Finite Group Databasebeta

← #14775427

Subgroups — #14775427

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#13078531C211yesmaximal, characteristic
2#13077337C211yesmaximal, characteristic
3#13077270C211yesmaximal, characteristic, complemented
4#13069369C211yesmaximal, characteristic, complemented
5#13069320C211yesmaximal, characteristic, complemented
6#13069265C211yesmaximal, characteristic, complemented
7#13069216C211yesmaximal, characteristic, complemented
8#13069216C211yesmaximal, characteristic, complemented
9#13069064C211yesmaximal, characteristic
10#13068894C211yesmaximal, characteristic, complemented
11#13068823C211yesmaximal, characteristic, complemented
12#13068495C211yesmaximal, characteristic, complemented
13#13068460C211yesmaximal, characteristic, complemented
14#13068326C211yesmaximal, characteristic, complemented
15C11×#1750C211yesmaximal, characteristic, complemented
16C2×C11×#117C2211yescharacteristic
17#10623322C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20C2×#66954C2211yescharacteristic
21C2×C11×C22⋊C8C2211yescharacteristic
22C2×C11×C22⋊C8C2211yescharacteristic
23C2×C11×#97C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25#10622820C2211yescharacteristic
26#10622726C2211yescharacteristic
27#10622726C2211yescharacteristic
28#10622723C2211yescharacteristic
29C2×#66883C2211yescharacteristic
30C2×#66883C2211yescharacteristic
31#10622719C2211yescharacteristic
32#10622719C2211yescharacteristic
33#10622715C2211yescharacteristic
34#10622715C2211yescharacteristic
35#10622715C2211yescharacteristic
36#10622714C2211yescharacteristic
37#10622714C2211yescharacteristic
38#10622714C2211yescharacteristic
39C2×#66869C2211yescharacteristic
40C2×#66869C2211yescharacteristic
41#10622350C411yescharacteristic, complemented
42#10622350C411yescharacteristic, complemented
43#10622349C411yescharacteristic, complemented
44#10622348C411yescharacteristic, complemented
45#10622343—21no—
46#10622342—21no—
47#10622341—21no—
48(C22⋊D11)⋊C8—21no—
49#10622336C411yescharacteristic, complemented
50#10622336C411yescharacteristic, complemented
51#10622335C411yescharacteristic, complemented
52#10622334C411yescharacteristic, complemented
53#10622333—21no—
54#10622333—21no—
55#10622332—21no—
56#10622331—21no—
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59#10622190C2211yescharacteristic
60#10622190C2211yescharacteristic
61#10622161C2211yescharacteristic
62#10622161C2211yescharacteristic
63#10622161C2211yescharacteristic
64#10622161C2211yescharacteristic
65#10622161C2211yescharacteristic
66#10622161C2211yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C2×#4339C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C11×#117—22no—
74C11×#117—41no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79#67006—21no—
80C2×C22⋊Dic11—21no—
81#66983C2×C411yescharacteristic
82#66983C2×C411yescharacteristic
83#66982—21no—
84C4×C22⋊D11—21no—
85C4×C22⋊D11—21no—
86#66979—21no—
87#66979—21no—
88#66979C2×C411yescharacteristic
89#66979C2×C411yescharacteristic
90#66979C2311yescharacteristic
91#66979C2311yescharacteristic
92#66979C2311yescharacteristic
93C2×C4⋊Dic11C2×C411yescharacteristic
94C2×C4⋊Dic11C2×C411yescharacteristic
95#66977C2×C411yescharacteristic
96#66977C2×C411yescharacteristic
97C2×C4×Dic11—21no—
98C2×#4318—21no—
99C2×#4318—22no—
100C2×#4318—41no—
101C2×#4318C2311yescharacteristic
102C2×#4318C2311yescharacteristic
103C2×#4318C2311yescharacteristic
104C2×#4318C2311yescharacteristic
105C22×C11⋊C8—21no—
106#66954—22no—
107#66954—41no—
108C2×#4313—21no—
109C2×C8×D11—21no—
110C11×C22⋊C8C2×C411yescharacteristic
111C11×C22⋊C8C2×C411yescharacteristic
