Finite Group Databasebeta

← #14765196

Subgroups — #14765196

Order 2816.

900 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#13077834C211yesmaximal, characteristic
2#13077319C211yesmaximal, characteristic, complemented
3#13069508C211yesmaximal, characteristic, complemented
4#13069503C211yesmaximal, characteristic, complemented
5#13069330C211yesmaximal, characteristic, complemented
6#13069323C211yesmaximal, characteristic, complemented
7#13069261C211yesmaximal, characteristic, complemented
8#13069261C211yesmaximal, characteristic, complemented
9#13068946C211yesmaximal, characteristic, complemented
10#13068946C211yesmaximal, characteristic, complemented
11#13068918C211yesmaximal, characteristic, complemented
12#13068821C211yesmaximal, characteristic, complemented
13#13068560C211yesmaximal, characteristic, complemented
14#13068397C211yesmaximal, characteristic, complemented
15C11×#2879C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C2×#67003C2211yescharacteristic
20C2×#67003C2211yescharacteristic
21#10623322C2211yescharacteristic
22C2×#66954C2211yescharacteristic, complemented
23C11×#408—21no—
24C11×#408—21no—
25C11×#408C2211yescharacteristic
26C11×#408C2211yescharacteristic
27C11×#408C2211yescharacteristic
28C11×#408C2211yescharacteristic
29C11×#407—21no—
30C11×#407—21no—
31#10622852C411yescharacteristic, complemented
32#10622852C411yescharacteristic, complemented
33#10622851C411yescharacteristic, complemented
34#10622851C411yescharacteristic, complemented
35C2×#66901C2211yescharacteristic
36C2×#66901C2211yescharacteristic
37C2×#66901C2211yescharacteristic
38C2×#66901C2211yescharacteristic
39#10622846C2211yescharacteristic
40#10622846C2211yescharacteristic
41#10622841C411yescharacteristic, complemented
42#10622840C411yescharacteristic, complemented
43#10622831C411yescharacteristic, complemented
44#10622830C411yescharacteristic, complemented
45C4×C22⋊Dic11C2211yescharacteristic
46#10622820C2211yescharacteristic
47C2×C22⋊(C11⋊C8)C2211yescharacteristic
48C2×#66889C2211yescharacteristic, complemented
49C2×#66889C2211yescharacteristic, complemented
50#10622741—21no—
51#10622741—21no—
52#10622740—21no—
53#10622740—21no—
54C2×#66886C2211yescharacteristic, complemented
55C2×#66886C2211yescharacteristic, complemented
56#10622723C2211yescharacteristic, complemented
57#10622715C2211yescharacteristic, complemented
58#10622714C2211yescharacteristic, complemented
59C2×#66879C2211yescharacteristic, complemented
60C2×C8×Dic11C2211yescharacteristic, complemented
61#10622196C2211yescharacteristic, complemented
62#10622196C2211yescharacteristic, complemented
63#10622193C2211yescharacteristic, complemented
64#10622193C2211yescharacteristic, complemented
65#10622188C2211yescharacteristic, complemented
66#10622188C2211yescharacteristic, complemented
67C2×C11×#41—21no—
68C2×C11×#41—21no—
69C2×C11×#41—41no—
70C2×C11×#41—41no—
71C2×C11×#41—41no—
72C2×C11×#41—41no—
73C2×C11×#41C2×C411yescharacteristic
74C2×C11×#41C2×C411yescharacteristic
75C2×C11×#41C2311yescharacteristic
