Finite Group Databasebeta

← #14765176

Subgroups — #14765176

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#13077836C211yesmaximal, characteristic
2#13077312C211yesmaximal, characteristic, complemented
3D11×#408C211yesmaximal, characteristic, complemented
4#13069502C211yesmaximal, characteristic, complemented
5#13069501C211yesmaximal, characteristic, complemented
6#13069322C211yesmaximal, characteristic, complemented
7#13069321C211yesmaximal, characteristic, complemented
8#13069264C211yesmaximal, characteristic, complemented
9#13068946C211yesmaximal, characteristic, complemented
10#13068942C211yesmaximal, characteristic, complemented
11#13068917C211yesmaximal, characteristic, complemented
12#13068819C211yesmaximal, characteristic, complemented
13#13068558C211yesmaximal, characteristic, complemented
14#13068386C211yesmaximal, characteristic, complemented
15C11×#1929C211yesmaximal, characteristic, complemented
16C2×#41×D11C2211yescharacteristic
17C2×#67003C2211yescharacteristic
18C2×M16×D11C2211yescharacteristic
19C2×#66957C2211yescharacteristic
20C2×#66954C2211yescharacteristic, complemented
21C22×C8×D11C2211yescharacteristic
22#10623055C2211yescharacteristic
23C2×C11×#108C2211yescharacteristic, complemented
24C2×C11×#104C2211yescharacteristic
25C11×#416C2211yescharacteristic
26C11×#408C2211yescharacteristic
27C11×#405C2211yescharacteristic, complemented
28C2×#66901C2211yescharacteristic
29#10622847C2211yescharacteristic
30C2×#66889C2211yescharacteristic
31C2×#66889C2211yescharacteristic, complemented
32#10622742C2211yescharacteristic
33#10622742C2211yescharacteristic, complemented
34#10622739C2211yescharacteristic
35C2×#66886C2211yescharacteristic, complemented
36#10622723C2211yescharacteristic
37C2×(C2×D11)⋊C8C2211yescharacteristic
38C2×C8×Dic11C2211yescharacteristic, complemented
39#10622615C2211yescharacteristic
40#10622612C2211yescharacteristic, complemented
41C4×(C2×D11)⋊C4C2211yescharacteristic
42C2×#66869C2211yescharacteristic
43C2×#66869C2211yescharacteristic, complemented
44C2×C4×C11⋊C8C2211yescharacteristic, complemented
45#10622424C411yescharacteristic, complemented
46#10622423C411yescharacteristic, complemented
47#10622421C411yescharacteristic, complemented
48#10622419C411yescharacteristic, complemented
49#10622396C411yescharacteristic, complemented
50#10622394C411yescharacteristic, complemented
51#10622389C411yescharacteristic, complemented
52#10622386C411yescharacteristic, complemented
53#10622340—21no—
54#10622340—21no—
55D11×C22⋊C8—21no—
56D11×C22⋊C8—21no—
57#10622319—21no—
58#10622319—21no—
59C8×D44—21no—
60C8×D44—21no—
61C11×#339C2211yescharacteristic, complemented
62C11×#336C2211yescharacteristic, complemented
63#10622196C2211yescharacteristic, complemented
64#10622190C2211yescharacteristic, complemented
65#10622188C2211yescharacteristic, complemented
66#10622170C2211yescharacteristic, complemented
67C2×C11×#41C2311yescharacteristic
68#41×D11—41no—
69#41×D11—41no—
70#41×D11—41no—
71#41×D11—41no—
72C2×#4343C2×C411yescharacteristic
73C2×Q8×D11C2×C411yescharacteristic
74C2×#4341—21no—
75C2×#4341C2×C411yescharacteristic
76C2×D4×D11—21no—
77C2×D4×D11C2×C411yescharacteristic
78C2×#4339—21no—
79C2×#4339C2311yescharacteristic
80C2×#4339C2311yescharacteristic
81C22×C4×D11—21no—
82C22×C4×D11C2311yescharacteristic
83C2×C11×M16C2311yescharacteristic
