Finite Group Databasebeta

← #15625012

Subgroups — #15625012

Order 2816.

2208 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
1#13081912C211yesmaximal, characteristic, complemented
2C2×#10623008C211yesmaximal, characteristic, complemented
3#13079594C214yesmaximal, complemented
4#13079583C214yesmaximal, complemented
5#13079574C212yesmaximal, complemented
6#13079566C211yesmaximal, characteristic, complemented
7#13079559C211yesmaximal, characteristic, complemented
8#13079551C212yesmaximal, complemented
9#13079543C211yesmaximal, characteristic, complemented
10#13079536C211yesmaximal, characteristic, complemented
11#13079044C212yesmaximal, complemented
12#13078939C212yesmaximal, complemented
13#13078073C214yesmaximal, complemented
14#13077838C214yesmaximal, complemented
15C2×C11×#431C211yesmaximal, characteristic, complemented
16C22×#4339C2212yes—
17C22×C42×C11C2211yescharacteristic
18#10623322—21no—
19#10623322—21no—
20#10623322C2212yes—
21C2×#66983—21no—
22C2×#66983—21no—
23C2×#66957C2218yescomplemented
24#10623010—21no—
25#10623010—21no—
26#10623010—21no—
27#10623010—21no—
28#10623010C2212yes—
29#10623010C2212yescomplemented
30#10623008—21no—
31#10623008—21no—
32#10623008—21no—
33#10623008—21no—
34#10623008C2212yes—
35#10623008C2212yes—
36#10623008C2212yes—
37#10623008C2212yes—
38#10623008C2211yescharacteristic
39#10623008C2211yescharacteristic, complemented
40#10623008C2211yescharacteristic, complemented
41C2×#66928C2212yes—
42C2×#66927C2211yescharacteristic
43C4×#4339—21no—
44C4×#4339—21no—
45C4×#4339C2212yescomplemented
46C2×C4×D44—21no—
47C2×C4×D44—21no—
48#10623001C2211yescharacteristic
49#10623001C2211yescharacteristic, complemented
50#10623001C2211yescharacteristic, complemented
51C2×#66922C2211yescharacteristic
52C11×#431C2211yescharacteristic
53C11×#431C2211yescharacteristic
54C11×#431C2212yes—
55C11×#431C2212yescomplemented
56C11×#431C2212yescomplemented
57C2×C11×C4⋊C8C2212yescomplemented
58C2×C11×C22⋊C8C2212yes—
59C2×C4×C8×C11C2212yescomplemented
60#10622726C2218yescomplemented
61#10622462C2214yescomplemented
62#10622461C2214yescomplemented
63#10622458C2218yescomplemented
64#10622457C2218yescomplemented
65#10622456C2214yescomplemented
66#10622454C2214yescomplemented
67#10622352C2214yes—
68#10622351C2214yes—
69#10622347C2218yescomplemented
70#10622346C2218yescomplemented
71#10622345C2214yes—
72#10622344C2214yes—
73#10622312C2212yescomplemented
74#10622310C2218yescomplemented
75#10622309C2218yescomplemented
76#10622308C2212yescomplemented
77#10622307C2212yescomplemented
78#10622307C2212yescomplemented
79#10622306C2212yescomplemented
80#10622306C2212yescomplemented
81#10622294C2212yescomplemented
82#10622294C2212yescomplemented
