Finite Group Databasebeta

← #14765170

Subgroups — #14765170

Order 2816.

926 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077830C211yesmaximal, characteristic
2#13077308C211yesmaximal, characteristic, complemented
3D11×#408C211yesmaximal, characteristic, complemented
4#13069505C211yesmaximal, characteristic, complemented
5#13069501C211yesmaximal, characteristic, complemented
6#13069318C211yesmaximal, characteristic, complemented
7#13069317C211yesmaximal, characteristic, complemented
8#13069265C211yesmaximal, characteristic, complemented
9#13069261C211yesmaximal, characteristic, complemented
10#13068943C211yesmaximal, characteristic, complemented
11#13068915C211yesmaximal, characteristic, complemented
12#13068822C211yesmaximal, characteristic, complemented
13#13068558C211yesmaximal, characteristic, complemented
14#13068386C211yesmaximal, characteristic, complemented
15C11×#1876C211yesmaximal, characteristic, complemented
16C2×#41×D11C2211yescharacteristic
17C2×C11×#135C2211yescharacteristic
18C2×C11×#131C2211yescharacteristic, complemented
19#10623359C2211yescharacteristic
20C2×#67003C2211yescharacteristic
21C2×M16×D11C2211yescharacteristic
22C22×C8×D11C2211yescharacteristic
23C2×C11×#104C2211yescharacteristic
24C2×C11×#104C2211yescharacteristic, complemented
25C11×#408C2211yescharacteristic
26C2×#66901C2211yescharacteristic
27C2×#66901C2211yescharacteristic, complemented
28#10622847C2211yescharacteristic
29#10622847C2211yescharacteristic, complemented
30#10622846C2211yescharacteristic
31#10622800C411yescharacteristic, complemented
32#10622799C411yescharacteristic, complemented
33#10622786C411yescharacteristic, complemented
34#10622785C411yescharacteristic, complemented
35#10622783C411yescharacteristic, complemented
36#10622782C411yescharacteristic, complemented
37#10622771C411yescharacteristic, complemented
38#10622769C411yescharacteristic, complemented
39C2×#66889C2211yescharacteristic
40#10622742C2211yescharacteristic
41#10622740—21no—
42#10622740—21no—
43#10622739C2211yescharacteristic
44C2×#66886C2211yescharacteristic, complemented
45#10622732C2211yescharacteristic, complemented
46#10622726C2211yescharacteristic
47#10622723C2211yescharacteristic
48C8×C22⋊D11—21no—
49C8×C22⋊D11—21no—
50C2×(C2×D11)⋊C8C2211yescharacteristic
51C2×#66883C2211yescharacteristic, complemented
52#10622714C2211yescharacteristic, complemented
53C2×C8×Dic11C2211yescharacteristic, complemented
54C4×(C2×D11)⋊C4C2211yescharacteristic
55C2×#66869C2211yescharacteristic
56C2×C4×C11⋊C8C2211yescharacteristic, complemented
57#10622340—21no—
58#10622340—21no—
59D11×C22⋊C8—21no—
60D11×C22⋊C8—21no—
61C11×#341C2211yescharacteristic, complemented
62C11×#336C2211yescharacteristic, complemented
63#10622196C2211yescharacteristic, complemented
64#10622193C2211yescharacteristic, complemented
