Finite Group Databasebeta

← #15633620

Subgroups — #15633620

Order 2816.

1880 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082211C211yesmaximal, characteristic, complemented
2#13081443C214yesmaximal, complemented
3#13081397C212yesmaximal, complemented
4#13081369C214yesmaximal, complemented
5#13081323C212yesmaximal, complemented
6#13081276C212yesmaximal, complemented
7#13081265C212yesmaximal, complemented
8#13079019C212yesmaximal, complemented
9#13079012C211yesmaximal, characteristic, complemented
10#13078434C212yesmaximal, complemented
11#13078425C211yesmaximal, characteristic, complemented
12#13078080C211yesmaximal, characteristic, complemented
13#13078080C212yesmaximal, complemented
14Q8×#4318C211yesmaximal, characteristic, complemented
15C4×#66985C211yesmaximal, characteristic, complemented
16C4×#66985C212yesmaximal, complemented
17C2×C11×#554C211yesmaximal, characteristic, complemented
18C11×#554—21no—
19C11×#554—21no—
20C11×#554—22no—
21C11×#554C2214yes—
22C11×#554C2212yes—
23C11×#554C2212yes—
24C2×C11×C4⋊Q8C2211yescharacteristic
25C2×C11×#125C2212yes—
26C2×C11×C22⋊Q8—21no—
27C2×C11×C22⋊Q8—22no—
28C2×C4×Q8×C11C2211yescharacteristic
29C2×C4×D4×C11C2212yes—
30C2×C4×D4×C11C2211yescharacteristic
31C22×C11×C4⋊C4—21no—
32#10623348—21no—
33C2×#66985C2211yescharacteristic
34C2×#66985C2212yes—
35#10623116C2212yescomplemented
36#10623116C2211yescharacteristic, complemented
37#10623115C2212yescomplemented
38#10623115C2211yescharacteristic, complemented
39#10623111—22no—
40#10623111—21no—
41#10623108C2211yescharacteristic, complemented
42C4×#4343—21no—
43#10623101C2211yescharacteristic, complemented
44#10623045—21no—
45#10623045—22no—
46#10623008C2211yescharacteristic
47#10623008C2212yes—
48C4×#4339C2211yescharacteristic
49C4×#4339C2212yes—
50#10622828C2211yescharacteristic
51#10622707C2212yescomplemented
52#10622706C2212yescomplemented
53#10622704C2212yescomplemented
54#10622702C2214yescomplemented
55#10622701C2212yescomplemented
56#10622700C2212yescomplemented
57#10622697C2212yescomplemented
58#10622682C2214yescomplemented
59#10622681C2214yescomplemented
60#10622681C2214yescomplemented
61#10622680C2214yescomplemented
62#10622679C2214yescomplemented
63#10622679C2214yescomplemented
64#10622676C2214yescomplemented
65#10622676C2214yescomplemented
66#10622637C2214yescomplemented
67#10622637C2212yescomplemented
68Q8×C11⋊C8C2212yescomplemented
69#10622632C2214yes—
70#10622632C2212yes—
71#10622631C2214yes—
72#10622631C2212yes—
73C4×#4324C2212yes—
74C4×#4324C2214yes—
75#10622629C2214yes—
76#10622629C2214yes—
77#10622629C2214yes—
78#10622628C2214yes—
79#10622628C2212yes—
80#10622627C2212yes—
81#10622627C2214yes—
82C4×#4323C2214yes—
83C4×#4323C2212yes—
84#10622579C2212yes—
85#10622579C2212yes—
86#10622579C2212yes—
87#10622579C2212yes—
88#10622579C2211yescharacteristic
89#10622577C2212yes—
