Finite Group Databasebeta

← #15634902

Subgroups — #15634902

Order 2816.

1922 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082483C211yesmaximal, characteristic, complemented
2#13081676C214yesmaximal, complemented
3#13081658C212yesmaximal, complemented
4#13081647C212yesmaximal, complemented
5#13081612C212yesmaximal, complemented
6#13081608C214yesmaximal, complemented
7#13081597C212yesmaximal, complemented
8#13079088C212yesmaximal, complemented
9#13079042C211yesmaximal, characteristic, complemented
10#13078166C212yesmaximal, complemented
11#13078151C212yesmaximal, complemented
12#13078084C211yesmaximal, characteristic, complemented
13#13078080C211yesmaximal, characteristic, complemented
14#13077551C211yesmaximal, characteristic, complemented
15#13077497C212yesmaximal, complemented
16C2×C4×#4324C211yesmaximal, characteristic, complemented
17C11×#3506C211yesmaximal, characteristic, complemented
18C11×#559C2214yes—
19C11×#556C2212yes—
20C11×#555—21no—
21C11×#553—22no—
22C11×#550C2212yes—
23C11×#547—21no—
24C11×#538—22no—
25C11×#535C2212yes—
26C11×#533C2211yescharacteristic
27C11×#532C2211yescharacteristic
28C11×#525—22no—
29C11×#520C2212yes—
30C2×C4×D4×C11C2211yescharacteristic
31C2×#67004C2212yes—
32C2×#67003C2212yes—
33C2×#67003C2212yes—
34C22×#4324C2211yescharacteristic
35C2×#66985C2212yes—
36#10623263—21no—
37#10623261—21no—
38#10623225—22no—
39#10623176—22no—
40#10623155—22no—
41#10623116C2212yescomplemented
42#10623115C2214yescomplemented
43#10623101C2212yescomplemented
44#10623057C2212yes—
45#10623054C2212yes—
46#10623008C2211yescharacteristic
47C2×C4×Dic22C2211yescharacteristic
48#10622845C2212yes—
49C2×#66896C2211yescharacteristic
50#10622705C2211yescharacteristic, complemented
51#10622703C2212yescomplemented
52#10622698C2211yescharacteristic, complemented
53#10622689C2214yes—
54#10622689C2211yescharacteristic, complemented
55#10622688C2214yes—
56#10622688C2212yescomplemented
57#10622687C2214yes—
58#10622686C2211yescharacteristic, complemented
59#10622685C2214yes—
60#10622673C2214yes—
61#10622672C2214yes—
62#10622672C2212yescomplemented
63#10622672C2212yescomplemented
64#10622670C2214yes—
65#10622667C2214yes—
66#10622667C2214yescomplemented
67#10622644C2214yescomplemented
68#10622643C2214yescomplemented
69#10622641C2214yescomplemented
70C4×#4325C2214yescomplemented
71#10622637C2212yescomplemented
72#10622637C2212yescomplemented
73Q8×C11⋊C8C2212yescomplemented
74Q8×C11⋊C8C2212yescomplemented
75#10622632C2212yes—
76#10622632C2214yescomplemented
77C4×#4324C2212yes—
78C4×#4324C2212yes—
79C4×#4324C2212yes—
80C4×#4324C2212yes—
81C4×#4324C2214yescomplemented
82#10622629C2214yes—
83#10622629C2214yescomplemented
