Finite Group Databasebeta

← #15649314

Subgroups — #15649314

Order 2816.

2238 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082399C211yesmaximal, characteristic, complemented
2D4×#4339C211yesmaximal, characteristic, complemented
3#13081466C212yesmaximal, complemented
4#13081250C212yesmaximal, complemented
5#13080962C212yesmaximal, complemented
6#13080961C214yesmaximal, complemented
7#13080426C212yesmaximal, complemented
8#13080425C214yesmaximal, complemented
9#13079926C211yesmaximal, characteristic, complemented
10#13079925C212yesmaximal, complemented
11#13079737C211yesmaximal, characteristic, complemented
12#13079736C212yesmaximal, complemented
13#13078618C212yesmaximal, complemented
14#13078616C211yesmaximal, characteristic, complemented
15D11×#474C212yesmaximal, complemented
16#13077725C211yesmaximal, characteristic, complemented
17C2×C11×#474C211yesmaximal, characteristic, complemented
18C2×#67040—21no—
19C22×#4339—21no—
20C2×C11×C4⋊Q8C2211yescharacteristic, complemented
21C2×C4×D4×C11C2211yescharacteristic
22#10623347—21no—
23D4×C22⋊D11C2212yes—
24#10623322—21no—
25#10623258—21no—
26#10623258C2212yescomplemented
27#10623257—21no—
28#10623257C2212yescomplemented
29#10623256C2212yescomplemented
30#10623255—22no—
31D11×C4⋊Q8C2212yescomplemented
32#10623084C2211yescharacteristic
33#10623083—21no—
34#10623082C2211yescharacteristic
35#10623081—21no—
36D4×D44C2211yescharacteristic
37#10623079C2212yes—
38#10623078—22no—
39C4×D4×D11C2212yes—
40D4×Dic22C2211yescharacteristic
41#10623038—22no—
42#10623038C2212yes—
43#10623038C2214yescomplemented
44#10623021—22no—
45#10623008C2211yescharacteristic
46#10623008C2211yescharacteristic, complemented
47C4×#4339C2211yescharacteristic
48C11×#474C2212yes—
49C11×#474C2212yes—
50C11×#474C2212yescomplemented
51C11×#474C2212yescomplemented
52C2×C11×#107C2212yescomplemented
53C2×C11×C4⋊C8C2211yescharacteristic, complemented
54C2×C11×#102C2212yes—
55#10622830C2212yes—
56#10622728C2214yescomplemented
57C8×C22⋊D11C2214yescomplemented
58#10622701C2212yescomplemented
59#10622700C2212yescomplemented
60#10622700C2212yescomplemented
61#10622691C2212yescomplemented
62#10622628C2211yescharacteristic
63#10622628C2211yescharacteristic, complemented
64C4×#4323C2212yes—
65C4×#4323C2212yescomplemented
66#10622620C2211yescharacteristic
67#10622620C2211yescharacteristic, complemented
68#10622580C2212yescomplemented
69#10622580C2214yescomplemented
70#10622538C2211yescharacteristic, complemented
71#10622503C2214yescomplemented
72#10622503C2214yescomplemented
73#10622496C2214yescomplemented
74#10622495C2214yescomplemented
75#10622495C2214yescomplemented
76D11×#107C2214yescomplemented
77#10622487C2214yescomplemented
