Finite Group Databasebeta

← #15626389

Subgroups — #15626389

Order 2816.

1682 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082512C211yesmaximal, characteristic
2#13079914C214yesmaximal, complemented
3#13079899C214yesmaximal, complemented
4#13079856C212yesmaximal, complemented
5#13079856C212yesmaximal, complemented
6#13079846C212yesmaximal, complemented
7#13079837C212yesmaximal, complemented
8#13079158C211yesmaximal, characteristic, complemented
9#13079138C211yesmaximal, characteristic, complemented
10#13079005C211yesmaximal, characteristic, complemented
11C2×#10622702C211yesmaximal, characteristic, complemented
12#13078585C212yesmaximal, complemented
13#13078574C212yesmaximal
14#13078452C212yesmaximal, complemented
15#13078441C212yesmaximal, complemented
16#13077267C211yesmaximal, characteristic, complemented
17C11×#3503C211yesmaximal, characteristic, complemented
18Q82×C11—21no—
19C11×#557—21no—
20C11×#554—22no—
21C11×#554—21no—
22D4×Q8×C11—22no—
23D4×Q8×C11—21no—
24C11×#544C2212yes—
25C11×#544C2214yescomplemented
26C11×#533C2211yescharacteristic
27C11×#533C2212yescomplemented
28C2×C11×C4⋊Q8C2211yescharacteristic
29C2×C11×C4⋊Q8C2212yescomplemented
30C11×#520C2212yes—
31C4×C11×#41C2211yescharacteristic
32#10623361C2211yescharacteristic
33#10623356C2211yescharacteristic
34#10623099—21no—
35#10623099—21no—
36#10623090—21no—
37#10623090—21no—
38#10623087—22no—
39#10623087—22no—
40#10623065C2212yes—
41#10623065C2212yes—
42#10623052C2211yescharacteristic
43#10623047C2211yescharacteristic
44#10623010C2212yes—
45#10623010C2212yes—
46C2×#66928C2211yescharacteristic
47#10623001C2211yescharacteristic
48#10622847C2212yes—
49#10622707C2214yescomplemented
50#10622704C2214yescomplemented
51#10622702C2212yes—
52#10622702C2212yes—
53#10622702C2212yes—
54#10622702C2212yes—
55#10622702C2214yes—
56#10622700C2214yes—
57#10622697C2214yes—
58#10622693C2211yescharacteristic, complemented
59#10622693C2212yescomplemented
60#10622693C2211yescharacteristic, complemented
61#10622693C2212yescomplemented
62#10622693C2211yescharacteristic, complemented
63#10622693C2211yescharacteristic, complemented
64#10622692C2212yescomplemented
65#10622691C2212yescomplemented
66#10622681C2214yes—
67#10622679C2214yes—
68#10622679C2214yes—
69#10622678C2212yescomplemented
70#10622678C2212yescomplemented
71#10622676C2214yescomplemented
72#10622676C2214yescomplemented
73#10622617C2212yes—
74#10622616C2214yes—
75#10622616C2214yes—
76#10622614C2212yes—
77#10622613C2214yescomplemented
78#10622612C2212yes—
79#10622611C2212yes—
80#10622611C2212yes—
81#10622609C2214yescomplemented
82#10622609C2214yescomplemented
83#10622584C2214yescomplemented
84#10622583C2214yescomplemented
85C2×#66874C2212yes—
