Finite Group Databasebeta

← #14730869

Subgroups — #14730869

Order 2816.

1084 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079942C211yesmaximal, characteristic, complemented
2#13079042C211yesmaximal, characteristic, complemented
3#13078707C211yesmaximal, characteristic, complemented
4#13067761C211yesmaximal, characteristic, complemented
5#13067750C211yesmaximal, characteristic, complemented
6#13067743C211yesmaximal, characteristic, complemented
7#13067732C211yesmaximal, characteristic, complemented
8#13067699C211yesmaximal, characteristic, complemented
9#13067688C211yesmaximal, characteristic, complemented
10#13067681C211yesmaximal, characteristic, complemented
11#13067670C211yesmaximal, characteristic, complemented
12#13067311C211yesmaximal, characteristic, complemented
13#13067076C211yesmaximal, characteristic, complemented
14C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
15C11×#3519C211yesmaximal, characteristic, complemented
16C11×#555C2211yescharacteristic
17C11×#554C2211yescharacteristic
18C11×#553—21no—
19C11×#553—21no—
20C11×#550C2211yescharacteristic
21C11×#546—22no—
22C11×#546—21no—
23D42×C11—21no—
24D42×C11C2211yescharacteristic
25C11×#540—21no—
26C11×#538—22no—
27C11×#532C2211yescharacteristic
28C11×#529C2211yescharacteristic
29C11×#525—21no—
30C2×C11×#121—21no—
31C11×#518—21no—
32C2×C4×D4×C11C2211yescharacteristic
33C2×#67003—22no—
34#10623008C2211yescharacteristic, complemented
35#10622830—21no—
36#10622705C2211yescharacteristic, complemented
37#10622698C2211yescharacteristic, complemented
38#10622689C2211yescharacteristic, complemented
39#10622686C2211yescharacteristic, complemented
40#10622679—21no—
41#10622672—22no—
42#10622670—21no—
43#10622661—21no—
44#10622651—21no—
45#10622640C2211yescharacteristic, complemented
46#10622634C2211yescharacteristic, complemented
47#10622628C2211yescharacteristic
48#10622628C2211yescharacteristic, complemented
49#10622628C2211yescharacteristic, complemented
50#10622627—21no—
51#10622627—21no—
52#10622621C2211yescharacteristic
53#10622621C2211yescharacteristic, complemented
54#10622621C2211yescharacteristic, complemented
55#10622581—21no—
56#10622539C2211yescharacteristic, complemented
57C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
58C2×C4×C11⋊C8C2211yescharacteristic, complemented
59#10622184C2211yescharacteristic, complemented
60#10622184C2211yescharacteristic, complemented
61#10622182C2211yescharacteristic, complemented
62#10622182C2211yescharacteristic, complemented
63Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
64Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
65D4⋊(C11⋊C8)C2211yescharacteristic
66D4⋊(C11⋊C8)C2211yescharacteristic
67D4⋊(C11⋊C8)C2211yescharacteristic, complemented
68D4⋊(C11⋊C8)C2211yescharacteristic, complemented
69D4⋊(C11⋊C8)C2211yescharacteristic, complemented
70D4⋊(C11⋊C8)C2211yescharacteristic, complemented
71C2×C11×#41—21no—
72C2×C11×#41D412yes—
73C22×D4×C11—22no—
74C22×D4×C11—21no—
75C22×D4×C11—21no—
