Finite Group Databasebeta

← #15638516

Subgroups — #15638516

Order 2816.

2142 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082455C211yesmaximal, characteristic, complemented
2C2×#10623083C211yesmaximal, characteristic, complemented
3#13080520C214yesmaximal, complemented
4#13080505C214yesmaximal, complemented
5#13080359C214yesmaximal, complemented
6#13080328C214yesmaximal, complemented
7#13079583C212yesmaximal, complemented
8#13079399C212yesmaximal, complemented
9#13079374C211yesmaximal, characteristic, complemented
10#13079367C211yesmaximal, characteristic, complemented
11#13078698C212yesmaximal, complemented
12#13077838C212yesmaximal, complemented
13C2×#10622352C211yesmaximal, characteristic, complemented
14C2×#10622351C211yesmaximal, characteristic, complemented
15C11×#2972C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic, complemented
17C23×Dic22C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19#10623335—21no—
20C2×#66992—21no—
21#10623322C2212yes—
22C2×#66983C2211yescharacteristic
23C2×#66983C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C2×#66977C2211yescharacteristic, complemented
26C22×Dic44C2212yescomplemented
27C2×#66957C2214yescomplemented
28C22×#4314C2212yescomplemented
29#10623096C2212yescomplemented
30#10623087—22no—
31#10623083—22no—
32#10623083—22no—
33#10623083C2214yes—
34#10623083C2212yescomplemented
35#10623083C2214yescomplemented
36#10623081C2212yescomplemented
37#10623072C2212yescomplemented
38#10623071—22no—
39#10623046—21no—
40C2×#66949—21no—
41#10623025—21no—
42C2×#66938—21no—
43#10623017—21no—
44C2×(C22⋊D11)⋊C4—21no—
45#10623010C2212yes—
46C2×#66928C2211yescharacteristic, complemented
47C2×C4×Dic22C2211yescharacteristic, complemented
48C8×D4×C11C2214yescomplemented
49C8×D4×C11C2214yescomplemented
50C11×#431C2212yescomplemented
51C2×C11×C22⋊C8C2211yescharacteristic
52C2×C11×C22⋊C8C2211yescharacteristic
53C2×C11×C22⋊C8C2212yescomplemented
54#10622729C2214yescomplemented
55#10622728C2214yescomplemented
56#10622727C2214yescomplemented
57#10622727C2214yescomplemented
58#10622726C2214yescomplemented
59C2×#66880C2212yescomplemented
60C2×#66880C2212yescomplemented
61#10622458C2214yescomplemented
62#10622458C2214yescomplemented
63#10622457C2214yescomplemented
64#10622442C2214yescomplemented
65#10622352C2214yescomplemented
66#10622352C2212yescomplemented
67#10622352C2212yescomplemented
68#10622351C2212yes—
69#10622351C2212yes—
70#10622351C2212yescomplemented
71#10622351C2214yescomplemented
72#10622349C2212yes—
73#10622349C2212yescomplemented
74#10622348C2212yescomplemented
75#10622347C2214yescomplemented
76#10622346C2214yescomplemented
