Finite Group Databasebeta

← #14756284

Subgroups — #14756284

Order 2816.

1050 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622506C211yesmaximal, characteristic, complemented
2C2×D11×#104C211yesmaximal, characteristic
3#13077131C211yesmaximal, characteristic
4#13077058C211yesmaximal, characteristic
5#13077032C211yesmaximal, characteristic, complemented
6#13069267C211yesmaximal, characteristic, complemented
7#13069266C211yesmaximal, characteristic, complemented
8#13069265C211yesmaximal, characteristic, complemented
9#13069264C211yesmaximal, characteristic, complemented
10#13069263C211yesmaximal, characteristic, complemented
11#13069262C211yesmaximal, characteristic, complemented
12#13069261C211yesmaximal, characteristic, complemented
13D11×#339C211yesmaximal, characteristic, complemented
14#13068308C211yesmaximal, characteristic, complemented
15C11×#1929C211yesmaximal, characteristic, complemented
16C2×#41×D11C2211yescharacteristic
17C2×M16×D11C2211yescharacteristic
18C2×M16×D11C2211yescharacteristic
19C22×#4313C2211yescharacteristic
20C22×#4313C2211yescharacteristic
21D11×#117C2211yescharacteristic
22C2×C42×D11C2211yescharacteristic
23C2×C11×#108C2211yescharacteristic, complemented
24C2×C11×#104C2211yescharacteristic
25C11×#416C2211yescharacteristic
26C11×#408C2211yescharacteristic
27C11×#405C2211yescharacteristic, complemented
28C2×#66901C2211yescharacteristic
29#10622847C2211yescharacteristic
30#10622846C2211yescharacteristic
31C2×#66889C2211yescharacteristic
32#10622742C2211yescharacteristic
33C2×#66886C2211yescharacteristic, complemented
34C2×#66886C2211yescharacteristic, complemented
35#10622735C2211yescharacteristic, complemented
36#10622726C2211yescharacteristic
37#10622723C2211yescharacteristic
38C2×#66883C2211yescharacteristic, complemented
39#10622714C2211yescharacteristic, complemented
40#10622615C2211yescharacteristic
41#10622610C2211yescharacteristic, complemented
42C2×#66869C2211yescharacteristic
43#10622506—24no—
44D11×#104—24no—
45#10622416C411yescharacteristic, complemented
46#10622416C411yescharacteristic, complemented
47#10622415C411yescharacteristic, complemented
48#10622415C411yescharacteristic, complemented
49#10622384C411yescharacteristic, complemented
50#10622384C411yescharacteristic, complemented
51#10622383C411yescharacteristic, complemented
52#10622383C411yescharacteristic, complemented
53#10622340—21no—
54#10622340—21no—
55#10622339—21no—
56#10622339—21no—
57#10622321—21no—
58#10622320—21no—
59#10622302—21no—
60C4×#4313—21no—
61C11×#339C2211yescharacteristic, complemented
62C11×#336C2211yescharacteristic, complemented
63#10622193C2211yescharacteristic, complemented
64#10622188C2211yescharacteristic, complemented
65#10622188C2211yescharacteristic, complemented
66#10622170C2211yescharacteristic, complemented