83C23×C4×C11D411yescharacteristic
84C23×C4×C11D411yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C22×C22⋊D11—22no—
87C2×#4339—21no—
88C2×#4339—21no—
89C2×#4339—22no—
90C2×#4339—22no—
91C2×#4339—48no—
92C2×#4339C2314yes—
93C2×#4339C2312yes—
94C2×#4339C2314yes—
95C22×D44—21no—
96C22×D44—21no—
97C22×D44C2312yes—
98C22×C4×D11—22no—
99C22×Dic22C2312yes—
100C22×C8×C11C2314yes—
101C2×C42×C11D411yescharacteristic
102C2×C42×C11D411yescharacteristic
103C2×C42×C11D411yescharacteristic
104C2×C42×C11D411yescharacteristic
105C2×C42×C11D411yescharacteristic
106C2×C42×C11D411yescharacteristic
107C2×C42×C11C2311yescharacteristic
108C2×C42×C11C2311yescharacteristic
109C2×C42×C11C2311yescharacteristic
110C2×C42×C11C2311yescharacteristic
111C2×C42×C11C2311yescharacteristic
112C2×C42×C11C2311yescharacteristic
113#67006—22no—
114#66983—22no—
115#66983—22no—
116#66983—22no—
117#66983—22no—
118#66983—22no—
119#66983—22no—
120#66983—22no—
121#66983—22no—
122#66983—21no—
123#66983—21no—
124#66983—21no—
125#66983—21no—
126#66983C2312yes—
127#66983C2312yes—
128#66982—22no—
129#66982—22no—
130#66982—22no—
131C4×C22⋊D11—22no—
132C4×C22⋊D11—22no—
133C4×C22⋊D11—22no—
134C4×C22⋊D11—22no—
135C4×C22⋊D11—22no—
136C4×C22⋊D11—22no—
137C2×(C2×D11)⋊C4—22no—
138C2×(C2×D11)⋊C4—22no—
139#66979—21no—
140#66979—21no—
141#66979C2312yes—
142C2×C4⋊Dic11—21no—
143C2×C4⋊Dic11—21no—
144#66977—21no—
145#66977—21no—
146#66977—21no—
147#66977—21no—
148#66977C2312yes—
149#66977C2312yes—
150C2×Dic44C2318yes—
151#66957—416no—
152C2×D88C2318yes—
153C2×#4314C2318yes—
154C2×#4314C2318yes—
155#66929—22no—
156#66929—22no—
157#66928—22no—
158#66928—22no—
159#66928—21no—
160#66928—21no—
161#66928C2314yes—
162#66928C2314yes—
163#66928C2312yes—
164#66927—21no—
165#66927—21no—
166#66927C2312yes—
167#66927C2312yes—
168#66927C2311yescharacteristic
169C4×D44—22no—
170C4×D44—22no—
171C4×D44—22no—
172C4×D44—22no—
173C4×D44—22no—
174C4×D44—22no—
175C4×D44—22no—
176C4×D44—22no—
177C4×D44—21no—
178C4×D44—21no—
179C4×D44—21no—
180C4×D44—21no—
181C4×D44C2312yes—
182C4×D44C2312yes—
183#66925—22no—
184#66925—22no—
185#66925—22no—
186C42×D11—22no—
187#66923—21no—
188#66923—21no—
189#66923C2312yes—
190#66922—21no—
191#66922—21no—
192#66922C2312yes—
193#66922C2312yes—
194#66922C2311yescharacteristic
195#66922C2311yescharacteristic
196#66922C2311yescharacteristic
197C4×Dic22—21no—
198C4×Dic22—21no—
199C4×Dic22—21no—
200C4×Dic22—21no—
201C4×Dic22C2312yes—
202C4×Dic22C2312yes—
203C11×C4⋊C8C2312yes—
204C11×C4⋊C8C2312yes—
205C11×C4⋊C8C2314yes—
206C11×C22⋊C8C2312yes—
207C11×C22⋊C8C2312yes—
208C11×C22⋊C8C2314yes—
209C4×C8×C11C2312yes—
210C4×C8×C11C2312yes—
211C4×C8×C11C2314yes—
212#66885C2318yes—
213#66885C2318yes—
