Finite Group Databasebeta

← #14765634

Subgroups — #14765634

Order 2816.

726 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078527C211yesmaximal, characteristic
2#13077308C211yesmaximal, characteristic
3D11×#424C211yesmaximal, characteristic, complemented
4#13069368C211yesmaximal, characteristic, complemented
5#13069367C211yesmaximal, characteristic, complemented
6#13069329C211yesmaximal, characteristic, complemented
7#13069324C211yesmaximal, characteristic, complemented
8#13069216C211yesmaximal, characteristic, complemented
9#13069212C211yesmaximal, characteristic, complemented
10#13068915C211yesmaximal, characteristic
11#13068891C211yesmaximal, characteristic, complemented
12#13068819C211yesmaximal, characteristic, complemented
13#13068714C211yesmaximal, characteristic, complemented
14#13068391C211yesmaximal, characteristic, complemented
15C11×#1866C211yesmaximal, characteristic, complemented
16C2×C11×#131C2211yescharacteristic
17#10623359C2211yescharacteristic
18C2×M16×D11C2211yescharacteristic
19C22×C8×D11C2211yescharacteristic
20D11×#117C2211yescharacteristic
21C2×C11×#108C2211yescharacteristic
22C11×#424C2211yescharacteristic
23C2×C11×#104C2211yescharacteristic
24C11×#416C2211yescharacteristic
25C2×#66901C2211yescharacteristic
26#10622847C2211yescharacteristic
27#10622846C2211yescharacteristic
28#10622740—21no—
29#10622740—21no—
30#10622739C2211yescharacteristic
31C2×#66886C2211yescharacteristic
32#10622732C2211yescharacteristic
33#10622732C2211yescharacteristic
34C8×C22⋊D11—21no—
35C8×C22⋊D11—21no—
36C2×(C2×D11)⋊C8C2211yescharacteristic
37#10622719C2211yescharacteristic
38#10622715C2211yescharacteristic
39#10622714C2211yescharacteristic
40C2×#66879C2211yescharacteristic
41#10622612C2211yescharacteristic
42#10622611C2211yescharacteristic
43C4×(C2×D11)⋊C4C2211yescharacteristic
44C2×#66867C2211yescharacteristic
45#10622452—21no—
46#10622452—21no—
47D11×C4⋊C8—21no—
48D11×C4⋊C8—21no—
49#10622428C411yescharacteristic, complemented
50#10622427C411yescharacteristic, complemented
51#10622422C411yescharacteristic, complemented
52#10622418C411yescharacteristic, complemented
53#10622397C411yescharacteristic, complemented
54#10622392C411yescharacteristic, complemented
55#10622390C411yescharacteristic, complemented
56#10622387C411yescharacteristic, complemented
57C11×#339C2211yescharacteristic
58C11×#336C2211yescharacteristic
59#10622196C2211yescharacteristic
60#10622193C2211yescharacteristic
61#10622193C2211yescharacteristic
62#10622190C2211yescharacteristic
63#10622188C2211yescharacteristic
64#10622170C2211yescharacteristic
65#10622161C2211yescharacteristic
66#10622161C2211yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C22×C4×D11C2311yescharacteristic
69C11×#131—41no—
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×C4×Dic11C2311yescharacteristic
91C2×#4318C2311yescharacteristic
92C2×#4318C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95M16×D11—41no—
96M16×D11—41no—
97C2×#4313—21no—
98C2×C8×D11—21no—
99C2×C8×D11—41no—
100C2×C8×D11—41no—
101C2×C8×D11D411yescharacteristic
102C2×C8×D11D411yescharacteristic
103C2×C8×D11D411yescharacteristic
104C2×C8×D11D411yescharacteristic
105#66945C2×C411yescharacteristic
106#66945C2×C411yescharacteristic
107C4⋊C4×D11C2×C411yescharacteristic
108C4⋊C4×D11C2×C411yescharacteristic
109C22⋊C4×D11—21no—
110#66930—21no—
111#66925—21no—
112C42×D11—21no—
113C11×#108—41no—
114C11×C4⋊C8—21no—
115C11×C4⋊C8—21no—
116C11×#104—41no—
117C11×#103C2×C411yescharacteristic
118C11×#103C2×C411yescharacteristic
