Finite Group Databasebeta

← #15633648

Subgroups — #15633648

Order 2816.

1804 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082211C211yesmaximal, characteristic
2#13081458C214yesmaximal, complemented
3#13081419C212yesmaximal, complemented
4#13081384C214yesmaximal, complemented
5#13081345C212yesmaximal, complemented
6#13081312C212yesmaximal, complemented
7#13081301C212yesmaximal, complemented
8#13079019C212yesmaximal, complemented
9#13079012C211yesmaximal, characteristic, complemented
10#13078434C212yesmaximal, complemented
11#13078425C211yesmaximal, characteristic, complemented
12#13078088C211yesmaximal, characteristic, complemented
13#13078088C212yesmaximal, complemented
14Q8×#4318C211yesmaximal, characteristic, complemented
15C4×#66995C211yesmaximal, characteristic, complemented
16C4×#66995C212yesmaximal, complemented
17C2×C11×#557C211yesmaximal, characteristic, complemented
18C11×#557—21no—
19C11×#557—21no—
20C11×#557—22no—
21C11×#557C2212yes—
22C11×#557C2214yes—
23C11×#557C2212yes—
24C2×C11×C4⋊Q8—21no—
25C2×C11×C4⋊Q8C2211yescharacteristic
26C2×C11×#125—22no—
27C2×C11×#125C2212yes—
28C2×C4×Q8×C11—21no—
29C2×C4×Q8×C11C2212yes—
30C2×C4×Q8×C11C2211yescharacteristic
31C2×C4×Q8×C11C2211yescharacteristic
32#10623348—21no—
33C2×#66995C2211yescharacteristic
34C2×#66995C2212yes—
35#10623116C2212yes—
36#10623116C2211yescharacteristic
37#10623115C2212yes—
38#10623115C2211yescharacteristic
39#10623111—22no—
40#10623111—21no—
41#10623108C2211yescharacteristic
42C4×#4343—21no—
43#10623101C2211yescharacteristic
44#10623045—21no—
45#10623045—22no—
46#10623008C2211yescharacteristic
47#10623008C2212yes—
48C4×#4339C2211yescharacteristic
49C4×#4339C2212yes—
50#10622838C2211yescharacteristic
51#10622707C2212yes—
52#10622706C2212yes—
53#10622704C2212yes—
54#10622702C2214yes—
55#10622701C2212yes—
56#10622700C2212yes—
57#10622697C2212yes—
58#10622682C2214yes—
59#10622681C2214yes—
60#10622681C2214yes—
61#10622680C2214yes—
62#10622679C2214yes—
63#10622679C2214yes—
64#10622676C2214yes—
65#10622676C2214yes—
66#10622644C2214yes—
67#10622644C2212yes—
68#10622643C2214yes—
69#10622643C2212yes—
70C4×#4326C2212yes—
71C4×#4326C2214yes—
72#10622641C2214yes—
73#10622641C2214yes—
74#10622641C2214yes—
75#10622640C2214yes—
76#10622640C2212yes—
77#10622639C2214yes—
78#10622639C2212yes—
79C4×#4325C2212yes—
80C4×#4325C2214yes—
81#10622637C2212yes—
82#10622637C2214yes—
83Q8×C11⋊C8C2212yes—
84#10622579C2212yes—
85#10622579C2212yes—
86#10622579C2212yes—
87#10622579C2212yes—
88#10622579C2211yescharacteristic
89#10622577C2212yes—
90#10622577C2211yescharacteristic
91#10622537C2211yescharacteristic
92#10622537C2212yes—
