Finite Group Databasebeta

← #14775426

Subgroups — #14775426

Order 2816.

730 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078527C211yesmaximal, characteristic
2#13077338C211yesmaximal, characteristic
3#13077271C211yesmaximal, characteristic, complemented
4#13069369C211yesmaximal, characteristic, complemented
5#13069317C211yesmaximal, characteristic, complemented
6#13069266C211yesmaximal, characteristic, complemented
7#13069215C211yesmaximal, characteristic, complemented
8#13069214C211yesmaximal, characteristic, complemented
9#13069061C211yesmaximal, characteristic
10#13068891C211yesmaximal, characteristic, complemented
11#13068822C211yesmaximal, characteristic, complemented
12#13068494C211yesmaximal, characteristic, complemented
13#13068385C211yesmaximal, characteristic, complemented
14#13068324C211yesmaximal, characteristic, complemented
15C11×#1765C211yesmaximal, characteristic, complemented
16C2×C11×#131C2211yescharacteristic
17#10623359C2211yescharacteristic
18C2×M16×D11C2211yescharacteristic
19D11×#117C2211yescharacteristic
20C2×#66925C2211yescharacteristic
21C2×C11×#104C2211yescharacteristic
22C11×#416C2211yescharacteristic
23C11×#405C2211yescharacteristic
24C2×C11×#97C2211yescharacteristic
25C2×#66901C2211yescharacteristic
26#10622847C2211yescharacteristic
27#10622846C2211yescharacteristic
28#10622741—21no—
29#10622740—21no—
30#10622739C2211yescharacteristic
31C2×#66886C2211yescharacteristic
32#10622735C2211yescharacteristic
33#10622732C2211yescharacteristic
34#10622724—21no—
35C8×C22⋊D11—21no—
36C2×(C2×D11)⋊C8C2211yescharacteristic
37C2×(C2×D11)⋊C8C2211yescharacteristic
38C2×#66883C2211yescharacteristic
39#10622719C2211yescharacteristic
40#10622715C2211yescharacteristic
41#10622715C2211yescharacteristic
42#10622611C2211yescharacteristic
43#10622610C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622428C411yescharacteristic, complemented
46#10622427C411yescharacteristic, complemented
47#10622422C411yescharacteristic, complemented
48#10622418C411yescharacteristic, complemented
49#10622397C411yescharacteristic, complemented
50#10622392C411yescharacteristic, complemented
51#10622390C411yescharacteristic, complemented
52#10622387C411yescharacteristic, complemented
53#10622322—21no—
54#10622318—21no—
55#10622303—21no—
56#10622298—21no—
57C11×#341C2211yescharacteristic
58C11×#339C2211yescharacteristic
59#10622196C2211yescharacteristic
60#10622193C2211yescharacteristic
61#10622193C2211yescharacteristic
62#10622188C2211yescharacteristic
63#10622188C2211yescharacteristic
64#10622170C2211yescharacteristic
65#10622161C2211yescharacteristic
66#10622161C2211yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C22×C4×D11C2311yescharacteristic
69C11×#131—22no—
70C11×#131—41no—
71C2×C11×M16—21no—
72C2×C11×M16C2311yescharacteristic
73C2×C11×M16C2311yescharacteristic
74C22×C8×C11—21no—
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C11×#117C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79#66999C2×C411yescharacteristic
80#66999C2×C411yescharacteristic
81#66991C2×C411yescharacteristic
82#66991C2×C411yescharacteristic
83#66990—21no—
84#66988—21no—
85C4×C22⋊D11—21no—
86C4×C22⋊D11—21no—
87C2×(C2×D11)⋊C4—21no—
88#66979C2311yescharacteristic