86#10622581C2214yes—
87#10622580C2214yes—
88C2×#66873C2212yes—
89#10622577C2212yes—
90#10622577C2212yes—
91#10622539C2212yescomplemented
92#10622539C2212yescomplemented
93C4×#4318C2211yescharacteristic
94C2×#66867C2211yescharacteristic
95C2×C11×#41C2311yescharacteristic
96C22×Q8×C11—21no—
97C22×Q8×C11—22no—
98C22×D44C2311yescharacteristic
99C22×Dic22C2311yescharacteristic
100C11×C4⋊Q8—22no—
101C11×C4⋊Q8—24no—
102C11×C4⋊Q8—21no—
103C11×C4⋊Q8—21no—
104C11×C4⋊Q8—22no—
105C11×C4⋊Q8—22no—
106C11×C4⋊Q8C2312yes—
107C11×C4⋊Q8C2312yes—
108C11×C4⋊Q8C2311yescharacteristic
109C11×C4⋊Q8C2314yes—
110C11×C4⋊Q8C2311yescharacteristic
111C11×#125—22no—
112C11×#125—24no—
113C11×#125C2312yes—
114C11×#125C2314yes—
115C11×C22⋊Q8—21no—
116C11×C22⋊Q8—21no—
117C11×C22⋊Q8—22no—
118C11×C22⋊Q8—22no—
119C11×C22⋊Q8—24no—
120C11×C22⋊Q8—24no—
121C11×C22⋊Q8—24no—
122C4×Q8×C11—22no—
123C4×Q8×C11—21no—
124C4×Q8×C11—21no—
125C4×Q8×C11—22no—
126C4×Q8×C11—22no—
127C4×Q8×C11D411yescharacteristic
128C4×Q8×C11D411yescharacteristic
129C4×D4×C11—24no—
130C4×D4×C11—22no—
131C4×D4×C11D412yes—
132C4×D4×C11D412yes—
133C4×D4×C11D411yescharacteristic
134C4×D4×C11D411yescharacteristic
135C11×#117C2314yes—
136C11×#117C2312yes—
137C11×#117C2311yescharacteristic
138C11×#117C2312yes—
139C2×C11×C4⋊C4—21no—
140C2×C11×C4⋊C4—22no—
141C2×C11×C4⋊C4C2312yes—
142C2×C11×C4⋊C4C2314yes—
143C2×C42×C11C2311yescharacteristic
144C2×C42×C11C2312yes—
145#67000—21no—
146#66997—21no—
147#66993—21no—
148#66990—22no—
149#66989—21no—
150#66988—22no—
151#66983C2312yes—
152#66983C2312yes—
153#66982—22no—
154#66982—22no—
155C4×C22⋊D11—22no—
156C4×C22⋊D11—22no—
157C2×(C2×D11)⋊C4—21no—
158C2×(C2×D11)⋊C4—21no—
159#66979C2311yescharacteristic
160#66979C2311yescharacteristic
161#66977—21no—
162#66977—21no—
163#66977C2312yes—
164#66977C2312yes—
165C2×#4318C2312yes—
166C22×C11⋊C8C2312yes—
167#66951—22no—
168#66951—22no—
169#66949—22no—
170#66949—22no—
171#66946—21no—
172#66946—21no—
173#66940—21no—
174#66940—21no—
175#66938—22no—
176#66938—22no—
177#66936—22no—
178#66936—22no—
179C22⋊C4×D11—22no—
180#66930—22no—
181#66929—22no—
182#66929—22no—
183#66928—21no—
184#66928—21no—
185#66928C2312yes—
186#66928C2312yes—
187C4×D44C2312yes—
188C4×D44C2312yes—
189#66925—22no—
190#66925—22no—
191#66923C2311yescharacteristic
192#66923C2311yescharacteristic
193#66922C2311yescharacteristic
194#66922C2311yescharacteristic
195C4×Dic22—21no—
196C4×Dic22—21no—
197C4×Dic22C2312yes—
198C4×Dic22C2312yes—
199C22⋊(C11⋊C8)C2314yes—
200C22⋊(C11⋊C8)C2314yes—
201#66874C2314yes—
202#66874C2314yes—
203#66874C2314yes—
204#66874C2314yes—
205#66873C2314yes—
206#66873C2314yes—
207#66873C2314yes—
208#66873C2314yes—
209#66872C2314yes—
210#66872C2314yes—