76C22×D4×C11D411yescharacteristic
77C23×C4×C11—21no—
78C2×#4339—21no—
79C11×C4⋊Q8C2311yescharacteristic
80C11×#127—21no—
81C11×#127C2311yescharacteristic
82C11×#126—22no—
83C11×#126—21no—
84C11×#125—21no—
85C11×#125D411yescharacteristic
86C11×#124—22no—
87C11×#124D411yescharacteristic
88C11×#124D412yes—
89C11×#123—22no—
90C11×#123—22no—
91C11×#123—22no—
92C11×#123—21no—
93C11×C22⋊Q8—21no—
94C11×C22⋊Q8—22no—
95C11×C22⋊Q8D411yescharacteristic
96C11×#121—22no—
97C11×#121—22no—
98C11×#121—22no—
99C11×#121—22no—
100C11×#121—21no—
101C11×#121—22no—
102C11×#121—21no—
103C11×#121—21no—
104C11×#121—21no—
105C11×#121—21no—
106C11×#121—21no—
107C11×#121—21no—
108C11×#121D411yescharacteristic
109C11×#120—22no—
110C11×#120—22no—
111C11×#120—22no—
112C4×Q8×C11C2311yescharacteristic
113C4×D4×C11—22no—
114C4×D4×C11—22no—
115C4×D4×C11—22no—
116C4×D4×C11—21no—
117C4×D4×C11—21no—
118C4×D4×C11—21no—
119C4×D4×C11—21no—
120C4×D4×C11—21no—
121C4×D4×C11—21no—
122C4×D4×C11—21no—
123C4×D4×C11D411yescharacteristic
124C4×D4×C11D411yescharacteristic
125C4×D4×C11C2311yescharacteristic
126C4×D4×C11C2311yescharacteristic
127C4×D4×C11C2311yescharacteristic
128C11×#117—21no—
129C11×#117—21no—
130C11×#117—21no—
131C2×C11×C4⋊C4—21no—
132C2×C11×C4⋊C4D411yescharacteristic
133C2×C11×C22⋊C4—22no—
134C2×C11×C22⋊C4—22no—
135C2×C11×C22⋊C4—21no—
136C2×C42×C11C2311yescharacteristic
137#67003—48no—
138C2×#4326—22no—
139C2×#4325—22no—
140C2×#4325—21no—
141C2×#4324—22no—
142C2×#4323—21no—
143C2×#4323—21no—
144C2×#4323—22no—
145C2×#4323—21no—
146#66983—21no—
147#66983—21no—
148C22×C11⋊C8—21no—
149C22×C11⋊C8—21no—
150#66928—21no—
151#66927C2311yescharacteristic
152C4×D44—21no—
153C4×D44—21no—
154#66922C2311yescharacteristic
155#66899—21no—
156#66896—21no—
157#66896—21no—
158#66896—21no—
159C22⋊(C11⋊C8)—21no—
160#66873—21no—
161#66873—21no—
162#66873—21no—
163#66873—21no—
164#66872—21no—
165#66872—21no—
166#66872—21no—
167#66871—21no—
168C4⋊(C11⋊C8)—21no—
169C4⋊(C11⋊C8)C2311yescharacteristic
170C4⋊(C11⋊C8)C2311yescharacteristic
171C4⋊(C11⋊C8)C2311yescharacteristic
172C4⋊(C11⋊C8)C2311yescharacteristic
173#66867—21no—
174C4×C11⋊C8—21no—
175C4×C11⋊C8C2311yescharacteristic
176C4×C11⋊C8C2311yescharacteristic
177#18618—111nomaximal, Sylow
178C24×C11—22no—
179C24×C11—21no—
180C11×#41—44no—
181C11×#41—81no—
182C11×#41—81no—
183C2×Q8×C11C2×D411yescharacteristic
184C2×Q8×C11C2×D412yes—
185C2×D4×C11—22no—
186C2×D4×C11—22no—
187C2×D4×C11—22no—
188C2×D4×C11—21no—
189C2×D4×C11—22no—
190C2×D4×C11—22no—
191C2×D4×C11—22no—
192C2×D4×C11—22no—
193C2×D4×C11—21no—
194C2×D4×C11—21no—
195C2×D4×C11—21no—
196C2×D4×C11—41no—
197C2×D4×C11—42no—
198C2×D4×C11—42no—
199C2×D4×C11—81no—
200C2×D4×C11—81no—
201C2×D4×C11—84no—
202C2×D4×C11C2×D411yescharacteristic
203C2×D4×C11C2×D411yescharacteristic
204C2×D4×C11C2×D411yescharacteristic
205C2×D4×C11C2×D412yes—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—22no—
214C22×C4×C11—21no—
215C22×C4×C11—81no—
216C22×C4×C11—81no—