84#10622628C2212yes—
85#10622627C2214yescomplemented
86#10622612C2212yes—
87#10622610C2212yes—
88C2×#66874C2211yescharacteristic
89#10622579C2212yes—
90C2×#66872C2211yescharacteristic
91#10622537C2211yescharacteristic
92C2×C4×C11⋊C8C2211yescharacteristic
93C2×C11×#41—22no—
94C2×C11×#41C2312yes—
95C22×D4×C11C2311yescharacteristic
96C23×C4×C11—21no—
97C2×#4339C2312yes—
98C22×Dic22C2311yescharacteristic
99C11×C4⋊Q8D411yescharacteristic
100C11×C4⋊Q8D411yescharacteristic
101C11×C4⋊Q8C2311yescharacteristic
102C11×#127C2311yescharacteristic
103C11×#127C2314yes—
104C11×#126—24no—
105C11×#125D412yes—
106C11×#124—24no—
107C11×#124C2312yes—
108C11×#124C2314yes—
109C11×#123—24no—
110C11×#123—24no—
111C11×C22⋊Q8—22no—
112C11×C22⋊Q8D412yes—
113C11×C22⋊Q8D412yes—
114C11×#121—21no—
115C11×#121—21no—
116C11×#121—22no—
117C11×#121—22no—
118C11×#121—22no—
119C11×#121—24no—
120C11×#120—24no—
121C4×Q8×C11C2314yes—
122C4×Q8×C11C2312yes—
123C4×Q8×C11C2312yes—
124C4×D4×C11—24no—
125C4×D4×C11—24no—
126C4×D4×C11—21no—
127C4×D4×C11—21no—
128C4×D4×C11—21no—
129C4×D4×C11—21no—
130C4×D4×C11C2312yes—
131C4×D4×C11C2312yes—
132C4×D4×C11C2314yes—
133C11×#117—22no—
134C11×#117—22no—
135C11×#117C2312yes—
136C2×C11×C4⋊C4—22no—
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C22⋊C4—21no—
139C2×C42×C11C2311yescharacteristic
140#67004—44no—
141#67003—28no—
142#67003—44no—
143#67000—22no—
144#66999—24no—
145Q8×Dic11—22no—
146C2×#4326C2312yes—
147C2×#4326C2312yes—
148C2×#4326C2314yes—
149C2×#4325C2312yes—
150C2×#4325C2312yes—
151C2×#4324—24no—
152C2×#4324C2312yes—
153C2×#4324C2312yes—
154C2×#4324C2312yes—
155C2×#4324C2314yes—
156C2×#4324C2312yes—
157C2×#4324C2314yes—
158#66985—44no—
159C2×#4323C2312yes—
160C2×#4323C2314yes—
161C2×#4323C2312yes—
162#66983—21no—
163#66983—21no—
164C2×C4⋊Dic11C2311yescharacteristic
165C2×Dic11⋊C4—21no—
166C2×C4×Dic11—21no—
167C2×#4318C2312yes—
168C22×C11⋊C8C2311yescharacteristic
169C22×C11⋊C8C2311yescharacteristic
170#66951—24no—
171#66951—24no—
172#66950—22no—
173#66950—22no—
174#66947—24no—
175#66946—22no—
176#66945—22no—
177#66945—24no—
178C4⋊C4×D11—22no—
179#66943—22no—
180#66943—24no—
181#66939—24no—
182(C22⋊D11)⋊C4—24no—
183#66928C2312yes—
184#66928C2314yes—
185#66927C2311yescharacteristic
186C4×D44—21no—
187C4×D44—21no—
188C4×D44C2314yes—
189#66922C2311yescharacteristic
190#66922C2314yes—
191C4×Dic22—21no—
192C4×Dic22—21no—
193C4×Dic22C2312yes—
194C4×Dic22C2312yes—
195C4×Dic22C2314yes—
196#66899C2314yes—
197#66896C2312yes—
198#66896C2312yes—
199#66896C2314yes—
200#66874C2314yes—
201#66874C2312yes—
202#66874C2312yes—
203#66873C2314yes—
204#66872C2312yes—
205#66872C2312yes—
206C4⋊(C11⋊C8)C2312yes—
207C4⋊(C11⋊C8)C2312yes—