67#10622162C2211yescharacteristic, complemented
68#10622161C2211yescharacteristic, complemented
69C2×C11×#41C2311yescharacteristic
70#41×D11—22no—
71#41×D11—22no—
72#41×D11—22no—
73#41×D11—22no—
74C2×#4343C2×C411yescharacteristic
75C2×Q8×D11C2×C411yescharacteristic
76C2×#4341—21no—
77C2×#4341C2×C411yescharacteristic
78C2×D4×D11—21no—
79C2×D4×D11C2×C411yescharacteristic
80C2×#4339—21no—
81C2×#4339C2311yescharacteristic
82C22×C4×D11—21no—
83C22×C4×D11—21no—
84C22×C4×D11C2311yescharacteristic
85C2×C11×M16C2311yescharacteristic
86C2×C11×M16C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C11×#117C2311yescharacteristic
90C2×C42×C11C2311yescharacteristic
91#66979C2311yescharacteristic
92C2×C4×Dic11—21no—
93C2×C4×Dic11C2311yescharacteristic
94C2×#4318C2311yescharacteristic
95C2×#4318C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98M16×D11—22no—
99M16×D11—22no—
100M16×D11—22no—
101M16×D11D414yes—
102C2×#4313—22no—
103C2×#4313—21no—
104C2×#4313—22no—
105C2×#4313—22no—
106C2×#4313—22no—
107C2×#4313—21no—
108C2×#4313C2×C411yescharacteristic
109C2×#4313C2×C411yescharacteristic
110C2×#4313C2×C411yescharacteristic
111C2×#4313C2×C411yescharacteristic
112C2×#4313D411yescharacteristic
113C2×#4313D411yescharacteristic
114C2×#4313D411yescharacteristic
115C2×#4313D411yescharacteristic
116C2×C8×D11—21no—
117C2×C8×D11—21no—
118#66945C2×C411yescharacteristic
119#66945C2×C411yescharacteristic
120C4⋊C4×D11C2×C411yescharacteristic
121C4⋊C4×D11C2×C411yescharacteristic
122C22⋊C4×D11—21no—
123#66930—21no—
124#66925—21no—
125C42×D11—21no—
126C42×D11—22no—
127C42×D11—22no—
128C11×#108—22no—
129C11×#104—22no—
130C11×#103C2×C411yescharacteristic, complemented
131C11×#103C2×C411yescharacteristic, complemented
132C11×#102C2×C411yescharacteristic, complemented
133C11×#102C2×C411yescharacteristic, complemented
134C11×C22⋊C8—21no—
135C11×C22⋊C8—21no—
136C11×#97—21no—
137C4×C8×C11—21no—
138#66901—22no—
139#66899C2×C411yescharacteristic, complemented
140#66899C2×C411yescharacteristic, complemented
141#66896C2×C411yescharacteristic, complemented
142#66896C2×C411yescharacteristic, complemented
143C22⋊(C11⋊C8)—21no—
144C22⋊(C11⋊C8)—21no—
145#66889—22no—
146#66886—22no—
147#66886—22no—
148#66885C2×C411yescharacteristic, complemented
149#66885C2×C411yescharacteristic, complemented
150(C2×D11)⋊C8—21no—
151(C2×D11)⋊C8—21no—
152(C2×D11)⋊C8—21no—
153(C2×D11)⋊C8—21no—
154#66883—22no—
155#66880C2×C411yescharacteristic, complemented
156#66880C2×C411yescharacteristic, complemented
157#66879—21no—
158#66879—21no—
159C8×Dic11—21no—
160C8×Dic11—21no—
161#66874C2×C411yescharacteristic, complemented
162#66874C2×C411yescharacteristic, complemented
163#66873C2×C411yescharacteristic, complemented
164#66873C2×C411yescharacteristic, complemented
165#66869—22no—
166#66867—21no—
