Finite Group Databasebeta

← #15638484

Subgroups — #15638484

Order 2816.

2282 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082457C211yesmaximal, characteristic, complemented
2C2×#10623337C211yesmaximal, characteristic, complemented
3#13080462C214yesmaximal, complemented
4#13080455C214yesmaximal, complemented
5#13080323C214yesmaximal, complemented
6#13080294C214yesmaximal, complemented
7#13079584C212yesmaximal, complemented
8#13079388C211yesmaximal, characteristic, complemented
9#13079384C212yesmaximal, complemented
10#13079374C211yesmaximal, characteristic, complemented
11#13078664C212yesmaximal, complemented
12#13077835C212yesmaximal, complemented
13C2×#10622830C211yesmaximal, characteristic, complemented
14#13077638C211yesmaximal, characteristic, complemented
15C2×C11×#450C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C22×#4341C2211yescharacteristic, complemented
18C22×C11×SD16C2212yescomplemented
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×#67006—21no—
21C22×C22⋊Dic11—21no—
22#10623348C2212yescomplemented
23#10623337—22no—
24#10623337—22no—
25#10623337C2214yes—
26#10623337C2214yescomplemented
27C2×#66992—21no—
28C2×#66991C2211yescharacteristic, complemented
29C2×#66989C2211yescharacteristic, complemented
30C2×#66988—21no—
31C2×D4×Dic11C2211yescharacteristic, complemented
32C22×#4323C2212yescomplemented
33C2×#66983C2211yescharacteristic
34C2×C4×C22⋊D11C2211yescharacteristic
35C2×#66977C2211yescharacteristic
36C2×#66969C2214yescomplemented
37#10623176—21no—
38#10623175—21no—
39#10623173C2212yescomplemented
40#10623168—22no—
41#10623161C2212yescomplemented
42#10623158C2212yescomplemented
43#10623155C2212yescomplemented
44#10623045—22no—
45#10623045C2212yescomplemented
46#10623024—21no—
47#10623017—21no—
48C11×#450C2212yescomplemented
49C11×#450C2212yescomplemented
50C11×#450C2214yescomplemented
51C2×C11×#102C2212yescomplemented
52C2×C11×C22⋊C8C2211yescharacteristic
53#10622841C2212yescomplemented
54#10622830C2212yes—
55#10622830C2212yes—
56#10622830C2214yescomplemented
57C2×#66896C2212yescomplemented
58C2×C22⋊(C11⋊C8)C2211yescharacteristic
59#10622786C2214yescomplemented
60#10622785C2214yescomplemented
61#10622784C2214yescomplemented
62#10622781C2214yescomplemented
63#10622779C2214yescomplemented
64#10622778C2214yescomplemented
65SD16×Dic11C2214yescomplemented
66#10622727C2214yescomplemented
67C8×C22⋊D11C2214yescomplemented
68#10622664C2214yescomplemented
69#10622663C2212yescomplemented
70#10622657C2212yescomplemented
71#10622583C2212yescomplemented
72#10622400C2214yescomplemented
73#10622394C2214yescomplemented
74#10622392C2214yescomplemented
75#10622388C2214yescomplemented
76#10622385C2214yescomplemented
77#10622381C2214yescomplemented
78#10622376C2214yescomplemented
