Finite Group Databasebeta

← #15645924

Subgroups — #15645924

Order 2816.

1942 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082492C211yesmaximal, characteristic, complemented
2#13081612C212yesmaximal, complemented
3#13081276C212yesmaximal, complemented
4#13080560C212yesmaximal, complemented
5#13080445C214yesmaximal, complemented
6#13080342C212yesmaximal, complemented
7#13080297C214yesmaximal, complemented
8#13079958C211yesmaximal, characteristic, complemented
9#13079942C212yesmaximal, complemented
10#13079588C212yesmaximal, complemented
11#13079554C211yesmaximal, characteristic, complemented
12#13078676C212yesmaximal, complemented
13#13078624C211yesmaximal, characteristic, complemented
14#13078071C212yesmaximal, complemented
15C2×#10622628C211yesmaximal, characteristic, complemented
16#13077727C211yesmaximal, characteristic, complemented
17C11×#3475C211yesmaximal, characteristic, complemented
18C11×#556C2211yescharacteristic, complemented
19C11×#555C2211yescharacteristic, complemented
20C11×#554C2211yescharacteristic, complemented
21C11×#553—21no—
22C11×#552—21no—
23C11×#552C2212yes—
24C11×#551—22no—
25C11×#547C2211yescharacteristic, complemented
26C11×#546C2212yes—
27C11×#533C2211yescharacteristic
28C11×#529—22no—
29C11×#529C2212yescomplemented
30C11×#525—21no—
31C4×C11×#41C2211yescharacteristic
32C4×C11×#41C2212yescomplemented
33C2×C4×D4×C11C2211yescharacteristic
34C2×C11×#117—21no—
35#10623361—21no—
36C2×#67003C2214yescomplemented
37C22×#4323C2212yes—
38#10623116—21no—
39#10623116C2212yescomplemented
40#10623084—21no—
41#10623084C2212yescomplemented
42#10623081—22no—
43#10623081C2214yes—
44#10623066—22no—
45#10623052—21no—
46#10623008C2212yescomplemented
47#10623008C2212yescomplemented
48C2×#66927C2211yescharacteristic
49#10623001C2211yescharacteristic
50#10622851C2214yescomplemented
51#10622831C2212yes—
52#10622704C2212yescomplemented
53#10622703C2212yescomplemented
54#10622701C2212yescomplemented
55#10622698C2212yescomplemented
56#10622681C2214yescomplemented
57#10622679C2214yescomplemented
58#10622672C2214yescomplemented
59#10622670C2214yescomplemented
60#10622664C2214yes—
61#10622661C2214yescomplemented
62#10622660C2214yescomplemented
63#10622659C2214yes—
64#10622651C2214yescomplemented
65#10622650C2214yescomplemented
66#10622644C2212yescomplemented
67#10622641C2214yescomplemented
68#10622640C2212yescomplemented
69#10622640C2212yescomplemented
70C4×#4325C2214yescomplemented
71Q8×C11⋊C8C2212yescomplemented
72#10622634C2212yescomplemented
73#10622632C2211yescharacteristic, complemented
74#10622632C2211yescharacteristic, complemented
75C4×#4324C2212yescomplemented
76C4×#4324C2212yescomplemented
77#10622629C2214yescomplemented