208C4⋊(C11⋊C8)C2314yes—
209C4⋊(C11⋊C8)C2314yes—
210#66867C2314yes—
211C4×C11⋊C8C2311yescharacteristic
212C4×C11⋊C8C2311yescharacteristic
213C4×C11⋊C8C2311yescharacteristic
214C4×C11⋊C8C2311yescharacteristic
215C4×C11⋊C8C2314yes—
216#61407—111nomaximal, Sylow
217C24×C11—21no—
218C11×#41—24no—
219C11×#41—24no—
220C11×#41—84no—
221C2×Q8×C11C2×D412yes—
222C2×Q8×C11C2×D412yes—
223C2×Q8×C11C2412yes—
224C2×D4×C11—22no—
225C2×D4×C11—21no—
226C2×D4×C11—21no—
227C2×D4×C11—24no—
228C2×D4×C11—21no—
229C2×D4×C11—24no—
230C2×D4×C11—22no—
231C2×D4×C11—22no—
232C2×D4×C11C2412yes—
233C2×D4×C11C2412yes—
234C22×C4×C11—21no—
235C22×C4×C11—22no—
236C22×C4×C11—22no—
237C22×C4×C11—24no—
238C22×C4×C11—22no—
239C22×C4×C11—82no—
240C22×C4×C11C2×D411yescharacteristic
241C22×C4×C11C2×D411yescharacteristic
242C22×C4×C11C2411yescharacteristic
243C2×C22⋊D11—22no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246#4339—24no—
247#4339—24no—
248C2×D44—21no—
249C2×D44—21no—
250C2×D44C2412yes—
251C2×C4×D11—22no—
252C2×C4×D11—24no—
253C2×Dic22—21no—
254C2×Dic22—22no—
255C2×Dic22—22no—
256C2×Dic22C2412yes—
257C2×Dic22C2412yes—
258C11×C4⋊C4—21no—
259C11×C4⋊C4—24no—
260C11×C4⋊C4—21no—
261C11×C4⋊C4—21no—
262C11×C4⋊C4C2×D412yes—
263C11×C4⋊C4C2×D414yes—
264C11×C4⋊C4C2×D412yes—
265C11×C4⋊C4C2×D412yes—
266C11×C4⋊C4C2×D414yes—
267C11×C4⋊C4C2×D412yes—
268C11×C4⋊C4C2412yes—
269C11×C22⋊C4—22no—
270C11×C22⋊C4—22no—
271C11×C22⋊C4—24no—
272C11×C22⋊C4—24no—
273C11×C22⋊C4—22no—
274C11×C22⋊C4—24no—
275C11×C22⋊C4—22no—
276C11×C22⋊C4C2×D414yes—
277C42×C11—24no—
278C42×C11C2×D411yescharacteristic
279C42×C11C2×D411yescharacteristic
280C42×C11C2411yescharacteristic
281C42×C11C2411yescharacteristic
282C42×C11C2414yes—
283#4326—24no—
284#4326—42no—
285#4326—44no—
286#4325—24no—
287#4325—42no—
288#4324—24no—
289#4324—24no—
290#4324—24no—
291#4324—44no—
292#4324—42no—
293#4324—44no—
294#4323—24no—
295#4323—44no—
296#4323—42no—
297(C2×D11)⋊C4—22no—
298(C2×D11)⋊C4—22no—
299(C2×D11)⋊C4—24no—
300(C2×D11)⋊C4—24no—
301(C2×D11)⋊C4—24no—
302C4⋊Dic11—21no—
303C4⋊Dic11—21no—
304C4⋊Dic11—21no—
305C4⋊Dic11—24no—
306C4⋊Dic11—24no—
307C4⋊Dic11C2412yes—
308Dic11⋊C4—22no—
309Dic11⋊C4—22no—
310Dic11⋊C4—24no—
311C4×Dic11—22no—
312C4×Dic11—22no—
313C4×Dic11—24no—
314#4318—24no—
315C2×C11⋊C8—22no—
316C2×C11⋊C8#4114yescomplemented
317C2×C11⋊C8C2411yescharacteristic
318C2×C11⋊C8C2411yescharacteristic
319C2×C11⋊C8C2414yes—
320C2×C11⋊C8C2411yescharacteristic
321C2×C11⋊C8C2411yescharacteristic
322#3507—111no—
323#3506D1111yescharacteristic, complemented
324#3401—114no—
325#3399—112no—
326#3398—112no—
327#3394—114no—
328#3394—112no—
329#3392—112no—
330#3154—112no—
331#3147—111no—
332#3046—112no—
333#3045—112no—
