Finite Group Databasebeta

← #15625949

Subgroups — #15625949

Order 2816.

1780 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081912C211yesmaximal, characteristic
2#13079856C214yesmaximal, complemented
3#13079846C212yesmaximal, complemented
4#13079837C212yesmaximal, complemented
5#13079830C212yesmaximal, complemented
6#13079822C212yesmaximal, complemented
7#13079814C212yesmaximal, complemented
8#13079806C212yesmaximal, complemented
9#13079138C212yesmaximal, complemented
10#13078964C212yesmaximal, complemented
11#13078529C214yesmaximal, complemented
12#13078398C214yesmaximal, complemented
13C2×#10622539C211yesmaximal, characteristic, complemented
14C2×C11×#533C211yesmaximal, characteristic, complemented
15C11×#533—21no—
16C11×#533—21no—
17C11×#533—21no—
18C11×#533—21no—
19C11×#533C2212yes—
20C11×#533C2212yes—
21C11×#533C2212yes—
22C11×#533C2212yes—
23C2×C11×C4⋊Q8C2211yescharacteristic
24C2×C11×C4⋊Q8C2211yescharacteristic
25C2×C11×#125C2212yes—
26C2×C11×C22⋊Q8—21no—
27C2×C11×C22⋊Q8—21no—
28C2×C4×Q8×C11—21no—
29C2×C4×Q8×C11—21no—
30C2×C11×#117C2212yes—
31C22×C42×C11C2211yescharacteristic
32#10623322—21no—
33#10623322—21no—
34#10623322C2212yes—
35#10623010—21no—
36#10623010—21no—
37#10623010—21no—
38#10623010—21no—
39#10623010C2212yes—
40#10623010C2212yes—
41#10623008C2211yescharacteristic
42#10623008C2211yescharacteristic
43#10623008C2211yescharacteristic
44C4×#4339—21no—
45C4×#4339—21no—
46C4×#4339C2212yes—
47#10623001C2211yescharacteristic
48#10623001C2211yescharacteristic
49#10623001C2211yescharacteristic
50C2×C22⋊(C11⋊C8)C2212yes—
51#10622707C2214yescomplemented
52#10622704C2214yescomplemented
53#10622702C2214yescomplemented
54#10622702C2214yescomplemented
55#10622700C2214yescomplemented
56#10622697C2214yescomplemented
57#10622693C2214yescomplemented
58#10622693C2214yescomplemented
59#10622682C2214yescomplemented
60#10622680C2214yescomplemented
61#10622679C2218yescomplemented
62#10622678C2214yescomplemented
63#10622678C2214yescomplemented
64#10622676C2218yescomplemented
65#10622616C2218yes—
66#10622615C2218yes—
67#10622611C2218yes—
68#10622609C2218yes—
69#10622584C2214yes—
70#10622583C2214yes—
71#10622581C2214yes—
72#10622580C2214yes—
73#10622539C2212yes—
74#10622539C2212yes—
75#10622539C2212yes—
76#10622539C2212yes—
77C2×C4⋊(C11⋊C8)C2212yes—
78C2×#66867C2212yes—
79C22×Q8×C11—21no—
80C22×Q8×C11—21no—
81C23×C4×C11D411yescharacteristic
82C23×C4×C11D411yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C2×#4339—21no—
85C2×#4339—21no—
86C2×#4339C2312yes—
87C11×C4⋊Q8—21no—
88C11×C4⋊Q8—21no—
89C11×C4⋊Q8—21no—
90C11×C4⋊Q8—21no—
91C11×C4⋊Q8C2312yes—