78#10622628C2212yes—
79#10622628C2212yes—
80#10622628C2212yes—
81#10622628C2212yes—
82C4×#4323C2214yescomplemented
83D4×C11⋊C8C2214yes—
84D4×C11⋊C8C2212yescomplemented
85#10622621C2211yescharacteristic, complemented
86#10622621C2211yescharacteristic, complemented
87#10622616C2214yescomplemented
88#10622615C2214yescomplemented
89#10622584C2212yes—
90C2×#66873C2212yes—
91#10622538C2211yescharacteristic
92#10622538C2212yescomplemented
93C2×C4⋊(C11⋊C8)C2211yescharacteristic
94C2×C4⋊(C11⋊C8)C2212yescomplemented
95C2×C11×#41D411yescharacteristic
96C2×C11×#41C2312yes—
97C22×D4×C11C2311yescharacteristic
98C23×C4×C11—21no—
99C2×#4339—22no—
100C2×#4339C2314yes—
101C22×D44—21no—
102C22×D44—21no—
103C22×D44C2312yes—
104C11×C4⋊Q8C2311yescharacteristic
105C11×C4⋊Q8C2311yescharacteristic
106C11×#126—22no—
107C11×#126—22no—
108C11×#126—22no—
109C11×#125—22no—
110C11×#125—21no—
111C11×#125C2312yes—
112C11×#124—22no—
113C11×#124C2312yes—
114C11×#123—22no—
115C11×#123—22no—
116C11×#123—22no—
117C11×#123—22no—
118C11×C22⋊Q8—21no—
119C11×C22⋊Q8—21no—
120C11×C22⋊Q8—21no—
121C11×C22⋊Q8—22no—
122C11×C22⋊Q8C2312yes—
123C11×C22⋊Q8C2312yes—
124C11×#121—21no—
125C11×#121—21no—
126C11×#121—22no—
127C11×#121C2312yes—
128C11×#120—22no—
129C4×Q8×C11—21no—
130C4×Q8×C11D411yescharacteristic
131C4×Q8×C11C2312yes—
132C4×Q8×C11C2312yes—
133C4×Q8×C11C2311yescharacteristic
134C4×D4×C11—22no—
135C4×D4×C11—22no—
136C4×D4×C11—22no—
137C4×D4×C11—21no—
138C4×D4×C11—21no—
139C4×D4×C11D412yes—
140C4×D4×C11D411yescharacteristic
141C4×D4×C11C2311yescharacteristic
142C4×D4×C11C2311yescharacteristic
143C4×D4×C11C2311yescharacteristic
144C4×D4×C11C2311yescharacteristic
145C4×D4×C11C2312yes—
146C4×D4×C11C2312yes—
147C4×D4×C11C2311yescharacteristic
148C11×#117—21no—
149C11×#117—21no—
150C11×#117—21no—
151C11×#117—22no—
152C11×#117—22no—
153C11×#117—22no—
154C11×#117D411yescharacteristic
155C11×#117D412yes—
156C11×#117C2312yes—
157C2×C11×C4⋊C4—21no—
158C2×C11×C4⋊C4—21no—
159C2×C11×C4⋊C4C2311yescharacteristic
160C2×C11×C22⋊C4—21no—
161C2×C11×C22⋊C4—22no—
162C2×C42×C11—22no—
163C2×C42×C11C2311yescharacteristic
164C2×C42×C11C2312yes—
165#67003—48no—
166#67000—22no—
167C2×#4326C2314yes—
168C2×#4325C2314yes—
169C2×#4325C2314yes—
170#66993—22no—
171#66990—24no—
172C2×#4324C2312yes—
173C2×#4324C2312yes—
174C2×#4323—44no—
175C2×#4323C2314yes—
176C2×#4323C2314yes—
177#66983—22no—
178#66983—22no—
179#66983—22no—
180#66983C2314yes—
181#66979—21no—
182#66977—21no—
183#66977C2312yes—
184C22×C11⋊C8C2312yes—
185C22×C11⋊C8C2314yes—
186#66947—24no—
187#66947—24no—
188#66946—22no—
189#66946—22no—
190#66937—24no—
191#66937—24no—
192C22⋊C4×D11—24no—
193#66928—22no—
194#66928C2314yes—
195#66927—21no—
196#66927—21no—
197#66927C2312yes—
