Finite Group Databasebeta

← #15626859

Subgroups — #15626859

Order 2816.

1932 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082492C211yesmaximal, characteristic, complemented
2#13080051C214yesmaximal, complemented
3#13080027C214yesmaximal, complemented
4#13079994C212yesmaximal, complemented
5#13079978C212yesmaximal, complemented
6#13079942C212yesmaximal, complemented
7#13079923C212yesmaximal, complemented
8#13078441C212yesmaximal, complemented
9#13078413C211yesmaximal, characteristic, complemented
10#13078404C211yesmaximal, characteristic, complemented
11#13078298C212yesmaximal, complemented
12#13078261C212yesmaximal, complemented
13#13078115C212yesmaximal, complemented
14#13078096C211yesmaximal, characteristic, complemented
15C2×#10622628C211yesmaximal, characteristic, complemented
16#13077184C211yesmaximal, characteristic, complemented
17C11×#3460C211yesmaximal, characteristic, complemented
18C11×#544C2211yescharacteristic
19C11×#542—21no—
20C11×#542C2212yescomplemented
21C11×#540—21no—
22C11×#540C2212yescomplemented
23C11×#538—22no—
24C11×#537C2211yescharacteristic
25C11×#535C2211yescharacteristic
26C11×#535C2211yescharacteristic
27C11×#532—21no—
28C11×#532C2212yescomplemented
29C11×#529—21no—
30C11×#529C2212yescomplemented
31C11×#525—22no—
32C4×C11×#41C2211yescharacteristic
33C4×C11×#41C2211yescharacteristic
34C2×C4×D4×C11C2211yescharacteristic
35#10623361C2212yes—
36C2×#67002C2212yes—
37C2×#67001C2212yes—
38C22×#4323C2212yes—
39#10623116—21no—
40#10623116—21no—
41#10623084—21no—
42#10623084—21no—
43#10623081—22no—
44#10623081—22no—
45#10623066C2214yescomplemented
46#10623052C2212yes—
47#10623008C2212yescomplemented
48#10623008C2212yescomplemented
49C2×#66927C2211yescharacteristic
50#10623001C2211yescharacteristic
51#10622846C2212yes—
52#10622828C2212yes—
53#10622700C2214yescomplemented
54#10622697C2214yescomplemented
55#10622685C2214yescomplemented
56#10622685C2214yescomplemented
57#10622679C2214yescomplemented
58#10622679C2214yescomplemented
59#10622670C2214yescomplemented
60#10622670C2214yescomplemented
61#10622662C2214yescomplemented
62#10622661C2214yescomplemented
63#10622652C2214yescomplemented
64#10622652C2214yescomplemented
65#10622652C2214yescomplemented
66#10622651C2214yescomplemented
67#10622651C2214yescomplemented
68#10622651C2214yescomplemented
69#10622640C2212yescomplemented
70#10622640C2212yescomplemented
71#10622635C2212yescomplemented
72#10622634C2211yescharacteristic, complemented
73#10622633C2211yescharacteristic, complemented
74#10622628C2212yes—
75#10622628C2212yes—
76#10622628C2214yes—
77#10622628C2212yescomplemented
78#10622628C2212yescomplemented