79#10622369C2214yescomplemented
80#10622351C2212yescomplemented
81#10622348C2212yescomplemented
82#10622344C2212yescomplemented
83(C22⋊D11)⋊C8C2214yescomplemented
84D11×C22⋊C8C2212yescomplemented
85#10622334C2212yescomplemented
86#10622331C2212yescomplemented
87C25×C11—21no—
88C22×Q8×C11C2311yescharacteristic
89C22×D4×C11—21no—
90C22×D4×C11—21no—
91C22×D4×C11—21no—
92C22×D4×C11—44no—
93C22×D4×C11C2311yescharacteristic
94C22×D4×C11C2312yes—
95C22×D4×C11C2312yes—
96C22×D4×C11C2311yescharacteristic
97C23×C4×C11C2311yescharacteristic
98C22×C22⋊D11—21no—
99C22×C22⋊D11—21no—
100C22×C22⋊D11—21no—
101C22×C22⋊D11D411yescharacteristic
102C23×Dic11—21no—
103C23×Dic11—21no—
104C2×#4343C2312yescomplemented
105C2×#4341—22no—
106C2×#4341—44no—
107C2×#4341C2314yes—
108C22×D44C2311yescharacteristic
109C22×C4×D11C2311yescharacteristic
110C22×Dic22C2311yescharacteristic
111C2×C11×SD16—44no—
112C2×C11×SD16C2314yes—
113C2×C11×SD16C2314yes—
114C22×C8×C11C2312yes—
115C11×C22⋊Q8—21no—
116C11×C22⋊Q8—21no—
117C11×C22⋊Q8C2312yes—
118C11×C22⋊Q8C2312yes—
119C2×C11×C4⋊C4—21no—
120C2×C11×C4⋊C4C2311yescharacteristic
121C2×C11×C22⋊C4—21no—
122#67006—24no—
123#67006—24no—
124C2×C22⋊Dic11—21no—
125C2×C22⋊Dic11—21no—
126C2×C22⋊Dic11—21no—
127C2×C22⋊Dic11—21no—
128C2×C22⋊Dic11—21no—
129C2×C22⋊Dic11—24no—
130C2×C22⋊Dic11—24no—
131C2×C22⋊Dic11D411yescharacteristic
132#67000—22no—
133#67000C2312yescomplemented
134#66999—22no—
135#66999C2312yescomplemented
136Q8×Dic11C2312yescomplemented
137C2×#4326C2314yescomplemented
138#66992—24no—
139#66992—24no—
140#66991—22no—
141#66991C2314yes—
142#66989—22no—
143#66989C2314yes—
144#66988—24no—
145#66988—24no—
146D4×Dic11—22no—
147D4×Dic11C2314yes—
148C2×#4323—44no—
149C2×#4323C2314yes—
150C2×#4323C2314yes—
151#66983—21no—
152#66983—21no—
153#66983—22no—
154#66983—22no—
155#66983C2312yes—
156#66983C2312yes—
157C4×C22⋊D11—22no—
158C4×C22⋊D11—22no—
159C4×C22⋊D11D412yes—
160C4×C22⋊D11D412yes—
161C4×C22⋊D11C2312yes—
162C4×C22⋊D11C2312yes—
163C2×(C2×D11)⋊C4—21no—
164C2×(C2×D11)⋊C4D411yescharacteristic
165C2×C4⋊Dic11C2311yescharacteristic
166C2×C4⋊Dic11C2311yescharacteristic
167#66977—21no—
168#66977—21no—
169#66977C2312yes—
170#66977C2312yes—
171C2×Dic11⋊C4—21no—
172C2×Dic11⋊C4D411yescharacteristic
173C2×C4×Dic11C2311yescharacteristic
174C22×C11⋊C8C2312yes—
175#66969—48no—
176C2×#4314C2314yescomplemented
177C2×C8×D11C2314yescomplemented
178#66951—22no—
179#66951—22no—
180#66951—22no—
181#66948—22no—
182#66948C2312yescomplemented
183#66947—22no—
184#66947—22no—
185#66947—22no—
186#66946—22no—
187#66946C2312yescomplemented
188#66945—22no—
189#66945C2312yescomplemented
190#66943—22no—
191#66943C2312yescomplemented
192#66939—22no—
193#66939—22no—
194#66935—22no—
195#66935—22no—
196(C22⋊D11)⋊C4—22no—
197(C22⋊D11)⋊C4—22no—
