Finite Group Databasebeta

← #15649417

Subgroups — #15649417

Order 2816.

1784 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082527C211yesmaximal, characteristic, complemented
2#13081487C212yesmaximal, complemented
3#13081272C212yesmaximal, complemented
4#13081023C212yesmaximal, complemented
5#13081012C214yesmaximal, complemented
6#13080566C212yesmaximal, complemented
7#13080518C214yesmaximal, complemented
8#13079942C212yesmaximal, complemented
9#13079923C211yesmaximal, characteristic, complemented
10#13079791C212yesmaximal, complemented
11#13079741C211yesmaximal, characteristic, complemented
12#13078676C212yesmaximal, complemented
13#13078647C211yesmaximal, characteristic, complemented
14#13078404C212yesmaximal, complemented
15C2×#10622634C211yesmaximal, characteristic, complemented
16#13077727C211yesmaximal, characteristic, complemented
17C11×#3480C211yesmaximal, characteristic, complemented
18C11×#559—21no—
19C11×#559C2211yescharacteristic
20C11×#557C2211yescharacteristic
21C11×#556—21no—
22C11×#556C2211yescharacteristic
23C11×#553—22no—
24C11×#553C2212yes—
25C11×#550C2211yescharacteristic
26C11×#548C2212yes—
27C11×#532—21no—
28C11×#532C2211yescharacteristic
29C11×#529—22no—
30C11×#529C2212yes—
31C4×C11×#41—21no—
32C4×C11×#41C2212yes—
33C4×C11×#41C2211yescharacteristic
34C2×C4×Q8×C11C2211yescharacteristic
35#10623364—21no—
36#10623115—21no—
37#10623110C2212yes—
38#10623096C2214yes—
39#10623094C2212yes—
40#10623083—22no—
41#10623082—21no—
42#10623065—22no—
43#10623054—21no—
44#10623008C2211yescharacteristic
45#10623008C2212yes—
46#10623001C2212yes—
47C2×#66922C2211yescharacteristic
48#10622851C2214yes—
49#10622846C2214yes—
50#10622840C2212yes—
51C2×#66899C2212yes—
52#10622700C2212yes—
53#10622692C2212yes—
54#10622685C2212yes—
55#10622683C2212yes—
56#10622679C2214yes—
57#10622677C2214yes—
58#10622670C2214yes—
59#10622669C2214yes—
60#10622661C2214yes—
61#10622658C2214yes—
62#10622651C2214yes—
63#10622651C2214yes—
64#10622648C2214yes—
65#10622647C2214yes—
66#10622640C2211yescharacteristic
67#10622640C2211yescharacteristic
68C4×#4325C2212yes—
69C4×#4325C2212yes—
70C4×#4325C2214yes—
71Q8×C11⋊C8C2212yes—
72#10622635C2214yes—
73#10622634C2212yes—
74#10622634C2212yes—
75#10622634C2212yes—
76#10622634C2212yes—
77#10622633C2211yescharacteristic
78#10622633C2211yescharacteristic
79#10622628C2212yes—
80C4×#4323C2214yes—
81D4×C11⋊C8C2214yes—
82D4×C11⋊C8C2212yes—
83#10622622C2214yes—
84#10622621C2212yes—
85#10622621C2212yes—
86#10622620C2212yes—
87#10622616C2214yes—
88#10622611C2214yes—
89#10622581C2212yes—
90C2×#66871C2212yes—
91#10622538C2211yescharacteristic
92#10622538C2212yes—
93C2×C4⋊(C11⋊C8)C2211yescharacteristic
94C2×C4⋊(C11⋊C8)C2212yes—