84C2×C11×M16C2311yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C22×C8×C11C2311yescharacteristic
87C11×#117C2311yescharacteristic
88C2×C42×C11C2311yescharacteristic
89#67003—41no—
90#67003—41no—
91C2×#4326C2×C411yescharacteristic
92C2×#4325C2×C411yescharacteristic
93C2×#4324C2×C411yescharacteristic
94C2×#4323C2×C411yescharacteristic
95C2×(C2×D11)⋊C4—21no—
96C2×C4×Dic11C2311yescharacteristic
97C2×#4318C2311yescharacteristic
98C2×#4318C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101M16×D11—41no—
102M16×D11—41no—
103C2×Dic44C2×C411yescharacteristic
104#66957—41no—
105#66957—41no—
106C2×D88C2×C411yescharacteristic
107C2×#4314C2×C411yescharacteristic
108C2×#4314C2×C411yescharacteristic
109#66954—41no—
110#66954—41no—
111C2×#4313—21no—
112C2×#4313—21no—
113C2×C8×D11—21no—
114C2×C8×D11—21no—
115C2×C8×D11—41no—
116C2×C8×D11—41no—
117C2×C8×D11D411yescharacteristic
118C2×C8×D11D411yescharacteristic
119C2×C8×D11D411yescharacteristic
120C2×C8×D11D411yescharacteristic
121#66950C2×C411yescharacteristic
122#66950C2×C411yescharacteristic
123#66948C2×C411yescharacteristic
124#66948C2×C411yescharacteristic
125#66939—21no—
126#66935—21no—
127C4×D44—21no—
128C4×D44—21no—
129C11×#108—41no—
130C11×#104—41no—
131C11×#103C2×C411yescharacteristic
132C11×#103C2×C411yescharacteristic
133C11×#102C2×C411yescharacteristic
134C11×#102C2×C411yescharacteristic
135C11×C22⋊C8—21no—
136C11×C22⋊C8—21no—
137C11×#97—21no—
138C4×C8×C11—21no—
139#66901—41no—
140C11⋊#95—21no—
141C22⋊(C11⋊C8)—21no—
142C22⋊(C11⋊C8)—21no—
143#66889—41no—
144#66889—41no—
145#66886—41no—
146(C2×D11)⋊C8—21no—
147(C2×D11)⋊C8—21no—
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
158C8×Dic11—41no—
159#66874C2×C411yescharacteristic
160#66874C2×C411yescharacteristic
161#66873C2×C411yescharacteristic
162#66873C2×C411yescharacteristic
163#66869—41no—
164#66869—41no—
165C4⋊(C11⋊C8)—21no—
166C4⋊(C11⋊C8)—21no—
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—
175C2×Q8×C11C22×C411yescharacteristic
176C2×D4×C11—21no—
177C2×D4×C11C22×C411yescharacteristic
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11C2411yescharacteristic
181C2×C22⋊D11—21no—
182C2×C22⋊D11—21no—
183C2×C22⋊D11—21no—
184C2×C22⋊D11—21no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11#4111yescharacteristic
188#4343—41no—
189#4343—41no—
190Q8×D11—41no—
191Q8×D11—41no—
192#4341—41no—
193#4341—41no—
194#4341—42no—
195#4341—42no—
196D4×D11—41no—
197D4×D11—41no—
198D4×D11—42no—
199D4×D11—42no—
200#4339—21no—
201#4339—21no—
202#4339—21no—
203#4339—21no—
204#4339—21no—
205#4339—21no—
206#4339—21no—
207#4339—21no—
208#4339—42no—
209#4339—42no—
210C2×D44—21no—
211C2×D44—21no—
212C2×D44—21no—
213C2×D44C22×C411yescharacteristic
214C2×D44C22×C411yescharacteristic
215C2×C4×D11—21no—
216C2×C4×D11—21no—
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—42no—
224C2×C4×D11—42no—
225C2×C4×D11C22×C411yescharacteristic
226C2×C4×D11C22×C411yescharacteristic
227C2×C4×D11C2×D411yescharacteristic
228C2×C4×D11C2×D411yescharacteristic
229C2×Dic22—21no—
230C2×Dic22C22×C411yescharacteristic
231C2×Dic22C22×C411yescharacteristic
232C11×M16—21no—
233C11×M16—21no—
234C11×M16—21no—
235C11×M16—21no—
236C2×C8×C11—21no—
237C2×C8×C11—21no—
238C2×C8×C11—21no—
239C2×C8×C11—21no—
240C2×C8×C11—21no—
241C2×C8×C11—21no—
242C2×C8×C11C22×C411yescharacteristic
243C2×C8×C11C22×C411yescharacteristic
244C2×C8×C11C2×D411yescharacteristic
245C2×C8×C11C2×D411yescharacteristic