211#66872C2312yes—
212#66872C2312yes—
213#66872C2312yes—
214#66872C2312yes—
215#66871C2314yes—
216#66871C2314yes—
217#66871C2312yes—
218#66871C2312yes—
219#66871C2312yes—
220#66871C2312yes—
221C4⋊(C11⋊C8)C2314yes—
222C4⋊(C11⋊C8)C2314yes—
223#66867C2311yescharacteristic
224#66867C2311yescharacteristic
225#66867C2312yes—
226#66867C2312yes—
227C4×C11⋊C8C2312yes—
228#60885—111nomaximal, Sylow
229C23×D11—21no—
230C11×#41—24no—
231C2×Q8×C11—21no—
232C2×Q8×C11—21no—
233C2×Q8×C11—22no—
234C2×Q8×C11—24no—
235C2×Q8×C11—22no—
236C2×Q8×C11—82no—
237C2×Q8×C11—84no—
238C2×Q8×C11C2×D411yescharacteristic
239C2×D4×C11C2×D412yes—
240C2×D4×C11C2×D411yescharacteristic
241C22×C4×C11—24no—
242C22×C4×C11—22no—
243C22×C4×C11C2×D411yescharacteristic
244C22×C4×C11C2×D411yescharacteristic
245C22×C4×C11C2×D412yes—
246C22×C4×C11C2×D412yes—
247C22×C4×C11C2412yes—
248C22×C4×C11C2411yescharacteristic
249C2×C22⋊D11—22no—
250C2×C22⋊D11—22no—
251C22×Dic11—21no—
252C2×D44—21no—
253C2×D44—24no—
254C2×D44C2412yes—
255C2×C4×D11—22no—
256C2×C4×D11—22no—
257C2×Dic22—21no—
258C2×Dic22—21no—
259C2×Dic22—21no—
260C2×Dic22—24no—
261C2×Dic22C2412yes—
262C11×C4⋊C4—22no—
263C11×C4⋊C4—21no—
264C11×C4⋊C4—24no—
265C11×C4⋊C4—22no—
266C11×C4⋊C4—24no—
267C11×C4⋊C4—22no—
268C11×C4⋊C4—21no—
269C11×C4⋊C4—24no—
270C11×C4⋊C4—22no—
271C11×C4⋊C4—24no—
272C11×C4⋊C4—22no—
273C11×C4⋊C4C2×D411yescharacteristic
274C11×C4⋊C4C2×D411yescharacteristic
275C11×C4⋊C4C2×D412yes—
276C11×C4⋊C4C2×D412yes—
277C11×C4⋊C4C2414yes—
278C11×C4⋊C4C2412yes—
279C11×C4⋊C4C2412yes—
280C11×C22⋊C4—24no—
281C11×C22⋊C4—22no—
282C11×C22⋊C4C2×D412yes—
283C11×C22⋊C4C2×D412yes—
284C11×C22⋊C4C2×D412yes—
285C42×C11—24no—
286C42×C11—22no—
287C42×C11C2×D411yescharacteristic
288C42×C11C2×D411yescharacteristic
289C42×C11C2×D412yes—
290C42×C11C2×D412yes—
291C42×C11C2411yescharacteristic
292C42×C11C2411yescharacteristic
293C42×C11C2412yes—
294C22⋊Dic11—21no—
295C22⋊Dic11—21no—
296C22⋊Dic11—22no—
297C22⋊Dic11—22no—
298(C2×D11)⋊C4—22no—
299(C2×D11)⋊C4—22no—
300(C2×D11)⋊C4—22no—
301(C2×D11)⋊C4—22no—
302(C2×D11)⋊C4—22no—
303(C2×D11)⋊C4—22no—
304(C2×D11)⋊C4—22no—
305(C2×D11)⋊C4—22no—
306C4⋊Dic11—21no—
307C4⋊Dic11—21no—
308C4⋊Dic11C2411yescharacteristic
309C4⋊Dic11C2411yescharacteristic
310C4⋊Dic11C2411yescharacteristic
311C4⋊Dic11C2411yescharacteristic
312Dic11⋊C4—21no—
313Dic11⋊C4—21no—
314Dic11⋊C4—21no—
315Dic11⋊C4—21no—
316Dic11⋊C4—22no—
317Dic11⋊C4—22no—
318Dic11⋊C4—22no—
319Dic11⋊C4—22no—
320C4×Dic11—21no—
321C4×Dic11—21no—
322C4×Dic11—22no—
323C4×Dic11—22no—
324#4318—24no—
325C2×C11⋊C8—24no—
326C2×C11⋊C8C2414yes—
327C2×C11⋊C8C2412yes—
328C2×C11⋊C8C2412yes—
329#3510—111no—
330#3503D1111yescharacteristic, complemented
331#3244—114no—
332#3243—114no—