65#10622188C2211yescharacteristic, complemented
66#10622161C2211yescharacteristic, complemented
67C2×C11×#41C2311yescharacteristic
68C2×C11×#41C2311yescharacteristic
69#41×D11—41no—
70#41×D11—41no—
71#41×D11—41no—
72#41×D11—41no—
73C2×#4343C2×C411yescharacteristic
74C2×Q8×D11C2×C411yescharacteristic
75C2×#4341—21no—
76C2×#4341C2×C411yescharacteristic
77C2×D4×D11—21no—
78C2×D4×D11C2×C411yescharacteristic
79C2×#4339—21no—
80C2×#4339C2311yescharacteristic
81C22×C4×D11—21no—
82C22×C4×D11C2311yescharacteristic
83C11×#135—41no—
84C11×#135—41no—
85C2×C11×Q16C2×C411yescharacteristic
86C2×C11×SD16C2×C411yescharacteristic
87C2×C11×SD16C2×C411yescharacteristic
88C2×C11×D8C2×C411yescharacteristic
89C11×#131—41no—
90C11×#131—41no—
91C2×C11×M16—21no—
92C2×C11×M16C2311yescharacteristic
93C2×C11×M16C2311yescharacteristic
94C22×C8×C11—21no—
95C22×C8×C11C2311yescharacteristic
96C22×C8×C11C2311yescharacteristic
97C2×C42×C11C2311yescharacteristic
98#67003—41no—
99#67003—41no—
100#66999C2×C411yescharacteristic
101#66999C2×C411yescharacteristic
102C2×#4326C2×C411yescharacteristic
103C2×#4325C2×C411yescharacteristic
104#66991C2×C411yescharacteristic
105#66991C2×C411yescharacteristic
106#66990—21no—
107#66988—21no—
108C2×#4324C2×C411yescharacteristic
109C2×#4323C2×C411yescharacteristic
110C4×C22⋊D11—21no—
111C4×C22⋊D11—21no—
112C2×(C2×D11)⋊C4—21no—
113#66979C2311yescharacteristic
114C2×C4×Dic11C2311yescharacteristic
115C2×#4318C2311yescharacteristic
116C2×#4318C2311yescharacteristic
117C22×C11⋊C8C2311yescharacteristic
118C22×C11⋊C8C2311yescharacteristic
119M16×D11—41no—
120M16×D11—41no—
121C2×#4313—21no—
122C2×C8×D11—21no—
123C2×C8×D11—41no—
124C2×C8×D11—41no—
125C2×C8×D11D411yescharacteristic
126C2×C8×D11D411yescharacteristic
127C2×C8×D11D411yescharacteristic
128C2×C8×D11D411yescharacteristic
129C11×#104—41no—
130C11×#104—41no—
131C11×C22⋊C8—21no—
132C11×C22⋊C8—21no—
133#66901—41no—
134#66901—41no—
135#66899C2×C411yescharacteristic
136#66899C2×C411yescharacteristic
137#66896C2×C411yescharacteristic
138#66896C2×C411yescharacteristic
139C11⋊#95—21no—
140C22⋊(C11⋊C8)—21no—
141C22⋊(C11⋊C8)—21no—
142C22⋊(C11⋊C8)—21no—
143C22⋊(C11⋊C8)—21no—
144#66889—41no—
145#66886—41no—
146#66885C2×C411yescharacteristic
147#66885C2×C411yescharacteristic
148(C2×D11)⋊C8—21no—
149(C2×D11)⋊C8—21no—
150(C2×D11)⋊C8—21no—
151(C2×D11)⋊C8—21no—
152(C2×D11)⋊C8—21no—
153(C2×D11)⋊C8—21no—
154(C2×D11)⋊C8C2×C411yescharacteristic
155(C2×D11)⋊C8C2×C411yescharacteristic
156(C2×D11)⋊C8C2×C411yescharacteristic
157(C2×D11)⋊C8C2×C411yescharacteristic
158#66883—41no—
159#66880C2×C411yescharacteristic
160#66880C2×C411yescharacteristic
161#66879—21no—
162Dic11⋊C8—21no—
163Dic11⋊C8—21no—
164C8×Dic11—21no—
165C8×Dic11—41no—
166#66869—41no—
167C4×C11⋊C8—41no—
168#22060—111nomaximal, Sylow
169C23×D11—21no—
