Finite Group Databasebeta

← #15625870

Subgroups — #15625870

Order 2816.

1800 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#13081912C211yesmaximal, characteristic
2C2×#10623001C211yesmaximal, characteristic, complemented
3#13079797C214yesmaximal, complemented
4#13079786C214yesmaximal, complemented
5#13079777C212yesmaximal, complemented
6#13079769C211yesmaximal, characteristic, complemented
7#13079762C211yesmaximal, characteristic, complemented
8#13079754C212yesmaximal, complemented
9#13079746C211yesmaximal, characteristic, complemented
10#13079739C211yesmaximal, characteristic, complemented
11#13079130C212yesmaximal, complemented
12#13078939C212yesmaximal, complemented
13#13078531C214yesmaximal, complemented
14#13078406C214yesmaximal, complemented
15C2×C11×#431C211yesmaximal, characteristic, complemented
16C22×C42×C11C2211yescharacteristic
17#10623322—21no—
18#10623322—21no—
19#10623322C2212yes—
20C2×#66979C2212yes—
21C2×#66977—21no—
22C2×#66977—21no—
23#10623010—21no—
24#10623010—21no—
25#10623010—21no—
26#10623010—21no—
27#10623010C2212yes—
28#10623010C2212yes—
29#10623008C2211yescharacteristic
30#10623008C2211yescharacteristic
31#10623008C2211yescharacteristic
32C4×#4339—21no—
33C4×#4339—21no—
34C4×#4339C2212yes—
35#10623001—21no—
36#10623001—21no—
37#10623001—21no—
38#10623001—21no—
39#10623001C2212yes—
40#10623001C2212yes—
41#10623001C2212yes—
42#10623001C2212yes—
43#10623001C2211yescharacteristic
44#10623001C2211yescharacteristic
45#10623001C2211yescharacteristic
46C2×#66923C2212yes—
47C2×#66922C2211yescharacteristic
48C2×#66922C2211yescharacteristic
49C2×C4×Dic22—21no—
50C2×C4×Dic22—21no—
51C11×#431C2211yescharacteristic
52C11×#431C2211yescharacteristic
53C11×#431C2212yes—
54C11×#431C2212yes—
55C11×#431C2212yes—
56C2×C11×C4⋊C8C2212yes—
57C2×C11×C22⋊C8C2212yes—
58C2×C4×C8×C11C2212yes—
59#10622726C2218yes—
60#10622719C2218yes—
61#10622464C2214yescomplemented
62#10622463C2214yescomplemented
63#10622460C2218yescomplemented
64#10622459C2214yescomplemented
65#10622455C2214yescomplemented
66#10622442C2218yescomplemented
67#10622350C2218yes—
68#10622349C2214yes—
69#10622348C2214yes—
70#10622336C2218yes—
71#10622335C2214yes—
72#10622334C2214yes—
73#10622310C2218yescomplemented
74#10622307C2212yescomplemented
75#10622307C2212yescomplemented
76#10622296C2218yescomplemented
77#10622295C2212yescomplemented
78#10622295C2212yescomplemented
79#10622294C2212yescomplemented
80#10622294C2212yescomplemented
81#10622293C2212yescomplemented
82#10622293C2212yescomplemented
83C23×C4×C11D411yescharacteristic
84C23×C4×C11D411yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C2×#4339—21no—
87C2×#4339—21no—
88C2×#4339C2312yes—