78#10622485C2214yescomplemented
79#10622459C2212yescomplemented
80#10622459C2212yescomplemented
81#10622456C2212yescomplemented
82#10622456C2212yescomplemented
83#10622447C2212yescomplemented
84#10622446C2212yescomplemented
85D11×C4⋊C8C2212yescomplemented
86#10622443C2212yescomplemented
87#10622399C2214yescomplemented
88#10622388C2214yescomplemented
89#10622387C2214yescomplemented
90#10622386C2214yes—
91D11×#102C2214yes—
92#10622373C2214yescomplemented
93#10622372C2214yes—
94#10622369C2214yes—
95C22×Q8×C11—21no—
96C22×D4×C11C2311yescharacteristic
97C23×C4×C11—21no—
98C22×C22⋊D11—22no—
99#67040—48no—
100C2×#4343—22no—
101C2×#4343—22no—
102C2×Q8×D11—22no—
103C2×Q8×D11—22no—
104C2×D4×D11C2312yes—
105C2×#4339—21no—
106C2×#4339—21no—
107C2×#4339—22no—
108C2×#4339—24no—
109C2×#4339—21no—
110C2×#4339—22no—
111C2×#4339—21no—
112C2×#4339—48no—
113C2×#4339D411yescharacteristic
114C22×D44—21no—
115C22×C4×D11—22no—
116C22×Dic22—21no—
117C22×C8×C11C2312yes—
118C11×C4⋊Q8—21no—
119C11×C4⋊Q8—21no—
120C11×C4⋊Q8C2312yes—
121C11×C4⋊Q8C2312yes—
122C4×D4×C11—21no—
123C4×D4×C11—21no—
124C4×D4×C11C2311yescharacteristic
125C4×D4×C11C2311yescharacteristic
126C4×D4×C11C2311yescharacteristic
127C4×D4×C11C2311yescharacteristic
128C2×C11×C4⋊C4—21no—
129C2×C11×C4⋊C4C2311yescharacteristic
130C2×C11×C4⋊C4C2312yes—
131C2×C11×C22⋊C4—21no—
132C2×C42×C11C2311yescharacteristic
133#67006—22no—
134#67000—22no—
135#66999—22no—
136#66999—22no—
137#66997—22no—
138#66993C2312yes—
139#66992—22no—
140#66991C2312yes—
141#66990—22no—
142D4×Dic11C2312yes—
143C2×#4323C2312yes—
144C2×#4323C2312yes—
145#66983—21no—
146#66983—21no—
147#66983—21no—
148#66983—21no—
149#66983C2312yes—
150#66983C2312yes—
151#66982—22no—
152#66982—24no—
153C4×C22⋊D11—22no—
154C4×C22⋊D11—22no—
155C4×C22⋊D11D412yes—
156C4×C22⋊D11C2312yes—
157#66979D411yescharacteristic
158#66977—21no—
159#66977—21no—
160C2×D88C2314yes—
161C2×C8×D11C2314yes—
162#66949—24no—
163#66949—24no—
164#66949—22no—
165#66948—22no—
166#66948C2314yes—
167#66948C2312yes—
168#66947—24no—
169#66947—24no—
170#66947—22no—
171#66946—22no—
172#66946C2312yes—
173#66946C2314yes—
174C4⋊C4×D11—22no—
175C4⋊C4×D11C2314yes—
176C4⋊C4×D11C2312yes—
177#66941—22no—
178#66941C2314yes—
179#66941C2312yes—
180#66938—22no—
181#66937—22no—
182#66937—22no—
183#66936—22no—
184#66935—22no—
185(C22⋊D11)⋊C4—22no—
186C22⋊C4×D11—22no—
187#66931—22no—
188#66928—21no—
189#66928—21no—
190#66927C2311yescharacteristic
191#66927C2311yescharacteristic
192C4×D44—21no—
193C4×D44—21no—
194C4×D44D411yescharacteristic
195C4×D44C2311yescharacteristic
196C4×D44C2312yes—
197C4×D44C2312yes—
198#66925D412yes—
199C42×D11C2312yes—
200#66922C2311yescharacteristic