95C2×C11×#41—21no—
96C2×C11×#41D411yescharacteristic
97C2×C11×#41C2312yes—
98C22×Q8×C11C2311yescharacteristic
99C2×#4339—21no—
100C2×#4339—22no—
101C22×Dic22—21no—
102C11×C4⋊Q8—21no—
103C11×C4⋊Q8C2311yescharacteristic
104C11×#127—21no—
105C11×#127C2311yescharacteristic
106C11×#126—22no—
107C11×#126—22no—
108C11×#126—22no—
109C11×#125—22no—
110C11×#125C2312yes—
111C11×#124—21no—
112C11×#124—21no—
113C11×#124—22no—
114C11×#124—21no—
115C11×#124C2312yes—
116C11×#123—22no—
117C11×#123—22no—
118C11×#123—22no—
119C11×C22⋊Q8—22no—
120C11×C22⋊Q8C2312yes—
121C11×#121—22no—
122C11×#121—22no—
123C11×#121—21no—
124C11×#121—22no—
125C11×#121C2312yes—
126C11×#121C2312yes—
127C4×Q8×C11—21no—
128C4×Q8×C11—21no—
129C4×Q8×C11—21no—
130C4×Q8×C11—21no—
131C4×Q8×C11D411yescharacteristic
132C4×Q8×C11C2311yescharacteristic
133C4×Q8×C11C2311yescharacteristic
134C4×Q8×C11C2311yescharacteristic
135C4×Q8×C11C2311yescharacteristic
136C4×Q8×C11C2312yes—
137C4×Q8×C11C2311yescharacteristic
138C4×D4×C11—22no—
139C4×D4×C11—22no—
140C4×D4×C11—22no—
141C4×D4×C11—21no—
142C4×D4×C11—21no—
143C4×D4×C11—22no—
144C4×D4×C11—22no—
145C4×D4×C11—21no—
146C4×D4×C11D411yescharacteristic
147C4×D4×C11D412yes—
148C4×D4×C11C2312yes—
149C4×D4×C11C2312yes—
150C4×D4×C11C2311yescharacteristic
151C4×D4×C11C2312yes—
152C11×#117—22no—
153C11×#117—22no—
154C11×#117D411yescharacteristic
155C11×#117D412yes—
156C11×#117C2312yes—
157C2×C11×C4⋊C4—21no—
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C42×C11—21no—
160C2×C42×C11—22no—
161C2×C42×C11C2311yescharacteristic
162C2×C42×C11C2312yes—
163#66999—22no—
164C2×#4325C2312yes—
165C2×#4325C2312yes—
166#66992—24no—
167#66991—22no—
168C2×#4323C2314yes—
169#66983—22no—
170#66983—21no—
171#66983C2312yes—
172#66983C2314yes—
173#66979C2314yes—
174C2×C4⋊Dic11—21no—
175C2×C4⋊Dic11C2312yes—
176#66977—22no—
177#66977—22no—
178C22×C11⋊C8C2312yes—
179C22×C11⋊C8C2314yes—
180#66951—24no—
181#66949—24no—
182#66945—22no—
183C4⋊C4×D11—22no—
184#66938—24no—
185#66936—24no—
186(C22⋊D11)⋊C4—24no—
187#66928—21no—
188#66928—22no—
189#66927C2311yescharacteristic
190C4×D44—22no—
191C4×D44—21no—
192C4×D44C2312yes—
193C4×D44C2314yes—
194#66923C2314yes—
195#66922—21no—
196#66922—21no—
197#66922C2312yes—
198#66922C2312yes—
199#66922C2311yescharacteristic
200C4×Dic22—22no—
201C4×Dic22—22no—
202#66899C2314yes—
203#66899C2314yes—
204#66899C2312yes—
205#66899C2312yes—
206#66896C2314yes—
207#66896C2314yes—
208#66896C2314yes—
209C22⋊(C11⋊C8)C2312yes—
210C22⋊(C11⋊C8)C2314yes—
211#66873C2312yes—
212#66873C2312yes—
213#66873C2314yes—
214#66872C2312yes—
215#66872C2312yes—
216#66872C2314yes—
217#66872C2314yes—
218#66871C2314yes—
219#66871C2314yes—
220#66871C2314yes—
221C4⋊(C11⋊C8)C2312yes—
