Finite Group Databasebeta

← #14765202

Subgroups — #14765202

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#13077832C211yesmaximal, characteristic
2#13077320C211yesmaximal, characteristic, complemented
3#13077060C211yesmaximal, characteristic, complemented
4#13069506C211yesmaximal, characteristic, complemented
5#13069501C211yesmaximal, characteristic, complemented
6#13069328C211yesmaximal, characteristic, complemented
7#13069321C211yesmaximal, characteristic, complemented
8#13069262C211yesmaximal, characteristic, complemented
9#13069262C211yesmaximal, characteristic, complemented
10#13068941C211yesmaximal, characteristic, complemented
11#13068941C211yesmaximal, characteristic, complemented
12#13068821C211yesmaximal, characteristic, complemented
13#13068561C211yesmaximal, characteristic, complemented
14#13068400C211yesmaximal, characteristic, complemented
15C11×#1871C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C11×#525C2211yescharacteristic
19C2×#67003C2211yescharacteristic
20C2×#67003C2211yescharacteristic
21C2×#67001C2211yescharacteristic, complemented
22C22×#4318C2211yescharacteristic
23C2×C11×#104C2211yescharacteristic, complemented
24C2×C11×#104C2211yescharacteristic, complemented
25C4×C11×C22⋊C4C2211yescharacteristic
26#10622847C2211yescharacteristic, complemented
27#10622820C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29#10622742C2211yescharacteristic
30#10622742C2211yescharacteristic
31#10622742C2211yescharacteristic
32#10622742C2211yescharacteristic
33#10622739—21no—
34#10622739—21no—
35C2×#66886C2211yescharacteristic, complemented
36C2×#66886C2211yescharacteristic, complemented
37#10622723—21no—
38#10622723—21no—
39#10622663C411yescharacteristic, complemented
40#10622660C411yescharacteristic, complemented
41#10622660C411yescharacteristic, complemented
42#10622659C411yescharacteristic, complemented
43#10622653C411yescharacteristic, complemented
44#10622650C411yescharacteristic, complemented
45#10622650C411yescharacteristic, complemented
46#10622649C411yescharacteristic, complemented
47#10622625—21no—
48#10622625—21no—
49#10622624—21no—
50#10622624—21no—
51#10622615C2211yescharacteristic
52#10622615C2211yescharacteristic
53#10622612C2211yescharacteristic, complemented
54#10622610C2211yescharacteristic, complemented
55C2×#66869C2211yescharacteristic
56C2×#66869C2211yescharacteristic
57C2×#66869C2211yescharacteristic
58C2×#66869C2211yescharacteristic
59C2×#66867C2211yescharacteristic, complemented
60C2×C4×C11⋊C8C2211yescharacteristic, complemented
61C11×#339C2211yescharacteristic, complemented
62C11×#339C2211yescharacteristic, complemented
63#10622196C2211yescharacteristic, complemented
64#10622196C2211yescharacteristic, complemented
65#10622162C2211yescharacteristic, complemented
66#10622162C2211yescharacteristic, complemented
67C2×C11×#41C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C22×C22⋊D11—21no—
70C2×#4339—21no—
71C2×#4339—21no—
72C2×#4339—41no—
73C2×#4339—41no—
74C2×#4339—41no—
75C2×#4339—41no—
76C2×#4339C2×C411yescharacteristic
77C2×#4339C2×C411yescharacteristic
78C2×#4339C2311yescharacteristic
79C2×#4339C2311yescharacteristic
80C22×D44C2×C411yescharacteristic
81C22×C4×D11—21no—
82C22×Dic22C2×C411yescharacteristic
83C2×C11×M16—21no—
84C2×C11×M16—41no—
85C2×C11×M16—41no—
86C2×C11×M16C2311yescharacteristic
87C2×C11×M16C2311yescharacteristic
88C22×C8×C11—21no—
89C11×#123—21no—
90C11×C22⋊Q8C2×C411yescharacteristic
91C11×C22⋊Q8C2×C411yescharacteristic
92C11×#121C2×C411yescharacteristic
93C11×#121C2×C411yescharacteristic
94C11×#120—21no—
95C4×D4×C11—21no—
96C4×D4×C11—21no—
97C11×#117C2311yescharacteristic