201#66922C2311yescharacteristic
202C4×Dic22D411yescharacteristic
203C4×Dic22C2311yescharacteristic
204C11×#107C2314yes—
205C11×#107C2314yes—
206C11×C4⋊C8C2312yes—
207C11×C4⋊C8C2312yes—
208C11×#102C2314yes—
209C11×#102C2314yes—
210#66896C2312yes—
211#66896C2312yes—
212C22⋊(C11⋊C8)C2312yes—
213#66885C2314yes—
214#66885C2314yes—
215(C2×D11)⋊C8C2314yes—
216#66882C2314yes—
217Dic11⋊C8C2314yes—
218C8×Dic11C2314yes—
219#66873C2312yes—
220#66873C2314yes—
221#66873C2312yes—
222#66873C2314yes—
223#66871C2312yes—
224#66871C2314yes—
225#66871C2312yes—
226#66871C2314yes—
227C4⋊(C11⋊C8)C2311yescharacteristic
228C4⋊(C11⋊C8)C2311yescharacteristic
229C4×C11⋊C8C2312yes—
230#62095—111nomaximal, Sylow
231C24×C11—21no—
232C23×D11—22no—
233C2×Q8×C11—22no—
234C2×Q8×C11—22no—
235C2×Q8×C11—44no—
236C2×D4×C11—22no—
237C2×D4×C11—21no—
238C2×D4×C11—41no—
239C2×D4×C11C2411yescharacteristic
240C2×D4×C11C2411yescharacteristic
241C22×C4×C11—21no—
242C22×C4×C11—22no—
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—44no—
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2411yescharacteristic
251C2×C22⋊D11—22no—
252C2×C22⋊D11—22no—
253C2×C22⋊D11—22no—
254C2×C22⋊D11—22no—
255C2×C22⋊D11—22no—
256C2×C22⋊D11—22no—
257C2×C22⋊D11—48no—
258C2×C22⋊D11C2×D412yes—
259C22×Dic11—22no—
260#4343—48no—
261#4343—48no—
262Q8×D11—48no—
263Q8×D11—48no—
264D4×D11—24no—
265D4×D11—42no—
266#4339—48no—
267#4339—416no—
268#4339—44no—
269#4339—48no—
270#4339—44no—
271#4339—44no—
272#4339—44no—
273#4339D818yescomplemented
274C2×D44—22no—
275C2×D44—24no—
276C2×D44—21no—
277C2×D44—21no—
278C2×D44—21no—
279C2×D44—21no—
280C2×D44—44no—
281C2×D44C2×D411yescharacteristic
282C2×D44C2412yes—
283C2×D44C2412yes—
284C2×C4×D11—22no—
285C2×C4×D11—24no—
286C2×C4×D11—22no—
287C2×C4×D11—24no—
288C2×C4×D11—22no—
289C2×C4×D11—22no—
290C2×C4×D11—48no—
291C2×C4×D11C2×D412yes—
292C2×C4×D11C2×D412yes—
293C2×C4×D11C2412yes—
294C2×Dic22—22no—
295C2×Dic22—24no—
296C2×Dic22—21no—
297C2×Dic22—21no—
298C2×Dic22—44no—
299C2×Dic22C2×D411yescharacteristic
300C2×C8×C11—42no—
301C2×C8×C11C2414yes—
302C11×C4⋊C4—22no—
303C11×C4⋊C4—22no—
304C11×C4⋊C4—21no—
305C11×C4⋊C4—22no—
306C11×C4⋊C4C2414yes—
307C11×C4⋊C4C2411yescharacteristic
308C11×C4⋊C4C2411yescharacteristic
309C11×C22⋊C4—21no—
310C11×C22⋊C4—21no—
311C11×C22⋊C4—21no—
312C11×C22⋊C4—21no—
313C42×C11C2×D411yescharacteristic
314C42×C11C2×D411yescharacteristic
315C42×C11C2411yescharacteristic
316C42×C11C2411yescharacteristic
317C22⋊Dic11—22no—
318C22⋊Dic11—22no—
319C22⋊Dic11C2×D412yes—
320#4323—24no—
321#4323—42no—
322(C2×D11)⋊C4—22no—
323(C2×D11)⋊C4—22no—
324(C2×D11)⋊C4—24no—
325(C2×D11)⋊C4—24no—
326(C2×D11)⋊C4—22no—
327(C2×D11)⋊C4—22no—
328(C2×D11)⋊C4—22no—
