Finite Group Databasebeta

← #14821925

Subgroups — #14821925

Order 2816.

782 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072955C211yesmaximal, characteristic, complemented
2#13071659C211yesmaximal, characteristic
3#13069803C211yesmaximal, characteristic
4#13069762C211yesmaximal, characteristic, complemented
5#13069616C211yesmaximal, characteristic
6#13069571C211yesmaximal, characteristic, complemented
7#13069289C211yesmaximal, characteristic, complemented
8#13069247C211yesmaximal, characteristic, complemented
9#13069221C211yesmaximal, characteristic, complemented
10#13069199C211yesmaximal, characteristic, complemented
11#13068952C211yesmaximal, characteristic, complemented
12#13068925C211yesmaximal, characteristic, complemented
13#13068710C211yesmaximal, characteristic, complemented
14#102×Dic11C211yesmaximal, characteristic, complemented
15C11×#2055C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C2×#66999C2211yescharacteristic
18C2×#66991C2211yescharacteristic
19C2×D4×Dic11C2211yescharacteristic
20C2×#66945C2211yescharacteristic
21C2×#66923C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C11×#391C2211yescharacteristic
26C11×#390C2211yescharacteristic
27#10622843C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×C8×Dic11C2211yescharacteristic
35#10622600C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37#10622586C2211yescharacteristic
38C2×#66872C2211yescharacteristic
39#10622571—21no—
40#10622570—21no—
41#10622558—21no—
42C22⋊C4×Dic11—21no—
43C4×(C2×D11)⋊C4C2211yescharacteristic
44C4×C4⋊Dic11C2211yescharacteristic
45#10622288—21no—
46#10622282—21no—
47#10622271—21no—
48#10622263—21no—
49C11×#340C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C22×C22⋊D11—21no—
62C23×Dic11—21no—
63C22×C4×D11C2311yescharacteristic
64C2×C11×SD16—22no—
65C2×C11×SD16—41no—
66C2×C11×SD16—41no—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C42×C11C2311yescharacteristic
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76#66999—22no—
77#66999—41no—
78#66991—22no—
79#66991—22no—
80D4×Dic11—22no—
81D4×Dic11—41no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4D411yescharacteristic
86C2×(C2×D11)⋊C4D411yescharacteristic
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×Dic11⋊C4—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101#66945—22no—
102#66945—41no—
103#66923—22no—
104#66923—41no—
105C11×C4⋊C8—41no—
106C11×#103—41no—
107C11×#102—22no—
108C11×#95—21no—
109C11×#95—21no—
110#66899—22no—
111#66899—22no—
112#66896—22no—
113#66896—41no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95D411yescharacteristic
121C11⋊#95D411yescharacteristic
122(C2×D11)⋊C8—41no—
123(C2×D11)⋊C8—41no—
124C8×Dic11—41no—
125#66872—22no—
126#26728—111nomaximal, Sylow
127C24×C11—21no—
128C23×D11C2×D411yescharacteristic
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×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11#4112yes—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C2×C22⋊D11—24no—
148C2×C22⋊D11—81no—
149C2×C22⋊D11—81no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—42no—
155C22×Dic11—42no—
156C22×Dic11—81no—
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C11×SD16—44no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C22⋊C4—42no—
178C11×C22⋊C4—81no—
179C42×C11—21no—
180C42×C11—21no—
181C22⋊Dic11—24no—
182C22⋊Dic11—42no—
183(C2×D11)⋊C4—22no—
184(C2×D11)⋊C4—41no—
185(C2×D11)⋊C4—42no—
186(C2×D11)⋊C4—42no—
187(C2×D11)⋊C4—42no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11#4112yes—
194C4⋊Dic11#4112yes—
195C4⋊Dic11#4112yes—
196Dic11⋊C4—42no—
197Dic11⋊C4—42no—
198Dic11⋊C4—42no—
199Dic11⋊C4—81no—
200C4×Dic11—21no—
201C4×Dic11—21no—
202C4×Dic11—42no—
203C4×Dic11—42no—
204C4×Dic11—81no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211#2489—111no—
212#2363—111no—
213#2055D1111yescharacteristic, complemented
214#2034—111no—
