Finite Group Databasebeta

← #15638693

Subgroups — #15638693

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#13082470C211yesmaximal, characteristic, complemented
2C2×#10623085C211yesmaximal, characteristic, complemented
3#13080769C214yesmaximal, complemented
4#13080657C214yesmaximal, complemented
5#13080158C214yesmaximal, complemented
6#13080147C214yesmaximal, complemented
7#13079615C211yesmaximal, characteristic, complemented
8#13079605C211yesmaximal, characteristic, complemented
9#13079451C212yesmaximal, complemented
10#13079386C212yesmaximal, complemented
11#13078707C211yesmaximal, characteristic, complemented
12#13077844C212yesmaximal, complemented
13#13077835C212yesmaximal, complemented
14#13077644C211yesmaximal, characteristic, complemented
15C11×#3110C211yesmaximal, characteristic, complemented
16C22×#4341C2211yescharacteristic
17C22×D4×D11C2211yescharacteristic
18C11×#533C2211yescharacteristic, complemented
19C2×C4×D4×C11C2211yescharacteristic
20C2×#66983—21no—
21C22×(C2×D11)⋊C4—21no—
22C2×#66969C2214yescomplemented
23C2×#66967C2214yescomplemented
24#10623265C2212yescomplemented
25#10623257C2212yescomplemented
26#10623226—22no—
27#10623175—21no—
28#10623175—21no—
29#10623158C2212yes—
30#10623158C2212yescomplemented
31#10623116—22no—
32#10623115C2212yescomplemented
33#10623108C2212yescomplemented
34#10623085—22no—
35#10623085—22no—
36#10623085C2214yes—
37#10623085C2214yes—
38#10623056—21no—
39#10623054—21no—
40C2×#66950C2211yescharacteristic
41C2×#66948C2211yescharacteristic
42C2×#66939—21no—
43C2×#66935—21no—
44#10623008C2211yescharacteristic, complemented
45C2×#66928C2211yescharacteristic
46C2×C4×D44C2211yescharacteristic
47C11×#484C2212yescomplemented
48C11×#474C2212yescomplemented
49C11×#461C2212yescomplemented
50C11×#450C2212yes—
51C11×#440C2214yescomplemented
52C11×#432C2211yescharacteristic, complemented
53#10622830C2212yes—
54#10622786C2214yescomplemented
55#10622782C2214yescomplemented
56#10622702C2212yescomplemented
57#10622699C2212yescomplemented
58#10622663C2212yescomplemented
59#10622659C2212yes—
60#10622641C2214yescomplemented
61#10622628C2212yescomplemented
62#10622627C2214yescomplemented
63#10622621C2212yescomplemented
64#10622581C2212yescomplemented
65#10622539C2211yescharacteristic, complemented
66#10622501C2214yescomplemented
67#10622499C2214yescomplemented
68#10622498C2214yescomplemented
69#10622496C2214yescomplemented
70#10622457C2214yescomplemented
71#10622449C2214yescomplemented
72#10622429C2214yescomplemented
73#10622424C2214yescomplemented
74#10622423C2214yescomplemented
75#10622420C2214yescomplemented
76#10622394C2214yescomplemented
77#10622386C2214yescomplemented
78#10622385C2214yescomplemented
79#10622383C2214yescomplemented
80#10622351C2212yescomplemented
81#10622345C2212yes—
82#10622339C2212yes—
83D11×C22⋊C8C2212yescomplemented