222C4⋊(C11⋊C8)C2311yescharacteristic
223C4⋊(C11⋊C8)C2314yes—
224C4⋊(C11⋊C8)C2312yes—
225C4⋊(C11⋊C8)C2311yescharacteristic
226C4×C11⋊C8C2314yes—
227C4×C11⋊C8C2312yes—
228#62102—111nomaximal, Sylow
229C11×#41—24no—
230C11×#41—24no—
231C11×#41—42no—
232C11×#41—44no—
233C2×Q8×C11—21no—
234C2×Q8×C11—21no—
235C2×Q8×C11—22no—
236C2×Q8×C11—41no—
237C2×Q8×C11C2×D411yescharacteristic
238C2×Q8×C11C2411yescharacteristic
239C2×Q8×C11C2411yescharacteristic
240C2×D4×C11—22no—
241C2×D4×C11—22no—
242C2×D4×C11—22no—
243C2×D4×C11—21no—
244C2×D4×C11—21no—
245C2×D4×C11C2×D411yescharacteristic
246C2×D4×C11C2×D412yes—
247C2×D4×C11C2412yes—
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11—22no—
251C22×C4×C11—22no—
252C22×C4×C11—22no—
253C22×C4×C11C2×D412yes—
254C22×C4×C11C2×D412yes—
255C22×C4×C11C2×D411yescharacteristic
256C22×C4×C11C2×D411yescharacteristic
257C22×C4×C11C2411yescharacteristic
258C22×C4×C11C2412yes—
259C2×C22⋊D11—22no—
260C2×C22⋊D11—24no—
261C22×Dic11—22no—
262#4339—44no—
263#4339—84no—
264C2×D44—21no—
265C2×D44—21no—
266C2×D44C2412yes—
267C2×C4×D11—22no—
268C2×C4×D11—24no—
269C2×Dic22—21no—
270C2×Dic22—22no—
271C2×Dic22—22no—
272C2×Dic22—82no—
273C11×C4⋊C4—21no—
274C11×C4⋊C4—21no—
275C11×C4⋊C4—21no—
276C11×C4⋊C4—21no—
277C11×C4⋊C4—21no—
278C11×C4⋊C4—22no—
279C11×C4⋊C4—22no—
280C11×C4⋊C4—22no—
281C11×C4⋊C4—21no—
282C11×C4⋊C4—22no—
283C11×C4⋊C4C2×D411yescharacteristic
284C11×C4⋊C4C2×D411yescharacteristic
285C11×C4⋊C4C2×D412yes—
286C11×C4⋊C4C2×D412yes—
287C11×C4⋊C4C2411yescharacteristic
288C11×C4⋊C4C2411yescharacteristic
289C11×C4⋊C4C2412yes—
290C11×C22⋊C4—22no—
291C11×C22⋊C4—22no—
292C11×C22⋊C4—22no—
293C11×C22⋊C4—22no—
294C11×C22⋊C4—22no—
295C11×C22⋊C4—22no—
296C11×C22⋊C4—22no—
297C11×C22⋊C4—22no—
298C11×C22⋊C4C2×D412yes—
299C11×C22⋊C4C2×D412yes—
300C11×C22⋊C4C2×D412yes—
301C42×C11—21no—
302C42×C11—21no—
303C42×C11—22no—
304C42×C11—22no—
305C42×C11—21no—
306C42×C11—21no—
307C42×C11C2×D412yes—
308C42×C11C2×D412yes—
309C42×C11C2×D411yescharacteristic
310C42×C11C2×D411yescharacteristic
311C42×C11C2411yescharacteristic
312C42×C11C2412yes—
313C42×C11C2411yescharacteristic
314C22⋊Dic11—24no—
315#4325—24no—
316#4325—42no—
317#4323—44no—
318(C2×D11)⋊C4—24no—
319(C2×D11)⋊C4—22no—
320(C2×D11)⋊C4—22no—
321(C2×D11)⋊C4—24no—
322C4⋊Dic11—21no—
323C4⋊Dic11—22no—
324C4⋊Dic11—22no—
325C4⋊Dic11—22no—
326C4⋊Dic11C2414yes—
327C4⋊Dic11C2412yes—
328Dic11⋊C4—24no—
329Dic11⋊C4—24no—
330C4×Dic11—24no—
331C2×C11⋊C8—42no—
332C2×C11⋊C8—44no—
333C2×C11⋊C8C2412yes—
334C2×C11⋊C8C2414yes—
335C2×C11⋊C8C2412yes—
336#3511—111no—
337#3480D1111yescharacteristic, complemented
338#3381—112no—
339#3361—112no—
340#3340—112no—
341#3339—114no—
342#3305—112no—
343#3301—114no—
