Finite Group Databasebeta

← #15624196

Subgroups — #15624196

Order 2816.

1898 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082527C211yesmaximal, characteristic, complemented
2#13079326C212yesmaximal, complemented
3#13079315C212yesmaximal, complemented
4#13079301C214yesmaximal, complemented
5#13079286C214yesmaximal, complemented
6#13079223C212yesmaximal, complemented
7#13079212C212yesmaximal, complemented
8C2×#10622678C211yesmaximal, characteristic, complemented
9#13079061C211yesmaximal, characteristic, complemented
10#13079019C211yesmaximal, characteristic, complemented
11#13079009C211yesmaximal, characteristic, complemented
12#13078283C212yesmaximal, complemented
13#13078275C212yesmaximal, complemented
14#13077497C212yesmaximal, complemented
15#13077489C212yesmaximal, complemented
16#13077044C211yesmaximal, characteristic, complemented
17C11×#3512C211yesmaximal, characteristic, complemented
18C11×#553—22no—
19C11×#553—22no—
20C11×#553—21no—
21C11×#553—21no—
22C11×#552—21no—
23C11×#552—21no—
24C11×#541C2212yes—
25C11×#540C2212yes—
26C11×#537C2211yescharacteristic
27C11×#537C2211yescharacteristic
28C11×#532C2211yescharacteristic
29C11×#529C2212yes—
30C11×#529C2212yes—
31C2×C11×#125C2211yescharacteristic
32C11×#520C2211yescharacteristic
33C11×#520C2211yescharacteristic
34C4×C11×#41C2211yescharacteristic
35#10623364C2212yes—
36C2×#67003C2212yes—
37C2×#67003C2212yes—
38C2×#67001C2212yes—
39#10623115—21no—
40#10623110—21no—
41#10623096—22no—
42#10623094—21no—
43#10623083—22no—
44#10623082—21no—
45#10623065C2214yes—
46#10623054C2212yes—
47#10623008C2211yescharacteristic
48#10623008C2212yes—
49#10623001C2212yes—
50C2×#66922C2211yescharacteristic
51#10622845C2212yes—
52#10622845C2212yes—
53#10622699C2212yes—
54#10622694C2212yes—
55#10622687C2212yes—
56#10622683C2212yes—
57#10622682C2212yes—
58#10622681C2214yes—
59#10622680C2212yes—
60#10622678C2214yes—
61#10622678C2212yes—
62#10622678C2212yes—
63#10622673C2211yescharacteristic
64#10622673C2211yescharacteristic
65#10622671C2211yescharacteristic
66#10622671C2211yescharacteristic
67#10622668C2212yes—
68#10622668C2212yes—
69#10622665C2214yes—
70#10622664C2214yes—
71#10622662C2214yes—
72#10622661C2214yes—
73#10622655C2214yes—
74#10622654C2214yes—
75#10622652C2214yes—
76#10622651C2214yes—
77#10622643C2214yes—
78C4×#4326C2214yes—
79#10622639C2214yes—
80C4×#4325C2214yes—
81#10622631C2214yes—
82C4×#4324C2214yes—
83#10622627C2214yes—
84C4×#4323C2214yes—
85#10622610C2214yes—
86#10622610C2212yes—
87#10622579C2212yes—
88#10622579C2212yes—
89C2×#66872C2212yes—
90C2×#66871C2212yes—
91C4×#4318C2212yes—
92C4×#4318C2211yescharacteristic
93C2×#66867C2212yes—
94C2×#66867C2211yescharacteristic
95C2×C11×#41C2311yescharacteristic