329(C2×D11)⋊C4—22no—
330(C2×D11)⋊C4C2×D412yes—
331(C2×D11)⋊C4C2×D412yes—
332C4⋊Dic11—21no—
333C4⋊Dic11—21no—
334C4⋊Dic11C2×D411yescharacteristic
335C4⋊Dic11C2×D411yescharacteristic
336C4⋊Dic11C2412yes—
337C4⋊Dic11C2412yes—
338Dic11⋊C4—22no—
339Dic11⋊C4—22no—
340Dic11⋊C4—24no—
341Dic11⋊C4—24no—
342Dic11⋊C4C2×D412yes—
343Dic11⋊C4C2×D412yes—
344C4×Dic11C2×D412yes—
345C4×Dic11C2×D412yes—
346C4×Dic11C2412yes—
347C2×C11⋊C8C2412yes—
348C2×C11⋊C8C2412yes—
349D88—44no—
350C8×D11—44no—
351#3499—111no—
352D4×#41—111no—
353Q8×D8—112no—
354#3358—112no—
355#3334—112no—
356#3334—114no—
357#3294—112no—
358#3294—114no—
359#3245—112no—
360#3245—111no—
361#3226—112no—
362#3226—111no—
363#3100—112no—
364#3100—111no—
365C2×#474—112no—
366C2×#474D1111yescharacteristic, complemented
367#2988—111no—
368C23×C11—21no—
369C23×C11—21no—
370C23×C11—42no—
371C23×C11—42no—
372C23×C11—81no—
373C23×C11C22×D411yescharacteristic
374C22×D11—22no—
375C22×D11—22no—
376C22×D11—44no—
377C22×D11—44no—
378C22×D11—82no—
379C22×D11C22×D412yes—
380Q8×C11—44no—
381Q8×C11—44no—
382D4×C11—21no—
383D4×C11—21no—
384D4×C11—21no—
385D4×C11—42no—
386D4×C112−1+412yescomplemented
387C2×C4×C11—21no—
388C2×C4×C11—21no—
389C2×C4×C11—21no—
390C2×C4×C11—21no—
391C2×C4×C11—24no—
392C2×C4×C11—41no—
393C2×C4×C11—42no—
394C2×C4×C11—44no—
395C2×C4×C11—42no—
396C2×C4×C11—42no—
397C2×C4×C11—42no—
398C2×C4×C11—42no—
399C2×C4×C11C2×D814yes—
400C2×C4×C11C22×D411yescharacteristic
401C2×C4×C11C22×D411yescharacteristic
402C2×C4×C11C22×D411yescharacteristic
403C2×C4×C11C22×D411yescharacteristic
404C2×C4×C11C22×D411yescharacteristic
405C2×C4×C11C2511yescharacteristic
406C22⋊D11—44no—
407C22⋊D11—44no—
408C22⋊D11—44no—
409C22⋊D11—44no—
410C22⋊D11—44no—
411C22⋊D11—82no—
412C22⋊D11C2×D818yes—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—44no—
416C2×Dic11C22×D412yes—
417C2×Dic11C22×D412yes—
418C2×Dic11C22×D412yes—
419D44—22no—
420D44—22no—
421D44—22no—
422D44—22no—
423D44—42no—
424D44—44no—
425D44—48no—
426D44—42no—
427D44—42no—
428D44—81no—
429D44C2×D814yes—
430C4×D11—22no—
431C4×D11—22no—
432C4×D11—42no—
433C4×D11—44no—
434C4×D11—48no—
435C4×D11—44no—
436C4×D11—44no—
437C4×D11—44no—
438C4×D11—48no—
439C4×D11C2×D818yes—
440Dic22—42no—
441Dic22—42no—
442Dic22—44no—
443Dic22—48no—
444Dic22C2×D814yes—
445C8×C11—24no—
446C11⋊C8—22no—
447C11⋊C8—22no—
448C2×2−1+4—221no—
449C22×#41—221no—
450#550—111no—
451D4×Q8—112no—
452D4×Q8—111no—
453D4×Q8—221no—
454#548—221no—
455#547—112no—
456#547—111no—
457#547—112no—
458#547—114no—
459#547—222no—
460#547—221no—
461#546—222no—
462#546—221no—
463D42—112no—
464D42—111no—
465#536—222no—
466#536—221no—
467#532—112no—
468#532—112no—
469#532—111no—
470#532—111no—
