Finite Group Databasebeta

← #14765192

Subgroups — #14765192

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#13077315C211yesmaximal, characteristic, complemented
3#13077061C211yesmaximal, characteristic, complemented
4#13069506C211yesmaximal, characteristic, complemented
5#13069501C211yesmaximal, characteristic, complemented
6#13069324C211yesmaximal, characteristic, complemented
7#13069317C211yesmaximal, characteristic, complemented
8#13069267C211yesmaximal, characteristic, complemented
9#13069267C211yesmaximal, characteristic, complemented
10#13068940C211yesmaximal, characteristic, complemented
11#13068940C211yesmaximal, characteristic, complemented
12#13068916C211yesmaximal, characteristic, complemented
13#13068820C211yesmaximal, characteristic, complemented
14#13068400C211yesmaximal, characteristic, complemented
15C11×#1789C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C2×#67003C2211yescharacteristic
18C2×#67003C2211yescharacteristic
19#10623322C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22C2×#66960C2211yescharacteristic, complemented
23C2×C11×#104C2211yescharacteristic
24C2×C11×#104C2211yescharacteristic
25C2×C11×#104C2211yescharacteristic
26C2×C11×#104C2211yescharacteristic
27C11×#407C2211yescharacteristic
28C4×C11×C22⋊C4C2211yescharacteristic
29#10622852C411yescharacteristic, complemented
30#10622852C411yescharacteristic, complemented
31#10622851C411yescharacteristic, complemented
32#10622851C411yescharacteristic, complemented
33#10622847—21no—
34#10622847—21no—
35#10622847C2211yescharacteristic
36#10622847C2211yescharacteristic
37#10622847C2211yescharacteristic
38#10622847C2211yescharacteristic
39#10622846C2211yescharacteristic
40#10622846C2211yescharacteristic
41#10622841C411yescharacteristic, complemented
42#10622840C411yescharacteristic, complemented
43#10622831C411yescharacteristic, complemented
44#10622830C411yescharacteristic, complemented
45#10622820—21no—
46#10622820—21no—
47C2×C22⋊(C11⋊C8)C2211yescharacteristic
48#10622742C2211yescharacteristic, complemented
49C2×#66886C2211yescharacteristic, complemented
50C2×#66886C2211yescharacteristic, complemented
51#10622735C2211yescharacteristic, complemented
52#10622732C2211yescharacteristic, complemented
53C2×#66869C2211yescharacteristic, complemented
54C2×#66869C2211yescharacteristic, complemented
55C2×#66867C2211yescharacteristic, complemented
56C2×C4×C11⋊C8C2211yescharacteristic, complemented
57#10622342—21no—
58#10622342—21no—
59#10622341—21no—
60#10622341—21no—
61#10622196C2211yescharacteristic, complemented
62#10622196C2211yescharacteristic, complemented
63#10622162C2211yescharacteristic, complemented
64#10622162C2211yescharacteristic, complemented
65#10622161C2211yescharacteristic, complemented
66#10622161C2211yescharacteristic, 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×M16C2311yescharacteristic
84C2×C11×M16C2311yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88#67006—21no—
89#67003—41no—
90#67003—41no—
91#67003—41no—
92#67003—41no—
93C2×#4326C2×C411yescharacteristic
94C2×#4326C2×C411yescharacteristic
95C2×#4325C2×C411yescharacteristic
96C2×#4325C2×C411yescharacteristic
97C2×#4324C2×C411yescharacteristic
98C2×#4324C2×C411yescharacteristic
99C2×#4323C2×C411yescharacteristic
100C2×#4323C2×C411yescharacteristic