214#66880C2318yes—
215#66880C2318yes—
216#60782—111nomaximal, Sylow
217C24×C11C2×D411yescharacteristic
218C23×D11—22no—
219C22×C4×C11—24no—
220C22×C4×C11—24no—
221C22×C4×C11—42no—
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×C11C2×D411yescharacteristic
235C22×C4×C11C2×D411yescharacteristic
236C22×C4×C11C2×D411yescharacteristic
237C22×C4×C11C2411yescharacteristic
238C22×C4×C11C2411yescharacteristic
239C22×C4×C11C2411yescharacteristic
240C2×C22⋊D11—22no—
241C2×C22⋊D11—22no—
242C2×C22⋊D11—22no—
243C2×C22⋊D11—24no—
244C2×C22⋊D11—24no—
245C2×C22⋊D11—48no—
246C22×Dic11—22no—
247#4339—28no—
248#4339—216no—
249#4339—48no—
250#4339—44no—
251#4339—48no—
252#4339—48no—
253#4339—44no—
254C2×D44—22no—
255C2×D44—22no—
256C2×D44—22no—
257C2×D44—22no—
258C2×D44—21no—
259C2×D44—21no—
260C2×D44—22no—
261C2×D44—44no—
262C2×D44—44no—
263C2×D44—44no—
264C2×D44C2414yes—
265C2×D44C2412yes—
266C2×C4×D11—22no—
267C2×C4×D11—22no—
268C2×C4×D11—22no—
269C2×C4×D11—24no—
270C2×C4×D11—24no—
271C2×C4×D11—48no—
272C2×Dic22—21no—
273C2×Dic22—21no—
274C2×Dic22—22no—
275C2×Dic22—44no—
276C2×Dic22C2414yes—
277C2×Dic22C2412yes—
278C2×C8×C11—28no—
279C2×C8×C11C2414yes—
280C2×C8×C11C2414yes—
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×C11C2×D411yescharacteristic
290C42×C11C2×D411yescharacteristic
291C42×C11C2×D411yescharacteristic
292C42×C11C2×D411yescharacteristic
293C42×C11C2411yescharacteristic
294C42×C11C2411yescharacteristic
295C42×C11C2411yescharacteristic
296C42×C11C2411yescharacteristic
297C22⋊Dic11—22no—
298C22⋊Dic11—22no—
299C22⋊Dic11—22no—
300(C2×D11)⋊C4—22no—
301(C2×D11)⋊C4—22no—
302(C2×D11)⋊C4—22no—
303(C2×D11)⋊C4—22no—
304(C2×D11)⋊C4—22no—
305(C2×D11)⋊C4—22no—
306(C2×D11)⋊C4—24no—
307(C2×D11)⋊C4—24no—
308(C2×D11)⋊C4—24no—
309(C2×D11)⋊C4—24no—
310C4⋊Dic11—21no—
311C4⋊Dic11—21no—
312C4⋊Dic11—21no—
313C4⋊Dic11—21no—
314C4⋊Dic11—22no—
315C4⋊Dic11—22no—
316C4⋊Dic11—22no—
317C4⋊Dic11—22no—
318C4⋊Dic11C2412yes—
319C4⋊Dic11C2412yes—
320Dic11⋊C4—22no—
321Dic11⋊C4—22no—
322Dic11⋊C4—22no—
323Dic11⋊C4—22no—
324Dic11⋊C4—22no—
325Dic11⋊C4—22no—
326C4×Dic11—22no—
327C4×Dic11—22no—
328C4×Dic11—22no—
329Dic44—48no—
330D88—48no—
331#4314—48no—
332#4314—48no—
333#3444—111no—
334C2×#532—111no—
335#3212—114no—
336#3211—114no—
337#3210—112no—
338#3209—111no—
339#3208—111no—
340#3207—112no—
341#3206—111no—
342#3205—111no—
343#3147—112no—
344#3131—112no—
345#3035—114no—
346#3002—114no—
347C2×#431D1111yescharacteristic, complemented
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—41no—
351C23×C11C22×D411yescharacteristic
352C23×C11C22×D411yescharacteristic
353C23×C11C22×D411yescharacteristic
354C22×D11—22no—
355C22×D11—24no—
356C22×D11—44no—
357C22×D11—44no—
358C22×D11—44no—
