Finite Group Databasebeta

← #15638606

Subgroups — #15638606

Order 2816.

2234 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082412C211yesmaximal, characteristic, complemented
2C2×#10623143C211yesmaximal, characteristic
3#13080700C214yesmaximal, complemented
4#13080692C214yesmaximal, complemented
5#13080133C214yesmaximal, complemented
6#13080129C214yesmaximal, complemented
7#13079616C212yesmaximal, complemented
8#13079422C211yesmaximal, characteristic, complemented
9#13079390C212yesmaximal, complemented
10#13078712C212yesmaximal, complemented
11#13077878C211yesmaximal, characteristic, complemented
12#13077874C211yesmaximal, characteristic, complemented
13D11×#450C212yesmaximal, complemented
14#13077643C211yesmaximal, characteristic, complemented
15C11×#3193C211yesmaximal, characteristic, complemented
16C22×D4×D11C2211yescharacteristic
17C22×#4339C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic, complemented
19C2×C11×#121C2211yescharacteristic
20Q8×C22⋊D11C2212yescomplemented
21C2×#66995C2212yescomplemented
22C2×#66991—21no—
23C2×#66990—21no—
24C2×#66989C2211yescharacteristic
25C2×C4×C22⋊D11C2211yescharacteristic
26C2×#66977C2211yescharacteristic, complemented
27C2×SD16×D11C2214yescomplemented
28C2×#66962C2212yescomplemented
29#10623167—22no—
30#10623166C2212yescomplemented
31#10623165—21no—
32#10623163C2212yescomplemented
33D11×C22⋊Q8C2212yes—
34#10623154—21no—
35#10623153C2212yescomplemented
36#10623143—22no—
37#10623143—22no—
38#10623143C2214yes—
39#10623143C2214yes—
40#10623042—22no—
41#10623042C2212yescomplemented
42C2×#66950C2211yescharacteristic
43C2×#66946C2211yescharacteristic
44C2×#66936—21no—
45#10623017—21no—
46C2×C22⋊C4×D11—21no—
47#10623014—21no—
48C11×#484C2212yescomplemented
49C11×#480C2212yescomplemented
50C11×#468C2214yescomplemented
51C11×#450C2212yes—
52C11×#448C2212yescomplemented
53C11×#407C2211yescharacteristic, complemented
54#10622831C2212yes—
55#10622820C2211yescharacteristic, complemented
56#10622782C2214yescomplemented
57#10622780C2214yescomplemented
58#10622779C2214yescomplemented
59#10622746C2212yescomplemented
60#10622740C2214yescomplemented
61#10622663C2212yescomplemented
62#10622660C2214yescomplemented
63#10622659C2212yes—
64#10622655C2214yescomplemented
65#10622653C2212yescomplemented
66#10622646C2212yescomplemented
67#10622583C2212yescomplemented
68#10622579C2212yescomplemented
69#10622503C2214yescomplemented
70#10622502C2214yescomplemented
71#10622500C2214yescomplemented
72#10622497C2214yescomplemented
73#10622431C2214yescomplemented
74#10622430C2214yescomplemented
75#10622426C2214yescomplemented
76#10622421C2214yescomplemented
77#10622389C2214yescomplemented
78D11×#102C2214yescomplemented
79#10622380C2214yescomplemented
80#10622378C2214yescomplemented
81#10622352C2212yescomplemented