89C22×Dic22—21no—
90C22×Dic22—21no—
91C22×C8×C11C2314yes—
92C2×C42×C11D411yescharacteristic
93C2×C42×C11D411yescharacteristic
94C2×C42×C11D411yescharacteristic
95C2×C42×C11D411yescharacteristic
96C2×C42×C11D411yescharacteristic
97C2×C42×C11D411yescharacteristic
98C2×C42×C11C2311yescharacteristic
99C2×C42×C11C2311yescharacteristic
100C2×C42×C11C2311yescharacteristic
101C2×C42×C11C2311yescharacteristic
102C2×C42×C11C2311yescharacteristic
103C2×C42×C11C2311yescharacteristic
104#67006—22no—
105C2×C22⋊Dic11—22no—
106#66983—21no—
107#66983—21no—
108#66983—21no—
109#66983—21no—
110#66983C2312yes—
111#66983C2312yes—
112#66982—22no—
113#66982—22no—
114#66982—22no—
115C4×C22⋊D11—22no—
116C4×C22⋊D11—22no—
117C4×C22⋊D11—22no—
118C4×C22⋊D11—22no—
119C4×C22⋊D11—22no—
120C4×C22⋊D11—22no—
121#66979—22no—
122#66979—22no—
123#66979—21no—
124#66979—21no—
125#66979C2314yes—
126#66979C2314yes—
127#66979C2312yes—
128C2×C4⋊Dic11—21no—
129C2×C4⋊Dic11—21no—
130C2×C4⋊Dic11C2312yes—
131C2×C4⋊Dic11C2312yes—
132#66977—22no—
133#66977—22no—
134#66977—22no—
135#66977—22no—
136#66977—22no—
137#66977—22no—
138#66977—22no—
139#66977—22no—
140#66977—21no—
141#66977—21no—
142#66977—21no—
143#66977—21no—
144#66977C2312yes—
145#66977C2312yes—
146C2×Dic11⋊C4—22no—
147C2×Dic11⋊C4—22no—
148C2×C4×Dic11—22no—
149#66929—22no—
150#66929—22no—
151#66928—21no—
152#66928—21no—
153#66928C2312yes—
154#66927C2311yescharacteristic
155C4×D44—21no—
156C4×D44—21no—
157C4×D44—21no—
158C4×D44—21no—
159C4×D44C2312yes—
160C4×D44C2312yes—
161#66925—22no—
162#66925—22no—
163#66925—22no—
164C42×D11—22no—
165#66923—22no—
166#66923—22no—
167#66923—21no—
168#66923—21no—
169#66923C2314yes—
170#66923C2314yes—
171#66923C2312yes—
172#66922—21no—
173#66922—21no—
174#66922—21no—
175#66922—21no—
176#66922C2311yescharacteristic
177#66922C2312yes—
178#66922C2312yes—
179#66922C2312yes—
180#66922C2312yes—
181#66922C2311yescharacteristic
182#66922C2311yescharacteristic
183C4×Dic22—22no—
184C4×Dic22—22no—
185C4×Dic22—22no—
186C4×Dic22—22no—
187C4×Dic22—22no—
188C4×Dic22—22no—
189C4×Dic22—22no—
190C4×Dic22—22no—
191C4×Dic22—21no—
192C4×Dic22—21no—
193C4×Dic22—21no—
194C4×Dic22—21no—
195C4×Dic22C2312yes—
196C4×Dic22C2312yes—
197C11×C4⋊C8C2312yes—
198C11×C4⋊C8C2314yes—
199C11×C4⋊C8C2312yes—
200C11×C22⋊C8C2312yes—
201C11×C22⋊C8C2312yes—
202C11×C22⋊C8C2314yes—
203C4×C8×C11C2312yes—
204C4×C8×C11C2312yes—
205C4×C8×C11C2314yes—
206#66885C2318yes—
207#66885C2318yes—
208#66882C2318yes—
209#66882C2318yes—
210#66881C2318yes—
211#66881C2318yes—
212#66880C2318yes—
213#66880C2318yes—
214#60846—111nomaximal, Sylow
215C24×C11C2×D411yescharacteristic
216C22×C4×C11—24no—
217C22×C4×C11—24no—