198#66927C2312yes—
199C4×D44—22no—
200C4×D44—22no—
201C4×D44—22no—
202C4×D44C2314yes—
203#66923—21no—
204#66922C2311yescharacteristic
205#66922C2311yescharacteristic
206C4×Dic22—21no—
207C4×Dic22C2312yes—
208#66899C2314yes—
209#66896C2312yes—
210#66896C2312yes—
211C22⋊(C11⋊C8)C2312yes—
212C22⋊(C11⋊C8)C2314yes—
213#66874C2312yes—
214#66874C2312yes—
215#66874C2314yes—
216#66873C2314yes—
217#66873C2314yes—
218#66873C2314yes—
219#66873C2314yes—
220#66872C2312yes—
221#66872C2312yes—
222#66871C2314yes—
223C4⋊(C11⋊C8)C2312yes—
224C4⋊(C11⋊C8)C2312yes—
225C4⋊(C11⋊C8)C2311yescharacteristic
226C4⋊(C11⋊C8)C2314yes—
227C4⋊(C11⋊C8)C2311yescharacteristic
228C4×C11⋊C8C2312yes—
229C4×C11⋊C8C2314yes—
230#61949—111nomaximal, Sylow
231C24×C11—21no—
232C23×D11—22no—
233C11×#41—24no—
234C11×#41—24no—
235C11×#41—42no—
236C2×Q8×C11—21no—
237C2×Q8×C11C2×D411yescharacteristic
238C2×Q8×C11C2412yes—
239C2×D4×C11—22no—
240C2×D4×C11—22no—
241C2×D4×C11—22no—
242C2×D4×C11—21no—
243C2×D4×C11—41no—
244C2×D4×C11C2×D412yes—
245C2×D4×C11C2×D411yescharacteristic
246C2×D4×C11C2411yescharacteristic
247C2×D4×C11C2411yescharacteristic
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11—22no—
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11—21no—
254C22×C4×C11—22no—
255C22×C4×C11—44no—
256C22×C4×C11C2×D412yes—
257C22×C4×C11C2×D411yescharacteristic
258C22×C4×C11C2×D412yes—
259C22×C4×C11C2×D411yescharacteristic
260C22×C4×C11C2411yescharacteristic
261C22×C4×C11C2412yes—
262C2×C22⋊D11—24no—
263C2×C22⋊D11—24no—
264#4339—44no—
265#4339—44no—
266#4339—84no—
267C2×D44—22no—
268C2×D44—22no—
269C2×D44—22no—
270C2×D44—22no—
271C2×D44—22no—
272C2×D44—42no—
273C2×D44—42no—
274C2×D44—44no—
275C2×D44—82no—
276C2×D44C2414yes—
277C2×C4×D11—24no—
278C2×C4×D11—24no—
279C2×Dic22—21no—
280C2×Dic22C2412yes—
281C11×C4⋊C4—21no—
282C11×C4⋊C4—21no—
283C11×C4⋊C4—22no—
284C11×C4⋊C4—22no—
285C11×C4⋊C4—21no—
286C11×C4⋊C4—22no—
287C11×C4⋊C4—22no—
288C11×C4⋊C4—22no—
289C11×C4⋊C4—22no—
290C11×C4⋊C4—21no—
291C11×C4⋊C4C2×D411yescharacteristic
292C11×C4⋊C4C2×D411yescharacteristic
293C11×C4⋊C4C2×D412yes—
294C11×C4⋊C4C2×D412yes—
295C11×C4⋊C4C2412yes—
296C11×C4⋊C4C2411yescharacteristic
297C11×C4⋊C4C2411yescharacteristic
298C11×C22⋊C4—22no—
299C11×C22⋊C4—22no—
300C11×C22⋊C4—22no—
301C11×C22⋊C4—21no—
302C11×C22⋊C4—22no—
303C11×C22⋊C4—22no—
304C11×C22⋊C4—21no—
305C11×C22⋊C4—21no—
306C11×C22⋊C4—21no—
307C11×C22⋊C4—22no—
308C11×C22⋊C4—22no—
309C11×C22⋊C4C2×D412yes—
310C11×C22⋊C4C2×D412yes—
311C11×C22⋊C4C2×D412yes—
312C42×C11—22no—
313C42×C11—22no—
314C42×C11—22no—
315C42×C11C2×D411yescharacteristic
316C42×C11C2×D411yescharacteristic
317C42×C11C2×D412yes—
318C42×C11C2×D412yes—
319C42×C11C2411yescharacteristic