170C23×D11#4111yescharacteristic
171C11×#41—21no—
172C11×#41—21no—
173C11×#41—21no—
174C11×#41—21no—
175C11×#41—21no—
176C11×#41—21no—
177C11×#41—21no—
178C11×#41—21no—
179C2×Q8×C11C22×C411yescharacteristic
180C2×Q8×C11C22×C411yescharacteristic
181C2×D4×C11—21no—
182C2×D4×C11—21no—
183C2×D4×C11C22×C411yescharacteristic
184C2×D4×C11C22×C411yescharacteristic
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11C2411yescharacteristic
189C2×C22⋊D11—21no—
190C2×C22⋊D11—21no—
191C2×C22⋊D11—21no—
192C2×C22⋊D11—21no—
193C2×C22⋊D11—21no—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11#4111yescharacteristic
197#4343—41no—
198#4343—41no—
199Q8×D11—41no—
200Q8×D11—41no—
201#4341—41no—
202#4341—41no—
203#4341—42no—
204#4341—42no—
205D4×D11—41no—
206D4×D11—41no—
207D4×D11—42no—
208D4×D11—42no—
209#4339—21no—
210#4339—21no—
211#4339—21no—
212#4339—21no—
213#4339—42no—
214#4339—42no—
215C2×D44—21no—
216C2×D44C22×C411yescharacteristic
217C2×C4×D11—21no—
218C2×C4×D11—21no—
219C2×C4×D11—21no—
220C2×C4×D11—21no—
221C2×C4×D11—21no—
222C2×C4×D11—21no—
223C2×C4×D11—21no—
224C2×C4×D11—42no—
225C2×C4×D11—42no—
226C2×C4×D11C22×C411yescharacteristic
227C2×C4×D11C22×C411yescharacteristic
228C2×C4×D11C2×D411yescharacteristic
229C2×C4×D11C2×D411yescharacteristic
230C2×Dic22—21no—
231C2×Dic22C22×C411yescharacteristic
232C11×Q16—41no—
233C11×SD16—41no—
234C11×SD16—41no—
235C11×D8—41no—
236C11×M16—21no—
237C11×M16—21no—
238C11×M16—21no—
239C11×M16—21no—
240C11×M16—42no—
241C2×C8×C11—21no—
242C2×C8×C11—21no—
243C2×C8×C11—21no—
244C2×C8×C11—21no—
245C2×C8×C11—21no—
246C2×C8×C11—21no—
247C2×C8×C11—42no—
248C2×C8×C11C22×C411yescharacteristic
249C2×C8×C11C22×C411yescharacteristic
250C2×C8×C11C2×D411yescharacteristic
251C2×C8×C11C2×D411yescharacteristic
252C42×C11—21no—
253C42×C11—21no—
254C22⋊Dic11—21no—
255C22⋊Dic11—21no—
256C22⋊Dic11—21no—
257#4326—41no—
258#4325—41no—
259#4324—41no—
260#4323—41no—
261(C2×D11)⋊C4—24no—
262(C2×D11)⋊C4—21no—
263(C2×D11)⋊C4—21no—
264C4⋊Dic11C22×C411yescharacteristic
265C4⋊Dic11C22×C411yescharacteristic
266Dic11⋊C4—21no—
267Dic11⋊C4—21no—
268C4×Dic11—21no—
269C4×Dic11—21no—
270C4×Dic11—21no—
271#4318—21no—
272#4318—21no—
273#4318—21no—
274#4318—21no—
275C2×C11⋊C8—21no—
276C2×C11⋊C8—21no—
277C2×C11⋊C8—21no—
278C2×C11⋊C8—21no—
279C2×C11⋊C8—21no—
280C2×C11⋊C8—21no—
281C2×C11⋊C8C22×C411yescharacteristic
282C2×C11⋊C8C22×C411yescharacteristic
283C2×C11⋊C8C2×D411yescharacteristic
284C2×C11⋊C8C2×D411yescharacteristic
285#4313—42no—
286C8×D11—41no—
287C8×D11—41no—
288C8×D11—41no—
289C8×D11—41no—
290C8×D11—42no—
291#3002—111no—
292#2929—111no—
293C2×#408—111no—
294#1974—111no—
295#1974—111no—
296#1937—111no—
297#1937—111no—
298#1929—111no—
299#1929—111no—
300#1876—111no—
301#1876D1111yescharacteristic, complemented
302#1871—111no—
303#1855—111no—