96C2×C11×#41C2311yescharacteristic
97C2×C11×#41C2311yescharacteristic
98C2×#4339—22no—
99C2×#4339C2312yes—
100C22×Dic22—21no—
101C11×C4⋊Q8C2311yescharacteristic
102C11×#127C2311yescharacteristic
103C11×#126—22no—
104C11×#126—22no—
105C11×#126—22no—
106C11×#126—22no—
107C11×#125—22no—
108C11×#125—22no—
109C11×#125—21no—
110C11×#125—21no—
111C11×#125C2312yes—
112C11×#125C2312yes—
113C11×#124C2311yescharacteristic
114C11×#124C2311yescharacteristic
115C11×#123—22no—
116C11×#123—22no—
117C11×#123—22no—
118C11×#123—22no—
119C11×C22⋊Q8—21no—
120C11×C22⋊Q8—21no—
121C11×C22⋊Q8C2312yes—
122C11×C22⋊Q8C2312yes—
123C11×#121—21no—
124C11×#121—21no—
125C11×#121—22no—
126C11×#121—22no—
127C11×#121—21no—
128C11×#121—21no—
129C11×#121—22no—
130C11×#121—22no—
131C11×#121C2312yes—
132C11×#121C2312yes—
133C4×Q8×C11D411yescharacteristic
134C4×Q8×C11D411yescharacteristic
135C4×Q8×C11C2312yes—
136C4×Q8×C11C2312yes—
137C4×D4×C11—22no—
138C4×D4×C11—22no—
139C4×D4×C11—22no—
140C4×D4×C11—22no—
141C4×D4×C11—21no—
142C4×D4×C11—21no—
143C4×D4×C11D411yescharacteristic
144C4×D4×C11D412yes—
145C4×D4×C11D411yescharacteristic
146C4×D4×C11D412yes—
147C4×D4×C11C2312yes—
148C4×D4×C11C2312yes—
149C11×#117—21no—
150C11×#117—21no—
151C11×#117—22no—
152C11×#117—22no—
153C11×#117C2311yescharacteristic
154C11×#117C2312yes—
155C2×C11×C4⋊C4—21no—
156C2×C11×C4⋊C4—21no—
157C2×C11×C4⋊C4—21no—
158C2×C11×C4⋊C4—21no—
159C2×C11×C4⋊C4C2311yescharacteristic
160C2×C11×C4⋊C4C2311yescharacteristic
161C2×C42×C11C2311yescharacteristic
162C2×C42×C11C2312yes—
163#67003—28no—
164#67003—28no—
165#67001—28no—
166#66999—22no—
167C2×#4326C2312yes—
168C2×#4326C2312yes—
169C2×#4325C2312yes—
170C2×#4325C2312yes—
171#66992—24no—
172#66991—22no—
173C2×#4324C2312yes—
174C2×#4324C2312yes—
175C2×#4323C2312yes—
176C2×#4323C2312yes—
177#66983—21no—
178#66983—22no—
179#66983—21no—
180#66983C2314yes—
181#66979—22no—
182C2×C4⋊Dic11—21no—
183C2×C4⋊Dic11C2312yes—
184#66977—22no—
185#66977C2314yes—
186C2×#4318C2312yes—
187C2×#4318C2314yes—
188C22×C11⋊C8C2314yes—
189C22×C11⋊C8C2312yes—
190#66951—24no—
191#66949—24no—
192#66945—22no—
193C4⋊C4×D11—22no—
194#66938—24no—
195#66936—24no—
196(C22⋊D11)⋊C4—24no—
197#66928—22no—
198#66928C2312yes—
199#66927C2311yescharacteristic
200C4×D44—21no—
201C4×D44—21no—
202C4×D44—22no—
203C4×D44C2314yes—
204#66923—22no—
205#66922—21no—
206#66922—21no—
207#66922C2311yescharacteristic
208#66922C2312yes—
209#66922C2312yes—
210C4×Dic22—22no—
211C4×Dic22C2314yes—
212#66899C2314yes—
213#66899C2314yes—
214#66896C2314yes—
215#66896C2314yes—
216#66874C2314yes—
217#66874C2314yes—
218#66873C2314yes—
219#66873C2314yes—
220#66872C2314yes—
221#66872C2314yes—
222#66871C2314yes—
223#66871C2314yes—