93C4×#4318C2211yescharacteristic
94C4×#4318C2212yes—
95C22×Q8×C11—21no—
96C22×Q8×C11D411yescharacteristic
97C22×Q8×C11C2311yescharacteristic
98C2×#4343—21no—
99C2×#4339C2311yescharacteristic
100C2×#4339C2312yes—
101C11×C4⋊Q8—22no—
102C11×C4⋊Q8—22no—
103C11×C4⋊Q8—24no—
104C11×C4⋊Q8—21no—
105C11×C4⋊Q8—21no—
106C11×C4⋊Q8C2312yes—
107C11×C4⋊Q8C2312yes—
108C11×#125—24no—
109C11×#125—24no—
110C11×#125—24no—
111C11×#125—24no—
112C11×#125—22no—
113C11×#125—22no—
114C11×#125C2314yes—
115C11×#125C2314yes—
116C4×Q8×C11—22no—
117C4×Q8×C11—22no—
118C4×Q8×C11—24no—
119C4×Q8×C11—22no—
120C4×Q8×C11—22no—
121C4×Q8×C11—21no—
122C4×Q8×C11—21no—
123C4×Q8×C11D411yescharacteristic
124C4×Q8×C11D412yes—
125C4×Q8×C11D411yescharacteristic
126C4×Q8×C11C2312yes—
127C4×Q8×C11C2314yes—
128C4×Q8×C11C2314yes—
129C4×Q8×C11C2312yes—
130C4×Q8×C11C2311yescharacteristic
131C4×Q8×C11C2311yescharacteristic
132C4×Q8×C11C2312yes—
133C2×C11×C4⋊C4—22no—
134C2×C11×C4⋊C4—21no—
135C2×C11×C4⋊C4—22no—
136C2×C11×C4⋊C4—21no—
137C2×C11×C4⋊C4—22no—
138C2×C11×C4⋊C4D411yescharacteristic
139C2×C11×C4⋊C4D412yes—
140C2×C11×C4⋊C4C2311yescharacteristic
141C2×C11×C4⋊C4C2312yes—
142C2×C42×C11—22no—
143C2×C42×C11—21no—
144C2×C42×C11C2312yes—
145C2×C42×C11C2311yescharacteristic
146#67000—21no—
147#67000—22no—
148#66999—21no—
149#66999—22no—
150Q8×Dic11—21no—
151C2×#4326C2314yes—
152C2×#4326C2312yes—
153#66995—24no—
154#66995—28no—
155C2×#4325C2312yes—
156C2×#4325C2314yes—
157#66983—22no—
158#66983—21no—
159#66983—21no—
160#66983—22no—
161C4×C22⋊D11—22no—
162C4×C22⋊D11—21no—
163C4×C22⋊D11—21no—
164C4×C22⋊D11—22no—
165#66979C2311yescharacteristic
166C2×#4318C2311yescharacteristic
167C2×#4318C2311yescharacteristic
168C2×#4318C2312yes—
169#66951—22no—
170#66951—22no—
171#66951—22no—
172#66948—21no—
173#66948—22no—
174#66947—22no—
175#66947—22no—
176#66947—22no—
177#66946—21no—
178#66946—22no—
179#66945—21no—
180#66945—22no—
181#66943—21no—
182#66943—22no—
183#66928C2312yes—
184#66928C2312yes—
185#66928C2312yes—
186#66927C2312yes—
187#66927C2311yescharacteristic
188C4×D44—22no—
189C4×D44—21no—
190C4×D44—22no—
191C4×D44—21no—
192C4×D44C2311yescharacteristic
193C4×D44C2312yes—
194C4×D44C2312yes—
195C4×D44C2311yescharacteristic
196#66925—22no—
197#66925—21no—
198C42×D11—22no—
199C42×D11—21no—
200#66922C2312yes—
201#66922C2311yescharacteristic
202C4×Dic22C2311yescharacteristic
203C4×Dic22C2312yes—
204C4×Dic22C2312yes—
205C4×Dic22C2311yescharacteristic
206#66899C2312yes—
207#66899C2312yes—
208#66874C2314yes—
209#66874C2314yes—
210#66874C2314yes—
211#66874C2312yes—
212#66874C2314yes—
213#66873C2312yes—
214#66873C2314yes—
215#66873C2314yes—
216#66873C2314yes—
217#66873C2314yes—