79#10622622C2212yescomplemented
80#10622622C2214yescomplemented
81#10622621C2211yescharacteristic, complemented
82#10622621C2212yescomplemented
83#10622620C2211yescharacteristic, complemented
84#10622620C2212yescomplemented
85#10622614C2212yes—
86#10622612C2212yes—
87#10622612C2214yescomplemented
88#10622611C2212yes—
89C2×#66873C2212yes—
90#10622577C2212yes—
91#10622537C2211yescharacteristic
92#10622537C2212yescomplemented
93C2×C4⋊(C11⋊C8)C2211yescharacteristic
94C2×C4⋊(C11⋊C8)C2212yescomplemented
95C2×C11×#41—22no—
96C2×C11×#41C2311yescharacteristic
97C2×C11×#41C2311yescharacteristic
98C22×D4×C11C2311yescharacteristic
99C23×C4×C11—21no—
100C2×#4339—22no—
101C2×#4339—22no—
102C22×D44—21no—
103C22×D44—21no—
104C22×D44C2312yes—
105C11×C4⋊Q8—21no—
106C11×C4⋊Q8C2312yes—
107C11×#127—21no—
108C11×#127C2312yes—
109C11×#126—22no—
110C11×#126—22no—
111C11×#125—21no—
112C11×#125C2312yes—
113C11×#124—21no—
114C11×#124—22no—
115C11×#124—22no—
116C11×#124C2312yes—
117C11×#123—22no—
118C11×#123—22no—
119C11×#123—22no—
120C11×#123—22no—
121C11×C22⋊Q8—21no—
122C11×C22⋊Q8—22no—
123C11×C22⋊Q8—22no—
124C11×C22⋊Q8C2312yes—
125C11×#121—22no—
126C11×#121—21no—
127C11×#121—22no—
128C11×#121—21no—
129C11×#121—21no—
130C11×#121—22no—
131C11×#121—22no—
132C11×#121C2312yes—
133C11×#121C2312yes—
134C11×#121C2312yes—
135C11×#120—22no—
136C11×#120—22no—
137C4×Q8×C11D411yescharacteristic
138C4×Q8×C11D411yescharacteristic
139C4×Q8×C11C2311yescharacteristic
140C4×Q8×C11C2311yescharacteristic
141C4×D4×C11—21no—
142C4×D4×C11—21no—
143C4×D4×C11—22no—
144C4×D4×C11—21no—
145C4×D4×C11—21no—
146C4×D4×C11—22no—
147C4×D4×C11D412yes—
148C4×D4×C11D412yes—
149C4×D4×C11D411yescharacteristic
150C4×D4×C11D411yescharacteristic
151C4×D4×C11C2312yes—
152C4×D4×C11C2312yes—
153C4×D4×C11C2311yescharacteristic
154C4×D4×C11C2311yescharacteristic
155C11×#117—21no—
156C11×#117—22no—
157C11×#117C2311yescharacteristic
158C11×#117C2311yescharacteristic
159C11×#117C2312yes—
160C2×C11×C4⋊C4C2311yescharacteristic
161C2×C11×C22⋊C4—21no—
162C2×C42×C11—21no—
163C2×C42×C11C2311yescharacteristic
164C2×C42×C11C2312yes—
165#67002—44no—
166#67001—44no—
167#67000—22no—
168C2×#4325C2314yes—
169#66993—22no—
170#66990—24no—
171C2×#4323—44no—
172C2×#4323C2314yes—
173C2×#4323C2314yes—
174C2×#4323C2314yes—
175#66983—22no—
176#66983—22no—
177#66983C2314yes—
178#66983C2314yes—
179#66979C2312yes—
180#66977—21no—
181#66977—21no—
182C2×#4318C2312yes—
183C2×#4318C2314yes—
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#66928—22no—
195#66927—21no—
196#66927—21no—
197#66927C2312yes—
198#66927C2312yes—
199C4×D44—22no—
200C4×D44—22no—
201C4×D44C2314yes—
202C4×D44C2314yes—