471C2×C4⋊Q8—112no—
472C2×C4⋊Q8C2×D1111yescharacteristic, complemented
473#525—222no—
474#525—221no—
475C4×#41—111no—
476C2×C4×D4—112no—
477C2×C4×D4C2×D1111yescharacteristic
478#500—112no—
479#500—114no—
480#486—112no—
481#486—114no—
482#480—112no—
483#480—114no—
484#480—114no—
485#480—114no—
486#480—114no—
487#474—112no—
488#474—112no—
489#474—111no—
490#474—111no—
491#474—114no—
492#474—114no—
493#474—112no—
494#474—112no—
495#474—114no—
496#474C2×D1112yes—
497#474C2×D1112yes—
498#474C2×D1112yescomplemented
499#474C2×D1112yescomplemented
500#466—114no—
501#466—114no—
502#466—114no—
503#459—111no—
504#459—111no—
505#459—112no—
506#459—112no—
507#459—114no—
508#447—112no—
509#447—114no—
510C8×Q8—112no—
511C4×D8—112no—
512C4×D8—112no—
513C4×D8—114no—
514C4×D8—114no—
515C8×D4—114no—
516C8×D4—112no—
517#431—111no—
518#431—112no—
519C2×#107—114no—
520C2×#107C2×D1112yescomplemented
521C2×C4⋊C8—112no—
522C2×C4⋊C8C2×D1111yescharacteristic, complemented
523C2×#102—114no—
524C2×#102C2×D1112yes—
525C22×C11—21no—
526C22×C11—21no—
527C22×C11—22no—
528C22×C11—41no—
529C22×C11—41no—
530C22×C11—41no—
531C22×C11—41no—
532C22×C11—41no—
533C22×C11—84no—
534C22×C11C22×D812yes—
535C22×C11C23×D411yescharacteristic
536C2×D11—22no—
537C2×D11—22no—
538C2×D11—42no—
539C2×D11—42no—
540C2×D11—42no—
541C2×D11—42no—
542C2×D11—42no—
543C2×D11—42no—
544C2×D11—88no—
545C2×D11C22×D814yes—
546C4×C11—21no—
547C4×C11—21no—
548C4×C11—21no—
549C4×C11—41no—
550C4×C11—41no—
551C4×C11—44no—
552C4×C11C22×D812yes—
553C4×C11C22×D812yes—
554C4×C11C2×2−1+411yescharacteristic
555C4×C11#58511yescharacteristic
556Dic11—22no—
557Dic11—22no—
558Dic11—42no—
559Dic11—42no—
560Dic11C22×D814yes—
5612−1+4—448no—
562C2×#41—111no—
563C2×#41—222no—
564C2×#41—222no—
565C2×#41—221no—
566C2×#41—224no—
567C2×#41—221no—
568C2×#41—222no—
569C2×#41—222no—
570C2×#41—221no—
571C2×#41—221no—
572C2×#41—448no—
573C22×Q8—21no—
574C22×Q8—221no—
575C22×Q8—222no—
576C22×Q8—222no—
577C22×D4—112no—
578C22×D4—221no—
579C22×D4—222no—
580C22×D4C22×D1111yescharacteristic
581C23×C4—21no—
582C23×C4—222no—
583C2×D8—112no—
584C2×D8—112no—
585C2×D8—114no—
586C22×C8—114no—
587C22×C8C22×D1112yes—
588C4⋊Q8—21no—
589C4⋊Q8—21no—
590C4⋊Q8—114no—
591C4⋊Q8—112no—
592C4⋊Q8—111no—
593C4⋊Q8—111no—
594C4⋊Q8—222no—
595C4⋊Q8—222no—
596C4⋊Q8C22×D1112yes—
597C4⋊Q8C22×D1112yes—
598#127—112no—
599#127—111no—
600#127—111no—
601#124—222no—
602#124—222no—
603#124—221no—
604#124—221no—
605#123—222no—
606#123—222no—
607#123—224no—
608#123—224no—
609#123—222no—
610#123—224no—
611C22⋊Q8—222no—
612C22⋊Q8—222no—
613C22⋊Q8—224no—
614C22⋊Q8—224no—
615C22⋊Q8—221no—
616C22⋊Q8—221no—
617C22⋊Q8—222no—
618C22⋊Q8—222no—
619#121—112no—
620#121—112no—