215#2025—111no—
216#2000—111no—
217#1989—111no—
218#1933—111no—
219#1927—111no—
220#1923—111no—
221#1920—111no—
222#1877—111no—
223#1873—111no—
224#1825—111no—
225C4×#102—111no—
226C23×C11—22no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11C22×D411yescharacteristic
234C22×D11—21no—
235C22×D11—21no—
236C22×D11—21no—
237C22×D11—21no—
238C22×D11—21no—
239C22×D11—21no—
240C22×D11—21no—
241Q8×C11—41no—
242Q8×C11—41no—
243Q8×C11—41no—
244Q8×C11—41no—
245D4×C11—22no—
246D4×C11—22no—
247D4×C11—41no—
248D4×C11—41no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
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×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11H(5,𝔽2)11yescharacteristic
269C2×C4×C11H(5,𝔽2)11yescharacteristic
270C22⋊D11—84no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—22no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—84no—
292C2×Dic11#13512yes—
293C4×D11—41no—
294C4×D11—41no—
295C4×D11—41no—
296C4×D11—41no—
297C8×C11—41no—
298C8×C11—41no—
299C11⋊C8—41no—
300C11⋊C8—41no—
301C22×SD16C2×D1111yescharacteristic
302C2×#125—111no—
303C2×C22⋊Q8—111no—
304C2×#121—111no—
305C2×C4×D4—111no—
306C2×#117—111no—
307C2×#106—111no—
308C2×C4⋊C8C2×D1111yescharacteristic
309C2×#103—111no—
310C2×#103—111no—
311C2×#103C2×D1111yescharacteristic
312C2×#102—111no—
313C2×#102—111no—
314C2×#102C2×D1111yescharacteristic
315C2×C22⋊C8—111no—
316C2×C22⋊C8—111no—
317C2×C4×C8—111no—
318#400—221no—
319#397—221no—
320#391—111no—
321#391C2×D1111yescharacteristic
322#390—221no—
323#390C2×D1111yescharacteristic
324#389—111no—
325#388—221no—
326#388—221no—
327#386—221no—
328#382—221no—
329#380—111no—
330C4×C4⋊C4—111no—
331C4×C4⋊C4—111no—
332C4×C22⋊C4—111no—
333C4×C22⋊C4—221no—
334#340—111no—
335#340—111no—
336#340—111no—
337#340—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340C2×D1111yescharacteristic
342#336—111no—
343#336—111no—
344C22×C11—42no—
345C22×C11—42no—
346C22×C11—42no—
347C22×C11—81no—
348C22×C11—81no—
349C22×C11—81no—
350C22×C11—81no—
351C22×C11#52511yescharacteristic
352C22×C11#54611yescharacteristic
353C22×C11#54611yescharacteristic
354C22×C11C2×#13511yescharacteristic
355C22×C11#57511yescharacteristic
356C22×C11#57711yescharacteristic
357C22×C11#57711yescharacteristic
358C2×D11—41no—
359C2×D11—41no—
360C2×D11—41no—
361C2×D11—41no—
362C2×D11—41no—
363C2×D11—41no—
364C2×D11—41no—
365C4×C11—41no—
366C4×C11—41no—
367C4×C11—81no—
368C4×C11—81no—
369C4×C11—81no—
370C4×C11#52911yescharacteristic
371C4×C11#53811yescharacteristic
372C4×C11#55511yescharacteristic
373C4×C11#55911yescharacteristic
374Dic11—22no—
375Dic11—42no—
376Dic11—41no—
377Dic11—42no—
378Dic11—42no—
379Dic11—41no—
380Dic11—81no—
381C22×Q8C22×D1111yescharacteristic
382C22×D4—221no—
383C22×D4C22×D1111yescharacteristic
384C23×C4—111no—
385C23×C4—221no—
386C2×SD16—22no—
387C2×SD16—41no—
388C2×SD16—41no—
389C22×C8—111no—
390C22×C8—111no—
391C22×C8C22×D1111yescharacteristic
392C22×C8C22×D1111yescharacteristic
393#125—222no—
394#125—441no—
395C22⋊Q8—222no—
396C22⋊Q8—441no—
397#121—222no—
398#121—222no—
399C4×D4—222no—
400C4×D4—441no—
401#117—222no—
402#117—441no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4C22×D1111yescharacteristic
412C2×C4⋊C4C22×D1111yescharacteristic
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—111no—
416C2×C22⋊C4—111no—
417C2×C22⋊C4—221no—
418C2×C22⋊C4—221no—
419C2×C22⋊C4—221no—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C42—111no—
423C2×C42—221no—
424C2×C42—221no—
425C2×C42—221no—
426C2×C42C22×D1111yescharacteristic
427#106—222no—
428C4⋊C8—41no—
429#103—41no—
430#103—222no—
431#103—222no—
432#102—22no—
433#102—222no—
434#102—441no—
435C22⋊C8—441no—
436C22⋊C8—441no—
437C4×C8—441no—
438#95—21no—
439#95—21no—
440#95—111no—
441#95—111no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448C2×C11—82no—
449C2×C11#245911yescharacteristic