76C2×C11×#41C2311yescharacteristic
77C22×Q8×C11C2×C411yescharacteristic
78C22×D4×C11—21no—
79C22×D4×C11C2×C411yescharacteristic
80C23×C4×C11—21no—
81C23×C4×C11C2311yescharacteristic
82C2×#4339C2311yescharacteristic
83C2×C11×M16—21no—
84C2×C11×M16—41no—
85C2×C11×M16—41no—
86C2×C11×M16—41no—
87C2×C11×M16—41no—
88C2×C11×M16D411yescharacteristic
89C2×C11×M16D411yescharacteristic
90C2×C11×M16D411yescharacteristic
91C2×C11×M16D411yescharacteristic
92C2×C11×M16C2311yescharacteristic
93C2×C11×M16C2311yescharacteristic
94C22×C8×C11—21no—
95C22×C8×C11C2311yescharacteristic
96C22×C8×C11C2311yescharacteristic
97#67006—21no—
98C2×C22⋊Dic11—21no—
99#67003—41no—
100#67003—41no—
101#67003—41no—
102#67003—41no—
103C2×#4326C2×C411yescharacteristic
104C2×#4326C2×C411yescharacteristic
105C2×#4325C2×C411yescharacteristic
106C2×#4325C2×C411yescharacteristic
107C2×#4324C2×C411yescharacteristic
108C2×#4324C2×C411yescharacteristic
109C2×#4323C2×C411yescharacteristic
110C2×#4323C2×C411yescharacteristic
111#66983C2×C411yescharacteristic
112#66983C2×C411yescharacteristic
113#66982—21no—
114C4×C22⋊D11—21no—
115C4×C22⋊D11—21no—
116#66979C2311yescharacteristic
117#66977C2×C411yescharacteristic
118#66977C2×C411yescharacteristic
119C2×C4×Dic11C2311yescharacteristic
120C2×C4×Dic11C2311yescharacteristic
121C2×#4318C2311yescharacteristic
122C2×#4318C2311yescharacteristic
123C22×C11⋊C8C2311yescharacteristic
124C22×C11⋊C8C2311yescharacteristic
125#66954—41no—
126#66954—41no—
127C2×#4313—21no—
128C2×C8×D11—21no—
129C11×C22⋊C8—21no—
130C11×C22⋊C8—21no—
131C11×C22⋊C8—21no—
132C11×C22⋊C8—21no—
133C11×C22⋊C8—21no—
134C11×C22⋊C8—21no—
135C11×C22⋊C8—21no—
136C11×C22⋊C8—21no—
137#66901—41no—
138#66901—41no—
139#66901—41no—
140#66901—41no—
141#66899C2×C411yescharacteristic
142#66899C2×C411yescharacteristic
143#66899C2×C411yescharacteristic
144#66899C2×C411yescharacteristic
145#66896C2×C411yescharacteristic
146#66896C2×C411yescharacteristic
147#66896C2×C411yescharacteristic
148#66896C2×C411yescharacteristic
149C11⋊#95—21no—
150C22⋊(C11⋊C8)—21no—
151C22⋊(C11⋊C8)—21no—
152C22⋊(C11⋊C8)C2×C411yescharacteristic
153C22⋊(C11⋊C8)C2×C411yescharacteristic
154C22⋊(C11⋊C8)C2×C411yescharacteristic
155C22⋊(C11⋊C8)C2×C411yescharacteristic
156#66889—41no—
157#66889—41no—
158#66886—41no—
159#66886—41no—
160(C2×D11)⋊C8—21no—
161(C2×D11)⋊C8—21no—
162#66879—21no—
163#66879—41no—
164Dic11⋊C8—21no—
165Dic11⋊C8—21no—
166C8×Dic11—21no—
167C8×Dic11—41no—
168#22062—111nomaximal, Sylow
169C24×C11—21no—
170C24×C11#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—
179C11×#41—41no—
180C11×#41—41no—
181C11×#41—41no—
182C11×#41—41no—
183C11×#41—42no—
184C11×#41—42no—
185C11×#41—42no—
186C11×#41—42no—
187C2×Q8×C11—21no—
188C2×Q8×C11—41no—
189C2×Q8×C11—41no—
190C2×Q8×C11C22×C411yescharacteristic
191C2×Q8×C11C22×C411yescharacteristic
192C2×D4×C11—21no—
193C2×D4×C11—21no—
194C2×D4×C11—21no—
195C2×D4×C11—21no—
196C2×D4×C11—21no—
197C2×D4×C11—41no—
198C2×D4×C11—41no—
199C2×D4×C11—42no—
200C2×D4×C11—42no—
201C2×D4×C11C22×C411yescharacteristic