198C22⋊C4×D11—22no—
199#66930—22no—
200C11×#102C2314yes—
201C11×#102C2314yes—
202C11×C22⋊C8C2312yes—
203C11×C22⋊C8C2312yes—
204#66899C2314yescomplemented
205#66896C2314yes—
206#66896C2314yes—
207C22⋊(C11⋊C8)C2312yes—
208C22⋊(C11⋊C8)C2312yes—
209#66885C2314yescomplemented
210(C2×D11)⋊C8C2314yescomplemented
211#66881C2314yescomplemented
212#66880C2314yescomplemented
213Dic11⋊C8C2314yescomplemented
214C8×Dic11C2314yescomplemented
215#66874C2314yescomplemented
216#66871C2314yescomplemented
217#61561—111nomaximal, Sylow
218C24×C11—21no—
219C24×C11—21no—
220C24×C11—22no—
221C24×C11—22no—
222C24×C11—44no—
223C24×C11—44no—
224C24×C11—82no—
225C24×C11C2×D411yescharacteristic
226C23×D11—21no—
227C23×D11C2×D411yescharacteristic
228C2×Q8×C11—21no—
229C2×Q8×C11—42no—
230C2×Q8×C11C2412yes—
231C2×D4×C11—24no—
232C2×D4×C11—24no—
233C2×D4×C11—24no—
234C2×D4×C11—21no—
235C2×D4×C11—22no—
236C2×D4×C11—22no—
237C2×D4×C11—21no—
238C2×D4×C11—42no—
239C2×D4×C11—42no—
240C2×D4×C11—42no—
241C2×D4×C11—44no—
242C2×D4×C11—44no—
243C2×D4×C11—44no—
244C2×D4×C11C2412yes—
245C2×D4×C11C2412yes—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—42no—
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2×D411yescharacteristic
252C22×C4×C11C2411yescharacteristic
253C22×C4×C11C2411yescharacteristic
254C22×C4×C11C2411yescharacteristic
255C2×C22⋊D11—24no—
256C2×C22⋊D11—22no—
257C2×C22⋊D11—22no—
258C2×C22⋊D11—24no—
259C2×C22⋊D11—24no—
260C2×C22⋊D11—44no—
261C2×C22⋊D11—44no—
262C2×C22⋊D11—82no—
263C2×C22⋊D11C2×D412yes—
264C2×C22⋊D11C2×D412yes—
265C22×Dic11—24no—
266C22×Dic11—24no—
267C22×Dic11—21no—
268C22×Dic11—21no—
269C22×Dic11—21no—
270C22×Dic11—44no—
271C22×Dic11—82no—
272C22×Dic11C2×D411yescharacteristic
273C22×Dic11C2×D411yescharacteristic
274C22×Dic11C2×D411yescharacteristic
275#4343—44no—
276#4341—28no—
277#4341—44no—
278#4341—48no—
279C2×D44—22no—
280C2×D44—22no—
281C2×D44—21no—
282C2×D44—42no—
283C2×D44C2412yes—
284C2×C4×D11—22no—
285C2×C4×D11—22no—
286C2×C4×D11—42no—
287C2×C4×D11C2×D412yes—
288C2×C4×D11C2412yes—
289C2×Dic22—21no—
290C2×Dic22—42no—
291C2×Dic22C2412yes—
292C11×SD16—28no—
293C11×SD16—44no—
294C2×C8×C11—42no—
295C2×C8×C11C2414yes—
296C11×C4⋊C4—22no—
297C11×C4⋊C4—22no—
298C11×C4⋊C4—21no—
299C11×C4⋊C4C2412yes—
300C11×C22⋊C4—22no—
301C11×C22⋊C4—22no—
302C22⋊Dic11—24no—
303C22⋊Dic11—24no—
304C22⋊Dic11—24no—
305C22⋊Dic11—24no—
306C22⋊Dic11—22no—
307C22⋊Dic11—22no—
308C22⋊Dic11C2×D412yes—
309C22⋊Dic11C2×D412yes—
310#4326—44no—
311#4323—28no—
312#4323—44no—
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—
319(C2×D11)⋊C4—22no—
320(C2×D11)⋊C4—22no—
321(C2×D11)⋊C4C2×D412yes—
322(C2×D11)⋊C4C2×D412yes—
323C4⋊Dic11—22no—
324C4⋊Dic11—22no—
325C4⋊Dic11—21no—
326C4⋊Dic11—21no—
327C4⋊Dic11C2412yes—
328C4⋊Dic11C2412yes—
329Dic11⋊C4—22no—
