Finite Group Databasebeta

← #15625280

Subgroups — #15625280

Order 2816.

2196 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623008C211yesmaximal, characteristic, complemented
2C2×#10623010C211yesmaximal, characteristic, complemented
3#13079655C214yesmaximal, complemented
4#13079645C212yesmaximal, complemented
5#13079636C212yesmaximal, complemented
6#13079594C214yesmaximal, complemented
7#13079583C214yesmaximal, complemented
8#13079082C212yesmaximal, complemented
9#13079017C212yesmaximal, complemented
10#13078090C212yesmaximal, complemented
11#13078082C212yesmaximal, complemented
12#13077878C212yesmaximal, complemented
13#13077870C212yesmaximal, complemented
14C11×#2920C211yesmaximal, characteristic, complemented
15C22×#4339C2212yes—
16C22×C42×C11C2211yescharacteristic
17C2×#66983—21no—
18C2×#66983—21no—
19C2×#66983C2211yescharacteristic
20C2×#66982—21no—
21C2×C4×C22⋊D11—21no—
22C2×#66977C2211yescharacteristic
23C2×#66962C2214yescomplemented
24C2×#66961C2214yescomplemented
25#10623010—21no—
26#10623010—21no—
27#10623010—21no—
28#10623010—21no—
29#10623010C2212yes—
30#10623010C2212yes—
31#10623010C2212yescomplemented
32#10623010C2212yescomplemented
33C2×#66929—21no—
34#10623008—21no—
35#10623008—21no—
36#10623008—21no—
37#10623008—21no—
38#10623008C2212yes—
39#10623008C2212yes—
40#10623008C2212yescomplemented
41#10623008C2212yescomplemented
42C2×#66928C2211yescharacteristic, complemented
43C2×#66928C2212yescomplemented
44C2×#66927C2211yescharacteristic, complemented
45C2×C4×D44—21no—
46C2×C4×D44—21no—
47C2×C4×D44C2211yescharacteristic, complemented
48C2×#66925—21no—
49C2×#66923C2211yescharacteristic, complemented
50C2×#66922C2211yescharacteristic, complemented
51C2×C4×Dic22C2211yescharacteristic, complemented
52C11×#432C2212yescomplemented
53C11×#432C2212yescomplemented
54C11×#431C2212yescomplemented
55C11×#431C2212yescomplemented
56C11×#423C2212yescomplemented
57C11×#407C2212yes—
58C4×C11×M16C2212yescomplemented
59#10622746C2214yescomplemented
60#10622746C2214yescomplemented
61#10622462C2214yescomplemented
62#10622461C2214yescomplemented
63#10622458C2218yescomplemented
64#10622457C2218yescomplemented
65#10622456C2214yescomplemented
66#10622454C2214yescomplemented
67#10622352C2214yescomplemented
68#10622351C2214yes—
69#10622347C2218yescomplemented
70#10622346C2218yescomplemented
71#10622345C2214yes—
72#10622344C2214yescomplemented
73#10622328C2214yescomplemented
74#10622326C2214yescomplemented
75#10622325C2214yescomplemented
76#10622316C2214yescomplemented
77#10622310C2218yescomplemented
78#10622309C2218yescomplemented
79C23×C4×C11D411yescharacteristic
80C23×C4×C11D411yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C22×C22⋊D11—21no—
83C22×C22⋊D11—22no—
84C2×#4339—22no—
85C2×#4339—22no—
86C2×#4339—48no—
87C2×#4339C2314yes—
88C2×#4339C2314yes—
89C22×D44—21no—
90C22×D44—21no—
91C22×D44C2311yescharacteristic
