Finite Group Databasebeta

← #15638689

Subgroups — #15638689

Order 2816.

2254 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082465C211yesmaximal, characteristic, complemented
2C2×#10623207C211yesmaximal, characteristic, complemented
3#13080779C214yesmaximal, complemented
4#13080651C214yesmaximal, complemented
5#13080155C214yesmaximal, complemented
6#13080136C214yesmaximal, complemented
7#13079619C211yesmaximal, characteristic, complemented
8#13079443C212yesmaximal, complemented
9#13079378C212yesmaximal, complemented
10#13078716C211yesmaximal, characteristic, complemented
11#13078703C211yesmaximal, characteristic, complemented
12#13077840C212yesmaximal, complemented
13#13077833C212yesmaximal, complemented
14#13077644C211yesmaximal, characteristic, complemented
15C11×#3213C211yesmaximal, characteristic, complemented
16C22×#4343C2211yescharacteristic
17C22×D4×D11C2211yescharacteristic
18C11×#532C2211yescharacteristic, complemented
19C2×C11×#124C2211yescharacteristic
20#10623361—21no—
21#10623358—21no—
22C2×#66999C2211yescharacteristic
23C2×#66991C2211yescharacteristic
24C2×#66969C2214yescomplemented
25C2×#66964C2214yescomplemented
26#10623263C2212yescomplemented
27#10623249C2212yescomplemented
28#10623212—22no—
29#10623207—22no—
30#10623207—22no—
31#10623207C2214yes—
32#10623207C2214yes—
33#10623148—21no—
34#10623148—21no—
35#10623137C2212yes—
36#10623137C2212yescomplemented
37#10623096—22no—
38#10623094C2212yescomplemented
39#10623086C2212yescomplemented
40C2×#66937—21no—
41C2×#66936—21no—
42C2×#66935—21no—
43C2×C22⋊C4×D11—21no—
44C2×C4×D44C2211yescharacteristic
45C2×C4×D44C2211yescharacteristic
46#10623001C2211yescharacteristic, complemented
47C11×#496C2212yescomplemented
48C11×#489C2212yescomplemented
49C11×#463C2214yescomplemented
50C11×#448C2212yescomplemented
51C11×#447C2212yes—
52C11×#432C2211yescharacteristic, complemented
53#10622841C2212yescomplemented
54#10622831C2212yes—
55#10622787C2214yescomplemented
56#10622786C2214yescomplemented
57#10622785C2214yescomplemented
58#10622771C2214yescomplemented
59#10622770C2214yescomplemented
60#10622769C2214yescomplemented
61#10622697C2212yescomplemented
62#10622685C2212yescomplemented
63#10622673C2212yescomplemented
64#10622668C2212yescomplemented
65#10622667C2214yescomplemented
66#10622649C2212yes—
67#10622647C2212yescomplemented
68#10622627C2214yescomplemented
69#10622539C2211yescharacteristic, complemented
70#10622459C2212yescomplemented
71#10622454C2212yescomplemented
72#10622449C2214yescomplemented
73#10622429C2214yescomplemented
74#10622427C2214yescomplemented
75#10622423C2214yescomplemented
76#10622417C2214yescomplemented
77#10622397C2214yescomplemented
78#10622391C2214yescomplemented