77#10622346C2214yescomplemented
78#10622345C2212yes—
79#10622345C2212yescomplemented
80#10622344C2212yescomplemented
81#10622336C2214yescomplemented
82#10622334C2212yescomplemented
83C4×Dic44C2214yescomplemented
84#10622310C2214yescomplemented
85#10622309C2214yescomplemented
86C4×#4314C2214yescomplemented
87C22×D4×C11D411yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C22×C22⋊D11—21no—
91C22×C22⋊D11—21no—
92C22×C22⋊D11—21no—
93C23×Dic11—21no—
94C2×#4339—22no—
95C2×#4339—44no—
96C2×#4339C2314yes—
97C2×#4339C2312yes—
98C22×D44C2311yescharacteristic
99C22×D44C2311yescharacteristic
100C22×C4×D11—21no—
101C22×Dic22—21no—
102C22×Dic22—21no—
103C22×Dic22—21no—
104C22×Dic22—44no—
105C22×Dic22C2311yescharacteristic
106C22×Dic22C2312yes—
107C22×Dic22C2312yes—
108C22×Dic22C2311yescharacteristic
109C22×Dic22C2311yescharacteristic
110C22×C8×C11C2314yes—
111C22×C8×C11C2312yes—
112C22×C8×C11C2312yes—
113C4×D4×C11D412yes—
114C4×D4×C11D412yes—
115C4×D4×C11C2312yes—
116C4×D4×C11C2312yes—
117C2×C11×C4⋊C4D411yescharacteristic
118C2×C11×C22⋊C4D411yescharacteristic
119C2×C11×C22⋊C4D411yescharacteristic
120C2×C42×C11C2311yescharacteristic
121#67006—22no—
122C2×C22⋊Dic11—21no—
123C2×C22⋊Dic11—21no—
124#66992—22no—
125#66992—22no—
126#66992—24no—
127#66992—24no—
128#66990—22no—
129#66988—22no—
130#66983—21no—
131#66983—21no—
132#66983—21no—
133#66983—21no—
134#66983C2312yes—
135#66983C2312yes—
136#66983C2312yes—
137#66983C2312yes—
138#66983C2312yes—
139#66982—22no—
140#66982—22no—
141C4×C22⋊D11—22no—
142C4×C22⋊D11—22no—
143C4×C22⋊D11—22no—
144C2×(C2×D11)⋊C4—21no—
145C2×(C2×D11)⋊C4—21no—
146C2×(C2×D11)⋊C4—21no—
147C2×(C2×D11)⋊C4—21no—
148#66979C2312yes—
149C2×C4⋊Dic11C2311yescharacteristic
150C2×C4⋊Dic11C2311yescharacteristic
151C2×C4⋊Dic11C2311yescharacteristic
152#66977—21no—
153#66977—21no—
154#66977—22no—
155#66977C2312yes—
156#66977C2314yes—
157#66977C2312yes—
158#66977C2312yes—
159C2×Dic11⋊C4—21no—
160C2×Dic11⋊C4—21no—
161C2×Dic11⋊C4—21no—
162C2×C4×Dic11—21no—
163C2×Dic44—44no—
164C2×Dic44C2314yes—
165C2×Dic44C2314yes—
166#66957—48no—
167C2×D88C2314yes—
168C2×#4314—44no—
169C2×#4314C2314yes—
170C2×#4314C2314yes—
171C2×#4314C2314yes—
172#66951—22no—
173#66949—24no—
174#66949—24no—
175#66949—22no—
176#66947—22no—
177#66942—22no—
178#66938—24no—
179#66938—24no—
180#66938—22no—
181#66937—22no—
182#66936—22no—
183(C22⋊D11)⋊C4—24no—
184(C22⋊D11)⋊C4—24no—
185(C22⋊D11)⋊C4—22no—
186(C22⋊D11)⋊C4—22no—
187C22⋊C4×D11—22no—
188#66932—22no—
189#66930—22no—
190#66929—22no—
191#66928—22no—
192#66928C2314yes—
193#66928C2312yes—
194C4×D44C2312yes—
195#66925—22no—
196#66923C2312yes—