92C22×D44C2312yes—
93C22×C4×D11—21no—
94C22×C4×D11—22no—
95C22×Dic22C2311yescharacteristic
96C22×Dic22C2312yes—
97C2×C11×M16C2314yes—
98C2×C42×C11D411yescharacteristic
99C2×C42×C11D411yescharacteristic
100C2×C42×C11D411yescharacteristic
101C2×C42×C11D411yescharacteristic
102C2×C42×C11D411yescharacteristic
103C2×C42×C11D411yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C2×C42×C11C2311yescharacteristic
106C2×C42×C11C2311yescharacteristic
107C2×C42×C11C2311yescharacteristic
108C2×C42×C11C2311yescharacteristic
109C2×C42×C11C2311yescharacteristic
110C2×C22⋊Dic11—21no—
111#66983—22no—
112#66983—22no—
113#66983—22no—
114#66983—22no—
115#66983—22no—
116#66983—22no—
117#66983—22no—
118#66983—22no—
119#66983—21no—
120#66983—21no—
121#66983C2312yes—
122#66983C2312yes—
123#66982—22no—
124#66982—22no—
125#66982—22no—
126#66982—22no—
127C4×C22⋊D11—22no—
128C4×C22⋊D11—22no—
129C4×C22⋊D11—22no—
130C4×C22⋊D11—22no—
131C2×(C2×D11)⋊C4—21no—
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4—22no—
134C2×(C2×D11)⋊C4—22no—
135C2×(C2×D11)⋊C4—21no—
136C2×(C2×D11)⋊C4—21no—
137C2×C4⋊Dic11—21no—
138C2×C4⋊Dic11—21no—
139C2×C4⋊Dic11C2311yescharacteristic
140C2×C4⋊Dic11C2311yescharacteristic
141#66977—21no—
142#66977—21no—
143#66977C2312yes—
144#66977C2312yes—
145C2×Dic11⋊C4—21no—
146C2×Dic11⋊C4—21no—
147C2×Dic11⋊C4—21no—
148C2×Dic11⋊C4—21no—
149C2×C4×Dic11—21no—
150#66962—48no—
151#66961—48no—
152C2×Dic44C2318yes—
153C2×D88C2318yes—
154C2×#4314C2318yes—
155C2×#4314C2318yes—
156#66929—22no—
157#66929—22no—
158#66929—22no—
159#66929—22no—
160#66928—22no—
161#66928—22no—
162#66928—21no—
163#66928—21no—
164#66928C2314yes—
165#66928C2314yes—
166#66928C2312yes—
167#66928C2312yes—
168#66927—21no—
169#66927—21no—
170#66927C2312yes—
171#66927C2312yes—
172C4×D44—22no—
173C4×D44—22no—
174C4×D44—22no—
175C4×D44—22no—
176C4×D44—22no—
177C4×D44—22no—
178C4×D44—22no—
179C4×D44—22no—
180C4×D44—21no—
181C4×D44—21no—
182C4×D44C2312yes—
183C4×D44C2312yes—
184#66925—22no—
185#66925—22no—
186#66925—22no—
187#66925—22no—
188#66923—21no—
189#66923—21no—
190#66923C2312yes—
191#66923C2312yes—
192#66922—21no—
193#66922—21no—
194#66922C2312yes—
195#66922C2312yes—
196C4×Dic22—21no—
197C4×Dic22—21no—
198C4×Dic22C2312yes—
199C4×Dic22C2312yes—
200C11×C4⋊C8C2314yes—
201C11×C4⋊C8C2314yes—
202C11×C22⋊C8C2314yes—
203C11×C22⋊C8C2314yes—
204C11×#97C2314yes—
205C4×C8×C11C2314yes—
206#66885C2318yes—
207#66885C2318yes—
208#66880C2318yes—
209#66880C2318yes—
210#60805—111nomaximal, Sylow
211C24×C11C2×D411yescharacteristic
212C23×D11—21no—
213C23×D11—22no—
214C22×C4×C11—24no—
215C22×C4×C11—42no—
216C22×C4×C11—42no—
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D411yescharacteristic
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×C11C2411yescharacteristic
233C22×C4×C11C2411yescharacteristic
234C22×C4×C11C2411yescharacteristic
235C2×C22⋊D11—22no—
236C2×C22⋊D11—22no—