84#10622327C2212yescomplemented
85#10622325C2212yescomplemented
86#10622319C2214yescomplemented
87C24×D11—21no—
88C22×D4×C11C2311yescharacteristic
89C23×C4×C11—21no—
90C22×C22⋊D11—21no—
91C22×C22⋊D11—21no—
92C23×Dic11—21no—
93C2×#4343C2312yes—
94C2×#4343C2312yescomplemented
95C2×#4341—22no—
96C2×#4341—44no—
97C2×#4341C2314yes—
98C2×D4×D11—22no—
99C2×D4×D11—44no—
100C2×D4×D11C2314yes—
101C2×#4339—21no—
102C22×D44—21no—
103C22×D44D411yescharacteristic
104C22×D44C2311yescharacteristic
105C22×C4×D11C2311yescharacteristic
106C22×C4×D11C2311yescharacteristic
107C22×Dic22C2311yescharacteristic
108C2×C11×SD16C2314yes—
109C11×C4⋊Q8C2311yescharacteristic, complemented
110C11×C4⋊Q8C2311yescharacteristic, complemented
111C11×#125—21no—
112C11×C22⋊Q8—21no—
113C11×C22⋊Q8C2312yes—
114C4×Q8×C11—21no—
115C4×Q8×C11C2312yescomplemented
116C4×D4×C11—21no—
117C4×D4×C11—21no—
118C4×D4×C11C2312yes—
119C4×D4×C11C2312yes—
120C11×#117—21no—
121C2×C11×C4⋊C4C2311yescharacteristic
122C2×C11×C22⋊C4—21no—
123C2×C42×C11C2311yescharacteristic
124#67000—22no—
125#67000—22no—
126#66999C2312yes—
127#66999C2312yescomplemented
128C2×#4326C2314yescomplemented
129C2×#4325C2314yes—
130C2×#4323C2314yes—
131#66983—21no—
132#66983—24no—
133#66983—24no—
134#66983C2312yes—
135C2×(C2×D11)⋊C4—21no—
136C2×(C2×D11)⋊C4—21no—
137C2×(C2×D11)⋊C4—21no—
138C2×(C2×D11)⋊C4—21no—
139C2×(C2×D11)⋊C4—24no—
140C2×(C2×D11)⋊C4—24no—
141C2×(C2×D11)⋊C4D411yescharacteristic
142C2×(C2×D11)⋊C4D411yescharacteristic
143C2×C4⋊Dic11—21no—
144C2×C4⋊Dic11D411yescharacteristic
145#66969—48no—
146#66967—48no—
147C2×D88C2314yes—
148C2×#4314C2314yescomplemented
149C2×#4313C2314yes—
150C2×C8×D11C2314yescomplemented
151#66951—22no—
152#66951—22no—
153#66950—22no—
154#66950C2314yes—
155#66948—22no—
156#66948—22no—
157#66948—22no—
158#66948—22no—
159#66948—22no—
160#66948C2314yes—
161#66948C2312yes—
162#66948C2312yescomplemented
163#66947—22no—
164#66947—22no—
165#66947—22no—
166#66947—22no—
167#66946—22no—
168#66946—22no—
169#66945—22no—
170#66945C2312yes—
171#66945C2312yescomplemented
172C4⋊C4×D11—22no—
173#66939—24no—
174#66939—24no—
175#66935—22no—
176#66935—22no—
177#66935—24no—
178#66935—24no—
179(C22⋊D11)⋊C4—22no—
180(C22⋊D11)⋊C4—22no—
181#66928—22no—
182#66928—21no—
183#66928—21no—
184#66928—21no—
185#66928C2312yes—
186#66928C2312yes—
187#66927—22no—
188#66927C2311yescharacteristic, complemented
189C4×D44—21no—
190C4×D44—22no—
191C4×D44D412yes—
192C4×D44D412yes—
193C4×D44C2312yes—
194C4×D44C2312yes—
195C4×D44C2312yescomplemented
196#66922C2311yescharacteristic, complemented
197C4×Dic22—22no—
198C11×#107C2314yescomplemented
199C11×C4⋊C8C2312yescomplemented
200C11×#103C2314yescomplemented
201C11×#102C2314yes—
202C11×C22⋊C8C2312yes—
203C11×#97C2312yescomplemented
204#66896C2314yes—
205C22⋊(C11⋊C8)C2312yes—
206#66885C2314yes—
207(C2×D11)⋊C8C2314yes—