203#66923C2312yes—
204#66922C2311yescharacteristic
205#66922C2311yescharacteristic
206C4×Dic22—21no—
207C4×Dic22—21no—
208#66899C2312yes—
209#66899C2312yes—
210#66896C2314yes—
211#66896C2314yes—
212#66896C2312yes—
213#66896C2312yes—
214#66873C2314yes—
215#66873C2314yes—
216#66873C2314yes—
217#66873C2314yes—
218#66872C2314yes—
219#66872C2312yes—
220#66872C2312yes—
221#66871C2314yes—
222#66871C2312yes—
223#66871C2312yes—
224C4⋊(C11⋊C8)C2311yescharacteristic
225C4⋊(C11⋊C8)C2311yescharacteristic
226C4⋊(C11⋊C8)C2312yes—
227C4⋊(C11⋊C8)C2312yes—
228C4⋊(C11⋊C8)C2314yes—
229C4⋊(C11⋊C8)C2312yes—
230C4⋊(C11⋊C8)C2314yes—
231#60922—111nomaximal, Sylow
232C24×C11—21no—
233C23×D11—22no—
234C11×#41—22no—
235C11×#41—22no—
236C11×#41—22no—
237C11×#41—22no—
238C11×#41—84no—
239C2×Q8×C11—22no—
240C2×Q8×C11C2×D411yescharacteristic
241C2×Q8×C11C2411yescharacteristic
242C2×D4×C11—21no—
243C2×D4×C11—22no—
244C2×D4×C11—22no—
245C2×D4×C11—22no—
246C2×D4×C11—21no—
247C2×D4×C11—22no—
248C2×D4×C11—22no—
249C2×D4×C11—22no—
250C2×D4×C11—22no—
251C2×D4×C11C2×D412yes—
252C2×D4×C11C2×D411yescharacteristic
253C2×D4×C11C2412yes—
254C2×D4×C11C2411yescharacteristic
255C22×C4×C11—21no—
256C22×C4×C11—21no—
257C22×C4×C11—21no—
258C22×C4×C11—22no—
259C22×C4×C11—21no—
260C22×C4×C11—22no—
261C22×C4×C11—82no—
262C22×C4×C11C2×D411yescharacteristic
263C22×C4×C11C2×D412yes—
264C22×C4×C11C2×D411yescharacteristic
265C22×C4×C11C2×D412yes—
266C22×C4×C11C2412yes—
267C22×C4×C11C2411yescharacteristic
268C2×C22⋊D11—24no—
269C2×C22⋊D11—24no—
270#4339—84no—
271#4339—84no—
272C2×D44—22no—
273C2×D44—22no—
274C2×D44—22no—
275C2×D44—22no—
276C2×D44—22no—
277C2×D44—24no—
278C2×D44—24no—
279C2×D44—82no—
280C2×D44—82no—
281C2×D44C2414yes—
282C2×C4×D11—24no—
283C2×C4×D11—24no—
284C2×Dic22—21no—
285C2×Dic22—21no—
286C11×C4⋊C4—21no—
287C11×C4⋊C4—21no—
288C11×C4⋊C4—21no—
289C11×C4⋊C4—22no—
290C11×C4⋊C4—22no—
291C11×C4⋊C4—22no—
292C11×C4⋊C4—22no—
293C11×C4⋊C4C2×D411yescharacteristic
294C11×C4⋊C4C2×D411yescharacteristic
295C11×C4⋊C4C2×D412yes—
296C11×C4⋊C4C2×D412yes—
297C11×C4⋊C4C2412yes—
298C11×C4⋊C4C2411yescharacteristic
299C11×C4⋊C4C2411yescharacteristic
300C11×C22⋊C4—21no—
301C11×C22⋊C4—22no—
302C11×C22⋊C4—22no—
303C11×C22⋊C4—22no—
304C11×C22⋊C4—21no—
305C11×C22⋊C4—21no—
306C11×C22⋊C4—22no—
307C11×C22⋊C4—22no—
308C11×C22⋊C4—22no—
309C11×C22⋊C4—22no—
310C11×C22⋊C4—22no—
311C11×C22⋊C4C2×D412yes—
312C11×C22⋊C4C2×D412yes—
313C11×C22⋊C4C2×D412yes—
314C42×C11—21no—
315C42×C11—21no—
316C42×C11—21no—
317C42×C11C2×D411yescharacteristic
318C42×C11C2×D411yescharacteristic
319C42×C11C2×D412yes—
320C42×C11C2×D412yes—
321C42×C11C2411yescharacteristic
322C42×C11C2411yescharacteristic