197C4×Dic22—22no—
198C4×Dic22C2314yes—
199C4×Dic22C2312yes—
200C11×C4⋊C8C2314yes—
201C11×C22⋊C8C2312yes—
202C11×C22⋊C8C2314yes—
203C11×C22⋊C8C2312yes—
204C11×C22⋊C8C2312yes—
205C11×C22⋊C8C2312yes—
206C4×C8×C11C2314yes—
207#66885C2314yes—
208#66885C2314yes—
209#66885C2314yes—
210#66882C2314yes—
211#66881C2314yes—
212#66880C2314yes—
213#66880C2314yes—
214#66880C2314yes—
215#66880C2314yes—
216#66880C2314yes—
217#61564—111nomaximal, Sylow
218C24×C11C2×D411yescharacteristic
219C24×C11C2×D411yescharacteristic
220C23×D11—21no—
221C23×D11—21no—
222C2×D4×C11—24no—
223C2×D4×C11C2×D412yes—
224C2×D4×C11C2×D412yes—
225C22×C4×C11—42no—
226C22×C4×C11—42no—
227C22×C4×C11C2×D411yescharacteristic
228C22×C4×C11C2×D411yescharacteristic
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2×D411yescharacteristic
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2×D412yes—
234C22×C4×C11C2411yescharacteristic
235C22×C4×C11C2412yes—
236C22×C4×C11C2411yescharacteristic
237C22×C4×C11C2411yescharacteristic
238C2×C22⋊D11—22no—
239C2×C22⋊D11—22no—
240C2×C22⋊D11—22no—
241C2×C22⋊D11—24no—
242C2×C22⋊D11—22no—
243C2×C22⋊D11—22no—
244C2×C22⋊D11—22no—
245C2×C22⋊D11—44no—
246C2×C22⋊D11—44no—
247C2×C22⋊D11—44no—
248C22×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—22no—
251C22×Dic11—22no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—44no—
257#4339—28no—
258#4339—44no—
259#4339—44no—
260#4339—48no—
261C2×D44—21no—
262C2×D44—21no—
263C2×D44—42no—
264C2×D44—42no—
265C2×D44C2412yes—
266C2×D44C2412yes—
267C2×C4×D11—24no—
268C2×C4×D11—22no—
269C2×C4×D11—22no—
270C2×C4×D11—44no—
271C2×Dic22—24no—
272C2×Dic22—24no—
273C2×Dic22—24no—
274C2×Dic22—21no—
275C2×Dic22—21no—
276C2×Dic22—22no—
277C2×Dic22—22no—
278C2×Dic22—21no—
279C2×Dic22—42no—
280C2×Dic22—42no—
281C2×Dic22—42no—
282C2×Dic22—42no—
283C2×Dic22—44no—
284C2×Dic22—44no—
285C2×Dic22—44no—
286C2×Dic22C2412yes—
287C2×Dic22C2412yes—
288C2×Dic22C2412yes—
289C2×C8×C11—42no—
290C2×C8×C11—44no—
291C2×C8×C11—42no—
292C2×C8×C11C2414yes—
293C2×C8×C11C2414yes—
294C11×C4⋊C4C2×D412yes—
295C11×C4⋊C4C2×D412yes—
296C11×C22⋊C4C2×D412yes—
297C11×C22⋊C4C2×D412yes—
298C11×C22⋊C4C2×D412yes—
299C11×C22⋊C4C2×D412yes—
300C42×C11C2×D412yes—
301C42×C11C2412yes—
302C22⋊Dic11—22no—
303C22⋊Dic11—22no—
304C22⋊Dic11—22no—
305C22⋊Dic11—24no—
306C22⋊Dic11—22no—
307(C2×D11)⋊C4—22no—
308(C2×D11)⋊C4—22no—
309(C2×D11)⋊C4—22no—
310(C2×D11)⋊C4—24no—
311(C2×D11)⋊C4—24no—
312(C2×D11)⋊C4—22no—
313(C2×D11)⋊C4—22no—
314(C2×D11)⋊C4—22no—
315(C2×D11)⋊C4—22no—
316(C2×D11)⋊C4—22no—
317C4⋊Dic11—21no—
318C4⋊Dic11—21no—
319C4⋊Dic11—21no—
320C4⋊Dic11C2412yes—
321C4⋊Dic11C2412yes—
322C4⋊Dic11C2412yes—