224#66867C2311yescharacteristic
225#66867C2312yes—
226#66867C2311yescharacteristic
227#66867C2314yes—
228#66867C2312yes—
229C4×C11⋊C8C2314yes—
230C4×C11⋊C8C2312yes—
231#60721—111nomaximal, Sylow
232C11×#41—24no—
233C11×#41—24no—
234C11×#41—24no—
235C2×Q8×C11C2×D411yescharacteristic
236C2×Q8×C11C2411yescharacteristic
237C2×Q8×C11C2411yescharacteristic
238C2×D4×C11—21no—
239C2×D4×C11—21no—
240C2×D4×C11—22no—
241C2×D4×C11—22no—
242C2×D4×C11—21no—
243C2×D4×C11—21no—
244C2×D4×C11C2×D411yescharacteristic
245C2×D4×C11C2×D412yes—
246C2×D4×C11C2411yescharacteristic
247C2×D4×C11C2411yescharacteristic
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11—21no—
251C22×C4×C11—21no—
252C22×C4×C11—22no—
253C22×C4×C11—22no—
254C22×C4×C11C2×D412yes—
255C22×C4×C11C2×D411yescharacteristic
256C22×C4×C11C2×D412yes—
257C22×C4×C11C2×D411yescharacteristic
258C22×C4×C11C2412yes—
259C22×C4×C11C2411yescharacteristic
260C2×C22⋊D11—22no—
261C2×C22⋊D11—24no—
262C22×Dic11—22no—
263#4339—24no—
264#4339—24no—
265#4339—84no—
266C2×D44—21no—
267C2×D44—21no—
268C2×D44C2412yes—
269C2×C4×D11—22no—
270C2×C4×D11—24no—
271C2×Dic22—22no—
272C2×Dic22—22no—
273C2×Dic22—82no—
274C2×Dic22C2412yes—
275C11×C4⋊C4—21no—
276C11×C4⋊C4—21no—
277C11×C4⋊C4—22no—
278C11×C4⋊C4—22no—
279C11×C4⋊C4—22no—
280C11×C4⋊C4—22no—
281C11×C4⋊C4—22no—
282C11×C4⋊C4—22no—
283C11×C4⋊C4—22no—
284C11×C4⋊C4—22no—
285C11×C4⋊C4—21no—
286C11×C4⋊C4—21no—
287C11×C4⋊C4C2×D411yescharacteristic
288C11×C4⋊C4C2×D411yescharacteristic
289C11×C4⋊C4C2×D412yes—
290C11×C4⋊C4C2×D412yes—
291C11×C4⋊C4C2412yes—
292C11×C4⋊C4C2412yes—
293C11×C22⋊C4—22no—
294C11×C22⋊C4—22no—
295C11×C22⋊C4—21no—
296C11×C22⋊C4—21no—
297C11×C22⋊C4—22no—
298C11×C22⋊C4—22no—
299C11×C22⋊C4—22no—
300C11×C22⋊C4—22no—
301C11×C22⋊C4—21no—
302C11×C22⋊C4—21no—
303C11×C22⋊C4C2×D412yes—
304C11×C22⋊C4C2×D412yes—
305C11×C22⋊C4C2×D412yes—
306C42×C11—22no—
307C42×C11—22no—
308C42×C11C2×D412yes—
309C42×C11C2×D411yescharacteristic
310C42×C11C2×D411yescharacteristic
311C42×C11C2×D412yes—
312C42×C11C2412yes—
313C42×C11C2411yescharacteristic
314C42×C11C2411yescharacteristic
315C22⋊Dic11—24no—
316#4326—24no—
317#4326—24no—
318#4325—24no—
319#4325—24no—
320#4324—24no—
321#4324—24no—
322#4323—24no—
323#4323—24no—
324(C2×D11)⋊C4—24no—
325(C2×D11)⋊C4—22no—
326(C2×D11)⋊C4—22no—
327(C2×D11)⋊C4—24no—
328C4⋊Dic11—21no—
329C4⋊Dic11—22no—
330C4⋊Dic11—22no—
331C4⋊Dic11—22no—
332C4⋊Dic11—21no—
333C4⋊Dic11C2414yes—
334Dic11⋊C4—24no—
335Dic11⋊C4—24no—
336C4×Dic11—24no—
337#4318—28no—
338#4318—24no—
339C2×C11⋊C8—28no—
340C2×C11⋊C8#4118yescomplemented
341C2×C11⋊C8C2414yes—
342C2×C11⋊C8C2412yes—
343C2×C11⋊C8C2412yes—
344#3512D1111yescharacteristic, complemented
345#3511—111no—
346#3181—112no—