79#10622389C2214yescomplemented
80#10622383C2214yescomplemented
81#10622344C2212yes—
82#10622339C2212yes—
83D11×C22⋊C8C2212yescomplemented
84#10622335C2212yescomplemented
85#10622323C2214yescomplemented
86#10622319C2214yescomplemented
87C24×D11—21no—
88C2×C11×#41—21no—
89C22×Q8×C11C2311yescharacteristic
90C22×D4×C11C2311yescharacteristic
91C22×C22⋊D11—21no—
92C22×C22⋊D11—21no—
93C2×#4343—22no—
94C2×#4343—44no—
95C2×#4343C2314yes—
96C2×#4341C2312yes—
97C2×#4341C2312yescomplemented
98C2×D4×D11—22no—
99C2×D4×D11—44no—
100C2×D4×D11C2314yes—
101C22×D44—21no—
102C22×D44D411yescharacteristic
103C22×D44C2311yescharacteristic
104C22×C4×D11—21no—
105C22×C4×D11—21no—
106C22×C4×D11C2311yescharacteristic
107C22×C4×D11C2311yescharacteristic
108C2×C11×SD16C2314yescomplemented
109C2×C11×D8C2314yes—
110C11×C4⋊Q8C2311yescharacteristic, complemented
111C11×#127C2311yescharacteristic, complemented
112C11×#124—21no—
113C11×#124—21no—
114C11×#124—21no—
115C11×#124C2312yes—
116C11×#124C2312yes—
117C11×#121—21no—
118C11×#121C2312yes—
119C4×D4×C11—21no—
120C4×D4×C11C2312yescomplemented
121C2×C11×C22⋊C4—21no—
122C2×C11×C22⋊C4—21no—
123C2×C42×C11C2311yescharacteristic
124C2×C22⋊Dic11—21no—
125#67000—22no—
126#66999—22no—
127#66999C2314yes—
128Q8×Dic11—22no—
129C2×#4326C2314yescomplemented
130#66993—22no—
131#66992—22no—
132#66992—22no—
133#66991—22no—
134#66991C2312yes—
135#66991C2314yes—
136#66991C2312yescomplemented
137#66990—22no—
138#66990—22no—
139D4×Dic11—22no—
140D4×Dic11—22no—
141D4×Dic11—22no—
142C2×#4324C2314yes—
143C2×#4323C2314yes—
144#66983—22no—
145#66983—22no—
146C2×(C2×D11)⋊C4—21no—
147C2×(C2×D11)⋊C4—21no—
148C2×(C2×D11)⋊C4D411yescharacteristic
149C2×(C2×D11)⋊C4D411yescharacteristic
150#66979—21no—
151#66979—22no—
152C2×C4⋊Dic11—22no—
153C2×C4⋊Dic11D411yescharacteristic
154C2×C4⋊Dic11C2311yescharacteristic
155#66977—21no—
156#66977C2312yes—
157C2×Dic11⋊C4—21no—
158#66969—48no—
159#66964—48no—
160C2×#4314C2314yes—
161C2×#4313C2314yes—
162C2×C8×D11C2314yescomplemented
163#66951—22no—
164#66951—22no—
165#66950C2312yes—
166#66950C2312yescomplemented
167#66945C2312yes—
168#66945C2312yescomplemented
169#66939—22no—
170#66939—22no—
171#66938—22no—
172#66938—22no—
173#66937—24no—
174#66937—24no—
175#66936—22no—
176#66936—22no—
177#66936—24no—
178#66936—24no—
179#66935—24no—
180#66935—24no—
181(C22⋊D11)⋊C4—22no—
182(C22⋊D11)⋊C4—22no—
183C22⋊C4×D11—24no—
184C22⋊C4×D11—24no—
185C4×D44—21no—
186C4×D44—21no—
187C4×D44D412yes—
188C4×D44D412yes—
189C4×D44C2312yes—
190C4×D44C2312yes—
191C4×D44C2312yes—
192C4×D44C2312yes—
193#66923—21no—
194#66922C2311yescharacteristic, complemented
195#66922C2311yescharacteristic, complemented
196C4×Dic22—21no—
197C4×Dic22C2312yescomplemented