119C11×#102C2×C411yescharacteristic
120C11×#102C2×C411yescharacteristic
121#66901—41no—
122#66899C2×C411yescharacteristic
123#66899C2×C411yescharacteristic
124#66896C2×C411yescharacteristic
125#66896C2×C411yescharacteristic
126C11⋊#95—21no—
127C22⋊(C11⋊C8)—21no—
128C22⋊(C11⋊C8)—21no—
129#66886—41no—
130(C2×D11)⋊C8—21no—
131(C2×D11)⋊C8—21no—
132(C2×D11)⋊C8C2×C411yescharacteristic
133(C2×D11)⋊C8C2×C411yescharacteristic
134(C2×D11)⋊C8C2×C411yescharacteristic
135(C2×D11)⋊C8C2×C411yescharacteristic
136#66882C2×C411yescharacteristic
137#66882C2×C411yescharacteristic
138#66881C2×C411yescharacteristic
139#66881C2×C411yescharacteristic
140#66879—21no—
141#66879—41no—
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
153C4⋊(C11⋊C8)—21no—
154C4⋊(C11⋊C8)—21no—
155#66867—41no—
156#22096—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—21no—
186C11×M16—42no—
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—21no—
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—
221C4×Dic11—21no—
222C4×Dic11—21no—
223C4×Dic11—21no—
224C4×Dic11—21no—
225C4×Dic11—21no—
226C4×Dic11—21no—
227#4318—21no—
228#4318—21no—
229#4318—21no—
230#4318—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8C22×C411yescharacteristic
238C2×C11⋊C8C22×C411yescharacteristic
239C2×C11⋊C8C2×D411yescharacteristic
240C2×C11⋊C8C2×D411yescharacteristic
241#4313—42no—
242C8×D11—41no—
243C8×D11—41no—
244C8×D11—41no—
245C8×D11—41no—
246C8×D11—42no—
247#3091—111no—
248#2929—111no—
249C2×#424—111no—
250#1946—111no—
251#1946—111no—
252#1938—111no—
253#1938—111no—
254#1922—111no—
255#1922—111no—
256#1871—111no—
257#1866—111no—
258#1866D1111yescharacteristic, complemented
259#1855—111no—
260#1826—111no—
261#1752—111no—
262C23×C11—21no—
263C23×C11C2×#4111yescharacteristic
264C22×D11—21no—
265C22×D11—21no—
266C22×D11—22no—
267C22×D11—41no—
268C22×D11C4×D411yescharacteristic
269C22×D11C4×D411yescharacteristic
270Q8×C11—21no—
271Q8×C11—21no—
272D4×C11—21no—
273D4×C11—21no—
274D4×C11—41no—
275D4×C11—41no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11C23×C411yescharacteristic
285C2×C4×C11C22×D411yescharacteristic
286C2×C4×C11H(5,𝔽2)11yescharacteristic
287C2×C4×C11H(5,𝔽2)11yescharacteristic
288C2×C4×C112−1+411yescharacteristic
289C2×C4×C112−1+411yescharacteristic
290C22⋊D11—42no—
291C22⋊D11—42no—
292C2×Dic11—21no—
293C2×Dic11—21no—
294C2×Dic11—21no—
295C2×Dic11—21no—
296C2×Dic11—21no—
297C2×Dic11—21no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11C4×D411yescharacteristic
302C2×Dic11C4×D411yescharacteristic
303C4×D11—21no—
304C4×D11—21no—
305C4×D11—21no—
306C4×D11—21no—
307C4×D11—21no—
308C4×D11—21no—
309C4×D11—21no—
310C4×D11—21no—
311C4×D11—42no—
312C4×D11—42no—
313C8×C11—21no—
314C8×C11—21no—
315C8×C11—21no—
316C8×C11—21no—
317C8×C11—41no—
318C8×C11—41no—
319C11⋊C8—21no—
320C11⋊C8—21no—
321C11⋊C8—21no—
322C11⋊C8—21no—
323C11⋊C8—41no—
324C11⋊C8—41no—
325C2×#131C2×D1111yescharacteristic
326C22×M16—111no—
327C23×C8—111no—
328#525—111no—
329C2×#117—111no—
330#485—111no—
331#485—111no—
332#484—111no—
333#483—111no—
334#482—111no—
335#482—111no—
336#481—111no—
337#480—111no—
338#435—221no—
339#435—221no—
340C8×D4—221no—
341C8×D4—221no—
342C2×#108—111no—
343C2×#108C2×D1111yescharacteristic
344#427—111no—
345#427—111no—
346#424—111no—
347#424—111no—
348#424—111no—
349#424—111no—
350#424—221no—
351#424—221no—
352#424C2×D1111yescharacteristic
353C2×C4⋊C8—221no—
354C2×C4⋊C8—221no—
355C2×#104—111no—
356C2×#104C2×D1111yescharacteristic
357#416—111no—
358#416C2×D1111yescharacteristic
359#408—111no—
360#407—111no—