101#66983C2×C411yescharacteristic
102#66983C2×C411yescharacteristic
103#66982—21no—
104C4×C22⋊D11—21no—
105C4×C22⋊D11—21no—
106#66979C2311yescharacteristic
107#66977C2×C411yescharacteristic
108#66977C2×C411yescharacteristic
109C2×#4318—21no—
110C2×#4318—41no—
111C2×#4318—41no—
112C2×#4318—41no—
113C2×#4318—41no—
114C2×#4318D411yescharacteristic
115C2×#4318D411yescharacteristic
116C2×#4318D411yescharacteristic
117C2×#4318D411yescharacteristic
118C2×#4318C2311yescharacteristic
119C2×#4318C2311yescharacteristic
120C22×C11⋊C8—21no—
121C22×C11⋊C8C2311yescharacteristic
122C22×C11⋊C8C2311yescharacteristic
123C22×C11⋊C8C2311yescharacteristic
124C22×C11⋊C8C2311yescharacteristic
125#66960—41no—
126#66960—41no—
127C2×#4313—21no—
128C2×C8×D11—21no—
129C11×#104—41no—
130C11×#104—41no—
131C11×#104—41no—
132C11×#104—41no—
133C11×C22⋊C8—21no—
134C11×C22⋊C8—21no—
135C11×#95—21no—
136#66899C2×C411yescharacteristic
137#66899C2×C411yescharacteristic
138#66899C2×C411yescharacteristic
139#66899C2×C411yescharacteristic
140#66896C2×C411yescharacteristic
141#66896C2×C411yescharacteristic
142#66896C2×C411yescharacteristic
143#66896C2×C411yescharacteristic
144C22⋊(C11⋊C8)—21no—
145C22⋊(C11⋊C8)—21no—
146C22⋊(C11⋊C8)—21no—
147C22⋊(C11⋊C8)—21no—
148C22⋊(C11⋊C8)—21no—
149C22⋊(C11⋊C8)—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#66886—41no—
157#66886—41no—
158(C2×D11)⋊C8—21no—
159(C2×D11)⋊C8—21no—
160#66879—21no—
161Dic11⋊C8—21no—
162Dic11⋊C8—21no—
163C8×Dic11—21no—
164#66869—41no—
165#66869—41no—
166#66867—41no—
167C4×C11⋊C8—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—21no—
213C22×C4×C11—21no—
214C22×C4×C11—42no—
215C22×C4×C11—42no—
216C22×C4×C11C22×C411yescharacteristic
217C22×C4×C11C22×C411yescharacteristic
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D411yescharacteristic
220C22×C4×C11#4111yescharacteristic
221C22×C4×C11C2411yescharacteristic
222C2×C22⋊D11—21no—
223C2×C22⋊D11—21no—
224C2×C22⋊D11—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—
236C2×C8×C11—21no—
237C2×C8×C11—21no—
238C11×C22⋊C4—42no—
239C42×C11—21no—
240C42×C11—21no—
241C42×C11—21no—
242C42×C11—21no—
243C22⋊Dic11—21no—
244C22⋊Dic11—21no—
245C22⋊Dic11—21no—
246#4326—41no—
247#4326—41no—
248#4325—41no—
249#4325—41no—
250#4324—41no—
251#4324—41no—
252#4323—41no—
253#4323—41no—
254(C2×D11)⋊C4—21no—
255(C2×D11)⋊C4—21no—
256C4⋊Dic11C22×C411yescharacteristic
257C4⋊Dic11C22×C411yescharacteristic
258Dic11⋊C4—21no—
259Dic11⋊C4—21no—
260C4×Dic11—21no—
261#4318—21no—
262#4318—21no—
263#4318—21no—
264#4318—21no—
265#4318—41no—
266#4318—41no—
267#4318—41no—
268#4318—41no—
269#4318—42no—
270C2×C11⋊C8—21no—
271C2×C11⋊C8—21no—
272C2×C11⋊C8—21no—
273C2×C11⋊C8—21no—
274C2×C11⋊C8—21no—
275C2×C11⋊C8—21no—
276C2×C11⋊C8—21no—
277C2×C11⋊C8—21no—
278C2×C11⋊C8—21no—
279C2×C11⋊C8—21no—
280C2×C11⋊C8—42no—
281C2×C11⋊C8C22×C411yescharacteristic
282C2×C11⋊C8C22×C411yescharacteristic
283C2×C11⋊C8C22×C411yescharacteristic
284C2×C11⋊C8C22×C411yescharacteristic
285C2×C11⋊C8C2×D411yescharacteristic
286C2×C11⋊C8C2×D411yescharacteristic
287C2×C11⋊C8C2×D411yescharacteristic
288C2×C11⋊C8C2×D411yescharacteristic
289#4313—42no—
290C8×D11—42no—
291#3002—111no—
292#2930—111no—
293#2879—111no—
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#1789D1111yescharacteristic, complemented