90#10622577C2211yescharacteristic
91#10622537C2211yescharacteristic
92#10622537C2212yes—
93C4×#4318C2211yescharacteristic
94C4×#4318C2212yes—
95C22×Q8×C11—21no—
96C22×Q8×C11D411yescharacteristic
97C22×D4×C11C2311yescharacteristic
98C23×C4×C11—21no—
99C23×C4×C11—22no—
100C2×#4343—21no—
101C2×#4339C2311yescharacteristic
102C2×#4339C2312yes—
103C11×C4⋊Q8—21no—
104C11×C4⋊Q8—21no—
105C11×C4⋊Q8C2312yes—
106C11×C4⋊Q8C2312yes—
107C11×#125—22no—
108C11×#125—22no—
109C11×#125C2314yes—
110C11×#125C2314yes—
111C11×C22⋊Q8—22no—
112C11×C22⋊Q8—22no—
113C11×C22⋊Q8—24no—
114C11×C22⋊Q8—24no—
115C11×C22⋊Q8—24no—
116C11×C22⋊Q8—24no—
117C11×C22⋊Q8—24no—
118C4×Q8×C11D411yescharacteristic
119C4×Q8×C11D412yes—
120C4×Q8×C11D411yescharacteristic
121C4×Q8×C11C2311yescharacteristic
122C4×Q8×C11C2311yescharacteristic
123C4×Q8×C11C2312yes—
124C4×D4×C11—22no—
125C4×D4×C11—21no—
126C4×D4×C11—22no—
127C4×D4×C11—21no—
128C4×D4×C11C2312yes—
129C4×D4×C11C2314yes—
130C4×D4×C11C2314yes—
131C4×D4×C11C2312yes—
132C2×C11×C4⋊C4—22no—
133C2×C11×C4⋊C4—21no—
134C2×C11×C4⋊C4—22no—
135C2×C11×C4⋊C4—22no—
136C2×C11×C4⋊C4—22no—
137C2×C11×C4⋊C4—24no—
138C2×C11×C4⋊C4D411yescharacteristic
139C2×C11×C4⋊C4D412yes—
140C2×C11×C4⋊C4C2311yescharacteristic
141C2×C11×C4⋊C4C2312yes—
142C2×C11×C22⋊C4—21no—
143C2×C11×C22⋊C4—22no—
144C2×C42×C11C2312yes—
145C2×C42×C11C2311yescharacteristic
146#67000—21no—
147#67000—22no—
148#66999—21no—
149#66999—22no—
150Q8×Dic11—21no—
151C2×#4324C2314yes—
152C2×#4324C2312yes—
153#66985—24no—
154#66985—28no—
155C2×#4323C2314yes—
156C2×#4323C2312yes—
157#66983—21no—
158#66983—22no—
159#66983—21no—
160#66983—22no—
161C4×C22⋊D11—21no—
162C4×C22⋊D11—22no—
163C4×C22⋊D11—21no—
164C4×C22⋊D11—22no—
165#66979C2311yescharacteristic
166C2×#4318C2311yescharacteristic
167C2×#4318C2311yescharacteristic
168C2×#4318C2312yes—
169#66951—22no—
170#66951—22no—
171#66951—22no—
172#66948—21no—
173#66948—22no—
174#66947—22no—
175#66947—22no—
176#66947—22no—
177#66946—21no—
178#66946—22no—
179#66945—21no—
180#66945—22no—
181#66943—21no—
182#66943—22no—
183#66928C2312yes—
184#66928C2312yes—
185#66928C2312yes—
186#66927C2312yes—
187#66927C2311yescharacteristic
188C4×D44—22no—
189C4×D44—21no—
190C4×D44—22no—
191C4×D44—21no—
192C4×D44C2311yescharacteristic
193C4×D44C2312yes—
194C4×D44C2312yes—
195C4×D44C2311yescharacteristic
196#66925—22no—
197#66925—21no—
198C42×D11—22no—
199C42×D11—21no—
200#66922C2312yes—
201#66922C2311yescharacteristic
202C4×Dic22C2311yescharacteristic
203C4×Dic22C2312yes—
204C4×Dic22C2312yes—
205C4×Dic22C2311yescharacteristic
206#66896C2312yes—
207#66896C2312yes—
208#66874C2314yes—
209#66874C2314yes—
210#66874C2314yes—
211#66874C2312yes—
212#66874C2314yes—
213#66873C2312yes—
214#66873C2314yes—
215#66873C2314yes—
216#66873C2314yes—
217#66873C2314yes—
218#66872C2312yes—
219#66872C2314yes—
220#66871C2312yes—
221#66871C2314yes—
222C4⋊(C11⋊C8)C2312yes—