334#3037—111no—
335#3036—111no—
336#2960—111no—
337#2952—112no—
338C2×C4×SD16—111no—
339C23×C11—22no—
340C23×C11—22no—
341C23×C11—42no—
342C23×C11—81no—
343C23×C11—81no—
344C23×C11C22×D411yescharacteristic
345C22×D11—22no—
346Q8×C11—24no—
347Q8×C11—22no—
348Q8×C11—22no—
349Q8×C11—42no—
350D4×C11—22no—
351D4×C11—22no—
352D4×C11—22no—
353D4×C11—22no—
354D4×C11—44no—
355D4×C11—42no—
356D4×C11—42no—
357D4×C11—81no—
358D4×C11—84no—
359D4×C11—84no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—41no—
364C2×C4×C11—44no—
365C2×C4×C11—44no—
366C2×C4×C11—82no—
367C2×C4×C11—84no—
368C2×C4×C11—81no—
369C2×C4×C11C22×D411yescharacteristic
370C2×C4×C11C22×D414yes—
371C2×C4×C11C22×D411yescharacteristic
372C2×C4×C11C22×D411yescharacteristic
373C2×C4×C11C22×D414yes—
374C2×C4×C11C22×D411yescharacteristic
375C2×C4×C11C22×D411yescharacteristic
376C2×C4×C11C2×#4112yes—
377C2×C4×C11H(5,𝔽2)12yes—
378C2×C4×C11C2511yescharacteristic
379C22⋊D11—44no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—42no—
384C2×Dic11—81no—
385D44—22no—
386D44—22no—
387D44—42no—
388D44—81no—
389C4×D11—44no—
390C4×D11—84no—
391Dic22—22no—
392Dic22—22no—
393Dic22—22no—
394Dic22—22no—
395Dic22—42no—
396C11⋊C8—21no—
397C11⋊C8—21no—
398C11⋊C8—24no—
399C11⋊C8C2×#4112yes—
400C11⋊C8C2×#4112yes—
401C2×#137—112no—
402C2×AGL(1,ℤ/8)—112no—
403C2×#135—112no—
404C2×#135—112no—
405C22×SD16—111no—
406#559—112no—
407#559C2×D1114yes—
408#557—112no—
409#556—114no—
410#556—221no—
411#556C2×D1112yes—
412#555—21no—
413#554—221no—
414#553—22no—
415#552—222no—
416#550C2×D1112yes—
417#547—21no—
418#539—222no—
419#538—22no—
420#536—112no—
421#535C2×D1112yes—
422#533C2×D1111yescharacteristic
423#532—111no—
424#532C2×D1111yescharacteristic
425#529—222no—
426#525—22no—
427#520—112no—
428#520C2×D1112yes—
429C2×C4×Q8—111no—
430C2×C4×D4C2×D1111yescharacteristic
431#497—114no—
432#496—114no—
433#495—112no—
434#495—114no—
435#495—112no—
436#494—111no—
437#493—111no—
438#492—111no—
439#492—111no—
440#492—114no—
441#464—114no—
442#464—114no—
443#464—114no—
444#463—114no—
445#463—114no—
446#463—114no—
447#462—112no—
448#462—114no—
449#461—112no—
450#461—114no—
451#460—112no—
452#460—114no—
453#459—114no—
454#459—112no—
455#446—112no—
456#446—112no—
457C8×Q8—112no—
458C8×Q8—112no—
459#442—114no—
460#441—114no—
461C4×SD16—114no—
462C4×SD16—112no—
463C4×SD16—114no—
464C4×SD16—112no—
465C4×SD16—112no—
466C4×SD16—112no—
467C2×#106—111no—
468#424—112no—
469#423—111no—
470#417—112no—
471#417—112no—
472C2×#103—111no—
473C2×#102—111no—
474#405—112no—
475C2×C4×C8—111no—
476C22×C11—21no—
477C22×C11—21no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—42no—
483C22×C11—42no—
484C22×C11—84no—