112C11×C22⋊C8C2×C411yescharacteristic
113C11×C22⋊C8C2×C411yescharacteristic
114C11×C22⋊C8D411yescharacteristic
115C11×C22⋊C8D411yescharacteristic
116C11×C22⋊C8D411yescharacteristic
117C11×C22⋊C8D411yescharacteristic
118C11×#97—41no—
119C4×C8×C11—22no—
120C22⋊(C11⋊C8)—21no—
121C22⋊(C11⋊C8)—21no—
122#66885C2×C411yescharacteristic
123#66885C2×C411yescharacteristic
124#66885C2×C411yescharacteristic
125#66885C2×C411yescharacteristic
126(C2×D11)⋊C8—21no—
127(C2×D11)⋊C8—21no—
128#66883—22no—
129#66883—41no—
130#66882C2×C411yescharacteristic
131#66882C2×C411yescharacteristic
132#66882C2×C411yescharacteristic
133#66882C2×C411yescharacteristic
134#66881C2×C411yescharacteristic
135#66881C2×C411yescharacteristic
136#66881C2×C411yescharacteristic
137#66881C2×C411yescharacteristic
138#66880C2×C411yescharacteristic
139#66880C2×C411yescharacteristic
140#66880C2×C411yescharacteristic
141#66880C2×C411yescharacteristic
142#66879—21no—
143#66879—21no—
144#66879—21no—
145Dic11⋊C8—21no—
146Dic11⋊C8—21no—
147Dic11⋊C8—21no—
148Dic11⋊C8—21no—
149Dic11⋊C8—21no—
150Dic11⋊C8—21no—
151C8×Dic11—21no—
152C8×Dic11—21no—
153C8×Dic11—21no—
154#66869—22no—
155#66869—41no—
156#22951—111nomaximal, Sylow
157C24×C11#4111yescharacteristic
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11C22×C411yescharacteristic
165C22×C4×C11C22×C411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11#4111yescharacteristic
169C22×C4×C11C2411yescharacteristic
170C2×C22⋊D11—21no—
171C2×C22⋊D11—21no—
172C2×C22⋊D11—21no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175#4339—21no—
176#4339—21no—
177#4339—21no—
178#4339—21no—
179C2×D44C22×C411yescharacteristic
180C2×C4×D11—21no—
181C2×Dic22C22×C411yescharacteristic
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11C22×C411yescharacteristic
191C2×C8×C11C22×C411yescharacteristic
192C2×C8×C11C22×C411yescharacteristic
193C2×C8×C11C22×C411yescharacteristic
194C2×C8×C11C2×D411yescharacteristic
195C2×C8×C11C2×D411yescharacteristic
196C2×C8×C11C2×D411yescharacteristic
197C2×C8×C11C2×D411yescharacteristic
198C11×C4⋊C4—42no—
199C11×C22⋊C4—42no—
200C42×C11—21no—
201C42×C11—21no—
202C42×C11—21no—
203C42×C11#4112yes—
204C22⋊Dic11—21no—
205C22⋊Dic11—21no—
206C22⋊Dic11—21no—
207C22⋊Dic11—21no—
208C22⋊Dic11—21no—
209C22⋊Dic11—21no—
210C22⋊Dic11—21no—
211(C2×D11)⋊C4—21no—
212(C2×D11)⋊C4—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11C22×C411yescharacteristic
216C4⋊Dic11C22×C411yescharacteristic
217C4⋊Dic11C22×C411yescharacteristic
218C4⋊Dic11C22×C411yescharacteristic
219C4⋊Dic11C22×C411yescharacteristic
220C4⋊Dic11C22×C411yescharacteristic
221Dic11⋊C4—21no—
222Dic11⋊C4—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—
232#4318—21no—
233#4318—21no—
234#4318—21no—
235#4318—42no—
236#4318#4112yes—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—42no—
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#1765—111no—
257#1750D1111yescharacteristic, complemented
258#1733—111no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11C4×D411yescharacteristic
264C23×C11C4×D411yescharacteristic
265C23×C11C2×#4111yescharacteristic
266C22×D11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—22no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11C4×D411yescharacteristic
284C2×C4×C11C4×D411yescharacteristic
285C2×C4×C11C23×C411yescharacteristic
286C2×C4×C11C22×D411yescharacteristic
287C2×C4×C11C2×#4111yescharacteristic
288C2×C4×C11C2×#4111yescharacteristic
289C2×C4×C11H(5,𝔽2)11yescharacteristic
290C2×C4×C112−1+411yescharacteristic
291C22⋊D11—42no—
292C22⋊D11—41no—
293C22⋊D11—41no—
294C22⋊D11—81no—
295C2×Dic11—21no—
296C2×Dic11—21no—
297C2×Dic11—21no—
298C2×Dic11—21no—