347#3180—112no—
348#3179—114no—
349#3178—114no—
350#3172—112no—
351#3171—112no—
352C2×#501—111no—
353#3150—111no—
354#3142—111no—
355#3141—111no—
356#3061—112no—
357#3060—112no—
358#2952—112no—
359#2951—112no—
360#2875—111no—
361C23×C11—21no—
362C23×C11—21no—
363C23×C11C22×D412yes—
364C23×C11C22×D411yescharacteristic
365C22×D11—22no—
366Q8×C11—22no—
367Q8×C11—22no—
368Q8×C11—22no—
369D4×C11—24no—
370D4×C11—22no—
371D4×C11—22no—
372D4×C11—22no—
373D4×C11—42no—
374D4×C11—42no—
375D4×C11—81no—
376D4×C11—81no—
377D4×C11—82no—
378D4×C11—82no—
379C2×C4×C11—24no—
380C2×C4×C11—21no—
381C2×C4×C11—21no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—41no—
385C2×C4×C11—42no—
386C2×C4×C11—42no—
387C2×C4×C11—41no—
388C2×C4×C11—42no—
389C2×C4×C11—42no—
390C2×C4×C11—82no—
391C2×C4×C11—82no—
392C2×C4×C11—81no—
393C2×C4×C11—81no—
394C2×C4×C11C22×D412yes—
395C2×C4×C11C22×D412yes—
396C2×C4×C11C22×D412yes—
397C2×C4×C11C22×D411yescharacteristic
398C2×C4×C11C22×D411yescharacteristic
399C2×C4×C11C22×D411yescharacteristic
400C2×C4×C11C22×D411yescharacteristic
401C2×C4×C11C22×D411yescharacteristic
402C2×C4×C11C2×#4114yes—
403C2×C4×C11C2511yescharacteristic
404C22⋊D11—44no—
405C22⋊D11—84no—
406C2×Dic11—22no—
407C2×Dic11—24no—
408C2×Dic11—82no—
409D44—22no—
410D44—22no—
411D44—42no—
412D44—42no—
413C4×D11—44no—
414C4×D11—84no—
415Dic22—22no—
416Dic22—22no—
417Dic22—44no—
418Dic22—82no—
419C11⋊C8—24no—
420C11⋊C8C2×#4114yes—
421C11⋊C8C2×#4114yes—
422C2×#135—112no—
423C2×#135—112no—
424C2×#131—112no—
425#556—221no—
426#555—221no—
427#554—221no—
428#553—22no—
429#553—22no—
430#553—21no—
431#553—21no—
432#553—222no—
433#552—21no—
434#552—21no—
435#548—222no—
436#547—221no—
437#542—114no—
438#541C2×D1112yes—
439#540C2×D1112yes—
440#537—112no—
441#537C2×D1111yescharacteristic
442#537C2×D1111yescharacteristic
443#533—112no—
444#532—112no—
445#532—111no—
446#532C2×D1111yescharacteristic
447C2×C4⋊Q8—111no—
448#529C2×D1112yes—
449#529C2×D1112yes—
450C2×#125C2×D1111yescharacteristic
451#520—112no—
452#520C2×D1111yescharacteristic
453#520C2×D1111yescharacteristic
454C4×#41C2×D1111yescharacteristic
455#501—112no—
456#501—114no—
457#501—112no—
458#497—112no—
459#497—111no—
460#497—111no—
461#496—112no—
462#496—111no—
463#496—111no—
464#491—112no—
465#490—112no—
466#489—112no—
467#489—112no—
468#488—114no—
469#487—112no—
470#486—112no—
471#470—114no—
472#469—114no—
473#468—114no—
474#468—114no—
475#467—114no—
476#466—114no—
477#465—114no—
478#465—114no—
479#442—114no—
480#441—114no—
481#440—114no—
482#440—114no—
483C4×Q16—114no—
484C4×SD16—114no—
485C4×SD16—114no—
486C4×D8—114no—
487C2×#107—112no—
488C2×#106—112no—
489#417—112no—
490#417—112no—
491#417—112no—
492#417—112no—
493#405—114no—