344#3247—112no—
345#3245—111no—
346#3233—112no—
347#3227—111no—
348#3106—112no—
349#3103—111no—
350#3076—112no—
351C2×#477—111no—
352#2988—111no—
353C23×C11—22no—
354C23×C11C22×D412yes—
355C23×C11C22×D411yescharacteristic
356C22×D11—22no—
357Q8×C11—22no—
358Q8×C11—21no—
359Q8×C11—21no—
360Q8×C11—21no—
361Q8×C11—42no—
362Q8×C11—42no—
363Q8×C112−1+412yes—
364D4×C11—24no—
365D4×C11—22no—
366D4×C11—22no—
367D4×C11—22no—
368D4×C11—44no—
369D4×C11—44no—
370D4×C11—42no—
371D4×C11—81no—
372D4×C11—82no—
373C2×C4×C11—21no—
374C2×C4×C11—24no—
375C2×C4×C11—21no—
376C2×C4×C11—22no—
377C2×C4×C11—21no—
378C2×C4×C11—22no—
379C2×C4×C11—21no—
380C2×C4×C11—21no—
381C2×C4×C11—22no—
382C2×C4×C11—21no—
383C2×C4×C11—41no—
384C2×C4×C11—42no—
385C2×C4×C11—44no—
386C2×C4×C11—42no—
387C2×C4×C11—44no—
388C2×C4×C11—82no—
389C2×C4×C11—81no—
390C2×C4×C11#13514yes—
391C2×C4×C11C22×D412yes—
392C2×C4×C11C22×D412yes—
393C2×C4×C11C22×D412yes—
394C2×C4×C11C22×D411yescharacteristic
395C2×C4×C11C22×D411yescharacteristic
396C2×C4×C11C22×D411yescharacteristic
397C2×C4×C11C22×D411yescharacteristic
398C2×C4×C11C22×D411yescharacteristic
399C2×C4×C11C2511yescharacteristic
400C22⋊D11—44no—
401C22⋊D11—84no—
402C2×Dic11—22no—
403C2×Dic11—24no—
404C2×Dic11—82no—
405D44—22no—
406D44—22no—
407D44—42no—
408D44—42no—
409C4×D11—44no—
410C4×D11—84no—
411Dic22—44no—
412Dic22—42no—
413Dic22—82no—
414C11⋊C8—22no—
415C11⋊C8—24no—
416C11⋊C8—22no—
417#559—21no—
418#559C2×D1111yescharacteristic
419#557C2×D1111yescharacteristic
420#556—21no—
421#556—221no—
422#556C2×D1111yescharacteristic
423#555—112no—
424#554—112no—
425#553—22no—
426#553—114no—
427#553C2×D1112yes—
428#550C2×D1111yescharacteristic
429#548—222no—
430#548C2×D1112yes—
431#547—221no—
432#542—222no—
433#537—221no—
434#533—112no—
435#532—21no—
436#532—111no—
437#532—112no—
438#532C2×D1111yescharacteristic
439C2×C4⋊Q8—111no—
440#529—22no—
441#529C2×D1112yes—
442#520—221no—
443C4×#41—21no—
444C4×#41C2×D1112yes—
445C4×#41C2×D1111yescharacteristic
446C2×C4×Q8C2×D1111yescharacteristic
447#499—114no—
448#498—112no—
449#488—114no—
450#486—112no—
451#485—114no—
452#482—114no—
453#482—114no—
454#481—114no—
455#481—112no—
456#479—114no—
457#478—114no—
458#478—114no—
459#477—112no—
460#477—112no—
461#477—112no—
462#477—112no—
463#476—112no—
464#476—112no—
465#475—111no—
466#475—111no—
467#474—112no—
468#474—112no—
469#466—114no—
470#466—114no—
471#465—114no—
472#463—114no—
473#460—111no—
474#460—111no—
475#459—112no—
476#459—112no—
477#449—114no—
478#448—112no—
479C8×Q8—112no—
480C4×SD16—112no—
481C4×SD16—112no—
482C4×SD16—114no—
483C4×D8—114no—
484C8×D4—114no—
485C8×D4—112no—
486#431—111no—
487#431—112no—
488#427—114no—
489C2×#107—112no—
490C2×C4⋊C8—111no—