92C11×C4⋊Q8C2312yes—
93C11×C4⋊Q8C2312yes—
94C11×C4⋊Q8C2312yes—
95C11×#125—22no—
96C11×#125—22no—
97C11×#125C2314yes—
98C11×#125C2314yes—
99C11×C22⋊Q8—22no—
100C11×C22⋊Q8—22no—
101C11×C22⋊Q8—22no—
102C11×C22⋊Q8—22no—
103C11×C22⋊Q8—22no—
104C11×C22⋊Q8—22no—
105C11×C22⋊Q8—22no—
106C11×C22⋊Q8—22no—
107C4×Q8×C11—22no—
108C4×Q8×C11—22no—
109C4×Q8×C11—22no—
110C4×Q8×C11—22no—
111C4×Q8×C11—22no—
112C4×Q8×C11—22no—
113C4×Q8×C11—22no—
114C4×Q8×C11—22no—
115C11×#117—22no—
116C11×#117—22no—
117C11×#117C2314yes—
118C11×#117C2314yes—
119C2×C11×C4⋊C4—22no—
120C2×C11×C4⋊C4—22no—
121C2×C11×C4⋊C4—21no—
122C2×C11×C4⋊C4—21no—
123C2×C11×C4⋊C4C2312yes—
124C2×C11×C4⋊C4C2312yes—
125C2×C11×C22⋊C4—22no—
126C2×C42×C11—22no—
127C2×C42×C11D411yescharacteristic
128C2×C42×C11D411yescharacteristic
129C2×C42×C11D411yescharacteristic
130C2×C42×C11D411yescharacteristic
131C2×C42×C11D411yescharacteristic
132C2×C42×C11D411yescharacteristic
133C2×C42×C11C2311yescharacteristic
134C2×C42×C11C2311yescharacteristic
135C2×C42×C11C2311yescharacteristic
136C2×C42×C11C2311yescharacteristic
137C2×C42×C11C2311yescharacteristic
138C2×C42×C11C2311yescharacteristic
139#67006—22no—
140#66983—21no—
141#66983—21no—
142#66983—21no—
143#66983—21no—
144#66983C2312yes—
145#66983C2312yes—
146#66982—22no—
147#66982—22no—
148#66982—22no—
149C4×C22⋊D11—22no—
150C4×C22⋊D11—22no—
151C4×C22⋊D11—22no—
152C4×C22⋊D11—22no—
153C4×C22⋊D11—22no—
154C4×C22⋊D11—22no—
155#66979—21no—
156#66979—21no—
157#66979C2312yes—
158#66977—21no—
159#66977—21no—
160#66977—21no—
161#66977—21no—
162#66977C2312yes—
163#66977C2312yes—
164C22×C11⋊C8C2314yes—
165#66929—22no—
166#66929—22no—
167#66928—21no—
168#66928—21no—
169#66928C2312yes—
170#66927C2311yescharacteristic
171C4×D44—21no—
172C4×D44—21no—
173C4×D44—21no—
174C4×D44—21no—
175C4×D44C2312yes—
176C4×D44C2312yes—
177#66925—22no—
178#66925—22no—
179#66925—22no—
180C42×D11—22no—
181#66923—21no—
182#66923—21no—
183#66923C2312yes—
184#66922C2311yescharacteristic
185#66922C2311yescharacteristic
186#66922C2311yescharacteristic
187C4×Dic22—21no—
188C4×Dic22—21no—
189C4×Dic22—21no—
190C4×Dic22—21no—
191C4×Dic22C2312yes—
192C4×Dic22C2312yes—
193C22⋊(C11⋊C8)C2314yes—
194C22⋊(C11⋊C8)C2314yes—
195#66874C2318yes—
196#66874C2318yes—
197#66873C2318yes—
198#66873C2318yes—
199#66872C2318yes—
200#66872C2318yes—
201#66871C2318yes—
202#66871C2318yes—
203C4⋊(C11⋊C8)C2314yes—
204C4⋊(C11⋊C8)C2314yes—
205#66867C2314yes—
206#66867C2314yes—
207#60854—111nomaximal, Sylow
208C24×C11C2×D411yescharacteristic
209C2×Q8×C11—22no—
210C2×Q8×C11—22no—
211C2×Q8×C11—22no—
212C2×Q8×C11—22no—
213C2×Q8×C11—44no—
214C2×Q8×C11—44no—