304#1789—111no—
305C8×C22⋊C4—111no—
306C23×C11—21no—
307C23×C11—21no—
308C23×C11C2×#4111yescharacteristic
309C22×D11—21no—
310C22×D11—21no—
311C22×D11—22no—
312C22×D11—21no—
313C22×D11—41no—
314C22×D11—42no—
315C22×D11—42no—
316C22×D11—42no—
317C22×D11C4×D411yescharacteristic
318C22×D11C4×D411yescharacteristic
319Q8×C11—21no—
320Q8×C11—21no—
321Q8×C11—21no—
322Q8×C11—21no—
323D4×C11—21no—
324D4×C11—21no—
325D4×C11—21no—
326D4×C11—21no—
327D4×C11—41no—
328D4×C11—41no—
329D4×C11—41no—
330D4×C11—41no—
331C2×C4×C11—22no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11C23×C411yescharacteristic
341C2×C4×C11C22×D411yescharacteristic
342C2×C4×C11H(5,𝔽2)11yescharacteristic
343C2×C4×C11H(5,𝔽2)11yescharacteristic
344C2×C4×C11H(5,𝔽2)11yescharacteristic
345C2×C4×C11H(5,𝔽2)11yescharacteristic
346C22⋊D11—42no—
347C22⋊D11—42no—
348C22⋊D11—42no—
349C22⋊D11—41no—
350C22⋊D11—41no—
351C22⋊D11—42no—
352C2×Dic11—21no—
353C2×Dic11—21no—
354C2×Dic11—22no—
355C2×Dic11—21no—
356C2×Dic11—21no—
357C2×Dic11—21no—
358C2×Dic11—42no—
359C2×Dic11—41no—
360C2×Dic11—41no—
361C2×Dic11C4×D411yescharacteristic
362C2×Dic11C4×D411yescharacteristic
363D44—21no—
364D44—21no—
365D44—42no—
366C4×D11—21no—
367C4×D11—21no—
368C4×D11—21no—
369C4×D11—21no—
370C4×D11—21no—
371C4×D11—21no—
372C4×D11—21no—
373C4×D11—21no—
374C4×D11—42no—
375C4×D11—42no—
376C4×D11—41no—
377C4×D11—41no—
378Dic22—21no—
379Dic22—21no—
380Dic22—42no—
381C8×C11—21no—
382C8×C11—21no—
383C8×C11—21no—
384C8×C11—21no—
385C8×C11—41no—
386C8×C11—41no—
387C11⋊C8—21no—
388C11⋊C8—21no—
389C11⋊C8—21no—
390C11⋊C8—21no—
391C11⋊C8—41no—
392C11⋊C8—41no—
393C22×#41—111no—
394C2×#135—111no—
395C2×#135C2×D1111yescharacteristic
396C2×#131C2×D1111yescharacteristic, complemented
397C22×M16—111no—
398C23×C8—111no—
399#525—111no—
400#452—111no—
401#452—111no—
402#451—111no—
403#450—111no—
404#449—111no—
405#449—111no—
406#448—111no—
407#447—111no—
408#435—221no—
409#435—221no—
410C8×D4—221no—
411C8×D4—221no—
412C2×#108—111no—
413C2×#108—111no—
414#424—111no—
415C2×#104—111no—
416C2×#104—111no—
417C2×#104—111no—
418C2×#104—111no—
419C2×#104C2×D1111yescharacteristic
420C2×#104C2×D1111yescharacteristic, complemented
421#416—111no—
422#416—111no—
423#408—111no—
424#408—111no—
425#408—111no—
426#408—111no—
427#408—221no—
428#408—221no—
429#408C2×D1111yescharacteristic
430#407—111no—
431C2×C22⋊C8—111no—
432C2×C22⋊C8—221no—
433C2×C22⋊C8—221no—
434#405—111no—
435C2×C4×C8—111no—
436C2×C4×C8—111no—
437C4×C22⋊C4—111no—
438#341—111no—
439#341C2×D1111yescharacteristic, complemented
440#339—111no—
441#339—111no—
442#336—111no—
443#336C2×D1111yescharacteristic, complemented
444C22×C11—21no—
445C22×C11—21no—
446C22×C11—41no—
447C22×C11—41no—
448C22×C11—41no—
449C22×C11—41no—
450C22×C11—41no—
451C22×C11—41no—
452C22×C11C2×C4×D411yescharacteristic