218C22×C4×C11—42no—
219C22×C4×C11C2×D411yescharacteristic
220C22×C4×C11C2×D411yescharacteristic
221C22×C4×C11C2×D411yescharacteristic
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2×D411yescharacteristic
224C22×C4×C11C2×D411yescharacteristic
225C22×C4×C11C2×D411yescharacteristic
226C22×C4×C11C2×D411yescharacteristic
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×D411yescharacteristic
234C22×C4×C11C2411yescharacteristic
235C22×C4×C11C2411yescharacteristic
236C22×C4×C11C2411yescharacteristic
237C2×C22⋊D11—22no—
238C2×C22⋊D11—22no—
239C2×C22⋊D11—22no—
240C22×Dic11—22no—
241C22×Dic11—22no—
242#4339—28no—
243#4339—44no—
244#4339—44no—
245C2×D44—21no—
246C2×D44—21no—
247C2×D44C2412yes—
248C2×C4×D11—22no—
249C2×C4×D11—22no—
250C2×C4×D11—22no—
251C2×Dic22—22no—
252C2×Dic22—22no—
253C2×Dic22—22no—
254C2×Dic22—22no—
255C2×Dic22—21no—
256C2×Dic22—21no—
257C2×Dic22—44no—
258C2×Dic22—44no—
259C2×Dic22C2412yes—
260C2×C8×C11—28no—
261C2×C8×C11C2414yes—
262C2×C8×C11C2414yes—
263C42×C11C2×D411yescharacteristic
264C42×C11C2×D411yescharacteristic
265C42×C11C2×D411yescharacteristic
266C42×C11C2×D411yescharacteristic
267C42×C11C2×D411yescharacteristic
268C42×C11C2×D411yescharacteristic
269C42×C11C2×D411yescharacteristic
270C42×C11C2×D411yescharacteristic
271C42×C11C2×D411yescharacteristic
272C42×C11C2×D411yescharacteristic
273C42×C11C2×D411yescharacteristic
274C42×C11C2×D411yescharacteristic
275C42×C11C2411yescharacteristic
276C42×C11C2411yescharacteristic
277C42×C11C2411yescharacteristic
278C42×C11C2411yescharacteristic
279C22⋊Dic11—24no—
280C22⋊Dic11—24no—
281C22⋊Dic11—22no—
282C22⋊Dic11—22no—
283C22⋊Dic11—22no—
284(C2×D11)⋊C4—22no—
285(C2×D11)⋊C4—22no—
286(C2×D11)⋊C4—22no—
287(C2×D11)⋊C4—22no—
288(C2×D11)⋊C4—22no—
289(C2×D11)⋊C4—22no—
290C4⋊Dic11—22no—
291C4⋊Dic11—22no—
292C4⋊Dic11—22no—
293C4⋊Dic11—22no—
294C4⋊Dic11—21no—
295C4⋊Dic11—21no—
296C4⋊Dic11—21no—
297C4⋊Dic11—21no—
298C4⋊Dic11—22no—
299C4⋊Dic11—22no—
300C4⋊Dic11C2414yes—
301C4⋊Dic11C2414yes—
302C4⋊Dic11C2412yes—
303C4⋊Dic11C2412yes—
304Dic11⋊C4—24no—
305Dic11⋊C4—24no—
306Dic11⋊C4—24no—
307Dic11⋊C4—24no—
308Dic11⋊C4—22no—
309Dic11⋊C4—22no—
310Dic11⋊C4—22no—
311Dic11⋊C4—22no—
312Dic11⋊C4—22no—
313Dic11⋊C4—22no—
314C4×Dic11—24no—
315C4×Dic11—24no—
316C4×Dic11—22no—
317C4×Dic11—22no—
318C4×Dic11—22no—
319#3444—111no—
320C2×#533—111no—
321#3233—114no—
322#3232—114no—
323#3231—112no—
324#3230—111no—
325#3229—111no—
326#3228—112no—
327#3227—111no—
328#3226—111no—
329#3160—112no—
330#3131—112no—
331#3091—114no—
332#3076—114no—
333C2×#431D1111yescharacteristic, complemented
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—41no—
337C23×C11C22×D411yescharacteristic
