Finite Group Databasebeta

← #15626893

Subgroups — #15626893

Order 2816.

1868 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082492C211yesmaximal, characteristic, complemented
2#13080057C214yesmaximal, complemented
3#13080027C214yesmaximal, complemented
4#13079999C212yesmaximal, complemented
5#13079978C212yesmaximal, complemented
6#13079942C212yesmaximal, complemented
7#13079928C212yesmaximal, complemented
8#13078441C212yesmaximal, complemented
9#13078421C211yesmaximal, characteristic, complemented
10#13078404C211yesmaximal, characteristic, complemented
11#13078298C212yesmaximal, complemented
12#13078257C212yesmaximal, complemented
13#13078124C212yesmaximal, complemented
14#13078096C211yesmaximal, characteristic, complemented
15C2×#10622640C211yesmaximal, characteristic, complemented
16#13077184C211yesmaximal, characteristic, complemented
17C11×#3461C211yesmaximal, characteristic, complemented
18C11×#544C2211yescharacteristic
19C11×#542—21no—
20C11×#542C2212yescomplemented
21C11×#541—21no—
22C11×#541C2212yescomplemented
23C11×#539—22no—
24C11×#537C2211yescharacteristic
25C11×#536C2211yescharacteristic
26C11×#536C2211yescharacteristic
27C11×#533—21no—
28C11×#533C2212yescomplemented
29C11×#529—22no—
30C11×#529—21no—
31C11×#529C2212yescomplemented
32C4×C11×#41C2211yescharacteristic
33C4×C11×#41C2211yescharacteristic
34C2×C4×Q8×C11C2211yescharacteristic
35#10623361C2212yes—
36C2×#67002C2212yes—
37C2×#67001C2212yes—
38C22×#4325C2212yes—
39#10623116—21no—
40#10623116—21no—
41#10623084—21no—
42#10623084—21no—
43#10623081—22no—
44#10623081—22no—
45#10623066C2214yes—
46#10623052C2212yes—
47#10623008C2212yes—
48#10623008C2212yes—
49C2×#66927C2211yescharacteristic
50#10623001C2211yescharacteristic
51#10622846C2212yes—
52#10622838C2212yes—
53#10622700C2214yescomplemented
54#10622697C2214yescomplemented
55#10622696C2214yescomplemented
56#10622696C2214yescomplemented
57#10622679C2214yescomplemented
58#10622679C2214yescomplemented
59#10622670C2214yescomplemented
60#10622670C2214yescomplemented
61#10622662C2214yescomplemented
62#10622662C2214yescomplemented
63#10622662C2214yescomplemented
64#10622661C2214yescomplemented
65#10622661C2214yescomplemented
66#10622661C2214yescomplemented
67#10622652C2214yescomplemented
68#10622651C2214yescomplemented
69#10622640C2212yes—
70#10622640C2212yes—
71#10622640C2214yes—
72#10622640C2212yes—
73#10622640C2212yes—
74#10622635C2212yescomplemented
75#10622635C2214yescomplemented
76#10622634C2211yescharacteristic, complemented
77#10622634C2212yescomplemented
78#10622633C2211yescharacteristic, complemented
79#10622633C2212yescomplemented
80#10622628C2212yes—
81#10622628C2212yes—
82#10622622C2212yescomplemented
83#10622621C2211yescharacteristic, complemented