491C2×C4⋊C8—112no—
492#416—114no—
493C2×#103—112no—
494C22×C11—21no—
495C22×C11—21no—
496C22×C11—22no—
497C22×C11—22no—
498C22×C11—22no—
499C22×C11—42no—
500C22×C11—42no—
501C22×C11—42no—
502C22×C11C2×#13512yes—
503C22×C11C23×D411yescharacteristic
504C2×D11—42no—
505C2×D11—42no—
506C2×D11—42no—
507C4×C11—21no—
508C4×C11—22no—
509C4×C11—21no—
510C4×C11—22no—
511C4×C11—21no—
512C4×C11—22no—
513C4×C11—22no—
514C4×C11—41no—
515C4×C11—41no—
516C4×C11—41no—
517C4×C11—42no—
518C4×C11C2×#13512yes—
519C4×C11C2×#13512yes—
520C4×C11C2×2−1+411yescharacteristic
521C4×C11#58511yescharacteristic
522Dic11—44no—
523Dic11—42no—
524C2×#41—21no—
525C2×#41—221no—
526C2×#41—222no—
527C2×#41C22⋊D1111yescharacteristic
528C2×#41C22×D1112yes—
529C22×Q8—221no—
530C22×Q8C22×D1111yescharacteristic
531C2×SD16—112no—
532C2×SD16—112no—
533C2×D8—114no—
534C22×C8—112no—
535C22×C8—114no—
536C4⋊Q8—21no—
537C4⋊Q8—112no—
538C4⋊Q8—112no—
539C4⋊Q8—111no—
540C4⋊Q8—221no—
541C4⋊Q8—221no—
542C4⋊Q8C22×D1111yescharacteristic
543#127—21no—
544#127—111no—
545#127C22×D1111yescharacteristic
546#126—22no—
547#126—22no—
548#126—22no—
549#126—224no—
550#125—22no—
551#125—114no—
552#125C22×D1112yes—
553#124—21no—
554#124—21no—
555#124—22no—
556#124—21no—
557#124—224no—
558#124—221no—
559#124—222no—
560#124C22×D1112yes—
561#123—22no—
562#123—22no—
563#123—22no—
564#123—224no—
565C22⋊Q8—22no—
566C22⋊Q8—222no—
567C22⋊Q8—222no—
568C22⋊Q8—222no—
569C22⋊Q8—224no—
570C22⋊Q8C22×D1112yes—
571#121—22no—
572#121—22no—
573#121—21no—
574#121—22no—
575#121—112no—
576#121—114no—
577#121—222no—
578#121—224no—
579#121—222no—
580#121—221no—
581#121C22×D1112yes—
582#121C22×D1112yes—
583C4×Q8—21no—
584C4×Q8—21no—
585C4×Q8—21no—
586C4×Q8—21no—
587C4×Q8—222no—
588C4×Q8—222no—
589C4×Q8C22⋊D1111yescharacteristic
590C4×Q8C22×D1111yescharacteristic
591C4×Q8C22×D1111yescharacteristic
592C4×Q8C22×D1111yescharacteristic
593C4×Q8C22×D1111yescharacteristic
594C4×Q8C22×D1112yes—
595C4×Q8C22×D1111yescharacteristic
596C4×D4—22no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—21no—
600C4×D4—21no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—21no—
604C4×D4—114no—
605C4×D4—112no—
606C4×D4—224no—
607C4×D4—222no—
608C4×D4—221no—
609C4×D4C22⋊D1111yescharacteristic
610C4×D4C22⋊D1112yes—
611C4×D4C22×D1112yes—
612C4×D4C22×D1112yes—
613C4×D4C22×D1112yes—
614C4×D4C22×D1111yescharacteristic
615#117—22no—
616#117—22no—
617#117—114no—
618#117—222no—
619#117C22⋊D1111yescharacteristic
620#117C22⋊D1112yes—
621#117C22×D1112yes—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—112no—
624C2×C4⋊C4—221no—
625C2×C4⋊C4—222no—
626C2×C4⋊C4C22×D1111yescharacteristic
627C2×C42—21no—
628C2×C42—22no—
629C2×C42C22×D1111yescharacteristic