320C42×C11C2412yes—
321C42×C11C2411yescharacteristic
322C22⋊Dic11—22no—
323#4326—44no—
324#4325—44no—
325#4325—44no—
326#4324—24no—
327#4324—42no—
328#4323—28no—
329#4323—44no—
330(C2×D11)⋊C4—24no—
331(C2×D11)⋊C4—24no—
332(C2×D11)⋊C4—24no—
333(C2×D11)⋊C4—24no—
334C4⋊Dic11—21no—
335C4⋊Dic11—21no—
336C4⋊Dic11—21no—
337C4⋊Dic11C2412yes—
338Dic11⋊C4—22no—
339Dic11⋊C4—22no—
340C4×Dic11—22no—
341C2×C11⋊C8—42no—
342C2×C11⋊C8—44no—
343C2×C11⋊C8C2412yes—
344C2×C11⋊C8C2414yes—
345C2×C11⋊C8C2412yes—
346#3508—111no—
347#3475D1111yescharacteristic, complemented
348#3394—112no—
349#3361—112no—
350#3305—112no—
351#3296—114no—
352#3284—112no—
353#3280—114no—
354#3249—111no—
355#3247—112no—
356#3212—112no—
357#3208—111no—
358#3106—112no—
359#3101—111no—
360#3035—112no—
361C2×#459—111no—
362#2988—111no—
363C23×C11—21no—
364C23×C11—21no—
365C23×C11—42no—
366C23×C11—42no—
367C23×C11—81no—
368C23×C11C22×D412yes—
369C23×C11C22×D411yescharacteristic
370C22×D11—24no—
371C22×D11—44no—
372C22×D11—82no—
373C22×D11—82no—
374Q8×C11—22no—
375Q8×C11—22no—
376Q8×C11—22no—
377Q8×C11—81no—
378D4×C11—24no—
379D4×C11—22no—
380D4×C11—21no—
381D4×C11—21no—
382D4×C11—21no—
383D4×C11—42no—
384D4×C11—44no—
385D4×C11—82no—
386D4×C11H(5,𝔽2)12yes—
387C2×C4×C11—24no—
388C2×C4×C11—21no—
389C2×C4×C11—22no—
390C2×C4×C11—21no—
391C2×C4×C11—22no—
392C2×C4×C11—21no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—21no—
396C2×C4×C11—41no—
397C2×C4×C11—42no—
398C2×C4×C11—44no—
399C2×C4×C11—42no—
400C2×C4×C11—42no—
401C2×C4×C11—42no—
402C2×C4×C11—42no—
403C2×C4×C11—42no—
404C2×C4×C11—82no—
405C2×C4×C11#13514yescomplemented
406C2×C4×C11C22×D411yescharacteristic
407C2×C4×C11C22×D411yescharacteristic
408C2×C4×C11C22×D411yescharacteristic
409C2×C4×C11C22×D412yes—
410C2×C4×C11C22×D412yes—
411C2×C4×C11C22×D412yes—
412C2×C4×C11C22×D411yescharacteristic
413C2×C4×C11C22×D411yescharacteristic
414C2×C4×C11C2511yescharacteristic
415C22⋊D11—84no—
416C22⋊D11—84no—
417C2×Dic11—22no—
418C2×Dic11—22no—
419D44—24no—
420D44—24no—
421D44—44no—
422D44—44no—
423D44—44no—
424D44—82no—
425D44—82no—
426C4×D11—84no—
427C4×D11—84no—
428Dic22—22no—
429Dic22—22no—
430Dic22—42no—
431C11⋊C8—24no—
432C11⋊C8—22no—
433C11⋊C8—22no—
434C2×#135—114no—
435C22×D8—112no—
436#559—112no—
437#559—221no—
438#556C2×D1111yescharacteristic, complemented
439#555C2×D1111yescharacteristic, complemented
440#554C2×D1111yescharacteristic, complemented
441#553—21no—
442#552—21no—
443#552C2×D1112yes—
444#551—22no—
445#550—112no—
446#550—221no—
447#547C2×D1111yescharacteristic, complemented
448#546—114no—
449#546—222no—
450#546C2×D1112yes—
451#540—222no—
452#535—221no—
453#533—111no—
454#533C2×D1111yescharacteristic
455#532—112no—
456#532—112no—
457C2×#127—111no—