323Dic11⋊C4—24no—
324Dic11⋊C4—22no—
325Dic11⋊C4—22no—
326Dic11⋊C4—22no—
327Dic11⋊C4—22no—
328Dic11⋊C4—22no—
329Dic11⋊C4—22no—
330Dic11⋊C4—24no—
331C4×Dic11—24no—
332C4×Dic11—22no—
333C4×Dic11—22no—
334Dic44—28no—
335Dic44—44no—
336D88—44no—
337#4314—28no—
338#4314—44no—
339#4314—44no—
340#3505—111no—
341C2×#548—111no—
342#3301—114no—
343#3300—114no—
344#3285—114no—
345#3282—114no—
346#3211—112no—
347#3190—112no—
348#3187—111no—
349#3186—111no—
350#3108—112no—
351#3002—112no—
352C2×#451—111no—
353C2×#448—111no—
354#2972D1111yescharacteristic, complemented
355C23×C11—22no—
356C23×C11—41no—
357C23×C11—41no—
358C23×C11—41no—
359C23×C11—41no—
360C23×C11#13514yescomplemented
361C23×C11C22×D412yes—
362C23×C11C22×D411yescharacteristic
363C23×C11C22×D411yescharacteristic
364C23×C11C22×D411yescharacteristic
365C22×D11—22no—
366C22×D11—22no—
367C22×D11—42no—
368C22×D11—42no—
369C22×D11—42no—
370C22×D11—42no—
371C22×D11—81no—
372C22×D11—81no—
373D4×C11—24no—
374D4×C11—24no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—24no—
379C2×C4×C11—22no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—42no—
385C2×C4×C11—41no—
386C2×C4×C11C22×D412yes—
387C2×C4×C11C22×D412yes—
388C2×C4×C11C22×D412yes—
389C2×C4×C11C22×D411yescharacteristic
390C2×C4×C11C22×D411yescharacteristic
391C2×C4×C11C22×D411yescharacteristic
392C2×C4×C11C2511yescharacteristic
393C22⋊D11—48no—
394C22⋊D11—44no—
395C22⋊D11—44no—
396C22⋊D11—44no—
397C22⋊D11—44no—
398C22⋊D11—82no—
399C22⋊D11—82no—
400C2×Dic11—24no—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—22no—
404C2×Dic11—22no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—44no—
408C2×Dic11—44no—
409C2×Dic11—42no—
410C2×Dic11—42no—
411C2×Dic11—42no—
412C2×Dic11—81no—
413C2×Dic11—81no—
414D44—24no—
415D44—24no—
416D44—42no—
417D44—81no—
418C4×D11—48no—
419C4×D11—82no—
420C4×D11—82no—
421Dic22—24no—
422Dic22—22no—
423Dic22—22no—
424Dic22—24no—
425Dic22—22no—
426Dic22—44no—
427Dic22—44no—
428Dic22—42no—
429Dic22—81no—
430Dic22H(5,𝔽2)14yes—
431C8×C11—24no—
432C8×C11—24no—
433C22×#41—111no—
434C23×Q8—111no—
435C2×#135—114no—
436C22×Q16—112no—
437C22×SD16—112no—
438#553—112no—
439#553—222no—
440#552—112no—
441#551—222no—
442#548—114no—
443#548—114no—
444#548—112no—
445#548—222no—
446#548—222no—
447#546—112no—
448#539—221no—
449#538—221no—
450#534—221no—
451#529—112no—
452C2×#124—111no—
453C2×#124—221no—
454#525—112no—
455C2×C22⋊Q8—111no—
456C2×C22⋊Q8—111no—
457C2×C22⋊Q8—221no—
458C2×#121—111no—
459C2×#121—111no—
460C2×#121—221no—
461#518—221no—
462C2×C4×Q8—111no—
463C2×C4×D4—221no—
464C2×C4×D4C2×D1111yescharacteristic
465#495—114no—
466#488—114no—