223C4⋊(C11⋊C8)C2314yes—
224C4⋊(C11⋊C8)C2314yes—
225C4⋊(C11⋊C8)C2312yes—
226#66867C2314yes—
227#66867C2312yes—
228C4×C11⋊C8C2314yes—
229C4×C11⋊C8C2312yes—
230#61318—111nomaximal, Sylow
231C24×C11—21no—
232C2×Q8×C11—22no—
233C2×Q8×C11—22no—
234C2×Q8×C11—42no—
235C2×Q8×C11—82no—
236C2×Q8×C11C2×D411yescharacteristic
237C2×Q8×C11C2×D411yescharacteristic
238C2×Q8×C11C2×D412yes—
239C2×D4×C11—21no—
240C2×D4×C11—22no—
241C2×D4×C11#4114yescomplemented
242C2×D4×C11C2412yes—
243C22×C4×C11—21no—
244C22×C4×C11—22no—
245C22×C4×C11—22no—
246C22×C4×C11—22no—
247C22×C4×C11—24no—
248C22×C4×C11—24no—
249C22×C4×C11—44no—
250C22×C4×C11—84no—
251C22×C4×C11C2×D411yescharacteristic
252C22×C4×C11C2×D412yes—
253C22×C4×C11C2×D411yescharacteristic
254C22×C4×C11C2×D412yes—
255C22×C4×C11C2411yescharacteristic
256C2×C22⋊D11—21no—
257C2×C22⋊D11—22no—
258#4343—44no—
259#4339—22no—
260#4339—24no—
261#4339—22no—
262#4339—24no—
263C2×D44—22no—
264C2×D44—21no—
265C2×D44—21no—
266C2×D44—22no—
267C2×D44C2411yescharacteristic
268C2×D44C2412yes—
269C2×C4×D11—22no—
270C2×C4×D11—21no—
271C2×C4×D11—22no—
272C2×C4×D11—21no—
273C2×C4×D11—21no—
274C2×C4×D11—22no—
275C2×Dic22C2412yes—
276C2×Dic22C2411yescharacteristic
277C11×C4⋊C4—24no—
278C11×C4⋊C4—24no—
279C11×C4⋊C4—22no—
280C11×C4⋊C4—22no—
281C11×C4⋊C4—24no—
282C11×C4⋊C4—24no—
283C11×C4⋊C4—21no—
284C11×C4⋊C4—22no—
285C11×C4⋊C4C2×D411yescharacteristic
286C11×C4⋊C4C2×D412yes—
287C11×C4⋊C4C2×D411yescharacteristic
288C11×C4⋊C4C2×D412yes—
289C11×C4⋊C4C2×D412yes—
290C11×C4⋊C4C2×D412yes—
291C11×C4⋊C4C2×D412yes—
292C11×C4⋊C4C2412yes—
293C11×C4⋊C4C2414yes—
294C11×C22⋊C4—22no—
295C11×C22⋊C4—22no—
296C11×C22⋊C4—24no—
297C11×C22⋊C4—24no—
298C42×C11C2×D412yes—
299C42×C11C2×D411yescharacteristic
300C42×C11C2×D412yes—
301C42×C11C2×D411yescharacteristic
302C42×C11C2411yescharacteristic
303C42×C11C2412yes—
304C42×C11C2412yes—
305C42×C11C2411yescharacteristic
306C22⋊Dic11—21no—
307#4324—28no—
308#4324—24no—
309#4323—28no—
310#4323—24no—
311(C2×D11)⋊C4—22no—
312(C2×D11)⋊C4—21no—
313(C2×D11)⋊C4—21no—
314(C2×D11)⋊C4—22no—
315(C2×D11)⋊C4—22no—
316(C2×D11)⋊C4—22no—
317(C2×D11)⋊C4—22no—
318(C2×D11)⋊C4—22no—
319(C2×D11)⋊C4—22no—
320(C2×D11)⋊C4—22no—
321C4⋊Dic11—21no—
322C4⋊Dic11—22no—
323C4⋊Dic11—22no—
324C4⋊Dic11—21no—
325C4⋊Dic11C2411yescharacteristic
326C4⋊Dic11C2411yescharacteristic
327Dic11⋊C4—21no—
328Dic11⋊C4—22no—
329Dic11⋊C4—22no—
330Dic11⋊C4—21no—
331C4×Dic11—22no—
332C4×Dic11—21no—
333C4×Dic11—21no—
334C4×Dic11—22no—
335C4×Dic11—21no—
336#4318—22no—
337#4318—24no—
338#4318—22no—
339C2×C11⋊C8C2412yes—
340C2×C11⋊C8C2414yes—
341C2×C11⋊C8C2412yes—
342#3480—111no—
343C2×#554D1111yescharacteristic, complemented
344#3376—114no—
345#3372—112no—
346#3370—114no—
347#3366—112no—
348#3361—112no—
349#3360—112no—
350#3142—112no—
351#3141—111no—
352#3080—112no—
353#3079—111no—
354#3036—111no—
355#3036—112no—