621#121—112no—
622#121—112no—
623#121—114no—
624#121—222no—
625#121—222no—
626#121—222no—
627#121—221no—
628#121—221no—
629#121—222no—
630#121—221no—
631#121—221no—
632#120—222no—
633#120—222no—
634#120—222no—
635C4×Q8—111no—
636C4×Q8—111no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—112no—
640C4×D4—112no—
641C4×D4—112no—
642C4×D4—112no—
643C4×D4—114no—
644C4×D4—111no—
645C4×D4—111no—
646C4×D4—112no—
647C4×D4—112no—
648C4×D4—222no—
649C4×D4—222no—
650C4×D4—222no—
651C4×D4—222no—
652C4×D4—221no—
653C4×D4—221no—
654C4×D4C22×D1111yescharacteristic
655C4×D4C22×D1111yescharacteristic
656C4×D4C22×D1111yescharacteristic
657C4×D4C22×D1111yescharacteristic
658#117—111no—
659#117—112no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—112no—
662C2×C4⋊C4—114no—
663C2×C4⋊C4—222no—
664C2×C4⋊C4C22×D1111yescharacteristic
665C2×C4⋊C4C22×D1112yes—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—222no—
668C2×C42—112no—
669C2×C42C22×D1111yescharacteristic
670#107—114no—
671#107—112no—
672#107—114no—
673#107—112no—
674#107—114no—
675#107C22×D1114yes—
676#107C22×D1114yes—
677C4⋊C8—114no—
678C4⋊C8—111no—
679C4⋊C8—111no—
680C4⋊C8C22×D1112yes—
681C4⋊C8C22×D1112yes—
682#102—112no—
683#102—112no—
684#102—114no—
685#102—114no—
686#102—114no—
687#102—112no—
688#102—114no—
689#102—112no—
690#102C22×D1114yes—
691#102C22×D1114yes—
692C22⋊C8—112no—
693C22⋊C8—114no—
694C4×C8—114no—
695C4×C8—112no—
696C2×C11—22no—
697C2×C11—42no—
698C2×C11—81no—
699C2×C11#348911yescharacteristic
700C2×C11C23×D811yescharacteristic
701C2×C11#358611yescharacteristic
702D11—24no—
703D11—82no—
704D11—82no—
705C24—21no—
706C24—222no—
707#41—118no—
708#41—448no—
709#41—448no—
710#41—444no—
711#41—4416no—
712#41—444no—
713#41—448no—
714#41—448no—
715#41—444no—
716#41—444no—
717C2×Q8—22no—
718C2×Q8—22no—
719C2×Q8—44no—
720C2×Q8—111no—
721C2×Q8—222no—
722C2×Q8—224no—
723C2×Q8—221no—
724C2×Q8—221no—
725C2×Q8—444no—
726C2×Q8—448no—
727C2×Q8—448no—
728C2×D4—22no—
729C2×D4—21no—
730C2×D4—41no—
731C2×D4—112no—
732C2×D4—111no—
733C2×D4—112no—
734C2×D4—112no—
735C2×D4—222no—
736C2×D4—224no—
737C2×D4—222no—
738C2×D4—222no—
739C2×D4—222no—
740C2×D4—224no—
741C2×D4—222no—
742C2×D4—222no—
743C2×D4—222no—
744C2×D4—221no—
745C2×D4—221no—
746C2×D4—221no—
747C2×D4—221no—
748C2×D4—444no—
749C2×D4—442no—
750C2×D4—448no—
751C2×D4C23×D1111yescharacteristic
752C2×D4C23×D1111yescharacteristic
753C22×C4—21no—
754C22×C4—22no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—44no—
760C22×C4—112no—
761C22×C4—112no—
762C22×C4—112no—
763C22×C4—222no—
764C22×C4—224no—
765C22×C4—222no—
766C22×C4—224no—
767C22×C4—222no—
768C22×C4—222no—
769C22×C4—222no—
770C22×C4—448no—
771C22×C4D4×D1111yescharacteristic