333#3240—112no—
334#3240—112no—
335#3239—112no—
336#3238—112no—
337#3165—111no—
338#3162—111no—
339#3140—111no—
340C2×#489—111no—
341#3097—112no—
342#3096—112no—
343#3082—112no—
344#3081—112no—
345#2923—111no—
346C23×C11C22×D412yes—
347C23×C11C22×D411yescharacteristic
348C22×D11—22no—
349C22×D11—42no—
350C22×D11—81no—
351C22×D11—81no—
352Q8×C11—22no—
353Q8×C11—42no—
354Q8×C11—42no—
355Q8×C11—44no—
356Q8×C11—82no—
357Q8×C11—84no—
358D4×C11—24no—
359D4×C11—22no—
360C2×C4×C11—24no—
361C2×C4×C11—22no—
362C2×C4×C11—24no—
363C2×C4×C11—22no—
364C2×C4×C11—41no—
365C2×C4×C11—42no—
366C2×C4×C11—41no—
367C2×C4×C11—42no—
368C2×C4×C11—82no—
369C2×C4×C11—84no—
370C2×C4×C11C22×D412yes—
371C2×C4×C11C22×D412yes—
372C2×C4×C11C22×D412yes—
373C2×C4×C11C22×D411yescharacteristic
374C2×C4×C11C22×D411yescharacteristic
375C2×C4×C11C22×D411yescharacteristic
376C2×C4×C11C22×D411yescharacteristic
377C2×C4×C11C22×D411yescharacteristic
378C2×C4×C112−1+414yes—
379C2×C4×C11C2511yescharacteristic
380C22⋊D11—82no—
381C22⋊D11—82no—
382C2×Dic11—21no—
383C2×Dic11—21no—
384C2×Dic11—22no—
385C2×Dic11—21no—
386C2×Dic11—21no—
387C2×Dic11—42no—
388D44—24no—
389D44—42no—
390C4×D11—82no—
391C4×D11—82no—
392Dic22—24no—
393Dic22—42no—
394Dic22—81no—
395Dic22—81no—
396C11⋊C8—22no—
397C11⋊C8—22no—
398C11⋊C8—24no—
399#559—221no—
400#559—221no—
401Q82—21no—
402#557—21no—
403#556—221no—
404#556—221no—
405#554—22no—
406#554—21no—
407#551—222no—
408#551—222no—
409D4×Q8—22no—
410D4×Q8—21no—
411#544C2×D1112yes—
412#544C2×D1114yescomplemented
413#542—112no—
414#542—112no—
415#536—111no—
416#535—111no—
417#533—111no—
418#533C2×D1111yescharacteristic
419#533C2×D1112yescomplemented
420C2×C4⋊Q8C2×D1111yescharacteristic
421C2×C4⋊Q8C2×D1112yescomplemented
422#529—112no—
423#529—112no—
424C2×#124—111no—
425#520C2×D1112yes—
426#519—111no—
427#518—111no—
428C4×#41C2×D1111yescharacteristic
429#501—111no—
430#501—111no—
431#501—111no—
432#501—111no—
433#501—112no—
434#501—112no—
435#501—112no—
436#501—112no—
437#500—112no—
438#498—112no—
439#489—112no—
440#489—112no—
441#489—114no—
442#489—112no—
443#489—112no—
444#488—114no—
445#485—114no—
446#485—114no—
447#484—114no—
448#483—114no—
449#482—114no—
450#482—114no—
451#481—114no—
452#480—114no—
453#479—114no—
454#479—114no—
455#478—114no—
456#478—114no—
457#477—114no—
458#476—114no—
459#475—114no—
460#474—114no—
461#433—114no—
462#432—112no—
463#432—112no—
464#428—112no—
465#428—112no—
466#427—112no—
467#427—112no—
468#424—112no—
469#419—112no—
470#418—112no—
471C2×#103—112no—
472C2×#102—112no—
473#408—112no—
474C4×M16—111no—
475C2×#97—111no—
476C22×C11—21no—
477C22×C11—21no—
478C22×C11—22no—
479C22×C11—22no—
480C22×C11—22no—
481C22×C11#53612yes—
482C22×C11C23×D411yescharacteristic