467#485—114no—
468#483—112no—
469#481—112no—
470#480—112no—
471#480—112no—
472#479—114no—
473#467—114no—
474#466—114no—
475#465—114no—
476#465—114no—
477#464—114no—
478#464—114no—
479#463—114no—
480#452—114no—
481#452—114no—
482#451—112no—
483#451—112no—
484#451—114no—
485#450—112no—
486#449—114no—
487#448—112no—
488#448—112no—
489#448—112no—
490#448—114no—
491#447—112no—
492#447—112no—
493C4×Q16—114no—
494C4×SD16—114no—
495C8×D4C2×D1114yescomplemented
496C8×D4C2×D1114yescomplemented
497#431C2×D1112yescomplemented
498#416—114no—
499C2×#103—112no—
500C2×#103—112no—
501C2×C22⋊C8C2×D1111yescharacteristic
502C2×C22⋊C8C2×D1111yescharacteristic
503C2×C22⋊C8C2×D1112yescomplemented
504C22×C11—21no—
505C22×C11—21no—
506C22×C11—21no—
507C22×C11—21no—
508C22×C11—21no—
509C22×C11—21no—
510C22×C11—22no—
511C22×C11—22no—
512C22×C11—22no—
513C22×C11—44no—
514C22×C11—82no—
515C22×C11C2×#13512yes—
516C22×C11C2×#13512yes—
517C22×C11C2×#13512yes—
518C22×C11C23×D411yescharacteristic
519C2×D11—42no—
520C2×D11—42no—
521C2×D11—42no—
522C2×D11—42no—
523C2×D11—42no—
524C2×D11—42no—
525C2×D11—84no—
526C2×D11—162no—
527C4×C11—22no—
528C4×C11—21no—
529C4×C11—21no—
530C4×C11—21no—
531C4×C11—22no—
532C4×C11—22no—
533C4×C11C2×H(5,𝔽2)12yes—
534Dic11—24no—
535Dic11—42no—
536Dic11—42no—
537Dic11—42no—
538Dic11—42no—
539Dic11—42no—
540C2×#41—114no—
541C2×#41—112no—
542C2×#41—222no—
543C2×#41—444no—
544C22×Q8—111no—
545C22×Q8—112no—
546C22×Q8—112no—
547C22×Q8—111no—
548C22×Q8—111no—
549C22×Q8—221no—
550C22×Q8—221no—
551C22×Q8—221no—
552C22×Q8—444no—
553C22×D4—111no—
554C22×D4—111no—
555C22×D4—221no—
556C22×D4—221no—
557C22×D4—221no—
558C22×D4D4411yescharacteristic
559C23×C4—221no—
560C23×C4—221no—
561C23×C4C22×D1111yescharacteristic
562C23×C4C22×D1111yescharacteristic
563#135—448no—
564C2×Q16—114no—
565C2×Q16—114no—
566C2×Q16—444no—
567C2×SD16—114no—
568C2×SD16—114no—
569C2×SD16—114no—
570C2×SD16—444no—
571C2×D8—114no—
572C22×C8C22×D1112yes—
573C22×C8C22×D1112yes—
574C22×C8C22×D1114yes—
575#126—222no—
576#126—222no—
577#126—222no—
578#125—112no—
579#125—222no—
580#124—114no—
581#124—112no—
582#124—224no—
583#124—224no—
584#124—222no—
585#124—222no—
586#123—222no—
587#123—222no—
588#123—222no—
589#123—222no—
590#123—222no—
591C22⋊Q8—112no—
592C22⋊Q8—112no—
593C22⋊Q8—114no—
594C22⋊Q8—112no—
595C22⋊Q8—221no—
596C22⋊Q8—222no—
597C22⋊Q8—221no—
598C22⋊Q8—224no—
599C22⋊Q8—224no—
600C22⋊Q8—222no—
601#121—112no—
602#121—112no—
603#121—112no—
604#121—112no—
605#121—112no—
606#121—224no—
607#121—224no—
608#121—222no—
609#121—222no—
610#121—221no—
611#121—221no—
612#121—221no—
613#121—221no—
614#121—222no—
615#120—222no—