450C2×C11#310211yescharacteristic
451C2×C11#312311yescharacteristic
452C2×C11#329611yescharacteristic
453C2×C11#330311yescharacteristic
454C2×C11#331711yescharacteristic
455C2×C11#332611yescharacteristic
456D11—81no—
457C24—21no—
458C24—111no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—224no—
471C2×D4—881no—
472C2×D4—881no—
473C2×D4#434112yes—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—111no—
478C22×C4—111no—
479C22×C4—111no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—442no—
491C22×C4—442no—
492C22×C4—881no—
493C22×C4D4×D1111yescharacteristic
494C22×C4D4×D1111yescharacteristic
495C22×C4C23×D1111yescharacteristic
496SD16—44no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—112no—
514C4⋊C4—112no—
515C4⋊C4—112no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—442no—
522C4⋊C4—442no—
523C4⋊C4—442no—
524C4⋊C4—881no—
525C22⋊C4—42no—
526C22⋊C4—81no—
527C22⋊C4—222no—
528C22⋊C4—224no—
529C22⋊C4—441no—
530C22⋊C4—442no—
531C22⋊C4—442no—
532C22⋊C4—442no—
533C22⋊C4—442no—
534C42—21no—
535C42—21no—
536C42—221no—
537C42—221no—
538C42—442no—
539C42—442no—
540C42—881no—
541C11#2672811yescharacteristic, complemented, Sylow
542C23—22no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—221no—
550C23—221no—
551C23—221no—
552C23—221no—
553C23—221no—
554C23—221no—
555C23—221no—
556C23C2×D4×D1111yescharacteristic
557Q8—41no—
558Q8—41no—
559Q8—41no—
560Q8—41no—
561D4—22no—
562D4—22no—
563D4—41no—
564D4—41no—
565D4—884no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—112no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—222no—
588C2×C4—222no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—222no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—884no—
607C2×C4C2×#434111yescharacteristic
608C2×C4#6703711yescharacteristic
609C2×C4#6703711yescharacteristic
610C2×C4#41×D1111yescharacteristic
611C2×C4#41×D1111yescharacteristic
612C2×C4#41×D1111yescharacteristic
613C8—41no—
614C8—41no—
615C8—441no—
616C8—441no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—81no—
621C22—81no—
622C22—81no—
623C22—81no—
624C22—441no—
625C22—441no—
626C22—441no—
627C22—441no—
628C22—441no—
629C22—441no—
630C22—441no—
631C22#1062313711yescharacteristic
632C22#1062314111yescharacteristic
633C22#1062314311yescharacteristic
634C22#1062329311yescharacteristic
635C22D11×#13511yescharacteristic
636C22#1062330411yescharacteristic
637C22#1062330911yescharacteristic
638C4—41no—
639C4—41no—
640C4—81no—
641C4—81no—
642C4—81no—
643C4—222no—
644C4—442no—
645C4—442no—
646C4—441no—
647C4—441no—
648C4—442no—
649C4—881no—
650C4#1062312411yescharacteristic
651C4#1062318011yescharacteristic
652C4#1062319511yescharacteristic
653C4#1062320111yescharacteristic
654C2—82no—
655C2—881no—
656C2#1307255411yescharacteristic
657C2#1307863111yescharacteristic
658C2#1307886611yescharacteristic
659C2#1308045811yescharacteristic
660C2#1308053911yescharacteristic
661C2#1308074911yescharacteristic
662C2#1308086411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2055C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
hypercenter#2055D11
hypocenterC11#26728
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2055

Complements

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

NH ≅ G/Ntype
1. #13072955C2semidirect
4. #13069762C2semidirect
6. #13069571C2semidirect
7. #13069289C2semidirect
8. #13069247C2semidirect
9. #13069221C2semidirect
10. #13069199C2semidirect
11. #13068952C2semidirect
12. #13068925C2semidirect
13. #13068710C2semidirect
14. #102×Dic11C2semidirect
15. C11×#2055C2semidirect
213. #2055D11semidirect
541. C11#26728semidirect

Maximal subgroups

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

subgroupindex
#130729552
#130716592
#130698032
#130697622
#130696162
#130695712
#130692892
#130692472
#130692212
#130691992
#130689522
#130689252
#130687102
#102×Dic112
C11×#20552
#2672811