84#10622620C2211yescharacteristic, complemented
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×#41C2311yescharacteristic
96C2×C11×#41C2311yescharacteristic
97C22×Q8×C11C2311yescharacteristic
98C2×#4339—22no—
99C2×#4339—22no—
100C22×D44—21no—
101C22×D44—21no—
102C22×D44C2312yes—
103C11×C4⋊Q8—21no—
104C11×C4⋊Q8—21no—
105C11×C4⋊Q8C2312yes—
106C11×C4⋊Q8C2312yes—
107C11×#126—22no—
108C11×#126—22no—
109C11×#126—22no—
110C11×#126—22no—
111C11×#125—22no—
112C11×#125—21no—
113C11×#125—22no—
114C11×#125—22no—
115C11×#125C2312yes—
116C11×#124—21no—
117C11×#124—22no—
118C11×#124C2312yes—
119C11×#123—22no—
120C11×#123—22no—
121C11×#123—22no—
122C11×#123—22no—
123C11×C22⋊Q8—21no—
124C11×C22⋊Q8—22no—
125C11×C22⋊Q8—21no—
126C11×C22⋊Q8—21no—
127C11×C22⋊Q8—22no—
128C11×C22⋊Q8—22no—
129C11×C22⋊Q8C2312yes—
130C11×C22⋊Q8C2312yes—
131C11×C22⋊Q8C2312yes—
132C11×#121—22no—
133C11×#121—21no—
134C11×#121C2312yes—
135C4×Q8×C11—21no—
136C4×Q8×C11—21no—
137C4×Q8×C11—22no—
138C4×Q8×C11D411yescharacteristic
139C4×Q8×C11D411yescharacteristic
140C4×Q8×C11C2312yes—
141C4×Q8×C11C2312yes—
142C4×Q8×C11C2311yescharacteristic
143C4×Q8×C11C2311yescharacteristic
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×C11C2311yescharacteristic
152C4×D4×C11C2311yescharacteristic
153C11×#117—22no—
154C11×#117—21no—
155C11×#117—22no—
156C11×#117C2311yescharacteristic
157C11×#117C2311yescharacteristic
158C11×#117C2312yes—
159C2×C11×C4⋊C4—21no—
160C2×C11×C4⋊C4C2311yescharacteristic
161C2×C42×C11—21no—
162C2×C42×C11—21no—
163C2×C42×C11C2311yescharacteristic
164C2×C42×C11C2312yes—
165#67002—44no—
166#67001—44no—
167#67000—22no—
168C2×#4325—44no—
169C2×#4325C2314yes—
170C2×#4325C2314yes—
171C2×#4325C2314yes—
172#66993—22no—
173#66990—24no—
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#66899C2314yes—
209#66899C2314yes—
210#66899C2312yes—
211#66899C2312yes—
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#60924—111nomaximal, Sylow
232C23×D11—22no—
233C11×#41—22no—
234C11×#41—22no—
235C11×#41—22no—
236C11×#41—22no—
237C2×Q8×C11—21no—
238C2×Q8×C11—22no—
239C2×Q8×C11—22no—
240C2×Q8×C11—22no—
241C2×Q8×C11C2×D411yescharacteristic
242C2×Q8×C11C2412yes—
243C2×Q8×C11C2411yescharacteristic
244C2×D4×C11—21no—
245C2×D4×C11—22no—
246C2×D4×C11C2×D412yes—
247C2×D4×C11C2×D411yescharacteristic
248C2×D4×C11C2411yescharacteristic
249C22×C4×C11—21no—
250C22×C4×C11—21no—
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11—21no—
254C22×C4×C11C2×D411yescharacteristic
255C22×C4×C11C2×D412yes—
256C22×C4×C11C2×D411yescharacteristic
257C22×C4×C11C2×D412yes—
258C22×C4×C11C2412yes—
259C22×C4×C11C2411yescharacteristic
260C2×C22⋊D11—24no—
261C2×C22⋊D11—24no—
262#4339—84no—
263#4339—84no—
264C2×D44—22no—
265C2×D44—22no—
266C2×D44—22no—
267C2×D44—22no—
268C2×D44—22no—