453C22×C11#53811yescharacteristic
454C22×C11#53811yescharacteristic
455C2×D11—21no—
456C2×D11—21no—
457C2×D11—21no—
458C2×D11—21no—
459C2×D11—21no—
460C2×D11—42no—
461C2×D11—42no—
462C2×D11—41no—
463C2×D11—41no—
464C2×D11—41no—
465C2×D11—84no—
466C2×D11#44312yes—
467C4×C11—42no—
468C4×C11—41no—
469C4×C11—41no—
470C4×C11#51811yescharacteristic
471C4×C11#51811yescharacteristic
472C4×C11#53411yescharacteristic
473C4×C11#53511yescharacteristic
474Dic11—21no—
475Dic11—21no—
476Dic11—42no—
477Dic11—41no—
478Dic11—41no—
479Dic11—41no—
480C2×#41—111no—
481C2×#41—111no—
482C2×#41—111no—
483C2×#41—221no—
484C2×#41—221no—
485C2×#41—441no—
486C2×#41—441no—
487C2×#41—441no—
488C2×#41—441no—
489C2×#41C22×D1111yescharacteristic
490C2×#41C22×D1111yescharacteristic
491C22×Q8—111no—
492C22×D4—111no—
493C22×D4—221no—
494C23×C4—111no—
495C23×C4—221no—
496#135—41no—
497#135—41no—
498#135—441no—
499#135—441no—
500C2×Q16—111no—
501C2×Q16C4×D1111yescharacteristic
502C2×SD16—111no—
503C2×SD16—111no—
504C2×SD16C4×D1111yescharacteristic
505C2×SD16C4×D1111yescharacteristic
506C2×D8—111no—
507C2×D8C4×D1111yescharacteristic
508#131—41no—
509#131—41no—
510C2×M16—21no—
511C2×M16—111no—
512C2×M16—111no—
513C2×M16—221no—
514C2×M16—441no—
515C2×M16—441no—
516C2×M16C22×D1111yescharacteristic
517C2×M16C22×D1111yescharacteristic
518C22×C8—21no—
519C22×C8—111no—
520C22×C8—111no—
521C22×C8—111no—
522C22×C8—111no—
523C22×C8—111no—
524C22×C8—111no—
525C22×C8—221no—
526C22×C8—441no—
527C22×C8—441no—
528C22×C8C22×D1111yescharacteristic
529C22×C8C22×D1111yescharacteristic
530#123—221no—
531C22⋊Q8—111no—
532C22⋊Q8—111no—
533#121—111no—
534#121—111no—
535#120—221no—
536C4×D4—221no—
537C4×D4—221no—
538#117—111no—
539C2×C22⋊C4—221no—
540C2×C42—111no—
541C2×C42C22×D1111yescharacteristic
542#108—441no—
543#108—441no—
544C4⋊C8—221no—
545C4⋊C8—221no—
546#104—41no—
547#104—41no—
548#104—441no—
549#104—441no—
550#104—441no—
551#104—441no—
552#103—111no—
553#103—111no—
554#103—111no—
555#103—111no—
556#102—111no—
557#102—111no—
558#102—111no—
559#102—111no—
560C22⋊C8—21no—
561C22⋊C8—21no—
562C22⋊C8—111no—
563C22⋊C8—111no—
564C22⋊C8—111no—
565C22⋊C8—111no—
566C22⋊C8—221no—
567C22⋊C8—221no—
568C22⋊C8—221no—
569C22⋊C8—221no—
570C22⋊C8—221no—
571C22⋊C8—221no—
572C22⋊C8—221no—
573C22⋊C8—221no—
574C22⋊C8—221no—
575C22⋊C8—221no—
576#97—221no—
577C4×C8—221no—
578C4×C8—441no—
579C4×C8—441no—
580#95—221no—
581C2×C11—21no—
582C2×C11—21no—
583C2×C11—81no—
584C2×C11—81no—
585C2×C11#232111yescharacteristic
586C2×C11C2×#44311yescharacteristic
587C2×C11#295511yescharacteristic
588D11—22no—
589D11—41no—
590D11—81no—
591C24—111no—
592C24—221no—
593#41—21no—
594#41—21no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—221no—
602#41—221no—
603#41—221no—
604#41—221no—
605#41—442no—
606#41—442no—
607#41—441no—
608#41—441no—