218#66872C2312yes—
219#66872C2314yes—
220#66871C2312yes—
221#66871C2314yes—
222C4⋊(C11⋊C8)C2312yes—
223C4⋊(C11⋊C8)C2314yes—
224C4⋊(C11⋊C8)C2314yes—
225C4⋊(C11⋊C8)C2312yes—
226#66867C2314yes—
227#66867C2312yes—
228C4×C11⋊C8C2314yes—
229C4×C11⋊C8C2312yes—
230#61320—111nomaximal, Sylow
231C2×Q8×C11—21no—
232C2×Q8×C11—22no—
233C2×Q8×C11—22no—
234C2×Q8×C11—22no—
235C2×Q8×C11—42no—
236C2×Q8×C11—44no—
237C2×Q8×C11C2×D411yescharacteristic
238C2×Q8×C11C2×D411yescharacteristic
239C2×Q8×C11C2×D412yes—
240C2×Q8×C11#4114yescomplemented
241C2×Q8×C11C2412yes—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—22no—
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2×D412yes—
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2×D412yes—
249C22×C4×C11C2411yescharacteristic
250C2×C22⋊D11—22no—
251C2×C22⋊D11—21no—
252#4343—44no—
253#4339—22no—
254#4339—24no—
255#4339—22no—
256#4339—24no—
257C2×D44—22no—
258C2×D44—21no—
259C2×D44—22no—
260C2×D44—21no—
261C2×D44C2411yescharacteristic
262C2×D44C2412yes—
263C2×C4×D11—22no—
264C2×C4×D11—21no—
265C2×C4×D11—22no—
266C2×C4×D11—21no—
267C2×C4×D11—22no—
268C2×C4×D11—21no—
269C2×Dic22C2412yes—
270C2×Dic22C2411yescharacteristic
271C11×C4⋊C4—24no—
272C11×C4⋊C4—24no—
273C11×C4⋊C4—22no—
274C11×C4⋊C4—22no—
275C11×C4⋊C4—24no—
276C11×C4⋊C4—24no—
277C11×C4⋊C4—22no—
278C11×C4⋊C4—22no—
279C11×C4⋊C4—24no—
280C11×C4⋊C4—24no—
281C11×C4⋊C4—21no—
282C11×C4⋊C4—22no—
283C11×C4⋊C4C2×D411yescharacteristic
284C11×C4⋊C4C2×D412yes—
285C11×C4⋊C4C2×D411yescharacteristic
286C11×C4⋊C4C2×D412yes—
287C11×C4⋊C4C2×D412yes—
288C11×C4⋊C4C2×D412yes—
289C11×C4⋊C4C2×D412yes—
290C11×C4⋊C4C2412yes—
291C11×C4⋊C4C2414yes—
292C42×C11—24no—
293C42×C11—24no—
294C42×C11—22no—
295C42×C11—22no—
296C42×C11C2×D412yes—
297C42×C11C2×D411yescharacteristic
298C42×C11C2×D412yes—
299C42×C11C2×D411yescharacteristic
300C42×C11C2411yescharacteristic
301C42×C11C2412yes—
302C42×C11C2412yes—
303C42×C11C2411yescharacteristic
304C22⋊Dic11—21no—
305#4326—28no—
306#4326—24no—
307#4325—24no—
308#4325—28no—
309(C2×D11)⋊C4—21no—
310(C2×D11)⋊C4—22no—
311(C2×D11)⋊C4—22no—
312(C2×D11)⋊C4—21no—
313(C2×D11)⋊C4—22no—
314(C2×D11)⋊C4—22no—
315(C2×D11)⋊C4—22no—
316(C2×D11)⋊C4—22no—
317(C2×D11)⋊C4—22no—
318(C2×D11)⋊C4—22no—
319C4⋊Dic11—22no—
320C4⋊Dic11—21no—
321C4⋊Dic11—22no—
322C4⋊Dic11—21no—
323C4⋊Dic11C2411yescharacteristic
324C4⋊Dic11C2411yescharacteristic
325Dic11⋊C4—22no—
326Dic11⋊C4—21no—
327Dic11⋊C4—21no—
328Dic11⋊C4—22no—
329C4×Dic11—22no—
330C4×Dic11—21no—
331C4×Dic11—22no—
332C4×Dic11—21no—
333C4×Dic11—21no—
334#4318—22no—
335#4318—24no—
336#4318—22no—
337C2×C11⋊C8C2412yes—
338C2×C11⋊C8C2414yes—
339C2×C11⋊C8C2412yes—
340#3480—111no—