323C42×C11C2412yes—
324C22⋊Dic11—22no—
325#4325—44no—
326#4323—44no—
327#4323—44no—
328#4323—44no—
329(C2×D11)⋊C4—24no—
330(C2×D11)⋊C4—24no—
331(C2×D11)⋊C4—24no—
332(C2×D11)⋊C4—24no—
333C4⋊Dic11—21no—
334C4⋊Dic11—21no—
335C4⋊Dic11C2412yes—
336C4⋊Dic11C2412yes—
337Dic11⋊C4—22no—
338Dic11⋊C4—22no—
339C4×Dic11—22no—
340#4318—24no—
341#4318—44no—
342C2×C11⋊C8—24no—
343C2×C11⋊C8—44no—
344C2×C11⋊C8C2412yes—
345C2×C11⋊C8C2414yes—
346C2×C11⋊C8C2412yes—
347#3508—111no—
348#3460D1111yescharacteristic, complemented
349#3259—114no—
350#3257—114no—
351#3253—112no—
352#3251—112no—
353#3247—112no—
354#3245—112no—
355#3081—112no—
356#3077—111no—
357#3076—111no—
358#3062—112no—
359#3058—112no—
360#3041—112no—
361#3038—111no—
362C2×#459—111no—
363#2906—111no—
364C23×C11—22no—
365C23×C11—21no—
366C23×C11—42no—
367C23×C11—81no—
368C23×C11—81no—
369C23×C11C22×D412yes—
370C23×C11C22×D411yescharacteristic
371C22×D11—24no—
372C22×D11—44no—
373C22×D11—82no—
374C22×D11—82no—
375Q8×C11—22no—
376Q8×C11—21no—
377Q8×C11—21no—
378Q8×C11—82no—
379D4×C11—24no—
380D4×C11—22no—
381D4×C11—22no—
382D4×C11—21no—
383D4×C11—22no—
384D4×C11—21no—
385D4×C11—42no—
386D4×C11—42no—
387D4×C11—82no—
388D4×C11—82no—
389D4×C11—82no—
390D4×C11—82no—
391D4×C11—82no—
392C2×C4×C11—22no—
393C2×C4×C11—24no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—21no—
397C2×C4×C11—21no—
398C2×C4×C11—21no—
399C2×C4×C11—22no—
400C2×C4×C11—41no—
401C2×C4×C11—42no—
402C2×C4×C11—42no—
403C2×C4×C11—44no—
404C2×C4×C11—42no—
405C2×C4×C11—81no—
406C2×C4×C11—82no—
407C2×C4×C11—81no—
408C2×C4×C11C22×D411yescharacteristic
409C2×C4×C11C22×D411yescharacteristic
410C2×C4×C11C22×D411yescharacteristic
411C2×C4×C11C22×D412yes—
412C2×C4×C11C22×D412yes—
413C2×C4×C11C22×D412yes—
414C2×C4×C11C22×D411yescharacteristic
415C2×C4×C11C22×D411yescharacteristic
416C2×C4×C11H(5,𝔽2)12yes—
417C2×C4×C112−1+412yes—
418C2×C4×C11C2511yescharacteristic
419C22⋊D11—84no—
420C22⋊D11—84no—
421C2×Dic11—22no—
422C2×Dic11—22no—
423D44—24no—
424D44—24no—
425D44—44no—
426D44—44no—
427D44—44no—
428D44—82no—
429D44—82no—
430C4×D11—84no—
431C4×D11—84no—
432Dic22—42no—
433Dic22—42no—
434C11⋊C8—22no—
435C11⋊C8—22no—
436C11⋊C8—24no—
437C2×AGL(1,ℤ/8)—112no—
438C22×D8—112no—
439C2×#131—112no—
440#559—221no—
441#559—221no—
442#550—221no—
443#550—221no—
444#546—222no—
445#546—222no—
446#544C2×D1111yescharacteristic
447#542—21no—
448#542C2×D1112yescomplemented
449#540—21no—
450#540—114no—
451#540C2×D1112yescomplemented
452#538—22no—
453#537C2×D1111yescharacteristic
454#535—112no—
455#535C2×D1111yescharacteristic
456#535C2×D1111yescharacteristic
457#533—111no—
458#532—21no—
459#532—112no—