202C2×D4×C11C22×C411yescharacteristic
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—42no—
213C22×C4×C11—42no—
214C22×C4×C11C22×C411yescharacteristic
215C22×C4×C11C22×C411yescharacteristic
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11#4111yescharacteristic
219C22×C4×C11C2411yescharacteristic
220C2×C22⋊D11—21no—
221C2×C22⋊D11—21no—
222C2×C22⋊D11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225#4339—21no—
226#4339—21no—
227#4339—21no—
228#4339—21no—
229C2×D44C22×C411yescharacteristic
230C2×C4×D11—21no—
231C2×Dic22C22×C411yescharacteristic
232C11×M16—21no—
233C11×M16—21no—
234C11×M16—21no—
235C11×M16—21no—
236C11×M16—41no—
237C11×M16—41no—
238C11×M16—41no—
239C11×M16—41no—
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×C11C2×D411yescharacteristic
249C2×C8×C11C2×D411yescharacteristic
250C2×C8×C11C2×D411yescharacteristic
251C2×C8×C11C2×D411yescharacteristic
252C22⋊Dic11—21no—
253C22⋊Dic11—21no—
254C22⋊Dic11—21no—
255C22⋊Dic11—42no—
256#4326—41no—
257#4326—41no—
258#4325—41no—
259#4325—41no—
260#4324—41no—
261#4324—41no—
262#4323—41no—
263#4323—41no—
264(C2×D11)⋊C4—21no—
265(C2×D11)⋊C4—21no—
266C4⋊Dic11C22×C411yescharacteristic
267C4⋊Dic11C22×C411yescharacteristic
268Dic11⋊C4—21no—
269Dic11⋊C4—21no—
270C4×Dic11—21no—
271C4×Dic11—21no—
272C4×Dic11—21no—
273C4×Dic11—21no—
274C4×Dic11—21no—
275#4318—21no—
276#4318—21no—
277#4318—21no—
278#4318—21no—
279C2×C11⋊C8—21no—
280C2×C11⋊C8—21no—
281C2×C11⋊C8—21no—
282C2×C11⋊C8—21no—
283C2×C11⋊C8—21no—
284C2×C11⋊C8—21no—
285C2×C11⋊C8C22×C411yescharacteristic
286C2×C11⋊C8C22×C411yescharacteristic
287C2×C11⋊C8C22×C411yescharacteristic
288C2×C11⋊C8C22×C411yescharacteristic
289#4313—42no—
290C8×D11—42no—
291#3002—111no—
292#2930—111no—
293#2879D1111yescharacteristic, complemented
294#1975—111no—
295#1974—111no—
296#1938—111no—
297#1937—111no—
298#1929—111no—
299#1929—111no—
300#1876—111no—
301#1876—111no—
302#1871—111no—
303#1855—111no—
304#1789—111no—
305#1753—111no—
306C23×C11—21no—
307C23×C11—21no—
308C23×C11—21no—
309C23×C11—21no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—42no—
313C23×C11—81no—
314C23×C11—81no—
315C23×C11C4×D411yescharacteristic
316C23×C11C4×D411yescharacteristic
317C23×C11C2×#4111yescharacteristic
318C22×D11—21no—
319Q8×C11—21no—
320Q8×C11—21no—
321Q8×C11—21no—
322Q8×C11—21no—
323Q8×C11—42no—
324D4×C11—21no—
325D4×C11—21no—
326D4×C11—21no—
327D4×C11—21no—
328D4×C11—42no—
329D4×C11—42no—
330D4×C11—42no—
331D4×C11—41no—
332D4×C11—41no—
333D4×C11—41no—
334D4×C11—41no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—21no—
338C2×C4×C11—21no—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—21no—
345C2×C4×C11—21no—
346C2×C4×C11—21no—
347C2×C4×C11—42no—
348C2×C4×C11—42no—
349C2×C4×C11—42no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11C4×D411yescharacteristic
355C2×C4×C11C4×D411yescharacteristic
356C2×C4×C11C23×C411yescharacteristic
357C2×C4×C11C22×D411yescharacteristic
358C2×C4×C11H(5,𝔽2)11yescharacteristic
359C2×C4×C11H(5,𝔽2)11yescharacteristic