458#529—22no—
459#529C2×D1112yescomplemented
460#525—21no—
461#518—221no—
462C4×#41C2×D1111yescharacteristic
463C4×#41C2×D1112yescomplemented
464C2×C4×D4C2×D1111yescharacteristic
465C2×#117—21no—
466#495—114no—
467#492—112no—
468#488—114no—
469#486—112no—
470#483—112no—
471#482—114no—
472#478—114no—
473#477—112no—
474#477—112no—
475#476—111no—
476#476—111no—
477#467—114no—
478#466—114no—
479#465—114no—
480#464—114no—
481#463—114no—
482#463—114no—
483#462—112no—
484#462—112no—
485#461—111no—
486#461—111no—
487#460—112no—
488#460—112no—
489#459—112no—
490#459—112no—
491#459—112no—
492#459—112no—
493#452—114no—
494#450—112no—
495#450—114no—
496#449—114no—
497#449—114no—
498C8×Q8—112no—
499C4×SD16—114no—
500C4×SD16—112no—
501C4×SD16—112no—
502C4×D8—114no—
503C8×D4—114no—
504C8×D4—112no—
505#431—111no—
506#431—112no—
507C2×C4⋊C8—111no—
508C2×C4⋊C8—112no—
509#416—114no—
510C2×#102—112no—
511C22×C11—21no—
512C22×C11—21no—
513C22×C11—22no—
514C22×C11—22no—
515C22×C11—22no—
516C22×C11—22no—
517C22×C11—41no—
518C22×C11—41no—
519C22×C11—41no—
520C22×C11—41no—
521C22×C11—41no—
522C22×C11—84no—
523C22×C11C2×#13512yes—
524C22×C11C23×D411yescharacteristic
525C2×D11—44no—
526C2×D11—44no—
527C2×D11—44no—
528C2×D11—164no—
529C4×C11—21no—
530C4×C11—22no—
531C4×C11—21no—
532C4×C11—22no—
533C4×C11—21no—
534C4×C11—22no—
535C4×C11—42no—
536C4×C11—42no—
537C4×C11—41no—
538C4×C11—41no—
539C4×C11C2×#13512yes—
540C4×C11C2×#13512yes—
541C4×C11C2×H(5,𝔽2)11yescharacteristic
542C4×C11#58511yescharacteristic
543Dic11—42no—
544Dic11—42no—
545C2×#41—114no—
546C2×#41—222no—
547C2×#41C22⋊D1111yescharacteristic
548C2×#41C22×D1112yes—
549C22×D4—112no—
550C22×D4—221no—
551C22×D4—221no—
552C22×D4C22×D1111yescharacteristic
553C23×C4—21no—
554#135—448no—
555C2×Q16—114no—
556C2×SD16—112no—
557C2×SD16—114no—
558C2×SD16—114no—
559C2×SD16—112no—
560C2×D8—114no—
561C2×D8—114no—
562C2×D8—444no—
563C22×C8—112no—
564C22×C8—114no—
565C4⋊Q8—111no—
566C4⋊Q8—111no—
567C4⋊Q8C22×D1111yescharacteristic
568C4⋊Q8C22×D1111yescharacteristic
569#127—112no—
570#127—112no—
571#127—222no—
572#127—221no—
573#127—221no—
574#126—22no—
575#126—22no—
576#126—22no—
577#125—22no—
578#125—21no—
579#125—221no—
580#125C22×D1112yes—
581#124—22no—
582#124—114no—
583#124—222no—
584#124—222no—
585#124C22×D1112yes—
586#123—22no—
587#123—22no—
588#123—22no—
589#123—22no—
590#123—224no—
591#123—224no—
592C22⋊Q8—21no—
593C22⋊Q8—21no—
594C22⋊Q8—21no—
595C22⋊Q8—22no—
596C22⋊Q8—112no—
597C22⋊Q8—221no—
598C22⋊Q8C22×D1112yes—
599C22⋊Q8C22×D1112yes—
600#121—21no—
601#121—21no—
602#121—22no—
603#121—114no—
604#121—222no—
605#121—222no—
606#121—222no—
607#121—224no—
608#121—224no—
609#121C22×D1112yes—
610#120—22no—
611#120—224no—