237C2×C22⋊D11—24no—
238C2×C22⋊D11—24no—
239C2×C22⋊D11—48no—
240C2×C22⋊D11—44no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—22no—
245#4339—28no—
246#4339—28no—
247#4339—44no—
248#4339—44no—
249#4339—48no—
250#4339—48no—
251C2×D44—22no—
252C2×D44—22no—
253C2×D44—22no—
254C2×D44—22no—
255C2×D44—21no—
256C2×D44—22no—
257C2×D44—24no—
258C2×D44—44no—
259C2×D44—44no—
260C2×D44—44no—
261C2×D44C2414yes—
262C2×D44C2412yes—
263C2×C4×D11—22no—
264C2×C4×D11—22no—
265C2×C4×D11—24no—
266C2×C4×D11—24no—
267C2×C4×D11—44no—
268C2×C4×D11—48no—
269C2×Dic22—21no—
270C2×Dic22—22no—
271C2×Dic22—24no—
272C2×Dic22—44no—
273C2×Dic22C2414yes—
274C2×Dic22C2412yes—
275C11×M16—28no—
276C2×C8×C11C2418yes—
277C42×C11C2×D411yescharacteristic
278C42×C11C2×D411yescharacteristic
279C42×C11C2×D411yescharacteristic
280C42×C11C2×D411yescharacteristic
281C42×C11C2×D411yescharacteristic
282C42×C11C2×D411yescharacteristic
283C42×C11C2×D411yescharacteristic
284C42×C11C2×D411yescharacteristic
285C42×C11C2×D411yescharacteristic
286C42×C11C2×D411yescharacteristic
287C42×C11C2×D411yescharacteristic
288C42×C11C2×D411yescharacteristic
289C42×C11C2411yescharacteristic
290C42×C11C2411yescharacteristic
291C42×C11C2411yescharacteristic
292C42×C11C2411yescharacteristic
293C22⋊Dic11—22no—
294C22⋊Dic11—22no—
295(C2×D11)⋊C4—22no—
296(C2×D11)⋊C4—22no—
297(C2×D11)⋊C4—22no—
298(C2×D11)⋊C4—22no—
299(C2×D11)⋊C4—24no—
300(C2×D11)⋊C4—24no—
301(C2×D11)⋊C4—24no—
302(C2×D11)⋊C4—24no—
303(C2×D11)⋊C4—22no—
304(C2×D11)⋊C4—22no—
305(C2×D11)⋊C4—22no—
306(C2×D11)⋊C4—22no—
307C4⋊Dic11—21no—
308C4⋊Dic11—22no—
309C4⋊Dic11—22no—
310C4⋊Dic11—22no—
311C4⋊Dic11—22no—
312C4⋊Dic11—21no—
313C4⋊Dic11C2412yes—
314C4⋊Dic11C2412yes—
315Dic11⋊C4—22no—
316Dic11⋊C4—22no—
317Dic11⋊C4—22no—
318Dic11⋊C4—22no—
319Dic11⋊C4—22no—
320Dic11⋊C4—22no—
321Dic11⋊C4—22no—
322Dic11⋊C4—22no—
323C4×Dic11—22no—
324C4×Dic11—22no—
325Dic44—48no—
326D88—48no—
327#4314—48no—
328#4314—48no—
329C2×#532—111no—
330C2×#529—111no—
331#3219—114no—
332#3218—112no—
333#3217—112no—
334#3212—114no—
335#3211—114no—
336#3153—112no—
337#3142—112no—
338#3037—112no—
339#3036—112no—
340#3007—112no—
341#3006—112no—
342#2920D1111yescharacteristic, complemented
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—41no—
346C23×C11C22×D411yescharacteristic
347C23×C11C22×D411yescharacteristic
348C23×C11C22×D411yescharacteristic
349C22×D11—22no—
350C22×D11—24no—
351C22×D11—44no—
352C22×D11—42no—
353C22×D11—44no—
354C22×D11—42no—
355C22×D11—42no—
356C22×D11—44no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11—41no—
373C2×C4×C11—41no—
374C2×C4×C11C22×D411yescharacteristic
375C2×C4×C11C22×D411yescharacteristic
376C2×C4×C11C22×D411yescharacteristic
377C2×C4×C11C22×D411yescharacteristic
378C2×C4×C11C22×D411yescharacteristic
379C2×C4×C11C22×D411yescharacteristic
380C2×C4×C11C22×D411yescharacteristic
381C2×C4×C11C22×D411yescharacteristic