360C2×C4×C11H(5,𝔽2)11yescharacteristic
361C2×C4×C11H(5,𝔽2)11yescharacteristic
362C22⋊D11—41no—
363C22⋊D11—41no—
364C22⋊D11—81no—
365C22⋊D11—81no—
366C2×Dic11—22no—
367C2×Dic11—21no—
368C2×Dic11—21no—
369C2×Dic11—21no—
370C2×Dic11—41no—
371C2×Dic11—41no—
372C2×Dic11—41no—
373C2×Dic11—41no—
374C2×Dic11—41no—
375D44—21no—
376D44—21no—
377C4×D11—41no—
378C4×D11—41no—
379Dic22—21no—
380Dic22—21no—
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×#41C2×D1111yescharacteristic
394C2×#135—111no—
395C2×#135—111no—
396C2×#131—111no—
397C22×M16C2×D1111yescharacteristic
398C22×M16C2×D1111yescharacteristic
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#436—221no—
409#436—221no—
410#435—221no—
411#435—221no—
412C2×#108—111no—
413C2×#108—111no—
414#424—111no—
415C2×#104—111no—
416C2×#104—111no—
417C2×#104—111no—
418C2×#104—111no—
419C2×#104—111no—
420C2×#104—111no—
421#416—111no—
422#416—111no—
423#408—21no—
424#408—21no—
425#408—111no—
426#408C2×D1111yescharacteristic
427#408C2×D1111yescharacteristic
428#408C2×D1111yescharacteristic
429#408C2×D1111yescharacteristic
430#407—21no—
431#407—21no—
432#407—111no—
433C2×C22⋊C8—111no—
434#405—111no—
435C2×#97—111no—
436C2×C4×C8—111no—
437C4×C22⋊C4—111no—
438#341—111no—
439#341—111no—
440#339—111no—
441#339—111no—
442#336—111no—
443#336—111no—
444C22×C11—21no—
445C22×C11—21no—
446C22×C11—21no—
447C22×C11—21no—
448C22×C11—21no—
449C22×C11—21no—
450C22×C11—21no—
451C22×C11—21no—
452C22×C11—41no—
453C22×C11—41no—
454C22×C11—41no—
455C22×C11—41no—
456C22×C11—41no—
457C22×C11—41no—
458C22×C11—81no—
459C22×C11—81no—
460C22×C11—84no—
461C22×C11C2×C4×D411yescharacteristic
462C22×C11#53811yescharacteristic
463C22×C11#53811yescharacteristic
464C2×D11—41no—
465C2×D11—41no—
466C2×D11—41no—
467C4×C11—21no—
468C4×C11—21no—
469C4×C11—41no—
470C4×C11—41no—
471C4×C11#51811yescharacteristic
472C4×C11#51811yescharacteristic
473C4×C11#53411yescharacteristic
474C4×C11#53511yescharacteristic
475Dic11—42no—
476Dic11—41no—
477Dic11—41no—
478Dic11—41no—
479Dic11—81no—
480C2×#41—21no—
481C2×#41—21no—
482C2×#41—41no—
483C2×#41—41no—
484C2×#41—41no—
485C2×#41—41no—
486C2×#41—111no—
487C2×#41C4×D1111yescharacteristic
488C2×#41C4×D1111yescharacteristic
489C2×#41C22×D1111yescharacteristic
490C2×#41C22×D1111yescharacteristic
491C22×Q8C4×D1111yescharacteristic
492C22×D4—21no—
493C22×D4C4×D1111yescharacteristic
494C23×C4—21no—
495C23×C4C22×D1111yescharacteristic
496#135—441no—
497#135—441no—
498#135—441no—
499#135—441no—
500C2×Q16—111no—
501C2×Q16—111no—
502C2×SD16—111no—
503C2×SD16—111no—
504C2×SD16—111no—
505C2×SD16—111no—
506C2×D8—111no—
507C2×D8—111no—
508#131—441no—
509#131—441no—
510C2×M16—21no—
511C2×M16—41no—
512C2×M16—41no—
513C2×M16—41no—
514C2×M16—41no—
515C2×M16—111no—
516C2×M16—111no—
517C2×M16—221no—
518C2×M16C22⋊D1111yescharacteristic
519C2×M16C22⋊D1111yescharacteristic
520C2×M16C22⋊D1111yescharacteristic
521C2×M16C22⋊D1111yescharacteristic
522C2×M16C22×D1111yescharacteristic
523C2×M16C22×D1111yescharacteristic
524C22×C8—21no—
525C22×C8—111no—
526C22×C8—111no—