356Q8×M16—111no—
357C4×AGL(1,ℤ/8)—111no—
358C4×AGL(1,ℤ/8)—112no—
359C23×C11—24no—
360C23×C11—22no—
361C23×C11—42no—
362C23×C11—42no—
363C23×C11C22×D411yescharacteristic
364C22×D11—22no—
365C22×D11—21no—
366Q8×C11—22no—
367Q8×C11—22no—
368Q8×C11—42no—
369Q8×C11—82no—
370Q8×C11—82no—
371D4×C11—24no—
372D4×C11—22no—
373D4×C11C2×#4114yes—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—24no—
377C2×C4×C11—42no—
378C2×C4×C11—42no—
379C2×C4×C11—41no—
380C2×C4×C11—44no—
381C2×C4×C11—42no—
382C2×C4×C11—44no—
383C2×C4×C11—44no—
384C2×C4×C11—84no—
385C2×C4×C11—84no—
386C2×C4×C11C22×D412yes—
387C2×C4×C11C22×D411yescharacteristic
388C2×C4×C11C22×D412yes—
389C2×C4×C11C22×D411yescharacteristic
390C2×C4×C11C22×D412yes—
391C2×C4×C11C22×D412yes—
392C2×C4×C11C22×D411yescharacteristic
393C2×C4×C11C22×D411yescharacteristic
394C2×C4×C11C22×D411yescharacteristic
395C2×C4×C11C2×#4112yes—
396C2×C4×C112−1+412yes—
397C2×C4×C11C2511yescharacteristic
398C22⋊D11—42no—
399C22⋊D11—44no—
400C2×Dic11—21no—
401C2×Dic11—21no—
402C2×Dic11—22no—
403C2×Dic11—21no—
404D44—21no—
405D44—22no—
406D44—21no—
407D44—22no—
408D44—44no—
409D44—42no—
410D44—82no—
411D44—81no—
412C4×D11—44no—
413C4×D11—44no—
414C4×D11—42no—
415C4×D11—42no—
416C4×D11—82no—
417C4×D11—81no—
418Dic22—22no—
419Dic22—21no—
420Dic22—22no—
421Dic22—21no—
422C11⋊C8—24no—
423C11⋊C8—22no—
424C11⋊C8—22no—
425C2×AGL(1,ℤ/8)—111no—
426C2×AGL(1,ℤ/8)—112no—
427#559—111no—
428#559—112no—
429#557—111no—
430#556—111no—
431#556—112no—
432#554—21no—
433#554—21no—
434#554—22no—
435#554C2×D1112yes—
436#554C2×D1112yes—
437#554C2×D1114yes—
438#553—221no—
439#553—222no—
440#550—111no—
441#548—221no—
442#532—111no—
443#532—112no—
444C2×C4⋊Q8C2×D1111yescharacteristic
445#529—222no—
446#529—221no—
447C2×#125C2×D1112yes—
448C2×C22⋊Q8—21no—
449C2×C22⋊Q8—22no—
450C4×#41—111no—
451C4×#41—112no—
452C4×#41—221no—
453C2×C4×Q8C2×D1111yescharacteristic
454C2×C4×D4C2×D1112yes—
455C2×C4×D4C2×D1111yescharacteristic
456C22×C4⋊C4—21no—
457#491—114no—
458#490—114no—
459#489—114no—
460#488—114no—
461#488—114no—
462#487—112no—
463#486—112no—
464#479—114no—
465#479—114no—
466#478—114no—
467#478—114no—
468#477—112no—
469#476—112no—
470#475—112no—
471#474—112no—
472#463—114no—
473#463—114no—
474#463—114no—
475#461—112no—
476#461—114no—
477#459—112no—
478#459—114no—
479#446—112no—
480#446—114no—
481C8×Q8—112no—
482#442—114no—
483#442—112no—
484#440—114no—
485#440—112no—
486C4×SD16—114no—
487C4×SD16—112no—
488C4×D8—112no—
489C4×D8—114no—
490#428—112no—
491#428—111no—
492#423—111no—
493#423—112no—
494#418—111no—
495#417—112no—
496#417—112no—
497#417—112no—
498#417—112no—
499#417—111no—
500C4×M16—111no—
501C4×M16—112no—
502C22×C11—21no—
503C22×C11—21no—
504C22×C11—24no—
505C22×C11—48no—
506C22×C11—42no—
507C22×C11—42no—
508C22×C11#54812yes—
509C22×C11C23×D411yescharacteristic
510C2×D11—42no—
511C2×D11—41no—
512C2×D11—42no—