269C2×D44—24no—
270C2×D44—24no—
271C2×D44—82no—
272C2×D44—82no—
273C2×D44C2414yes—
274C2×C4×D11—24no—
275C2×C4×D11—24no—
276C2×Dic22—21no—
277C2×Dic22—21no—
278C11×C4⋊C4—22no—
279C11×C4⋊C4—22no—
280C11×C4⋊C4—21no—
281C11×C4⋊C4—21no—
282C11×C4⋊C4—21no—
283C11×C4⋊C4—22no—
284C11×C4⋊C4—22no—
285C11×C4⋊C4—22no—
286C11×C4⋊C4—22no—
287C11×C4⋊C4—22no—
288C11×C4⋊C4—22no—
289C11×C4⋊C4—22no—
290C11×C4⋊C4—22no—
291C11×C4⋊C4C2×D411yescharacteristic
292C11×C4⋊C4C2×D411yescharacteristic
293C11×C4⋊C4C2×D412yes—
294C11×C4⋊C4C2×D412yes—
295C11×C4⋊C4C2412yes—
296C11×C4⋊C4C2411yescharacteristic
297C11×C4⋊C4C2411yescharacteristic
298C11×C22⋊C4—22no—
299C11×C22⋊C4—22no—
300C11×C22⋊C4—21no—
301C11×C22⋊C4—22no—
302C11×C22⋊C4—21no—
303C11×C22⋊C4—21no—
304C11×C22⋊C4—22no—
305C11×C22⋊C4—22no—
306C11×C22⋊C4—22no—
307C11×C22⋊C4C2×D412yes—
308C11×C22⋊C4C2×D412yes—
309C11×C22⋊C4C2×D412yes—
310C42×C11—22no—
311C42×C11—21no—
312C42×C11—21no—
313C42×C11—21no—
314C42×C11—22no—
315C42×C11C2×D411yescharacteristic
316C42×C11C2×D411yescharacteristic
317C42×C11C2×D412yes—
318C42×C11C2×D412yes—
319C42×C11C2411yescharacteristic
320C42×C11C2411yescharacteristic
321C42×C11C2412yes—
322C22⋊Dic11—22no—
323#4325—44no—
324#4325—44no—
325#4325—44no—
326#4323—44no—
327(C2×D11)⋊C4—24no—
328(C2×D11)⋊C4—24no—
329(C2×D11)⋊C4—24no—
330(C2×D11)⋊C4—24no—
331C4⋊Dic11—21no—
332C4⋊Dic11—21no—
333C4⋊Dic11C2412yes—
334C4⋊Dic11C2412yes—
335Dic11⋊C4—22no—
336Dic11⋊C4—22no—
337C4×Dic11—22no—
338#4318—24no—
339#4318—44no—
340C2×C11⋊C8—24no—
341C2×C11⋊C8—44no—
342C2×C11⋊C8C2412yes—
343C2×C11⋊C8C2414yes—
344C2×C11⋊C8C2412yes—
345#3508—111no—
346#3461D1111yescharacteristic, complemented
347#3260—114no—
348#3257—114no—
349#3254—112no—
350#3251—112no—
351#3247—112no—
352#3246—112no—
353#3081—112no—
354#3078—111no—
355#3076—111no—
356#3062—112no—
357#3057—112no—
358#3042—112no—
359#3038—111no—
360C2×#460—111no—
361#2906—111no—
362C23×C11—21no—
363C23×C11C22×D412yes—
364C23×C11C22×D411yescharacteristic
365C22×D11—24no—
366C22×D11—44no—
367C22×D11—82no—
368C22×D11—82no—
369Q8×C11—22no—
370Q8×C11—22no—
371Q8×C11—21no—
372Q8×C11—22no—
373Q8×C11—21no—
374Q8×C11—42no—
375Q8×C11—82no—
376D4×C11—24no—
377D4×C11—22no—
378D4×C11—21no—
379D4×C11—21no—
380D4×C11—42no—
381D4×C11—82no—
382C2×C4×C11—22no—
383C2×C4×C11—24no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—21no—
387C2×C4×C11—22no—
388C2×C4×C11—21no—
389C2×C4×C11—21no—
390C2×C4×C11—22no—
391C2×C4×C11—41no—
392C2×C4×C11—42no—
393C2×C4×C11—42no—
394C2×C4×C11—42no—
395C2×C4×C11—42no—
396C2×C4×C11—81no—
397C2×C4×C11—81no—
398C2×C4×C11C22×D411yescharacteristic
399C2×C4×C11C22×D411yescharacteristic
400C2×C4×C11C22×D411yescharacteristic
401C2×C4×C11C22×D412yes—
402C2×C4×C11C22×D412yes—
403C2×C4×C11C22×D412yes—