612C4×Q8—21no—
613C4×Q8—112no—
614C4×Q8—221no—
615C4×Q8C22⋊D1111yescharacteristic
616C4×Q8C22×D1112yes—
617C4×Q8C22×D1112yes—
618C4×Q8C22×D1111yescharacteristic
619C4×D4—22no—
620C4×D4—22no—
621C4×D4—22no—
622C4×D4—21no—
623C4×D4—21no—
624C4×D4—114no—
625C4×D4—222no—
626C4×D4—222no—
627C4×D4—222no—
628C4×D4—222no—
629C4×D4—222no—
630C4×D4C22⋊D1112yes—
631C4×D4C22⋊D1111yescharacteristic
632C4×D4C22×D1111yescharacteristic
633C4×D4C22×D1111yescharacteristic
634C4×D4C22×D1111yescharacteristic
635C4×D4C22×D1111yescharacteristic
636C4×D4C22×D1112yes—
637C4×D4C22×D1112yes—
638C4×D4C22×D1111yescharacteristic
639#117—21no—
640#117—21no—
641#117—21no—
642#117—22no—
643#117—22no—
644#117—22no—
645#117—221no—
646#117C22⋊D1111yescharacteristic
647#117C22⋊D1112yes—
648#117C22×D1112yes—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4C22×D1111yescharacteristic
652C2×C22⋊C4—21no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—224no—
655C2×C42—22no—
656C2×C42C22×D1111yescharacteristic
657C2×C42C22×D1112yes—
658#107—114no—
659#106—112no—
660#106—112no—
661C4⋊C8—112no—
662C4⋊C8—111no—
663C4⋊C8—112no—
664C4⋊C8—114no—
665C4⋊C8—111no—
666#103—114no—
667#103—112no—
668#103—114no—
669#103—112no—
670#102—112no—
671#102—112no—
672#102—114no—
673#102—114no—
674#102—114no—
675#102—114no—
676C22⋊C8—114no—
677C22⋊C8—112no—
678C4×C8—114no—
679C4×C8—112no—
680C2×C11—22no—
681C2×C11—42no—
682C2×C11—42no—
683C2×C11—81no—
684C2×C11#348811yescharacteristic
685C2×C11C22×#13511yescharacteristic
686C2×C11#358511yescharacteristic
687D11—84no—
688C24—21no—
689C24—222no—
690#41—24no—
691#41—24no—
692#41—42no—
693#41—444no—
694#41—444no—
695#41—884no—
696C2×Q8—21no—
697C2×Q8—112no—
698C2×Q8—221no—
699C2×Q8C2×C22⋊D1111yescharacteristic
700C2×Q8C23×D1112yes—
701C2×D4—22no—
702C2×D4—22no—
703C2×D4—22no—
704C2×D4—21no—
705C2×D4—41no—
706C2×D4—114no—
707C2×D4—224no—
708C2×D4—224no—
709C2×D4—222no—
710C2×D4—222no—
711C2×D4—222no—
712C2×D4—222no—
713C2×D4—222no—
714C2×D4—442no—
715C2×D4—442no—
716C2×D4—444no—
717C2×D4—882no—
718C2×D4C2×C22⋊D1112yes—
719C2×D4C2×C22⋊D1111yescharacteristic
720C2×D4C23×D1111yescharacteristic
721C2×D4C23×D1111yescharacteristic
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—22no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—22no—
729C22×C4—44no—
730C22×C4—224no—
731C22×C4—224no—
732C22×C4C2×C22⋊D1112yes—
733C22×C4C2×C22⋊D1111yescharacteristic
734C22×C4C2×C22⋊D1112yes—
735C22×C4C2×C22⋊D1111yescharacteristic
736C22×C4C23×D1111yescharacteristic
737C22×C4C23×D1112yes—
738Q16—444no—
739SD16—224no—
740SD16—442no—
741SD16—444no—
742SD16—444no—
743D8—228no—
744D8—444no—
745C2×C8—112no—
746C2×C8—112no—
747C2×C8—114no—
748C2×C8—442no—