630C2×C42C22×D1112yes—
631#107—114no—
632#107—114no—
633#107—114no—
634#106—112no—
635#106—114no—
636#106—112no—
637#106—114no—
638C4⋊C8—112no—
639C4⋊C8—111no—
640C4⋊C8—112no—
641C4⋊C8—114no—
642C4⋊C8—111no—
643#103—114no—
644#103—114no—
645#103—112no—
646#103—112no—
647#102—114no—
648#102—114no—
649#102—114no—
650#102—112no—
651#102—114no—
652#102—112no—
653C22⋊C8—112no—
654C22⋊C8—114no—
655C4×C8—114no—
656C4×C8—112no—
657C2×C11—22no—
658C2×C11—42no—
659C2×C11—82no—
660C2×C11#348911yescharacteristic
661C2×C11C22×#13511yescharacteristic
662C2×C11#358511yescharacteristic
663D11—82no—
664#41—24no—
665#41—24no—
666#41—42no—
667#41—44no—
668#41—444no—
669#41—884no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—22no—
673C2×Q8—41no—
674C2×Q8—221no—
675C2×Q8—222no—
676C2×Q8—222no—
677C2×Q8—882no—
678C2×Q8C2×C22⋊D1111yescharacteristic
679C2×Q8C23×D1111yescharacteristic
680C2×Q8C23×D1111yescharacteristic
681C2×D4—22no—
682C2×D4—22no—
683C2×D4—22no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—112no—
687C2×D4—222no—
688C2×D4—224no—
689C2×D4—221no—
690C2×D4—221no—
691C2×D4C2×C22⋊D1112yes—
692C2×D4C2×C22⋊D1111yescharacteristic
693C2×D4C23×D1112yes—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—222no—
700C22×C4—222no—
701C22×C4—224no—
702C22×C4C2×C22⋊D1112yes—
703C22×C4C2×C22⋊D1111yescharacteristic
704C22×C4C2×C22⋊D1112yes—
705C22×C4C2×C22⋊D1111yescharacteristic
706C22×C4C23×D1111yescharacteristic
707C22×C4C23×D1112yes—
708SD16—224no—
709SD16—442no—
710D8—444no—
711C2×C8—112no—
712C2×C8—112no—
713C2×C8—114no—
714C2×C8—442no—
715C2×C8—444no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—22no—
722C4⋊C4—22no—
723C4⋊C4—22no—
724C4⋊C4—21no—
725C4⋊C4—22no—
726C4⋊C4—114no—
727C4⋊C4—112no—
728C4⋊C4—222no—
729C4⋊C4—222no—
730C4⋊C4—222no—
731C4⋊C4—224no—
732C4⋊C4—221no—
733C4⋊C4—224no—
734C4⋊C4C2×C22⋊D1111yescharacteristic
735C4⋊C4C2×C22⋊D1111yescharacteristic
736C4⋊C4C2×C22⋊D1112yes—
737C4⋊C4C2×C22⋊D1112yes—
738C4⋊C4C23×D1112yes—
739C4⋊C4C23×D1111yescharacteristic
740C4⋊C4C23×D1111yescharacteristic
741C22⋊C4—22no—
742C22⋊C4—22no—
743C22⋊C4—22no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—22no—
748C22⋊C4—22no—
749C22⋊C4—224no—
750C22⋊C4—224no—
751C22⋊C4—224no—
752C22⋊C4—222no—
753C22⋊C4—222no—
754C22⋊C4C2×C22⋊D1112yes—
755C22⋊C4C2×C22⋊D1112yes—
756C22⋊C4C2×C22⋊D1112yes—
757C42—21no—
758C42—21no—
759C42—22no—
760C42—22no—
761C42—21no—
762C42—21no—
763C42—224no—
764C42C2×C22⋊D1112yes—
765C42C2×C22⋊D1112yes—
766C42C2×C22⋊D1111yescharacteristic
767C42C2×C22⋊D1111yescharacteristic
768C42C23×D1112yes—
769C42C23×D1111yescharacteristic
770C42C23×D1111yescharacteristic
771C11#6210211yescharacteristic, complemented, Sylow
772C23—22no—