167C4×C11⋊C8—21no—
168#21071—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—
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11#4111yescharacteristic
187#4343—22no—
188#4343—22no—
189Q8×D11—22no—
190Q8×D11—22no—
191#4341—22no—
192#4341—22no—
193#4341—42no—
194#4341—42no—
195D4×D11—22no—
196D4×D11—22no—
197D4×D11—42no—
198D4×D11—42no—
199#4339—21no—
200#4339—21no—
201#4339—21no—
202#4339—21no—
203#4339—42no—
204#4339—42no—
205C2×D44—21no—
206C2×D44C22×C411yescharacteristic
207C2×C4×D11—21no—
208C2×C4×D11—21no—
209C2×C4×D11—21no—
210C2×C4×D11—21no—
211C2×C4×D11—21no—
212C2×C4×D11—42no—
213C2×C4×D11—42no—
214C2×C4×D11—42no—
215C2×C4×D11—42no—
216C2×C4×D11—42no—
217C2×C4×D11C22×C411yescharacteristic
218C2×C4×D11C22×C411yescharacteristic
219C2×C4×D11C2×D411yescharacteristic
220C2×C4×D11C2×D411yescharacteristic
221C2×C4×D11C2×D412yes—
222C2×C4×D11#4112yes—
223C2×C4×D11#4112yes—
224C2×C4×D11#4112yes—
225C2×Dic22—21no—
226C2×Dic22C22×C411yescharacteristic
227C11×M16—21no—
228C11×M16—21no—
229C11×M16—21no—
230C11×M16C2×D412yes—
231C2×C8×C11—21no—
232C2×C8×C11—21no—
233C2×C8×C11—21no—
234C2×C8×C11—21no—
235C2×C8×C11—21no—
236C2×C8×C11—21no—
237C2×C8×C11C22×C411yescharacteristic
238C2×C8×C11C22×C411yescharacteristic
239C2×C8×C11C2×D411yescharacteristic
240C2×C8×C11C2×D411yescharacteristic
241C11×C4⋊C4C22×C411yescharacteristic
242C11×C4⋊C4C22×C411yescharacteristic
243C11×C22⋊C4—21no—
244C42×C11—21no—
245C42×C11—21no—
246C42×C11—21no—
247C22⋊Dic11—21no—
248(C2×D11)⋊C4—21no—
249(C2×D11)⋊C4—21no—
250C4⋊Dic11C22×C411yescharacteristic
251C4⋊Dic11C22×C411yescharacteristic
252Dic11⋊C4—21no—
253Dic11⋊C4—21no—
254C4×Dic11—21no—
255C4×Dic11—21no—
256C4×Dic11—21no—
257C4×Dic11—21no—
258C4×Dic11—21no—
259C4×Dic11—42no—
260#4318—21no—
261#4318—21no—
262#4318—21no—
263#4318C2×D412yes—
264C2×C11⋊C8—21no—
265C2×C11⋊C8—21no—
266C2×C11⋊C8—21no—
267C2×C11⋊C8—21no—
268C2×C11⋊C8—21no—
269C2×C11⋊C8—21no—
270C2×C11⋊C8C22×C411yescharacteristic
271C2×C11⋊C8C22×C411yescharacteristic
272C2×C11⋊C8C2×D411yescharacteristic
273C2×C11⋊C8C2×D411yescharacteristic
274#4313—22no—
275#4313—22no—
276#4313—22no—
277#4313—22no—
278#4313—24no—
279#4313—22no—
280#4313—22no—
281#4313—22no—
282#4313—22no—
283#4313—42no—
284C8×D11—24no—
285C8×D11—42no—
286C2×#430—111no—
287C22×#104—111no—
288#2896—111no—
289#2879—111no—
290#2873—111no—
291#1929—111no—
292#1929—111no—
293#1929—111no—
294#1929—111no—
295#1929—111no—
296#1929—111no—
297#1929—111no—
298#1929D1111yescharacteristic, complemented
299C2×#339—111no—
300#1728—111no—
301C23×C11—21no—
302C23×C11C2×#4111yescharacteristic
303C22×D11—21no—
304C22×D11—41no—
305C22×D11—41no—
306C22×D11—42no—
307C22×D11—81no—
308C22×D11—81no—
309C22×D11C4×D411yescharacteristic
310C22×D11C4×D411yescharacteristic
311C22×D11#12412yes—
312C22×D11#12612yes—
