Finite Group Databasebeta

← #15638483

Subgroups — #15638483

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#13082455C211yesmaximal, characteristic, complemented
2C2×#10623081C211yesmaximal, characteristic, complemented
3#13080468C214yesmaximal, complemented
4#13080453C214yesmaximal, complemented
5#13080328C214yesmaximal, complemented
6#13080303C214yesmaximal, complemented
7#13079583C212yesmaximal, complemented
8#13079391C211yesmaximal, characteristic, complemented
9#13079383C212yesmaximal, complemented
10#13079374C211yesmaximal, characteristic, complemented
11#13078665C212yesmaximal, complemented
12#13077838C212yesmaximal, complemented
13C2×#10622344C211yesmaximal, characteristic, complemented
14C2×#10622345C211yesmaximal, characteristic, complemented
15C11×#2972C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic, complemented
17C23×D44C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19#10623335—21no—
20C2×#66990—21no—
21#10623322C2212yescomplemented
22C2×#66983C2211yescharacteristic
23C2×#66983C2211yescharacteristic, complemented
24C2×#66977C2211yescharacteristic
25C2×#66977C2211yescharacteristic
26C2×#66957C2214yescomplemented
27C22×D88C2212yescomplemented
28C22×#4314C2212yescomplemented
29#10623096C2212yescomplemented
30#10623087—22no—
31#10623083C2212yescomplemented
32#10623081—22no—
33#10623081—22no—
34#10623081C2214yes—
35#10623081C2214yescomplemented
36#10623081C2212yescomplemented
37#10623072C2212yescomplemented
38#10623071—22no—
39#10623046—21no—
40C2×#66947—21no—
41#10623025—21no—
42C2×#66937—21no—
43#10623017—21no—
44C2×C22⋊C4×D11—21no—
45#10623010C2212yescomplemented
46C2×#66928C2211yescharacteristic, complemented
47C2×C4×D44C2211yescharacteristic, complemented
48C8×D4×C11C2214yescomplemented
49C8×D4×C11C2214yescomplemented
50C11×#431C2212yescomplemented
51C2×C11×C22⋊C8C2211yescharacteristic
52C2×C11×C22⋊C8C2211yescharacteristic
53C2×C11×C22⋊C8C2212yescomplemented
54#10622729C2214yescomplemented
55#10622728C2214yescomplemented
56#10622727C2214yescomplemented
57#10622727C2214yescomplemented
58#10622726C2214yescomplemented
59C2×#66885C2212yescomplemented
60C2×#66885C2212yescomplemented
61#10622460C2214yescomplemented
62#10622458C2214yescomplemented
63#10622457C2214yescomplemented
64#10622457C2214yescomplemented
65#10622352C2212yescomplemented
66#10622352C2212yescomplemented
67#10622351C2212yescomplemented
68#10622350C2214yescomplemented
69#10622348C2212yescomplemented
70#10622347C2214yescomplemented
71#10622347C2214yescomplemented
72#10622346C2214yescomplemented
73#10622345C2212yes—
74#10622345C2212yes—
75#10622345C2214yescomplemented
76#10622344C2212yescomplemented
77#10622344C2212yescomplemented
78#10622344C2214yescomplemented