98C2×C11×C22⋊C4—21no—
99C2×C42×C11C2311yescharacteristic
100C2×C42×C11C2311yescharacteristic
101#67003—41no—
102#67003—41no—
103#67003—41no—
104#67003—41no—
105#67001—41no—
106#67001—41no—
107C2×#4326C2×C411yescharacteristic
108C2×#4326C2×C411yescharacteristic
109C2×#4325C2×C411yescharacteristic
110C2×#4325C2×C411yescharacteristic
111C2×#4324C2×C411yescharacteristic
112C2×#4324C2×C411yescharacteristic
113C2×#4323C2×C411yescharacteristic
114C2×#4323C2×C411yescharacteristic
115C2×#4318—21no—
116C2×#4318—41no—
117C2×#4318—41no—
118C2×#4318D411yescharacteristic
119C2×#4318D411yescharacteristic
120C2×#4318D411yescharacteristic
121C2×#4318D411yescharacteristic
122C2×#4318C2311yescharacteristic
123C2×#4318C2311yescharacteristic
124C22×C11⋊C8—21no—
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128C22×C11⋊C8C2311yescharacteristic
129C11×#104—41no—
130C11×#104—41no—
131C11×#95—21no—
132C22⋊(C11⋊C8)—21no—
133C22⋊(C11⋊C8)—21no—
134C22⋊(C11⋊C8)—21no—
135C22⋊(C11⋊C8)—21no—
136C22⋊(C11⋊C8)C2×C411yescharacteristic
137C22⋊(C11⋊C8)C2×C411yescharacteristic
138C22⋊(C11⋊C8)C2×C411yescharacteristic
139C22⋊(C11⋊C8)C2×C411yescharacteristic
140#66886—41no—
141#66886—41no—
142(C2×D11)⋊C8—21no—
143(C2×D11)⋊C8—21no—
144(C2×D11)⋊C8—21no—
145(C2×D11)⋊C8—21no—
146(C2×D11)⋊C8—21no—
147(C2×D11)⋊C8—21no—
148(C2×D11)⋊C8—21no—
149(C2×D11)⋊C8—21no—
150#66874C2×C411yescharacteristic
151#66874C2×C411yescharacteristic
152#66874C2×C411yescharacteristic
153#66874C2×C411yescharacteristic
154#66873C2×C411yescharacteristic
155#66873C2×C411yescharacteristic
156#66873C2×C411yescharacteristic
157#66873C2×C411yescharacteristic
158#66869—41no—
159#66869—41no—
160#66869—41no—
161#66869—41no—
162C4⋊(C11⋊C8)—21no—
163C4⋊(C11⋊C8)—21no—
164#66867—21no—
165#66867—41no—
166C4×C11⋊C8—21no—
167C4×C11⋊C8—41no—
168#22062—111nomaximal, Sylow
169C24×C11#4111yescharacteristic
170C23×D11—21no—
171C11×#41—21no—
172C11×#41—21no—
173C11×#41—21no—
174C11×#41—21no—
175C2×Q8×C11C22×C411yescharacteristic
176C2×D4×C11—21no—
177C2×D4×C11—21no—
178C2×D4×C11—21no—
179C2×D4×C11C22×C411yescharacteristic
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11C22×C411yescharacteristic
188C22×C4×C11C22×C411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11#4111yescharacteristic
192C22×C4×C11C2411yescharacteristic
193C2×C22⋊D11—21no—
194C2×C22⋊D11—21no—
195C2×C22⋊D11—21no—
196C2×C22⋊D11—21no—
197C2×C22⋊D11—42no—
198C2×C22⋊D11—42no—
199C22×Dic11—21no—
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—41no—
209#4339—41no—
210#4339—41no—
211#4339—41no—
212#4339—42no—
213#4339—42no—
214#4339—42no—
215#4339—42no—
216C2×D44—21no—
217C2×D44—41no—
218C2×D44—41no—
219C2×D44C22×C411yescharacteristic
220C2×D44C22×C411yescharacteristic
221C2×C4×D11—21no—
222C2×C4×D11—21no—
223C2×C4×D11—21no—
224C2×C4×D11—21no—
225C2×C4×D11—42no—
226C2×C4×D11—42no—
227C2×Dic22—21no—
228C2×Dic22—41no—
229C2×Dic22—41no—
230C2×Dic22C22×C411yescharacteristic
231C2×Dic22C22×C411yescharacteristic
232C11×M16—21no—
233C11×M16—21no—
234C11×M16—21no—
235C11×M16—21no—
236C11×M16—42no—
237C2×C8×C11—21no—
238C2×C8×C11—21no—
239C2×C8×C11—42no—
240C11×C4⋊C4—21no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4C22×C411yescharacteristic
243C11×C4⋊C4C22×C411yescharacteristic
244C11×C22⋊C4—21no—
245C11×C22⋊C4—21no—
246C11×C22⋊C4—21no—
247C11×C22⋊C4—21no—
248C11×C22⋊C4—21no—
249C11×C22⋊C4—42no—
250C42×C11—21no—
251C42×C11—21no—
252C42×C11—21no—
253C42×C11—21no—
254C42×C11—21no—
255#4326—41no—
256#4326—41no—
257#4325—41no—
258#4325—41no—
259#4324—41no—
260#4324—41no—
261#4323—41no—
262#4323—41no—
263#4318—21no—
264#4318—21no—
265#4318—21no—
266#4318—21no—
267#4318—41no—