198C11×C4⋊C8C2312yescomplemented
199C11×#103C2314yescomplemented
200C11×#102C2314yes—
201C11×C22⋊C8C2312yes—
202C11×#97C2312yescomplemented
203#66899C2314yescomplemented
204#66896C2314yes—
205#66896C2314yescomplemented
206C22⋊(C11⋊C8)C2312yes—
207#66885C2314yes—
208(C2×D11)⋊C8C2314yes—
209(C2×D11)⋊C8C2314yescomplemented
210#66882C2314yescomplemented
211#66880C2314yescomplemented
212#66873C2314yes—
213#66872C2314yescomplemented
214C4⋊(C11⋊C8)C2312yescomplemented
215#66867C2312yescomplemented
216#61576—111nomaximal, Sylow
217C24×C11—21no—
218C23×D11—21no—
219C23×D11—24no—
220C23×D11—44no—
221C23×D11—44no—
222C23×D11—82no—
223C23×D11C2×D411yescharacteristic
224C23×D11C2×D411yescharacteristic
225C11×#41—44no—
226C2×Q8×C11—21no—
227C2×Q8×C11—21no—
228C2×Q8×C11—42no—
229C2×Q8×C11C2412yes—
230C2×D4×C11—22no—
231C2×D4×C11—21no—
232C2×D4×C11—21no—
233C2×D4×C11—21no—
234C2×D4×C11—42no—
235C2×D4×C11C2412yes—
236C2×D4×C11C2412yes—
237C22×C4×C11—21no—
238C22×C4×C11—22no—
239C22×C4×C11C2×D411yescharacteristic
240C22×C4×C11C2×D411yescharacteristic
241C22×C4×C11C2411yescharacteristic
242C2×C22⋊D11—24no—
243C2×C22⋊D11—22no—
244C2×C22⋊D11—22no—
245C2×C22⋊D11—24no—
246C2×C22⋊D11—22no—
247C2×C22⋊D11—22no—
248C2×C22⋊D11—44no—
249C2×C22⋊D11—82no—
250C22×Dic11—22no—
251C22×Dic11—22no—
252C22×Dic11—21no—
253C22×Dic11C2×D411yescharacteristic
254C22×Dic11C2×D411yescharacteristic
255#4343—28no—
256#4343—44no—
257#4343—48no—
258#4341—44no—
259#4341—44no—
260D4×D11—28no—
261D4×D11—44no—
262D4×D11—48no—
263C2×D44—24no—
264C2×D44—24no—
265C2×D44—21no—
266C2×D44—42no—
267C2×D44—44no—
268C2×D44C2×D412yes—
269C2×D44C2×D412yes—
270C2×D44C2412yes—
271C2×C4×D11—24no—
272C2×C4×D11—22no—
273C2×C4×D11—22no—
274C2×C4×D11—42no—
275C2×C4×D11—42no—
276C2×C4×D11—44no—
277C2×C4×D11—82no—
278C2×C4×D11C2×D412yes—
279C2×C4×D11C2×D412yes—
280C2×C4×D11C2412yes—
281C2×C4×D11C2412yes—
282C2×Dic22—21no—
283C2×Dic22C2412yes—
284C11×SD16—44no—
285C11×D8—44no—
286C2×C8×C11C2414yes—
287C11×C4⋊C4—21no—
288C11×C4⋊C4C2412yes—
289C11×C22⋊C4—22no—
290C11×C22⋊C4—22no—
291C11×C22⋊C4—22no—
292C11×C22⋊C4—22no—
293C11×C22⋊C4—22no—
294C11×C22⋊C4—22no—
295C42×C11C2×D411yescharacteristic
296C42×C11C2×D411yescharacteristic
297C42×C11C2411yescharacteristic
298C42×C11C2411yescharacteristic
299C22⋊Dic11—24no—
300C22⋊Dic11—22no—
301C22⋊Dic11—22no—
302C22⋊Dic11—22no—
303#4326—44no—
304#4324—44no—
305#4323—28no—
306(C2×D11)⋊C4—24no—
307(C2×D11)⋊C4—22no—
308(C2×D11)⋊C4—22no—
309(C2×D11)⋊C4—22no—
310(C2×D11)⋊C4—22no—
311(C2×D11)⋊C4—22no—
312(C2×D11)⋊C4—22no—
313(C2×D11)⋊C4C2×D412yes—
314(C2×D11)⋊C4C2×D412yes—
315(C2×D11)⋊C4C2×D412yes—
316(C2×D11)⋊C4C2×D412yes—
317C4⋊Dic11—22no—
318C4⋊Dic11—22no—
319C4⋊Dic11—21no—
320C4⋊Dic11—21no—
321C4⋊Dic11—21no—