82#10622346C2214yescomplemented
83#10622344C2212yes—
84#10622341C2214yescomplemented
85D11×C22⋊C8C2212yes—
86#10622332C2212yescomplemented
87C24×D11—21no—
88C22×Q8×C11C2311yescharacteristic, complemented
89C22×D4×C11—21no—
90C22×D4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C22×C22⋊D11—21no—
93C22×C22⋊D11—21no—
94C22×C22⋊D11D411yescharacteristic
95C2×Q8×D11C2312yes—
96C2×D4×D11—22no—
97C2×D4×D11—44no—
98C2×D4×D11C2314yes—
99C2×#4339—21no—
100C2×#4339—21no—
101C2×#4339—44no—
102C2×#4339C2312yes—
103C2×#4339C2312yes—
104C22×D44C2311yescharacteristic
105C22×C4×D11—21no—
106C22×C4×D11—21no—
107C22×C4×D11C2311yescharacteristic
108C22×Dic22C2311yescharacteristic
109C22×Dic22C2311yescharacteristic, complemented
110C2×C11×SD16C2314yes—
111C2×C11×M16C2312yescomplemented
112C11×C22⋊Q8—21no—
113C11×C22⋊Q8—21no—
114C11×C22⋊Q8C2312yes—
115C11×C22⋊Q8C2312yescomplemented
116C11×#121—21no—
117C11×#121—21no—
118C11×#121C2312yes—
119C11×#121C2312yes—
120C2×C11×C4⋊C4—21no—
121C2×C11×C4⋊C4C2311yescharacteristic
122C2×C11×C4⋊C4C2311yescharacteristic, complemented
123C2×C11×C22⋊C4—21no—
124C2×C11×C22⋊C4—21no—
125C2×C22⋊Dic11—21no—
126C2×C22⋊Dic11—21no—
127C2×C22⋊Dic11—21no—
128C2×C22⋊Dic11D411yescharacteristic
129#66999—22no—
130#66999C2312yes—
131Q8×Dic11C2312yescomplemented
132#66997—22no—
133#66997C2312yescomplemented
134C2×#4326C2314yescomplemented
135#66995—44no—
136C2×#4325C2314yes—
137#66991—24no—
138#66991—24no—
139#66990—24no—
140#66990—24no—
141#66989—22no—
142#66989C2314yes—
143C2×#4324C2314yes—
144C4×C22⋊D11—22no—
145C4×C22⋊D11—22no—
146C4×C22⋊D11D412yes—
147C4×C22⋊D11D412yes—
148C4×C22⋊D11C2312yes—
149C4×C22⋊D11C2312yes—
150C2×(C2×D11)⋊C4—21no—
151C2×(C2×D11)⋊C4—21no—
152C2×(C2×D11)⋊C4D411yescharacteristic
153C2×C4⋊Dic11—21no—
154C2×C4⋊Dic11C2311yescharacteristic, complemented
155#66977—21no—
156#66977—21no—
157#66977—22no—
158#66977—22no—
159#66977C2312yes—
160#66977C2312yescomplemented
161C2×Dic11⋊C4—21no—
162C2×Dic11⋊C4D411yescharacteristic
163C2×C4×Dic11C2311yescharacteristic
164C2×#4318C2312yescomplemented
165SD16×D11—48no—
166#66962—44no—
167C2×Dic44C2314yescomplemented
168C2×#4314C2314yes—
169C2×C8×D11C2314yes—
170#66950—22no—
171#66950—22no—
172#66950C2314yes—
173#66950C2312yes—
174#66949—22no—
175#66949—22no—
176#66949—22no—
177#66946—22no—
178#66946C2314yes—
179C4⋊C4×D11—22no—
180C4⋊C4×D11C2312yes—
181#66942—22no—
182#66942—22no—
183#66942—22no—
184#66941—22no—
185#66941C2312yescomplemented
186#66940—22no—
187#66940C2312yescomplemented
188#66936—24no—
189#66936—24no—
190(C22⋊D11)⋊C4—22no—
191(C22⋊D11)⋊C4—22no—
192C22⋊C4×D11—22no—
193C22⋊C4×D11—24no—
194C22⋊C4×D11—24no—
195#66931—22no—
196#66931—22no—
197#66931—22no—
198#66931—22no—
199#66930—22no—
200C11×#107C2314yescomplemented
201C11×#103C2314yescomplemented