341C2×#557D1111yescharacteristic, complemented
342#3377—114no—
343#3374—112no—
344#3371—114no—
345#3368—112no—
346#3365—112no—
347#3364—112no—
348#3142—112no—
349#3141—111no—
350#3080—112no—
351#3079—111no—
352#3037—111no—
353#3037—112no—
354Q8×M16—111no—
355C4×#137—111no—
356C4×#137—112no—
357C23×C11C22×D411yescharacteristic
358C22×D11—22no—
359C22×D11—21no—
360Q8×C11—24no—
361Q8×C11—22no—
362Q8×C11—22no—
363Q8×C11—22no—
364Q8×C11—42no—
365Q8×C11—44no—
366Q8×C11—44no—
367Q8×C11C2×#4114yes—
368C2×C4×C11—24no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—24no—
373C2×C4×C11—42no—
374C2×C4×C11—41no—
375C2×C4×C11—42no—
376C2×C4×C11—42no—
377C2×C4×C11—44no—
378C2×C4×C11C22×D412yes—
379C2×C4×C11C22×D412yes—
380C2×C4×C11C22×D411yescharacteristic
381C2×C4×C11C22×D412yes—
382C2×C4×C11C22×D411yescharacteristic
383C2×C4×C11C22×D411yescharacteristic
384C2×C4×C11C22×D412yes—
385C2×C4×C11C22×D411yescharacteristic
386C2×C4×C11C22×D411yescharacteristic
387C2×C4×C11C2×#4112yes—
388C2×C4×C112−1+412yes—
389C2×C4×C11C2511yescharacteristic
390C22⋊D11—42no—
391C22⋊D11—44no—
392C2×Dic11—21no—
393C2×Dic11—21no—
394C2×Dic11—22no—
395C2×Dic11—21no—
396D44—21no—
397D44—22no—
398D44—21no—
399D44—22no—
400D44—44no—
401D44—42no—
402D44—82no—
403D44—81no—
404C4×D11—44no—
405C4×D11—44no—
406C4×D11—42no—
407C4×D11—42no—
408C4×D11—82no—
409C4×D11—81no—
410Dic22—22no—
411Dic22—21no—
412Dic22—22no—
413Dic22—21no—
414C11⋊C8—24no—
415C11⋊C8—22no—
416C11⋊C8—22no—
417C2×#137—111no—
418C2×#137—112no—
419#559—111no—
420#559—112no—
421#557—21no—
422#557—21no—
423#557—22no—
424#557—111no—
425#557C2×D1112yes—
426#557C2×D1112yes—
427#557C2×D1114yes—
428#556—111no—
429#556—112no—
430#553—221no—
431#553—222no—
432#550—111no—
433#548—221no—
434#532—111no—
435#532—112no—
436C2×C4⋊Q8—21no—
437C2×C4⋊Q8C2×D1111yescharacteristic
438#529—222no—
439#529—221no—
440C2×#125—22no—
441C2×#125C2×D1112yes—
442C4×#41—111no—
443C4×#41—112no—
444C4×#41—221no—
445C2×C4×Q8—21no—
446C2×C4×Q8C2×D1112yes—
447C2×C4×Q8C2×D1111yescharacteristic
448C2×C4×Q8C2×D1111yescharacteristic
449#491—114no—
450#490—114no—
451#489—114no—
452#488—114no—
453#488—114no—
454#487—112no—
455#486—112no—
456#479—114no—
457#479—114no—
458#478—114no—
459#478—114no—
460#477—112no—
461#476—112no—
462#475—112no—
463#474—112no—
464#464—114no—
465#464—114no—
466#464—114no—
467#462—112no—
468#462—114no—
469#460—112no—
470#460—114no—
471#446—112no—
472#446—114no—
473C8×Q8—112no—
474#441—114no—
475#441—112no—
476#440—114no—
477#440—112no—
478C4×Q16—114no—
479C4×Q16—112no—
480C4×SD16—112no—
481C4×SD16—114no—
482#428—112no—
483#428—111no—
484#423—111no—
485#423—112no—
486#419—111no—