483C2×D11—42no—
484C2×D11—42no—
485C2×D11—42no—
486C2×D11—162no—
487C4×C11—21no—
488C4×C11—21no—
489C4×C11—22no—
490C4×C11—21no—
491C4×C11—21no—
492C4×C11—22no—
493C4×C11—22no—
494C4×C11—44no—
495C4×C11—42no—
496C4×C11—42no—
497C4×C11#53612yes—
498C4×C11C2×2−1+412yes—
499Dic11—41no—
500Dic11—41no—
501Dic11—41no—
502Dic11—41no—
503Dic11—42no—
504C2×#41C22×D1111yescharacteristic
505C22×Q8—21no—
506C22×Q8—22no—
507C22×Q8—111no—
508C22×D4—111no—
509C2×M16—112no—
510C22×C8—112no—
511C4⋊Q8—22no—
512C4⋊Q8—24no—
513C4⋊Q8—21no—
514C4⋊Q8—21no—
515C4⋊Q8—22no—
516C4⋊Q8—22no—
517C4⋊Q8—111no—
518C4⋊Q8—111no—
519C4⋊Q8—221no—
520C4⋊Q8C22×D1112yes—
521C4⋊Q8C22×D1112yes—
522C4⋊Q8C22×D1111yescharacteristic
523C4⋊Q8C22×D1114yes—
524C4⋊Q8C22×D1111yescharacteristic
525#127—221no—
526#126—222no—
527#126—222no—
528#126—222no—
529#126—222no—
530#125—22no—
531#125—24no—
532#125—111no—
533#125—111no—
534#125C22×D1112yes—
535#125C22×D1114yes—
536#124—112no—
537#124—112no—
538#124—221no—
539#124—221no—
540#124—222no—
541#124—222no—
542#124—221no—
543#124—221no—
544#123—222no—
545#123—222no—
546#123—222no—
547#123—222no—
548#123—222no—
549C22⋊Q8—21no—
550C22⋊Q8—21no—
551C22⋊Q8—22no—
552C22⋊Q8—22no—
553C22⋊Q8—24no—
554C22⋊Q8—24no—
555C22⋊Q8—24no—
556C22⋊Q8—112no—
557C22⋊Q8—112no—
558C22⋊Q8—221no—
559C22⋊Q8—221no—
560C22⋊Q8—222no—
561C22⋊Q8—222no—
562#121—112no—
563#121—112no—
564#120—222no—
565C4×Q8—22no—
566C4×Q8—21no—
567C4×Q8—21no—
568C4×Q8—22no—
569C4×Q8—22no—
570C4×Q8—112no—
571C4×Q8—112no—
572C4×Q8—221no—
573C4×Q8—221no—
574C4×Q8—221no—
575C4×Q8—221no—
576C4×Q8C22⋊D1111yescharacteristic
577C4×Q8C22⋊D1111yescharacteristic
578C4×D4—24no—
579C4×D4—22no—
580C4×D4—112no—
581C4×D4—112no—
582C4×D4—222no—
583C4×D4—222no—
584C4×D4—221no—
585C4×D4—221no—
586C4×D4C22⋊D1112yes—
587C4×D4C22⋊D1111yescharacteristic
588C4×D4C22⋊D1112yes—
589C4×D4C22⋊D1111yescharacteristic
590#117—111no—
591#117—111no—
592#117—222no—
593#117—222no—
594#117—222no—
595#117C22×D1112yes—
596#117C22×D1114yes—
597#117C22×D1111yescharacteristic
598#117C22×D1112yes—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4C22×D1112yes—
602C2×C4⋊C4C22×D1114yes—
603C2×C22⋊C4—221no—
604C2×C22⋊C4—221no—
605C2×C22⋊C4—222no—
606C2×C42C22×D1111yescharacteristic
607C2×C42C22×D1112yes—
608#107—112no—
609#107—112no—
610#107—112no—
611#107—112no—
612#107—114no—
613#107—114no—
614#106—112no—
615#106—112no—
616#106—112no—
617#106—112no—
618#106—114no—
619#106—114no—
620C4⋊C8—114no—
621C4⋊C8—114no—
622#103—114no—
623#103—114no—
624#103—114no—
625#103—114no—
626#102—114no—
627#102—114no—
628#102—114no—
629#102—114no—
630C22⋊C8—114no—
631C22⋊C8—114no—
632#97—111no—
633#97—111no—
634#97—112no—
635#97—112no—
636C4×C8—112no—