215C22×C4×C11—24no—
216C22×C4×C11—22no—
217C22×C4×C11—22no—
218C22×C4×C11—42no—
219C22×C4×C11—42no—
220C22×C4×C11C2×D411yescharacteristic
221C22×C4×C11C2×D411yescharacteristic
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2×D411yescharacteristic
224C22×C4×C11C2×D411yescharacteristic
225C22×C4×C11C2×D411yescharacteristic
226C22×C4×C11C2×D411yescharacteristic
227C22×C4×C11C2×D411yescharacteristic
228C22×C4×C11C2×D411yescharacteristic
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2×D411yescharacteristic
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2×D411yescharacteristic
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2411yescharacteristic
236C22×C4×C11C2411yescharacteristic
237C22×C4×C11C2411yescharacteristic
238C2×C22⋊D11—22no—
239C2×C22⋊D11—22no—
240C2×C22⋊D11—22no—
241#4339—28no—
242#4339—44no—
243#4339—44no—
244C2×D44—21no—
245C2×D44—21no—
246C2×D44C2412yes—
247C2×C4×D11—22no—
248C2×C4×D11—22no—
249C2×C4×D11—22no—
250C2×Dic22—21no—
251C2×Dic22—21no—
252C2×Dic22C2412yes—
253C11×C4⋊C4—24no—
254C11×C4⋊C4—24no—
255C11×C4⋊C4—24no—
256C11×C4⋊C4—24no—
257C11×C4⋊C4—22no—
258C11×C4⋊C4—22no—
259C11×C4⋊C4—22no—
260C11×C4⋊C4—22no—
261C11×C4⋊C4—22no—
262C11×C4⋊C4—22no—
263C11×C4⋊C4C2414yes—
264C11×C4⋊C4C2414yes—
265C11×C22⋊C4—24no—
266C11×C22⋊C4—24no—
267C42×C11—24no—
268C42×C11—24no—
269C42×C11C2×D411yescharacteristic
270C42×C11C2×D411yescharacteristic
271C42×C11C2×D411yescharacteristic
272C42×C11C2×D411yescharacteristic
273C42×C11C2×D411yescharacteristic
274C42×C11C2×D411yescharacteristic
275C42×C11C2×D411yescharacteristic
276C42×C11C2×D411yescharacteristic
277C42×C11C2×D411yescharacteristic
278C42×C11C2×D411yescharacteristic
279C42×C11C2×D411yescharacteristic
280C42×C11C2×D411yescharacteristic
281C42×C11C2411yescharacteristic
282C42×C11C2411yescharacteristic
283C42×C11C2411yescharacteristic
284C42×C11C2411yescharacteristic
285C22⋊Dic11—22no—
286C22⋊Dic11—22no—
287C22⋊Dic11—22no—
288(C2×D11)⋊C4—22no—
289(C2×D11)⋊C4—22no—
290(C2×D11)⋊C4—22no—
291(C2×D11)⋊C4—22no—
292(C2×D11)⋊C4—22no—
293(C2×D11)⋊C4—22no—
294C4⋊Dic11—21no—
295C4⋊Dic11—21no—
296C4⋊Dic11—21no—
297C4⋊Dic11—21no—
298C4⋊Dic11C2412yes—
299C4⋊Dic11C2412yes—
300Dic11⋊C4—22no—
301Dic11⋊C4—22no—
302Dic11⋊C4—22no—
303Dic11⋊C4—22no—
304Dic11⋊C4—22no—
305Dic11⋊C4—22no—
306C4×Dic11—22no—
307C4×Dic11—22no—
308C4×Dic11—22no—
309C2×C11⋊C8—28no—
310C2×C11⋊C8C2418yes—
311#3444—111no—
312C2×#533D1111yescharacteristic, complemented
313#3240—114no—
314#3239—112no—
315#3238—112no—
316#3237—112no—
317#3236—112no—
318#3235—112no—
319#3234—112no—
320#3162—112no—
321#3135—112no—
322#3091—114no—
323#3076—114no—