322C4⋊Dic11—21no—
323C4⋊Dic11C2×D412yes—
324C4⋊Dic11C2×D412yes—
325C4⋊Dic11C2412yes—
326C4⋊Dic11C2412yes—
327Dic11⋊C4—24no—
328Dic11⋊C4—22no—
329Dic11⋊C4—22no—
330C4×Dic11—22no—
331C4×Dic11—22no—
332C4×Dic11—22no—
333C2×C11⋊C8C2414yes—
334#4314—28no—
335#4313—44no—
336C8×D11—44no—
337#3506—111no—
338C2×#546—111no—
339#3319—114no—
340#3311—114no—
341#3268—114no—
342#3267—114no—
343#3215—111no—
344#3213D1111yescharacteristic, complemented
345#3196—112no—
346#3188—112no—
347#3110—111no—
348#3109—111no—
349#3003—112no—
350#3002—112no—
351#2973—111no—
352C23×C11—22no—
353C23×C11—22no—
354C23×C11—42no—
355C23×C11—42no—
356C23×C11—42no—
357C23×C11C22×D411yescharacteristic
358C22×D11—24no—
359C22×D11—22no—
360C22×D11—22no—
361C22×D11—22no—
362C22×D11—41no—
363C22×D11—41no—
364C22×D11—41no—
365C22×D11—41no—
366C22×D11—48no—
367C22×D11—48no—
368C22×D11—42no—
369C22×D11—42no—
370C22×D11—84no—
371C22×D11—816no—
372C22×D11C22×D412yes—
373C22×D11C22×D412yes—
374Q8×C11—24no—
375Q8×C11—42no—
376Q8×C11—42no—
377D4×C11—24no—
378D4×C11—24no—
379D4×C11—42no—
380D4×C11—42no—
381D4×C11—44no—
382D4×C11—81no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—41no—
388C2×C4×C11—44no—
389C2×C4×C11—42no—
390C2×C4×C11C22×D411yescharacteristic
391C2×C4×C11C22×D411yescharacteristic
392C2×C4×C11C22×D411yescharacteristic
393C2×C4×C11C22×D411yescharacteristic
394C2×C4×C11C22×D411yescharacteristic
395C2×C4×C11C2511yescharacteristic
396C22⋊D11—48no—
397C22⋊D11—82no—
398C22⋊D11—82no—
399C22⋊D11—82no—
400C22⋊D11—82no—
401C22⋊D11—84no—
402C2×Dic11—22no—
403C2×Dic11—22no—
404C2×Dic11—22no—
405C2×Dic11—41no—
406C2×Dic11—41no—
407C2×Dic11—42no—
408C2×Dic11—82no—
409C2×Dic11—82no—
410C2×Dic11C22×D412yes—
411C2×Dic11C22×D412yes—
412D44—24no—
413D44—22no—
414D44—42no—
415D44—42no—
416D44—48no—
417D44H(5,𝔽2)14yes—
418C4×D11—24no—
419C4×D11—24no—
420C4×D11—42no—
421C4×D11—42no—
422C4×D11—48no—
423C4×D11—82no—
424C4×D11—82no—
425Dic22—24no—
426Dic22—81no—
427C8×C11—24no—
428C11⋊C8—24no—
429C22×#41—111no—
430C23×D4—111no—
431C2×AGL(1,ℤ/8)—114no—
432C2×#135—114no—
433#559—222no—
434#556—112no—
435#555—112no—
436#553—222no—
437#550—112no—
438#547—112no—
439#546—114no—
440#546—114no—
441#546—222no—
442#546—222no—
443#538—221no—
444#538—221no—
445#535—221no—
446#533—111no—
447#532C2×D1111yescharacteristic, complemented
448C2×#124C2×D1111yescharacteristic
449#525—112no—
450#525—112no—
451C2×#123—221no—
452C2×C22⋊Q8—111no—
453C2×#121—111no—
454C2×#121—221no—
455C2×#120—221no—
456#520—221no—
457C2×C4×D4—111no—
458C2×C4×D4—111no—
459C22×C22⋊C4—221no—
460#497—112no—
461#496C2×D1112yescomplemented
462#489—112no—
463#489C2×D1112yescomplemented
464#485—114no—
465#484—112no—
466#482—114no—
467#481—112no—
468#476—112no—