330Dic11⋊C4—22no—
331Dic11⋊C4—22no—
332Dic11⋊C4—22no—
333Dic11⋊C4C2×D412yes—
334Dic11⋊C4C2×D412yes—
335C4×Dic11—22no—
336C4×Dic11—22no—
337C4×Dic11C2×D412yes—
338C4×Dic11C2412yes—
339C2×C11⋊C8—42no—
340C2×C11⋊C8C2414yes—
341#4314—44no—
342C8×D11—44no—
343#3505—111no—
344C2×#546—111no—
345#3297—114no—
346#3296—114no—
347#3282—114no—
348#3280—114no—
349#3211—112no—
350#3189—111no—
351#3188—112no—
352#3187—111no—
353#3105—112no—
354#3002—112no—
355C2×#450D1111yescharacteristic, complemented
356C2×#447—111no—
357#2972—111no—
358C23×C11—24no—
359C23×C11—22no—
360C23×C11—22no—
361C23×C11—41no—
362C23×C11—41no—
363C23×C11—44no—
364C23×C11—44no—
365C23×C11—42no—
366C23×C11—42no—
367C23×C11—42no—
368C23×C11—42no—
369C23×C11—44no—
370C23×C11—44no—
371C23×C11—42no—
372C23×C11—82no—
373C23×C11—82no—
374C23×C11—816no—
375C23×C11#13514yescomplemented
376C23×C11C22×D411yescharacteristic
377C23×C11C22×D411yescharacteristic
378C23×C11C22×D411yescharacteristic
379C22×D11—22no—
380C22×D11—22no—
381C22×D11—41no—
382C22×D11—41no—
383C22×D11—42no—
384C22×D11—81no—
385C22×D11—81no—
386C22×D11C22×D412yes—
387Q8×C11—24no—
388Q8×C11—81no—
389D4×C11—24no—
390D4×C11—22no—
391D4×C11—22no—
392D4×C11—22no—
393D4×C11—44no—
394D4×C11—44no—
395D4×C11—42no—
396D4×C11H(5,𝔽2)14yes—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—22no—
402C2×C4×C11—41no—
403C2×C4×C11—41no—
404C2×C4×C11—41no—
405C2×C4×C11—81no—
406C2×C4×C11—81no—
407C2×C4×C11C22×D411yescharacteristic
408C2×C4×C11C22×D411yescharacteristic
409C2×C4×C11C22×D411yescharacteristic
410C2×C4×C11C2511yescharacteristic
411C22⋊D11—24no—
412C22⋊D11—24no—
413C22⋊D11—48no—
414C22⋊D11—44no—
415C22⋊D11—44no—
416C22⋊D11—84no—
417C2×Dic11—22no—
418C2×Dic11—22no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—41no—
422C2×Dic11—41no—
423C2×Dic11—48no—
424C2×Dic11—42no—
425C2×Dic11—42no—
426C2×Dic11—42no—
427C2×Dic11—84no—
428C2×Dic11C22×D412yes—
429C2×Dic11C22×D412yes—
430C2×Dic11C22×D412yes—
431D44—24no—
432D44—81no—
433D44—82no—
434D44—82no—
435C4×D11—24no—
436C4×D11—42no—
437C4×D11—82no—
438C4×D11—82no—
439Dic22—24no—
440Dic22—42no—
441C8×C11—24no—
442C11⋊C8—24no—
443C22×#41—111no—
444C23×D4C2×D1111yescharacteristic
445C2×#135—114no—
446C22×SD16C2×D1112yescomplemented
447C22×D8—112no—
448#553—112no—
449#553—222no—
450#552—112no—
451#551—222no—
452#548—112no—
453#546—114no—
454#546—114no—
455#546—112no—
456#546—222no—
457#546—222no—
458#539—221no—
459#538—221no—
460#534—221no—
461#529—112no—
462C2×#124—111no—
463#525—112no—
464C2×#123—221no—
465C2×C22⋊Q8—111no—
466C2×C22⋊Q8C2×D1111yescharacteristic
467C2×#121—111no—
468C2×#121—111no—
469C2×#121—221no—
470C2×#120—221no—
471#518—221no—
472C2×C4×D4—111no—
473C2×C4×D4—111no—
474C22×C22⋊C4—221no—
475#495—114no—
476#488—114no—
477#484—112no—