313Q8×C11—21no—
314Q8×C11—21no—
315D4×C11—21no—
316D4×C11—21no—
317D4×C11—41no—
318D4×C11—41no—
319C2×C4×C11—22no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11C23×C411yescharacteristic
328C2×C4×C11C22×D411yescharacteristic
329C2×C4×C11C22×D411yescharacteristic
330C2×C4×C11C2×#4111yescharacteristic
331C2×C4×C11C2×#4111yescharacteristic
332C2×C4×C11C2×#4111yescharacteristic
333C22⋊D11—41no—
334C22⋊D11—41no—
335C22⋊D11—42no—
336C22⋊D11—42no—
337C2×Dic11—22no—
338C2×Dic11—21no—
339C2×Dic11—21no—
340C2×Dic11—21no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343C2×Dic11—42no—
344C2×Dic11C4×D411yescharacteristic
345C2×Dic11C4×D411yescharacteristic
346C2×Dic11#12412yes—
347C2×Dic11#12612yes—
348D44—21no—
349D44—21no—
350D44—42no—
351C4×D11—48no—
352C4×D11—42no—
353C4×D11—41no—
354C4×D11—41no—
355C4×D11—42no—
356C4×D11—81no—
357C4×D11—81no—
358C4×D11#11712yes—
359C4×D11#11712yes—
360C4×D11C4×D412yes—
361C4×D11C4×D412yes—
362C4×D11#12112yes—
363C4×D11#12112yes—
364C4×D11#12312yes—
365C4×D11#12312yes—
366Dic22—21no—
367Dic22—21no—
368Dic22—42no—
369C8×C11—21no—
370C8×C11—21no—
371C8×C11—22no—
372C8×C11—21no—
373C8×C11—21no—
374C8×C11—41no—
375C11⋊C8—21no—
376C11⋊C8—21no—
377C11⋊C8—22no—
378C11⋊C8—21no—
379C11⋊C8—21no—
380C11⋊C8—41no—
381C22×#41—111no—
382C22×M16—111no—
383C22×M16—111no—
384C22×M16—111no—
385C22×M16—111no—
386C2×#117—111no—
387C22×C42—111no—
388#430—224no—
389C2×#108—111no—
390C2×#108—111no—
391C2×#108—111no—
392C2×#108C2×D1111yescharacteristic, complemented
393C2×#104—111no—
394C2×#104—111no—
395C2×#104—111no—
396C2×#104—224no—
397C2×#104C2×D1111yescharacteristic
398#419—111no—
399#419—111no—
400#418—111no—
401#418—111no—
402#417—111no—
403#417—111no—
404#417—111no—
405#417—111no—
406#416—111no—
407#416—111no—
408#416—111no—
409#416C2×D1111yescharacteristic
410#408—111no—
411#408—111no—
412#408—111no—
413#408—221no—
414#408—221no—
415#408C2×D1111yescharacteristic
416#407—221no—
417#407—221no—
418#405—111no—
419#405—111no—
420#405—111no—
421#405—221no—
422#405—221no—
423#405C2×D1111yescharacteristic, complemented
424C4×M16—221no—
425C4×M16—221no—
426#339—111no—
427#339—111no—
428#339—111no—
429#339C2×D1111yescharacteristic, complemented
430#336—111no—
431#336—111no—
432#336—111no—
433#336C2×D1111yescharacteristic, complemented
434C22×C11—21no—
435C22×C11—21no—
436C22×C11—41no—
437C22×C11—41no—
438C22×C11—41no—
439C22×C11C2×C4×D411yescharacteristic
440C22×C11C2×#12411yescharacteristic
441C22×C11C2×#12611yescharacteristic
442C2×D11—21no—
443C2×D11—21no—
444C2×D11—21no—
445C2×D11—21no—
446C2×D11—42no—
447C2×D11—42no—
448C2×D11—41no—
449C2×D11—41no—
450C2×D11—41no—
451C2×D11—84no—
452C2×D11#38812yes—
453C2×D11#38812yes—
454C4×C11—42no—
455C4×C11—41no—
456C4×C11—41no—
457C4×C11—41no—
458C4×C11C2×#11711yescharacteristic