338C23×C11C22×D411yescharacteristic
339C23×C11C22×D411yescharacteristic
340C22×D11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11#13514yes—
358C2×C4×C11C22×D411yescharacteristic
359C2×C4×C11C22×D411yescharacteristic
360C2×C4×C11C22×D411yescharacteristic
361C2×C4×C11C22×D411yescharacteristic
362C2×C4×C11C22×D411yescharacteristic
363C2×C4×C11C22×D411yescharacteristic
364C2×C4×C11C22×D411yescharacteristic
365C2×C4×C11C22×D411yescharacteristic
366C2×C4×C11C22×D411yescharacteristic
367C2×C4×C11C22×D411yescharacteristic
368C2×C4×C11C22×D411yescharacteristic
369C2×C4×C112−1+414yes—
370C2×C4×C11C2511yescharacteristic
371C22⋊D11—44no—
372C22⋊D11—44no—
373C22⋊D11—44no—
374C2×Dic11—24no—
375C2×Dic11—24no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—44no—
380C2×Dic11—44no—
381D44—24no—
382D44—42no—
383D44—42no—
384C4×D11—44no—
385C4×D11—44no—
386C4×D11—44no—
387Dic22—24no—
388Dic22—44no—
389Dic22—44no—
390Dic22—44no—
391Dic22—42no—
392Dic22—44no—
393Dic22—42no—
394C8×C11—24no—
395C8×C11—24no—
396#533—112no—
397#533—112no—
398#533—111no—
399#533—112no—
400#533—112no—
401#533—111no—
402#533—111no—
403#533—221no—
404#533—221no—
405#533—221no—
406#533—221no—
407#532—111no—
408#532—111no—
409#532—111no—
410C2×C4⋊Q8—111no—
411C2×C4⋊Q8—111no—
412#529—112no—
413#529—112no—
414#529—221no—
415#529—221no—
416#529—221no—
417#529—221no—
418C2×#125—112no—
419#525—112no—
420#525—221no—
421#525—221no—
422C2×C22⋊Q8—221no—
423C2×C22⋊Q8—221no—
424C4×#41—112no—
425C4×#41—221no—
426C4×#41—221no—
427C2×C4×Q8—221no—
428C2×C4×Q8—221no—
429C2×#117—112no—
430C22×C42C2×D1111yescharacteristic
431#500—112no—
432#500—112no—
433#499—118no—
434#498—112no—
435#498—112no—
436#488—118no—
437#487—112no—
438#487—112no—
439#486—112no—
440#486—112no—
441#485—118no—
442#484—114no—
443#483—114no—
444#482—118no—
445#481—114no—
446#480—114no—
447#479—118no—
448#478—118no—
449#477—114no—
450#476—114no—
451#475—114no—
452#474—114no—
453#431C2×D1111yescharacteristic
454#431C2×D1111yescharacteristic
455#431C2×D1112yes—
456#431C2×D1112yes—
457#431C2×D1112yes—
458#427—118no—
459C2×C4⋊C8C2×D1112yes—
460#416—118no—
461C2×C22⋊C8C2×D1112yes—
462C2×C4×C8C2×D1112yes—
463C22×C11—21no—
464C22×C11—21no—
465C22×C11—21no—
466C22×C11—21no—
467C22×C11—21no—
468C22×C11—21no—
469C22×C11—21no—
470C22×C11—44no—
471C22×C11#53612yes—
472C22×C11C2×#13512yes—
473C22×C11C23×D411yescharacteristic
474C2×D11—42no—
475C2×D11—42no—
476C2×D11—42no—
477C4×C11—21no—
478C4×C11—21no—
479C4×C11—21no—
480C4×C11—21no—
481C4×C11—21no—
482C4×C11—21no—
483C4×C11—21no—
484C4×C11#53612yes—
485C4×C11C2×#13512yes—
486C4×C11C2×#13512yes—
487C4×C11#57512yes—
488C4×C11C2×2−1+412yes—
489Dic11—42no—
490Dic11—44no—