478#484—112no—
479#483—112no—
480#482—114no—
481#481—112no—
482#478—114no—
483#467—114no—
484#466—114no—
485#465—114no—
486#465—114no—
487#464—114no—
488#463—114no—
489#463—114no—
490#452—114no—
491#451—112no—
492#451—112no—
493#450—112no—
494#450C2×D1112yescomplemented
495#450C2×D1112yescomplemented
496#450C2×D1114yescomplemented
497#449—114no—
498#449—114no—
499#448—112no—
500#447—112no—
501#447—112no—
502#447—114no—
503C4×SD16—114no—
504C4×D8—114no—
505C8×D4—114no—
506C8×D4—114no—
507#431—112no—
508#416—114no—
509C2×#102—112no—
510C2×#102C2×D1112yescomplemented
511C2×C22⋊C8—111no—
512C2×C22⋊C8—112no—
513C2×C22⋊C8C2×D1111yescharacteristic
514C22×C11—21no—
515C22×C11—21no—
516C22×C11—21no—
517C22×C11—21no—
518C22×C11—21no—
519C22×C11—21no—
520C22×C11—24no—
521C22×C11—44no—
522C22×C11—48no—
523C22×C11—42no—
524C22×C11—42no—
525C22×C11—42no—
526C22×C11—42no—
527C22×C11—42no—
528C22×C11—88no—
529C22×C11—88no—
530C22×C11—84no—
531C22×C11C2×#13512yes—
532C22×C11C2×#13512yes—
533C22×C11C2×#13512yes—
534C22×C11C23×D411yescharacteristic
535C2×D11—22no—
536C2×D11—22no—
537C2×D11—22no—
538C2×D11—42no—
539C2×D11—42no—
540C2×D11—42no—
541C2×D11—82no—
542C2×D11—162no—
543C4×C11—21no—
544C4×C11—21no—
545C4×C11—21no—
546C4×C11—42no—
547C4×C11—42no—
548C4×C11C2×H(5,𝔽2)12yes—
549Dic11—22no—
550Dic11—22no—
551Dic11—22no—
552Dic11—42no—
553Dic11—42no—
554Dic11—42no—
555C25—21no—
556C2×#41—112no—
557C2×#41—114no—
558C2×#41—222no—
559C2×#41—444no—
560C22×Q8—111no—
561C22×Q8C22×D1111yescharacteristic
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—44no—
566C22×D4—111no—
567C22×D4—111no—
568C22×D4—221no—
569C22×D4—221no—
570C22×D4—221no—
571C22×D4C22×D1111yescharacteristic
572C22×D4C22×D1112yes—
573C22×D4C22×D1112yes—
574C22×D4C22×D1111yescharacteristic
575C23×C4—111no—
576C23×C4—221no—
577C23×C4—221no—
578C23×C4C22×D1111yescharacteristic
579#135—448no—
580C2×Q16—114no—
581C2×SD16—44no—
582C2×SD16—114no—
583C2×SD16C22×D1114yes—
584C2×SD16C22×D1114yes—
585C2×D8—114no—
586C2×D8—114no—
587C2×D8—444no—
588C22×C8—112no—
589C22×C8—114no—
590C22×C8C22×D1112yes—
591#126—222no—
592#126—222no—
593#126—222no—
594#125—112no—
595#125—222no—
596#124—112no—
597#124—114no—
598#124—222no—
599#124—222no—
600#123—222no—
601#123—222no—
602#123—222no—
603#123—222no—
604#123—222no—
605#123—224no—
606#123—224no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—112no—
610C22⋊Q8—112no—
611C22⋊Q8—112no—
612C22⋊Q8—222no—
613C22⋊Q8—221no—
614C22⋊Q8—221no—
615C22⋊Q8C22×D1112yes—
616C22⋊Q8C22×D1112yes—
617#121—114no—
618#121—112no—
619#121—112no—
620#121—112no—
621#121—222no—
622#121—224no—
623#121—224no—
624#121—222no—
625#121—222no—
626#121—222no—
627#121—221no—
628#121—221no—
629#120—222no—
630#120—222no—
631#120—224no—
632#120—224no—
633C4×Q8—112no—