208(C2×D11)⋊C8C2314yescomplemented
209#66880C2314yescomplemented
210#66874C2314yescomplemented
211#66873C2314yes—
212#66873C2314yescomplemented
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
225C2×Q8×C11—21no—
226C2×Q8×C11C2412yes—
227C2×D4×C11—24no—
228C2×D4×C11—21no—
229C2×D4×C11C2412yes—
230C22×C4×C11—21no—
231C22×C4×C11—22no—
232C22×C4×C11—22no—
233C22×C4×C11—82no—
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2×D411yescharacteristic
236C22×C4×C11C2411yescharacteristic
237C2×C22⋊D11—24no—
238C2×C22⋊D11—22no—
239C2×C22⋊D11—24no—
240C2×C22⋊D11—44no—
241C2×C22⋊D11—44no—
242C22×Dic11—24no—
243C22×Dic11—21no—
244C22×Dic11—44no—
245C22×Dic11C2×D411yescharacteristic
246C22×Dic11C2×D411yescharacteristic
247#4343—44no—
248#4343—44no—
249#4341—28no—
250#4341—44no—
251#4341—48no—
252D4×D11—28no—
253D4×D11—44no—
254D4×D11—48no—
255#4339—44no—
256C2×D44—22no—
257C2×D44—22no—
258C2×D44—22no—
259C2×D44—22no—
260C2×D44—24no—
261C2×D44—21no—
262C2×D44—21no—
263C2×D44—21no—
264C2×D44—42no—
265C2×D44—42no—
266C2×D44—82no—
267C2×D44C2×D412yes—
268C2×D44C2×D412yes—
269C2×D44C2412yes—
270C2×D44C2412yes—
271C2×C4×D11—22no—
272C2×C4×D11—22no—
273C2×C4×D11—22no—
274C2×C4×D11—42no—
275C2×C4×D11—42no—
276C2×C4×D11C2×D412yes—
277C2×C4×D11C2×D412yes—
278C2×C4×D11C2412yes—
279C2×C4×D11C2412yes—
280C2×Dic22—21no—
281C2×Dic22—21no—
282C2×Dic22—42no—
283C2×Dic22C2412yes—
284C11×SD16—28no—
285C2×C8×C11C2414yes—
286C11×C4⋊C4—21no—
287C11×C4⋊C4—21no—
288C11×C4⋊C4—22no—
289C11×C4⋊C4—21no—
290C11×C4⋊C4—21no—
291C11×C4⋊C4—22no—
292C11×C4⋊C4C2412yes—
293C11×C4⋊C4C2412yes—
294C11×C22⋊C4—22no—
295C11×C22⋊C4—22no—
296C11×C22⋊C4—22no—
297C42×C11—22no—
298C42×C11C2×D411yescharacteristic
299C42×C11C2×D411yescharacteristic
300C42×C11C2411yescharacteristic
301C42×C11C2411yescharacteristic
302#4326—44no—
303#4325—44no—
304#4323—28no—
305(C2×D11)⋊C4—22no—
306(C2×D11)⋊C4—22no—
307(C2×D11)⋊C4—24no—
308(C2×D11)⋊C4—22no—
309(C2×D11)⋊C4—22no—
310(C2×D11)⋊C4—22no—
311(C2×D11)⋊C4—22no—
312(C2×D11)⋊C4—24no—
313(C2×D11)⋊C4—22no—
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)⋊C4C2×D412yes—
320(C2×D11)⋊C4C2×D412yes—
321(C2×D11)⋊C4C2×D412yes—
322(C2×D11)⋊C4C2×D412yes—
323C4⋊Dic11—24no—
324C4⋊Dic11—21no—
325C4⋊Dic11C2×D412yes—
326C4⋊Dic11C2×D412yes—
327C4⋊Dic11C2412yes—
328Dic11⋊C4—22no—
329Dic11⋊C4—22no—
330C4×Dic11—22no—
331C4×Dic11—22no—
332C2×C11⋊C8C2414yes—
333D88—44no—
334#4314—44no—
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#3213—111no—
345#3196—112no—
346#3188—112no—
347#3110D1111yescharacteristic, complemented
348#3109—111no—
349#3003—112no—
350#3002—112no—
351#2973—111no—
352C23×C11—24no—
353C23×C11—22no—
354C23×C11—42no—
355C23×C11—42no—
356C23×C11C22×D411yescharacteristic
357C22×D11—22no—
358C22×D11—22no—
359C22×D11—22no—
360C22×D11—22no—
361C22×D11—41no—
362C22×D11—41no—