469#474—112no—
470#470—114no—
471#468—114no—
472#466—114no—
473#465—114no—
474#464—114no—
475#463C2×D1114yescomplemented
476#461—112no—
477#459—112no—
478#452—114no—
479#452—114no—
480#451—112no—
481#450—112no—
482#450—114no—
483#450—112no—
484#449—114no—
485#449—114no—
486#448C2×D1112yescomplemented
487#447—114no—
488#447—112no—
489#447C2×D1112yes—
490#442—114no—
491#440—114no—
492#435—114no—
493#435—114no—
494#432—111no—
495#432C2×D1111yescharacteristic, complemented
496#418—114no—
497#416—114no—
498#407—112no—
499C2×C22⋊C8—112no—
500C22×C11—21no—
501C22×C11—21no—
502C22×C11—42no—
503C22×C11—42no—
504C22×C11—42no—
505C22×C11—42no—
506C22×C11—42no—
507C22×C11—42no—
508C22×C11—84no—
509C22×C11#57512yes—
510C22×C11C23×D411yescharacteristic
511C2×D11—22no—
512C2×D11—22no—
513C2×D11—24no—
514C2×D11—22no—
515C2×D11—22no—
516C2×D11—22no—
517C2×D11—22no—
518C2×D11—48no—
519C2×D11—44no—
520C2×D11—42no—
521C2×D11—42no—
522C2×D11—82no—
523C2×D11—816no—
524C4×C11—21no—
525C4×C11—21no—
526C4×C11—21no—
527C4×C11—21no—
528C4×C11—21no—
529C4×C11—42no—
530C4×C11—42no—
531C4×C11C2×H(5,𝔽2)12yes—
532Dic11—22no—
533Dic11—22no—
534Dic11—42no—
535Dic11—42no—
536Dic11—42no—
537C25—221no—
538C2×#41—21no—
539C2×#41—114no—
540C2×#41—112no—
541C2×#41—112no—
542C2×#41—222no—
543C2×#41—444no—
544C22×Q8C22×D1111yescharacteristic
545C22×D4—114no—
546C22×D4—111no—
547C22×D4—111no—
548C22×D4—221no—
549C22×D4—222no—
550C22×D4—221no—
551C22×D4—221no—
552C22×D4—444no—
553C22×D4C22×D1111yescharacteristic
554C23×C4—111no—
555C23×C4—111no—
556C23×C4—221no—
557C23×C4—221no—
558AGL(1,ℤ/8)—448no—
559#135—448no—
560C2×Q16—114no—
561C2×SD16—114no—
562C2×SD16—114no—
563C2×SD16C22×D1114yescomplemented
564C2×D8—114no—
565C2×D8C22×D1114yes—
566C2×M16—114no—
567C22×C8—114no—
568C4⋊Q8—111no—
569C4⋊Q8—111no—
570C4⋊Q8C22×D1111yescharacteristic, complemented
571#127—222no—
572#127C22×D1111yescharacteristic, complemented
573#126—222no—
574#126—222no—
575#125—221no—
576#124—21no—
577#124—21no—
578#124—21no—
579#124—222no—
580#124—222no—
581#124—222no—
582#124C22×D1112yes—
583#124C22×D1112yes—
584#123—222no—
585#123—222no—
586#123—224no—
587#123—224no—
588#123—222no—
589#123—222no—
590C22⋊Q8—114no—
591C22⋊Q8—112no—
592C22⋊Q8—112no—
593C22⋊Q8—112no—
594C22⋊Q8—222no—
595C22⋊Q8—221no—
596#121—21no—
597#121—114no—
598#121—112no—
599#121—112no—
600#121—224no—
601#121—224no—
602#121—222no—
603#121—222no—
604#121—222no—
605#121—222no—
606#121—222no—
607#121C22×D1112yes—
608#120—224no—
609#120—224no—
610#120—222no—
611#120—222no—
612C4×Q8—112no—
613C4×Q8—222no—
614C4×Q8—221no—
615C4×D4—21no—
616C4×D4—112no—
617C4×D4—112no—
618C4×D4—112no—
619C4×D4—112no—
620C4×D4—112no—
621C4×D4—112no—
622C4×D4—222no—
623C4×D4—222no—