460#532—112no—
461#532C2×D1112yescomplemented
462C2×#127—111no—
463#529—21no—
464#529C2×D1112yescomplemented
465#525—22no—
466#518—112no—
467C4×#41C2×D1111yescharacteristic
468C4×#41C2×D1111yescharacteristic
469C2×C4×D4C2×D1111yescharacteristic
470#479—112no—
471#478—114no—
472#478—114no—
473#478—112no—
474#478—114no—
475#477—111no—
476#476—114no—
477#476—111no—
478#476—112no—
479#475—111no—
480#474—114no—
481#474—111no—
482#474—112no—
483#469—114no—
484#469—114no—
485#469—114no—
486#468—114no—
487#466—114no—
488#466—114no—
489#466—114no—
490#465—114no—
491#463—114no—
492#463—114no—
493#460—112no—
494#460—112no—
495#459—114no—
496#459—114no—
497#459—112no—
498#459—112no—
499#459—114no—
500#459—112no—
501#459—112no—
502#428—112no—
503#427—112no—
504#424—112no—
505#424—114no—
506#423—111no—
507#423—112no—
508C2×C4⋊C8—111no—
509C2×C4⋊C8—112no—
510#418—112no—
511#418—112no—
512#416—112no—
513C2×#102—112no—
514C22×C11—21no—
515C22×C11—21no—
516C22×C11—22no—
517C22×C11—22no—
518C22×C11—22no—
519C22×C11—41no—
520C22×C11—42no—
521C22×C11—41no—
522C22×C11—42no—
523C22×C11—42no—
524C22×C11—41no—
525C22×C11—84no—
526C22×C11#53712yes—
527C22×C11C23×D411yescharacteristic
528C2×D11—44no—
529C2×D11—44no—
530C2×D11—44no—
531C2×D11—164no—
532C4×C11—21no—
533C4×C11—21no—
534C4×C11—22no—
535C4×C11—22no—
536C4×C11—21no—
537C4×C11—22no—
538C4×C11—41no—
539C4×C11—41no—
540C4×C11—42no—
541C4×C11—41no—
542C4×C11#53712yes—
543C4×C11#57612yes—
544C4×C11C2×H(5,𝔽2)11yescharacteristic
545C4×C11C2×2−1+411yescharacteristic
546Dic11—42no—
547Dic11—42no—
548C2×#41—22no—
549C2×#41—222no—
550C2×#41—222no—
551C2×#41C22×D1111yescharacteristic
552C2×#41C22×D1111yescharacteristic
553C22×D4—112no—
554C22×D4—221no—
555C22×D4—221no—
556C22×D4C22×D1111yescharacteristic
557C23×C4—21no—
558AGL(1,ℤ/8)—444no—
559C2×SD16—114no—
560C2×D8—114no—
561C2×D8—114no—
562C2×D8—114no—
563C2×D8—444no—
564#131—444no—
565C2×M16—112no—
566C2×M16—114no—
567C22×C8—112no—
568C22×C8—114no—
569C4⋊Q8—21no—
570C4⋊Q8—111no—
571C4⋊Q8—111no—
572C4⋊Q8C22×D1112yes—
573#127—21no—
574#127—112no—
575#127—112no—
576#127—222no—
577#127—221no—
578#127—221no—
579#127C22×D1112yes—
580#126—22no—
581#126—22no—
582#125—21no—
583#125—112no—
584#125C22×D1112yes—
585#124—21no—
586#124—22no—
587#124—22no—
588#124—222no—
589#124—222no—
590#124—222no—
591#124C22×D1112yes—
592#123—22no—
593#123—22no—
594#123—22no—
595#123—22no—
596#123—224no—
597#123—224no—
598C22⋊Q8—21no—
599C22⋊Q8—22no—
600C22⋊Q8—22no—
601C22⋊Q8—221no—
602C22⋊Q8—221no—
603C22⋊Q8C22×D1112yes—
604#121—22no—
605#121—21no—
606#121—22no—
607#121—21no—
608#121—21no—
609#121—22no—
610#121—22no—
611#121—114no—