202C11×#102C2314yes—
203C11×C22⋊C8C2312yes—
204C11×C22⋊C8C2312yescomplemented
205#66896C2314yes—
206C22⋊(C11⋊C8)C2312yes—
207C22⋊(C11⋊C8)C2312yescomplemented
208#66885C2314yes—
209(C2×D11)⋊C8C2314yes—
210#66880C2314yescomplemented
211#66879C2314yescomplemented
212Dic11⋊C8C2314yescomplemented
213#66874C2314yescomplemented
214#66874C2314yescomplemented
215#66873C2314yes—
216#66871C2314yescomplemented
217#61570—111nomaximal, Sylow
218C24×C11—21no—
219C24×C11C2×D411yescharacteristic
220C23×D11—21no—
221C23×D11—24no—
222C23×D11—44no—
223C23×D11—44no—
224C23×D11—82no—
225C23×D11C2×D411yescharacteristic
226C2×Q8×C11—21no—
227C2×Q8×C11—42no—
228C2×Q8×C11C2412yes—
229C2×D4×C11—22no—
230C2×D4×C11—22no—
231C2×D4×C11—21no—
232C2×D4×C11—42no—
233C2×D4×C11—82no—
234C2×D4×C11C2412yes—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—21no—
238C22×C4×C11—42no—
239C22×C4×C11C2×D411yescharacteristic
240C22×C4×C11C2×D411yescharacteristic
241C22×C4×C11C2×D411yescharacteristic
242C22×C4×C11C2411yescharacteristic
243C22×C4×C11C2411yescharacteristic
244C22×C4×C11C2411yescharacteristic
245C2×C22⋊D11—24no—
246C2×C22⋊D11—22no—
247C2×C22⋊D11—22no—
248C2×C22⋊D11—24no—
249C2×C22⋊D11—44no—
250C2×C22⋊D11—44no—
251C2×C22⋊D11C2×D412yes—
252C2×C22⋊D11C2×D412yes—
253C22×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11C2×D411yescharacteristic
257C22×Dic11C2×D411yescharacteristic
258C22×Dic11C2×D411yescharacteristic
259Q8×D11—44no—
260D4×D11—28no—
261D4×D11—44no—
262D4×D11—48no—
263#4339—24no—
264#4339—24no—
265#4339—42no—
266#4339—42no—
267#4339—44no—
268#4339—44no—
269C2×D44—24no—
270C2×D44—21no—
271C2×D44C2412yes—
272C2×C4×D11—24no—
273C2×C4×D11—22no—
274C2×C4×D11—22no—
275C2×C4×D11—22no—
276C2×C4×D11—22no—
277C2×C4×D11—42no—
278C2×C4×D11—44no—
279C2×C4×D11—82no—
280C2×C4×D11C2×D412yes—
281C2×C4×D11C2412yes—
282C2×Dic22—22no—
283C2×Dic22—22no—
284C2×Dic22—21no—
285C2×Dic22—21no—
286C2×Dic22—42no—
287C2×Dic22—42no—
288C2×Dic22C2412yes—
289C2×Dic22C2412yes—
290C11×SD16—44no—
291C11×M16—42no—
292C2×C8×C11C2414yes—
293C11×C4⋊C4—22no—
294C11×C4⋊C4—22no—
295C11×C4⋊C4—21no—
296C11×C4⋊C4—21no—
297C11×C4⋊C4C2412yes—
298C11×C4⋊C4C2412yes—
299C11×C22⋊C4—22no—
300C11×C22⋊C4—22no—
301C11×C22⋊C4—22no—
302C11×C22⋊C4—22no—
303C22⋊Dic11—24no—
304C22⋊Dic11—24no—
305C22⋊Dic11—22no—
306C22⋊Dic11—22no—
307C22⋊Dic11C2×D412yes—
308C22⋊Dic11C2×D412yes—
309#4326—44no—
310#4325—28no—
311#4324—44no—
312(C2×D11)⋊C4—24no—
313(C2×D11)⋊C4—24no—
314(C2×D11)⋊C4—22no—
315(C2×D11)⋊C4—22no—
316(C2×D11)⋊C4C2×D412yes—
317(C2×D11)⋊C4C2×D412yes—
318C4⋊Dic11—22no—
319C4⋊Dic11—22no—
320C4⋊Dic11—24no—
321C4⋊Dic11—21no—
322C4⋊Dic11C2412yes—
323Dic11⋊C4—22no—
324Dic11⋊C4—22no—
325Dic11⋊C4—22no—
326Dic11⋊C4—22no—
327Dic11⋊C4—22no—
328Dic11⋊C4—22no—
329Dic11⋊C4—22no—
330Dic11⋊C4—22no—
331Dic11⋊C4C2×D412yes—