527C22×C8—221no—
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×C42—111no—
542#108—441no—
543#108—441no—
544C4⋊C8—221no—
545C4⋊C8—221no—
546#104—441no—
547#104—441no—
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—21no—
563C22⋊C8—21no—
564C22⋊C8—21no—
565C22⋊C8—21no—
566C22⋊C8—21no—
567C22⋊C8—21no—
568C22⋊C8—111no—
569C22⋊C8—111no—
570C22⋊C8—111no—
571C22⋊C8—111no—
572C22⋊C8—221no—
573C22⋊C8—221no—
574C22⋊C8—221no—
575C22⋊C8—221no—
576#97—221no—
577#97—441no—
578C4×C8—221no—
579C4×C8—441no—
580#95—221no—
581C2×C11—21no—
582C2×C11—21no—
583C2×C11—41no—
584C2×C11—41no—
585C2×C11—81no—
586C2×C11—81no—
587C2×C11#232111yescharacteristic
588C2×C11#295611yescharacteristic
589C2×C11#295711yescharacteristic
590D11—81no—
591C24—21no—
592C24#433911yescharacteristic
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—41no—
602#41—41no—
603#41—41no—
604#41—41no—
605#41—42no—
606#41—42no—
607#41—42no—
608#41—42no—
609#41—221no—
610#41—221no—
611#41—221no—
612#41—221no—
613C2×Q8—21no—
614C2×Q8—41no—
615C2×Q8—41no—
616C2×Q8—111no—
617C2×Q8C2×C4×D1111yescharacteristic
618C2×Q8C2×C4×D1111yescharacteristic
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—41no—
625C2×D4—41no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—111no—
629C2×D4—221no—
630C2×D4—221no—
631C2×D4—221no—
632C2×D4C2×C4×D1111yescharacteristic
633C2×D4C2×C4×D1111yescharacteristic
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—221no—
646C22×C4—221no—
647C22×C4—221no—
648C22×C4C2×C4×D1111yescharacteristic
649C22×C4C2×C4×D1111yescharacteristic
650C22×C4#433911yescharacteristic
651C22×C4C2×C22⋊D1111yescharacteristic
652C22×C4C2×C22⋊D1111yescharacteristic
653C22×C4C23×D1111yescharacteristic
654Q16—441no—
655Q16—441no—
656SD16—441no—
657SD16—441no—
658SD16—441no—
659SD16—441no—
660D8—441no—
661D8—441no—
662M16—21no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—41no—
667M16—41no—
668M16—41no—
669M16—41no—
670M16—42no—
671M16—221no—
672M16—221no—
673M16—221no—
674M16—221no—
675M16—442no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—42no—
683C2×C8—111no—
684C2×C8—111no—
685C2×C8—111no—
686C2×C8—111no—
687C2×C8—221no—
688C2×C8—221no—
689C2×C8—221no—
690C2×C8—221no—
691C2×C8—221no—
692C2×C8—221no—
693C2×C8—442no—
694C2×C8C2×C22⋊D1111yescharacteristic
695C2×C8C2×C22⋊D1111yescharacteristic
696C2×C8C2×C22⋊D1111yescharacteristic
697C2×C8C2×C22⋊D1111yescharacteristic
698C4⋊C4—111no—
699C4⋊C4—111no—
700C4⋊C4—221no—
701C4⋊C4—221no—
702C22⋊C4—221no—
703C22⋊C4—221no—
704C22⋊C4—221no—
705C22⋊C4—221no—
706C22⋊C4—221no—
707C22⋊C4—442no—
708C42—221no—
709C42—221no—
710C42—221no—
711C42—221no—
712C42—221no—
713C11#2206211yescharacteristic, complemented, Sylow
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—41no—
719C23—41no—
720C23—42no—
721C23—81no—
722C23—81no—
723C23—221no—
724C23C4×C22⋊D1111yescharacteristic
725C23C4×C22⋊D1111yescharacteristic
726C23C2×#433911yescharacteristic
727Q8—21no—
728Q8—21no—
729Q8—21no—
730Q8—21no—
731Q8—42no—
732Q8—221no—
733Q8—221no—
734D4—21no—