246C11×C4⋊C4C22×C411yescharacteristic
247C11×C4⋊C4C22×C411yescharacteristic
248C11×C22⋊C4—21no—
249C42×C11—21no—
250C42×C11—21no—
251C42×C11—21no—
252#4326—41no—
253#4325—41no—
254#4324—41no—
255#4323—41no—
256(C2×D11)⋊C4—24no—
257(C2×D11)⋊C4—21no—
258(C2×D11)⋊C4—21no—
259(C2×D11)⋊C4—21no—
260(C2×D11)⋊C4—21no—
261C4⋊Dic11—21no—
262C4⋊Dic11—21no—
263C4×Dic11—21no—
264C4×Dic11—21no—
265#4318—21no—
266#4318—21no—
267#4318—21no—
268#4318—21no—
269C2×C11⋊C8—21no—
270C2×C11⋊C8—21no—
271C2×C11⋊C8—21no—
272C2×C11⋊C8—21no—
273C2×C11⋊C8—21no—
274C2×C11⋊C8—21no—
275C2×C11⋊C8C22×C411yescharacteristic
276C2×C11⋊C8C22×C411yescharacteristic
277C2×C11⋊C8C2×D411yescharacteristic
278C2×C11⋊C8C2×D411yescharacteristic
279Dic44—41no—
280D88—41no—
281#4314—41no—
282#4314—41no—
283#4313—42no—
284#4313—42no—
285C8×D11—41no—
286C8×D11—41no—
287C8×D11—41no—
288C8×D11—41no—
289C8×D11—42no—
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#1929D1111yescharacteristic, complemented
300#1876—111no—
301#1876—111no—
302#1871—111no—
303#1855—111no—
304#1789—111no—
305C8×C22⋊C4—111no—
306C23×C11—21no—
307C23×C11C2×#4111yescharacteristic
308C22×D11—21no—
309C22×D11—21no—
310C22×D11—22no—
311C22×D11—21no—
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—
321D4×C11—21no—
322D4×C11—21no—
323D4×C11—41no—
324D4×C11—41no—
325C2×C4×C11—22no—
326C2×C4×C11—21no—
327C2×C4×C11—21no—
328C2×C4×C11—21no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11C23×C411yescharacteristic
334C2×C4×C11C22×D411yescharacteristic
335C2×C4×C11H(5,𝔽2)11yescharacteristic
336C2×C4×C11H(5,𝔽2)11yescharacteristic
337C2×C4×C11H(5,𝔽2)11yescharacteristic
338C2×C4×C11H(5,𝔽2)11yescharacteristic
339C22⋊D11—42no—
340C22⋊D11—42no—
341C22⋊D11—41no—
342C22⋊D11—41no—
343C22⋊D11—41no—
344C22⋊D11—41no—
345C2×Dic11—21no—
346C2×Dic11—21no—
347C2×Dic11—22no—
348C2×Dic11—21no—
349C2×Dic11—21no—
350C2×Dic11—42no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11C4×D411yescharacteristic
354C2×Dic11C4×D411yescharacteristic
355D44—21no—
356D44—21no—
357D44—21no—
358D44—21no—
359D44—42no—
360D44—42no—
361D44—42no—
362C4×D11—21no—
363C4×D11—21no—
364C4×D11—21no—
365C4×D11—21no—
366C4×D11—21no—
367C4×D11—21no—
368C4×D11—21no—
369C4×D11—21no—
370C4×D11—42no—
371C4×D11—42no—
372C4×D11—41no—
373C4×D11—41no—
374C4×D11—41no—
375C4×D11—41no—
376Dic22—21no—
377Dic22—21no—
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×#135—111no—
396C2×#131—111no—
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×#108C2×D1111yescharacteristic, complemented
414#424—111no—
415C2×#104—111no—
416C2×#104—111no—
417C2×#104—111no—
418C2×#104—111no—
419C2×#104—111no—
420C2×#104C2×D1111yescharacteristic
421#416—111no—
422#416C2×D1111yescharacteristic
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#405C2×D1111yescharacteristic, complemented
435C2×C4×C8—111no—
436C2×C4×C8—111no—
437C4×C22⋊C4—111no—
438#341—111no—
439#341—111no—
440#339—111no—
441#339C2×D1111yescharacteristic, complemented
442#336—111no—
443#336C2×D1111yescharacteristic, complemented
444C22×C11—21no—
445C22×C11—21no—
446C22×C11—41no—
447C22×C11—41no—
448C22×C11—41no—
449C22×C11C2×C4×D411yescharacteristic
450C22×C11#53811yescharacteristic
451C22×C11#53811yescharacteristic
452C2×D11—21no—
453C2×D11—21no—
454C2×D11—21no—
455C2×D11—21no—
456C2×D11—21no—
457C2×D11—42no—
458C2×D11—42no—
459C2×D11—41no—
460C2×D11—41no—
461C2×D11—41no—