634C4×D4—112no—
635C4×D4—112no—
636C4×D4—112no—
637C4×D4—112no—
638C4×D4—114no—
639C4×D4—112no—
640C4×D4—222no—
641C4×D4—222no—
642C4×D4—222no—
643C4×D4—222no—
644C4×D4—222no—
645C4×D4—222no—
646#117—112no—
647#117—222no—
648#117—222no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—111no—
651C2×C4⋊C4—111no—
652C2×C4⋊C4—111no—
653C2×C4⋊C4—221no—
654C2×C4⋊C4C22×D1111yescharacteristic
655C2×C22⋊C4—21no—
656C2×C22⋊C4—111no—
657C2×C22⋊C4—111no—
658C2×C22⋊C4—222no—
659C2×C22⋊C4—224no—
660C2×C22⋊C4—224no—
661C2×C22⋊C4—221no—
662C2×C22⋊C4—221no—
663C2×C22⋊C4—221no—
664C2×C22⋊C4—221no—
665C2×C22⋊C4—221no—
666C2×C22⋊C4—221no—
667C2×C42—111no—
668#107—114no—
669#106—114no—
670C4⋊C8—114no—
671#103—114no—
672#103—114no—
673#103—114no—
674#102—114no—
675#102—114no—
676#102—114no—
677#102C22×D1114yes—
678#102C22×D1114yes—
679C22⋊C8—112no—
680C22⋊C8—112no—
681C22⋊C8—114no—
682C22⋊C8C22×D1112yes—
683C22⋊C8C22×D1112yes—
684C4×C8—114no—
685C2×C11—22no—
686C2×C11—22no—
687C2×C11—22no—
688C2×C11—44no—
689C2×C11—82no—
690C2×C11#348411yescharacteristic
691C2×C11C22×#13511yescharacteristic
692C2×C11#358511yescharacteristic
693D11—42no—
694D11—82no—
695C24—21no—
696C24—21no—
697C24—22no—
698C24—22no—
699C24—44no—
700C24—44no—
701C24—82no—
702C24—111no—
703C24—221no—
704C24D4×D1111yescharacteristic
705#41—228no—
706#41—444no—
707#41—444no—
708#41—448no—
709C2×Q8—21no—
710C2×Q8—42no—
711C2×Q8—112no—
712C2×Q8—221no—
713C2×Q8—442no—
714C2×Q8C23×D1112yes—
715C2×D4—24no—
716C2×D4—24no—
717C2×D4—24no—
718C2×D4—21no—
719C2×D4—22no—
720C2×D4—22no—
721C2×D4—21no—
722C2×D4—42no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—44no—
726C2×D4—44no—
727C2×D4—44no—
728C2×D4—112no—
729C2×D4—112no—
730C2×D4—112no—
731C2×D4—222no—
732C2×D4—222no—
733C2×D4—224no—
734C2×D4—224no—
735C2×D4—222no—
736C2×D4—222no—
737C2×D4—224no—
738C2×D4—221no—
739C2×D4—442no—
740C2×D4—444no—
741C2×D4—444no—
742C2×D4—882no—
743C2×D4C23×D1112yes—
744C2×D4C23×D1112yes—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—42no—
748C22×C4—111no—
749C22×C4—111no—
750C22×C4—111no—
751C22×C4—112no—
752C22×C4—112no—
753C22×C4—222no—
754C22×C4—222no—
755C22×C4—224no—
756C22×C4—224no—
757C22×C4—221no—
758C22×C4—221no—
759C22×C4—221no—
760C22×C4—442no—
761C22×C4—444no—
762C22×C4—882no—
763C22×C4D4×D1111yescharacteristic
764C22×C4D4×D1111yescharacteristic
765C22×C4D4×D1111yescharacteristic
766C22×C4C23×D1111yescharacteristic
767C22×C4C23×D1111yescharacteristic
768C22×C4C23×D1111yescharacteristic
769Q16—444no—
770SD16—28no—
771SD16—44no—
772SD16—444no—
773D8—228no—
774D8—444no—
775C2×C8—42no—
776C2×C8—114no—
777C2×C8—444no—
778C2×C8—442no—
779C2×C8C23×D1114yes—
780C4⋊C4—22no—
781C4⋊C4—22no—
782C4⋊C4—21no—
783C4⋊C4—112no—
784C4⋊C4—112no—
785C4⋊C4—112no—
786C4⋊C4—112no—
