511yescharacteristic
622C2#1307883111yescharacteristic
623C2#1308045811yescharacteristic
624C2#1308068911yescharacteristic
625C2#1308160111yescharacteristic
626C2#1308168111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2015C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2015D11
hypocenterC11#27070
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. #13073222C2semidirect
6. #13069478C2semidirect
7. #13069253C2semidirect
8. #13069247C2semidirect
9. #13069209C2semidirect
10. #13069172C2semidirect
11. #13068959C2semidirect
13. #13068629C2semidirect
517. C11#27070semidirect

Maximal subgroups

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

subgroupindex
#130732222
#130716912
#130701352
#130699292
#130698522
#130694782
#130692532
#130692472
#130692092
#130691722
#130689592
#130689522
#130686292
#102×Dic112
C11×#20152
#2707011