487#417—112no—
488#417—112no—
489#417—112no—
490#417—112no—
491#417—111no—
492C4×M16—111no—
493C4×M16—112no—
494C22×C11—21no—
495C22×C11—21no—
496C22×C11#54812yes—
497C22×C11C23×D411yescharacteristic
498C2×D11—42no—
499C2×D11—41no—
500C2×D11—42no—
501C2×D11—41no—
502C2×D11—42no—
503C2×D11—41no—
504C4×C11—22no—
505C4×C11—21no—
506C4×C11—22no—
507C4×C11—21no—
508C4×C11—24no—
509C4×C11—21no—
510C4×C11—22no—
511C4×C11—22no—
512C4×C11—42no—
513C4×C11—44no—
514C4×C11#54812yes—
515C4×C11#57512yes—
516C4×C11C22×#4111yescharacteristic
517C4×C11C2×2−1+411yescharacteristic
518Dic11—41no—
519Dic11—42no—
520Dic11—41no—
521Dic11—41no—
522C2×#41—111no—
523C2×#41—112no—
524C2×#41—221no—
525C22×Q8—21no—
526C22×Q8C22⋊D1111yescharacteristic
527C22×Q8C22×D1111yescharacteristic
528#137—224no—
529#137—228no—
530C2×Q16—114no—
531C2×Q16—112no—
532C2×SD16—112no—
533C2×SD16—114no—
534C2×M16—111no—
535C2×M16—112no—
536C2×M16—111no—
537C4⋊Q8—22no—
538C4⋊Q8—22no—
539C4⋊Q8—24no—
540C4⋊Q8—21no—
541C4⋊Q8—21no—
542C4⋊Q8—111no—
543C4⋊Q8—112no—
544C4⋊Q8C22×D1112yes—
545C4⋊Q8C22×D1112yes—
546#127—111no—
547#127—112no—
548#126—222no—
549#126—222no—
550#126—222no—
551#125—24no—
552#125—24no—
553#125—24no—
554#125—24no—
555#125—22no—
556#125—22no—
557#125—221no—
558#125—222no—
559#125C22×D1114yes—
560#125C22×D1114yes—
561#124—112no—
562#124—112no—
563#124—112no—
564#124—221no—
565#124—222no—
566#123—222no—
567#123—222no—
568#123—222no—
569C22⋊Q8—221no—
570C22⋊Q8—222no—
571#121—221no—
572#121—222no—
573#121—222no—
574#121—221no—
575#121—221no—
576#121—222no—
577C4×Q8—22no—
578C4×Q8—22no—
579C4×Q8—24no—
580C4×Q8—22no—
581C4×Q8—22no—
582C4×Q8—21no—
583C4×Q8—21no—
584C4×Q8—112no—
585C4×Q8—111no—
586C4×Q8—111no—
587C4×Q8—112no—
588C4×Q8—221no—
589C4×Q8C22⋊D1111yescharacteristic
590C4×Q8C22⋊D1112yes—
591C4×Q8C22⋊D1111yescharacteristic
592C4×Q8C22×D1112yes—
593C4×Q8C22×D1114yes—
594C4×Q8C22×D1114yes—
595C4×Q8C22×D1112yes—
596C4×Q8C22×D1111yescharacteristic
597C4×Q8C22×D1111yescharacteristic
598C4×Q8C22×D1112yes—
599C4×D4—111no—
600C4×D4—112no—
601C4×D4—112no—
602C4×D4—111no—
603C4×D4—221no—
604C4×D4—222no—
605C4×D4—222no—
606C4×D4—221no—
607C4×D4—221no—
608C4×D4—222no—
609C4×D4—222no—
610C4×D4—221no—
611C4×D4—222no—
612C4×D4—221no—
613#117—111no—
614#117—221no—
615#117—222no—
616#117—222no—
617#117—221no—
618C2×C4⋊C4—22no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—22no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—22no—
623C2×C4⋊C4C22⋊D1111yescharacteristic
624C2×C4⋊C4C22⋊D1112yes—
625C2×C4⋊C4C22×D1111yescharacteristic
626C2×C4⋊C4C22×D1112yes—
627C2×C42—22no—
628C2×C42—21no—
629C2×C42—222no—
630C2×C42—221no—
631C2×C42C22×D1112yes—