79#10622344C2212yescomplemented
80#10622335C2212yescomplemented
81#10622335C2212yescomplemented
82#10622334C2212yescomplemented
83#10622310C2214yescomplemented
84#10622309C2214yescomplemented
85C4×D88C2214yescomplemented
86C4×#4314C2214yescomplemented
87C24×D11—21no—
88C22×D4×C11D411yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C22×C22⋊D11—21no—
92C22×C22⋊D11—21no—
93C22×C22⋊D11—21no—
94C2×#4339—22no—
95C2×#4339—44no—
96C2×#4339C2314yes—
97C2×#4339C2312yescomplemented
98C22×D44—21no—
99C22×D44—21no—
100C22×D44—21no—
101C22×D44—44no—
102C22×D44C2311yescharacteristic
103C22×D44C2312yes—
104C22×D44C2312yes—
105C22×D44C2311yescharacteristic
106C22×D44C2311yescharacteristic
107C22×C4×D11—21no—
108C22×C4×D11—21no—
109C22×Dic22C2311yescharacteristic
110C22×Dic22C2311yescharacteristic
111C22×C8×C11C2312yes—
112C22×C8×C11C2312yes—
113C22×C8×C11C2314yescomplemented
114C4×D4×C11D412yes—
115C4×D4×C11D412yes—
116C4×D4×C11C2312yes—
117C4×D4×C11C2312yes—
118C2×C11×C4⋊C4D411yescharacteristic
119C2×C11×C22⋊C4D411yescharacteristic
120C2×C11×C22⋊C4D411yescharacteristic
121C2×C42×C11C2311yescharacteristic
122#67006—22no—
123C2×C22⋊Dic11—21no—
124C2×C22⋊Dic11—21no—
125#66992—22no—
126#66992—22no—
127#66990—24no—
128#66990—24no—
129#66990—22no—
130#66988—22no—
131#66983—21no—
132#66983—21no—
133#66983—22no—
134#66983C2312yes—
135#66983C2314yes—
136#66983C2312yes—
137#66983C2312yescomplemented
138#66982—22no—
139#66982—22no—
140C4×C22⋊D11—22no—
141C4×C22⋊D11—22no—
142C4×C22⋊D11—22no—
143C2×(C2×D11)⋊C4—21no—
144C2×(C2×D11)⋊C4—21no—
145C2×(C2×D11)⋊C4—21no—
146C2×(C2×D11)⋊C4—21no—
147C2×(C2×D11)⋊C4—21no—
148#66979C2312yescomplemented
149C2×C4⋊Dic11C2311yescharacteristic
150C2×C4⋊Dic11C2311yescharacteristic
151C2×C4⋊Dic11C2311yescharacteristic
152#66977—21no—
153#66977—21no—
154#66977—21no—
155#66977—21no—
156#66977C2312yes—
157#66977C2312yes—
158#66977C2312yes—
159#66977C2312yes—
160#66977C2312yescomplemented
161C2×Dic11⋊C4—21no—
162C2×Dic11⋊C4—21no—
163C2×Dic44C2314yescomplemented
164#66957—48no—
165C2×D88—44no—
166C2×D88C2314yes—
167C2×D88C2314yes—
168C2×#4314—44no—
169C2×#4314C2314yes—
170C2×#4314C2314yes—
171C2×#4314C2314yescomplemented
172#66951—22no—
173#66949—22no—
174#66947—24no—
175#66947—24no—
176#66947—22no—
177#66942—22no—
178#66938—22no—
179#66937—24no—
180#66937—24no—
181#66937—22no—
182#66936—22no—
183(C22⋊D11)⋊C4—22no—
184(C22⋊D11)⋊C4—22no—
185C22⋊C4×D11—24no—
186C22⋊C4×D11—24no—
187C22⋊C4×D11—22no—
188#66932—22no—
189#66930—22no—
190#66929—22no—
191#66928—22no—
192#66928C2314yes—
193#66928C2312yescomplemented
194C4×D44—22no—
195C4×D44C2314yes—
196C4×D44C2312yescomplemented
197#66925—22no—
198#66923C2312yescomplemented
199C4×Dic22C2312yescomplemented