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—41no—
471C4×C11#51811yescharacteristic
472C4×C11#51811yescharacteristic
473C4×C11#53411yescharacteristic
474C4×C11#53511yescharacteristic
475Dic11—21no—
476Dic11—21no—
477Dic11—42no—
478Dic11—41no—
479Dic11—41no—
480C2×#41—111no—
481C2×#41—111no—
482C2×#41—111no—
483C2×#41—111no—
484C2×#41—221no—
485C2×#41—221no—
486C2×#41—441no—
487C2×#41—441no—
488C2×#41—441no—
489C2×#41—441no—
490C2×#41C22×D1111yescharacteristic
491C22×Q8—111no—
492C22×D4—111no—
493C22×D4—221no—
494C23×C4—111no—
495C23×C4—221no—
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—111no—
511C2×M16—111no—
512C2×M16—221no—
513C2×M16—221no—
514C2×M16—441no—
515C2×M16—441no—
516C2×M16C22×D1111yescharacteristic
517C2×M16C22×D1111yescharacteristic
518C22×C8—111no—
519C22×C8—111no—
520C22×C8—111no—
521C22×C8—111no—
522C22×C8—111no—
523C22×C8—111no—
524C22×C8—221no—
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#117C22×D1111yescharacteristic
539C2×C22⋊C4—221no—
540C2×C42—111no—
541C2×C42C22×D1111yescharacteristic
542#108—41no—
543#108—441no—
544C4⋊C8—221no—
545C4⋊C8—221no—
546#104—41no—
547#104—441no—
548#104—441no—
549#104—441no—
550#104—441no—
551#104—441no—
552#103—111no—
553#103—111no—
554#103C4×D1111yescharacteristic
555#103C4×D1111yescharacteristic
556#102—111no—
557#102—111no—
558#102C4×D1111yescharacteristic
559#102C4×D1111yescharacteristic
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—21no—
577C4×C8—21no—
578C4×C8—441no—
579C4×C8—441no—
580#95—221no—
581C2×C11—21no—
582C2×C11—21no—
583C2×C11—81no—
584C2×C11#232111yescharacteristic
585C2×C11C2×#44311yescharacteristic
586C2×C11#295511yescharacteristic
587D11—22no—
588D11—41no—
589D11—81no—
590D11—81no—
591C24—111no—
592C24—221no—
593#41—21no—
594#41—21no—
595#41—21no—
596#41—21no—
597#41—221no—
598#41—221no—
599#41—221no—
600#41—221no—
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—111no—
615C2×Q8—221no—
616C2×Q8—441no—
617C2×Q8—441no—
618C2×Q8C2×C4×D1111yescharacteristic
619C2×D4—21no—
620C2×D4—111no—
621C2×D4—111no—
622C2×D4—221no—
623C2×D4—221no—
624C2×D4—221no—
625C2×D4—221no—
626C2×D4—221no—
627C2×D4—221no—
628C2×D4—221no—
629C2×D4—441no—
630C2×D4—441no—
631C2×D4—442no—
632C2×D4—442no—
633C2×D4C2×C4×D1111yescharacteristic
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—111no—
637C22×C4—111no—
638C22×C4—111no—
639C22×C4—111no—
640C22×C4—111no—
641C22×C4—221no—
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—441no—
655Q16—441no—
656SD16—441no—
657SD16—441no—
658SD16—441no—
659SD16—441no—
660D8—441no—
661D8—441no—
662M16—21no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—221no—
667M16—221no—
668M16—221no—
669M16—221no—
670M16—442no—
671M16—442no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—111no—
679C2×C8—111no—
680C2×C8—111no—
681C2×C8—111no—
682C2×C8—221no—
683C2×C8—221no—
684C2×C8—221no—
685C2×C8—221no—
686C2×C8—221no—
687C2×C8—221no—
688C2×C8—441no—
689C2×C8—441no—
690C2×C8—441no—
691C2×C8—441no—
692C2×C8—442no—
693C2×C8—442no—
694C2×C8C2×C4×D1111yescharacteristic
695C2×C8C2×C4×D1111yescharacteristic
696C2×C8D4×D1111yescharacteristic
697C2×C8D4×D1111yescharacteristic
698C4⋊C4—221no—
699C4⋊C4—221no—
700C4⋊C4C2×C4×D1111yescharacteristic
701C4⋊C4C2×C4×D1111yescharacteristic
702C22⋊C4—21no—
703C22⋊C4—221no—
704C22⋊C4—221no—
705C22⋊C4—221no—
706C22⋊C4—221no—
707C22⋊C4—224no—
708C42—21no—
709C42—21no—
710C42—21no—