324C2×#432—111no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—41no—
328C23×C11C22×D411yescharacteristic
329C23×C11C22×D411yescharacteristic
330C23×C11C22×D411yescharacteristic
331C22×D11—22no—
332Q8×C11—44no—
333Q8×C11—44no—
334Q8×C11—44no—
335Q8×C11—44no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—24no—
347C2×C4×C11—24no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—44no—
356C2×C4×C11—44no—
357C2×C4×C11C22×D411yescharacteristic
358C2×C4×C11C22×D411yescharacteristic
359C2×C4×C11C22×D411yescharacteristic
360C2×C4×C11C22×D411yescharacteristic
361C2×C4×C11C22×D411yescharacteristic
362C2×C4×C11C22×D411yescharacteristic
363C2×C4×C11C22×D411yescharacteristic
364C2×C4×C11C22×D411yescharacteristic
365C2×C4×C11C22×D411yescharacteristic
366C2×C4×C11C22×D411yescharacteristic
367C2×C4×C11C22×D411yescharacteristic
368C2×C4×C112−1+414yes—
369C2×C4×C11C2511yescharacteristic
370C22⋊D11—44no—
371C22⋊D11—44no—
372C22⋊D11—44no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376D44—24no—
377D44—42no—
378D44—42no—
379C4×D11—44no—
380C4×D11—44no—
381C4×D11—44no—
382Dic22—24no—
383Dic22—42no—
384Dic22—42no—
385C11⋊C8—28no—
386#533—21no—
387#533—21no—
388#533—21no—
389#533—21no—
390#533—111no—
391#533—111no—
392#533—111no—
393#533C2×D1112yes—
394#533C2×D1112yes—
395#533C2×D1112yes—
396#533C2×D1112yes—
397#532—111no—
398#532—111no—
399#532—111no—
400C2×C4⋊Q8C2×D1111yescharacteristic
401C2×C4⋊Q8C2×D1111yescharacteristic
402#529—112no—
403#529—112no—
404#529—221no—
405#529—221no—
406#529—221no—
407#529—221no—
408C2×#125C2×D1112yes—
409#525—112no—
410#525—221no—
411#525—221no—
412C2×C22⋊Q8—21no—
413C2×C22⋊Q8—21no—
414C4×#41—112no—
415C4×#41—221no—
416C4×#41—221no—
417C2×C4×Q8—21no—
418C2×C4×Q8—21no—
419C2×#117C2×D1112yes—
420C22×C42C2×D1111yescharacteristic
421#501—114no—
422#501—114no—
423#501—114no—
424#501—114no—
425#491—114no—
426#490—114no—
427#489—114no—
428#489—114no—
429#485—118no—
430#484—114no—
431#483—114no—
432#482—118no—
433#481—114no—
434#480—114no—
435#479—118no—
436#478—118no—
437#477—114no—
438#476—114no—
439#475—114no—
440#474—114no—
441#432—112no—
442#432—112no—
443#432—112no—
444#432—112no—
445#427—118no—
446C2×C4⋊C8—112no—
447#416—118no—
448C2×C22⋊C8—112no—
449C2×#97—112no—
450C22×C11—21no—
451C22×C11—21no—
452C22×C11—21no—
453C22×C11—21no—
454C22×C11—21no—
455C22×C11—21no—
456C22×C11—21no—
457C22×C11—44no—
458C22×C11#53612yes—
459C22×C11#57512yes—
460C22×C11C23×D411yescharacteristic
461C2×D11—42no—
462C2×D11—42no—
463C2×D11—42no—
464C4×C11—21no—
465C4×C11—21no—
466C4×C11—21no—
467C4×C11—21no—
468C4×C11—21no—
469C4×C11—21no—
470C4×C11—21no—