200C11×C4⋊C8C2314yescomplemented
201C11×C22⋊C8C2312yes—
202C11×C22⋊C8C2312yes—
203C11×C22⋊C8C2312yes—
204C11×C22⋊C8C2312yes—
205C11×C22⋊C8C2314yescomplemented
206C4×C8×C11C2314yescomplemented
207#66885C2314yes—
208#66885C2314yes—
209#66885C2314yes—
210#66885C2314yes—
211#66885C2314yescomplemented
212#66882C2314yescomplemented
213#66881C2314yescomplemented
214#66880C2314yescomplemented
215#66880C2314yescomplemented
216#66880C2314yescomplemented
217#61561—111nomaximal, Sylow
218C24×C11C2×D411yescharacteristic
219C24×C11C2×D411yescharacteristic
220C23×D11—21no—
221C23×D11—21no—
222C23×D11—22no—
223C23×D11—22no—
224C23×D11—21no—
225C23×D11—44no—
226C23×D11—44no—
227C23×D11—82no—
228C2×D4×C11—24no—
229C2×D4×C11C2×D412yes—
230C2×D4×C11C2×D412yes—
231C22×C4×C11—42no—
232C22×C4×C11—42no—
233C22×C4×C11C2×D411yescharacteristic
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2×D411yescharacteristic
236C22×C4×C11C2×D411yescharacteristic
237C22×C4×C11C2×D411yescharacteristic
238C22×C4×C11C2×D411yescharacteristic
239C22×C4×C11C2×D412yes—
240C22×C4×C11C2411yescharacteristic
241C22×C4×C11C2411yescharacteristic
242C22×C4×C11C2411yescharacteristic
243C22×C4×C11C2412yes—
244C2×C22⋊D11—22no—
245C2×C22⋊D11—24no—
246C2×C22⋊D11—22no—
247C2×C22⋊D11—22no—
248C2×C22⋊D11—24no—
249C2×C22⋊D11—22no—
250C2×C22⋊D11—44no—
251C2×C22⋊D11—44no—
252C2×C22⋊D11—82no—
253C22×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258#4339—28no—
259#4339—44no—
260#4339—44no—
261#4339—48no—
262C2×D44—24no—
263C2×D44—24no—
264C2×D44—24no—
265C2×D44—21no—
266C2×D44—21no—
267C2×D44—22no—
268C2×D44—22no—
269C2×D44—21no—
270C2×D44—42no—
271C2×D44—42no—
272C2×D44—42no—
273C2×D44—42no—
274C2×D44—44no—
275C2×D44—44no—
276C2×D44—44no—
277C2×D44C2412yes—
278C2×D44C2412yes—
279C2×D44C2412yes—
280C2×C4×D11—24no—
281C2×C4×D11—22no—
282C2×C4×D11—24no—
283C2×C4×D11—22no—
284C2×C4×D11—44no—
285C2×C4×D11—82no—
286C2×Dic22—21no—
287C2×Dic22—21no—
288C2×Dic22—42no—
289C2×Dic22—42no—
290C2×Dic22C2412yes—
291C2×Dic22C2412yes—
292C2×C8×C11—42no—
293C2×C8×C11—42no—
294C2×C8×C11—44no—
295C2×C8×C11C2414yes—
296C2×C8×C11C2414yes—
297C11×C4⋊C4C2×D412yes—
298C11×C4⋊C4C2×D412yes—
299C11×C22⋊C4C2×D412yes—
300C11×C22⋊C4C2×D412yes—
301C11×C22⋊C4C2×D412yes—
302C11×C22⋊C4C2×D412yes—
303C42×C11C2×D412yes—
304C42×C11C2412yes—
305C22⋊Dic11—22no—
306C22⋊Dic11—22no—
307C22⋊Dic11—22no—
308C22⋊Dic11—22no—
309C22⋊Dic11—22no—
310C22⋊Dic11—22no—
311(C2×D11)⋊C4—22no—
312(C2×D11)⋊C4—22no—
313(C2×D11)⋊C4—24no—
314(C2×D11)⋊C4—22no—
315(C2×D11)⋊C4—24no—
316(C2×D11)⋊C4—24no—
317(C2×D11)⋊C4—22no—
318(C2×D11)⋊C4—24no—
319(C2×D11)⋊C4—22no—
320(C2×D11)⋊C4—22no—
321C4⋊Dic11—21no—
322C4⋊Dic11—21no—
323C4⋊Dic11—21no—
324C4⋊Dic11C2412yes—
325C4⋊Dic11C2412yes—