773C23—222no—
774C23C22×C22⋊D1112yes—
775C23C22×C22⋊D1111yescharacteristic
776Q8—22no—
777Q8—21no—
778Q8—21no—
779Q8—21no—
780Q8—42no—
781Q8—42no—
782Q8—444no—
783Q8—442no—
784Q8—882no—
785Q8#6704312yes—
786D4—24no—
787D4—22no—
788D4—22no—
789D4—22no—
790D4—44no—
791D4—44no—
792D4—42no—
793D4—81no—
794D4—82no—
795D4—222no—
796D4—222no—
797D4—442no—
798D4—444no—
799D4—442no—
800D4—884no—
801C2×C4—21no—
802C2×C4—24no—
803C2×C4—21no—
804C2×C4—22no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—22no—
810C2×C4—21no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—44no—
814C2×C4—42no—
815C2×C4—44no—
816C2×C4—82no—
817C2×C4—81no—
818C2×C4—222no—
819C2×C4—224no—
820C2×C4—444no—
821C2×C4—884no—
822C2×C4—882no—
823C2×C4#6700314yes—
824C2×C4C22×C22⋊D1112yes—
825C2×C4C22×C22⋊D1112yes—
826C2×C4C22×C22⋊D1111yescharacteristic
827C2×C4C22×C22⋊D1111yescharacteristic
828C2×C4C22×C22⋊D1112yes—
829C2×C4C22×C22⋊D1111yescharacteristic
830C2×C4C22×C22⋊D1111yescharacteristic
831C2×C4C22×C22⋊D1111yescharacteristic
832C2×C4C24×D1111yescharacteristic
833C8—222no—
834C8—224no—
835C8—222no—
836C22—21no—
837C22—21no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—442no—
845C22—442no—
846C22—442no—
847C22C2×#6700312yes—
848C22C23×C22⋊D1111yescharacteristic
849C4—21no—
850C4—22no—
851C4—21no—
852C4—22no—
853C4—21no—
854C4—22no—
855C4—22no—
856C4—41no—
857C4—41no—
858C4—41no—
859C4—42no—
860C4—444no—
861C4—442no—
862C4C2×#6700312yes—
863C4C2×#6700312yes—
864C4C2×#6704311yescharacteristic
865C4#1062345311yescharacteristic
866C2—22no—
867C2—42no—
868C2—82no—
869C2—882no—
870C2#1308229611yescharacteristic
871C2C22×#6700311yescharacteristic
872C2#1308339511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3480C2
socleC22×C11C23×D4
hypercenter#3480D11
hypocenterC11#62102
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3480

Complements

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

NH ≅ G/Ntype
1. #13082527C2semidirect
2. #13081487C2semidirect
3. #13081272C2semidirect
4. #13081023C2semidirect
5. #13081012C2semidirect
6. #13080566C2semidirect
7. #13080518C2semidirect
8. #13079942C2semidirect
9. #13079923C2semidirect
10. #13079791C2semidirect
11. #13079741C2semidirect
12. #13078676C2semidirect
13. #13078647C2semidirect
14. #13078404C2semidirect
15. C2×#10622634C2semidirect
16. #13077727C2semidirect
17. C11×#3480C2semidirect
337. #3480D11semidirect
771. C11#62102semidirect

Maximal subgroups

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

subgroupindex
#130825272
#130814872
#130812722
#130810232
#130810122
#130805662
#130805182
#130799422
#130799232
#130797912
#130797412
#130786762
#130786472
#130784042
C2×#106226342
#130777272
C11×#34802
#6210211