609#41—442no—
610#41—442no—
611#41—441no—
612#41—441no—
613C2×Q8—111no—
614C2×Q8—221no—
615C2×Q8—441no—
616C2×Q8—441no—
617C2×Q8C2×C4×D1111yescharacteristic
618C2×Q8C2×C4×D1111yescharacteristic
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—111no—
622C2×D4—221no—
623C2×D4—221no—
624C2×D4—221no—
625C2×D4—221no—
626C2×D4—221no—
627C2×D4—221no—
628C2×D4—441no—
629C2×D4—441no—
630C2×D4—442no—
631C2×D4—442no—
632C2×D4C2×C4×D1111yescharacteristic
633C2×D4C2×C4×D1111yescharacteristic
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—111no—
638C22×C4—111no—
639C22×C4—111no—
640C22×C4—111no—
641C22×C4—111no—
642C22×C4—221no—
643C22×C4—221no—
644C22×C4—221no—
645C22×C4—221no—
646C22×C4—221no—
647C22×C4—221no—
648C22×C4—221no—
649C22×C4—221no—
650C22×C4—221no—
651C22×C4—442no—
652C22×C4—442no—
653C22×C4C23×D1111yescharacteristic
654Q16—41no—
655Q16—441no—
656SD16—41no—
657SD16—41no—
658SD16—441no—
659SD16—441no—
660D8—41no—
661D8—441no—
662M16—21no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—42no—
667M16—221no—
668M16—221no—
669M16—221no—
670M16—221no—
671M16—442no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—42no—
679C2×C8—111no—
680C2×C8—111no—
681C2×C8—111no—
682C2×C8—111no—
683C2×C8—221no—
684C2×C8—221no—
685C2×C8—221no—
686C2×C8—221no—
687C2×C8—221no—
688C2×C8—221no—
689C2×C8—441no—
690C2×C8—441no—
691C2×C8—441no—
692C2×C8—441no—
693C2×C8—442no—
694C2×C8C2×C4×D1111yescharacteristic
695C2×C8C2×C4×D1111yescharacteristic
696C2×C8D4×D1111yescharacteristic
697C2×C8D4×D1111yescharacteristic
698C4⋊C4—111no—
699C4⋊C4—111no—
700C4⋊C4—221no—
701C4⋊C4—221no—
702C22⋊C4—221no—
703C22⋊C4—221no—
704C22⋊C4—224no—
705C22⋊C4—221no—
706C22⋊C4—221no—
707C22⋊C4—221no—
708C42—21no—
709C42—21no—
710C42—221no—
711C42—221no—
712C42—221no—
713C11#2206011yescharacteristic, complemented, Sylow
714C23—21no—
715C23—21no—
716C23—111no—
717C23—111no—
718C23—222no—
719C23—221no—
720C23—221no—
721C23—221no—
722C23—441no—
723C23—442no—
724C23—442no—
725C23—442no—
726C23#41×D1111yescharacteristic
727Q8—21no—
728Q8—21no—
729Q8—21no—
730Q8—21no—
731Q8—221no—
732Q8—221no—
733Q8—442no—
734D4—21no—
735D4—21no—
736D4—21no—
737D4—21no—
738D4—41no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—221no—
743D4—221no—
744D4—442no—
745D4—442no—
746D4—442no—
747D4—442no—
748D4—442no—
749D4—441no—
750D4—441no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—111no—
761C2×C4—111no—
762C2×C4—221no—
763C2×C4—221no—
764C2×C4—221no—
765C2×C4—221no—
766C2×C4—221no—
767C2×C4—221no—
768C2×C4—221no—
769C2×C4—221no—
770C2×C4—221no—
771C2×C4—221no—
772C2×C4—222no—
773C2×C4—221no—
774C2×C4—221no—
775C2×C4—221no—
776C2×C4—442no—
777C2×C4—442no—
778C2×C4—442no—
779C2×C4—441no—
780C2×C4—441no—
781C2×C4—441no—
782C2×C4—441no—
783C2×C4C22×C4×D1111yescharacteristic
784C2×C4C2×D4×D1111yescharacteristic