326C4⋊Dic11C2412yes—
327Dic11⋊C4—22no—
328Dic11⋊C4—22no—
329Dic11⋊C4—22no—
330Dic11⋊C4—22no—
331Dic11⋊C4—22no—
332Dic11⋊C4—22no—
333Dic11⋊C4—22no—
334Dic11⋊C4—22no—
335C4×Dic11—22no—
336C4×Dic11—22no—
337Dic44—44no—
338D88—28no—
339D88—44no—
340#4314—28no—
341#4314—44no—
342#4314—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×#450—111no—
356C2×#447—111no—
357#2972D1111yescharacteristic, complemented
358C23×C11—22no—
359C23×C11—41no—
360C23×C11—41no—
361C23×C11—41no—
362C23×C11—41no—
363C23×C11#13514yescomplemented
364C23×C11C22×D412yes—
365C23×C11C22×D411yescharacteristic
366C23×C11C22×D411yescharacteristic
367C23×C11C22×D411yescharacteristic
368C22×D11—24no—
369C22×D11—22no—
370C22×D11—22no—
371C22×D11—22no—
372C22×D11—44no—
373C22×D11—44no—
374C22×D11—42no—
375C22×D11—42no—
376C22×D11—42no—
377C22×D11—42no—
378C22×D11—44no—
379C22×D11—44no—
380C22×D11—42no—
381C22×D11—42no—
382C22×D11—82no—
383C22×D11—82no—
384C22×D11—81no—
385C22×D11—81no—
386C22×D11—816no—
387D4×C11—24no—
388D4×C11—24no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—24no—
393C2×C4×C11—22no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11—42no—
400C2×C4×C11C22×D412yes—
401C2×C4×C11C22×D412yes—
402C2×C4×C11C22×D411yescharacteristic
403C2×C4×C11C22×D411yescharacteristic
404C2×C4×C11C22×D411yescharacteristic
405C2×C4×C11C22×D412yes—
406C2×C4×C11C2511yescharacteristic
407C22⋊D11—48no—
408C22⋊D11—44no—
409C22⋊D11—44no—
410C22⋊D11—82no—
411C22⋊D11—82no—
412C22⋊D11—84no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—22no—
417C2×Dic11—22no—
418C2×Dic11—42no—
419C2×Dic11—42no—
420C2×Dic11—42no—
421C2×Dic11—81no—
422C2×Dic11—81no—
423D44—24no—
424D44—22no—
425D44—22no—
426D44—24no—
427D44—22no—
428D44—44no—
429D44—44no—
430D44—42no—
431D44—81no—
432D44H(5,𝔽2)14yes—
433C4×D11—48no—
434C4×D11—82no—
435C4×D11—84no—
436C4×D11—82no—
437Dic22—24no—
438Dic22—24no—
439Dic22—42no—
440Dic22—81no—
441C8×C11—24no—
442C8×C11—24no—
443C22×#41—111no—
444C23×D4—111no—
445C2×#135—114no—
446C22×SD16—112no—
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⋊Q8—111no—
467C2×#121—111no—
468C2×#121—111no—
469C2×#121—221no—
470C2×#120—221no—
471#518—221no—
472C2×C4×D4—111no—
473C2×C4×D4C2×D1111yescharacteristic
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#450—112no—
495#450—112no—
496#450—114no—
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×D4C2×D1114yescomplemented
506C8×D4C2×D1114yescomplemented
507#431C2×D1112yescomplemented
508#416—114no—
509C2×#102—112no—
510C2×#102—112no—
511C2×C22⋊C8C2×D1111yescharacteristic
512C2×C22⋊C8C2×D1111yescharacteristic
513C2×C22⋊C8C2×D1112yescomplemented
514C22×C11—21no—
515C22×C11—21no—
516C22×C11—21no—
517C22×C11—21no—
518C22×C11—21no—