787C4⋊C4—222no—
788C4⋊C4—222no—
789C4⋊C4—222no—
790C4⋊C4—222no—
791C4⋊C4—221no—
792C4⋊C4—221no—
793C4⋊C4—222no—
794C4⋊C4—222no—
795C4⋊C4C23×D1112yes—
796C22⋊C4—22no—
797C22⋊C4—22no—
798C22⋊C4—112no—
799C22⋊C4—112no—
800C22⋊C4—112no—
801C22⋊C4—112no—
802C22⋊C4—222no—
803C22⋊C4—222no—
804C22⋊C4—222no—
805C22⋊C4—222no—
806C22⋊C4—222no—
807C22⋊C4—222no—
808C22⋊C4—224no—
809C22⋊C4—224no—
810C22⋊C4—224no—
811C22⋊C4—224no—
812C22⋊C4—222no—
813C22⋊C4—222no—
814C22⋊C4—222no—
815C22⋊C4—222no—
816C42—112no—
817C42—112no—
818C42—222no—
819C42—222no—
820C11#6156111yescharacteristic, complemented, Sylow
821C23—24no—
822C23—22no—
823C23—22no—
824C23—41no—
825C23—41no—
826C23—44no—
827C23—44no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—44no—
833C23—44no—
834C23—42no—
835C23—82no—
836C23—82no—
837C23—816no—
838C23—112no—
839C23—222no—
840C23—222no—
841C23—441no—
842C23—441no—
843C23—442no—
844C23—881no—
845C23—881no—
846C23#6696914yescomplemented
847C23C2×D4×D1111yescharacteristic
848C23C2×D4×D1111yescharacteristic
849C23C2×D4×D1111yescharacteristic
850Q8—24no—
851Q8—81no—
852Q8—224no—
853Q8—442no—
854D4—24no—
855D4—22no—
856D4—22no—
857D4—22no—
858D4—44no—
859D4—44no—
860D4—42no—
861D4—224no—
862D4—224no—
863D4—224no—
864D4—448no—
865D4—444no—
866D4—444no—
867D4—881no—
868D4—882no—
869D4—882no—
870D4—884no—
871D4#6703714yes—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—112no—
883C2×C4—112no—
884C2×C4—112no—
885C2×C4—222no—
886C2×C4—224no—
887C2×C4—222no—
888C2×C4—222no—
889C2×C4—222no—
890C2×C4—442no—
891C2×C4—441no—
892C2×C4—441no—
893C2×C4—448no—
894C2×C4—442no—
895C2×C4—442no—
896C2×C4—442no—
897C2×C4—882no—
898C2×C4—882no—
899C2×C4—884no—
900C2×C4C2×D4×D1111yescharacteristic
901C2×C4C2×D4×D1111yescharacteristic
902C2×C4C2×D4×D1111yescharacteristic
903C2×C4C24×D1111yescharacteristic
904C8—24no—
905C8—224no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—21no—
910C22—21no—
911C22—21no—
912C22—24no—
913C22—44no—
914C22—48no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—88no—
921C22—88no—
922C22—84no—
923C22—222no—
924C22—222no—
925C22—222no—
926C22—442no—
927C22—442no—
928C22—442no—
929C22—882no—
930C22—1762no—
931C22C2×#6696912yes—
932C22C2×#6696912yes—
933C22C2×#6696912yes—
934C22C22×D4×D1111yescharacteristic
935C4—21no—
936C4—21no—
937C4—21no—
938C4—42no—
939C4—42no—
940C4—222no—
941C4—222no—
942C4—222no—
943C4—442no—
944C4—442no—
945C4—442no—
946C4C2×#6703712yes—
947C2—22no—
948C2—22no—
949C2—22no—
950C2—44no—
951C2—82no—
952C2—442no—
953C2—882no—
954C2#1308224511yescharacteristic
955C2C22×#6696911yescharacteristic
956C2#1308339211yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#450C2
socleC22×C11C23×D4
hypercenterC2×#450D11
hypocenterC11#61561
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