459C4×C11C2×C4×D411yescharacteristic
460C4×C11C2×#12111yescharacteristic
461C4×C11C2×#12311yescharacteristic
462Dic11—42no—
463Dic11—41no—
464Dic11—41no—
465Dic11—41no—
466Dic11#38812yes—
467Dic11#38812yes—
468C2×#41—111no—
469C2×#41—111no—
470C2×#41—111no—
471C2×#41—221no—
472C2×#41—221no—
473C2×#41—222no—
474C2×#41—222no—
475C2×#41—222no—
476C2×#41—222no—
477C2×#41C22×D1111yescharacteristic
478C22×Q8—111no—
479C22×D4—111no—
480C22×D4—221no—
481C23×C4—111no—
482C23×C4—221no—
483C23×C4—221no—
484C2×M16—111no—
485C2×M16—111no—
486C2×M16—111no—
487C2×M16—111no—
488C2×M16—111no—
489C2×M16—111no—
490C2×M16—111no—
491C2×M16—111no—
492C2×M16—111no—
493C2×M16—114no—
494C2×M16—111no—
495C2×M16—222no—
496C2×M16—222no—
497C2×M16—222no—
498C2×M16—221no—
499C2×M16—222no—
500C2×M16—221no—
501C2×M16—222no—
502C2×M16—222no—
503C2×M16—222no—
504C2×M16C22×D1111yescharacteristic
505C2×M16C22×D1111yescharacteristic
506C22×C8—111no—
507C22×C8—111no—
508C22×C8—221no—
509C22×C8—221no—
510C22×C8C22×D1111yescharacteristic
511C22×C8C22×D1111yescharacteristic
512#117—111no—
513#117—111no—
514#117—111no—
515#117—221no—
516#117—221no—
517#117C22×D1111yescharacteristic
518C2×C4⋊C4—111no—
519C2×C4⋊C4—111no—
520C2×C22⋊C4—221no—
521C2×C42—111no—
522C2×C42—221no—
523C2×C42—222no—
524C2×C42—222no—
525C2×C42—221no—
526C2×C42C22×D1111yescharacteristic
527#108—22no—
528#108—222no—
529#108—222no—
530#108—222no—
531#104—22no—
532#104—222no—
533#104—222no—
534#104—222no—
535#103—111no—
536#103—111no—
537#103—111no—
538#103—111no—
539#103—111no—
540#103—111no—
541#103C4×D1111yescharacteristic, complemented
542#103C4×D1111yescharacteristic, complemented
543#102—111no—
544#102—111no—
545#102—111no—
546#102—111no—
547#102—111no—
548#102—111no—
549#102C4×D1111yescharacteristic, complemented
550#102C4×D1111yescharacteristic, complemented
551C22⋊C8—21no—
552C22⋊C8—21no—
553C22⋊C8—221no—
554C22⋊C8—221no—
555C22⋊C8—221no—
556C22⋊C8—221no—
557C22⋊C8—221no—
558C22⋊C8—221no—
559#97—21no—
560#97—221no—
561#97—221no—
562#97—221no—
563C4×C8—21no—
564C4×C8—221no—
565C4×C8—221no—
566C4×C8—221no—
567C2×C11—21no—
568C2×C11—21no—
569C2×C11—81no—
570C2×C11C2×#38811yescharacteristic
571C2×C11#295611yescharacteristic
572C2×C11#295611yescharacteristic
573D11—22no—
574D11—22no—
575D11—81no—
576C24—111no—
577C24—221no—
578#41—21no—
579#41—21no—
580#41—21no—
581#41—21no—
582#41—222no—
583#41—222no—
584#41—222no—
585#41—222no—
586#41—221no—
587#41—221no—
588#41—221no—
589#41—221no—
590#41—442no—
591#41—442no—
592#41—442no—
593#41—442no—
594C2×Q8—111no—
595C2×Q8—221no—
596C2×Q8—222no—
597C2×Q8—222no—
598C2×Q8C2×C4×D1111yescharacteristic
599C2×D4—21no—
600C2×D4—111no—
601C2×D4—221no—
602C2×D4—222no—
603C2×D4—222no—
604C2×D4—221no—
605C2×D4—221no—
606C2×D4—221no—
607C2×D4—442no—
608C2×D4—442no—
609C2×D4C2×C4×D1111yescharacteristic