616#120—222no—
617C4×Q8—114no—
618C4×Q8—112no—
619C4×Q8—222no—
620C4×D4—112no—
621C4×D4—222no—
622C4×D4—222no—
623C4×D4—222no—
624C4×D4—224no—
625C4×D4—224no—
626C4×D4—222no—
627C4×D4—222no—
628C4×D4D4412yes—
629C4×D4D4412yes—
630C4×D4C22×D1112yes—
631C4×D4C22×D1112yes—
632#117—112no—
633#117—222no—
634#117—222no—
635C2×C4⋊C4—111no—
636C2×C4⋊C4—111no—
637C2×C4⋊C4—111no—
638C2×C4⋊C4—221no—
639C2×C4⋊C4—221no—
640C2×C4⋊C4—221no—
641C2×C4⋊C4D4411yescharacteristic
642C2×C22⋊C4—221no—
643C2×C22⋊C4—221no—
644C2×C22⋊C4—221no—
645C2×C22⋊C4—221no—
646C2×C22⋊C4—221no—
647C2×C22⋊C4—221no—
648C2×C22⋊C4—222no—
649C2×C22⋊C4D4411yescharacteristic
650C2×C22⋊C4D4411yescharacteristic
651C2×C42—221no—
652C2×C42C22×D1111yescharacteristic
653#107—114no—
654#106—114no—
655C4⋊C8C22×D1114yes—
656#103—114no—
657#103—114no—
658#103—114no—
659#103—114no—
660#103—114no—
661#102—114no—
662#102—114no—
663#102—114no—
664C22⋊C8C22×D1112yes—
665C22⋊C8C22×D1112yes—
666C22⋊C8C22×D1112yes—
667C22⋊C8C22×D1112yes—
668C22⋊C8C22×D1114yes—
669C4×C8C22×D1114yes—
670C2×C11—22no—
671C2×C11—22no—
672C2×C11—22no—
673C2×C11—42no—
674C2×C11#348411yescharacteristic
675C2×C11C22×#13511yescharacteristic
676C2×C11#358611yescharacteristic
677D11—82no—
678D11—82no—
679C24—221no—
680C24—221no—
681C24C2×D4411yescharacteristic
682C24C2×D4411yescharacteristic
683#41—228no—
684#41—444no—
685#41—444no—
686#41—448no—
687C2×Q8—112no—
688C2×Q8—112no—
689C2×Q8—112no—
690C2×Q8—224no—
691C2×Q8—224no—
692C2×Q8—224no—
693C2×Q8—221no—
694C2×Q8—222no—
695C2×Q8—222no—
696C2×Q8—221no—
697C2×Q8—221no—
698C2×Q8—442no—
699C2×Q8—442no—
700C2×Q8—442no—
701C2×Q8—442no—
702C2×Q8—444no—
703C2×Q8—444no—
704C2×Q8—444no—
705C2×D4—24no—
706C2×D4—112no—
707C2×D4—112no—
708C2×D4—222no—
709C2×D4—222no—
710C2×D4—222no—
711C2×D4—222no—
712C2×D4—224no—
713C2×D4—222no—
714C2×D4—222no—
715C2×D4—221no—
716C2×D4—221no—
717C2×D4—442no—
718C2×D4—442no—
719C2×D4—444no—
720C2×D4—444no—
721C2×D4—444no—
722C2×D4C2×D4412yes—
723C2×D4C2×D4412yes—
724C22×C4—42no—
725C22×C4—42no—
726C22×C4—221no—
727C22×C4—221no—
728C22×C4—221no—
729C22×C4—221no—
730C22×C4—222no—
731C22×C4—222no—
732C22×C4—221no—
733C22×C4—221no—
734C22×C4—224no—
735C22×C4—222no—
736C22×C4—222no—
737C22×C4—444no—
738C22×C4—444no—
739C22×C4C2×D4411yescharacteristic
740C22×C4C2×D4411yescharacteristic
741C22×C4C2×D4411yescharacteristic
742C22×C4C2×D4411yescharacteristic
743C22×C4C2×D4411yescharacteristic
744C22×C4C2×D4411yescharacteristic
745C22×C4C2×D4412yes—
746C22×C4C23×D1111yescharacteristic
747C22×C4C23×D1111yescharacteristic
748C22×C4C23×D1111yescharacteristic
749C22×C4C23×D1112yes—
750Q16—228no—
751Q16—444no—