513C2×D11—41no—
514C2×D11—42no—
515C2×D11—41no—
516C4×C11—22no—
517C4×C11—22no—
518C4×C11—21no—
519C4×C11—21no—
520C4×C11—21no—
521C4×C11—22no—
522C4×C11—22no—
523C4×C11—44no—
524C4×C11—42no—
525C4×C11#54812yes—
526C4×C11#57512yes—
527C4×C11C22×#4111yescharacteristic
528C4×C11C2×2−1+411yescharacteristic
529Dic11—41no—
530Dic11—42no—
531Dic11—41no—
532Dic11—41no—
533C2×#41—111no—
534C2×#41—112no—
535C2×#41—221no—
536C22×Q8—21no—
537C22×Q8C22⋊D1111yescharacteristic
538C22×D4C22×D1111yescharacteristic
539C23×C4—21no—
540C23×C4—22no—
541AGL(1,ℤ/8)—224no—
542AGL(1,ℤ/8)—228no—
543C2×SD16—114no—
544C2×SD16—112no—
545C2×D8—112no—
546C2×D8—114no—
547C2×M16—111no—
548C2×M16—112no—
549C2×M16—111no—
550C4⋊Q8—21no—
551C4⋊Q8—21no—
552C4⋊Q8—111no—
553C4⋊Q8—112no—
554C4⋊Q8C22×D1112yes—
555C4⋊Q8C22×D1112yes—
556#127—111no—
557#127—112no—
558#126—222no—
559#126—222no—
560#126—222no—
561#125—22no—
562#125—22no—
563#125—221no—
564#125—222no—
565#125C22×D1114yes—
566#125C22×D1114yes—
567#124—112no—
568#124—112no—
569#124—112no—
570#124—221no—
571#124—222no—
572#123—222no—
573#123—222no—
574#123—222no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—24no—
578C22⋊Q8—24no—
579C22⋊Q8—24no—
580C22⋊Q8—24no—
581C22⋊Q8—24no—
582C22⋊Q8—221no—
583C22⋊Q8—222no—
584#121—221no—
585#121—222no—
586#121—221no—
587#121—222no—
588#121—221no—
589#121—222no—
590C4×Q8—112no—
591C4×Q8—111no—
592C4×Q8—111no—
593C4×Q8—112no—
594C4×Q8—221no—
595C4×Q8C22⋊D1111yescharacteristic
596C4×Q8C22⋊D1112yes—
597C4×Q8C22⋊D1111yescharacteristic
598C4×Q8C22×D1111yescharacteristic
599C4×Q8C22×D1111yescharacteristic
600C4×Q8C22×D1112yes—
601C4×D4—22no—
602C4×D4—21no—
603C4×D4—22no—
604C4×D4—21no—
605C4×D4—111no—
606C4×D4—112no—
607C4×D4—112no—
608C4×D4—111no—
609C4×D4—221no—
610C4×D4—222no—
611C4×D4—221no—
612C4×D4—222no—
613C4×D4—221no—
614C4×D4—222no—
615C4×D4—222no—
616C4×D4—221no—
617C4×D4—222no—
618C4×D4—221no—
619C4×D4C22×D1112yes—
620C4×D4C22×D1114yes—
621C4×D4C22×D1114yes—
622C4×D4C22×D1112yes—
623#117—111no—
624#117—221no—
625#117—222no—
626#117—222no—
627#117—221no—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—22no—
633C2×C4⋊C4—24no—
634C2×C4⋊C4C22⋊D1111yescharacteristic
635C2×C4⋊C4C22⋊D1112yes—
636C2×C4⋊C4C22×D1111yescharacteristic
637C2×C4⋊C4C22×D1112yes—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—22no—
640C2×C42—222no—
641C2×C42—221no—
642C2×C42C22×D1112yes—
643C2×C42C22×D1111yescharacteristic
644#107—114no—
645#107—112no—
646#106—114no—
647#106—112no—
648C4⋊C8—112no—
649C4⋊C8—114no—
650C4⋊C8—114no—
651C4⋊C8—112no—
652#103—114no—
653#103—112no—
654#103—114no—
655#103—114no—
656#103—114no—
657#102—112no—
658#102—112no—
659#102—114no—
660#102—112no—
661#102—114no—
662#102—114no—
663#102—114no—
664#97—112no—
665#97—114no—
666C4×C8—112no—
667C4×C8—114no—
668C2×C11—22no—
669C2×C11—44no—
670C2×C11C2×#54811yescharacteristic