632C2×C42C22×D1111yescharacteristic
633#107—114no—
634#107—112no—
635#106—114no—
636#106—112no—
637C4⋊C8—112no—
638C4⋊C8—114no—
639C4⋊C8—114no—
640C4⋊C8—112no—
641#103—112no—
642#103—112no—
643#103—114no—
644#103—112no—
645#103—114no—
646#103—114no—
647#103—114no—
648#102—114no—
649#102—112no—
650#102—114no—
651#102—114no—
652#102—114no—
653#97—112no—
654#97—114no—
655C4×C8—112no—
656C4×C8—114no—
657C2×C11—22no—
658C2×C11C2×#54811yescharacteristic
659C2×C11C2×#57511yescharacteristic
660C2×C11#358611yescharacteristic
661D11—82no—
662D11—81no—
663#41—222no—
664#41—224no—
665#41—222no—
666#41—224no—
667#41—444no—
668C2×Q8—22no—
669C2×Q8—21no—
670C2×Q8—22no—
671C2×Q8—22no—
672C2×Q8—42no—
673C2×Q8—44no—
674C2×Q8—112no—
675C2×Q8—111no—
676C2×Q8#434314yescomplemented
677C2×Q8C2×C22⋊D1111yescharacteristic
678C2×Q8C2×C22⋊D1111yescharacteristic
679C2×Q8C2×C22⋊D1112yes—
680C2×Q8C23×D1112yes—
681C2×D4—112no—
682C2×D4—111no—
683C2×D4—221no—
684C2×D4—222no—
685C2×D4—222no—
686C2×D4—221no—
687C2×D4—222no—
688C2×D4—221no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—22no—
692C22×C4—222no—
693C22×C4—221no—
694C22×C4—222no—
695C22×C4—221no—
696C22×C4—222no—
697C22×C4—221no—
698C22×C4C2×C22⋊D1111yescharacteristic
699C22×C4C2×C22⋊D1112yes—
700C22×C4C2×C22⋊D1111yescharacteristic
701C22×C4C2×C22⋊D1112yes—
702C22×C4C23×D1111yescharacteristic
703Q16—228no—
704Q16—224no—
705SD16—224no—
706SD16—228no—
707M16—222no—
708M16—224no—
709M16—222no—
710C2×C8—112no—
711C2×C8—112no—
712C2×C8—114no—
713C4⋊C4—24no—
714C4⋊C4—24no—
715C4⋊C4—22no—
716C4⋊C4—22no—
717C4⋊C4—24no—
718C4⋊C4—24no—
719C4⋊C4—22no—
720C4⋊C4—22no—
721C4⋊C4—24no—
722C4⋊C4—24no—
723C4⋊C4—21no—
724C4⋊C4—22no—
725C4⋊C4—111no—
726C4⋊C4—111no—
727C4⋊C4—221no—
728C4⋊C4—222no—
729C4⋊C4—222no—
730C4⋊C4—221no—
731C4⋊C4—222no—
732C4⋊C4—221no—
733C4⋊C4—222no—
734C4⋊C4—221no—
735C4⋊C4C2×C22⋊D1111yescharacteristic
736C4⋊C4C2×C22⋊D1112yes—
737C4⋊C4C2×C22⋊D1111yescharacteristic
738C4⋊C4C2×C22⋊D1112yes—
739C4⋊C4C2×C22⋊D1112yes—
740C4⋊C4C2×C22⋊D1112yes—
741C4⋊C4C2×C22⋊D1112yes—
742C4⋊C4C23×D1112yes—
743C4⋊C4C23×D1114yes—
744C22⋊C4—221no—
745C22⋊C4—222no—
746C22⋊C4—221no—
747C22⋊C4—221no—
748C22⋊C4—222no—
749C22⋊C4—222no—
750C22⋊C4—222no—
751C22⋊C4—222no—
752C22⋊C4—222no—
753C22⋊C4—222no—
754C22⋊C4—222no—
755C42—24no—
756C42—24no—
757C42—22no—
758C42—22no—
759C42—221no—
760C42—222no—
761C42—221no—
762C42—222no—
763C42—221no—
764C42C2×C22⋊D1112yes—
765C42C2×C22⋊D1111yescharacteristic
766C42C2×C22⋊D1112yes—
767C42C2×C22⋊D1111yescharacteristic
768C42C23×D1112yes—
769C42C23×D1111yescharacteristic
770C42C23×D1111yescharacteristic
771C42C23×D1112yes—