89#66979C2311yescharacteristic
90C2×Dic11⋊C4—21no—
91C2×C4×Dic11C2311yescharacteristic
92C2×#4318C2311yescharacteristic
93C2×#4318C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96M16×D11—22no—
97M16×D11—41no—
98C2×#4313—21no—
99C2×C8×D11—21no—
100#66945C2×C411yescharacteristic
101#66945C2×C411yescharacteristic
102C4⋊C4×D11C2×C411yescharacteristic
103C4⋊C4×D11C2×C411yescharacteristic
104C22⋊C4×D11—21no—
105#66930—21no—
106#66925—21no—
107#66925—22no—
108#66925—41no—
109C42×D11—21no—
110C11×#104—22no—
111C11×#103C2×C411yescharacteristic
112C11×#103C2×C411yescharacteristic
113C11×#102C2×C411yescharacteristic
114C11×#102C2×C411yescharacteristic
115C11×#97—21no—
116C11×#97—41no—
117C4×C8×C11—21no—
118#66901—41no—
119#66899C2×C411yescharacteristic
120#66899C2×C411yescharacteristic
121#66896C2×C411yescharacteristic
122#66896C2×C411yescharacteristic
123C22⋊(C11⋊C8)—21no—
124C22⋊(C11⋊C8)—21no—
125#66886—22no—
126(C2×D11)⋊C8—21no—
127(C2×D11)⋊C8—21no—
128(C2×D11)⋊C8C2×C411yescharacteristic
129(C2×D11)⋊C8C2×C411yescharacteristic
130(C2×D11)⋊C8C2×C411yescharacteristic
131(C2×D11)⋊C8C2×C411yescharacteristic
132(C2×D11)⋊C8D411yescharacteristic
133(C2×D11)⋊C8D411yescharacteristic
134(C2×D11)⋊C8D411yescharacteristic
135(C2×D11)⋊C8D411yescharacteristic
136#66883—41no—
137#66882C2×C411yescharacteristic
138#66882C2×C411yescharacteristic
139#66881C2×C411yescharacteristic
140#66881C2×C411yescharacteristic
141#66879—21no—
142Dic11⋊C8—21no—
143Dic11⋊C8—21no—
144Dic11⋊C8—21no—
145Dic11⋊C8—21no—
146Dic11⋊C8—21no—
147Dic11⋊C8—21no—
148C8×Dic11—21no—
149#66872C2×C411yescharacteristic
150#66872C2×C411yescharacteristic
151#66871C2×C411yescharacteristic
152#66871C2×C411yescharacteristic
153#66867—21no—
154C4×C11⋊C8—22no—
155C4×C11⋊C8—21no—
156#22951—111nomaximal, Sylow
157C23×D11#4111yescharacteristic
158C11×#41—21no—
159C11×#41—21no—
160C11×#41—21no—
161C11×#41—21no—
162C2×Q8×C11C22×C411yescharacteristic
163C2×D4×C11—21no—
164C2×D4×C11C22×C411yescharacteristic
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11C2411yescharacteristic
168C2×C22⋊D11—21no—
169C2×C22⋊D11—21no—
170C22×Dic11—21no—
171C22×Dic11#4111yescharacteristic
172C2×C4×D11—21no—
173C2×C4×D11—21no—
174C2×C4×D11—21no—
175C2×C4×D11—21no—
176C2×C4×D11—21no—
177C2×C4×D11—21no—
178C2×C4×D11C22×C411yescharacteristic
179C2×C4×D11C22×C411yescharacteristic
180C2×C4×D11C2×D411yescharacteristic
181C2×C4×D11C2×D411yescharacteristic
182C11×M16—21no—
183C11×M16—21no—
184C11×M16—21no—
185C11×M16—42no—
186C11×M16#4112yes—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—42no—
194C2×C8×C11C22×C411yescharacteristic
195C2×C8×C11C22×C411yescharacteristic
196C2×C8×C11C2×D411yescharacteristic
197C2×C8×C11C2×D411yescharacteristic
198C11×C4⋊C4C22×C411yescharacteristic
199C11×C4⋊C4C22×C411yescharacteristic
200C11×C22⋊C4—21no—
201C42×C11—21no—
202C42×C11—21no—
203C42×C11#4112yes—
204C22⋊Dic11—21no—
205C22⋊Dic11—21no—
206C22⋊Dic11—21no—
207C22⋊Dic11—21no—
208(C2×D11)⋊C4—21no—
209(C2×D11)⋊C4—21no—
210(C2×D11)⋊C4—21no—
211(C2×D11)⋊C4—21no—
212(C2×D11)⋊C4—42no—
213C4⋊Dic11C22×C411yescharacteristic
214C4⋊Dic11C22×C411yescharacteristic
215C4⋊Dic11C22×C411yescharacteristic
216C4⋊Dic11C22×C411yescharacteristic
217Dic11⋊C4—21no—
218Dic11⋊C4—21no—
219Dic11⋊C4—21no—