471C4×C11—21no—
472C4×C11—21no—
473C4×C11—44no—
474C4×C11—44no—
475C4×C11#53612yes—
476C4×C11#57512yes—
477C4×C11C2×2−1+412yes—
478Dic11—42no—
479Dic11—42no—
480Dic11—42no—
481C2×#41—112no—
482C2×#41—221no—
483C2×#41—221no—
484C22×Q8—21no—
485C22×Q8—21no—
486C23×C4C22⋊D1111yescharacteristic
487C23×C4C22⋊D1111yescharacteristic
488C23×C4C22×D1111yescharacteristic
489C22×C8—114no—
490C4⋊Q8—21no—
491C4⋊Q8—21no—
492C4⋊Q8—21no—
493C4⋊Q8—21no—
494C4⋊Q8—111no—
495C4⋊Q8—111no—
496C4⋊Q8—111no—
497C4⋊Q8C22×D1112yes—
498C4⋊Q8C22×D1112yes—
499C4⋊Q8C22×D1112yes—
500C4⋊Q8C22×D1112yes—
501#127—111no—
502#126—222no—
503#126—222no—
504#125—22no—
505#125—22no—
506#125—112no—
507#125—221no—
508#125—221no—
509#125C22×D1114yes—
510#125C22×D1114yes—
511#124—112no—
512#124—221no—
513#124—221no—
514#123—222no—
515#123—222no—
516#123—222no—
517C22⋊Q8—22no—
518C22⋊Q8—22no—
519C22⋊Q8—22no—
520C22⋊Q8—22no—
521C22⋊Q8—22no—
522C22⋊Q8—22no—
523C22⋊Q8—22no—
524C22⋊Q8—22no—
525C22⋊Q8—112no—
526C22⋊Q8—112no—
527C22⋊Q8—221no—
528C22⋊Q8—221no—
529C22⋊Q8—221no—
530C22⋊Q8—221no—
531#121—112no—
532#121—112no—
533#121—221no—
534#121—221no—
535#121—221no—
536#121—221no—
537#120—222no—
538C4×Q8—22no—
539C4×Q8—22no—
540C4×Q8—22no—
541C4×Q8—22no—
542C4×Q8—22no—
543C4×Q8—22no—
544C4×Q8—22no—
545C4×Q8—22no—
546C4×Q8—112no—
547C4×Q8—112no—
548C4×Q8—221no—
549C4×Q8—221no—
550C4×Q8—221no—
551C4×Q8—221no—
552C4×D4—112no—
553C4×D4—112no—
554C4×D4—222no—
555C4×D4—222no—
556C4×D4—222no—
557C4×D4—222no—
558C4×D4—222no—
559C4×D4—222no—
560C4×D4—221no—
561C4×D4—221no—
562C4×D4—221no—
563C4×D4—221no—
564#117—22no—
565#117—22no—
566#117—112no—
567#117—221no—
568#117—221no—
569#117—222no—
570#117—222no—
571#117—222no—
572#117C22×D1114yes—
573#117C22×D1114yes—
574C2×C4⋊C4—22no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4C22×D1112yes—
579C2×C4⋊C4C22×D1112yes—
580C2×C22⋊C4—22no—
581C2×C42—22no—
582C2×C42—222no—
583C2×C42C22⋊D1111yescharacteristic
584C2×C42C22⋊D1111yescharacteristic
585C2×C42C22⋊D1111yescharacteristic
586C2×C42C22⋊D1111yescharacteristic
587C2×C42C22⋊D1111yescharacteristic
588C2×C42C22⋊D1111yescharacteristic
589C2×C42C22×D1111yescharacteristic
590C2×C42C22×D1111yescharacteristic
591C2×C42C22×D1111yescharacteristic
592C2×C42C22×D1111yescharacteristic
593C2×C42C22×D1111yescharacteristic
594C2×C42C22×D1111yescharacteristic
595#107—118no—
596#107—118no—
597#106—118no—
598#106—118no—
599C4⋊C8—114no—
600C4⋊C8—114no—
601#103—118no—
602#103—118no—
603#102—118no—
604#102—118no—
605C22⋊C8—114no—
606C22⋊C8—114no—
607#97—114no—
608#97—114no—
609C2×C11—22no—
610C2×C11—22no—
611C2×C11—41no—
612C2×C11C2×#53611yescharacteristic