772C11#6132011yescharacteristic, complemented, Sylow
773C23—222no—
774C23—221no—
775C23C22×C22⋊D1111yescharacteristic
776Q8—24no—
777Q8—22no—
778Q8—22no—
779Q8—22no—
780Q8—42no—
781Q8—44no—
782Q8—44no—
783Q8—222no—
784Q8—221no—
785Q8—222no—
786Q8—221no—
787Q8C2×#434314yes—
788D4—222no—
789D4—221no—
790D4—222no—
791D4—221no—
792D4—444no—
793D4—442no—
794D4—444no—
795D4—442no—
796D4—882no—
797D4—881no—
798C2×C4—24no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—24no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—44no—
808C2×C4—221no—
809C2×C4—221no—
810C2×C4—222no—
811C2×C4—221no—
812C2×C4—444no—
813C2×C4—444no—
814C2×C4—442no—
815C2×C4—442no—
816C2×C4—882no—
817C2×C4—881no—
818C2×C4C2×#434312yes—
819C2×C4#6704012yes—
820C2×C4C22×C22⋊D1112yes—
821C2×C4C22×C22⋊D1111yescharacteristic
822C2×C4C22×C22⋊D1112yes—
823C2×C4C22×C22⋊D1111yescharacteristic
824C2×C4C22×C22⋊D1112yes—
825C2×C4C22×C22⋊D1112yes—
826C2×C4C22×C22⋊D1111yescharacteristic
827C2×C4C22×C22⋊D1111yescharacteristic
828C2×C4C22×C22⋊D1111yescharacteristic
829C2×C4C24×D1111yescharacteristic
830C8—222no—
831C8—224no—
832C8—222no—
833C22—21no—
834C22—21no—
835C22—442no—
836C22—441no—
837C22—442no—
838C22—441no—
839C22—442no—
840C22—441no—
841C22#1062334812yes—
842C22C23×C22⋊D1111yescharacteristic
843C4—22no—
844C4—21no—
845C4—22no—
846C4—21no—
847C4—21no—
848C4—22no—
849C4—22no—
850C4—24no—
851C4—42no—
852C4—44no—
853C4—441no—
854C4—441no—
855C4—442no—
856C4—441no—
857C4#1062334812yes—
858C4#1062335312yes—
859C4C22×#434311yescharacteristic
860C4C2×#6704011yescharacteristic
861C2—22no—
862C2—882no—
863C2—881no—
864C2C2×#1062334811yescharacteristic
865C2C2×#1062335311yescharacteristic
866C2#1308340311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#557C2
socleC22×C11C23×D4
prime radical#13082211C2
hypercenterC2×#557D11
hypocenterC11#61320
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
2. #13081458C2semidirect
3. #13081419C2semidirect
4. #13081384C2semidirect
5. #13081345C2semidirect
6. #13081312C2semidirect
7. #13081301C2semidirect
8. #13079019C2semidirect
9. #13079012C2semidirect
10. #13078434C2semidirect
11. #13078425C2semidirect
12. #13078088C2semidirect
13. #13078088C2semidirect
14. Q8×#4318C2semidirect
15. C4×#66995C2semidirect
16. C4×#66995C2semidirect
17. C2×C11×#557C2semidirect
240. C2×Q8×C11#41semidirect
341. C2×#557D11semidirect
676. C2×Q8#4343semidirect
772. C11#61320semidirect

Maximal subgroups

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

subgroupindex
#130822112
#130814582
#130814192
#130813842
#130813452
#130813122
#130813012
#130790192
#130790122
#130784342
#130784252
#130780882
Q8×#43182
C4×#669952
C2×C11×#5572
#6132011