299C2×Dic11—21no—
300C2×Dic11—21no—
301C2×Dic11—21no—
302C2×Dic11—42no—
303C2×Dic11—81no—
304D44—21no—
305D44—21no—
306C4×D11—41no—
307C4×D11—41no—
308Dic22—21no—
309Dic22—21no—
310C8×C11—21no—
311C8×C11—21no—
312C8×C11—21no—
313C8×C11—21no—
314C8×C11—21no—
315C8×C11—21no—
316C8×C11—21no—
317C8×C11—21no—
318C11⋊C8—22no—
319C11⋊C8—41no—
320C11⋊C8—41no—
321C11⋊C8—41no—
322C2×#131—111no—
323C22×M16—111no—
324#525—111no—
325C2×#117—111no—
326C2×#117C2×D1111yescharacteristic
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×#104—111no—
352#416—111no—
353#416—111no—
354#408—111no—
355#407—111no—
356C2×C22⋊C8C2×D1111yescharacteristic
357C2×C22⋊C8C2×D1111yescharacteristic
358#405—111no—
359#405—111no—
360#405—111no—
361C2×#97C2×D1111yescharacteristic
362C2×C4×C8C2×D1111yescharacteristic
363#341—111no—
364#341—111no—
365#339—111no—
366#339—111no—
367#339—111no—
368#339—111no—
369#339—111no—
370#339—111no—
371#336C2×D1111yescharacteristic
372#336C2×D1111yescharacteristic
373C22×C11—21no—
374C22×C11—21no—
375C22×C11—21no—
376C22×C11—21no—
377C22×C11—21no—
378C22×C11—21no—
379C22×C11—21no—
380C22×C11—21no—
381C22×C11—81no—
382C22×C11—81no—
383C22×C11C2×C4×D411yescharacteristic
384C22×C11#55111yescharacteristic
385C22×C11#55211yescharacteristic
386C2×D11—41no—
387C2×D11—41no—
388C2×D11—41no—
389C4×C11—21no—
390C4×C11—21no—
391C4×C11—42no—
392C4×C11—81no—
393C4×C11C4×#4111yescharacteristic
394C4×C11#52011yescharacteristic
395C4×C11#54611yescharacteristic
396C4×C11#54711yescharacteristic
397Dic11—41no—
398Dic11—41no—
399Dic11—41no—
400Dic11—41no—
401Dic11—41no—
402Dic11—41no—
403Dic11—41no—
404C2×#41—111no—
405C23×C4C22×D1111yescharacteristic
406#131—222no—
407#131—441no—
408C2×M16—111no—
409C2×M16—111no—
410C2×M16—111no—
411C2×M16—111no—
412C2×M16—221no—
413C2×M16—221no—
414C2×M16—222no—
415C2×M16—441no—
416C22×C8—221no—
417C22×C8—221no—
418C22×C8C22×D1111yescharacteristic
419C22×C8C22×D1111yescharacteristic
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—22no—
431#117—41no—
432#117—111no—
433#117—111no—
434#117—111no—
435#117—111no—
436#117—111no—
437#117—221no—
438#117—221no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—111no—
441C2×C4⋊C4—111no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—221no—
444C2×C42—221no—
445C2×C42C22×D1111yescharacteristic
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—222no—
464#104—441no—
465#103—111no—
466#103—111no—
467#103—111no—
468#103—111no—
469#102—111no—
470#102—111no—
471#102—111no—
472#102—111no—
473C22⋊C8—221no—
474C22⋊C8—221no—
475C22⋊C8—221no—
476C22⋊C8—221no—
477C22⋊C8C4×D1111yescharacteristic
478C22⋊C8C4×D1111yescharacteristic
479C22⋊C8C4×D1111yescharacteristic
480C22⋊C8C4×D1111yescharacteristic
481C22⋊C8D4411yescharacteristic
482C22⋊C8D4411yescharacteristic
483C22⋊C8D4411yescharacteristic
484C22⋊C8D4411yescharacteristic
485#97—41no—
486#97—221no—
487#97—221no—
488#97—221no—
489C4×C8—22no—
490C4×C8—221no—
491C4×C8—221no—
492C4×C8—221no—
493C2×C11—21no—
494C2×C11—21no—
495C2×C11—41no—
496C2×C11—41no—
497C2×C11#235911yescharacteristic
498C2×C11#295511yescharacteristic
499C2×C11#295711yescharacteristic
500D11—81no—
501C24#433911yescharacteristic
502#41—221no—
503#41—221no—
504#41—221no—
505#41—221no—
506C2×Q8—111no—
507C2×D4—111no—
508C2×D4—221no—
509C2×D4—221no—
510C2×D4—221no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4C2×C4×D1111yescharacteristic
521C22×C4C2×C4×D1111yescharacteristic
522C22×C4C2×D4411yescharacteristic
523C22×C4C2×D4411yescharacteristic
524C22×C4#433911yescharacteristic
525C22×C4C23×D1111yescharacteristic
526M16—112no—
527M16—221no—
528M16—221no—
529M16—221no—
530M16—221no—