494#405—112no—
495C4×M16—111no—
496C4×M16—112no—
497C2×#97—111no—
498C2×#97—112no—
499C22×C11—21no—
500C22×C11—21no—
501C22×C11—22no—
502C22×C11—22no—
503C22×C11—22no—
504C22×C11—41no—
505C22×C11—41no—
506C22×C11—41no—
507C22×C11—41no—
508C22×C11—41no—
509C22×C11—41no—
510C22×C11#53212yes—
511C22×C11C23×D411yescharacteristic
512C2×D11—42no—
513C2×D11—42no—
514C2×D11—42no—
515C4×C11—21no—
516C4×C11—22no—
517C4×C11—21no—
518C4×C11—21no—
519C4×C11—22no—
520C4×C11—21no—
521C4×C11—22no—
522C4×C11—42no—
523C4×C11—42no—
524C4×C11—41no—
525C4×C11—41no—
526C4×C11#53212yes—
527C4×C11C22×#4112yes—
528Dic11—44no—
529Dic11—42no—
530C2×#41—112no—
531C2×#41—222no—
532C2×#41C22×D1111yescharacteristic
533C2×#41C22×D1111yescharacteristic
534C2×#41C22×D1111yescharacteristic
535C22×Q8—221no—
536#135—228no—
537#135—228no—
538C2×Q16—112no—
539C2×Q16—112no—
540C2×SD16—112no—
541C2×SD16—112no—
542C2×SD16—112no—
543C2×SD16—112no—
544C2×D8—112no—
545C2×D8—112no—
546#131—228no—
547C2×M16—112no—
548C2×M16—114no—
549C22×C8—112no—
550C22×C8—114no—
551C4⋊Q8—112no—
552C4⋊Q8—112no—
553C4⋊Q8—111no—
554C4⋊Q8—221no—
555C4⋊Q8—221no—
556C4⋊Q8C22×D1111yescharacteristic
557#127—111no—
558#127C22×D1111yescharacteristic
559#126—22no—
560#126—22no—
561#126—22no—
562#126—22no—
563#126—224no—
564#125—22no—
565#125—22no—
566#125—21no—
567#125—21no—
568#125—222no—
569#125C22×D1112yes—
570#125C22×D1112yes—
571#124—112no—
572#124—224no—
573#124—222no—
574#124C22×D1111yescharacteristic
575#124C22×D1111yescharacteristic
576#123—22no—
577#123—22no—
578#123—22no—
579#123—22no—
580#123—224no—
581C22⋊Q8—21no—
582C22⋊Q8—21no—
583C22⋊Q8—114no—
584C22⋊Q8—222no—
585C22⋊Q8—222no—
586C22⋊Q8—224no—
587C22⋊Q8C22×D1112yes—
588C22⋊Q8C22×D1112yes—
589#121—21no—
590#121—21no—
591#121—22no—
592#121—22no—
593#121—21no—
594#121—21no—
595#121—22no—
596#121—22no—
597#121—114no—
598#121—222no—
599#121—224no—
600#121—221no—
601#121—221no—
602#121—222no—
603#121C22×D1112yes—
604#121C22×D1112yes—
605C4×Q8—114no—
606C4×Q8—222no—
607C4×Q8C22⋊D1111yescharacteristic
608C4×Q8C22⋊D1111yescharacteristic
609C4×Q8C22×D1112yes—
610C4×Q8C22×D1112yes—
611C4×D4—22no—
612C4×D4—22no—
613C4×D4—22no—
614C4×D4—22no—
615C4×D4—21no—
616C4×D4—21no—
617C4×D4—114no—
618C4×D4—224no—
619C4×D4—221no—
620C4×D4—222no—
621C4×D4—221no—
622C4×D4C22⋊D1111yescharacteristic
623C4×D4C22⋊D1112yes—
624C4×D4C22⋊D1112yes—
625C4×D4C22⋊D1111yescharacteristic
626C4×D4C22×D1112yes—
627C4×D4C22×D1112yes—
628#117—21no—
629#117—21no—
630#117—22no—
631#117—22no—
632#117—222no—
633#117—222no—
634#117C22×D1111yescharacteristic
635#117C22×D1112yes—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—112no—
641C2×C4⋊C4—221no—
642C2×C4⋊C4—222no—
643C2×C4⋊C4C22×D1111yescharacteristic