752SD16—228no—
753SD16—444no—
754SD16—444no—
755D8—444no—
756C2×C8—42no—
757C2×C8—42no—
758C2×C8—44no—
759C2×C8C23×D1114yes—
760C2×C8C23×D1114yes—
761C4⋊C4—112no—
762C4⋊C4—112no—
763C4⋊C4—112no—
764C4⋊C4—221no—
765C4⋊C4—221no—
766C4⋊C4—221no—
767C4⋊C4—222no—
768C4⋊C4—224no—
769C4⋊C4—224no—
770C4⋊C4—222no—
771C4⋊C4—222no—
772C4⋊C4—222no—
773C4⋊C4—222no—
774C4⋊C4—222no—
775C4⋊C4C2×D4412yes—
776C4⋊C4C2×D4412yes—
777C22⋊C4—222no—
778C22⋊C4—222no—
779C22⋊C4—224no—
780C22⋊C4—222no—
781C22⋊C4—222no—
782C22⋊C4—222no—
783C22⋊C4—222no—
784C22⋊C4—222no—
785C22⋊C4—224no—
786C22⋊C4—222no—
787C22⋊C4—222no—
788C22⋊C4—222no—
789C22⋊C4—224no—
790C22⋊C4—222no—
791C22⋊C4—222no—
792C22⋊C4C2×D4412yes—
793C22⋊C4C2×D4412yes—
794C22⋊C4C2×D4412yes—
795C22⋊C4C2×D4412yes—
796C42—224no—
797C42—222no—
798C42—222no—
799C42C2×D4412yes—
800C42C23×D1112yes—
801C11#6156411yescharacteristic, complemented, Sylow
802C23—22no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—222no—
808C23—222no—
809C23—442no—
810C23—442no—
811C23—442no—
812C23—442no—
813C23—881no—
814C23—881no—
815C23#6695714yescomplemented
816C23C22×D4412yes—
817C23C22×D4411yescharacteristic
818C23C22×D4411yescharacteristic
819C23C22×D4411yescharacteristic
820Q8—114no—
821Q8—224no—
822Q8—222no—
823Q8—222no—
824Q8—224no—
825Q8—222no—
826Q8—444no—
827Q8—444no—
828Q8—442no—
829Q8—881no—
830D4—24no—
831D4—24no—
832D4—224no—
833D4—224no—
834D4—442no—
835D4—448no—
836D4—444no—
837D4—444no—
838D4—444no—
839D4—444no—
840D4—881no—
841D4—882no—
842D4—882no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—24no—
847C2×C4—22no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—42no—
853C2×C4—41no—
854C2×C4—224no—
855C2×C4—222no—
856C2×C4—222no—
857C2×C4—222no—
858C2×C4—222no—
859C2×C4—222no—
860C2×C4—222no—
861C2×C4—448no—
862C2×C4—444no—
863C2×C4—444no—
864C2×C4—442no—
865C2×C4—442no—
866C2×C4—442no—
867C2×C4—882no—
868C2×C4—882no—
869C2×C4—881no—
870C2×C4—881no—
871C2×C4C22×D4412yes—
872C2×C4C22×D4412yes—
873C2×C4C22×D4411yescharacteristic
874C2×C4C22×D4412yes—
875C2×C4C22×D4411yescharacteristic
876C2×C4C22×D4411yescharacteristic
877C2×C4C24×D1111yescharacteristic
878C8—24no—
879C8—24no—
880C22—21no—
881C22—21no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—22no—
887C22—22no—
888C22—22no—
889C22—44no—
890C22—82no—
891C22—442no—
892C22—442no—
893C22—442no—
894C22—442no—
895C22—442no—
896C22—442no—
897C22—884no—
898C22—1762no—
899C22C2×#6695712yes—
900C22C2×#6695712yes—
901C22C2×#6695712yes—
902C22C23×D4411yescharacteristic
903C4—22no—
904C4—21no—
905C4—22no—
906C4—21no—
907C4—21no—
908C4—22no—
909C4—224no—
910C4—442no—
911C4—442no—