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D411yescharacteristic
220C2×C22⋊D11—41no—
221#4339—44no—
222C2×D44—21no—
223C2×D44—21no—
224C2×D44—21no—
225C2×C4×D11—41no—
226C2×Dic22—21no—
227C11×C4⋊C4—22no—
228C11×C4⋊C4—22no—
229C11×C4⋊C4—21no—
230C11×C4⋊C4—21no—
231C11×C4⋊C4—21no—
232C11×C4⋊C4—21no—
233C11×C4⋊C4—21no—
234C11×C4⋊C4—21no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4C2×D411yescharacteristic
237C11×C4⋊C4C2×D411yescharacteristic
238C11×C4⋊C4C2×D411yescharacteristic
239C11×C4⋊C4C2×D411yescharacteristic
240C11×C22⋊C4—22no—
241C11×C22⋊C4—22no—
242C11×C22⋊C4—22no—
243C11×C22⋊C4—22no—
244C11×C22⋊C4—22no—
245C11×C22⋊C4—21no—
246C11×C22⋊C4—21no—
247C11×C22⋊C4—21no—
248C11×C22⋊C4—21no—
249C11×C22⋊C4—22no—
250C11×C22⋊C4—21no—
251C11×C22⋊C4—21no—
252C11×C22⋊C4—22no—
253C11×C22⋊C4—21no—
254C11×C22⋊C4—21no—
255C11×C22⋊C4—21no—
256C42×C11—22no—
257C42×C11—21no—
258C42×C11C2×D411yescharacteristic
259C42×C11C2×D411yescharacteristic
260C42×C11C2×D411yescharacteristic
261C42×C11C2411yescharacteristic
262#4326—44no—
263#4325—44no—
264#4325—81no—
265#4324—44no—
266#4323—42no—
267#4323—44no—
268#4323—42no—
269#4323—81no—
270(C2×D11)⋊C4—41no—
271(C2×D11)⋊C4—41no—
272C4⋊Dic11—21no—
273C4⋊Dic11—21no—
274C2×C11⋊C8—24no—
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—81no—
282#3519D1111yescharacteristic, complemented
283#3247—111no—
284#3147—111no—
285#3109—111no—
286#1634—111no—
287#1632—111no—
288#1631—111no—
289#1629—111no—
290#1624—111no—
291#1622—111no—
292#1621—111no—
293#1619—111no—
294#1551—111no—
295#1494—111no—
296C2×D4⋊C8—111no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—22no—
301C23×C11—42no—
302C23×C11—44no—
303C23×C11—42no—
304C23×C11—81no—
305C23×C11—82no—
306C23×C11—82no—
307C23×C11#12011yescharacteristic
308C22×D11—41no—
309Q8×C11—21no—
310Q8×C11—21no—
311Q8×C11—42no—
312D4×C11—21no—
313D4×C11—21no—
314D4×C11—21no—
315D4×C11—21no—
316D4×C11—21no—
317D4×C11—42no—
318D4×C11—42no—
319D4×C11—44no—
320D4×C11—42no—
321D4×C11—44no—
322D4×C11—41no—
323D4×C11—41no—
324D4×C11—41no—
325D4×C11—41no—
326D4×C11—82no—
327D4×C11—82no—
328D4×C11—82no—
329D4×C11—82no—
330D4×C11#13512yescomplemented
331C2×C4×C11—22no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—21no—
338C2×C4×C11—21no—
339C2×C4×C11—22no—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
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×C11—81no—
349C2×C4×C11—81no—
350C2×C4×C11—82no—
351C2×C4×C11—81no—
352C2×C4×C11—82no—
353C2×C4×C11—82no—
354C2×C4×C11#12011yescharacteristic
355C2×C4×C11#12011yescharacteristic
356C2×C4×C11#12011yescharacteristic
357C2×C4×C11C22×D411yescharacteristic
358C2×C4×C11C22×D411yescharacteristic
359C2×C4×C11C22×D411yescharacteristic
360C22⋊D11—82no—
361C2×Dic11—41no—
362D44—42no—
363D44—41no—
364D44—41no—
365D44—41no—
366D44—41no—
367C4×D11—82no—
368Dic22—42no—
369C11⋊C8—22no—
370C11⋊C8—22no—
371C11⋊C8—41no—
372C11⋊C8—41no—
373C11⋊C8—41no—
374C11⋊C8—41no—
375C2×#135—222no—
376#555C2×D1111yescharacteristic
377#554C2×D1111yescharacteristic