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—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—41no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11#13514yescomplemented
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×C11C22×D411yescharacteristic
386C2×C4×C11C22×D411yescharacteristic
387C2×C4×C11H(5,𝔽2)14yes—
388C2×C4×C11C2511yescharacteristic
389C22⋊D11—48no—
390C22⋊D11—44no—
391C22⋊D11—48no—
392C22⋊D11—44no—
393C22⋊D11—44no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—22no—
397C2×Dic11—24no—
398C2×Dic11—44no—
399D44—24no—
400D44—28no—
401D44—44no—
402D44—44no—
403D44—44no—
404D44—44no—
405D44—42no—
406D44—44no—
407D44—42no—
408C4×D11—48no—
409C4×D11—44no—
410C4×D11—48no—
411C4×D11—44no—
412C4×D11—44no—
413Dic22—24no—
414Dic22—28no—
415Dic22—44no—
416Dic22—42no—
417Dic22—42no—
418C8×C11—24no—
419C8×C11—24no—
420C22×#41—112no—
421C2×#135—118no—
422#533—111no—
423#533—111no—
424#533—111no—
425#532—111no—
426#532—111no—
427#532—112no—
428#532—112no—
429#532—112no—
430#532—112no—
431#532—111no—
432#532—221no—
433#532—221no—
434#532—221no—
435#532—221no—
436C2×C4⋊Q8—111no—
437C2×#127—111no—
438#529—112no—
439#529—112no—
440#529—221no—
441#529—221no—
442#529—221no—
443#529—221no—
444C2×#124—112no—
445#525—112no—
446#525—221no—
447#525—221no—
448C2×#121—221no—
449C2×#121—221no—
450C4×#41—112no—
451C4×#41—221no—
452C4×#41—221no—
453C2×C4×D4—221no—
454C2×C4×D4—221no—
455C22×C42C2×D1111yescharacteristic
456#495—118no—
457#494—112no—
458#493—112no—
459#492—112no—
460#492—112no—
461#488—118no—
462#487—112no—
463#487—112no—
464#486—112no—
465#486—112no—
466#464—118no—
467#463—118no—
468#462—114no—
469#461—114no—
470#460—114no—
471#459—114no—
472#452—118no—
473#451—114no—
474#450—114no—
475#449—118no—
476#448—114no—
477#447—114no—
478#431C2×D1111yescharacteristic
479#431C2×D1111yescharacteristic
480#431C2×D1112yes—
481#431C2×D1112yescomplemented
482#431C2×D1112yescomplemented
483C2×C4⋊C8C2×D1112yescomplemented
484#416—118no—
485C2×C22⋊C8C2×D1112yes—
486C2×C4×C8C2×D1112yescomplemented
487C22×C11—21no—
488C22×C11—21no—
489C22×C11—21no—
490C22×C11—21no—
491C22×C11—21no—
492C22×C11—21no—
493C22×C11—21no—
494C22×C11—44no—
495C22×C11#53512yes—
496C22×C11C2×#13512yes—
497C22×C11C23×D411yescharacteristic
498C2×D11—44no—
499C2×D11—42no—
500C2×D11—44no—
501C2×D11—42no—
502C2×D11—44no—
503C2×D11—42no—
504C2×D11—88no—
505C4×C11—21no—
506C4×C11—21no—
507C4×C11—21no—
508C4×C11—21no—
509C4×C11—21no—
510C4×C11—21no—
511C4×C11—21no—
512C4×C11#53512yes—
513C4×C11C2×#13512yes—
514C4×C11C2×#13512yes—
515C4×C11#57512yes—
516C4×C11C2×H(5,𝔽2)12yes—
517Dic11—44no—
518Dic11—42no—
519Dic11—42no—
520Dic11—42no—
521C2×#41—112no—
522C2×#41—114no—