772C22×C4D4×D1111yescharacteristic
773C22×C4C23×D1111yescharacteristic
774D8—224no—
775D8—444no—
776D8—442no—
777C2×C8—42no—
778C2×C8—112no—
779C2×C8—112no—
780C2×C8—444no—
781C2×C8C23×D1114yes—
782C4⋊C4—22no—
783C4⋊C4—22no—
784C4⋊C4—21no—
785C4⋊C4—22no—
786C4⋊C4—112no—
787C4⋊C4—112no—
788C4⋊C4—111no—
789C4⋊C4—111no—
790C4⋊C4—112no—
791C4⋊C4—112no—
792C4⋊C4—222no—
793C4⋊C4—224no—
794C4⋊C4—224no—
795C4⋊C4—222no—
796C4⋊C4—221no—
797C4⋊C4—221no—
798C4⋊C4C23×D1114yes—
799C4⋊C4C23×D1111yescharacteristic
800C4⋊C4C23×D1111yescharacteristic
801C22⋊C4—21no—
802C22⋊C4—21no—
803C22⋊C4—21no—
804C22⋊C4—21no—
805C22⋊C4—112no—
806C22⋊C4—112no—
807C22⋊C4—112no—
808C22⋊C4—222no—
809C22⋊C4—224no—
810C22⋊C4—222no—
811C22⋊C4—224no—
812C22⋊C4—222no—
813C22⋊C4—222no—
814C22⋊C4—222no—
815C22⋊C4—222no—
816C22⋊C4—222no—
817C22⋊C4—222no—
818C42—112no—
819C42—112no—
820C42—112no—
821C42D4×D1111yescharacteristic
822C42D4×D1111yescharacteristic
823C42C23×D1111yescharacteristic
824C42C23×D1111yescharacteristic
825C11#6209511yescharacteristic, complemented, Sylow
826C23—21no—
827C23—21no—
828C23—42no—
829C23—42no—
830C23—81no—
831C23—112no—
832C23—222no—
833C23—222no—
834C23—444no—
835C23—444no—
836C23—882no—
837C23C2×D4×D1111yescharacteristic
838Q8—44no—
839Q8—44no—
840Q8—114no—
841Q8—448no—
842Q8—444no—
843Q8—442no—
844Q8—442no—
845D4—21no—
846D4—21no—
847D4—21no—
848D4—42no—
849D4—118no—
850D4—114no—
851D4—222no—
852D4—222no—
853D4—222no—
854D4—222no—
855D4—442no—
856D4—444no—
857D4—448no—
858D4—444no—
859D4—444no—
860D4—444no—
861D4—444no—
862D4—444no—
863D4—442no—
864D4—442no—
865D4—881no—
866D4—882no—
867D4#6704012yescomplemented
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—24no—
873C2×C4—41no—
874C2×C4—42no—
875C2×C4—44no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—112no—
881C2×C4—118no—
882C2×C4—112no—
883C2×C4—112no—
884C2×C4—222no—
885C2×C4—222no—
886C2×C4—222no—
887C2×C4—222no—
888C2×C4—442no—
889C2×C4—444no—
890C2×C4—448no—
891C2×C4—444no—
892C2×C4—448no—
893C2×C4—444no—
894C2×C4—444no—
895C2×C4—444no—
896C2×C4D8×D1114yes—
897C2×C4C2×D4×D1111yescharacteristic
898C2×C4C2×D4×D1111yescharacteristic
899C2×C4C2×D4×D1111yescharacteristic
900C2×C4C2×D4×D1111yescharacteristic
901C2×C4C2×D4×D1111yescharacteristic
902C2×C4C24×D1111yescharacteristic
903C8—24no—
904C8—222no—
905C8—222no—
906C22—21no—
907C22—21no—
908C22—22no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—84no—
915C22—114no—
916C22—222no—
917C22—222no—
918C22—442no—
919C22—442no—
920C22—442no—
921C22—442no—
922C22—442no—
923C22—442no—
924C22—888no—
925C22C2×D8×D1112yes—
926C22C22×D4×D1111yescharacteristic
927C4—21no—
928C4—21no—
929C4—21no—
930C4—41no—
931C4—41no—