613C2×C11C2×#57511yescharacteristic
614C2×C11C2×#57511yescharacteristic
615D11—82no—
616C24C2×C22⋊D1111yescharacteristic
617#41—228no—
618#41—444no—
619#41—444no—
620C2×Q8—22no—
621C2×Q8—22no—
622C2×Q8—22no—
623C2×Q8—22no—
624C2×Q8—44no—
625C2×Q8—44no—
626C2×Q8—112no—
627C2×Q8—221no—
628C2×Q8—221no—
629C2×D4—112no—
630C2×D4—222no—
631C2×D4—222no—
632C2×D4—222no—
633C2×D4—221no—
634C2×D4—221no—
635C22×C4—24no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—222no—
641C22×C4—222no—
642C22×C4—222no—
643C22×C4C2×C22⋊D1111yescharacteristic
644C22×C4C2×C22⋊D1111yescharacteristic
645C22×C4C2×C22⋊D1111yescharacteristic
646C22×C4C2×C22⋊D1111yescharacteristic
647C22×C4C2×C22⋊D1111yescharacteristic
648C22×C4C2×C22⋊D1111yescharacteristic
649C22×C4C2×C22⋊D1111yescharacteristic
650C22×C4C2×C22⋊D1111yescharacteristic
651C22×C4C2×C22⋊D1111yescharacteristic
652C22×C4C2×C22⋊D1111yescharacteristic
653C22×C4C2×C22⋊D1111yescharacteristic
654C22×C4C2×C22⋊D1111yescharacteristic
655C22×C4C2×C22⋊D1111yescharacteristic
656C22×C4C2×C22⋊D1111yescharacteristic
657C22×C4C2×C22⋊D1111yescharacteristic
658C22×C4C23×D1111yescharacteristic
659C22×C4C23×D1111yescharacteristic
660C22×C4C23×D1111yescharacteristic
661C2×C8—118no—
662C2×C8—228no—
663C4⋊C4—24no—
664C4⋊C4—24no—
665C4⋊C4—24no—
666C4⋊C4—24no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—112no—
674C4⋊C4—112no—
675C4⋊C4—222no—
676C4⋊C4—222no—
677C4⋊C4—221no—
678C4⋊C4—221no—
679C4⋊C4—221no—
680C4⋊C4—221no—
681C4⋊C4—222no—
682C4⋊C4—222no—
683C4⋊C4—222no—
684C4⋊C4—222no—
685C4⋊C4C23×D1114yes—
686C4⋊C4C23×D1114yes—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—222no—
690C22⋊C4—222no—
691C22⋊C4—222no—
692C22⋊C4—222no—
693C22⋊C4—222no—
694C22⋊C4—222no—
695C22⋊C4—222no—
696C22⋊C4—222no—
697C22⋊C4—222no—
698C42—24no—
699C42—24no—
700C42—222no—
701C42—222no—
702C42—222no—
703C42C2×C22⋊D1111yescharacteristic
704C42C2×C22⋊D1111yescharacteristic
705C42C2×C22⋊D1111yescharacteristic
706C42C2×C22⋊D1111yescharacteristic
707C42C2×C22⋊D1111yescharacteristic
708C42C2×C22⋊D1111yescharacteristic
709C42C2×C22⋊D1111yescharacteristic
710C42C2×C22⋊D1111yescharacteristic
711C42C2×C22⋊D1111yescharacteristic
712C42C2×C22⋊D1111yescharacteristic
713C42C2×C22⋊D1111yescharacteristic
714C42C2×C22⋊D1111yescharacteristic
715C42C23×D1111yescharacteristic
716C42C23×D1111yescharacteristic
717C42C23×D1111yescharacteristic
718C42C23×D1111yescharacteristic
719C11#6085411yescharacteristic, complemented, Sylow
720C23—22no—
721C23—22no—
722C23—41no—
723C23—222no—
724C23C22×C22⋊D1111yescharacteristic
725C23C22×C22⋊D1111yescharacteristic