612#121—114no—
613#121—222no—
614#121—222no—
615#121—224no—
616#121—224no—
617#121C22×D1112yes—
618#121C22×D1112yes—
619#121C22×D1112yes—
620#120—22no—
621#120—22no—
622#120—224no—
623C4×Q8—221no—
624C4×Q8—221no—
625C4×Q8C22⋊D1111yescharacteristic
626C4×Q8C22⋊D1111yescharacteristic
627C4×Q8C22×D1111yescharacteristic
628C4×Q8C22×D1111yescharacteristic
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—22no—
632C4×D4—21no—
633C4×D4—21no—
634C4×D4—22no—
635C4×D4—114no—
636C4×D4—114no—
637C4×D4—222no—
638C4×D4—222no—
639C4×D4—222no—
640C4×D4—222no—
641C4×D4C22⋊D1112yes—
642C4×D4C22⋊D1111yescharacteristic
643C4×D4C22⋊D1112yes—
644C4×D4C22⋊D1111yescharacteristic
645C4×D4C22×D1112yes—
646C4×D4C22×D1112yes—
647C4×D4C22×D1111yescharacteristic
648C4×D4C22×D1111yescharacteristic
649#117—21no—
650#117—22no—
651#117—112no—
652#117C22×D1111yescharacteristic
653#117C22×D1111yescharacteristic
654#117C22×D1112yes—
655C2×C4⋊C4C22×D1111yescharacteristic
656C2×C22⋊C4—21no—
657C2×C22⋊C4—224no—
658C2×C42—21no—
659C2×C42C22×D1111yescharacteristic
660C2×C42C22×D1112yes—
661#107—112no—
662#107—112no—
663#107—114no—
664#106—112no—
665#106—112no—
666#106—114no—
667C4⋊C8—111no—
668C4⋊C8—111no—
669C4⋊C8—112no—
670C4⋊C8—112no—
671C4⋊C8—114no—
672C4⋊C8—112no—
673C4⋊C8—114no—
674#103—112no—
675#103—112no—
676#102—112no—
677#102—112no—
678#102—114no—
679#102—114no—
680#102—114no—
681#102—114no—
682#102—114no—
683#102—114no—
684C2×C11—22no—
685C2×C11—42no—
686C2×C11—81no—
687C2×C11—82no—
688C2×C11C2×#53711yescharacteristic
689C2×C11C2×#57611yescharacteristic
690C2×C11#358511yescharacteristic
691D11—84no—
692C24—21no—
693C24—222no—
694#41—22no—
695#41—22no—
696#41—22no—
697#41—22no—
698#41—84no—
699#41—884no—
700#41—884no—
701C2×Q8—22no—
702C2×Q8—221no—
703C2×Q8—221no—
704C2×Q8C2×C22⋊D1111yescharacteristic
705C2×Q8C23×D1111yescharacteristic
706C2×D4—21no—
707C2×D4—22no—
708C2×D4—22no—
709C2×D4—22no—
710C2×D4—22no—
711C2×D4—22no—
712C2×D4—21no—
713C2×D4—22no—
714C2×D4—22no—
715C2×D4—114no—
716C2×D4—224no—
717C2×D4—224no—
718C2×D4—224no—
719C2×D4—224no—
720C2×D4—222no—
721C2×D4—222no—
722C2×D4—222no—
723C2×D4—222no—
724C2×D4—222no—
725C2×D4—882no—
726C2×D4—882no—
727C2×D4C2×C22⋊D1112yes—
728C2×D4C2×C22⋊D1111yescharacteristic
729C2×D4C23×D1112yes—
730C2×D4C23×D1111yescharacteristic
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—22no—
735C22×C4—21no—
736C22×C4—22no—
737C22×C4—82no—
738C22×C4—224no—
739C22×C4—224no—
740C22×C4C2×C22⋊D1112yes—
741C22×C4C2×C22⋊D1111yescharacteristic
742C22×C4C2×C22⋊D1111yescharacteristic
743C22×C4C2×C22⋊D1112yes—
744C22×C4C23×D1112yes—
745C22×C4C23×D1111yescharacteristic
746SD16—444no—
747D8—444no—