332Dic11⋊C4C2×D412yes—
333C4×Dic11—22no—
334C4×Dic11—22no—
335C4×Dic11C2×D412yes—
336C4×Dic11C2412yes—
337#4318—42no—
338C2×C11⋊C8C2414yes—
339Dic44—44no—
340#4314—28no—
341C8×D11—44no—
342#3501—111no—
343C2×#546—111no—
344#3314—114no—
345#3314—114no—
346#3266—114no—
347#3266—114no—
348#3215—112no—
349#3193—111no—
350#3193D1111yescharacteristic, complemented
351#3189—112no—
352#3110—112no—
353#3007—111no—
354#3007—111no—
355C2×#450—112no—
356#2973—111no—
357C23×C11—22no—
358C23×C11—22no—
359C23×C11—41no—
360C23×C11—41no—
361C23×C11—42no—
362C23×C11—42no—
363C23×C11—42no—
364C23×C11C22×D411yescharacteristic
365C23×C11C22×D411yescharacteristic
366C23×C11C22×D411yescharacteristic
367C22×D11—24no—
368C22×D11—22no—
369C22×D11—41no—
370C22×D11—41no—
371C22×D11—48no—
372C22×D11—42no—
373C22×D11—42no—
374C22×D11—48no—
375C22×D11—84no—
376C22×D11—816no—
377C22×D11#13714yescomplemented
378C22×D11C22×D412yes—
379Q8×C11—24no—
380Q8×C11—81no—
381D4×C11—24no—
382D4×C11—42no—
383D4×C11—82no—
384D4×C11—82no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—42no—
395C2×C4×C11—81no—
396C2×C4×C11—81no—
397C2×C4×C11C22×D411yescharacteristic
398C2×C4×C11C22×D411yescharacteristic
399C2×C4×C11C22×D411yescharacteristic
400C2×C4×C11C2511yescharacteristic
401C22⋊D11—24no—
402C22⋊D11—24no—
403C22⋊D11—48no—
404C22⋊D11—44no—
405C22⋊D11—44no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408C2×Dic11—22no—
409C2×Dic11—22no—
410C2×Dic11—41no—
411C2×Dic11—41no—
412C2×Dic11—42no—
413C2×Dic11—81no—
414C2×Dic11—81no—
415C2×Dic11C22×D412yes—
416C2×Dic11C22×D412yes—
417C2×Dic11C22×D412yes—
418D44—24no—
419D44—22no—
420D44H(5,𝔽2)14yes—
421C4×D11—24no—
422C4×D11—42no—
423C4×D11—44no—
424C4×D11—44no—
425C4×D11—84no—
426C4×D11—82no—
427C4×D11—82no—
428Dic22—24no—
429Dic22—22no—
430Dic22—22no—
431Dic22—42no—
432Dic22—82no—
433Dic22—82no—
434Dic22—81no—
435C8×C11—24no—
436C11⋊C8—24no—
437C22×#41—111no—
438C23×D4—111no—
439C2×#137—112no—
440C2×#137—112no—
441C22×SD16—114no—
442#554—112no—
443#554—112no—
444#554—222no—
445#554—222no—
446D4×Q8—112no—
447D4×Q8—112no—
448#546—114no—
449#546—114no—
450#546—222no—
451#546—222no—
452#544—221no—
453#543—221no—
454#543—221no—
455#533—112no—
456C2×#124—111no—
457C2×#123—221no—
458C2×C22⋊Q8—111no—
459C2×C22⋊Q8—112no—
460C2×C22⋊Q8—111no—
461C2×C22⋊Q8C2×D1111yescharacteristic, complemented
462C2×#121—221no—
463C2×#121C2×D1111yescharacteristic
464C2×#120—221no—
465#518—221no—
466C2×C4×D4—111no—
467C2×C4×D4—111no—
468C22×C22⋊C4—221no—
469#497—114no—
470#489—114no—
471#484—112no—
472#484—114no—
473#484C2×D1112yescomplemented
474#480—112no—
475#480C2×D1112yescomplemented
476#474—114no—
477#468—114no—
478#468C2×D1114yescomplemented
479#467—114no—
480#467—114no—
481#464—114no—
482#464—114no—
483#461—114no—
484#452—114no—
485#452—114no—