361C2×C22⋊C8—111no—
362#405—111no—
363C2×#97—111no—
364C2×#97—111no—
365C4×C22⋊C4—111no—
366#341—111no—
367#341—111no—
368#339—111no—
369#339—111no—
370#339—111no—
371#339—111no—
372#339—111no—
373#339C2×D1111yescharacteristic
374#336—111no—
375#336C2×D1111yescharacteristic
376C22×C11—21no—
377C22×C11—21no—
378C22×C11—41no—
379C22×C11—41no—
380C22×C11—41no—
381C22×C11C2×C4×D411yescharacteristic
382C22×C11#53911yescharacteristic
383C22×C11#53911yescharacteristic
384C2×D11—21no—
385C2×D11—21no—
386C2×D11—21no—
387C2×D11—21no—
388C2×D11—21no—
389C2×D11—42no—
390C2×D11—42no—
391C2×D11#44412yes—
392C4×C11—41no—
393C4×C11—41no—
394C4×C11—41no—
395C4×C11—81no—
396C4×C11#52011yescharacteristic
397C4×C11#52011yescharacteristic
398C4×C11#53411yescharacteristic
399C4×C11#53611yescharacteristic
400Dic11—21no—
401Dic11—21no—
402Dic11—41no—
403Dic11—41no—
404Dic11—41no—
405Dic11—41no—
406Dic11—81no—
407C2×#41C22×D1111yescharacteristic
408C23×C4—111no—
409#131—41no—
410#131—41no—
411C2×M16—21no—
412C2×M16—111no—
413C2×M16—111no—
414C2×M16—221no—
415C2×M16—441no—
416C2×M16—441no—
417C2×M16C22×D1111yescharacteristic
418C2×M16C22×D1111yescharacteristic
419C22×C8—21no—
420C22×C8—111no—
421C22×C8—111no—
422C22×C8—111no—
423C22×C8—111no—
424C22×C8—111no—
425C22×C8—111no—
426C22×C8—221no—
427C22×C8—441no—
428C22×C8—441no—
429C22×C8C22×D1111yescharacteristic
430C22×C8C22×D1111yescharacteristic
431#123—221no—
432C22⋊Q8—111no—
433C22⋊Q8—111no—
434#121—111no—
435#121—111no—
436#120—221no—
437C4×D4—221no—
438C4×D4—221no—
439#117—111no—
440#117—111no—
441#117—111no—
442#117—111no—
443#117—221no—
444#117—221no—
445#117C22×D1111yescharacteristic
446C2×C4⋊C4—111no—
447C2×C4⋊C4—111no—
448C2×C22⋊C4—221no—
449C2×C22⋊C4—221no—
450C2×C42—111no—
451C2×C42—221no—
452C2×C42C22×D1111yescharacteristic
453#108—41no—
454#108—441no—
455#107—111no—
456#107—111no—
457#107—111no—
458#107—111no—
459#106—111no—
460#106—111no—
461#106—111no—
462#106—111no—
463C4⋊C8—21no—
464C4⋊C8—21no—
465C4⋊C8—221no—
466C4⋊C8—221no—
467C4⋊C8—221no—
468C4⋊C8—221no—
469C4⋊C8—221no—
470C4⋊C8—221no—
471C4⋊C8—221no—
472C4⋊C8—221no—
473#104—41no—
474#104—441no—
475#103—111no—
476#103—111no—
477#103C4×D1111yescharacteristic
478#103C4×D1111yescharacteristic
479#102—111no—
480#102—111no—
481#102C4×D1111yescharacteristic
482#102C4×D1111yescharacteristic
483C22⋊C8—111no—
484C22⋊C8—111no—
485C22⋊C8—111no—
486C22⋊C8—111no—
487C22⋊C8—221no—
488C22⋊C8—221no—
489C22⋊C8—221no—
490C22⋊C8—221no—
491#97—221no—
492#97—441no—
493#97—441no—
494C4×C8—221no—
495#95—221no—
496C2×C11—21no—
497C2×C11—21no—
498C2×C11—81no—
499C2×C11#232211yescharacteristic
500C2×C11C2×#44411yescharacteristic
501C2×C11#295511yescharacteristic
502D11—22no—
503D11—41no—
504C24—111no—
505#41—21no—
506#41—21no—
507#41—21no—
508#41—21no—
509C2×Q8C2×C4×D1111yescharacteristic
510C2×D4—21no—
511C2×D4—221no—
512C2×D4—221no—
513C2×D4C2×C4×D1111yescharacteristic
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—111no—
517C22×C4—111no—
518C22×C4—111no—
519C22×C4—111no—
520C22×C4—111no—
521C22×C4—221no—
522C22×C4—221no—
523C22×C4—221no—
524C22×C4—221no—
525C22×C4—221no—
526C22×C4—221no—
527C22×C4—221no—
528C22×C4C23×D1111yescharacteristic
529M16—21no—
530M16—21no—
531M16—21no—
532M16—21no—
533M16—42no—
534M16—221no—
535M16—221no—
536M16—221no—
537M16—221no—
538M16—442no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—42no—
546C2×C8—111no—
547C2×C8—111no—
548C2×C8—111no—
549C2×C8—111no—
550C2×C8—221no—
551C2×C8—221no—
552C2×C8—221no—
553C2×C8—221no—
554C2×C8—221no—