671C2×C11C2×#57511yescharacteristic
672C2×C11#358511yescharacteristic
673D11—82no—
674D11—81no—
675C24—21no—
676#41—222no—
677#41—224no—
678#41—222no—
679#41—224no—
680#41—444no—
681C2×Q8—22no—
682C2×Q8—22no—
683C2×Q8—42no—
684C2×Q8—82no—
685C2×Q8—112no—
686C2×Q8—111no—
687C2×Q8C2×C22⋊D1111yescharacteristic
688C2×Q8C2×C22⋊D1111yescharacteristic
689C2×Q8C2×C22⋊D1112yes—
690C2×D4—22no—
691C2×D4—21no—
692C2×D4—112no—
693C2×D4—111no—
694C2×D4—221no—
695C2×D4—222no—
696C2×D4—222no—
697C2×D4—221no—
698C2×D4—221no—
699C2×D4—222no—
700C2×D4#434314yescomplemented
701C2×D4C23×D1112yes—
702C22×C4—21no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—24no—
707C22×C4—24no—
708C22×C4—44no—
709C22×C4—84no—
710C22×C4—222no—
711C22×C4—221no—
712C22×C4—222no—
713C22×C4—221no—
714C22×C4—221no—
715C22×C4—222no—
716C22×C4C2×C22⋊D1111yescharacteristic
717C22×C4C2×C22⋊D1112yes—
718C22×C4C2×C22⋊D1111yescharacteristic
719C22×C4C2×C22⋊D1112yes—
720C22×C4C23×D1111yescharacteristic
721SD16—228no—
722SD16—224no—
723D8—224no—
724D8—228no—
725M16—222no—
726M16—224no—
727M16—222no—
728C2×C8—112no—
729C2×C8—112no—
730C2×C8—114no—
731C4⋊C4—24no—
732C4⋊C4—24no—
733C4⋊C4—22no—
734C4⋊C4—22no—
735C4⋊C4—24no—
736C4⋊C4—24no—
737C4⋊C4—21no—
738C4⋊C4—22no—
739C4⋊C4—111no—
740C4⋊C4—111no—
741C4⋊C4—222no—
742C4⋊C4—221no—
743C4⋊C4—221no—
744C4⋊C4—222no—
745C4⋊C4—222no—
746C4⋊C4—221no—
747C4⋊C4—221no—
748C4⋊C4—222no—
749C4⋊C4C2×C22⋊D1111yescharacteristic
750C4⋊C4C2×C22⋊D1111yescharacteristic
751C4⋊C4C2×C22⋊D1112yes—
752C4⋊C4C2×C22⋊D1112yes—
753C4⋊C4C2×C22⋊D1112yes—
754C4⋊C4C2×C22⋊D1112yes—
755C4⋊C4C2×C22⋊D1112yes—
756C4⋊C4C23×D1112yes—
757C4⋊C4C23×D1114yes—
758C22⋊C4—22no—
759C22⋊C4—22no—
760C22⋊C4—24no—
761C22⋊C4—24no—
762C22⋊C4—221no—
763C22⋊C4—221no—
764C22⋊C4—222no—
765C22⋊C4—222no—
766C22⋊C4—221no—
767C22⋊C4—222no—
768C22⋊C4—222no—
769C22⋊C4—222no—
770C22⋊C4—222no—
771C22⋊C4—222no—
772C22⋊C4—222no—
773C42—221no—
774C42—221no—
775C42—222no—
776C42—222no—
777C42—221no—
778C42C2×C22⋊D1112yes—
779C42C2×C22⋊D1111yescharacteristic
780C42C2×C22⋊D1112yes—
781C42C2×C22⋊D1111yescharacteristic
782C42C23×D1112yes—
783C42C23×D1111yescharacteristic
784C42C23×D1111yescharacteristic
785C42C23×D1112yes—
786C11#6131811yescharacteristic, complemented, Sylow
787C23—24no—
788C23—22no—
789C23—42no—
790C23—42no—
791C23—222no—
792C23—221no—
793C23C22×C22⋊D1111yescharacteristic
794Q8—22no—
795Q8—22no—
796Q8—42no—
797Q8—82no—
798Q8—82no—
799Q8—222no—
800Q8—221no—
801Q8—222no—
802Q8—221no—
803D4—24no—
804D4—22no—
805D4—222no—
806D4—221no—
807D4—222no—
808D4—221no—
809D4—444no—
810D4—442no—
811D4—444no—
812D4—442no—
813D4—882no—
814D4—881no—
815D4C2×#434314yes—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—24no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—41no—
822C2×C4—44no—
823C2×C4—42no—
824C2×C4—44no—
825C2×C4—44no—
826C2×C4—84no—