220Dic11⋊C4—21no—
221Dic11⋊C4—42no—
222C4×Dic11—21no—
223C4×Dic11—21no—
224C4×Dic11—21no—
225C4×Dic11—21no—
226C4×Dic11—21no—
227C4×Dic11—21no—
228#4318—21no—
229#4318—21no—
230#4318—21no—
231#4318—21no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8C22×C411yescharacteristic
239C2×C11⋊C8C22×C411yescharacteristic
240C2×C11⋊C8C2×D411yescharacteristic
241C2×C11⋊C8C2×D411yescharacteristic
242#4313—42no—
243C8×D11—42no—
244#3091—111no—
245#2933—111no—
246#2924—111no—
247#1946—111no—
248#1937—111no—
249#1929—111no—
250#1922—111no—
251#1922—111no—
252#1897—111no—
253#1866—111no—
254#1855—111no—
255#1772—111no—
256#1765D1111yescharacteristic, complemented
257#1750—111no—
258#1733—111no—
259C23×C11—21no—
260C23×C11C2×#4111yescharacteristic
261C22×D11—21no—
262C22×D11—21no—
263C22×D11—41no—
264C22×D11—41no—
265C22×D11C4×D411yescharacteristic
266C22×D11C4×D411yescharacteristic
267Q8×C11—21no—
268Q8×C11—21no—
269D4×C11—21no—
270D4×C11—21no—
271D4×C11—41no—
272D4×C11—41no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—22no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11C23×C411yescharacteristic
282C2×C4×C11C22×D411yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11C2×#4111yescharacteristic
285C2×C4×C11H(5,𝔽2)11yescharacteristic
286C2×C4×C112−1+411yescharacteristic
287C22⋊D11—42no—
288C22⋊D11—81no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—21no—
294C2×Dic11—21no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11C4×D411yescharacteristic
299C2×Dic11C4×D411yescharacteristic
300C4×D11—21no—
301C4×D11—21no—
302C4×D11—21no—
303C4×D11—21no—
304C4×D11—21no—
305C4×D11—21no—
306C4×D11—21no—
307C4×D11—21no—
308C4×D11—42no—
309C4×D11—81no—
310C8×C11—21no—
311C8×C11—21no—
312C8×C11—22no—
313C8×C11—21no—
314C8×C11—21no—
315C8×C11—41no—
316C11⋊C8—21no—
317C11⋊C8—21no—
318C11⋊C8—21no—
319C11⋊C8—21no—
320C11⋊C8—41no—
321C11⋊C8—41no—
322C2×#131C2×D1111yescharacteristic
323C22×M16—111no—
324#525—111no—
325C2×#117—111no—
326C2×#117—111no—
327#485—111no—
328#485—111no—
329#484—111no—
330#483—111no—
331#482—111no—
332#482—111no—
333#481—111no—
334#480—111no—
335#436—221no—
336#435—221no—
337#435—221no—
338C8×D4—221no—
339#433—221no—
340#433—221no—
341#432—221no—
342#431—221no—
343C2×#108—111no—
344C2×#108—111no—
345#427—111no—
346#427—111no—
347#424—111no—
348#424—111no—
349#424—111no—
350C2×#104—111no—
351C2×#104C2×D1111yescharacteristic
352#416—111no—
353#416C2×D1111yescharacteristic
354#408—111no—
355#407—111no—
356C2×C22⋊C8—111no—
357C2×C22⋊C8—111no—
358#405—111no—
359#405—111no—
360#405C2×D1111yescharacteristic
361C2×#97C2×D1111yescharacteristic
362C2×C4×C8—111no—
363#341—111no—
364#341C2×D1111yescharacteristic
365#339—111no—
366#339—111no—
367#339—111no—
368#339—111no—
369#339—111no—
370#339C2×D1111yescharacteristic
371#336—111no—
372#336—111no—
373C22×C11—21no—
374C22×C11—21no—
375C22×C11—41no—
376C22×C11—41no—
377C22×C11—41no—
378C22×C11C2×C4×D411yescharacteristic
379C22×C11#55111yescharacteristic
380C22×C11#55211yescharacteristic
381C2×D11—21no—
382C2×D11—21no—
383C2×D11—21no—
384C2×D11—21no—
385C2×D11—21no—
386C2×D11—21no—
387C2×D11—81no—
388C2×D11—81no—
389C4×C11—42no—
390C4×C11—41no—
391C4×C11—41no—
392C4×C11—41no—
393C4×C11C4×#4111yescharacteristic
