Finite Group Databasebeta

← #14821841

Subgroups — #14821841

Order 2816.

848 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072993C211yesmaximal, characteristic, complemented
2#13071634C211yesmaximal, characteristic
3#13069934C211yesmaximal, characteristic, complemented
4#13069808C211yesmaximal, characteristic
5#13069749C211yesmaximal, characteristic, complemented
6#13069622C211yesmaximal, characteristic
7#13069293C211yesmaximal, characteristic, complemented
8#13069250C211yesmaximal, characteristic, complemented
9#13069221C211yesmaximal, characteristic, complemented
10#13069197C211yesmaximal, characteristic, complemented
11#13068951C211yesmaximal, characteristic, complemented
12#13068922C211yesmaximal, characteristic, complemented
13#13068701C211yesmaximal, characteristic, complemented
14#13068430C211yesmaximal, characteristic, complemented
15C11×#1987C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C22×#4314C2211yescharacteristic
18C2×#66950C2211yescharacteristic
19C2×#66948C2211yescharacteristic
20C2×#66946C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×C4×D44—21no—
23C2×C11×C4⋊C8C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25#10622844—21no—
26#10622843—21no—
27C2×#66885C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×#66880C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32#10622603—21no—
33#10622600C2211yescharacteristic
34#10622599—21no—
35#10622598C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37#10622587C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43#10622553—21no—
44#10622552C2211yescharacteristic
45C4×(C2×D11)⋊C4C2211yescharacteristic
46#10622542C2211yescharacteristic
47#10622281—21no—
48#10622278—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11—21no—
60C22×D44—21no—
61C22×D44C2311yescharacteristic
62C22×C4×D11—21no—
63C22×C4×D11—21no—
64C22×C4×D11C2311yescharacteristic
65C22×Dic22C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×C4⋊Q8—22no—
69C11×C4⋊Q8—41no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C42×C11—21no—
76C2×C42×C11C2311yescharacteristic
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4D411yescharacteristic
84C2×(C2×D11)⋊C4D411yescharacteristic
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×Dic11⋊C4—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C2×#4314—22no—
95C2×#4314—41no—
96C2×#4314—41no—
97#66950—22no—
98#66950—41no—
99#66948—22no—
100#66948—22no—
101#66946—22no—
102#66946—41no—
103C4⋊C4×D11—22no—
104C4⋊C4×D11—41no—
105C4×D44—44no—
106C11×C4⋊C8—41no—
107C11×#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95D411yescharacteristic
116C11⋊#95D411yescharacteristic
117#66885—22no—
118(C2×D11)⋊C8—41no—
119(C2×D11)⋊C8—41no—
120#66880—41no—
121C8×Dic11—41no—
122#66874—22no—
123#66874—22no—
124#66873—22no—
125#66873—41no—
126#66872—22no—
127#26722—111nomaximal, Sylow
128C23×D11—21no—
129C23×D11C2×D411yescharacteristic
130C2×Q8×C11—42no—
131C2×Q8×C11—42no—
132C2×Q8×C11—81no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11C2×D411yescharacteristic
144C22×Dic11C2×D411yescharacteristic
145C22×Dic11C2×D411yescharacteristic
146C2×D44—24no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—42no—
153C2×D44—42no—
154C2×D44#4112yes—
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—42no—
162C2×C4×D11—42no—
163C2×C4×D11—42no—
164C2×C4×D11—42no—
165C2×C4×D11—81no—
166C2×C4×D11—81no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—42no—
185C11×C4⋊C4#4112yes—
186C11×C4⋊C4#4112yes—
187C11×C4⋊C4#4112yes—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—42no—
191(C2×D11)⋊C4—24no—
192(C2×D11)⋊C4—41no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—42no—
195(C2×D11)⋊C4—42no—
196(C2×D11)⋊C4—81no—
197(C2×D11)⋊C4—81no—
198(C2×D11)⋊C4SD1614yescomplemented
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—42no—
204C4⋊Dic11—42no—
205Dic11⋊C4—42no—
206C4×Dic11—21no—
207C4×Dic11—21no—
208C4×Dic11—81no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215#4314—44no—
216#2492—111no—
217#2361—111no—
218#2055—111no—
219#2034—111no—
220#2023—111no—
221#2000—111no—