485C22×C11#55012yes—
486C22×C11C23×D411yescharacteristic
487C2×D11—42no—
488C2×D11—42no—
489C2×D11—42no—
490C4×C11—21no—
491C4×C11—21no—
492C4×C11—24no—
493C4×C11—21no—
494C4×C11—24no—
495C4×C11—42no—
496C4×C11—42no—
497C4×C11#55012yes—
498C4×C11#57712yes—
499C4×C11C22×#4111yescharacteristic
500C4×C11C2×H(5,𝔽2)11yescharacteristic
501Dic11—42no—
502Dic11—42no—
503Dic11—42no—
504C2×#41—22no—
505C2×#41—112no—
506C2×#41C22×D1112yes—
507C22×Q8—111no—
508C22×D4C22×D1111yescharacteristic
509C23×C4—21no—
510#137—444no—
511AGL(1,ℤ/8)—444no—
512#135—228no—
513#135—444no—
514C2×Q16—112no—
515C2×Q16—112no—
516C2×Q16—114no—
517C2×SD16—112no—
518C2×SD16—112no—
519C2×SD16—112no—
520C2×SD16—112no—
521C2×SD16—112no—
522C2×SD16—112no—
523C2×SD16—114no—
524C2×SD16—114no—
525C2×SD16—224no—
526C2×D8—112no—
527C2×D8—112no—
528C2×D8—114no—
529C2×M16—112no—
530C22×C8—111no—
531C22×C8—111no—
532C4⋊Q8—111no—
533C4⋊Q8—114no—
534C4⋊Q8C22⋊D1111yescharacteristic
535C4⋊Q8C22⋊D1111yescharacteristic
536C4⋊Q8C22×D1111yescharacteristic
537#127—111no—
538#127C22×D1111yescharacteristic
539#127C22×D1114yes—
540#126—24no—
541#126—224no—
542#126—224no—
543#125—222no—
544#125—224no—
545#125C22⋊D1112yes—
546#124—24no—
547#124—112no—
548#124—114no—
549#124—222no—
550#124C22×D1112yes—
551#124C22×D1114yes—
552#123—24no—
553#123—24no—
554#123—224no—
555#123—224no—
556C22⋊Q8—22no—
557C22⋊Q8—224no—
558C22⋊Q8—222no—
559C22⋊Q8—222no—
560C22⋊Q8C22⋊D1112yes—
561C22⋊Q8C22⋊D1112yes—
562#121—21no—
563#121—21no—
564#121—22no—
565#121—22no—
566#121—22no—
567#121—24no—
568#121—221no—
569#121—221no—
570#120—24no—
571C4×Q8—112no—
572C4×Q8—112no—
573C4×Q8—114no—
574C4×Q8—222no—
575C4×Q8—221no—
576C4×Q8—221no—
577C4×Q8C22×D1114yes—
578C4×Q8C22×D1112yes—
579C4×Q8C22×D1112yes—
580C4×D4—24no—
581C4×D4—24no—
582C4×D4—21no—
583C4×D4—21no—
584C4×D4—21no—
585C4×D4—21no—
586C4×D4—114no—
587C4×D4—222no—
588C4×D4—224no—
589C4×D4—221no—
590C4×D4—221no—
591C4×D4C22×D1112yes—
592C4×D4C22×D1112yes—
593C4×D4C22×D1114yes—
594#117—22no—
595#117—22no—
596#117—222no—
597#117—224no—
598#117C22×D1112yes—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—111no—
601C2×C4⋊C4—221no—
602C2×C4⋊C4—222no—
603C2×C4⋊C4C22×D1111yescharacteristic
604C2×C22⋊C4—21no—
605C2×C42—221no—
606C2×C42C22×D1111yescharacteristic
607#106—112no—
608#106—112no—
609C4⋊C8—112no—
610C4⋊C8—112no—
611C4⋊C8—114no—
612C4⋊C8—114no—
613#103—114no—
614#103—112no—
615#103—112no—
616#103—114no—
617#102—112no—
618#102—112no—
619#102—114no—
620#102—114no—
621#97—114no—
622C4×C8—111no—
623C4×C8—111no—
624C4×C8—111no—
625C4×C8—111no—
626C4×C8—114no—
627C2×C11—22no—
628C2×C11—82no—
629C2×C11—82no—
630C2×C11C2×#55011yescharacteristic