531M16—221no—
532M16—221no—
533M16—221no—
534M16—442no—
535M16—442no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—221no—
545C2×C8—221no—
546C2×C8—221no—
547C2×C8—221no—
548C2×C8—442no—
549C2×C8—442no—
550C2×C8C2×C4×D1111yescharacteristic
551C2×C8C2×C4×D1111yescharacteristic
552C2×C8C2×C4×D1111yescharacteristic
553C2×C8C2×C4×D1111yescharacteristic
554C2×C8C2×D4411yescharacteristic
555C2×C8C2×D4411yescharacteristic
556C2×C8C2×D4411yescharacteristic
557C2×C8C2×D4411yescharacteristic
558C4⋊C4—42no—
559C4⋊C4—111no—
560C4⋊C4—111no—
561C4⋊C4—111no—
562C4⋊C4—111no—
563C4⋊C4—111no—
564C4⋊C4—111no—
565C4⋊C4—221no—
566C4⋊C4—221no—
567C4⋊C4—221no—
568C4⋊C4—221no—
569C22⋊C4—42no—
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—221no—
579C42—21no—
580C42—21no—
581C42—21no—
582C42—221no—
583C42—221no—
584C42—221no—
585C42—221no—
586C42—221no—
587C42#434112yes—
588C11#2295111yescharacteristic, complemented, Sylow
589C23—21no—
590C23—21no—
591C23—41no—
592C23—41no—
593C23—221no—
594C23C4×D4411yescharacteristic
595C23C4×D4411yescharacteristic
596C23C2×#433911yescharacteristic
597Q8—221no—
598Q8—221no—
599D4—221no—
600D4—221no—
601D4—442no—
602D4—441no—
603D4—441no—
604D4—881no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—221no—
622C2×C4—221no—
623C2×C4—221no—
624C2×C4—221no—
625C2×C4—221no—
626C2×C4—221no—
627C2×C4—221no—
628C2×C4—442no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—881no—
632C2×C4C4×D4411yescharacteristic
633C2×C4C4×D4411yescharacteristic
634C2×C4C22×C4×D1111yescharacteristic
635C2×C4C22×D4411yescharacteristic
636C2×C4C2×#434111yescharacteristic
637C2×C4#6703711yescharacteristic
638C2×C4#41×D1111yescharacteristic
639C2×C4#6704311yescharacteristic
640C8—21no—
641C8—21no—
642C8—21no—
643C8—21no—
644C8—21no—
645C8—21no—
646C8—21no—
647C8—21no—
648C8—222no—
649C8—441no—
650C8—441no—
651C8—441no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—21no—
660C22—81no—
661C22—81no—
662C22—441no—
663C22—441no—
664C22—441no—
665C22C2×C4×D4411yescharacteristic
666C22#1062302611yescharacteristic
667C22#1062306211yescharacteristic
668C4—21no—
669C4—21no—
670C4—42no—
671C4—81no—
672C4—441no—
673C4—441no—
674C4—441no—
675C4—441no—
676C4—441no—
677C4—441no—
678C4—441no—
679C4C4×#434111yescharacteristic
680C4#1062307711yescharacteristic
681C4#1062308511yescharacteristic
682C4#1062308611yescharacteristic
683C2—21no—
684C2—21no—
685C2—41no—
686C2—41no—
687C2—881no—
688C2#1307161011yescharacteristic
689C2#1307752011yescharacteristic
690C2#1307753411yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1750C2
socleC22×C11C2×C4×D4
prime radical#10623322C22
cosocleC22×C4×C11C24
hypercenter#1750D11
hypocenterC11#22951
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #1750

Complements

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

NH ≅ G/Ntype
3. #13077270C2semidirect
4. #13069369C2semidirect
5. #13069320C2semidirect
6. #13069265C2semidirect
7. #13069216C2semidirect
8. #13069216C2semidirect
10. #13068894C2semidirect
11. #13068823C2semidirect
12. #13068495C2semidirect
13. #13068460C2semidirect
14. #13068326C2semidirect
15. C11×#1750C2semidirect
41. #10622350C4semidirect
42. #10622350C4semidirect
43. #10622349C4semidirect
44. #10622348C4semidirect
49. #10622336C4semidirect
50. #10622336C4semidirect
51. #10622335C4semidirect
52. #10622334C4semidirect
257. #1750D11semidirect
588. C11#22951semidirect

Maximal subgroups

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

subgroupindex
#130785312
#130773372
#130772702
#130693692
#130693202
#130692652
#130692162
#130690642
#130688942
#130688232
#130684952
#130684602
#130683262
C11×#17502
#2295111