726C23C22×C22⋊D1111yescharacteristic
727Q8—44no—
728Q8—44no—
729Q8—44no—
730Q8—44no—
731Q8—224no—
732Q8—442no—
733Q8—442no—
734D4—224no—
735D4—442no—
736D4—442no—
737D4—444no—
738D4—444no—
739D4—444no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—222no—
762C2×C4—222no—
763C2×C4—222no—
764C2×C4—444no—
765C2×C4—444no—
766C2×C4—444no—
767C2×C4#6704014yes—
768C2×C4C22×C22⋊D1111yescharacteristic
769C2×C4C22×C22⋊D1111yescharacteristic
770C2×C4C22×C22⋊D1111yescharacteristic
771C2×C4C22×C22⋊D1111yescharacteristic
772C2×C4C22×C22⋊D1111yescharacteristic
773C2×C4C22×C22⋊D1111yescharacteristic
774C2×C4C22×C22⋊D1111yescharacteristic
775C2×C4C22×C22⋊D1111yescharacteristic
776C2×C4C22×C22⋊D1111yescharacteristic
777C2×C4C22×C22⋊D1111yescharacteristic
778C2×C4C22×C22⋊D1111yescharacteristic
779C2×C4C24×D1111yescharacteristic
780C8—228no—
781C22—21no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—21no—
788C22—44no—
789C22—442no—
790C22—442no—
791C22—442no—
792C22#1062334712yes—
793C22#1062335312yes—
794C22C23×C22⋊D1111yescharacteristic
795C4—21no—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—21no—
803C4—21no—
804C4—44no—
805C4—44no—
806C4—442no—
807C4—442no—
808C4—442no—
809C4#1062334712yes—
810C4#1062335312yes—
811C4C2×#6704012yes—
812C2—22no—
813C2—22no—
814C2—41no—
815C2—882no—
816C2C2×#1062334711yescharacteristic
817C2C2×#1062335311yescharacteristic
818C2C2×#1062335311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#533C2
socleC22×C11C23×D4
prime radical#13081912C2
hypercenterC2×#533D11
hypocenterC11#60854
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
2. #13079856C2semidirect
3. #13079846C2semidirect
4. #13079837C2semidirect
5. #13079830C2semidirect
6. #13079822C2semidirect
7. #13079814C2semidirect
8. #13079806C2semidirect
9. #13079138C2semidirect
10. #13078964C2semidirect
11. #13078529C2semidirect
12. #13078398C2semidirect
13. C2×#10622539C2semidirect
14. C2×C11×#533C2semidirect
51. #10622707C22semidirect
52. #10622704C22semidirect
53. #10622702C22semidirect
54. #10622702C22semidirect
55. #10622700C22semidirect
56. #10622697C22semidirect
57. #10622693C22semidirect
58. #10622693C22semidirect
59. #10622682C22semidirect
60. #10622680C22semidirect
61. #10622679C22semidirect
62. #10622678C22semidirect
63. #10622678C22semidirect
64. #10622676C22semidirect
312. C2×#533D11semidirect
719. C11#60854semidirect

Maximal subgroups

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

subgroupindex
#130819122
#130798562
#130798462
#130798372
#130798302
#130798222
#130798142
#130798062
#130791382
#130789642
#130785292
#130783982
C2×#106225392
C2×C11×#5332
#6085411