519C22×C11—21no—
520C22×C11—22no—
521C22×C11—22no—
522C22×C11—22no—
523C22×C11—44no—
524C22×C11—82no—
525C22×C11C2×#13512yes—
526C22×C11C2×#13512yes—
527C22×C11C2×#13512yes—
528C22×C11C23×D411yescharacteristic
529C2×D11—24no—
530C2×D11—48no—
531C2×D11—42no—
532C2×D11—42no—
533C2×D11—42no—
534C2×D11—42no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—42no—
539C2×D11—88no—
540C2×D11—88no—
541C2×D11—84no—
542C2×D11—162no—
543C4×C11—22no—
544C4×C11—21no—
545C4×C11—21no—
546C4×C11—22no—
547C4×C11—21no—
548C4×C11—22no—
549C4×C11C2×H(5,𝔽2)12yes—
550Dic11—42no—
551Dic11—42no—
552Dic11—42no—
553Dic11—42no—
554Dic11—42no—
555C25—221no—
556C2×#41—114no—
557C2×#41—112no—
558C2×#41—222no—
559C2×#41—444no—
560C22×Q8—111no—
561C22×Q8—111no—
562C22×D4—111no—
563C22×D4—112no—
564C22×D4—112no—
565C22×D4—111no—
566C22×D4—111no—
567C22×D4—221no—
568C22×D4—221no—
569C22×D4—221no—
570C22×D4—221no—
571C22×D4—221no—
572C22×D4—221no—
573C22×D4—444no—
574C22×D4D4411yescharacteristic
575C23×C4—221no—
576C23×C4—221no—
577C23×C4C22×D1111yescharacteristic
578C23×C4C22×D1111yescharacteristic
579#135—448no—
580C2×Q16—114no—
581C2×SD16—114no—
582C2×SD16—114no—
583C2×SD16—114no—
584C2×SD16—444no—
585C2×D8—114no—
586C2×D8—114no—
587C2×D8—444no—
588C22×C8C22×D1112yes—
589C22×C8C22×D1112yes—
590C22×C8C22×D1114yescomplemented
591#126—222no—
592#126—222no—
593#126—222no—
594#125—112no—
595#125—222no—
596#124—114no—
597#124—112no—
598#124—222no—
599#124—222no—
600#123—222no—
601#123—222no—
602#123—222no—
603#123—224no—
604#123—224no—
605#123—222no—
606#123—222no—
607C22⋊Q8—112no—
608C22⋊Q8—112no—
609C22⋊Q8—112no—
610C22⋊Q8—112no—
611C22⋊Q8—112no—
612C22⋊Q8—221no—
613C22⋊Q8—221no—
614C22⋊Q8—221no—
615C22⋊Q8—221no—
616C22⋊Q8—222no—
617#121—112no—
618#121—114no—
619#121—112no—
620#121—112no—
621#121—222no—
622#121—222no—
623#121—221no—
624#121—222no—
625#121—221no—
626#121—224no—
627#121—224no—
628#121—222no—
629#120—222no—
630#120—224no—
631#120—224no—
632#120—222no—
633C4×Q8—112no—
634C4×D4—114no—
635C4×D4—112no—
636C4×D4—222no—
637C4×D4—222no—
638C4×D4—222no—
639C4×D4—222no—
640C4×D4—222no—
641C4×D4—222no—
642C4×D4D4412yes—
643C4×D4D4412yes—
644C4×D4C22×D1112yes—
645C4×D4C22×D1112yes—
646#117—112no—
647#117—222no—
648#117—222no—
649C2×C4⋊C4—111no—
650C2×C4⋊C4—111no—
651C2×C4⋊C4—111no—
652C2×C4⋊C4—221no—
653C2×C4⋊C4—221no—
654C2×C4⋊C4D4411yescharacteristic
655C2×C22⋊C4—221no—
656C2×C22⋊C4—221no—
657C2×C22⋊C4—221no—
658C2×C22⋊C4—221no—
659C2×C22⋊C4—221no—
660C2×C22⋊C4—221no—
661C2×C22⋊C4—221no—
662C2×C22⋊C4—224no—
663C2×C22⋊C4—224no—
664C2×C22⋊C4—222no—
665C2×C22⋊C4D4411yescharacteristic
666C2×C22⋊C4D4411yescharacteristic
667C2×C42C22×D1111yescharacteristic
668#107—114no—
669#106—114no—