404C2×C4×C11C22×D411yescharacteristic
405C2×C4×C11C22×D411yescharacteristic
406C2×C4×C11H(5,𝔽2)12yes—
407C2×C4×C112−1+412yes—
408C2×C4×C11C2511yescharacteristic
409C22⋊D11—84no—
410C22⋊D11—84no—
411C2×Dic11—22no—
412C2×Dic11—22no—
413D44—24no—
414D44—24no—
415D44—44no—
416D44—44no—
417D44—44no—
418D44—82no—
419D44—82no—
420C4×D11—84no—
421C4×D11—84no—
422Dic22—42no—
423Dic22—42no—
424C11⋊C8—22no—
425C11⋊C8—22no—
426C11⋊C8—24no—
427C2×AGL(1,ℤ/8)—112no—
428C22×SD16—112no—
429C2×#131—112no—
430#559—221no—
431#559—221no—
432#550—221no—
433#550—221no—
434#546—222no—
435#546—222no—
436#544C2×D1111yescharacteristic
437#542—21no—
438#542C2×D1112yescomplemented
439#541—21no—
440#541C2×D1112yescomplemented
441#540—114no—
442#539—22no—
443#537C2×D1111yescharacteristic
444#536C2×D1111yescharacteristic
445#536C2×D1111yescharacteristic
446#535—112no—
447#533—21no—
448#533—111no—
449#533C2×D1112yescomplemented
450#532—112no—
451#532—112no—
452C2×#127—111no—
453#529—22no—
454#529—21no—
455#529C2×D1112yescomplemented
456#518—112no—
457C4×#41C2×D1111yescharacteristic
458C4×#41C2×D1111yescharacteristic
459C2×C4×Q8C2×D1111yescharacteristic
460#479—112no—
461#479—114no—
462#478—114no—
463#478—114no—
464#478—112no—
465#477—111no—
466#477—112no—
467#476—114no—
468#476—111no—
469#475—111no—
470#475—112no—
471#474—114no—
472#474—111no—
473#469—114no—
474#468—114no—
475#468—114no—
476#468—114no—
477#466—114no—
478#465—114no—
479#465—114no—
480#465—114no—
481#463—114no—
482#463—114no—
483#461—114no—
484#461—114no—
485#460—112no—
486#460—112no—
487#460—112no—
488#460—114no—
489#460—112no—
490#459—112no—
491#459—112no—
492#428—112no—
493#427—112no—
494#424—112no—
495#424—114no—
496#423—111no—
497#423—112no—
498C2×C4⋊C8—111no—
499C2×C4⋊C8—112no—
500#419—112no—
501#418—112no—
502#416—112no—
503C2×#102—112no—
504C22×C11—21no—
505C22×C11—21no—
506C22×C11—22no—
507C22×C11—22no—
508C22×C11—22no—
509C22×C11—41no—
510C22×C11—41no—
511C22×C11—41no—
512C22×C11#53712yes—
513C22×C11C23×D411yescharacteristic
514C2×D11—44no—
515C2×D11—44no—
516C2×D11—44no—
517C2×D11—164no—
518C4×C11—21no—
519C4×C11—21no—
520C4×C11—22no—
521C4×C11—22no—
522C4×C11—22no—
523C4×C11—21no—
524C4×C11—42no—
525C4×C11—41no—
526C4×C11—41no—
527C4×C11—42no—
528C4×C11—41no—
529C4×C11#53712yes—
530C4×C11#57712yes—
531C4×C11C2×H(5,𝔽2)11yescharacteristic
532C4×C11C2×2−1+411yescharacteristic
533Dic11—42no—
534Dic11—42no—
535C2×#41—222no—
536C2×#41—222no—
537C2×#41C22×D1111yescharacteristic
538C2×#41C22×D1111yescharacteristic
539C22×Q8C22×D1111yescharacteristic
540C22×D4—112no—
541C22×D4—221no—
542C22×D4—221no—
543AGL(1,ℤ/8)—444no—
544C2×SD16—114no—
545C2×SD16—114no—
546C2×SD16—114no—
547C2×SD16—444no—
548C2×D8—114no—
549#131—444no—
550C2×M16—112no—
551C2×M16—114no—
552C22×C8—112no—