827C2×C4—84no—
828C2×C4—221no—
829C2×C4—221no—
830C2×C4—221no—
831C2×C4—222no—
832C2×C4—444no—
833C2×C4—444no—
834C2×C4—442no—
835C2×C4—442no—
836C2×C4—882no—
837C2×C4—881no—
838C2×C4C2×#434312yes—
839C2×C4#6704012yes—
840C2×C4C22×C22⋊D1111yescharacteristic
841C2×C4C22×C22⋊D1112yes—
842C2×C4C22×C22⋊D1112yes—
843C2×C4C22×C22⋊D1112yes—
844C2×C4C22×C22⋊D1111yescharacteristic
845C2×C4C22×C22⋊D1111yescharacteristic
846C2×C4C22×C22⋊D1112yes—
847C2×C4C22×C22⋊D1111yescharacteristic
848C2×C4C22×C22⋊D1111yescharacteristic
849C2×C4C24×D1111yescharacteristic
850C8—222no—
851C8—224no—
852C8—222no—
853C22—21no—
854C22—21no—
855C22—24no—
856C22—48no—
857C22—42no—
858C22—42no—
859C22—442no—
860C22—441no—
861C22—442no—
862C22—441no—
863C22—442no—
864C22—441no—
865C22#1062334812yes—
866C22C23×C22⋊D1111yescharacteristic
867C4—22no—
868C4—22no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—22no—
873C4—22no—
874C4—44no—
875C4—42no—
876C4—441no—
877C4—441no—
878C4—441no—
879C4—442no—
880C4#1062334812yes—
881C4#1062335312yes—
882C4C22×#434311yescharacteristic
883C4C2×#6704011yescharacteristic
884C2—22no—
885C2—44no—
886C2—882no—
887C2—881no—
888C2C2×#1062334811yescharacteristic
889C2C2×#1062335311yescharacteristic
890C2#1308339611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#554C2
socleC22×C11C23×D4
hypercenterC2×#554D11
hypocenterC11#61318
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #13082211C2semidirect
2. #13081443C2semidirect
3. #13081397C2semidirect
4. #13081369C2semidirect
5. #13081323C2semidirect
6. #13081276C2semidirect
7. #13081265C2semidirect
8. #13079019C2semidirect
9. #13079012C2semidirect
10. #13078434C2semidirect
11. #13078425C2semidirect
12. #13078080C2semidirect
13. #13078080C2semidirect
14. Q8×#4318C2semidirect
15. C4×#66985C2semidirect
16. C4×#66985C2semidirect
17. C2×C11×#554C2semidirect
35. #10623116C22semidirect
36. #10623116C22semidirect
37. #10623115C22semidirect
38. #10623115C22semidirect
41. #10623108C22semidirect
43. #10623101C22semidirect
51. #10622707C22semidirect
52. #10622706C22semidirect
53. #10622704C22semidirect
54. #10622702C22semidirect
55. #10622701C22semidirect
56. #10622700C22semidirect
57. #10622697C22semidirect
58. #10622682C22semidirect
59. #10622681C22semidirect
60. #10622681C22semidirect
61. #10622680C22semidirect
62. #10622679C22semidirect
63. #10622679C22semidirect
64. #10622676C22semidirect
65. #10622676C22semidirect
66. #10622637C22semidirect
67. #10622637C22semidirect
68. Q8×C11⋊C8C22semidirect
241. C2×D4×C11#41semidirect
343. C2×#554D11semidirect
700. C2×D4#4343semidirect
786. C11#61318semidirect

Maximal subgroups

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

subgroupindex
#130822112
#130814432
#130813972
#130813692
#130813232
#130812762
#130812652
#130790192
#130790122
#130784342
#130784252
#130780802
Q8×#43182
C4×#669852
C2×C11×#5542
#6131811