394C4×C11#52011yescharacteristic
395C4×C11#54611yescharacteristic
396C4×C11#54711yescharacteristic
397Dic11—21no—
398Dic11—21no—
399Dic11—41no—
400Dic11—41no—
401Dic11—41no—
402Dic11—41no—
403Dic11—81no—
404C2×#41C22×D1111yescharacteristic
405C23×C4—111no—
406#131—22no—
407#131—41no—
408C2×M16—21no—
409C2×M16—111no—
410C2×M16—111no—
411C2×M16—221no—
412C2×M16—222no—
413C2×M16—441no—
414C2×M16C22×D1111yescharacteristic
415C2×M16C22×D1111yescharacteristic
416C22×C8—21no—
417C22×C8—111no—
418C22×C8—111no—
419C22×C8—221no—
420C22×C8C22×D1111yescharacteristic
421C22×C8C22×D1111yescharacteristic
422#123—221no—
423C22⋊Q8—111no—
424C22⋊Q8—111no—
425#121—111no—
426#121—111no—
427#120—221no—
428C4×D4—221no—
429C4×D4—221no—
430#117—111no—
431#117—111no—
432#117—111no—
433#117—111no—
434#117—221no—
435#117—221no—
436#117—222no—
437#117—441no—
438#117C22×D1111yescharacteristic
439C2×C4⋊C4—111no—
440C2×C4⋊C4—111no—
441C2×C4⋊C4—221no—
442C2×C22⋊C4—221no—
443C2×C22⋊C4—221no—
444C2×C42—111no—
445C2×C42—221no—
446C2×C42C22×D1111yescharacteristic
447#108—222no—
448#108—441no—
449#107—111no—
450#107—111no—
451#107—111no—
452#107—111no—
453#106—111no—
454#106—111no—
455#106—111no—
456#106—111no—
457C4⋊C8—221no—
458C4⋊C8—221no—
459C4⋊C8—221no—
460C4⋊C8—221no—
461C4⋊C8—221no—
462C4⋊C8—221no—
463#104—22no—
464#104—441no—
465#103—111no—
466#103—111no—
467#103C4×D1111yescharacteristic
468#103C4×D1111yescharacteristic
469#102—111no—
470#102—111no—
471#102C4×D1111yescharacteristic
472#102C4×D1111yescharacteristic
473C22⋊C8—111no—
474C22⋊C8—111no—
475C22⋊C8—111no—
476C22⋊C8—111no—
477C22⋊C8—111no—
478C22⋊C8—111no—
479C22⋊C8—111no—
480C22⋊C8—111no—
481C22⋊C8—221no—
482C22⋊C8—221no—
483C22⋊C8—221no—
484C22⋊C8—221no—
485#97—21no—
486#97—41no—
487#97—221no—
488#97—221no—
489C4×C8—21no—
490C4×C8—221no—
491C4×C8—221no—
492C4×C8—222no—
493C2×C11—21no—
494C2×C11—21no—
495C2×C11—81no—
496C2×C11#235911yescharacteristic
497C2×C11#295511yescharacteristic
498C2×C11#295711yescharacteristic
499D11—41no—
500D11—41no—
501C24—111no—
502#41—21no—
503#41—21no—
504#41—21no—
505#41—21no—
506C2×Q8C2×C4×D1111yescharacteristic
507C2×D4—21no—
508C2×D4—221no—
509C2×D4—221no—
510C2×D4C2×C4×D1111yescharacteristic
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—111no—
514C22×C4—111no—
515C22×C4—111no—
516C22×C4—111no—
517C22×C4—111no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4—221no—
521C22×C4—221no—
522C22×C4—221no—
523C22×C4—221no—
524C22×C4—221no—
525C22×C4C23×D1111yescharacteristic
526M16—21no—
527M16—21no—
528M16—21no—
529M16—42no—
530M16—221no—
531M16—221no—
532M16—221no—
533M16—221no—
534M16—442no—
535M16#433912yes—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—42no—
543C2×C8—111no—
544C2×C8—111no—
545C2×C8—111no—
546C2×C8—111no—
547C2×C8—221no—
548C2×C8—221no—
549C2×C8—221no—
550C2×C8—221no—
551C2×C8—221no—
552C2×C8—221no—
553C2×C8—442no—
554C2×C8C2×C4×D1111yescharacteristic
555C2×C8C2×C4×D1111yescharacteristic
556C2×C8D4×D1111yescharacteristic
557C2×C8D4×D1111yescharacteristic
558C4⋊C4—111no—
559C4⋊C4—111no—
560C4⋊C4—111no—
561C4⋊C4—111no—
562C4⋊C4—221no—
563C4⋊C4—221no—
564C4⋊C4—221no—
565C4⋊C4—221no—
566C4⋊C4—442no—
567C4⋊C4C2×C4×D1111yescharacteristic
568C4⋊C4C2×C4×D1111yescharacteristic