748D8—444no—
749D8—444no—
750M16—224no—
751M16—444no—
752C2×C8—114no—
753C2×C8—112no—
754C2×C8—112no—
755C2×C8—224no—
756C2×C8—444no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—22no—
761C4⋊C4—22no—
762C4⋊C4—22no—
763C4⋊C4—22no—
764C4⋊C4—112no—
765C4⋊C4—112no—
766C4⋊C4—221no—
767C4⋊C4—221no—
768C4⋊C4—222no—
769C4⋊C4—222no—
770C4⋊C4C2×C22⋊D1111yescharacteristic
771C4⋊C4C2×C22⋊D1111yescharacteristic
772C4⋊C4C2×C22⋊D1112yes—
773C4⋊C4C2×C22⋊D1112yes—
774C4⋊C4C23×D1112yes—
775C4⋊C4C23×D1111yescharacteristic
776C4⋊C4C23×D1111yescharacteristic
777C22⋊C4—21no—
778C22⋊C4—22no—
779C22⋊C4—22no—
780C22⋊C4—22no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—22no—
784C22⋊C4—22no—
785C22⋊C4—22no—
786C22⋊C4—22no—
787C22⋊C4—22no—
788C22⋊C4—222no—
789C22⋊C4—224no—
790C22⋊C4—224no—
791C22⋊C4—224no—
792C22⋊C4—224no—
793C22⋊C4C2×C22⋊D1112yes—
794C22⋊C4C2×C22⋊D1112yes—
795C22⋊C4C2×C22⋊D1112yes—
796C42—21no—
797C42—21no—
798C42—21no—
799C42—222no—
800C42C2×C22⋊D1111yescharacteristic
801C42C2×C22⋊D1112yes—
802C42C2×C22⋊D1111yescharacteristic
803C42C2×C22⋊D1112yes—
804C42C23×D1111yescharacteristic
805C42C23×D1112yes—
806C42C23×D1111yescharacteristic
807C11#6092211yescharacteristic, complemented, Sylow
808C23—22no—
809C23—21no—
810C23—42no—
811C23—81no—
812C23—81no—
813C23—224no—
814C23—444no—
815C23—882no—
816C23—882no—
817C23C22×C22⋊D1112yes—
818C23C22×C22⋊D1111yescharacteristic
819Q8—22no—
820Q8—21no—
821Q8—21no—
822Q8—82no—
823Q8—442no—
824Q8—442no—
825D4—24no—
826D4—22no—
827D4—22no—
828D4—21no—
829D4—22no—
830D4—21no—
831D4—42no—
832D4—42no—
833D4—82no—
834D4—82no—
835D4—82no—
836D4—82no—
837D4—82no—
838D4—224no—
839D4—224no—
840D4—444no—
841D4—444no—
842D4—444no—
843D4—882no—
844D4—882no—
845D4—884no—
846D4—884no—
847C2×C4—22no—
848C2×C4—24no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—41no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—44no—
859C2×C4—42no—
860C2×C4—81no—
861C2×C4—82no—
862C2×C4—81no—
863C2×C4—222no—
864C2×C4—222no—
865C2×C4—884no—
866C2×C4—884no—
867C2×C4#6704212yes—
868C2×C4#6704312yes—
869C2×C4C22×C22⋊D1111yescharacteristic
870C2×C4C22×C22⋊D1111yescharacteristic
871C2×C4C22×C22⋊D1112yes—
872C2×C4C22×C22⋊D1112yes—
873C2×C4C22×C22⋊D1112yes—
874C2×C4C22×C22⋊D1111yescharacteristic
875C2×C4C22×C22⋊D1111yescharacteristic
876C2×C4C22×C22⋊D1111yescharacteristic
877C2×C4C24×D1111yescharacteristic
878C8—222no—
879C8—222no—
880C8—224no—
881C22—21no—
882C22—21no—
883C22—22no—
884C22—22no—
885C22—22no—
886C22—41no—
887C22—42no—
888C22—41no—
889C22—42no—
890C22—42no—
891C22—41no—
892C22—84no—
893C22—444no—
894C22—444no—
895C22—444no—
896C22—1764no—
897C22#1062336412yes—