555C2×C8—221no—
556C2×C8—441no—
557C2×C8—441no—
558C2×C8—441no—
559C2×C8—441no—
560C2×C8—442no—
561C2×C8C2×C4×D1111yescharacteristic
562C2×C8C2×C4×D1111yescharacteristic
563C2×C8D4×D1111yescharacteristic
564C2×C8D4×D1111yescharacteristic
565C4⋊C4—111no—
566C4⋊C4—111no—
567C4⋊C4—111no—
568C4⋊C4—111no—
569C4⋊C4—221no—
570C4⋊C4—221no—
571C4⋊C4—221no—
572C4⋊C4—221no—
573C4⋊C4C2×C4×D1111yescharacteristic
574C4⋊C4C2×C4×D1111yescharacteristic
575C22⋊C4—21no—
576C22⋊C4—221no—
577C22⋊C4—221no—
578C22⋊C4—221no—
579C22⋊C4—221no—
580C22⋊C4—221no—
581C22⋊C4—221no—
582C22⋊C4—221no—
583C22⋊C4—221no—
584C22⋊C4—442no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—221no—
589C42—221no—
590C42—221no—
591C42—221no—
592C42—221no—
593C42—221no—
594C11#2209611yescharacteristic, complemented, Sylow
595C23—21no—
596C23—111no—
597C23—111no—
598C23—222no—
599C23—221no—
600C23—221no—
601C23—441no—
602C23#41×D1111yescharacteristic
603Q8—21no—
604Q8—21no—
605D4—21no—
606D4—21no—
607D4—41no—
608D4—41no—
609D4—442no—
610D4—442no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—111no—
620C2×C4—111no—
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—221no—
630C2×C4—221no—
631C2×C4—221no—
632C2×C4—221no—
633C2×C4—221no—
634C2×C4—221no—
635C2×C4—442no—
636C2×C4—442no—
637C2×C4—441no—
638C2×C4—441no—
639C2×C4—441no—
640C2×C4C22×C4×D1111yescharacteristic
641C2×C4C2×D4×D1111yescharacteristic
642C2×C4#6703711yescharacteristic
643C2×C4#6703711yescharacteristic
644C2×C4#6704011yescharacteristic
645C2×C4#6704311yescharacteristic
646C8—21no—
647C8—21no—
648C8—21no—
649C8—21no—
650C8—41no—
651C8—41no—
652C8—221no—
653C8—221no—
654C8—221no—
655C8—221no—
656C8—441no—
657C8—441no—
658C22—21no—
659C22—21no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—112no—
664C22—221no—
665C22—221no—
666C22—221no—
667C22—221no—
668C22—221no—
669C22—442no—
670C22—442no—
671C22C4×D4×D1111yescharacteristic
672C22#1062316911yescharacteristic
673C22#1062319111yescharacteristic
674C4—41no—
675C4—41no—
676C4—41no—
677C4—81no—
678C4—221no—
679C4—221no—
680C4—441no—
681C4—441no—
682C4—441no—
683C4—441no—
684C4—881no—
685C4#1062303511yescharacteristic
686C4#1062307711yescharacteristic
687C4#1062312011yescharacteristic
688C4#1062315911yescharacteristic
689C2—21no—
690C2—21no—
691C2—81no—
692C2—222no—
693C2—441no—
694C2#1307128311yescharacteristic
695C2D11×#44411yescharacteristic
696C2#1307751411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1866C2
socleC22×C11C2×C4×D4
prime radical#10623359C22
cosocleC22×C4×C11C24
hypercenter#1866D11
hypocenterC11#22096
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1866

Complements

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

NH ≅ G/Ntype
3. D11×#424C2semidirect
4. #13069368C2semidirect
5. #13069367C2semidirect
6. #13069329C2semidirect
7. #13069324C2semidirect
8. #13069216C2semidirect
9. #13069212C2semidirect
11. #13068891C2semidirect
12. #13068819C2semidirect
13. #13068714C2semidirect
14. #13068391C2semidirect
15. C11×#1866C2semidirect
49. #10622428C4semidirect
50. #10622427C4semidirect
51. #10622422C4semidirect
52. #10622418C4semidirect
53. #10622397C4semidirect
54. #10622392C4semidirect
55. #10622390C4semidirect
56. #10622387C4semidirect
258. #1866D11semidirect
594. C11#22096semidirect

Maximal subgroups

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

subgroupindex
#130785272
#130773082
D11×#4242
#130693682
#130693672
#130693292
#130693242
#130692162
#130692122
#130689152
#130688912
#130688192
#130687142
#130683912
C11×#18662
#2209611