222#1987D1111yescharacteristic, complemented
223#1933—111no—
224#1927—111no—
225#1923—111no—
226#1919—111no—
227#1877—111no—
228#1872—111no—
229#1823—111no—
230C4×#102—111no—
231C23×C11C22×D411yescharacteristic
232C22×D11—21no—
233C22×D11—21no—
234C22×D11—21no—
235C22×D11—21no—
236C22×D11—21no—
237C22×D11—21no—
238C22×D11—22no—
239C22×D11—41no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—41no—
245C22×D11C2×SD1612yes—
246Q8×C11—84no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11C2×SD1612yes—
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11H(5,𝔽2)11yescharacteristic
270C2×C4×C11H(5,𝔽2)11yescharacteristic
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11C2×SD1612yes—
289D44—22no—
290D44—22no—
291D44—48no—
292D44—41no—
293D44—41no—
294C4×D11—41no—
295C4×D11—41no—
296C4×D11—41no—
297C4×D11—41no—
298C4×D11—84no—
299C4×D11—84no—
300Dic22—41no—
301Dic22—41no—
302Dic22—41no—
303Dic22—41no—
304C8×C11—41no—
305C8×C11—41no—
306C11⋊C8—41no—
307C11⋊C8—41no—
308C22×SD16—111no—
309C2×C4⋊Q8C2×D1111yescharacteristic
310C2×C22⋊Q8—111no—
311C2×#121—111no—
312C2×C4×D4—111no—
313C2×C4×D4—221no—
314C22×C4⋊C4—111no—
315C2×#106—111no—
316C2×C4⋊C8C2×D1111yescharacteristic
317C2×#103—111no—
318C2×#103—111no—
319C2×#103—111no—
320C2×#102—111no—
321C2×#102—111no—
322C2×#102—111no—
323C2×C22⋊C8—111no—
324C2×C22⋊C8—111no—
325C2×C4×C8—111no—
326#400—221no—
327#393—221no—
328#391—111no—
329#391—111no—
330#391—221no—
331#390—111no—
332#389—111no—
333#388—221no—
334#388—221no—
335#386—221no—
336#385—221no—
337#380—111no—
338C4×C4⋊C4—111no—
339C4×C4⋊C4C2×D1111yescharacteristic
340C4×C22⋊C4—111no—
341#340—111no—
342#340—111no—
343#340—111no—
344#340—111no—
345#340C2×D1111yescharacteristic
346#340C2×D1111yescharacteristic
347#340C2×D1111yescharacteristic
348#340C2×D1111yescharacteristic
349#336—111no—
350#336—111no—
351C22×C11#52511yescharacteristic
352C22×C11#54611yescharacteristic
353C22×C11#54611yescharacteristic
354C22×C11C22×SD1611yescharacteristic
355C22×C11#57511yescharacteristic
356C22×C11#57611yescharacteristic
357C22×C11#57811yescharacteristic
358C2×D11—22no—
359C2×D11—22no—
360C2×D11—22no—
361C2×D11—41no—
362C2×D11—41no—
363C2×D11—41no—
364C2×D11—41no—
365C2×D11—42no—
366C2×D11—42no—
367C2×D11—42no—
368C2×D11—81no—
369C2×D11—81no—
370C2×D11—81no—
371C2×D11—81no—
372C4×C11—22no—
373C4×C11—42no—
374C4×C11—42no—
375C4×C11—41no—
376C4×C11—42no—
377C4×C11—81no—
378C4×C11#52911yescharacteristic
379C4×C11#53811yescharacteristic
380C4×C11#55511yescharacteristic
381C4×C11#55911yescharacteristic
382Dic11—22no—
383Dic11—41no—
384Dic11—41no—
385Dic11—81no—
386Dic11—81no—
387Dic11—81no—
388C22×Q8—21no—
389C22×Q8—111no—
390C22×D4—111no—
391C22×D4—221no—
392C23×C4—111no—
393C23×C4—221no—
394C23×C4—221no—
395C2×SD16—222no—
396C2×SD16—441no—
397C2×SD16—441no—
398C22×C8—111no—
399C22×C8—111no—
400C22×C8C22×D1111yescharacteristic
401C22×C8C22×D1111yescharacteristic
402C4⋊Q8—22no—
403C4⋊Q8—41no—
404C22⋊Q8—222no—
405C22⋊Q8—441no—
406#121—222no—
407#121—222no—
408C4×D4—222no—
409C4×D4—444no—
410C4×D4—441no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—222no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—441no—
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C4⋊C4C22×D1111yescharacteristic
421C2×C4⋊C4C22×D1111yescharacteristic
422C2×C4⋊C4C22×D1111yescharacteristic
423C2×C22⋊C4—111no—
424C2×C22⋊C4—111no—
425C2×C22⋊C4—221no—
426C2×C22⋊C4—221no—
427C2×C22⋊C4—221no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C42—21no—
432C2×C42—111no—
433C2×C42—221no—
434C2×C42C22×D1111yescharacteristic
435#106—222no—
436C4⋊C8—41no—
437#103—222no—
438#103—222no—
439#103—441no—
440#102—222no—
441#102—222no—
442#102—441no—
443C22⋊C8—441no—
444C22⋊C8—441no—
445C4×C8—441no—
446#95—21no—
447#95—111no—
448#95—111no—
449#95—221no—
450#95—221no—
451#95—221no—
452#95—221no—
453#95—221no—
454#95—221no—
455#95—221no—
456C2×C11#245911yescharacteristic
457C2×C11#310111yescharacteristic
458C2×C11#312411yescharacteristic
459C2×C11#329511yescharacteristic
460C2×C11#329811yescharacteristic
461C2×C11#331311yescharacteristic