363C22×D11—41no—
364C22×D11—41no—
365C22×D11—48no—
366C22×D11—48no—
367C22×D11—42no—
368C22×D11—42no—
369C22×D11—42no—
370C22×D11—84no—
371C22×D11—816no—
372C22×D11C22×D412yes—
373C22×D11C22×D412yes—
374Q8×C11—24no—
375Q8×C11—81no—
376D4×C11—24no—
377D4×C11—22no—
378D4×C11H(5,𝔽2)14yes—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—41no—
385C2×C4×C11—42no—
386C2×C4×C11—82no—
387C2×C4×C11—82no—
388C2×C4×C11C22×D411yescharacteristic
389C2×C4×C11C22×D411yescharacteristic
390C2×C4×C11C22×D411yescharacteristic
391C2×C4×C11C22×D411yescharacteristic
392C2×C4×C11C22×D411yescharacteristic
393C2×C4×C11C2511yescharacteristic
394C22⋊D11—48no—
395C22⋊D11—48no—
396C22⋊D11—44no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—41no—
400C2×Dic11—41no—
401C2×Dic11—48no—
402C2×Dic11—42no—
403C2×Dic11C22×D412yes—
404C2×Dic11C22×D412yes—
405D44—24no—
406D44—24no—
407D44—42no—
408D44—42no—
409D44—42no—
410D44—42no—
411D44—81no—
412D44—82no—
413D44—82no—
414D44—84no—
415D44—82no—
416D44—82no—
417C4×D11—24no—
418C4×D11—24no—
419C4×D11—42no—
420C4×D11—42no—
421C4×D11—44no—
422C4×D11—82no—
423C4×D11—82no—
424Dic22—24no—
425Dic22—42no—
426Dic22—42no—
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#533C2×D1111yescharacteristic, complemented
447#532—111no—
448C2×#124—111no—
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×D4C2×D1111yescharacteristic
459C22×C22⋊C4—221no—
460#497—112no—
461#496—112no—
462#489—112no—
463#489—112no—
464#485—114no—
465#484C2×D1112yescomplemented
466#482—114no—
467#481—112no—
468#476—112no—
469#474C2×D1112yescomplemented
470#470—114no—
471#468—114no—
472#466—114no—
473#465—114no—
474#464—114no—
475#463—114no—
476#461C2×D1112yescomplemented
477#459—112no—
478#452—114no—
479#452—114no—
480#451—112no—
481#450—114no—
482#450—112no—
483#450C2×D1112yes—
484#449—114no—
485#449—114no—
486#448—112no—
487#447—112no—
488#447—114no—
489#447—112no—
490#442—114no—
491#440C2×D1114yescomplemented
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—24no—
503C22×C11—48no—
504C22×C11—42no—
505C22×C11—42no—
506C22×C11#57512yes—
507C22×C11C23×D411yescharacteristic
508C2×D11—22no—
509C2×D11—22no—
510C2×D11—22no—
511C2×D11—22no—
512C2×D11—22no—
513C2×D11—22no—
514C2×D11—44no—
515C2×D11—42no—
516C2×D11—42no—
517C2×D11—42no—
518C2×D11—42no—
519C2×D11—42no—
520C2×D11—42no—
521C2×D11—82no—
522C2×D11—816no—
523C2×D11—84no—
524C4×C11—21no—
525C4×C11—21no—
526C4×C11—21no—
527C4×C11—21no—
528C4×C11—21no—
529C4×C11—42no—
530C4×C11—42no—
531C4×C11—42no—
532C4×C11C2×H(5,𝔽2)12yes—
533Dic11—22no—
534Dic11—22no—
535Dic11—42no—
536Dic11—42no—
537C25—221no—
538C2×#41—112no—
539C2×#41—112no—
540C2×#41—114no—
541C2×#41—222no—
542C2×#41—221no—
543C2×#41—444no—
544C22×Q8—111no—
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—21no—
555C23×C4—111no—
556C23×C4—111no—
557C23×C4—221no—