1. #13082457C2semidirect
2. C2×#10623337C2semidirect
3. #13080462C2semidirect
4. #13080455C2semidirect
5. #13080323C2semidirect
6. #13080294C2semidirect
7. #13079584C2semidirect
8. #13079388C2semidirect
9. #13079384C2semidirect
10. #13079374C2semidirect
11. #13078664C2semidirect
12. #13077835C2semidirect
13. C2×#10622830C2semidirect
14. #13077638C2semidirect
15. C2×C11×#450C2semidirect
17. C22×#4341C22semidirect
18. C22×C11×SD16C22semidirect
22. #10623348C22semidirect
26. #10623337C22semidirect
28. C2×#66991C22semidirect
29. C2×#66989C22semidirect
31. C2×D4×Dic11C22semidirect
32. C22×#4323C22semidirect
36. C2×#66969C22semidirect
39. #10623173C22semidirect
41. #10623161C22semidirect
42. #10623158C22semidirect
43. #10623155C22semidirect
45. #10623045C22semidirect
48. C11×#450C22semidirect
49. C11×#450C22semidirect
50. C11×#450C22semidirect
51. C2×C11×#102C22semidirect
53. #10622841C22semidirect
56. #10622830C22semidirect
57. C2×#66896C22semidirect
59. #10622786C22semidirect
60. #10622785C22semidirect
61. #10622784C22semidirect
62. #10622781C22semidirect
63. #10622779C22semidirect
64. #10622778C22semidirect
65. SD16×Dic11C22semidirect
66. #10622727C22semidirect
67. C8×C22⋊D11C22semidirect
68. #10622664C22semidirect
69. #10622663C22semidirect
70. #10622657C22semidirect
71. #10622583C22semidirect
72. #10622400C22semidirect
73. #10622394C22semidirect
74. #10622392C22semidirect
75. #10622388C22semidirect
76. #10622385C22semidirect
77. #10622381C22semidirect
78. #10622376C22semidirect
79. #10622369C22semidirect
80. #10622351C22semidirect
81. #10622348C22semidirect
82. #10622344C22semidirect
83. (C22⋊D11)⋊C8C22semidirect
84. D11×C22⋊C8C22semidirect
85. #10622334C22semidirect
86. #10622331C22semidirect
104. C2×#4343C23semidirect
133. #67000C23semidirect
135. #66999C23semidirect
136. Q8×Dic11C23semidirect
137. C2×#4326C23semidirect
176. C2×#4314C23semidirect
177. C2×C8×D11C23semidirect
182. #66948C23semidirect
187. #66946C23semidirect
189. #66945C23semidirect
191. #66943C23semidirect
204. #66899C23semidirect
209. #66885C23semidirect
210. (C2×D11)⋊C8C23semidirect
211. #66881C23semidirect
212. #66880C23semidirect
213. Dic11⋊C8C23semidirect
214. C8×Dic11C23semidirect
215. #66874C23semidirect
216. #66871C23semidirect
355. C2×#450D11semidirect
375. C23×C11#135semidirect
446. C22×SD16C2×D11semidirect
494. #450C2×D11semidirect
495. #450C2×D11semidirect
496. #450C2×D11semidirect
510. C2×#102C2×D11semidirect
820. C11#61561semidirect
846. C23#66969semidirect

Maximal subgroups

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

subgroupindex
#130824572
C2×#106233372
#130804622
#130804552
#130803232
#130802942
#130795842
#130793882
#130793842
#130793742
#130786642
#130778352
C2×#106228302
#130776382
C2×C11×#4502
#6156111