378#553—21no—
379#553—21no—
380#550C2×D1111yescharacteristic
381#546—22no—
382#546—21no—
383D42—21no—
384D42C2×D1111yescharacteristic
385#540—21no—
386#538—22no—
387#532—111no—
388#532C2×D1111yescharacteristic
389#529C2×D1111yescharacteristic
390#525—21no—
391C2×#121—21no—
392#518—21no—
393C2×C4×D4C2×D1111yescharacteristic
394#495—222no—
395#494—111no—
396#493—111no—
397#492—111no—
398#492—111no—
399#481—221no—
400#478—221no—
401#477—111no—
402#476—111no—
403#476—111no—
404#476—111no—
405#466—221no—
406#465—221no—
407#463—221no—
408#460—111no—
409#459—111no—
410#459—111no—
411#459—111no—
412#447—221no—
413#442—221no—
414#442—221no—
415#432—111no—
416C2×C4⋊C8—111no—
417C2×C4×C8—111no—
418#333—111no—
419#333—111no—
420#331—111no—
421#331—111no—
422Q8⋊C8—111no—
423Q8⋊C8—111no—
424D4⋊C8—111no—
425D4⋊C8—111no—
426D4⋊C8—111no—
427D4⋊C8—111no—
428D4⋊C8—111no—
429D4⋊C8—111no—
430C22×C11—21no—
431C22×C11—21no—
432C22×C11—22no—
433C22×C11—41no—
434C22×C11—41no—
435C22×C11—41no—
436C22×C11—41no—
437C22×C11—42no—
438C22×C11—41no—
439C22×C11—42no—
440C22×C11—41no—
441C22×C11—42no—
442C22×C11—41no—
443C22×C11—41no—
444C22×C11—84no—
445C22×C11—164no—
446C22×C11#45312yes—
447C22×C11C2×#12011yescharacteristic
448C2×D11—81no—
449C2×D11—81no—
450C2×D11—81no—
451C4×C11—21no—
452C4×C11—21no—
453C4×C11—21no—
454C4×C11—21no—
455C4×C11—41no—
456C4×C11—41no—
457C4×C11—41no—
458C4×C11—41no—
459C4×C11—41no—
460C4×C11—42no—
461C4×C11C2×#13511yescharacteristic
462C4×C11#57511yescharacteristic
463C4×C11#57611yescharacteristic
464C4×C11#57711yescharacteristic
465Dic11—81no—
466C2×#41—21no—
467C2×#41—221no—
468C2×#41C22⋊D1112yes—
469C22×D4—22no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4C22⋊D1111yescharacteristic
473C23×C4—21no—
474#135—448no—
475C2×Q16—222no—
476C2×SD16—222no—
477C2×SD16—222no—
478C2×SD16—221no—
479C2×D8—222no—
480C2×D8—221no—
481C2×D8—221no—
482C2×D8—221no—
483C22×C8—221no—
484C22×C8—221no—
485C4⋊Q8—111no—
486C4⋊Q8C22×D1111yescharacteristic
487#127—21no—
488#127—111no—
489#127C22×D1111yescharacteristic
490#126—22no—
491#126—21no—
492#125—21no—
493#125C22⋊D1111yescharacteristic
494#124—22no—
495#124—221no—
496#124C22⋊D1111yescharacteristic
497#124C22⋊D1112yes—
498#123—22no—
499#123—22no—
500#123—22no—
501#123—21no—
502C22⋊Q8—21no—
503C22⋊Q8—22no—
504C22⋊Q8C22⋊D1111yescharacteristic
505#121—22no—
506#121—22no—
507#121—22no—
508#121—22no—
509#121—21no—
510#121—22no—
511#121—21no—
512#121—21no—
513#121—21no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—221no—
518#121—221no—
519#121C22⋊D1111yescharacteristic
520#120—22no—
521#120—22no—
522#120—22no—
523C4×Q8C22×D1111yescharacteristic
524C4×D4—22no—
525C4×D4—22no—
526C4×D4—22no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—21no—
533C4×D4—21no—
534C4×D4—221no—
535C4×D4—221no—
536C4×D4C22⋊D1111yescharacteristic
537C4×D4C22⋊D1111yescharacteristic
538C4×D4C22×D1111yescharacteristic
539C4×D4C22×D1111yescharacteristic
540C4×D4C22×D1111yescharacteristic
541#117—21no—