558AGL(1,ℤ/8)—448no—
559#135—448no—
560C2×Q16—114no—
561C2×SD16—114no—
562C2×SD16—114no—
563C2×SD16C22×D1114yes—
564C2×D8—114no—
565C2×D8—114no—
566C2×M16—114no—
567C22×C8—114no—
568C4⋊Q8—111no—
569C4⋊Q8C22×D1111yescharacteristic, complemented
570C4⋊Q8C22×D1111yescharacteristic, complemented
571#127—111no—
572#127—222no—
573#126—222no—
574#126—222no—
575#125—21no—
576#124—112no—
577#124—112no—
578#124—222no—
579#124—222no—
580#124—222no—
581#124—221no—
582#124—221no—
583#124—221no—
584#123—224no—
585#123—224no—
586#123—222no—
587#123—222no—
588#123—222no—
589#123—222no—
590C22⋊Q8—21no—
591C22⋊Q8—112no—
592C22⋊Q8—112no—
593C22⋊Q8—114no—
594C22⋊Q8—222no—
595C22⋊Q8C22×D1112yes—
596#121—112no—
597#121—114no—
598#121—112no—
599#121—112no—
600#121—222no—
601#121—222no—
602#121—224no—
603#121—224no—
604#121—222no—
605#121—222no—
606#121—222no—
607#121—221no—
608#120—224no—
609#120—224no—
610#120—222no—
611#120—222no—
612C4×Q8—21no—
613C4×Q8—222no—
614C4×Q8C22×D1112yescomplemented
615C4×D4—21no—
616C4×D4—21no—
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×D4C22×D1112yes—
629C4×D4C22×D1112yes—
630#117—21no—
631#117—112no—
632#117—112no—
633#117—222no—
634C2×C4⋊C4—111no—
635C2×C4⋊C4—222no—
636C2×C4⋊C4—221no—
637C2×C4⋊C4C22×D1111yescharacteristic
638C2×C22⋊C4—21no—
639C2×C22⋊C4—111no—
640C2×C22⋊C4—111no—
641C2×C22⋊C4—224no—
642C2×C22⋊C4—224no—
643C2×C22⋊C4—221no—
644C2×C22⋊C4—221no—
645C2×C22⋊C4—221no—
646C2×C22⋊C4—221no—
647C2×C42C22×D1111yescharacteristic
648#107C22×D1114yescomplemented
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—44no—
668C2×C11#348411yescharacteristic
669C2×C11C2×#57511yescharacteristic
670C2×C11#358511yescharacteristic
671D11—42no—
672D11—42no—
673D11—82no—
674D11—82no—
675C24—21no—
676C24—111no—
677C24—111no—
678C24—224no—
679C24—221no—
680C24—444no—
681C24—444no—
682C24—882no—
683#41—228no—
684#41—444no—
685#41—444no—
686#41—444no—
687#41—444no—
688#41—448no—
689C2×Q8—21no—
690C2×Q8—112no—
691C2×Q8—221no—
692C2×Q8—221no—
693C2×Q8—442no—
694C2×Q8C23×D1112yes—
695C2×D4—24no—
696C2×D4—21no—
697C2×D4—112no—
698C2×D4—112no—
699C2×D4—112no—
700C2×D4—112no—
701C2×D4—222no—
702C2×D4—222no—
703C2×D4—224no—
704C2×D4—222no—
705C2×D4—222no—
706C2×D4—224no—
707C2×D4—228no—
708C2×D4—224no—
709C2×D4—222no—
710C2×D4—221no—
711C2×D4—221no—
712C2×D4—221no—
713C2×D4—442no—
714C2×D4—442no—
715C2×D4—444no—
716C2×D4—448no—
717C2×D4—444no—
718C2×D4—444no—
719C2×D4—882no—
720C2×D4C23×D1112yes—
721C22×C4—21no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—82no—
725C22×C4—111no—
726C22×C4—111no—
727C22×C4—112no—
728C22×C4—112no—
729C22×C4—112no—
730C22×C4—112no—
731C22×C4—222no—
732C22×C4—222no—
733C22×C4—224no—
734C22×C4—221no—
735C22×C4—222no—
736C22×C4—442no—
737C22×C4—442no—
738C22×C4—444no—
739C22×C4D4×D1111yescharacteristic
740C22×C4D4×D1111yescharacteristic