486#451—112no—
487#451—114no—
488#451—112no—
489#450—112no—
490#450—114no—
491#450—112no—
492#450—114no—
493#450—112no—
494#450C2×D1112yes—
495#448—112no—
496#448C2×D1112yescomplemented
497#440—114no—
498#440—114no—
499#435—114no—
500#435—114no—
501#432—112no—
502#417—112no—
503#417—112no—
504C2×#102—114no—
505#407—111no—
506#407C2×D1111yescharacteristic, complemented
507C2×C22⋊C8—112no—
508C22×C11—21no—
509C22×C11—21no—
510C22×C11—21no—
511C22×C11—21no—
512C22×C11—21no—
513C22×C11—21no—
514C22×C11—21no—
515C22×C11—21no—
516C22×C11—42no—
517C22×C11—42no—
518C22×C11—42no—
519C22×C11—82no—
520C22×C11—84no—
521C22×C11C2×#13712yes—
522C22×C11C23×D411yescharacteristic
523C2×D11—22no—
524C2×D11—22no—
525C2×D11—24no—
526C2×D11—44no—
527C2×D11—48no—
528C2×D11—42no—
529C2×D11—42no—
530C2×D11—816no—
531C2×D11C2×#13714yes—
532C4×C11—21no—
533C4×C11—21no—
534C4×C11—21no—
535C4×C11—42no—
536C4×C11—42no—
537C4×C11—42no—
538C4×C11C2×H(5,𝔽2)12yes—
539Dic11—22no—
540Dic11—22no—
541Dic11—22no—
542Dic11—42no—
543Dic11—42no—
544Dic11—42no—
545C25—221no—
546C2×#41—112no—
547C2×#41—112no—
548C2×#41—221no—
549C2×#41—221no—
550C2×#41—444no—
551C22×Q8—112no—
552C22×Q8—111no—
553C22×Q8—111no—
554C22×Q8C22×D1111yescharacteristic, complemented
555C22×D4—21no—
556C22×D4—111no—
557C22×D4—114no—
558C22×D4—111no—
559C22×D4—222no—
560C22×D4—221no—
561C22×D4—221no—
562C22×D4—444no—
563C22×D4C22×D1111yescharacteristic
564C23×C4—111no—
565C23×C4—221no—
566C23×C4—221no—
567C23×C4C22×D1111yescharacteristic
568#137—444no—
569#137—444no—
570C2×Q16—114no—
571C2×Q16—114no—
572C2×SD16—114no—
573C2×SD16—114no—
574C2×SD16—114no—
575C2×SD16—448no—
576C2×SD16C22×D1114yes—
577C2×M16—112no—
578C2×M16C22×D1112yescomplemented
579C22×C8—114no—
580C4⋊Q8—112no—
581C4⋊Q8—112no—
582C4⋊Q8—222no—
583C4⋊Q8—222no—
584#125—222no—
585#125—222no—
586#125—222no—
587#124—114no—
588#124—222no—
589#123—224no—
590#123—224no—
591C22⋊Q8—21no—
592C22⋊Q8—21no—
593C22⋊Q8—112no—
594C22⋊Q8—112no—
595C22⋊Q8—112no—
596C22⋊Q8—114no—
597C22⋊Q8—112no—
598C22⋊Q8—222no—
599C22⋊Q8—222no—
600C22⋊Q8—222no—
601C22⋊Q8—222no—
602C22⋊Q8—222no—
603C22⋊Q8—222no—
604C22⋊Q8—222no—
605C22⋊Q8—222no—
606C22⋊Q8—222no—
607C22⋊Q8—222no—
608C22⋊Q8—222no—
609C22⋊Q8—222no—
610C22⋊Q8—221no—
611C22⋊Q8—221no—
612C22⋊Q8C22×D1112yes—
613C22⋊Q8C22×D1112yescomplemented
614#121—21no—
615#121—21no—
616#121—224no—
617#121—224no—
618#121C22×D1112yes—
619#121C22×D1112yes—
620#120—224no—
621#120—224no—
622C4×Q8—112no—
623C4×Q8—112no—
624C4×Q8—222no—
625C4×D4—112no—
626C4×D4—112no—
627C4×D4—112no—
628C4×D4—112no—
629C4×D4—114no—
630C4×D4—222no—
631C4×D4—222no—
632C4×D4—222no—
633C4×D4—222no—
634C4×D4—222no—
635#117—222no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—111no—
638C2×C4⋊C4—111no—
639C2×C4⋊C4—112no—
640C2×C4⋊C4—222no—
641C2×C4⋊C4—221no—