462C2×C11#332211yescharacteristic
463D11—42no—
464D11—82no—
465C24—111no—
466C24—221no—
467C2×Q8—42no—
468C2×Q8—42no—
469C2×Q8—81no—
470C2×Q8—221no—
471C2×Q8—221no—
472C2×Q8—221no—
473C2×Q8—221no—
474C2×Q8—221no—
475C2×Q8—221no—
476C2×D4—112no—
477C2×D4—224no—
478C2×D4—221no—
479C2×D4—221no—
480C2×D4—221no—
481C2×D4—221no—
482C2×D4—221no—
483C2×D4—442no—
484C2×D4—442no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—111no—
490C22×C4—111no—
491C22×C4—111no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—442no—
502C22×C4—442no—
503C22×C4—442no—
504C22×C4—442no—
505C22×C4—881no—
506C22×C4—881no—
507C22×C4D4×D1111yescharacteristic
508C22×C4D4×D1111yescharacteristic
509C22×C4C23×D1111yescharacteristic
510SD16—444no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—221no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—42no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—442no—
534C4⋊C4—442no—
535C4⋊C4—442no—
536C4⋊C4#433912yes—
537C4⋊C4#434312yes—
538C4⋊C4#434312yes—
539C22⋊C4—114no—
540C22⋊C4—224no—
541C22⋊C4—441no—
542C22⋊C4—442no—
543C22⋊C4—442no—
544C22⋊C4—442no—
545C22⋊C4—881no—
546C22⋊C4—881no—
547C42—21no—
548C42—21no—
549C42—42no—
550C42—221no—
551C42—221no—
552C42—881no—
553C11#2672211yescharacteristic, complemented, Sylow
554C23—112no—
555C23—221no—
556C23—221no—
557C23—221no—
558C23—221no—
559C23—221no—
560C23—221no—
561C23—222no—
562C23—441no—
563C23—441no—
564C23—441no—
565C23—441no—
566C23—441no—
567C23—441no—
568C23C2×D4×D1111yescharacteristic
569Q8—84no—
570Q8—441no—
571Q8—441no—
572Q8—441no—
573Q8—441no—
574D4—222no—
575D4—222no—
576D4—448no—
577D4—441no—
578D4—441no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—112no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—221no—
604C2×C4—221no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—884no—
619C2×C4—884no—
620C2×C4SD16×D1112yes—
621C2×C4C2×#433911yescharacteristic
622C2×C4#6703711yescharacteristic
623C2×C4C2×#434311yescharacteristic
624C2×C4C2×#434311yescharacteristic
625C2×C4#41×D1111yescharacteristic
626C2×C4#6704211yescharacteristic
627C8—41no—
628C8—41no—
629C8—441no—
630C8—441no—
631C22—222no—
632C22—222no—
633C22—222no—
634C22—441no—
635C22—441no—
636C22—441no—
637C22—441no—
638C22—442no—
639C22—442no—
640C22—442no—
641C22—881no—
642C22—881no—
643C22—881no—
644C22—881no—
645C22#1062302111yescharacteristic
646C22#1062315811yescharacteristic
647C22#1062316111yescharacteristic
648C22C2×SD16×D1111yescharacteristic
649C22#1062329711yescharacteristic
650C22#1062330411yescharacteristic
651C22#1062330511yescharacteristic
652C4—22no—
653C4—42no—
654C4—42no—
655C4—41no—
656C4—42no—
657C4—81no—
658C4—222no—
659C4—441no—
660C4—441no—
661C4—881no—
662C4—881no—
663C4—881no—
664C4#1062311111yescharacteristic
665C4#1062311611yescharacteristic
666C4#1062320911yescharacteristic
667C4#1062326511yescharacteristic
668C2—442no—
669C2—882no—
670C2#1307256011yescharacteristic
671C2#1307862611yescharacteristic
672C2#1307888511yescharacteristic
673C2#1308043711yescharacteristic
674C2#1308047711yescharacteristic
675C2#1308067911yescharacteristic
676C2#1308081311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1987C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
hypercenter#1987D11
hypocenterC11#26722
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1987

Complements

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

NH ≅ G/Ntype
1. #13072993C2semidirect
3. #13069934C2semidirect
5. #13069749C2semidirect
7. #13069293C2semidirect
8. #13069250C2semidirect
9. #13069221C2semidirect
10. #13069197C2semidirect
11. #13068951C2semidirect
12. #13068922C2semidirect
13. #13068701C2semidirect
14. #13068430C2semidirect
15. C11×#1987C2semidirect
198. (C2×D11)⋊C4SD16semidirect
222. #1987D11semidirect
553. C11#26722semidirect

Maximal subgroups

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

subgroupindex
#130729932
#130716342
#130699342
#130698082
#130697492
#130696222
#130692932
#130692502
#130692212
#130691972
#130689512
#130689222
#130687012
#130684302
C11×#19872
#2672211