741C22×C4C23×D1111yescharacteristic
742Q16—444no—
743SD16—28no—
744SD16—444no—
745SD16—444no—
746D8—228no—
747D8—444no—
748M16—444no—
749C2×C8—114no—
750C2×C8—444no—
751C2×C8C23×D1114yes—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—22no—
756C4⋊C4—21no—
757C4⋊C4—22no—
758C4⋊C4—112no—
759C4⋊C4—112no—
760C4⋊C4—112no—
761C4⋊C4—222no—
762C4⋊C4—222no—
763C4⋊C4—224no—
764C4⋊C4—221no—
765C4⋊C4C23×D1112yes—
766C4⋊C4C23×D1112yes—
767C22⋊C4—22no—
768C22⋊C4—22no—
769C22⋊C4—22no—
770C22⋊C4—112no—
771C22⋊C4—112no—
772C22⋊C4—112no—
773C22⋊C4—112no—
774C22⋊C4—224no—
775C22⋊C4—222no—
776C22⋊C4—222no—
777C22⋊C4—224no—
778C22⋊C4—222no—
779C22⋊C4—222no—
780C22⋊C4—222no—
781C22⋊C4—222no—
782C22⋊C4—222no—
783C22⋊C4—222no—
784C22⋊C4—222no—
785C22⋊C4—222no—
786C22⋊C4—222no—
787C22⋊C4—222no—
788C42—22no—
789C42—222no—
790C42—222no—
791C42D4×D1111yescharacteristic
792C42D4×D1111yescharacteristic
793C42C23×D1111yescharacteristic
794C42C23×D1111yescharacteristic
795C11#6157611yescharacteristic, complemented, Sylow
796C23—24no—
797C23—22no—
798C23—42no—
799C23—42no—
800C23—112no—
801C23—112no—
802C23—222no—
803C23—222no—
804C23—222no—
805C23—222no—
806C23—441no—
807C23—441no—
808C23—441no—
809C23—441no—
810C23—448no—
811C23—442no—
812C23—442no—
813C23—448no—
814C23—442no—
815C23—884no—
816C23—8816no—
817C23C2×D4×D1111yescharacteristic
818Q8—24no—
819Q8—81no—
820Q8—224no—
821Q8—442no—
822Q8—442no—
823D4—24no—
824D4—22no—
825D4—224no—
826D4—224no—
827D4—442no—
828D4—442no—
829D4—442no—
830D4—442no—
831D4—448no—
832D4—448no—
833D4—444no—
834D4—881no—
835D4—884no—
836D4—882no—
837D4—882no—
838D4—882no—
839D4—882no—
840D4#6704214yes—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—41no—
847C2×C4—42no—
848C2×C4—82no—
849C2×C4—82no—
850C2×C4—112no—
851C2×C4—112no—
852C2×C4—224no—
853C2×C4—224no—
854C2×C4—222no—
855C2×C4—222no—
856C2×C4—442no—
857C2×C4—442no—
858C2×C4—444no—
859C2×C4—441no—
860C2×C4—441no—
861C2×C4—448no—
862C2×C4—442no—
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—24no—
876C22—48no—
877C22—42no—
878C22—42no—
879C22—222no—
880C22—222no—
881C22—222no—
882C22—222no—
883C22—222no—
884C22—222no—
885C22—444no—
886C22—442no—
887C22—442no—
888C22—442no—
889C22—442no—
890C22—442no—
891C22—442no—
892C22—882no—
893C22—884no—
894C22—8816no—
895C22#1062330812yes—
896C22C22×D4×D1111yescharacteristic
897C4—21no—
898C4—21no—
899C4—21no—
900C4—21no—
901C4—21no—
902C4—42no—
903C4—42no—
904C4—42no—
905C4—222no—
906C4—222no—
907C4—442no—
908C4—442no—
909C4C2×#6704212yes—
910C2—22no—
911C2—44no—
912C2—442no—
913C2—442no—
914C2—882no—
915C2—882no—
916C2#1308224911yescharacteristic
917C2C2×#1062330811yescharacteristic
918C2#1308339211yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3110C2
socleC22×C11C23×D4
hypercenter#3110D11
hypocenterC11#61576
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3110