553C22×C8—114no—
554C4⋊Q8—21no—
555C4⋊Q8—21no—
556C4⋊Q8—111no—
557C4⋊Q8—111no—
558C4⋊Q8C22×D1112yes—
559C4⋊Q8C22×D1112yes—
560#127—112no—
561#127—112no—
562#127—222no—
563#127—221no—
564#127—221no—
565#126—22no—
566#126—22no—
567#126—22no—
568#126—22no—
569#125—22no—
570#125—21no—
571#125—22no—
572#125—22no—
573#125—112no—
574#125C22×D1112yes—
575#124—21no—
576#124—22no—
577#124—222no—
578#124—222no—
579#124—222no—
580#124C22×D1112yes—
581#123—22no—
582#123—22no—
583#123—22no—
584#123—22no—
585#123—224no—
586#123—224no—
587C22⋊Q8—21no—
588C22⋊Q8—22no—
589C22⋊Q8—21no—
590C22⋊Q8—21no—
591C22⋊Q8—22no—
592C22⋊Q8—22no—
593C22⋊Q8—221no—
594C22⋊Q8—221no—
595C22⋊Q8C22×D1112yes—
596C22⋊Q8C22×D1112yes—
597C22⋊Q8C22×D1112yes—
598#121—22no—
599#121—21no—
600#121—114no—
601#121—114no—
602#121—222no—
603#121—222no—
604#121—224no—
605#121—224no—
606#121C22×D1112yes—
607#120—224no—
608C4×Q8—21no—
609C4×Q8—21no—
610C4×Q8—22no—
611C4×Q8—221no—
612C4×Q8—221no—
613C4×Q8C22⋊D1111yescharacteristic
614C4×Q8C22⋊D1111yescharacteristic
615C4×Q8C22×D1112yes—
616C4×Q8C22×D1112yes—
617C4×Q8C22×D1111yescharacteristic
618C4×Q8C22×D1111yescharacteristic
619C4×D4—21no—
620C4×D4—21no—
621C4×D4—22no—
622C4×D4—114no—
623C4×D4—114no—
624C4×D4—222no—
625C4×D4—222no—
626C4×D4—222no—
627C4×D4—222no—
628C4×D4C22⋊D1112yes—
629C4×D4C22⋊D1111yescharacteristic
630C4×D4C22⋊D1112yes—
631C4×D4C22⋊D1111yescharacteristic
632C4×D4C22×D1111yescharacteristic
633C4×D4C22×D1111yescharacteristic
634#117—22no—
635#117—21no—
636#117—22no—
637#117—112no—
638#117C22×D1111yescharacteristic
639#117C22×D1111yescharacteristic
640#117C22×D1112yes—
641C2×C4⋊C4—21no—
642C2×C4⋊C4C22×D1111yescharacteristic
643C2×C22⋊C4—224no—
644C2×C42—21no—
645C2×C42—21no—
646C2×C42C22×D1111yescharacteristic
647C2×C42C22×D1112yes—
648#107—112no—
649#107—112no—
650#107—114no—
651#106—112no—
652#106—112no—
653#106—114no—
654C4⋊C8—111no—
655C4⋊C8—112no—
656C4⋊C8—111no—
657C4⋊C8—112no—
658C4⋊C8—114no—
659C4⋊C8—112no—
660C4⋊C8—114no—
661#103—112no—
662#103—112no—
663#103—114no—
664#103—114no—
665#102—112no—
666#102—112no—
667#102—114no—
668#102—114no—
669#102—114no—
670#102—114no—
671C2×C11—22no—
672C2×C11—42no—
673C2×C11—81no—
674C2×C11C2×#53711yescharacteristic
675C2×C11C2×#57711yescharacteristic
676C2×C11#358511yescharacteristic
677D11—84no—
678C24—222no—
679#41—22no—
680#41—22no—
681#41—22no—
682#41—22no—
683#41—884no—
684#41—884no—
685C2×Q8—21no—
686C2×Q8—22no—
687C2×Q8—22no—
688C2×Q8—22no—
689C2×Q8—221no—
690C2×Q8—221no—
691C2×Q8C2×C22⋊D1111yescharacteristic
692C2×Q8C23×D1112yes—
693C2×Q8C23×D1111yescharacteristic
694C2×D4—21no—
695C2×D4—22no—
696C2×D4—114no—
697C2×D4—224no—
698C2×D4—224no—
699C2×D4—224no—
700C2×D4—224no—
701C2×D4—222no—
702C2×D4—222no—
703C2×D4—222no—
704C2×D4—222no—