491Dic11—42no—
492Dic11—44no—
493Dic11—42no—
494C2×#41—112no—
495C2×#41—221no—
496C2×#41—221no—
497C22×Q8—221no—
498C22×Q8—221no—
499C23×C4D4411yescharacteristic
500C23×C4D4411yescharacteristic
501C23×C4C22×D1111yescharacteristic
502C22×C8C22×D1114yes—
503C4⋊Q8—112no—
504C4⋊Q8—112no—
505C4⋊Q8—112no—
506C4⋊Q8—112no—
507C4⋊Q8—111no—
508C4⋊Q8—111no—
509C4⋊Q8—111no—
510C4⋊Q8—221no—
511C4⋊Q8—221no—
512C4⋊Q8—221no—
513C4⋊Q8—221no—
514#127—111no—
515#126—222no—
516#126—222no—
517#125—114no—
518#125—114no—
519#125—112no—
520#125—222no—
521#125—222no—
522#125—221no—
523#125—221no—
524#124—112no—
525#124—221no—
526#124—221no—
527#123—222no—
528#123—222no—
529#123—222no—
530C22⋊Q8—112no—
531C22⋊Q8—112no—
532C22⋊Q8—222no—
533C22⋊Q8—222no—
534C22⋊Q8—222no—
535C22⋊Q8—222no—
536C22⋊Q8—222no—
537C22⋊Q8—222no—
538C22⋊Q8—222no—
539C22⋊Q8—222no—
540C22⋊Q8—221no—
541C22⋊Q8—221no—
542C22⋊Q8—221no—
543C22⋊Q8—221no—
544#121—112no—
545#121—112no—
546#121—221no—
547#121—221no—
548#121—221no—
549#121—221no—
550#120—222no—
551C4×Q8—112no—
552C4×Q8—112no—
553C4×Q8—222no—
554C4×Q8—222no—
555C4×Q8—222no—
556C4×Q8—222no—
557C4×Q8—222no—
558C4×Q8—222no—
559C4×Q8—222no—
560C4×Q8—222no—
561C4×Q8—221no—
562C4×Q8—221no—
563C4×Q8—221no—
564C4×Q8—221no—
565C4×D4—112no—
566C4×D4—112no—
567C4×D4—222no—
568C4×D4—222no—
569C4×D4—222no—
570C4×D4—222no—
571C4×D4—222no—
572C4×D4—222no—
573C4×D4—221no—
574C4×D4—221no—
575C4×D4—221no—
576C4×D4—221no—
577#117—114no—
578#117—114no—
579#117—112no—
580#117—222no—
581#117—222no—
582#117—221no—
583#117—221no—
584#117—222no—
585#117—222no—
586#117—222no—
587C2×C4⋊C4—112no—
588C2×C4⋊C4—112no—
589C2×C4⋊C4—222no—
590C2×C4⋊C4—222no—
591C2×C4⋊C4—221no—
592C2×C4⋊C4—221no—
593C2×C22⋊C4—222no—
594C2×C42—222no—
595C2×C42—222no—
596C2×C42D4411yescharacteristic
597C2×C42D4411yescharacteristic
598C2×C42D4411yescharacteristic
599C2×C42D4411yescharacteristic
600C2×C42D4411yescharacteristic
601C2×C42D4411yescharacteristic
602C2×C42C22×D1111yescharacteristic
603C2×C42C22×D1111yescharacteristic
604C2×C42C22×D1111yescharacteristic
605C2×C42C22×D1111yescharacteristic
606C2×C42C22×D1111yescharacteristic
607C2×C42C22×D1111yescharacteristic
608#107—118no—
609#107—118no—
610#106—118no—
611#106—118no—
612C4⋊C8C22×D1112yes—
613C4⋊C8C22×D1112yes—
614C4⋊C8C22×D1114yes—
615#103—118no—
616#103—118no—
617#102—118no—
618#102—118no—
619C22⋊C8C22×D1112yes—
620C22⋊C8C22×D1112yes—
621C22⋊C8C22×D1114yes—
622C4×C8C22×D1112yes—
623C4×C8C22×D1112yes—
624C4×C8C22×D1114yes—
625C2×C11—22no—
626C2×C11—22no—
627C2×C11—41no—
628C2×C11C2×#53611yescharacteristic
629C2×C11C22×#13511yescharacteristic
630C2×C11C2×#57511yescharacteristic
631D11—82no—