Complements

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

NH ≅ G/Ntype
1. #13082470C2semidirect
2. C2×#10623085C2semidirect
3. #13080769C2semidirect
4. #13080657C2semidirect
5. #13080158C2semidirect
6. #13080147C2semidirect
7. #13079615C2semidirect
8. #13079605C2semidirect
9. #13079451C2semidirect
10. #13079386C2semidirect
11. #13078707C2semidirect
12. #13077844C2semidirect
13. #13077835C2semidirect
14. #13077644C2semidirect
15. C11×#3110C2semidirect
18. C11×#533C22semidirect
22. C2×#66969C22semidirect
23. C2×#66967C22semidirect
24. #10623265C22semidirect
25. #10623257C22semidirect
30. #10623158C22semidirect
32. #10623115C22semidirect
33. #10623108C22semidirect
44. #10623008C22semidirect
47. C11×#484C22semidirect
48. C11×#474C22semidirect
49. C11×#461C22semidirect
51. C11×#440C22semidirect
52. C11×#432C22semidirect
54. #10622786C22semidirect
55. #10622782C22semidirect
56. #10622702C22semidirect
57. #10622699C22semidirect
58. #10622663C22semidirect
60. #10622641C22semidirect
61. #10622628C22semidirect
62. #10622627C22semidirect
63. #10622621C22semidirect
64. #10622581C22semidirect
65. #10622539C22semidirect
66. #10622501C22semidirect
67. #10622499C22semidirect
68. #10622498C22semidirect
69. #10622496C22semidirect
70. #10622457C22semidirect
71. #10622449C22semidirect
72. #10622429C22semidirect
73. #10622424C22semidirect
74. #10622423C22semidirect
75. #10622420C22semidirect
76. #10622394C22semidirect
77. #10622386C22semidirect
78. #10622385C22semidirect
79. #10622383C22semidirect
80. #10622351C22semidirect
83. D11×C22⋊C8C22semidirect
84. #10622327C22semidirect
85. #10622325C22semidirect
86. #10622319C22semidirect
94. C2×#4343C23semidirect
109. C11×C4⋊Q8C23semidirect
110. C11×C4⋊Q8C23semidirect
115. C4×Q8×C11C23semidirect
127. #66999C23semidirect
128. C2×#4326C23semidirect
148. C2×#4314C23semidirect
150. C2×C8×D11C23semidirect
162. #66948C23semidirect
171. #66945C23semidirect
188. #66927C23semidirect
195. C4×D44C23semidirect
196. #66922C23semidirect
198. C11×#107C23semidirect
199. C11×C4⋊C8C23semidirect
200. C11×#103C23semidirect
203. C11×#97C23semidirect
208. (C2×D11)⋊C8C23semidirect
209. #66880C23semidirect
210. #66874C23semidirect
212. #66873C23semidirect
213. #66872C23semidirect
214. C4⋊(C11⋊C8)C23semidirect
215. #66867C23semidirect
347. #3110D11semidirect
446. #533C2×D11semidirect
465. #484C2×D11semidirect
469. #474C2×D11semidirect
476. #461C2×D11semidirect
491. #440C2×D11semidirect
495. #432C2×D11semidirect
569. C4⋊Q8C22×D11semidirect
570. C4⋊Q8C22×D11semidirect
614. C4×Q8C22×D11semidirect
648. #107C22×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
#130824702
C2×#106230852
#130807692
#130806572
#130801582
#130801472
#130796152
#130796052
#130794512
#130793862
#130787072
#130778442
#130778352
#130776442
C11×#31102
#6157611