705C2×D4—222no—
706C2×D4—882no—
707C2×D4—882no—
708C2×D4C2×C22⋊D1112yes—
709C2×D4C2×C22⋊D1111yescharacteristic
710C2×D4C23×D1111yescharacteristic
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—224no—
717C22×C4—224no—
718C22×C4C2×C22⋊D1111yescharacteristic
719C22×C4C2×C22⋊D1112yes—
720C22×C4C2×C22⋊D1111yescharacteristic
721C22×C4C2×C22⋊D1112yes—
722C22×C4C23×D1112yes—
723C22×C4C23×D1111yescharacteristic
724SD16—444no—
725SD16—444no—
726SD16—444no—
727D8—444no—
728M16—224no—
729M16—444no—
730C2×C8—112no—
731C2×C8—112no—
732C2×C8—114no—
733C2×C8—224no—
734C2×C8—444no—
735C4⋊C4—22no—
736C4⋊C4—22no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—22no—
741C4⋊C4—22no—
742C4⋊C4—22no—
743C4⋊C4—22no—
744C4⋊C4—22no—
745C4⋊C4—22no—
746C4⋊C4—22no—
747C4⋊C4—22no—
748C4⋊C4—112no—
749C4⋊C4—112no—
750C4⋊C4—221no—
751C4⋊C4—221no—
752C4⋊C4—222no—
753C4⋊C4—222no—
754C4⋊C4C2×C22⋊D1111yescharacteristic
755C4⋊C4C2×C22⋊D1111yescharacteristic
756C4⋊C4C2×C22⋊D1112yes—
757C4⋊C4C2×C22⋊D1112yes—
758C4⋊C4C23×D1112yes—
759C4⋊C4C23×D1111yescharacteristic
760C4⋊C4C23×D1111yescharacteristic
761C22⋊C4—22no—
762C22⋊C4—22no—
763C22⋊C4—21no—
764C22⋊C4—22no—
765C22⋊C4—21no—
766C22⋊C4—21no—
767C22⋊C4—22no—
768C22⋊C4—22no—
769C22⋊C4—22no—
770C22⋊C4—222no—
771C22⋊C4—224no—
772C22⋊C4—224no—
773C22⋊C4—224no—
774C22⋊C4—224no—
775C22⋊C4C2×C22⋊D1112yes—
776C22⋊C4C2×C22⋊D1112yes—
777C22⋊C4C2×C22⋊D1112yes—
778C42—22no—
779C42—21no—
780C42—21no—
781C42—21no—
782C42—22no—
783C42—222no—
784C42C2×C22⋊D1111yescharacteristic
785C42C2×C22⋊D1112yes—
786C42C2×C22⋊D1111yescharacteristic
787C42C2×C22⋊D1112yes—
788C42C23×D1111yescharacteristic
789C42C23×D1112yes—
790C42C23×D1111yescharacteristic
791C11#6092411yescharacteristic, complemented, Sylow
792C23—21no—
793C23—224no—
794C23—444no—
795C23—882no—
796C23—882no—
797C23C22×C22⋊D1112yes—
798C23C22×C22⋊D1111yescharacteristic
799Q8—22no—
800Q8—22no—
801Q8—21no—
802Q8—22no—
803Q8—21no—
804Q8—42no—
805Q8—82no—
806Q8—442no—
807Q8—442no—
808D4—24no—
809D4—22no—
810D4—21no—
811D4—21no—
812D4—42no—
813D4—82no—
814D4—224no—
815D4—224no—
816D4—444no—
817D4—444no—
818D4—444no—
819D4—882no—
820D4—882no—
821D4—884no—
822D4—884no—
823C2×C4—22no—
824C2×C4—24no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—21no—
828C2×C4—22no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—22no—
832C2×C4—41no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—81no—
838C2×C4—81no—
839C2×C4—222no—
840C2×C4—222no—
841C2×C4—884no—
842C2×C4—884no—
843C2×C4#6704212yes—
844C2×C4#6704312yes—
845C2×C4C22×C22⋊D1111yescharacteristic
846C2×C4C22×C22⋊D1111yescharacteristic
847C2×C4C22×C22⋊D1111yescharacteristic
848C2×C4C22×C22⋊D1112yes—
849C2×C4C22×C22⋊D1112yes—
850C2×C4C22×C22⋊D1112yes—
851C2×C4C22×C22⋊D1111yescharacteristic