898C22C23×C22⋊D1111yescharacteristic
899C4—21no—
900C4—21no—
901C4—22no—
902C4—22no—
903C4—21no—
904C4—22no—
905C4—41no—
906C4—41no—
907C4—42no—
908C4—41no—
909C4—442no—
910C4—442no—
911C4#1062336412yes—
912C4#1062336612yes—
913C4C2×#6704211yescharacteristic
914C4C2×#6704311yescharacteristic
915C2—22no—
916C2—42no—
917C2—82no—
918C2—81no—
919C2—884no—
920C2C2×#1062336411yescharacteristic
921C2C2×#1062336611yescharacteristic
922C2#1308339511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3460C2
socleC22×C11C23×D4
hypercenter#3460D11
hypocenterC11#60922
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3460

Complements

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

NH ≅ G/Ntype
1. #13082492C2semidirect
2. #13080051C2semidirect
3. #13080027C2semidirect
4. #13079994C2semidirect
5. #13079978C2semidirect
6. #13079942C2semidirect
7. #13079923C2semidirect
8. #13078441C2semidirect
9. #13078413C2semidirect
10. #13078404C2semidirect
11. #13078298C2semidirect
12. #13078261C2semidirect
13. #13078115C2semidirect
14. #13078096C2semidirect
15. C2×#10622628C2semidirect
16. #13077184C2semidirect
17. C11×#3460C2semidirect
20. C11×#542C22semidirect
22. C11×#540C22semidirect
28. C11×#532C22semidirect
30. C11×#529C22semidirect
45. #10623066C22semidirect
47. #10623008C22semidirect
48. #10623008C22semidirect
53. #10622700C22semidirect
54. #10622697C22semidirect
55. #10622685C22semidirect
56. #10622685C22semidirect
57. #10622679C22semidirect
58. #10622679C22semidirect
59. #10622670C22semidirect
60. #10622670C22semidirect
61. #10622662C22semidirect
62. #10622661C22semidirect
63. #10622652C22semidirect
64. #10622652C22semidirect
65. #10622652C22semidirect
66. #10622651C22semidirect
67. #10622651C22semidirect
68. #10622651C22semidirect
69. #10622640C22semidirect
70. #10622640C22semidirect
71. #10622635C22semidirect
72. #10622634C22semidirect
73. #10622633C22semidirect
77. #10622628C22semidirect
78. #10622628C22semidirect
79. #10622622C22semidirect
80. #10622622C22semidirect
81. #10622621C22semidirect
82. #10622621C22semidirect
83. #10622620C22semidirect
84. #10622620C22semidirect
87. #10622612C22semidirect
92. #10622537C22semidirect
94. C2×C4⋊(C11⋊C8)C22semidirect
348. #3460D11semidirect
448. #542C2×D11semidirect
451. #540C2×D11semidirect
461. #532C2×D11semidirect
464. #529C2×D11semidirect
807. C11#60922semidirect

Maximal subgroups

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

subgroupindex
#130824922
#130800512
#130800272
#130799942
#130799782
#130799422
#130799232
#130784412
#130784132
#130784042
#130782982
#130782612
#130781152
#130780962
C2×#106226282
#130771842
C11×#34602
#6092211