382C2×C4×C11C22×D411yescharacteristic
383C2×C4×C11C22×D411yescharacteristic
384C2×C4×C11C22×D411yescharacteristic
385C2×C4×C11H(5,𝔽2)14yes—
386C2×C4×C11C2511yescharacteristic
387C22⋊D11—48no—
388C22⋊D11—44no—
389C22⋊D11—48no—
390C22⋊D11—44no—
391C2×Dic11—22no—
392C2×Dic11—22no—
393C2×Dic11—22no—
394C2×Dic11—24no—
395C2×Dic11—44no—
396C2×Dic11—42no—
397C2×Dic11—42no—
398C2×Dic11—42no—
399D44—24no—
400D44—24no—
401D44—24no—
402D44—44no—
403D44—44no—
404D44—44no—
405D44—44no—
406D44—42no—
407D44—44no—
408C4×D11—44no—
409C4×D11—48no—
410C4×D11—48no—
411C4×D11—44no—
412Dic22—24no—
413Dic22—24no—
414Dic22—24no—
415Dic22—44no—
416Dic22—42no—
417C8×C11—28no—
418C22×#41—112no—
419C2×#137—114no—
420C2×AGL(1,ℤ/8)—114no—
421#532—112no—
422#532—112no—
423#532—112no—
424#532—112no—
425#532—221no—
426#532—221no—
427#532—221no—
428#532—221no—
429C2×C4⋊Q8—111no—
430C2×#127—111no—
431#529—112no—
432#529—112no—
433#529—112no—
434#529—112no—
435#529—221no—
436#529—221no—
437#529—221no—
438#529—221no—
439C2×#126—221no—
440C2×#125—111no—
441C2×#124—111no—
442C2×#124—112no—
443C2×#123—221no—
444C2×C22⋊Q8—111no—
445C2×#121—111no—
446C2×#121—221no—
447C2×#121—221no—
448C2×C4×Q8—111no—
449C2×C4×D4—111no—
450C2×C4×D4—221no—
451C2×C4×D4—221no—
452C2×C4×D4—221no—
453C2×#117—221no—
454C22×C42C2×D1111yescharacteristic
455#497—114no—
456#496—114no—
457#495—118no—
458#491—114no—
459#490—114no—
460#488—118no—
461#464—118no—
462#463—118no—
463#462—114no—
464#461—114no—
465#460—114no—
466#459—114no—
467#452—118no—
468#451—114no—
469#450—114no—
470#449—118no—
471#448—114no—
472#447—114no—
473#432C2×D1112yescomplemented
474#432C2×D1112yescomplemented
475#431C2×D1112yescomplemented
476#431C2×D1112yescomplemented
477#423C2×D1112yescomplemented
478#417—114no—
479#417—114no—
480#407C2×D1112yes—
481C4×M16C2×D1112yescomplemented
482C22×C11—21no—
483C22×C11—21no—
484C22×C11—21no—
485C22×C11—21no—
486C22×C11—21no—
487C22×C11—21no—
488C22×C11—21no—
489C22×C11—44no—
490C22×C11#53512yes—
491C22×C11#57512yes—
492C22×C11C23×D411yescharacteristic
493C2×D11—44no—
494C2×D11—42no—
495C2×D11—42no—
496C2×D11—44no—
497C2×D11—44no—
498C2×D11—42no—
499C2×D11—88no—
500C2×D11—84no—
501C4×C11—21no—
502C4×C11—21no—
503C4×C11—21no—
504C4×C11—21no—
505C4×C11—21no—
506C4×C11—21no—
507C4×C11—21no—
508C4×C11—21no—
509C4×C11—21no—
510C4×C11#53512yes—
511C4×C11#57512yes—
512C4×C11C2×H(5,𝔽2)12yes—
513Dic11—44no—
514Dic11—42no—
515Dic11—42no—
516Dic11—42no—
517C2×#41—114no—
518C2×#41—114no—
519C2×#41—222no—
520C2×#41—222no—
521C2×#41—448no—
522C22×Q8—111no—
523C22×Q8—112no—
524C22×D4—111no—
525C22×D4—112no—
526C22×D4—221no—
527C22×D4—222no—
528C22×D4—221no—
529C22×D4—221no—
530C23×C4—221no—
531C23×C4—222no—
532C23×C4D4411yescharacteristic
533C23×C4D4411yescharacteristic
534C23×C4C22×D1111yescharacteristic
535#137—448no—
536AGL(1,ℤ/8)—448no—
537C2×Q16—118no—
538C2×SD16—118no—
539C2×SD16—118no—