670C4⋊C8C22×D1114yescomplemented
671#103—114no—
672#103—114no—
673#103—114no—
674#102—114no—
675#102—114no—
676#102—114no—
677#102—114no—
678#102—114no—
679C22⋊C8C22×D1112yes—
680C22⋊C8C22×D1112yes—
681C22⋊C8C22×D1112yes—
682C22⋊C8C22×D1112yes—
683C22⋊C8C22×D1114yescomplemented
684C4×C8C22×D1114yescomplemented
685C2×C11—22no—
686C2×C11—22no—
687C2×C11—22no—
688C2×C11—42no—
689C2×C11#348411yescharacteristic
690C2×C11C22×#13511yescharacteristic
691C2×C11#358511yescharacteristic
692D11—44no—
693D11—82no—
694D11—82no—
695C24—221no—
696C24—221no—
697C24—222no—
698C24—222no—
699C24—221no—
700C24—444no—
701C24—444no—
702C24—882no—
703C24C2×D4411yescharacteristic
704C24C2×D4411yescharacteristic
705#41—228no—
706#41—444no—
707#41—444no—
708#41—448no—
709C2×Q8—112no—
710C2×Q8—112no—
711C2×Q8—221no—
712C2×Q8—221no—
713C2×Q8—442no—
714C2×Q8—442no—
715C2×D4—24no—
716C2×D4—112no—
717C2×D4—112no—
718C2×D4—112no—
719C2×D4—224no—
720C2×D4—224no—
721C2×D4—224no—
722C2×D4—222no—
723C2×D4—222no—
724C2×D4—224no—
725C2×D4—222no—
726C2×D4—224no—
727C2×D4—222no—
728C2×D4—221no—
729C2×D4—222no—
730C2×D4—222no—
731C2×D4—221no—
732C2×D4—221no—
733C2×D4—442no—
734C2×D4—442no—
735C2×D4—442no—
736C2×D4—442no—
737C2×D4—444no—
738C2×D4—444no—
739C2×D4—444no—
740C2×D4—444no—
741C2×D4—444no—
742C2×D4—882no—
743C2×D4C2×D4412yes—
744C2×D4C2×D4412yes—
745C22×C4—42no—
746C22×C4—42no—
747C22×C4—221no—
748C22×C4—221no—
749C22×C4—221no—
750C22×C4—221no—
751C22×C4—221no—
752C22×C4—224no—
753C22×C4—224no—
754C22×C4—222no—
755C22×C4—222no—
756C22×C4—444no—
757C22×C4—882no—
758C22×C4C2×D4411yescharacteristic
759C22×C4C2×D4411yescharacteristic
760C22×C4C2×D4411yescharacteristic
761C22×C4C2×D4411yescharacteristic
762C22×C4C2×D4411yescharacteristic
763C22×C4C2×D4411yescharacteristic
764C22×C4C2×D4412yes—
765C22×C4C23×D1111yescharacteristic
766C22×C4C23×D1111yescharacteristic
767C22×C4C23×D1111yescharacteristic
768C22×C4C23×D1112yes—
769Q16—444no—
770SD16—228no—
771SD16—444no—
772SD16—444no—
773D8—228no—
774D8—444no—
775C2×C8—42no—
776C2×C8—42no—
777C2×C8—44no—
778C2×C8C23×D1114yes—
779C2×C8C23×D1114yes—
780C4⋊C4—112no—
781C4⋊C4—112no—
782C4⋊C4—112no—
783C4⋊C4—221no—
784C4⋊C4—221no—
785C4⋊C4—221no—
786C4⋊C4—222no—
787C4⋊C4—222no—
788C4⋊C4—222no—
789C4⋊C4—222no—
790C4⋊C4—222no—
791C4⋊C4—222no—
792C4⋊C4—222no—
793C4⋊C4—222no—
794C4⋊C4C2×D4412yes—
795C4⋊C4C2×D4412yes—
796C22⋊C4—222no—
797C22⋊C4—222no—
798C22⋊C4—222no—
799C22⋊C4—222no—
800C22⋊C4—222no—
801C22⋊C4—222no—
802C22⋊C4—224no—
803C22⋊C4—224no—
804C22⋊C4—222no—
805C22⋊C4—224no—
806C22⋊C4—222no—
807C22⋊C4—222no—
808C22⋊C4—224no—
809C22⋊C4—222no—
810C22⋊C4—222no—
811C22⋊C4—222no—
812C22⋊C4C2×D4412yes—
813C22⋊C4C2×D4412yes—
814C22⋊C4C2×D4412yes—