631C2×C11C2×#57711yescharacteristic
632C2×C11#358411yescharacteristic
633D11—82no—
634C24—21no—
635#41—24no—
636#41—24no—
637#41—84no—
638#41—224no—
639#41—224no—
640C2×Q8—112no—
641C2×Q8—112no—
642C2×Q8—221no—
643C2×Q8—222no—
644C2×Q8—222no—
645C2×Q8C2×C22⋊D1112yes—
646C2×Q8C2×C22⋊D1112yes—
647C2×Q8C23×D1112yes—
648C2×D4—22no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—24no—
654C2×D4—21no—
655C2×D4—24no—
656C2×D4—112no—
657C2×D4—222no—
658C2×D4—221no—
659C2×D4—221no—
660C2×D4C23×D1112yes—
661C2×D4C23×D1112yes—
662C22×C4—21no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—24no—
666C22×C4—22no—
667C22×C4—82no—
668C22×C4—221no—
669C22×C4—221no—
670C22×C4—222no—
671C22×C4—224no—
672C22×C4C2×C22⋊D1111yescharacteristic
673C22×C4C2×C22⋊D1111yescharacteristic
674C22×C4C23×D1111yescharacteristic
675Q16—224no—
676Q16—442no—
677Q16—444no—
678SD16—224no—
679SD16—224no—
680SD16—224no—
681SD16—224no—
682SD16—442no—
683SD16—444no—
684SD16—444no—
685SD16—442no—
686D8—224no—
687D8—442no—
688D8—444no—
689M16—224no—
690C2×C8—114no—
691C2×C8—111no—
692C2×C8—111no—
693C2×C8—111no—
694C2×C8—111no—
695C2×C8—114no—
696C2×C8—222no—
697C4⋊C4—21no—
698C4⋊C4—24no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—112no—
702C4⋊C4—221no—
703C4⋊C4—224no—
704C4⋊C4—222no—
705C4⋊C4—222no—
706C4⋊C4—224no—
707C4⋊C4—221no—
708C4⋊C4—221no—
709C4⋊C4—224no—
710C4⋊C4C2×C22⋊D1112yes—
711C4⋊C4C2×C22⋊D1112yes—
712C4⋊C4C2×C22⋊D1112yes—
713C4⋊C4C2×C22⋊D1114yes—
714C4⋊C4C2×C22⋊D1114yes—
715C4⋊C4C2×C22⋊D1112yes—
716C4⋊C4C23×D1112yes—
717C22⋊C4—22no—
718C22⋊C4—22no—
719C22⋊C4—24no—
720C22⋊C4—24no—
721C22⋊C4—22no—
722C22⋊C4—24no—
723C22⋊C4—22no—
724C22⋊C4—222no—
725C22⋊C4—224no—
726C22⋊C4—224no—
727C22⋊C4—222no—
728C22⋊C4—224no—
729C22⋊C4C2×C22⋊D1114yes—
730C42—24no—
731C42—222no—
732C42—222no—
733C42—224no—
734C42C2×C22⋊D1111yescharacteristic
735C42C2×C22⋊D1111yescharacteristic
736C42C23×D1111yescharacteristic
737C42C23×D1111yescharacteristic
738C42C23×D1114yes—
739C11#6140711yescharacteristic, complemented, Sylow
740C23—22no—
741C23—22no—
742C23—42no—
743C23—81no—
744C23—81no—
745C23—222no—
746C23C22×C22⋊D1111yescharacteristic
747Q8—24no—
748Q8—22no—
749Q8—22no—
750Q8—42no—
751Q8—222no—
752Q8—222no—
753Q8—222no—
754Q8—222no—
755Q8—442no—
756D4—22no—
757D4—22no—
758D4—22no—
759D4—22no—
760D4—44no—
761D4—42no—
762D4—42no—
763D4—81no—
764D4—84no—
765D4—84no—
766D4—222no—
767D4—222no—
768D4—444no—
769D4—442no—
770D4—881no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—41no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—82no—
778C2×C4—84no—
779C2×C4—81no—
780C2×C4—222no—
781C2×C4—222no—
782C2×C4—222no—
783C2×C4—442no—
784C2×C4—444no—
785C2×C4—884no—