624C4×D4—222no—
625C4×D4—222no—
626C4×D4—222no—
627C4×D4—221no—
628C4×D4—221no—
629C4×D4C22×D1112yescomplemented
630#117—112no—
631#117—112no—
632#117—222no—
633#117—221no—
634C2×C4⋊C4—111no—
635C2×C4⋊C4—111no—
636C2×C4⋊C4—222no—
637C2×C4⋊C4—221no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—111no—
641C2×C22⋊C4—111no—
642C2×C22⋊C4—224no—
643C2×C22⋊C4—224no—
644C2×C22⋊C4—221no—
645C2×C22⋊C4—221no—
646C2×C22⋊C4—221no—
647C2×C42C22×D1111yescharacteristic
648#107—114no—
649#106—114no—
650C4⋊C8—112no—
651C4⋊C8C22×D1112yescomplemented
652#103—114no—
653#103—114no—
654#103C22×D1114yescomplemented
655#102—114no—
656#102—114no—
657#102—114no—
658#102—114no—
659#102C22×D1114yes—
660C22⋊C8—112no—
661C22⋊C8—114no—
662C22⋊C8—114no—
663C22⋊C8C22×D1112yes—
664#97—112no—
665#97C22×D1112yescomplemented
666C2×C11—22no—
667C2×C11—82no—
668C2×C11—82no—
669C2×C11#348411yescharacteristic
670C2×C11C2×#57511yescharacteristic
671C2×C11#358511yescharacteristic
672D11—42no—
673D11—42no—
674D11—44no—
675C24—21no—
676C24—111no—
677C24—111no—
678C24—224no—
679C24—221no—
680C24—444no—
681C24—444no—
682C24—882no—
683#41—44no—
684#41—228no—
685#41—444no—
686#41—444no—
687#41—444no—
688#41—448no—
689C2×Q8—21no—
690C2×Q8—21no—
691C2×Q8—42no—
692C2×Q8—112no—
693C2×Q8—221no—
694C2×Q8C23×D1112yes—
695C2×D4—22no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—42no—
700C2×D4—112no—
701C2×D4—112no—
702C2×D4—112no—
703C2×D4—224no—
704C2×D4—224no—
705C2×D4—224no—
706C2×D4—228no—
707C2×D4—222no—
708C2×D4—222no—
709C2×D4—224no—
710C2×D4—222no—
711C2×D4—222no—
712C2×D4—221no—
713C2×D4—442no—
714C2×D4—444no—
715C2×D4—444no—
716C2×D4—448no—
717C2×D4—444no—
718C2×D4—882no—
719C2×D4C23×D1112yes—
720C2×D4C23×D1112yes—
721C22×C4—21no—
722C22×C4—22no—
723C22×C4—111no—
724C22×C4—111no—
725C22×C4—112no—
726C22×C4—112no—
727C22×C4—112no—
728C22×C4—112no—
729C22×C4—224no—
730C22×C4—222no—
731C22×C4—222no—
732C22×C4—221no—
733C22×C4—222no—
734C22×C4—222no—
735C22×C4—442no—
736C22×C4—442no—
737C22×C4—444no—
738C22×C4—882no—
739C22×C4D4×D1111yescharacteristic
740C22×C4D4×D1111yescharacteristic
741C22×C4C23×D1111yescharacteristic
742Q16—444no—
743SD16—44no—
744SD16—228no—
745SD16—444no—
746D8—44no—
747D8—228no—
748M16—444no—
749C2×C8—114no—
750C2×C8—444no—
751C2×C8C23×D1114yes—
752C4⋊C4—21no—
753C4⋊C4—112no—
754C4⋊C4—112no—
755C4⋊C4—112no—
756C4⋊C4—112no—
757C4⋊C4—222no—
758C4⋊C4—222no—
759C4⋊C4—224no—
760C4⋊C4—221no—
761C4⋊C4—221no—
762C4⋊C4—221no—
763C4⋊C4—222no—
764C4⋊C4—222no—
765C4⋊C4—221no—
766C4⋊C4C23×D1112yes—
767C22⋊C4—22no—
768C22⋊C4—22no—
769C22⋊C4—22no—
770C22⋊C4—22no—
771C22⋊C4—22no—
772C22⋊C4—22no—
773C22⋊C4—112no—
774C22⋊C4—112no—
775C22⋊C4—112no—
776C22⋊C4—112no—
777C22⋊C4—224no—