540C2×D8—118no—
541C2×M16C22×D1114yes—
542C4⋊Q8—112no—
543C4⋊Q8—112no—
544C4⋊Q8—221no—
545C4⋊Q8—221no—
546#127—112no—
547#127—112no—
548#127—221no—
549#127—221no—
550#126—222no—
551#126—222no—
552#126—222no—
553#126—222no—
554#125—112no—
555#125—112no—
556#125—221no—
557#125—221no—
558#124—112no—
559#124—112no—
560#124—114no—
561#124—114no—
562#124—221no—
563#124—221no—
564#124—222no—
565#124—222no—
566#123—222no—
567#123—222no—
568#123—222no—
569#123—222no—
570C22⋊Q8—112no—
571C22⋊Q8—112no—
572C22⋊Q8—221no—
573C22⋊Q8—221no—
574#121—112no—
575#121—112no—
576#121—221no—
577#121—221no—
578#121—222no—
579#121—222no—
580#121—222no—
581#121—222no—
582#121—222no—
583#121—222no—
584#121—222no—
585#121—222no—
586C4×Q8—112no—
587C4×Q8—112no—
588C4×Q8—221no—
589C4×Q8—221no—
590C4×D4—112no—
591C4×D4—112no—
592C4×D4—222no—
593C4×D4—222no—
594C4×D4—222no—
595C4×D4—222no—
596C4×D4—221no—
597C4×D4—221no—
598C4×D4—222no—
599C4×D4—222no—
600C4×D4—222no—
601C4×D4—222no—
602C4×D4—222no—
603C4×D4—222no—
604C4×D4—222no—
605C4×D4—222no—
606#117—222no—
607#117—222no—
608#117—222no—
609#117—222no—
610C2×C4⋊C4—111no—
611C2×C4⋊C4—111no—
612C2×C4⋊C4—221no—
613C2×C4⋊C4—221no—
614C2×C4⋊C4—221no—
615C2×C4⋊C4—221no—
616C2×C4⋊C4—221no—
617C2×C4⋊C4—221no—
618C2×C22⋊C4—221no—
619C2×C22⋊C4—221no—
620C2×C22⋊C4—221no—
621C2×C22⋊C4—221no—
622C2×C22⋊C4—222no—
623C2×C22⋊C4—222no—
624C2×C22⋊C4—221no—
625C2×C42—221no—
626C2×C42D4411yescharacteristic
627C2×C42D4411yescharacteristic
628C2×C42D4411yescharacteristic
629C2×C42D4411yescharacteristic
630C2×C42D4411yescharacteristic
631C2×C42D4411yescharacteristic
632C2×C42C22×D1111yescharacteristic
633C2×C42C22×D1111yescharacteristic
634C2×C42C22×D1111yescharacteristic
635C2×C42C22×D1111yescharacteristic
636C2×C42C22×D1111yescharacteristic
637C2×C42C22×D1111yescharacteristic
638C4⋊C8C22×D1114yes—
639C4⋊C8C22×D1114yes—
640#103—118no—
641#103—118no—
642#102—118no—
643#102—118no—
644C22⋊C8C22×D1114yes—
645C22⋊C8C22×D1114yes—
646#97C22×D1114yes—
647C4×C8C22×D1114yes—
648C2×C11—22no—
649C2×C11—22no—
650C2×C11—41no—
651C2×C11C2×#53511yescharacteristic
652C2×C11C2×#57511yescharacteristic
653C2×C11C2×#57511yescharacteristic
654D11—84no—
655D11—82no—
656C24—221no—
657C24—222no—
658C24C2×D4411yescharacteristic
659#41—228no—
660#41—228no—
661#41—444no—
662#41—444no—
663#41—448no—
664#41—448no—
665C2×Q8—114no—
666C2×Q8—112no—
667C2×Q8—221no—
668C2×Q8—222no—
669C2×Q8—224no—
670C2×Q8—444no—
671C2×D4—114no—
672C2×D4—112no—
673C2×D4—222no—
674C2×D4—222no—
675C2×D4—224no—
676C2×D4—224no—
677C2×D4—221no—
678C2×D4—222no—
679C2×D4—222no—
680C2×D4—222no—
681C2×D4—222no—
682C2×D4—222no—
683C2×D4—224no—
684C2×D4—444no—
685C2×D4—444no—
686C2×D4—444no—
687C2×D4—448no—
688C2×D4—444no—
689C22×C4—24no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—221no—
693C22×C4—221no—
694C22×C4—221no—
695C22×C4—222no—
696C22×C4—222no—
697C22×C4—222no—
698C22×C4—224no—