268#4318—41no—
269#4318—41no—
270#4318—41no—
271#4318—42no—
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—21no—
281C2×C11⋊C8—21no—
282C2×C11⋊C8—42no—
283C2×C11⋊C8C22×C411yescharacteristic
284C2×C11⋊C8C22×C411yescharacteristic
285C2×C11⋊C8C22×C411yescharacteristic
286C2×C11⋊C8C22×C411yescharacteristic
287C2×C11⋊C8C2×D411yescharacteristic
288C2×C11⋊C8C2×D411yescharacteristic
289C2×C11⋊C8C2×D411yescharacteristic
290C2×C11⋊C8C2×D411yescharacteristic
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#1871D1111yescharacteristic, complemented
303#1855—111no—
304#1789—111no—
305#1753—111no—
306C23×C11—21no—
307C23×C11—21no—
308C23×C11—21no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11C4×D411yescharacteristic
312C23×C11C4×D411yescharacteristic
313C23×C11C2×#4111yescharacteristic
314C22×D11—21no—
315C22×D11—21no—
316C22×D11—42no—
317C22×D11—81no—
318C22×D11—81no—
319Q8×C11—21no—
320Q8×C11—21no—
321D4×C11—21no—
322D4×C11—21no—
323D4×C11—41no—
324D4×C11—41no—
325D4×C11—81no—
326D4×C11—81no—
327C2×C4×C11—21no—
328C2×C4×C11—21no—
329C2×C4×C11—21no—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—22no—
338C2×C4×C11—21no—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11C4×D411yescharacteristic
349C2×C4×C11C4×D411yescharacteristic
350C2×C4×C11C23×C411yescharacteristic
351C2×C4×C11C22×D411yescharacteristic
352C2×C4×C11H(5,𝔽2)11yescharacteristic
353C2×C4×C11H(5,𝔽2)11yescharacteristic
354C2×C4×C11H(5,𝔽2)11yescharacteristic
355C2×C4×C11H(5,𝔽2)11yescharacteristic
356C22⋊D11—42no—
357C22⋊D11—42no—
358C22⋊D11—41no—
359C22⋊D11—41no—
360C22⋊D11—41no—
361C22⋊D11—41no—
362C2×Dic11—21no—
363C2×Dic11—21no—
364C2×Dic11—42no—
365D44—21no—
366D44—21no—
367D44—21no—
368D44—21no—
369D44—42no—
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—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×#41—111no—
394C2×#135—111no—
395C2×#135—111no—
396C2×#131—111no—
397C22×M16—111no—
398C22×M16C2×D1111yescharacteristic
399#525C2×D1111yescharacteristic
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×#104C2×D1111yescharacteristic, complemented
420C2×#104C2×D1111yescharacteristic, complemented
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—111no—
431#407—221no—
432#407—221no—
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#339C2×D1111yescharacteristic, complemented
441#339C2×D1111yescharacteristic, complemented
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—81no—
456C22×C11—81no—
457C22×C11C2×C4×D411yescharacteristic
458C22×C11#53811yescharacteristic
459C22×C11#53811yescharacteristic
460C2×D11—41no—
461C2×D11—41no—
462C2×D11—41no—
463C2×D11—41no—
464C2×D11—41no—
465C2×D11—41no—
466C2×D11—84no—
467C4×C11—21no—
468C4×C11—21no—
469C4×C11—42no—
470C4×C11—41no—
471C4×C11—41no—
472C4×C11—41no—
473C4×C11—81no—
474C4×C11#51811yescharacteristic
475C4×C11#51811yescharacteristic
476C4×C11#53411yescharacteristic
477C4×C11#53511yescharacteristic
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—221no—
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—111no—
514C2×M16—111no—
515C2×M16—111no—
516C2×M16—111no—
517C2×M16—111no—
518C2×M16—111no—
519C2×M16—221no—
520C2×M16—441no—
521C2×M16—441no—
522C2×M16C22×D1111yescharacteristic
523C2×M16C22×D1111yescharacteristic
524C22×C8—21no—
525C22×C8—111no—
526C22×C8—111no—
527C22×C8—111no—
528C22×C8—111no—
529C22×C8—221no—
530#123—21no—
531C22⋊Q8C4×D1111yescharacteristic
532C22⋊Q8C4×D1111yescharacteristic
533#121C4×D1111yescharacteristic
534#121C4×D1111yescharacteristic
535#120—21no—
536C4×D4—21no—
537C4×D4—21no—
538#117C22×D1111yescharacteristic
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—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—111no—