778C22⋊C4—222no—
779C22⋊C4—222no—
780C22⋊C4—222no—
781C22⋊C4—222no—
782C22⋊C4—224no—
783C22⋊C4—222no—
784C22⋊C4—222no—
785C22⋊C4—222no—
786C22⋊C4—222no—
787C22⋊C4—222no—
788C42—222no—
789C42—222no—
790C42—222no—
791C42D4×D1111yescharacteristic
792C42D4×D1111yescharacteristic
793C42C23×D1111yescharacteristic
794C42C23×D1111yescharacteristic
795C11#6157611yescharacteristic, complemented, Sylow
796C23—22no—
797C23—22no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—112no—
802C23—112no—
803C23—224no—
804C23—222no—
805C23—222no—
806C23—222no—
807C23—441no—
808C23—441no—
809C23—441no—
810C23—441no—
811C23—442no—
812C23—448no—
813C23—448no—
814C23—442no—
815C23—884no—
816C23—8816no—
817C23C2×D4×D1111yescharacteristic
818Q8—24no—
819Q8—42no—
820Q8—42no—
821Q8—224no—
822Q8—881no—
823D4—24no—
824D4—24no—
825D4—42no—
826D4—42no—
827D4—44no—
828D4—81no—
829D4—114no—
830D4—224no—
831D4—222no—
832D4—442no—
833D4—442no—
834D4—448no—
835D4—448no—
836D4—884no—
837D4—882no—
838D4—882no—
839D4—882no—
840D4—882no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—41no—
846C2×C4—44no—
847C2×C4—42no—
848C2×C4—112no—
849C2×C4—112no—
850C2×C4—224no—
851C2×C4—224no—
852C2×C4—222no—
853C2×C4—222no—
854C2×C4—222no—
855C2×C4—442no—
856C2×C4—442no—
857C2×C4—448no—
858C2×C4—441no—
859C2×C4—441no—
860C2×C4—442no—
861C2×C4—882no—
862C2×C4—882no—
863C2×C4—882no—
864C2×C4—882no—
865C2×C4C2×D4×D1111yescharacteristic
866C2×C4C2×D4×D1111yescharacteristic
867C2×C4C2×D4×D1111yescharacteristic
868C2×C4C2×D4×D1111yescharacteristic
869C2×C4C2×D4×D1111yescharacteristic
870C2×C4C24×D1111yescharacteristic
871C8—24no—
872C8—224no—
873C22—21no—
874C22—21no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22—84no—
882C22—222no—
883C22—222no—
884C22—222no—
885C22—222no—
886C22—224no—
887C22—222no—
888C22—222no—
889C22—444no—
890C22—448no—
891C22—442no—
892C22—442no—
893C22—882no—
894C22—8816no—
895C22#1062330412yes—
896C22C22×D4×D1111yescharacteristic
897C4—21no—
898C4—21no—
899C4—21no—
900C4—21no—
901C4—21no—
902C4—42no—
903C4—42no—
904C4—222no—
905C4—222no—
906C4—442no—
907C4—442no—
908C4—442no—
909C4D11×H(5,𝔽2)12yes—
910C2—22no—
911C2—82no—
912C2—82no—
913C2—442no—
914C2—442no—
915C2—444no—
916C2#1308225011yescharacteristic
917C2C2×#1062330411yescharacteristic
918C2#1308339311yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3213C2
socleC22×C11C23×D4
hypercenter#3213D11
hypocenterC11#61576
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3213

Complements

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

NH ≅ G/Ntype
1. #13082465C2semidirect
2. C2×#10623207C2semidirect
3. #13080779C2semidirect
4. #13080651C2semidirect
5. #13080155C2semidirect
6. #13080136C2semidirect