699C22×C4—224no—
700C22×C4—448no—
701C22×C4—444no—
702C22×C4C2×D4411yescharacteristic
703C22×C4C2×D4411yescharacteristic
704C22×C4C2×D4411yescharacteristic
705C22×C4C2×D4411yescharacteristic
706C22×C4C2×D4411yescharacteristic
707C22×C4C2×D4411yescharacteristic
708C22×C4C2×D4411yescharacteristic
709C22×C4C2×D4411yescharacteristic
710C22×C4C2×D4411yescharacteristic
711C22×C4C2×D4411yescharacteristic
712C22×C4C2×D4411yescharacteristic
713C22×C4C2×D4411yescharacteristic
714C22×C4C2×D4411yescharacteristic
715C22×C4C2×D4411yescharacteristic
716C22×C4C2×D4411yescharacteristic
717C22×C4C23×D1111yescharacteristic
718C22×C4C23×D1111yescharacteristic
719C22×C4C23×D1111yescharacteristic
720Q16—448no—
721SD16—448no—
722SD16—448no—
723D8—448no—
724M16—28no—
725C2×C8C23×D1118yes—
726C4⋊C4—112no—
727C4⋊C4—112no—
728C4⋊C4—221no—
729C4⋊C4—221no—
730C4⋊C4—222no—
731C4⋊C4—222no—
732C4⋊C4—222no—
733C4⋊C4—222no—
734C4⋊C4—222no—
735C4⋊C4—222no—
736C4⋊C4—222no—
737C4⋊C4—222no—
738C4⋊C4—222no—
739C4⋊C4—222no—
740C4⋊C4—222no—
741C4⋊C4—222no—
742C22⋊C4—222no—
743C22⋊C4—222no—
744C22⋊C4—222no—
745C22⋊C4—222no—
746C22⋊C4—222no—
747C22⋊C4—222no—
748C22⋊C4—222no—
749C22⋊C4—222no—
750C22⋊C4—224no—
751C22⋊C4—224no—
752C22⋊C4—224no—
753C22⋊C4—224no—
754C22⋊C4—222no—
755C22⋊C4—222no—
756C42—222no—
757C42—222no—
758C42C2×D4411yescharacteristic
759C42C2×D4411yescharacteristic
760C42C2×D4411yescharacteristic
761C42C2×D4411yescharacteristic
762C42C2×D4411yescharacteristic
763C42C2×D4411yescharacteristic
764C42C2×D4411yescharacteristic
765C42C2×D4411yescharacteristic
766C42C2×D4411yescharacteristic
767C42C2×D4411yescharacteristic
768C42C2×D4411yescharacteristic
769C42C2×D4411yescharacteristic
770C42C23×D1111yescharacteristic
771C42C23×D1111yescharacteristic
772C42C23×D1111yescharacteristic
773C42C23×D1111yescharacteristic
774C11#6080511yescharacteristic, complemented, Sylow
775C23—22no—
776C23—22no—
777C23—41no—
778C23—222no—
779C23—224no—
780C23—444no—
781C23—442no—
782C23—444no—
783C23—442no—
784C23—444no—
785C23—442no—
786C23C22×D4411yescharacteristic
787C23C22×D4411yescharacteristic
788C23C22×D4411yescharacteristic
789Q8—224no—
790Q8—224no—
791Q8—224no—
792Q8—444no—
793Q8—442no—
794D4—224no—
795D4—224no—
796D4—224no—
797D4—444no—
798D4—444no—
799D4—444no—
800D4—444no—
801D4—448no—
802D4—444no—
803D4—444no—
804D4—448no—
805D4—444no—
806D4—442no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—222no—
825C2×C4—222no—
826C2×C4—222no—
827C2×C4—224no—
828C2×C4—448no—
829C2×C4—444no—
830C2×C4—444no—
831C2×C4—442no—
832C2×C4—442no—
833C2×C4—442no—
834C2×C4—444no—
835C2×C4—448no—
836C2×C4C22×D4411yescharacteristic
837C2×C4C22×D4411yescharacteristic
838C2×C4C22×D4411yescharacteristic
839C2×C4C22×D4411yescharacteristic
840C2×C4C22×D4411yescharacteristic
841C2×C4C22×D4411yescharacteristic
842C2×C4C22×D4411yescharacteristic
843C2×C4C22×D4411yescharacteristic