785C2×C4#6703711yescharacteristic
786C2×C4#6703711yescharacteristic
787C2×C4#6703711yescharacteristic
788C2×C4#6704211yescharacteristic
789C8—21no—
790C8—21no—
791C8—21no—
792C8—21no—
793C8—41no—
794C8—41no—
795C8—221no—
796C8—221no—
797C8—221no—
798C8—221no—
799C8—441no—
800C8—441no—
801C22—21no—
802C22—21no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—112no—
810C22—221no—
811C22—221no—
812C22—221no—
813C22—221no—
814C22—221no—
815C22—442no—
816C22—442no—
817C22—441no—
818C22—441no—
819C22—441no—
820C22—884no—
821C22C4×D4×D1111yescharacteristic
822C22#1062314411yescharacteristic
823C22#1062318811yescharacteristic
824C4—42no—
825C4—41no—
826C4—41no—
827C4—221no—
828C4—221no—
829C4—442no—
830C4—441no—
831C4—441no—
832C4—441no—
833C4#1062301711yescharacteristic
834C4#1062307611yescharacteristic
835C4#1062312011yescharacteristic
836C4#1062313811yescharacteristic
837C2—21no—
838C2—21no—
839C2—81no—
840C2—81no—
841C2—222no—
842C2—441no—
843C2—881no—
844C2#1307127211yescharacteristic
845C2D11×#44311yescharacteristic
846C2#1307751611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1876C2
socleC22×C11C2×C4×D4
prime radical#13077830C2
cosocleC22×C4×C11C24
hypercenter#1876D11
hypocenterC11#22060
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1876

Complements

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

NH ≅ G/Ntype
2. #13077308C2semidirect
3. D11×#408C2semidirect
4. #13069505C2semidirect
5. #13069501C2semidirect
6. #13069318C2semidirect
7. #13069317C2semidirect
8. #13069265C2semidirect
9. #13069261C2semidirect
10. #13068943C2semidirect
11. #13068915C2semidirect
12. #13068822C2semidirect
13. #13068558C2semidirect
14. #13068386C2semidirect
15. C11×#1876C2semidirect
18. C2×C11×#131C22semidirect
24. C2×C11×#104C22semidirect
27. C2×#66901C22semidirect
29. #10622847C22semidirect
31. #10622800C4semidirect
32. #10622799C4semidirect
33. #10622786C4semidirect
34. #10622785C4semidirect
35. #10622783C4semidirect
36. #10622782C4semidirect
37. #10622771C4semidirect
38. #10622769C4semidirect
44. C2×#66886C22semidirect
45. #10622732C22semidirect
51. C2×#66883C22semidirect
52. #10622714C22semidirect
53. C2×C8×Dic11C22semidirect
56. C2×C4×C11⋊C8C22semidirect
61. C11×#341C22semidirect
62. C11×#336C22semidirect
63. #10622196C22semidirect
64. #10622193C22semidirect
65. #10622188C22semidirect
66. #10622161C22semidirect
301. #1876D11semidirect
396. C2×#131C2×D11semidirect
420. C2×#104C2×D11semidirect
439. #341C2×D11semidirect
443. #336C2×D11semidirect
713. C11#22060semidirect

Maximal subgroups

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

subgroupindex
#130778302
#130773082
D11×#4082
#130695052
#130695012
#130693182
#130693172
#130692652
#130692612
#130689432
#130689152
#130688222
#130685582
#130683862
C11×#18762
#2206011