7. #13079619C2semidirect
8. #13079443C2semidirect
9. #13079378C2semidirect
10. #13078716C2semidirect
11. #13078703C2semidirect
12. #13077840C2semidirect
13. #13077833C2semidirect
14. #13077644C2semidirect
15. C11×#3213C2semidirect
18. C11×#532C22semidirect
24. C2×#66969C22semidirect
25. C2×#66964C22semidirect
26. #10623263C22semidirect
27. #10623249C22semidirect
36. #10623137C22semidirect
38. #10623094C22semidirect
39. #10623086C22semidirect
46. #10623001C22semidirect
47. C11×#496C22semidirect
48. C11×#489C22semidirect
49. C11×#463C22semidirect
50. C11×#448C22semidirect
52. C11×#432C22semidirect
53. #10622841C22semidirect
55. #10622787C22semidirect
56. #10622786C22semidirect
57. #10622785C22semidirect
58. #10622771C22semidirect
59. #10622770C22semidirect
60. #10622769C22semidirect
61. #10622697C22semidirect
62. #10622685C22semidirect
63. #10622673C22semidirect
64. #10622668C22semidirect
65. #10622667C22semidirect
67. #10622647C22semidirect
68. #10622627C22semidirect
69. #10622539C22semidirect
70. #10622459C22semidirect
71. #10622454C22semidirect
72. #10622449C22semidirect
73. #10622429C22semidirect
74. #10622427C22semidirect
75. #10622423C22semidirect
76. #10622417C22semidirect
77. #10622397C22semidirect
78. #10622391C22semidirect
79. #10622389C22semidirect
80. #10622383C22semidirect
83. D11×C22⋊C8C22semidirect
84. #10622335C22semidirect
85. #10622323C22semidirect
86. #10622319C22semidirect
97. C2×#4341C23semidirect
108. C2×C11×SD16C23semidirect
110. C11×C4⋊Q8C23semidirect
111. C11×#127C23semidirect
120. C4×D4×C11C23semidirect
129. C2×#4326C23semidirect
136. #66991C23semidirect
162. C2×C8×D11C23semidirect
166. #66950C23semidirect
168. #66945C23semidirect
194. #66922C23semidirect
195. #66922C23semidirect
197. C4×Dic22C23semidirect
198. C11×C4⋊C8C23semidirect
199. C11×#103C23semidirect
202. C11×#97C23semidirect
203. #66899C23semidirect
205. #66896C23semidirect
209. (C2×D11)⋊C8C23semidirect
210. #66882C23semidirect
211. #66880C23semidirect
213. #66872C23semidirect
214. C4⋊(C11⋊C8)C23semidirect
215. #66867C23semidirect
344. #3213D11semidirect
447. #532C2×D11semidirect
461. #496C2×D11semidirect
463. #489C2×D11semidirect
475. #463C2×D11semidirect
486. #448C2×D11semidirect
495. #432C2×D11semidirect
563. C2×SD16C22×D11semidirect
570. C4⋊Q8C22×D11semidirect
572. #127C22×D11semidirect
629. C4×D4C22×D11semidirect
651. C4⋊C8C22×D11semidirect
654. #103C22×D11semidirect
665. #97C22×D11semidirect
795. C11#61576semidirect

Maximal subgroups

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

subgroupindex
#130824652
C2×#106232072
#130807792
#130806512
#130801552
#130801362
#130796192
#130794432
#130793782
#130787162
#130787032
#130778402
#130778332
#130776442
C11×#32132
#6157611