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—111no—
613C22×C4—111no—
614C22×C4—111no—
615C22×C4—112no—
616C22×C4—111no—
617C22×C4—111no—
618C22×C4—112no—
619C22×C4—112no—
620C22×C4—112no—
621C22×C4—221no—
622C22×C4—221no—
623C22×C4—221no—
624C22×C4—221no—
625C22×C4—221no—
626C22×C4—221no—
627C22×C4—221no—
628C22×C4—442no—
629C22×C4—442no—
630C22×C4—442no—
631C22×C4—442no—
632C22×C4—442no—
633C22×C4C23×D1111yescharacteristic
634M16—21no—
635M16—21no—
636M16—21no—
637M16—112no—
638M16—222no—
639M16—222no—
640M16—222no—
641M16—222no—
642M16—224no—
643M16—222no—
644M16—222no—
645M16—222no—
646M16—222no—
647M16—221no—
648M16—221no—
649M16—221no—
650M16—442no—
651M16D4×D1112yes—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—111no—
659C2×C8—111no—
660C2×C8—111no—
661C2×C8—111no—
662C2×C8—224no—
663C2×C8—221no—
664C2×C8—221no—
665C2×C8—221no—
666C2×C8—221no—
667C2×C8—221no—
668C2×C8—221no—
669C2×C8—442no—
670C2×C8C2×C4×D1111yescharacteristic
671C2×C8C2×C4×D1111yescharacteristic
672C2×C8D4×D1111yescharacteristic
673C2×C8D4×D1111yescharacteristic
674C4⋊C4—111no—
675C4⋊C4—111no—
676C4⋊C4—221no—
677C4⋊C4—221no—
678C4⋊C4C2×C4×D1111yescharacteristic
679C4⋊C4C2×C4×D1111yescharacteristic
680C22⋊C4—21no—
681C22⋊C4—221no—
682C22⋊C4—221no—
683C22⋊C4—221no—
684C42—21no—
685C42—21no—
686C42—21no—
687C42—221no—
688C42—221no—
689C42—221no—
690C42—221no—
691C42—221no—
692C42—442no—
693C11#2107111yescharacteristic, complemented, Sylow
694C23—21no—
695C23—111no—
696C23—111no—
697C23—112no—
698C23—112no—
699C23—221no—
700C23—441no—
701C23—441no—
702C23—442no—
703C23—881no—
704C23—881no—
705C23#41×D1111yescharacteristic
706Q8—21no—
707Q8—21no—
708Q8—221no—
709Q8—221no—
710Q8—442no—
711D4—21no—
712D4—21no—
713D4—41no—
714D4—41no—
715D4—221no—
716D4—221no—
717D4—442no—
718D4—442no—
719D4—442no—
720D4—441no—
721D4—441no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—112no—
731C2×C4—111no—
732C2×C4—111no—
733C2×C4—112no—
734C2×C4—112no—
735C2×C4—112no—
736C2×C4—112no—
737C2×C4—112no—
738C2×C4—112no—
739C2×C4—112no—
740C2×C4—112no—
741C2×C4—112no—
742C2×C4—222no—
743C2×C4—221no—
744C2×C4—221no—
745C2×C4—221no—
746C2×C4—442no—
747C2×C4—442no—
748C2×C4—448no—
749C2×C4—442no—
750C2×C4—441no—
751C2×C4—441no—
752C2×C4—441no—
753C2×C4—441no—
754C2×C4—881no—
755C2×C4—881no—
756C2×C4C22×C4×D1111yescharacteristic
757C2×C4C2×D4×D1111yescharacteristic
758C2×C4C2×D4×D1111yescharacteristic
759C2×C4#41×D1111yescharacteristic
760C2×C4#41×D1111yescharacteristic
761C2×C4#41×D1111yescharacteristic
762C8—21no—
763C8—21no—
764C8—22no—
765C8—21no—
766C8—21no—
767C8—41no—
768C8—221no—
769C8—221no—
770C8—222no—
771C8—221no—
772C8—221no—
773C8—441no—
774C22—21no—
775C22—21no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—112no—
780C22—112no—
781C22—221no—