844C2×C4C22×D4411yescharacteristic
845C2×C4C22×D4411yescharacteristic
846C2×C4C22×D4411yescharacteristic
847C2×C4#6704214yes—
848C2×C4C24×D1111yescharacteristic
849C8—28no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—44no—
858C22—444no—
859C22—442no—
860C22—442no—
861C22—444no—
862C22—442no—
863C22—444no—
864C22—888no—
865C22—884no—
866C22#1062305612yes—
867C22#1062327912yes—
868C22C23×D4411yescharacteristic
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—444no—
879C4—442no—
880C4—442no—
881C4—442no—
882C4#1062305612yes—
883C4#1062327912yes—
884C4C2×#6704212yes—
885C2—22no—
886C2—22no—
887C2—41no—
888C2—884no—
889C2—882no—
890C2C2×#1062305611yescharacteristic
891C2C2×#1062327911yescharacteristic
892C2C2×#1062327911yescharacteristic
subgroupG/H
centerC22C23×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#2920C2
socleC22×C11C23×D4
hypercenter#2920D11
hypocenterC11#60805
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C42 ◁ #2920

Complements

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

NH ≅ G/Ntype
1. C2×#10623008C2semidirect
2. C2×#10623010C2semidirect
3. #13079655C2semidirect
4. #13079645C2semidirect
5. #13079636C2semidirect
6. #13079594C2semidirect
7. #13079583C2semidirect
8. #13079082C2semidirect
9. #13079017C2semidirect
10. #13078090C2semidirect
11. #13078082C2semidirect
12. #13077878C2semidirect
13. #13077870C2semidirect
14. C11×#2920C2semidirect
23. C2×#66962C22semidirect
24. C2×#66961C22semidirect
31. #10623010C22semidirect
32. #10623010C22semidirect
40. #10623008C22semidirect
41. #10623008C22semidirect
42. C2×#66928C22semidirect
43. C2×#66928C22semidirect
44. C2×#66927C22semidirect
47. C2×C4×D44C22semidirect
49. C2×#66923C22semidirect
50. C2×#66922C22semidirect
51. C2×C4×Dic22C22semidirect
52. C11×#432C22semidirect
53. C11×#432C22semidirect
54. C11×#431C22semidirect
55. C11×#431C22semidirect
56. C11×#423C22semidirect
58. C4×C11×M16C22semidirect
59. #10622746C22semidirect
60. #10622746C22semidirect
61. #10622462C22semidirect
62. #10622461C22semidirect
63. #10622458C22semidirect
64. #10622457C22semidirect
65. #10622456C22semidirect
66. #10622454C22semidirect
67. #10622352C22semidirect
69. #10622347C22semidirect
70. #10622346C22semidirect
72. #10622344C22semidirect
73. #10622328C22semidirect
74. #10622326C22semidirect
75. #10622325C22semidirect
76. #10622316C22semidirect
77. #10622310C22semidirect
78. #10622309C22semidirect
342. #2920D11semidirect
473. #432C2×D11semidirect
474. #432C2×D11semidirect
475. #431C2×D11semidirect
476. #431C2×D11semidirect
477. #423C2×D11semidirect
481. C4×M16C2×D11semidirect
774. C11#60805semidirect

Maximal subgroups

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

subgroupindex
C2×#106230082
C2×#106230102
#130796552
#130796452
#130796362
#130795942
#130795832
#130790822
#130790172
#130780902
#130780822
#130778782
#130778702
C11×#29202
#6080511