542#117—21no—
543#117—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4C22⋊D1111yescharacteristic
546C2×C22⋊C4—22no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—21no—
549C2×C42C22×D1111yescharacteristic
550#107—221no—
551#106—221no—
552#106—221no—
553#106—221no—
554C4⋊C8—111no—
555C4⋊C8—111no—
556C4⋊C8—111no—
557C4⋊C8—111no—
558C4⋊C8—221no—
559#103—221no—
560#102—221no—
561#102—221no—
562#102—221no—
563#102—221no—
564#102—221no—
565#102—221no—
566#102—221no—
567C22⋊C8—221no—
568#97—221no—
569C4×C8—111no—
570C4×C8—111no—
571C4×C8—221no—
572C2×C11—22no—
573C2×C11—42no—
574C2×C11—81no—
575C2×C11—82no—
576C2×C11—81no—
577C2×C11#300211yescharacteristic
578C2×C11#301211yescharacteristic
579C2×C11C2×#45311yescharacteristic
580D11—161no—
581C24—22no—
582C24—21no—
583#41—44no—
584#41—81no—
585#41—81no—
586#41—444no—
587C2×Q8—221no—
588C2×Q8C2×C22⋊D1111yescharacteristic
589C2×Q8C2×C22⋊D1112yes—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—21no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—41no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—81no—
605C2×D4—81no—
606C2×D4—84no—
607C2×D4—221no—
608C2×D4—221no—
609C2×D4—221no—
610C2×D4—441no—
611C2×D4C2×C22⋊D1111yescharacteristic
612C2×D4C2×C22⋊D1111yescharacteristic
613C2×D4C2×C22⋊D1111yescharacteristic
614C2×D4C2×C22⋊D1112yes—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—21no—
624C22×C4—81no—
625C22×C4—81no—
626C22×C4—441no—
627C22×C4C2×C22⋊D1111yescharacteristic
628C22×C4C2×C22⋊D1111yescharacteristic
629C22×C4C2×C22⋊D1111yescharacteristic
630Q16—444no—
631SD16—444no—
632SD16—444no—
633SD16—881no—
634D8—444no—
635D8—442no—
636D8—442no—
637D8—881no—
638C2×C8—224no—
639C2×C8—221no—
640C2×C8—221no—
641C2×C8—221no—
642C2×C8—221no—
643C2×C8—221no—
644C2×C8—221no—
645C2×C8—881no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—221no—
656C4⋊C4—221no—
657C4⋊C4C2×C22⋊D1111yescharacteristic
658C4⋊C4C2×C22⋊D1111yescharacteristic
659C4⋊C4C2×C22⋊D1111yescharacteristic
660C4⋊C4C2×C22⋊D1111yescharacteristic
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—22no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—22no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—22no—
674C22⋊C4—21no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—441no—
678C22⋊C4—441no—
679C42—22no—
680C42—21no—
681C42C2×C22⋊D1111yescharacteristic
682C42C2×C22⋊D1111yescharacteristic
683C42C2×C22⋊D1111yescharacteristic
684C42C23×D1111yescharacteristic
685C11#1861811yescharacteristic, complemented, Sylow
686C23—21no—
687C23—21no—
688C23—21no—
689C23—22no—
690C23—42no—
691C23—44no—
692C23—42no—
693C23—81no—
694C23—82no—
695C23—82no—
696C23—441no—
697C23#6700611yescharacteristic
698Q8—21no—
699Q8—21no—
700Q8—42no—
701Q8—442no—
702D4—21no—
703D4—21no—
704D4—21no—
705D4—21no—
706D4—21no—
707D4—42no—
708D4—42no—
709D4—44no—
710D4—42no—
711D4—44no—
712D4—41no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—82no—
717D4—82no—
718D4—82no—
719D4—82no—
720D4—442no—
721D4—441no—