523C2×#41—114no—
524C2×#41—221no—
525C2×#41—221no—
526C2×#41—222no—
527C2×#41—222no—
528C2×#41—448no—
529C22×Q8—112no—
530C22×D4—112no—
531C22×D4—222no—
532C22×D4—221no—
533C22×D4—221no—
534C23×C4—222no—
535C23×C4D4411yescharacteristic
536C23×C4D4411yescharacteristic
537C23×C4C22×D1111yescharacteristic
538#135—4416no—
539C2×Q16—118no—
540C2×SD16—118no—
541C2×SD16—118no—
542C2×D8—118no—
543C22×C8C22×D1114yes—
544C4⋊Q8—111no—
545C4⋊Q8—111no—
546C4⋊Q8—112no—
547C4⋊Q8—112no—
548C4⋊Q8—111no—
549C4⋊Q8—221no—
550C4⋊Q8—221no—
551#127—112no—
552#127—112no—
553#127—111no—
554#127—221no—
555#127—221no—
556#126—222no—
557#126—222no—
558#125—112no—
559#125—221no—
560#125—221no—
561#124—114no—
562#124—114no—
563#124—112no—
564#124—222no—
565#124—222no—
566#124—221no—
567#124—221no—
568#123—222no—
569#123—222no—
570#123—222no—
571C22⋊Q8—112no—
572C22⋊Q8—112no—
573C22⋊Q8—221no—
574C22⋊Q8—221no—
575C22⋊Q8—221no—
576C22⋊Q8—221no—
577#121—112no—
578#121—112no—
579#121—222no—
580#121—222no—
581#121—222no—
582#121—222no—
583#121—222no—
584#121—222no—
585#121—222no—
586#121—222no—
587#121—221no—
588#121—221no—
589#121—221no—
590#121—221no—
591#120—222no—
592C4×Q8—112no—
593C4×Q8—112no—
594C4×Q8—221no—
595C4×Q8—221no—
596C4×Q8—221no—
597C4×Q8—221no—
598C4×D4—112no—
599C4×D4—112no—
600C4×D4—222no—
601C4×D4—222no—
602C4×D4—222no—
603C4×D4—222no—
604C4×D4—222no—
605C4×D4—222no—
606C4×D4—222no—
607C4×D4—222no—
608C4×D4—222no—
609C4×D4—222no—
610C4×D4—222no—
611C4×D4—222no—
612C4×D4—222no—
613C4×D4—222no—
614C4×D4—221no—
615C4×D4—221no—
616C4×D4—221no—
617C4×D4—221no—
618#117—112no—
619#117—221no—
620#117—221no—
621#117—222no—
622#117—222no—
623#117—222no—
624C2×C4⋊C4—221no—
625C2×C4⋊C4—221no—
626C2×C22⋊C4—222no—
627C2×C22⋊C4—222no—
628C2×C42—222no—
629C2×C42D4411yescharacteristic
630C2×C42D4411yescharacteristic
631C2×C42D4411yescharacteristic
632C2×C42D4411yescharacteristic
633C2×C42D4411yescharacteristic
634C2×C42D4411yescharacteristic
635C2×C42C22×D1111yescharacteristic
636C2×C42C22×D1111yescharacteristic
637C2×C42C22×D1111yescharacteristic
638C2×C42C22×D1111yescharacteristic
639C2×C42C22×D1111yescharacteristic
640C2×C42C22×D1111yescharacteristic
641C4⋊C8C22×D1112yes—
642C4⋊C8C22×D1112yes—
643C4⋊C8C22×D1114yes—
644#103—118no—
645#103—118no—
646#102—118no—
647#102—118no—
648C22⋊C8C22×D1112yes—
649C22⋊C8C22×D1112yes—
650C22⋊C8C22×D1114yes—
651C4×C8C22×D1112yes—
652C4×C8C22×D1112yes—
653C4×C8C22×D1114yes—
654C2×C11—22no—
655C2×C11—22no—
656C2×C11—41no—
657C2×C11C2×#53511yescharacteristic
658C2×C11C22×#13511yescharacteristic
659C2×C11C2×#57511yescharacteristic
660D11—82no—
661D11—84no—
662C24—222no—
663C24C2×D4411yescharacteristic
664#41—228no—
665#41—2216no—