644C2×C4⋊C4C22×D1111yescharacteristic
645C2×C42C22×D1111yescharacteristic
646C2×C42C22×D1112yes—
647#107—114no—
648#107—114no—
649#106—114no—
650#106—114no—
651#103—114no—
652#103—114no—
653#103—114no—
654#103—114no—
655#102—114no—
656#102—114no—
657#102—114no—
658#102—114no—
659#97—111no—
660#97—112no—
661#97—111no—
662#97—114no—
663#97—112no—
664C4×C8—114no—
665C4×C8—112no—
666C2×C11—22no—
667C2×C11—42no—
668C2×C11—81no—
669C2×C11—81no—
670C2×C11C2×#53211yescharacteristic
671C2×C11#358511yescharacteristic
672C2×C11#358611yescharacteristic
673D11—82no—
674#41—24no—
675#41—24no—
676#41—24no—
677#41—224no—
678#41—224no—
679#41—884no—
680C2×Q8—112no—
681C2×Q8—222no—
682C2×Q8—222no—
683C2×Q8—882no—
684C2×Q8C2×C22⋊D1111yescharacteristic
685C2×Q8C23×D1111yescharacteristic
686C2×Q8C23×D1111yescharacteristic
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—22no—
690C2×D4—22no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—112no—
694C2×D4—222no—
695C2×D4—224no—
696C2×D4—221no—
697C2×D4—221no—
698C2×D4C2×C22⋊D1112yes—
699C2×D4C2×C22⋊D1111yescharacteristic
700C2×D4C23×D1111yescharacteristic
701C2×D4C23×D1111yescharacteristic
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—222no—
709C22×C4—222no—
710C22×C4—224no—
711C22×C4C2×C22⋊D1111yescharacteristic
712C22×C4C2×C22⋊D1111yescharacteristic
713C22×C4C2×C22⋊D1112yes—
714C22×C4C2×C22⋊D1112yes—
715C22×C4C23×D1112yes—
716C22×C4C23×D1111yescharacteristic
717Q16—224no—
718Q16—224no—
719SD16—224no—
720SD16—224no—
721SD16—224no—
722SD16—224no—
723D8—224no—
724D8—224no—
725M16—228no—
726M16—224no—
727C2×C8—118no—
728C2×C8—112no—
729C2×C8—112no—
730C2×C8—114no—
731C2×C8—228no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—22no—
735C4⋊C4—22no—
736C4⋊C4—22no—
737C4⋊C4—22no—
738C4⋊C4—22no—
739C4⋊C4—22no—
740C4⋊C4—22no—
741C4⋊C4—22no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—114no—
745C4⋊C4—222no—
746C4⋊C4—222no—
747C4⋊C4—224no—
748C4⋊C4—222no—
749C4⋊C4—221no—
750C4⋊C4—221no—
751C4⋊C4—224no—
752C4⋊C4C2×C22⋊D1111yescharacteristic
753C4⋊C4C2×C22⋊D1111yescharacteristic
754C4⋊C4C2×C22⋊D1112yes—
755C4⋊C4C2×C22⋊D1112yes—
756C4⋊C4C23×D1112yes—
757C4⋊C4C23×D1112yes—
758C22⋊C4—22no—
759C22⋊C4—22no—
760C22⋊C4—21no—
761C22⋊C4—21no—
762C22⋊C4—22no—
763C22⋊C4—22no—
764C22⋊C4—22no—
765C22⋊C4—22no—
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—224no—
769C22⋊C4—224no—
770C22⋊C4—224no—
771C22⋊C4—222no—
772C22⋊C4—222no—
773C22⋊C4C2×C22⋊D1112yes—
774C22⋊C4C2×C22⋊D1112yes—
775C22⋊C4C2×C22⋊D1112yes—
776C42—22no—
777C42—22no—
778C42—224no—
779C42C2×C22⋊D1112yes—
780C42C2×C22⋊D1112yes—
781C42C2×C22⋊D1111yescharacteristic
782C42C2×C22⋊D1111yescharacteristic
783C42C23×D1112yes—
784C42C23×D1111yescharacteristic