632C24C2×D4411yescharacteristic
633#41—228no—
634#41—444no—
635#41—444no—
636C2×Q8—112no—
637C2×Q8—221no—
638C2×Q8—221no—
639C2×Q8—222no—
640C2×Q8—222no—
641C2×Q8—222no—
642C2×Q8—222no—
643C2×Q8—444no—
644C2×Q8—444no—
645C2×D4—112no—
646C2×D4—222no—
647C2×D4—222no—
648C2×D4—222no—
649C2×D4—221no—
650C2×D4—221no—
651C22×C4—24no—
652C22×C4—24no—
653C22×C4—42no—
654C22×C4—222no—
655C22×C4—222no—
656C22×C4—222no—
657C22×C4—222no—
658C22×C4—222no—
659C22×C4C2×D4411yescharacteristic
660C22×C4C2×D4411yescharacteristic
661C22×C4C2×D4411yescharacteristic
662C22×C4C2×D4411yescharacteristic
663C22×C4C2×D4411yescharacteristic
664C22×C4C2×D4411yescharacteristic
665C22×C4C2×D4411yescharacteristic
666C22×C4C2×D4411yescharacteristic
667C22×C4C2×D4411yescharacteristic
668C22×C4C2×D4411yescharacteristic
669C22×C4C2×D4411yescharacteristic
670C22×C4C2×D4411yescharacteristic
671C22×C4C2×D4411yescharacteristic
672C22×C4C2×D4411yescharacteristic
673C22×C4C2×D4411yescharacteristic
674C22×C4C23×D1111yescharacteristic
675C22×C4C23×D1111yescharacteristic
676C22×C4C23×D1111yescharacteristic
677C2×C8—28no—
678C2×C8C23×D1114yes—
679C2×C8C23×D1114yes—
680C4⋊C4—114no—
681C4⋊C4—114no—
682C4⋊C4—112no—
683C4⋊C4—112no—
684C4⋊C4—222no—
685C4⋊C4—222no—
686C4⋊C4—224no—
687C4⋊C4—224no—
688C4⋊C4—224no—
689C4⋊C4—224no—
690C4⋊C4—222no—
691C4⋊C4—222no—
692C4⋊C4—222no—
693C4⋊C4—222no—
694C4⋊C4—222no—
695C4⋊C4—222no—
696C4⋊C4—221no—
697C4⋊C4—221no—
698C4⋊C4—221no—
699C4⋊C4—221no—
700C4⋊C4—222no—
701C4⋊C4—222no—
702C4⋊C4—222no—
703C4⋊C4—222no—
704C22⋊C4—224no—
705C22⋊C4—224no—
706C22⋊C4—222no—
707C22⋊C4—222no—
708C22⋊C4—222no—
709C22⋊C4—222no—
710C22⋊C4—222no—
711C22⋊C4—222no—
712C22⋊C4—222no—
713C22⋊C4—222no—
714C22⋊C4—222no—
715C42—224no—
716C42—222no—
717C42—222no—
718C42—222no—
719C42—224no—
720C42C2×D4411yescharacteristic
721C42C2×D4411yescharacteristic
722C42C2×D4411yescharacteristic
723C42C2×D4411yescharacteristic
724C42C2×D4411yescharacteristic
725C42C2×D4411yescharacteristic
726C42C2×D4411yescharacteristic
727C42C2×D4411yescharacteristic
728C42C2×D4411yescharacteristic
729C42C2×D4411yescharacteristic
730C42C2×D4411yescharacteristic
731C42C2×D4411yescharacteristic
732C42C23×D1111yescharacteristic
733C42C23×D1111yescharacteristic
734C42C23×D1111yescharacteristic
735C42C23×D1111yescharacteristic
736C11#6084611yescharacteristic, complemented, Sylow
737C23—22no—
738C23—22no—
739C23—41no—
740C23—222no—
741C23C22×D4411yescharacteristic
742C23C22×D4411yescharacteristic
743C23C22×D4411yescharacteristic
744Q8—224no—
745Q8—444no—
746Q8—444no—
747Q8—444no—
748Q8—442no—
749Q8—444no—
750Q8—442no—
751D4—224no—
752D4—444no—
753D4—444no—
754D4—444no—
755D4—442no—