666#41—448no—
667#41—448no—
668#41—448no—
669#41—444no—
670#41—444no—
671C2×Q8—114no—
672C2×Q8—112no—
673C2×Q8—221no—
674C2×Q8—221no—
675C2×Q8—222no—
676C2×Q8—444no—
677C2×D4—114no—
678C2×D4—112no—
679C2×D4—222no—
680C2×D4—222no—
681C2×D4—222no—
682C2×D4—224no—
683C2×D4—224no—
684C2×D4—221no—
685C2×D4—221no—
686C2×D4—222no—
687C2×D4—222no—
688C2×D4—222no—
689C2×D4—222no—
690C2×D4—222no—
691C2×D4—444no—
692C2×D4—444no—
693C2×D4—448no—
694C2×D4—444no—
695C22×C4—24no—
696C22×C4—24no—
697C22×C4—42no—
698C22×C4—222no—
699C22×C4—222no—
700C22×C4—222no—
701C22×C4—224no—
702C22×C4—222no—
703C22×C4—224no—
704C22×C4—448no—
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×C4C2×D4411yescharacteristic
718C22×C4C2×D4411yescharacteristic
719C22×C4C2×D4411yescharacteristic
720C22×C4C23×D1111yescharacteristic
721C22×C4C23×D1111yescharacteristic
722C22×C4C23×D1111yescharacteristic
723Q16—448no—
724SD16—448no—
725SD16—448no—
726D8—448no—
727C2×C8—28no—
728C2×C8C23×D1114yes—
729C2×C8C23×D1114yes—
730C4⋊C4—112no—
731C4⋊C4—112no—
732C4⋊C4—222no—
733C4⋊C4—222no—
734C4⋊C4—222no—
735C4⋊C4—222no—
736C4⋊C4—222no—
737C4⋊C4—222no—
738C4⋊C4—221no—
739C4⋊C4—221no—
740C4⋊C4—221no—
741C4⋊C4—221no—
742C4⋊C4—222no—
743C4⋊C4—222no—
744C4⋊C4—222no—
745C4⋊C4—222no—
746C22⋊C4—222no—
747C22⋊C4—222no—
748C22⋊C4—222no—
749C22⋊C4—224no—
750C22⋊C4—224no—
751C22⋊C4—224no—
752C22⋊C4—224no—
753C22⋊C4—222no—
754C22⋊C4—222no—
755C22⋊C4—222no—
756C22⋊C4—222no—
757C22⋊C4—222no—
758C22⋊C4—222no—
759C42—222no—
760C42—222no—
761C42—222no—
762C42C2×D4411yescharacteristic
763C42C2×D4411yescharacteristic
764C42C2×D4411yescharacteristic
765C42C2×D4411yescharacteristic
766C42C2×D4411yescharacteristic
767C42C2×D4411yescharacteristic
768C42C2×D4411yescharacteristic
769C42C2×D4411yescharacteristic
770C42C2×D4411yescharacteristic
771C42C2×D4411yescharacteristic
772C42C2×D4411yescharacteristic
773C42C2×D4411yescharacteristic
774C42C23×D1111yescharacteristic
775C42C23×D1111yescharacteristic
776C42C23×D1111yescharacteristic
777C42C23×D1111yescharacteristic
778C11#6078211yescharacteristic, complemented, Sylow
779C23—22no—
780C23—22no—
781C23—41no—
782C23—222no—
783C23—224no—
784C23—444no—
785C23—444no—
786C23—444no—
787C23C22×D4411yescharacteristic
788C23C22×D4411yescharacteristic
789C23C22×D4411yescharacteristic
790Q8—224no—
791Q8—228no—
792Q8—444no—
793Q8—442no—
794Q8—442no—
795D4—224no—
796D4—228no—
797D4—444no—
798D4—444no—
799D4—448no—
800D4—444no—
801D4—444no—
802D4—448no—
803D4—444no—
804D4—444no—
805D4—444no—
806D4—442no—
807D4—444no—
808D4—442no—
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—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—222no—
826C2×C4—222no—
827C2×C4—222no—