852C2×C4C22×C22⋊D1111yescharacteristic
853C2×C4C24×D1111yescharacteristic
854C8—222no—
855C8—222no—
856C8—224no—
857C22—21no—
858C22—21no—
859C22—22no—
860C22—22no—
861C22—22no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—444no—
866C22—444no—
867C22—444no—
868C22—1764no—
869C22#1062336412yes—
870C22C23×C22⋊D1111yescharacteristic
871C4—21no—
872C4—21no—
873C4—22no—
874C4—22no—
875C4—22no—
876C4—21no—
877C4—42no—
878C4—41no—
879C4—41no—
880C4—42no—
881C4—41no—
882C4—442no—
883C4—442no—
884C4#1062336412yes—
885C4#1062336812yes—
886C4C2×#6704211yescharacteristic
887C4C2×#6704311yescharacteristic
888C2—22no—
889C2—42no—
890C2—81no—
891C2—884no—
892C2C2×#1062336411yescharacteristic
893C2C2×#1062336811yescharacteristic
894C2#1308339511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3461C2
socleC22×C11C23×D4
hypercenter#3461D11
hypocenterC11#60924
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3461

Complements

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

NH ≅ G/Ntype
1. #13082492C2semidirect
2. #13080057C2semidirect
3. #13080027C2semidirect
4. #13079999C2semidirect
5. #13079978C2semidirect
6. #13079942C2semidirect
7. #13079928C2semidirect
8. #13078441C2semidirect
9. #13078421C2semidirect
10. #13078404C2semidirect
11. #13078298C2semidirect
12. #13078257C2semidirect
13. #13078124C2semidirect
14. #13078096C2semidirect
15. C2×#10622640C2semidirect
16. #13077184C2semidirect
17. C11×#3461C2semidirect
20. C11×#542C22semidirect
22. C11×#541C22semidirect
28. C11×#533C22semidirect
31. C11×#529C22semidirect
53. #10622700C22semidirect
54. #10622697C22semidirect
55. #10622696C22semidirect
56. #10622696C22semidirect
57. #10622679C22semidirect
58. #10622679C22semidirect
59. #10622670C22semidirect
60. #10622670C22semidirect
61. #10622662C22semidirect
62. #10622662C22semidirect
63. #10622662C22semidirect
64. #10622661C22semidirect
65. #10622661C22semidirect
66. #10622661C22semidirect
67. #10622652C22semidirect
68. #10622651C22semidirect
74. #10622635C22semidirect
75. #10622635C22semidirect
76. #10622634C22semidirect
77. #10622634C22semidirect
78. #10622633C22semidirect
79. #10622633C22semidirect
82. #10622622C22semidirect
83. #10622621C22semidirect
84. #10622620C22semidirect
87. #10622612C22semidirect
92. #10622537C22semidirect
94. C2×C4⋊(C11⋊C8)C22semidirect
346. #3461D11semidirect
438. #542C2×D11semidirect
440. #541C2×D11semidirect
449. #533C2×D11semidirect
455. #529C2×D11semidirect
791. C11#60924semidirect

Maximal subgroups

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

subgroupindex
#130824922
#130800572
#130800272
#130799992
#130799782
#130799422
#130799282
#130784412
#130784212
#130784042
#130782982
#130782572
#130781242
#130780962
C2×#106226402
#130771842
C11×#34612
#6092411