749C2×C8—444no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—22no—
753C4⋊C4—22no—
754C4⋊C4—21no—
755C4⋊C4—22no—
756C4⋊C4—22no—
757C4⋊C4—22no—
758C4⋊C4—22no—
759C4⋊C4—21no—
760C4⋊C4—112no—
761C4⋊C4—221no—
762C4⋊C4—221no—
763C4⋊C4—221no—
764C4⋊C4—222no—
765C4⋊C4—222no—
766C4⋊C4C2×C22⋊D1111yescharacteristic
767C4⋊C4C2×C22⋊D1111yescharacteristic
768C4⋊C4C2×C22⋊D1112yes—
769C4⋊C4C2×C22⋊D1112yes—
770C4⋊C4C23×D1111yescharacteristic
771C4⋊C4C23×D1111yescharacteristic
772C4⋊C4C23×D1112yes—
773C22⋊C4—22no—
774C22⋊C4—22no—
775C22⋊C4—22no—
776C22⋊C4—21no—
777C22⋊C4—22no—
778C22⋊C4—22no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—22no—
783C22⋊C4—22no—
784C22⋊C4—222no—
785C22⋊C4—224no—
786C22⋊C4—224no—
787C22⋊C4—224no—
788C22⋊C4—224no—
789C22⋊C4C2×C22⋊D1112yes—
790C22⋊C4C2×C22⋊D1112yes—
791C22⋊C4C2×C22⋊D1112yes—
792C42—22no—
793C42—22no—
794C42—22no—
795C42—222no—
796C42C2×C22⋊D1112yes—
797C42C2×C22⋊D1112yes—
798C42C2×C22⋊D1111yescharacteristic
799C42C2×C22⋊D1111yescharacteristic
800C42C23×D1112yes—
801C42C23×D1111yescharacteristic
802C42C23×D1111yescharacteristic
803C11#6194911yescharacteristic, complemented, Sylow
804C23—21no—
805C23—21no—
806C23—42no—
807C23—42no—
808C23—81no—
809C23—224no—
810C23—444no—
811C23—882no—
812C23—882no—
813C23C22×C22⋊D1112yes—
814C23C22×C22⋊D1111yescharacteristic
815Q8—22no—
816Q8—22no—
817Q8—22no—
818Q8—81no—
819Q8—222no—
820Q8—222no—
821Q8—442no—
822D4—24no—
823D4—22no—
824D4—21no—
825D4—21no—
826D4—21no—
827D4—42no—
828D4—44no—
829D4—82no—
830D4—224no—
831D4—224no—
832D4—444no—
833D4—444no—
834D4—444no—
835D4—882no—
836D4—882no—
837D4—884no—
838D4—884no—
839D4#6704212yes—
840C2×C4—24no—
841C2×C4—21no—
842C2×C4—22no—
843C2×C4—21no—
844C2×C4—22no—
845C2×C4—21no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—21no—
849C2×C4—41no—
850C2×C4—42no—
851C2×C4—44no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—82no—
858C2×C4—222no—
859C2×C4—222no—
860C2×C4—884no—
861C2×C4—884no—
862C2×C4#6700314yescomplemented
863C2×C4C22×C22⋊D1112yes—
864C2×C4C22×C22⋊D1112yes—
865C2×C4C22×C22⋊D1111yescharacteristic
866C2×C4C22×C22⋊D1111yescharacteristic
867C2×C4C22×C22⋊D1112yes—
868C2×C4C22×C22⋊D1111yescharacteristic
869C2×C4C22×C22⋊D1111yescharacteristic
870C2×C4C22×C22⋊D1111yescharacteristic
871C2×C4C24×D1111yescharacteristic
872C8—224no—
873C8—222no—
874C8—222no—
875C22—21no—
876C22—21no—
877C22—22no—
878C22—22no—
879C22—22no—
880C22—22no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—84no—
887C22—444no—
888C22—444no—
889C22—444no—
890C22—1764no—
891C22C2×#6700312yes—
892C22C23×C22⋊D1111yescharacteristic
893C4—21no—
894C4—22no—
895C4—21no—
896C4—22no—
897C4—21no—
898C4—22no—
899C4—42no—
900C4—42no—
901C4—41no—
902C4—41no—
903C4—442no—