735D4—21no—
736D4—21no—
737D4—21no—
738D4—42no—
739D4—42no—
740D4—42no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—221no—
746D4—221no—
747D4—441no—
748D4—441no—
749D4—881no—
750D4—881no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—222no—
771C2×C4—221no—
772C2×C4—221no—
773C2×C4—221no—
774C2×C4—441no—
775C2×C4—441no—
776C2×C4—441no—
777C2×C4—441no—
778C2×C4—441no—
779C2×C4—441no—
780C2×C4—441no—
781C2×C4C4×C22⋊D1111yescharacteristic
782C2×C4C4×C22⋊D1111yescharacteristic
783C2×C4C22×C4×D1111yescharacteristic
784C2×C4#6703711yescharacteristic
785C2×C4#6703711yescharacteristic
786C2×C4#6703711yescharacteristic
787C2×C4#6703711yescharacteristic
788C2×C4C22×C22⋊D1111yescharacteristic
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—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—81no—
816C22—81no—
817C22—84no—
818C22—441no—
819C22—441no—
820C22—441no—
821C22#1062302511yescharacteristic
822C22#1062302511yescharacteristic
823C22C2×C4×C22⋊D1111yescharacteristic
824C4—21no—
825C4—21no—
826C4—41no—
827C4—41no—
828C4—442no—
829C4—441no—
830C4—441no—
831C4—441no—
832C4—881no—
833C4#1062301711yescharacteristic
834C4#1062301711yescharacteristic
835C4#1062333511yescharacteristic
836C4#1062333611yescharacteristic
837C2—21no—
838C2—21no—
839C2—41no—
840C2—41no—
841C2—81no—
842C2—81no—
843C2—881no—
844C2#1307127411yescharacteristic
845C2#1307752311yescharacteristic
846C2#1307753111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2879C2
socleC22×C11C2×C4×D4
prime radical#13077834C2
cosocleC22×C4×C11C24
hypercenter#2879D11
hypocenterC11#22062
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×M16 ◁ #2879

Complements

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

NH ≅ G/Ntype
2. #13077319C2semidirect
3. #13069508C2semidirect
4. #13069503C2semidirect
5. #13069330C2semidirect
6. #13069323C2semidirect
7. #13069261C2semidirect
8. #13069261C2semidirect
9. #13068946C2semidirect
10. #13068946C2semidirect
11. #13068918C2semidirect
12. #13068821C2semidirect
13. #13068560C2semidirect
14. #13068397C2semidirect
15. C11×#2879C2semidirect
22. C2×#66954C22semidirect
31. #10622852C4semidirect
32. #10622852C4semidirect
33. #10622851C4semidirect
34. #10622851C4semidirect
41. #10622841C4semidirect
42. #10622840C4semidirect
43. #10622831C4semidirect
44. #10622830C4semidirect
48. C2×#66889C22semidirect
49. C2×#66889C22semidirect
54. C2×#66886C22semidirect
55. C2×#66886C22semidirect
56. #10622723C22semidirect
57. #10622715C22semidirect
58. #10622714C22semidirect
59. C2×#66879C22semidirect
60. C2×C8×Dic11C22semidirect
61. #10622196C22semidirect
62. #10622196C22semidirect
63. #10622193C22semidirect
64. #10622193C22semidirect
65. #10622188C22semidirect
66. #10622188C22semidirect
293. #2879D11semidirect
713. C11#22062semidirect

Maximal subgroups

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

subgroupindex
#130778342
#130773192
#130695082
#130695032
#130693302
#130693232
#130692612
#130689462
#130689182
#130688212
#130685602
#130683972
C11×#28792
#2206211