756D4—442no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—222no—
774C2×C4—222no—
775C2×C4—222no—
776C2×C4—224no—
777C2×C4—224no—
778C2×C4—444no—
779C2×C4—444no—
780C2×C4—444no—
781C2×C4—444no—
782C2×C4—444no—
783C2×C4#6695714yes—
784C2×C4C22×D4411yescharacteristic
785C2×C4C22×D4411yescharacteristic
786C2×C4C22×D4411yescharacteristic
787C2×C4C22×D4411yescharacteristic
788C2×C4C22×D4411yescharacteristic
789C2×C4C22×D4411yescharacteristic
790C2×C4C22×D4411yescharacteristic
791C2×C4C22×D4411yescharacteristic
792C2×C4C22×D4411yescharacteristic
793C2×C4C22×D4411yescharacteristic
794C2×C4C22×D4411yescharacteristic
795C2×C4#6704314yes—
796C2×C4C24×D1111yescharacteristic
797C8—24no—
798C8—24no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—44no—
807C22—442no—
808C22—442no—
809C22—442no—
810C22#1062305712yes—
811C22C2×#6695712yes—
812C22C23×D4411yescharacteristic
813C4—21no—
814C4—21no—
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—21no—
820C4—442no—
821C4—442no—
822C4—444no—
823C4—442no—
824C4—444no—
825C4#1062305712yes—
826C4C2×#6695712yes—
827C4C2×#6695712yes—
828C4#1062327912yes—
829C4C2×#6704312yes—
830C2—22no—
831C2—22no—
832C2—41no—
833C2—882no—
834C2C2×#1062305711yescharacteristic
835C2C22×#6695711yescharacteristic
836C2C2×#1062327911yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#431C2
socleC22×C11C23×D4
prime radical#13081912C2
hypercenterC2×#431D11
hypocenterC11#60846
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C2×#431

Complements

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

NH ≅ G/Ntype
2. C2×#10623001C2semidirect
3. #13079797C2semidirect
4. #13079786C2semidirect
5. #13079777C2semidirect
6. #13079769C2semidirect
7. #13079762C2semidirect
8. #13079754C2semidirect
9. #13079746C2semidirect
10. #13079739C2semidirect
11. #13079130C2semidirect
12. #13078939C2semidirect
13. #13078531C2semidirect
14. #13078406C2semidirect
15. C2×C11×#431C2semidirect
61. #10622464C22semidirect
62. #10622463C22semidirect
63. #10622460C22semidirect
64. #10622459C22semidirect
65. #10622455C22semidirect
66. #10622442C22semidirect
73. #10622310C22semidirect
74. #10622307C22semidirect
75. #10622307C22semidirect
76. #10622296C22semidirect
77. #10622295C22semidirect
78. #10622295C22semidirect
79. #10622294C22semidirect
80. #10622294C22semidirect
81. #10622293C22semidirect
82. #10622293C22semidirect
333. C2×#431D11semidirect
736. C11#60846semidirect

Maximal subgroups

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

subgroupindex
#130819122
C2×#106230012
#130797972
#130797862
#130797772
#130797692
#130797622
#130797542
#130797462
#130797392
#130791302
#130789392
#130785312
#130784062
C2×C11×#4312
#6084611