904C4—442no—
905C4C2×#6700312yes—
906C4C2×#6700312yes—
907C4C2×#6704211yescharacteristic
908C4#1062345311yescharacteristic
909C2—22no—
910C2—42no—
911C2—42no—
912C2—81no—
913C2—884no—
914C2#1308228511yescharacteristic
915C2C22×#6700311yescharacteristic
916C2#1308339511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3475C2
socleC22×C11C23×D4
hypercenter#3475D11
hypocenterC11#61949
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3475

Complements

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

NH ≅ G/Ntype
1. #13082492C2semidirect
2. #13081612C2semidirect
3. #13081276C2semidirect
4. #13080560C2semidirect
5. #13080445C2semidirect
6. #13080342C2semidirect
7. #13080297C2semidirect
8. #13079958C2semidirect
9. #13079942C2semidirect
10. #13079588C2semidirect
11. #13079554C2semidirect
12. #13078676C2semidirect
13. #13078624C2semidirect
14. #13078071C2semidirect
15. C2×#10622628C2semidirect
16. #13077727C2semidirect
17. C11×#3475C2semidirect
18. C11×#556C22semidirect
19. C11×#555C22semidirect
20. C11×#554C22semidirect
25. C11×#547C22semidirect
29. C11×#529C22semidirect
32. C4×C11×#41C22semidirect
36. C2×#67003C22semidirect
39. #10623116C22semidirect
41. #10623084C22semidirect
46. #10623008C22semidirect
47. #10623008C22semidirect
50. #10622851C22semidirect
52. #10622704C22semidirect
53. #10622703C22semidirect
54. #10622701C22semidirect
55. #10622698C22semidirect
56. #10622681C22semidirect
57. #10622679C22semidirect
58. #10622672C22semidirect
59. #10622670C22semidirect
61. #10622661C22semidirect
62. #10622660C22semidirect
64. #10622651C22semidirect
65. #10622650C22semidirect
66. #10622644C22semidirect
67. #10622641C22semidirect
68. #10622640C22semidirect
69. #10622640C22semidirect
70. C4×#4325C22semidirect
71. Q8×C11⋊C8C22semidirect
72. #10622634C22semidirect
73. #10622632C22semidirect
74. #10622632C22semidirect
75. C4×#4324C22semidirect
76. C4×#4324C22semidirect
77. #10622629C22semidirect
82. C4×#4323C22semidirect
84. D4×C11⋊C8C22semidirect
85. #10622621C22semidirect
86. #10622621C22semidirect
87. #10622616C22semidirect
88. #10622615C22semidirect
92. #10622538C22semidirect
94. C2×C4⋊(C11⋊C8)C22semidirect
347. #3475D11semidirect
405. C2×C4×C11#135semidirect
438. #556C2×D11semidirect
439. #555C2×D11semidirect
440. #554C2×D11semidirect
447. #547C2×D11semidirect
459. #529C2×D11semidirect
463. C4×#41C2×D11semidirect
803. C11#61949semidirect
862. C2×C4#67003semidirect

Maximal subgroups

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

subgroupindex
#130824922
#130816122
#130812762
#130805602
#130804452
#130803422
#130802972
#130799582
#130799422
#130795882
#130795542
#130786762
#130786242
#130780712
C2×#106226282
#130777272
C11×#34752
#6194911