785C42C23×D1111yescharacteristic
786C11#6072111yescharacteristic, complemented, Sylow
787C23—21no—
788C23—21no—
789C23—222no—
790C23C22×C22⋊D1112yes—
791C23C22×C22⋊D1111yescharacteristic
792Q8—22no—
793Q8—22no—
794Q8—22no—
795Q8—222no—
796Q8—222no—
797Q8—444no—
798Q8—882no—
799D4—24no—
800D4—22no—
801D4—22no—
802D4—22no—
803D4—42no—
804D4—42no—
805D4—81no—
806D4—81no—
807D4—82no—
808D4—82no—
809D4—222no—
810D4—222no—
811D4—442no—
812D4—442no—
813D4—444no—
814D4—884no—
815C2×C4—24no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—42no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—82no—
827C2×C4—82no—
828C2×C4—81no—
829C2×C4—81no—
830C2×C4—222no—
831C2×C4—224no—
832C2×C4—444no—
833C2×C4—884no—
834C2×C4—882no—
835C2×C4#41×D1114yes—
836C2×C4C22×C22⋊D1112yes—
837C2×C4C22×C22⋊D1112yes—
838C2×C4C22×C22⋊D1111yescharacteristic
839C2×C4C22×C22⋊D1111yescharacteristic
840C2×C4C22×C22⋊D1112yes—
841C2×C4C22×C22⋊D1111yescharacteristic
842C2×C4C22×C22⋊D1111yescharacteristic
843C2×C4C22×C22⋊D1111yescharacteristic
844C2×C4C24×D1111yescharacteristic
845C8—114no—
846C8—114no—
847C8—224no—
848C22—21no—
849C22—21no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—442no—
860C22—442no—
861C22—442no—
862C22#1062336312yes—
863C22C23×C22⋊D1111yescharacteristic
864C4—21no—
865C4—22no—
866C4—21no—
867C4—21no—
868C4—22no—
869C4—21no—
870C4—22no—
871C4—42no—
872C4—42no—
873C4—41no—
874C4—41no—
875C4—444no—
876C4—442no—
877C4#1062336312yes—
878C4C2×#41×D1112yes—
879C2—22no—
880C2—42no—
881C2—81no—
882C2—81no—
883C2—882no—
884C2C2×#1062336311yescharacteristic
885C2#1308339511yescharacteristic
886C2#1308340211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3512C2
socleC22×C11C23×D4
hypercenter#3512D11
hypocenterC11#60721
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3512

Complements

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

NH ≅ G/Ntype
1. #13082527C2semidirect
2. #13079326C2semidirect
3. #13079315C2semidirect
4. #13079301C2semidirect
5. #13079286C2semidirect
6. #13079223C2semidirect
7. #13079212C2semidirect
8. C2×#10622678C2semidirect
9. #13079061C2semidirect
10. #13079019C2semidirect
11. #13079009C2semidirect
12. #13078283C2semidirect
13. #13078275C2semidirect
14. #13077497C2semidirect
15. #13077489C2semidirect
16. #13077044C2semidirect
17. C11×#3512C2semidirect
340. C2×C11⋊C8#41semidirect
344. #3512D11semidirect
786. C11#60721semidirect

Maximal subgroups

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

subgroupindex
#130825272
#130793262
#130793152
#130793012
#130792862
#130792232
#130792122
C2×#106226782
#130790612
#130790192
#130790092
#130782832
#130782752
#130774972
#130774892
#130770442
C11×#35122
#6072111