932C4—44no—
933C4—114no—
934C4—222no—
935C4—222no—
936C4—442no—
937C4—442no—
938C4C2×D8×D1112yes—
939C4C2×D8×D1112yes—
940C4C2×#6704011yescharacteristic
941C4#1062345311yescharacteristic
942C2—22no—
943C2—42no—
944C2—81no—
945C2—224no—
946C2—882no—
947C2—882no—
948C2#1308229211yescharacteristic
949C2C22×D8×D1111yescharacteristic
950C2#1308339911yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#474C2
socleC22×C11C23×D4
hypercenterC2×#474D11
hypocenterC11#62095
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. #13082399C2semidirect
2. D4×#4339C2semidirect
3. #13081466C2semidirect
4. #13081250C2semidirect
5. #13080962C2semidirect
6. #13080961C2semidirect
7. #13080426C2semidirect
8. #13080425C2semidirect
9. #13079926C2semidirect
10. #13079925C2semidirect
11. #13079737C2semidirect
12. #13079736C2semidirect
13. #13078618C2semidirect
14. #13078616C2semidirect
15. D11×#474C2semidirect
16. #13077725C2semidirect
17. C2×C11×#474C2semidirect
20. C2×C11×C4⋊Q8C22semidirect
26. #10623258C22semidirect
28. #10623257C22semidirect
29. #10623256C22semidirect
31. D11×C4⋊Q8C22semidirect
43. #10623038C22semidirect
46. #10623008C22semidirect
50. C11×#474C22semidirect
51. C11×#474C22semidirect
52. C2×C11×#107C22semidirect
53. C2×C11×C4⋊C8C22semidirect
56. #10622728C22semidirect
57. C8×C22⋊D11C22semidirect
58. #10622701C22semidirect
59. #10622700C22semidirect
60. #10622700C22semidirect
61. #10622691C22semidirect
63. #10622628C22semidirect
65. C4×#4323C22semidirect
67. #10622620C22semidirect
68. #10622580C22semidirect
69. #10622580C22semidirect
70. #10622538C22semidirect
71. #10622503C22semidirect
72. #10622503C22semidirect
73. #10622496C22semidirect
74. #10622495C22semidirect
75. #10622495C22semidirect
76. D11×#107C22semidirect
77. #10622487C22semidirect
78. #10622485C22semidirect
79. #10622459C22semidirect
80. #10622459C22semidirect
81. #10622456C22semidirect
82. #10622456C22semidirect
83. #10622447C22semidirect
84. #10622446C22semidirect
85. D11×C4⋊C8C22semidirect
86. #10622443C22semidirect
87. #10622399C22semidirect
88. #10622388C22semidirect
89. #10622387C22semidirect
92. #10622373C22semidirect
273. #4339D8semidirect
366. C2×#474D11semidirect
386. D4×C112−1+4semidirect
472. C2×C4⋊Q8C2×D11semidirect
498. #474C2×D11semidirect
499. #474C2×D11semidirect
520. C2×#107C2×D11semidirect
522. C2×C4⋊C8C2×D11semidirect
825. C11#62095semidirect
867. D4#67040semidirect

Maximal subgroups

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

subgroupindex
#130823992
D4×#43392
#130814662
#130812502
#130809622
#130809612
#130804262
#130804252
#130799262
#130799252
#130797372
#130797362
#130786182
#130786162
D11×#4742
#130777252
C2×C11×#4742
#6209511