782C22—221no—
783C22—221no—
784C22—221no—
785C22—442no—
786C22—442no—
787C22—441no—
788C22—441no—
789C22—441no—
790C22—884no—
791C22C4×D4×D1111yescharacteristic
792C22D11×#12411yescharacteristic
793C22D11×#12611yescharacteristic
794C4—42no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—112no—
799C4—112no—
800C4—442no—
801C4—441no—
802C4—441no—
803C4—441no—
804C4D11×#11711yescharacteristic
805C4C4×D4×D1111yescharacteristic
806C4D11×#12111yescharacteristic
807C4D11×#12311yescharacteristic
808C2—21no—
809C2—21no—
810C2—81no—
811C2—222no—
812C2—222no—
813C2—881no—
814C2D11×#38811yescharacteristic
815C2#1307752111yescharacteristic
816C2#1307752411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1929C2
socleC22×C11C2×C4×D4
prime radicalC2×#41×D11C22
cosocleC22×C4×C11C24
hypercenter#1929D11
hypocenterC11#21071
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
1. C2×#10622506C2semidirect
5. #13077032C2semidirect
6. #13069267C2semidirect
7. #13069266C2semidirect
8. #13069265C2semidirect
9. #13069264C2semidirect
10. #13069263C2semidirect
11. #13069262C2semidirect
12. #13069261C2semidirect
13. D11×#339C2semidirect
14. #13068308C2semidirect
15. C11×#1929C2semidirect
23. C2×C11×#108C22semidirect
27. C11×#405C22semidirect
33. C2×#66886C22semidirect
34. C2×#66886C22semidirect
35. #10622735C22semidirect
38. C2×#66883C22semidirect
39. #10622714C22semidirect
41. #10622610C22semidirect
45. #10622416C4semidirect
46. #10622416C4semidirect
47. #10622415C4semidirect
48. #10622415C4semidirect
49. #10622384C4semidirect
50. #10622384C4semidirect
51. #10622383C4semidirect
52. #10622383C4semidirect
61. C11×#339C22semidirect
62. C11×#336C22semidirect
63. #10622193C22semidirect
64. #10622188C22semidirect
65. #10622188C22semidirect
66. #10622170C22semidirect
67. #10622162C22semidirect
68. #10622161C22semidirect
130. C11×#103C2×C4semidirect
131. C11×#103C2×C4semidirect
132. C11×#102C2×C4semidirect
133. C11×#102C2×C4semidirect
139. #66899C2×C4semidirect
140. #66899C2×C4semidirect
141. #66896C2×C4semidirect
142. #66896C2×C4semidirect
148. #66885C2×C4semidirect
149. #66885C2×C4semidirect
155. #66880C2×C4semidirect
156. #66880C2×C4semidirect
161. #66874C2×C4semidirect
162. #66874C2×C4semidirect
163. #66873C2×C4semidirect
164. #66873C2×C4semidirect
298. #1929D11semidirect
392. C2×#108C2×D11semidirect
423. #405C2×D11semidirect
429. #339C2×D11semidirect
433. #336C2×D11semidirect
541. #103C4×D11semidirect
542. #103C4×D11semidirect
549. #102C4×D11semidirect
550. #102C4×D11semidirect
693. C11#21071semidirect

Maximal subgroups

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

subgroupindex
C2×#106225062
C2×D11×#1042
#130771312
#130770582
#130770322
#130692672
#130692662
#130692652
#130692642
#130692632
#130692622
#130692612
D11×#3392
#130683082
C11×#19292
#2107111