912C4—442no—
913C4—442no—
914C4—442no—
915C4D11×H(5,𝔽2)12yes—
916C2—22no—
917C2—22no—
918C2—22no—
919C2—42no—
920C2—882no—
921C2—882no—
922C2#1308225211yescharacteristic
923C2C22×#6695711yescharacteristic
924C2#1308340411yescharacteristic
subgroupG/H
centerC22C23×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#2972C2
socleC22×C11C23×D4
hypercenter#2972D11
hypocenterC11#61564
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2972

Complements

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

NH ≅ G/Ntype
1. #13082455C2semidirect
2. C2×#10623083C2semidirect
3. #13080520C2semidirect
4. #13080505C2semidirect
5. #13080359C2semidirect
6. #13080328C2semidirect
7. #13079583C2semidirect
8. #13079399C2semidirect
9. #13079374C2semidirect
10. #13079367C2semidirect
11. #13078698C2semidirect
12. #13077838C2semidirect
13. C2×#10622352C2semidirect
14. C2×#10622351C2semidirect
15. C11×#2972C2semidirect
16. C22×#4339C22semidirect
25. C2×#66977C22semidirect
26. C22×Dic44C22semidirect
27. C2×#66957C22semidirect
28. C22×#4314C22semidirect
29. #10623096C22semidirect
34. #10623083C22semidirect
35. #10623083C22semidirect
36. #10623081C22semidirect
37. #10623072C22semidirect
46. C2×#66928C22semidirect
47. C2×C4×Dic22C22semidirect
48. C8×D4×C11C22semidirect
49. C8×D4×C11C22semidirect
50. C11×#431C22semidirect
53. C2×C11×C22⋊C8C22semidirect
54. #10622729C22semidirect
55. #10622728C22semidirect
56. #10622727C22semidirect
57. #10622727C22semidirect
58. #10622726C22semidirect
59. C2×#66880C22semidirect
60. C2×#66880C22semidirect
61. #10622458C22semidirect
62. #10622458C22semidirect
63. #10622457C22semidirect
64. #10622442C22semidirect
65. #10622352C22semidirect
66. #10622352C22semidirect
67. #10622352C22semidirect
70. #10622351C22semidirect
71. #10622351C22semidirect
73. #10622349C22semidirect
74. #10622348C22semidirect
75. #10622347C22semidirect
76. #10622346C22semidirect
77. #10622346C22semidirect
79. #10622345C22semidirect
80. #10622344C22semidirect
81. #10622336C22semidirect
82. #10622334C22semidirect
83. C4×Dic44C22semidirect
84. #10622310C22semidirect
85. #10622309C22semidirect
86. C4×#4314C22semidirect
354. #2972D11semidirect
360. C23×C11#135semidirect
495. C8×D4C2×D11semidirect
496. C8×D4C2×D11semidirect
497. #431C2×D11semidirect
503. C2×C22⋊C8C2×D11semidirect
801. C11#61564semidirect
815. C23#66957semidirect

Maximal subgroups

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

subgroupindex
#130824552
C2×#106230832
#130805202
#130805052
#130803592
#130803282
#130795832
#130793992
#130793742
#130793672
#130786982
#130778382
C2×#106223522
C2×#106223512
C11×#29722
#6156411