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—22no—
346C2×C4×C11—21no—
347C2×C4×C11—21no—
348C2×C4×C11—42no—
349C2×C4×C11—42no—
350C2×C4×C11—41no—
351C2×C4×C11—42no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11—41no—
360C2×C4×C11C4×D411yescharacteristic
361C2×C4×C11C4×D411yescharacteristic
362C2×C4×C11C23×C411yescharacteristic
363C2×C4×C11C22×D411yescharacteristic
364C2×C4×C11H(5,𝔽2)11yescharacteristic
365C2×C4×C11H(5,𝔽2)11yescharacteristic
366C2×C4×C11H(5,𝔽2)11yescharacteristic
367C2×C4×C11H(5,𝔽2)11yescharacteristic
368C22⋊D11—41no—
369C22⋊D11—41no—
370C22⋊D11—81no—
371C22⋊D11—81no—
372C2×Dic11—21no—
373C2×Dic11—21no—
374C2×Dic11—21no—
375D44—21no—
376D44—21no—
377C4×D11—41no—
378C4×D11—41no—
379Dic22—21no—
380Dic22—21no—
381C8×C11—41no—
382C8×C11—41no—
383C11⋊C8—21no—
384C11⋊C8—21no—
385C11⋊C8—21no—
386C11⋊C8—21no—
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×M16—111no—
398C22×M16—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#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×#104C2×D1111yescharacteristic
418C2×#104C2×D1111yescharacteristic
419C2×#104C2×D1111yescharacteristic
420C2×#104C2×D1111yescharacteristic
421#416—111no—
422#416—111no—
423#408—111no—
424#408—111no—
425#408—111no—
426#408—111no—
427#408—111no—
428#408—221no—
429#408—221no—
430#407—221no—
431#407—221no—
432#407C2×D1111yescharacteristic
433C2×C22⋊C8—111no—
434#405—111no—
435C2×#97—111no—
436C2×C4×C8—111no—
437C4×C22⋊C4C2×D1111yescharacteristic
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—42no—
470C4×C11—41no—
471C4×C11—41no—
472C4×C11—81no—
473C4×C11#51811yescharacteristic
474C4×C11#51811yescharacteristic
475C4×C11#53411yescharacteristic
476C4×C11#53511yescharacteristic
477Dic11—41no—
478Dic11—41no—
479Dic11—41no—
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—111no—
511C2×M16—111no—
512C2×M16—111no—
513C2×M16—111no—
514C2×M16—111no—
515C2×M16—111no—
516C2×M16—221no—
517C2×M16—221no—
518C2×M16—441no—
519C2×M16—441no—
520C2×M16—441no—
521C2×M16—441no—
522C2×M16C22×D1111yescharacteristic
523C2×M16C22×D1111yescharacteristic
524C22×C8—111no—
525C22×C8—111no—
526C22×C8—111no—
527C22×C8—111no—
528C22×C8—221no—
529C22×C8—221no—
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—21no—
540C2×C42C22×D1111yescharacteristic
541C2×C42C22×D1111yescharacteristic
542#108—441no—
543#108—441no—
544C4⋊C8—221no—
545C4⋊C8—221no—
546#104—41no—
547#104—41no—
548#104—41no—
549#104—41no—
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—
577#97—441no—
578C4×C8—221no—
579C4×C8—441no—
580#95—21no—
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#434111yescharacteristic
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—21no—
644C22×C4—21no—
645C22×C4—42no—
646C22×C4—42no—
647C22×C4—221no—
648C22×C4C2×C4×D1111yescharacteristic
649C22×C4C2×C4×D1111yescharacteristic
650C22×C4D4×D1111yescharacteristic
651C22×C4D4×D1111yescharacteristic
652C22×C4#434111yescharacteristic
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—441no—
672M16—441no—
673M16—441no—
674M16—441no—
675M16—442no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—111no—
679C2×C8—111no—
680C2×C8—111no—
681C2×C8—111no—
682C2×C8—111no—
683C2×C8—111no—
684C2×C8—111no—
685C2×C8—111no—
686C2×C8—221no—
687C2×C8—221no—