815C22⋊C4C2×D4412yes—
816C42—222no—
817C42—222no—
818C42C2×D4412yes—
819C42C23×D1112yes—
820C11#6156111yescharacteristic, complemented, Sylow
821C23—22no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—224no—
827C23—222no—
828C23—222no—
829C23—222no—
830C23—444no—
831C23—444no—
832C23—442no—
833C23—442no—
834C23—442no—
835C23—442no—
836C23—444no—
837C23—444no—
838C23—442no—
839C23—442no—
840C23—882no—
841C23—882no—
842C23—881no—
843C23—881no—
844C23—8816no—
845C23#6695714yescomplemented
846C23C22×D4412yes—
847C23C22×D4411yescharacteristic
848C23C22×D4411yescharacteristic
849C23C22×D4411yescharacteristic
850Q8—224no—
851Q8—224no—
852Q8—442no—
853Q8—881no—
854D4—24no—
855D4—24no—
856D4—114no—
857D4—224no—
858D4—222no—
859D4—224no—
860D4—222no—
861D4—222no—
862D4—444no—
863D4—444no—
864D4—442no—
865D4—448no—
866D4—444no—
867D4—444no—
868D4—881no—
869D4—884no—
870D4—882no—
871D4—882no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—24no—
876C2×C4—22no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—42no—
882C2×C4—41no—
883C2×C4—222no—
884C2×C4—222no—
885C2×C4—222no—
886C2×C4—222no—
887C2×C4—222no—
888C2×C4—448no—
889C2×C4—442no—
890C2×C4—442no—
891C2×C4—442no—
892C2×C4—884no—
893C2×C4—882no—
894C2×C4—882no—
895C2×C4—881no—
896C2×C4—881no—
897C2×C4C22×D4412yes—
898C2×C4C22×D4412yes—
899C2×C4C22×D4411yescharacteristic
900C2×C4C22×D4412yes—
901C2×C4C22×D4411yescharacteristic
902C2×C4C22×D4411yescharacteristic
903C2×C4C24×D1111yescharacteristic
904C8—24no—
905C8—24no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—21no—
910C22—21no—
911C22—21no—
912C22—22no—
913C22—22no—
914C22—22no—
915C22—44no—
916C22—82no—
917C22—224no—
918C22—448no—
919C22—442no—
920C22—442no—
921C22—442no—
922C22—442no—
923C22—442no—
924C22—442no—
925C22—442no—
926C22—442no—
927C22—888no—
928C22—888no—
929C22—884no—
930C22—1762no—
931C22C2×#6695712yes—
932C22C2×#6695712yes—
933C22C2×#6695712yes—
934C22C23×D4411yescharacteristic
935C4—22no—
936C4—21no—
937C4—22no—
938C4—21no—
939C4—21no—
940C4—22no—
941C4—442no—
942C4—442no—
943C4—442no—
944C4—442no—
945C4—442no—
946C4D11×H(5,𝔽2)12yes—
947C2—22no—
948C2—22no—
949C2—22no—
950C2—42no—
951C2—444no—
952C2—882no—
953C2—882no—
954C2#1308225211yescharacteristic
955C2C22×#6695711yescharacteristic
956C2#1308339711yescharacteristic
subgroupG/H
centerC22C23×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#2972C2
socleC22×C11C23×D4
hypercenter#2972D11
hypocenterC11#61561
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2972

Complements

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

NH ≅ G/Ntype
1. #13082455C2semidirect
2. C2×#10623081C2semidirect
3. #13080468C2semidirect
4. #13080453C2semidirect
5. #13080328C2semidirect