828C2×C4—224no—
829C2×C4—448no—
830C2×C4—444no—
831C2×C4—444no—
832C2×C4—444no—
833C2×C4—448no—
834C2×C4—444no—
835C2×C4#6695714yescomplemented
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—24no—
850C8—24no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—44no—
859C22—444no—
860C22—442no—
861C22—442no—
862C22—444no—
863C22—442no—
864C22—444no—
865C22—888no—
866C22#1062305612yes—
867C22C2×#6695712yes—
868C22C23×D4411yescharacteristic
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—21no—
875C4—21no—
876C4—444no—
877C4—442no—
878C4—442no—
879C4—442no—
880C4#1062305612yes—
881C4C2×#6695712yes—
882C4C2×#6695712yes—
883C4#1062327912yes—
884C4C2×#6704212yes—
885C2—22no—
886C2—22no—
887C2—41no—
888C2—884no—
889C2—882no—
890C2C2×#1062305611yescharacteristic
891C2C22×#6695711yescharacteristic
892C2C2×#1062327911yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#431C2
socleC22×C11C23×D4
hypercenterC2×#431D11
hypocenterC11#60782
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
1. #13081912C2semidirect
2. C2×#10623008C2semidirect
3. #13079594C2semidirect
4. #13079583C2semidirect
5. #13079574C2semidirect
6. #13079566C2semidirect
7. #13079559C2semidirect
8. #13079551C2semidirect
9. #13079543C2semidirect
10. #13079536C2semidirect
11. #13079044C2semidirect
12. #13078939C2semidirect
13. #13078073C2semidirect
14. #13077838C2semidirect
15. C2×C11×#431C2semidirect
23. C2×#66957C22semidirect
29. #10623010C22semidirect
39. #10623008C22semidirect
40. #10623008C22semidirect
45. C4×#4339C22semidirect
49. #10623001C22semidirect
50. #10623001C22semidirect
55. C11×#431C22semidirect
56. C11×#431C22semidirect
57. C2×C11×C4⋊C8C22semidirect
59. C2×C4×C8×C11C22semidirect
60. #10622726C22semidirect
61. #10622462C22semidirect
62. #10622461C22semidirect
63. #10622458C22semidirect
64. #10622457C22semidirect
65. #10622456C22semidirect
66. #10622454C22semidirect
69. #10622347C22semidirect
70. #10622346C22semidirect
73. #10622312C22semidirect
74. #10622310C22semidirect
75. #10622309C22semidirect
76. #10622308C22semidirect
77. #10622307C22semidirect
78. #10622307C22semidirect
79. #10622306C22semidirect
80. #10622306C22semidirect
81. #10622294C22semidirect
82. #10622294C22semidirect
347. C2×#431D11semidirect
375. C2×C4×C11#135semidirect
481. #431C2×D11semidirect
482. #431C2×D11semidirect
483. C2×C4⋊C8C2×D11semidirect
486. C2×C4×C8C2×D11semidirect
778. C11#60782semidirect
835. C2×C4#66957semidirect

Maximal subgroups

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

subgroupindex
#130819122
C2×#106230082
#130795942
#130795832
#130795742
#130795662
#130795592
#130795512
#130795432
#130795362
#130790442
#130789392
#130780732
#130778382
C2×C11×#4312
#6078211