637C2×C11—22no—
638C2×C11—42no—
639C2×C11C2×#53611yescharacteristic
640C2×C11#358511yescharacteristic
641C2×C11#358611yescharacteristic
642D11—82no—
643C24—221no—
644#41—24no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—22no—
648C2×Q8—24no—
649C2×Q8—22no—
650C2×Q8—82no—
651C2×Q8—84no—
652C2×Q8—112no—
653C2×Q8—221no—
654C2×Q8—221no—
655C2×Q8—221no—
656C2×Q8—224no—
657C2×Q8C2×C22⋊D1111yescharacteristic
658C2×D4—112no—
659C2×D4—222no—
660C2×D4—222no—
661C2×D4—224no—
662C2×D4—221no—
663C2×D4C2×C22⋊D1112yes—
664C2×D4C2×C22⋊D1111yescharacteristic
665C22×C4—24no—
666C22×C4—22no—
667C22×C4—221no—
668C22×C4—222no—
669C22×C4—222no—
670C22×C4C2×C22⋊D1111yescharacteristic
671C22×C4C2×C22⋊D1111yescharacteristic
672C22×C4C2×C22⋊D1112yes—
673C22×C4C2×C22⋊D1112yes—
674C22×C4C23×D1112yes—
675C22×C4C23×D1111yescharacteristic
676M16—224no—
677C2×C8—114no—
678C2×C8—112no—
679C2×C8—112no—
680C2×C8—224no—
681C4⋊C4—22no—
682C4⋊C4—21no—
683C4⋊C4—24no—
684C4⋊C4—22no—
685C4⋊C4—24no—
686C4⋊C4—22no—
687C4⋊C4—21no—
688C4⋊C4—24no—
689C4⋊C4—22no—
690C4⋊C4—24no—
691C4⋊C4—22no—
692C4⋊C4—111no—
693C4⋊C4—111no—
694C4⋊C4—111no—
695C4⋊C4—111no—
696C4⋊C4—221no—
697C4⋊C4—221no—
698C4⋊C4—222no—
699C4⋊C4—222no—
700C4⋊C4—222no—
701C4⋊C4—222no—
702C4⋊C4—221no—
703C4⋊C4—221no—
704C4⋊C4—221no—
705C4⋊C4—221no—
706C4⋊C4C2×C22⋊D1111yescharacteristic
707C4⋊C4C2×C22⋊D1111yescharacteristic
708C4⋊C4C2×C22⋊D1112yes—
709C4⋊C4C2×C22⋊D1112yes—
710C4⋊C4C23×D1114yes—
711C4⋊C4C23×D1112yes—
712C4⋊C4C23×D1112yes—
713C22⋊C4—24no—
714C22⋊C4—22no—
715C22⋊C4—221no—
716C22⋊C4—221no—
717C22⋊C4—222no—
718C22⋊C4—222no—
719C22⋊C4—222no—
720C22⋊C4—222no—
721C22⋊C4—222no—
722C22⋊C4—222no—
723C22⋊C4—222no—
724C22⋊C4—222no—
725C22⋊C4—222no—
726C22⋊C4—222no—
727C22⋊C4C2×C22⋊D1112yes—
728C22⋊C4C2×C22⋊D1112yes—
729C22⋊C4C2×C22⋊D1112yes—
730C42—24no—
731C42—22no—
732C42—221no—
733C42—221no—
734C42—222no—
735C42—222no—
736C42C2×C22⋊D1112yes—
737C42C2×C22⋊D1112yes—
738C42C2×C22⋊D1111yescharacteristic
739C42C2×C22⋊D1111yescharacteristic
740C42C23×D1111yescharacteristic
741C42C23×D1111yescharacteristic
742C42C23×D1112yes—
743C11#6088511yescharacteristic, complemented, Sylow
744C23—222no—
745C23—442no—
746C23—881no—
747C23—881no—
748C23C22×C22⋊D1112yes—
749C23C22×C22⋊D1111yescharacteristic
750Q8—22no—
751Q8—42no—
752Q8—42no—
753Q8—44no—
754Q8—84no—
755Q8—82no—
756Q8—224no—
757Q8—442no—
758Q8—881no—
759Q8—881no—
760D4—24no—
761D4—22no—
762D4—224no—
763D4—442no—
764D4—882no—
765D4—882no—
766C2×C4—24no—
767C2×C4—22no—
768C2×C4—24no—
769C2×C4—22no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—42no—
773C2×C4—41no—
774C2×C4—82no—
775C2×C4—84no—
776C2×C4—221no—
777C2×C4—221no—
778C2×C4—222no—
779C2×C4—221no—