561C22⋊C8—111no—
562C22⋊C8—111no—
563C22⋊C8—111no—
564C22⋊C8—221no—
565C22⋊C8—221no—
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#232111yescharacteristic
587C2×C11#295611yescharacteristic
588C2×C11#295711yescharacteristic
589D11—81no—
590D11—81no—
591C24—221no—
592C24#434111yescharacteristic
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—441no—
606#41—441no—
607#41—441no—
608#41—441no—
609#41—442no—
610#41—442no—
611#41—442no—
612#41—442no—
613C2×Q8—111no—
614C2×Q8—111no—
615C2×Q8—221no—
616C2×Q8—441no—
617C2×Q8—441no—
618C2×Q8C2×C4×D1111yescharacteristic
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—111no—
623C2×D4—111no—
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—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—221no—
642C22×C4—221no—
643C22×C4—221no—
644C22×C4—221no—
645C22×C4—221no—
646C22×C4—442no—
647C22×C4—442no—
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—42no—
667M16—221no—
668M16—221no—
669M16—221no—
670M16—221no—
671M16—441no—
672M16—441no—
673M16—441no—
674M16—441no—
675M16—442no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—42no—
679C2×C8—111no—
680C2×C8—111no—
681C2×C8—111no—
682C2×C8—111no—
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—221no—
694C2×C8—221no—
695C2×C8—221no—
696C2×C8—221no—
697C2×C8—442no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4C2×C4×D1111yescharacteristic
701C4⋊C4C2×C4×D1111yescharacteristic
702C22⋊C4—21no—
703C22⋊C4—21no—
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—42no—
708C42—21no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42—21no—
713C11#2206211yescharacteristic, complemented, Sylow
714C23—21no—
715C23—21no—
716C23—21no—
717C23—41no—
718C23—41no—
719C23—221no—
720C23—221no—
721C23—442no—
722C23—881no—
723C23—881no—
724C23(C22⋊D11)⋊C411yescharacteristic
725C23(C22⋊D11)⋊C411yescharacteristic
726C23C2×#434111yescharacteristic
727Q8—21no—
728Q8—21no—
729Q8—221no—
730Q8—221no—
731Q8—221no—
732Q8—221no—
733Q8—442no—
734D4—21no—
735D4—21no—
736D4—41no—
737D4—41no—
738D4—81no—
739D4—81no—
740D4—221no—
741D4—221no—
742D4—221no—
743D4—221no—
744D4—442no—
745D4—442no—
746D4—442no—
747D4—441no—
748D4—441no—
749D4—441no—
750D4—441no—
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—21no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
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(C22⋊D11)⋊C411yescharacteristic
782C2×C4(C22⋊D11)⋊C411yescharacteristic
783C2×C4C22×C4×D1111yescharacteristic
784C2×C4C2×D4×D1111yescharacteristic
785C2×C4#6703711yescharacteristic
786C2×C4#6703711yescharacteristic
787C2×C4#6704211yescharacteristic
788C2×C4#6704211yescharacteristic
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—81no—
813C22—81no—
814C22—441no—
815C22—441no—
816C22—441no—
817C22—441no—
818C22—441no—
819C22—441no—
820C22—884no—
821C22C2×(C22⋊D11)⋊C411yescharacteristic
822C22#1062314811yescharacteristic
823C22#1062314811yescharacteristic
824C4—21no—
825C4—21no—
826C4—42no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—81no—
831C4—441no—
832C4—441no—
833C4#1062307611yescharacteristic
834C4#1062307611yescharacteristic
835C4#1062312311yescharacteristic
836C4#1062318411yescharacteristic
837C2—21no—
838C2—21no—
839C2—41no—
840C2—41no—
841C2—81no—
842C2—881no—
843C2—881no—
844C2#1307127911yescharacteristic
845C2#1307752211yescharacteristic
846C2#1307752911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1871C2
socleC22×C11C2×C4×D4
prime radical#13077832C2
cosocleC22×C4×C11C24
hypercenter#1871D11
hypocenterC11#22062
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1871