6. #13080303C2semidirect
7. #13079583C2semidirect
8. #13079391C2semidirect
9. #13079383C2semidirect
10. #13079374C2semidirect
11. #13078665C2semidirect
12. #13077838C2semidirect
13. C2×#10622344C2semidirect
14. C2×#10622345C2semidirect
15. C11×#2972C2semidirect
16. C22×#4339C22semidirect
21. #10623322C22semidirect
23. C2×#66983C22semidirect
26. C2×#66957C22semidirect
27. C22×D88C22semidirect
28. C22×#4314C22semidirect
29. #10623096C22semidirect
31. #10623083C22semidirect
35. #10623081C22semidirect
36. #10623081C22semidirect
37. #10623072C22semidirect
45. #10623010C22semidirect
46. C2×#66928C22semidirect
47. C2×C4×D44C22semidirect
48. C8×D4×C11C22semidirect
49. C8×D4×C11C22semidirect
50. C11×#431C22semidirect
53. C2×C11×C22⋊C8C22semidirect
54. #10622729C22semidirect
55. #10622728C22semidirect
56. #10622727C22semidirect
57. #10622727C22semidirect
58. #10622726C22semidirect
59. C2×#66885C22semidirect
60. C2×#66885C22semidirect
61. #10622460C22semidirect
62. #10622458C22semidirect
63. #10622457C22semidirect
64. #10622457C22semidirect
65. #10622352C22semidirect
66. #10622352C22semidirect
67. #10622351C22semidirect
68. #10622350C22semidirect
69. #10622348C22semidirect
70. #10622347C22semidirect
71. #10622347C22semidirect
72. #10622346C22semidirect
75. #10622345C22semidirect
76. #10622344C22semidirect
77. #10622344C22semidirect
78. #10622344C22semidirect
79. #10622344C22semidirect
80. #10622335C22semidirect
81. #10622335C22semidirect
82. #10622334C22semidirect
83. #10622310C22semidirect
84. #10622309C22semidirect
85. C4×D88C22semidirect
86. C4×#4314C22semidirect
97. C2×#4339C23semidirect
113. C22×C8×C11C23semidirect
137. #66983C23semidirect
148. #66979C23semidirect
160. #66977C23semidirect
163. C2×Dic44C23semidirect
171. C2×#4314C23semidirect
193. #66928C23semidirect
196. C4×D44C23semidirect
198. #66923C23semidirect
199. C4×Dic22C23semidirect
200. C11×C4⋊C8C23semidirect
205. C11×C22⋊C8C23semidirect
206. C4×C8×C11C23semidirect
211. #66885C23semidirect
212. #66882C23semidirect
213. #66881C23semidirect
214. #66880C23semidirect
215. #66880C23semidirect
216. #66880C23semidirect
357. #2972D11semidirect
363. C23×C11#135semidirect
505. C8×D4C2×D11semidirect
506. C8×D4C2×D11semidirect
507. #431C2×D11semidirect
513. C2×C22⋊C8C2×D11semidirect
590. C22×C8C22×D11semidirect
670. C4⋊C8C22×D11semidirect
683. C22⋊C8C22×D11semidirect
684. C4×C8C22×D11semidirect
820. C11#61561semidirect
845. C23#66957semidirect

Maximal subgroups

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

subgroupindex
#130824552
C2×#106230812
#130804682
#130804532
#130803282
#130803032
#130795832
#130793912
#130793832
#130793742
#130786652
#130778382
C2×#106223442
C2×#106223452
C11×#29722
#6156111