780C2×C4—221no—
781C2×C4—442no—
782C2×C4—882no—
783C2×C4—882no—
784C2×C4#6704014yes—
785C2×C4C22×C22⋊D1112yes—
786C2×C4C22×C22⋊D1112yes—
787C2×C4C22×C22⋊D1112yes—
788C2×C4C22×C22⋊D1111yescharacteristic
789C2×C4C22×C22⋊D1111yescharacteristic
790C2×C4C22×C22⋊D1111yescharacteristic
791C2×C4C22×C22⋊D1111yescharacteristic
792C2×C4C22×C22⋊D1111yescharacteristic
793C2×C4C24×D1111yescharacteristic
794C8—222no—
795C8—222no—
796C8—224no—
797C22—21no—
798C22—21no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—442no—
803C22—442no—
804C22—442no—
805C22—1762no—
806C22#1062334712yes—
807C22C23×C22⋊D1111yescharacteristic
808C4—21no—
809C4—22no—
810C4—21no—
811C4—21no—
812C4—22no—
813C4—21no—
814C4—22no—
815C4—44no—
816C4—42no—
817C4—42no—
818C4—441no—
819C4—441no—
820C4—441no—
821C4—441no—
822C4—442no—
823C4#1062334712yes—
824C4C2×#6704012yes—
825C2—22no—
826C2—42no—
827C2—882no—
828C2C2×#1062334711yescharacteristic
829C2#1308339611yescharacteristic
830C2#1308340311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3503C2
socleC22×C11C23×D4
prime radical#10623361C22
hypercenter#3503D11
hypocenterC11#60885
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3503

Complements

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

NH ≅ G/Ntype
2. #13079914C2semidirect
3. #13079899C2semidirect
4. #13079856C2semidirect
5. #13079856C2semidirect
6. #13079846C2semidirect
7. #13079837C2semidirect
8. #13079158C2semidirect
9. #13079138C2semidirect
10. #13079005C2semidirect
11. C2×#10622702C2semidirect
12. #13078585C2semidirect
14. #13078452C2semidirect
15. #13078441C2semidirect
16. #13077267C2semidirect
17. C11×#3503C2semidirect
25. C11×#544C22semidirect
27. C11×#533C22semidirect
29. C2×C11×C4⋊Q8C22semidirect
49. #10622707C22semidirect
50. #10622704C22semidirect
58. #10622693C22semidirect
59. #10622693C22semidirect
60. #10622693C22semidirect
61. #10622693C22semidirect
62. #10622693C22semidirect
63. #10622693C22semidirect
64. #10622692C22semidirect
65. #10622691C22semidirect
69. #10622678C22semidirect
70. #10622678C22semidirect
71. #10622676C22semidirect
72. #10622676C22semidirect
77. #10622613C22semidirect
81. #10622609C22semidirect
82. #10622609C22semidirect
83. #10622584C22semidirect
84. #10622583C22semidirect
91. #10622539C22semidirect
92. #10622539C22semidirect
330. #3503D11semidirect
412. #544C2×D11semidirect
419. #533C2×D11semidirect
421. C2×C4⋊Q8C2×D11semidirect
743. C11#60885semidirect

Maximal subgroups

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

subgroupindex
#130825122
#130799142
#130798992
#130798562
#130798462
#130798372
#130791582
#130791382
#130790052
C2×#106227022
#130785852
#130785742
#130784522
#130784412
#130772672
C11×#35032
#6088511