711C42—221no—
712C42—221no—
713C11#2206011yescharacteristic, complemented, Sylow
714C23—21no—
715C23—111no—
716C23—111no—
717C23—222no—
718C23—221no—
719C23—221no—
720C23—221no—
721C23—221no—
722C23—441no—
723C23—442no—
724C23—442no—
725C23—442no—
726C23#41×D1111yescharacteristic
727Q8—21no—
728Q8—21no—
729Q8—221no—
730Q8—221no—
731Q8—221no—
732Q8—221no—
733Q8—442no—
734D4—21no—
735D4—21no—
736D4—41no—
737D4—41no—
738D4—221no—
739D4—221no—
740D4—221no—
741D4—221no—
742D4—442no—
743D4—442no—
744D4—442no—
745D4—442no—
746D4—442no—
747D4—441no—
748D4—441no—
749D4—441no—
750D4—441no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—111no—
760C2×C4—111no—
761C2×C4—221no—
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—222no—
772C2×C4—221no—
773C2×C4—221no—
774C2×C4—442no—
775C2×C4—442no—
776C2×C4—442no—
777C2×C4—441no—
778C2×C4—441no—
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#6704211yescharacteristic
787C2×C4#6704211yescharacteristic
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—112no—
807C22—221no—
808C22—221no—
809C22—221no—
810C22—221no—
811C22—221no—
812C22—442no—
813C22—442no—
814C22—441no—
815C22—441no—
816C22—441no—
817C22—441no—
818C22—441no—
819C22—441no—
820C22—884no—
821C22C4×D4×D1111yescharacteristic
822C22#1062320911yescharacteristic
823C22#1062323511yescharacteristic
824C4—42no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—221no—
829C4—221no—
830C4—442no—
831C4—441no—
832C4—441no—
833C4#1062305211yescharacteristic
834C4#1062307611yescharacteristic
835C4#1062313811yescharacteristic
836C4#1062318411yescharacteristic
837C2—21no—
838C2—21no—
839C2—81no—
840C2—222no—
841C2—441no—
842C2—881no—
843C2—881no—
844C2#1307127811yescharacteristic
845C2D11×#44311yescharacteristic
846C2#1307751611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1929C2
socleC22×C11C2×C4×D4
prime radical#13077836C2
cosocleC22×C4×C11C24
hypercenter#1929D11
hypocenterC11#22060
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1929

Complements

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

NH ≅ G/Ntype
2. #13077312C2semidirect
3. D11×#408C2semidirect
4. #13069502C2semidirect
5. #13069501C2semidirect
6. #13069322C2semidirect
7. #13069321C2semidirect
8. #13069264C2semidirect
9. #13068946C2semidirect
10. #13068942C2semidirect
11. #13068917C2semidirect
12. #13068819C2semidirect
13. #13068558C2semidirect
14. #13068386C2semidirect
15. C11×#1929C2semidirect
20. C2×#66954C22semidirect
23. C2×C11×#108C22semidirect
27. C11×#405C22semidirect
31. C2×#66889C22semidirect
33. #10622742C22semidirect
35. C2×#66886C22semidirect
38. C2×C8×Dic11C22semidirect
40. #10622612C22semidirect
43. C2×#66869C22semidirect
44. C2×C4×C11⋊C8C22semidirect
45. #10622424C4semidirect
46. #10622423C4semidirect
47. #10622421C4semidirect
48. #10622419C4semidirect
49. #10622396C4semidirect
50. #10622394C4semidirect
51. #10622389C4semidirect
52. #10622386C4semidirect
61. C11×#339C22semidirect
62. C11×#336C22semidirect
63. #10622196C22semidirect
64. #10622190C22semidirect
65. #10622188C22semidirect
66. #10622170C22semidirect
299. #1929D11semidirect
413. C2×#108C2×D11semidirect
434. #405C2×D11semidirect
441. #339C2×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
#130778362
#130773122
D11×#4082
#130695022
#130695012
#130693222
#130693212
#130692642
#130689462
#130689422
#130689172
#130688192
#130685582
#130683862
C11×#19292
#2206011