688C2×C8—221no—
689C2×C8—221no—
690C2×C8—221no—
691C2×C8—221no—
692C2×C8—221no—
693C2×C8—221no—
694C2×C8—221no—
695C2×C8—221no—
696C2×C8—442no—
697C2×C8—442no—
698C4⋊C4—111no—
699C4⋊C4—111no—
700C4⋊C4—221no—
701C4⋊C4—221no—
702C22⋊C4—42no—
703C22⋊C4—221no—
704C22⋊C4—221no—
705C22⋊C4—221no—
706C22⋊C4—221no—
707C22⋊C4—221no—
708C42—21no—
709C42—21no—
710C42—21no—
711C42—21no—
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—
724C23(C22⋊D11)⋊C411yescharacteristic
725C23(C22⋊D11)⋊C411yescharacteristic
726C23C2×#434111yescharacteristic
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—22no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—41no—
767C2×C4—42no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—221no—
777C2×C4—221no—
778C2×C4—221no—
779C2×C4—441no—
780C2×C4—441no—
781C2×C4(C22⋊D11)⋊C411yescharacteristic
782C2×C4(C22⋊D11)⋊C411yescharacteristic
783C2×C4C22×C4×D1111yescharacteristic
784C2×C4C2×D4×D1111yescharacteristic
785C2×C4#6703711yescharacteristic
786C2×C4#6703711yescharacteristic
787C2×C4#6703711yescharacteristic
788C2×C4#6703711yescharacteristic
789C8—41no—
790C8—41no—
791C8—221no—
792C8—221no—
793C8—221no—
794C8—221no—
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—
821C22C2×(C22⋊D11)⋊C411yescharacteristic
822C22#1062312411yescharacteristic
823C22#1062312411yescharacteristic
824C4—21no—
825C4—21no—
826C4—42no—
827C4—41no—
828C4—41no—
829C4—81no—
830C4—441no—
831C4—441no—
832C4—441no—
833C4#1062301711yescharacteristic
834C4#1062301711yescharacteristic
835C4#1062312011yescharacteristic
836C4#1062312311yescharacteristic
837C2—21no—
838C2—21no—
839C2—41no—
840C2—41no—
841C2—81no—
842C2—81no—
843C2—881no—
844C2#1307127111yescharacteristic
845C2#1307752211yescharacteristic
846C2#1307752911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1789C2
socleC22×C11C2×C4×D4
prime radical#13077834C2
cosocleC22×C4×C11C24
hypercenter#1789D11
hypocenterC11#22062
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
2. #13077315C2semidirect
3. #13077061C2semidirect
4. #13069506C2semidirect
5. #13069501C2semidirect
6. #13069324C2semidirect
7. #13069317C2semidirect
8. #13069267C2semidirect
9. #13069267C2semidirect
10. #13068940C2semidirect
11. #13068940C2semidirect
12. #13068916C2semidirect
13. #13068820C2semidirect
14. #13068400C2semidirect
15. C11×#1789C2semidirect
22. C2×#66960C22semidirect
29. #10622852C4semidirect
30. #10622852C4semidirect
31. #10622851C4semidirect
32. #10622851C4semidirect
41. #10622841C4semidirect
42. #10622840C4semidirect
43. #10622831C4semidirect
44. #10622830C4semidirect
48. #10622742C22semidirect
49. C2×#66886C22semidirect
50. C2×#66886C22semidirect
51. #10622735C22semidirect
52. #10622732C22semidirect
53. C2×#66869C22semidirect
54. C2×#66869C22semidirect
55. C2×#66867C22semidirect
56. C2×C4×C11⋊C8C22semidirect
61. #10622196C22semidirect
62. #10622196C22semidirect
63. #10622162C22semidirect
64. #10622162C22semidirect
65. #10622161C22semidirect
66. #10622161C22semidirect
304. #1789D11semidirect
713. C11#22062semidirect

Maximal subgroups

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

subgroupindex
#130778342
#130773152
#130770612
#130695062
#130695012
#130693242
#130693172
#130692672
#130689402
#130689162
#130688202
#130684002
C11×#17892
#2206211