722D4—441no—
723D4—441no—
724D4—441no—
725D4—882no—
726D4#6700312yescomplemented
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—81no—
745C2×C4—81no—
746C2×C4—82no—
747C2×C4—81no—
748C2×C4—82no—
749C2×C4—82no—
750C2×C4—441no—
751C2×C4—882no—
752C2×C4#6700611yescharacteristic
753C2×C4#6700611yescharacteristic
754C2×C4#6700611yescharacteristic
755C2×C4C22×C22⋊D1111yescharacteristic
756C2×C4C22×C22⋊D1111yescharacteristic
757C2×C4C22×C22⋊D1111yescharacteristic
758C8—222no—
759C8—222no—
760C8—441no—
761C8—441no—
762C8—441no—
763C8—441no—
764C22—21no—
765C22—21no—
766C22—22no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—42no—
772C22—41no—
773C22—42no—
774C22—41no—
775C22—42no—
776C22—41no—
777C22—41no—
778C22—84no—
779C22—164no—
780C22—881no—
781C22—881no—
782C22—881no—
783C22#1062285412yes—
784C22C2×#6700611yescharacteristic
785C4—21no—
786C4—21no—
787C4—21no—
788C4—21no—
789C4—41no—
790C4—41no—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—42no—
795C4—881no—
796C4C2×#6700311yescharacteristic
797C4#1062335311yescharacteristic
798C4#1062336611yescharacteristic
799C4#1062336711yescharacteristic
800C2—22no—
801C2—42no—
802C2—81no—
803C2—81no—
804C2—82no—
805C2—1761no—
806C2#1307783411yescharacteristic
807C2#1307792011yescharacteristic
808C2C2×#1062285411yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3519C2
socleC22×C11C2×#120
hypercenter#3519D11
hypocenterC11#18618
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3519

Complements

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

NH ≅ G/Ntype
1. #13079942C2semidirect
2. #13079042C2semidirect
3. #13078707C2semidirect
4. #13067761C2semidirect
5. #13067750C2semidirect
6. #13067743C2semidirect
7. #13067732C2semidirect
8. #13067699C2semidirect
9. #13067688C2semidirect
10. #13067681C2semidirect
11. #13067670C2semidirect
12. #13067311C2semidirect
13. #13067076C2semidirect
14. C2×D4⋊(C11⋊C8)C2semidirect
15. C11×#3519C2semidirect
34. #10623008C22semidirect
36. #10622705C22semidirect
37. #10622698C22semidirect
38. #10622689C22semidirect
39. #10622686C22semidirect
45. #10622640C22semidirect
46. #10622634C22semidirect
48. #10622628C22semidirect
49. #10622628C22semidirect
53. #10622621C22semidirect
54. #10622621C22semidirect
56. #10622539C22semidirect
57. C2×C4⋊(C11⋊C8)C22semidirect
58. C2×C4×C11⋊C8C22semidirect
59. #10622184C22semidirect
60. #10622184C22semidirect
61. #10622182C22semidirect
62. #10622182C22semidirect
63. Q8⋊(C11⋊C8)C22semidirect
64. Q8⋊(C11⋊C8)C22semidirect
67. D4⋊(C11⋊C8)C22semidirect
68. D4⋊(C11⋊C8)C22semidirect
69. D4⋊(C11⋊C8)C22semidirect
70. D4⋊(C11⋊C8)C22semidirect
282. #3519D11semidirect
330. D4×C11#135semidirect
685. C11#18618semidirect
726. D4#67003semidirect

Maximal subgroups

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

subgroupindex
#130799422
#130790422
#130787072
#130677612
#130677502
#130677432
#130677322
#130676992
#130676882
#130676812
#130676702
#130673112
#130670762
C2×D4⋊(C11⋊C8)2
C11×#35192
#1861811