569C22⋊C4—21no—
570C22⋊C4—221no—
571C22⋊C4—221no—
572C22⋊C4—221no—
573C22⋊C4—221no—
574C22⋊C4—221no—
575C22⋊C4—221no—
576C22⋊C4—221no—
577C22⋊C4—221no—
578C22⋊C4—442no—
579C42—21no—
580C42—21no—
581C42—221no—
582C42—221no—
583C42—221no—
584C42—221no—
585C42—221no—
586C42—221no—
587C42#433912yes—
588C11#2295111yescharacteristic, complemented, Sylow
589C23—21no—
590C23—111no—
591C23—111no—
592C23—221no—
593C23—221no—
594C23—441no—
595C23—441no—
596C23#41×D1111yescharacteristic
597Q8—21no—
598Q8—21no—
599D4—21no—
600D4—21no—
601D4—41no—
602D4—41no—
603D4—442no—
604D4—881no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—22no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—111no—
614C2×C4—111no—
615C2×C4—221no—
616C2×C4—221no—
617C2×C4—221no—
618C2×C4—221no—
619C2×C4—221no—
620C2×C4—221no—
621C2×C4—221no—
622C2×C4—221no—
623C2×C4—221no—
624C2×C4—221no—
625C2×C4—221no—
626C2×C4—221no—
627C2×C4—221no—
628C2×C4—221no—
629C2×C4—442no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—881no—
634C2×C4C22×C4×D1111yescharacteristic
635C2×C4C2×#433911yescharacteristic
636C2×C4C2×#433911yescharacteristic
637C2×C4C2×D4×D1111yescharacteristic
638C2×C4#6703711yescharacteristic
639C2×C4#6704311yescharacteristic
640C8—21no—
641C8—21no—
642C8—22no—
643C8—21no—
644C8—21no—
645C8—41no—
646C8—221no—
647C8—221no—
648C8—221no—
649C8—221no—
650C8—441no—
651C8—441no—
652C22—21no—
653C22—21no—
654C22—41no—
655C22—41no—
656C22—41no—
657C22—221no—
658C22—221no—
659C22—221no—
660C22—221no—
661C22—221no—
662C22—221no—
663C22—881no—
664C22—881no—
665C22#1062306011yescharacteristic
666C22C4×D4×D1111yescharacteristic
667C22#1062308711yescharacteristic
668C4—42no—
669C4—41no—
670C4—41no—
671C4—41no—
672C4—221no—
673C4—221no—
674C4—441no—
675C4—441no—
676C4—441no—
677C4—441no—
678C4—881no—
679C4C4×#433911yescharacteristic
680C4#1062302111yescharacteristic
681C4#1062307711yescharacteristic
682C4#1062308211yescharacteristic
683C2—21no—
684C2—21no—
685C2—81no—
686C2—441no—
687C2—441no—
688C2#1307160911yescharacteristic
689C2#1307751611yescharacteristic
690C2#1307753011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1765C2
socleC22×C11C2×C4×D4
prime radical#10623359C22
cosocleC22×C4×C11C24
hypercenter#1765D11
hypocenterC11#22951
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1765

Complements

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

NH ≅ G/Ntype
3. #13077271C2semidirect
4. #13069369C2semidirect
5. #13069317C2semidirect
6. #13069266C2semidirect
7. #13069215C2semidirect
8. #13069214C2semidirect
10. #13068891C2semidirect
11. #13068822C2semidirect
12. #13068494C2semidirect
13. #13068385C2semidirect
14. #13068324C2semidirect
15. C11×#1765C2semidirect
45. #10622428C4semidirect
46. #10622427C4semidirect
47. #10622422C4semidirect
48. #10622418C4semidirect
49. #10622397C4semidirect
50. #10622392C4semidirect
51. #10622390C4semidirect
52. #10622387C4semidirect
256. #1765D11semidirect
588. C11#22951semidirect

Maximal subgroups

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

subgroupindex
#130785272
#130773382
#130772712
#130693692
#130693172
#130692662
#130692152
#130692142
#130690612
#130688912
#130688222
#130684942
#130683852
#130683242
C11×#17652
#2295111