Complements

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

NH ≅ G/Ntype
2. #13077320C2semidirect
3. #13077060C2semidirect
4. #13069506C2semidirect
5. #13069501C2semidirect
6. #13069328C2semidirect
7. #13069321C2semidirect
8. #13069262C2semidirect
9. #13069262C2semidirect
10. #13068941C2semidirect
11. #13068941C2semidirect
12. #13068821C2semidirect
13. #13068561C2semidirect
14. #13068400C2semidirect
15. C11×#1871C2semidirect
21. C2×#67001C22semidirect
23. C2×C11×#104C22semidirect
24. C2×C11×#104C22semidirect
26. #10622847C22semidirect
35. C2×#66886C22semidirect
36. C2×#66886C22semidirect
39. #10622663C4semidirect
40. #10622660C4semidirect
41. #10622660C4semidirect
42. #10622659C4semidirect
43. #10622653C4semidirect
44. #10622650C4semidirect
45. #10622650C4semidirect
46. #10622649C4semidirect
53. #10622612C22semidirect
54. #10622610C22semidirect
59. C2×#66867C22semidirect
60. C2×C4×C11⋊C8C22semidirect
61. C11×#339C22semidirect
62. C11×#339C22semidirect
63. #10622196C22semidirect
64. #10622196C22semidirect
65. #10622162C22semidirect
66. #10622162C22semidirect
302. #1871D11semidirect
419. C2×#104C2×D11semidirect
420. C2×#104C2×D11semidirect
440. #339C2×D11semidirect
441. #339C2×D11semidirect
713. C11#22062semidirect

Maximal subgroups

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

subgroupindex
#130778322
#130773202
#130770602
#130695062
#130695012
#130693282
#130693212
#130692622
#130689412
#130688212
#130685612
#130684002
C11×#18712
#2206211