786C2×C4—881no—
787C2×C4#41×D1112yes—
788C2×C4#6704212yes—
789C2×C4C22×C22⋊D1114yes—
790C2×C4C22×C22⋊D1111yescharacteristic
791C2×C4C22×C22⋊D1114yes—
792C2×C4C22×C22⋊D1111yescharacteristic
793C2×C4C22×C22⋊D1111yescharacteristic
794C2×C4C22×C22⋊D1111yescharacteristic
795C2×C4C22×C22⋊D1111yescharacteristic
796C2×C4C24×D1111yescharacteristic
797C8—112no—
798C8—112no—
799C8—221no—
800C8—221no—
801C8—224no—
802C22—21no—
803C22—21no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—84no—
811C22—442no—
812C22—442no—
813C22—442no—
814C22#1062336512yes—
815C22C23×C22⋊D1111yescharacteristic
816C4—21no—
817C4—24no—
818C4—21no—
819C4—21no—
820C4—24no—
821C4—42no—
822C4—42no—
823C4—442no—
824C4—442no—
825C4—442no—
826C4#1062336512yes—
827C4#1062336712yes—
828C4C2×#41×D1111yescharacteristic
829C4C2×#6704211yescharacteristic
830C2—22no—
831C2—82no—
832C2—82no—
833C2—882no—
834C2C2×#1062336511yescharacteristic
835C2C2×#1062336711yescharacteristic
836C2#1308338711yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3506C2
socleC22×C11C23×D4
hypercenter#3506D11
hypocenterC11#61407
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #533 ◁ #3506

Complements

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

NH ≅ G/Ntype
1. #13082483C2semidirect
2. #13081676C2semidirect
3. #13081658C2semidirect
4. #13081647C2semidirect
5. #13081612C2semidirect
6. #13081608C2semidirect
7. #13081597C2semidirect
8. #13079088C2semidirect
9. #13079042C2semidirect
10. #13078166C2semidirect
11. #13078151C2semidirect
12. #13078084C2semidirect
13. #13078080C2semidirect
14. #13077551C2semidirect
15. #13077497C2semidirect
16. C2×C4×#4324C2semidirect
17. C11×#3506C2semidirect
41. #10623116C22semidirect
42. #10623115C22semidirect
43. #10623101C22semidirect
50. #10622705C22semidirect
51. #10622703C22semidirect
52. #10622698C22semidirect
54. #10622689C22semidirect
56. #10622688C22semidirect
58. #10622686C22semidirect
62. #10622672C22semidirect
63. #10622672C22semidirect
66. #10622667C22semidirect
67. #10622644C22semidirect
68. #10622643C22semidirect
69. #10622641C22semidirect
70. C4×#4325C22semidirect
71. #10622637C22semidirect
72. #10622637C22semidirect
73. Q8×C11⋊C8C22semidirect
74. Q8×C11⋊C8C22semidirect
76. #10622632C22semidirect
81. C4×#4324C22semidirect
83. #10622629C22semidirect
85. #10622627C22semidirect
316. C2×C11⋊C8#41semidirect
323. #3506D11semidirect
739. C11#61407semidirect

Maximal subgroups

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

subgroupindex
#130824832
#130816762
#130816582
#130816472
#130816122
#130816082
#130815972
#130790882
#130790422
#130781662
#130781512
#130780842
#130780802
#130775512
#130774972
C2×C4×#43242
C11×#35062
#6140711