642C2×C4⋊C4—221no—
643C2×C4⋊C4C22×D1111yescharacteristic
644C2×C4⋊C4C22×D1111yescharacteristic, complemented
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—111no—
648C2×C22⋊C4—111no—
649C2×C22⋊C4—224no—
650C2×C22⋊C4—224no—
651C2×C22⋊C4—222no—
652C2×C22⋊C4—221no—
653C2×C22⋊C4—221no—
654C2×C22⋊C4—221no—
655C2×C22⋊C4—221no—
656C2×C22⋊C4—221no—
657C2×C42—111no—
658#107—114no—
659#107C22×D1114yescomplemented
660C4⋊C8—114no—
661#103—114no—
662#103—114no—
663#103—114no—
664#103C22×D1114yescomplemented
665#102—114no—
666#102—114no—
667#102—114no—
668#102C22×D1114yes—
669C22⋊C8—112no—
670C22⋊C8—112no—
671C22⋊C8—114no—
672C22⋊C8C22×D1112yes—
673C22⋊C8C22×D1112yescomplemented
674#97—114no—
675C2×C11—22no—
676C2×C11—41no—
677C2×C11—41no—
678C2×C11—82no—
679C2×C11#348411yescharacteristic
680C2×C11C22×#13711yescharacteristic
681C2×C11#358511yescharacteristic
682D11—24no—
683D11—44no—
684C24—21no—
685C24—111no—
686C24—224no—
687C24—221no—
688C24—444no—
689C24—444no—
690C24—882no—
691C24D4×D1111yescharacteristic
692#41—224no—
693#41—224no—
694#41—442no—
695#41—442no—
696#41—444no—
697#41—444no—
698C2×Q8—21no—
699C2×Q8—42no—
700C2×Q8—112no—
701C2×Q8—112no—
702C2×Q8—222no—
703C2×Q8—222no—
704C2×Q8—221no—
705C2×Q8—221no—
706C2×Q8—442no—
707C2×Q8—442no—
708C2×Q8—444no—
709C2×Q8C23×D1112yes—
710C2×D4—22no—
711C2×D4—22no—
712C2×D4—21no—
713C2×D4—42no—
714C2×D4—82no—
715C2×D4—112no—
716C2×D4—112no—
717C2×D4—112no—
718C2×D4—224no—
719C2×D4—224no—
720C2×D4—228no—
721C2×D4—224no—
722C2×D4—222no—
723C2×D4—222no—
724C2×D4—221no—
725C2×D4—444no—
726C2×D4—448no—
727C2×D4—444no—
728C2×D4—444no—
729C2×D4C23×D1112yes—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—42no—
734C22×C4—111no—
735C22×C4—111no—
736C22×C4—111no—
737C22×C4—112no—
738C22×C4—112no—
739C22×C4—224no—
740C22×C4—222no—
741C22×C4—222no—
742C22×C4—221no—
743C22×C4—221no—
744C22×C4—221no—
745C22×C4—222no—
746C22×C4—222no—
747C22×C4—442no—
748C22×C4—444no—
749C22×C4—882no—
750C22×C4D4×D1111yescharacteristic
751C22×C4D4×D1111yescharacteristic
752C22×C4D4×D1111yescharacteristic
753C22×C4C23×D1111yescharacteristic
754C22×C4C23×D1111yescharacteristic
755C22×C4C23×D1111yescharacteristic
756Q16—444no—
757Q16—444no—
758SD16—44no—
759SD16—228no—
760SD16—228no—
761SD16—444no—
762M16—42no—
763M16—442no—
764C2×C8—114no—
765C2×C8—444no—
766C2×C8C23×D1114yes—
767C4⋊C4—22no—
768C4⋊C4—22no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—112no—
772C4⋊C4—112no—
773C4⋊C4—112no—
774C4⋊C4—222no—
775C4⋊C4—224no—
776C4⋊C4—222no—
777C4⋊C4—222no—
778C4⋊C4—222no—
779C4⋊C4—222no—
780C4⋊C4—222no—
781C4⋊C4—222no—
782C4⋊C4—222no—
783C4⋊C4—221no—
784C4⋊C4—222no—
785C4⋊C4—222no—
786C4⋊C4C23×D1112yes—
787C4⋊C4C23×D1112yes—
788C22⋊C4—22no—
789C22⋊C4—22no—
790C22⋊C4—22no—
791C22⋊C4—22no—
792C22⋊C4—112no—
793C22⋊C4—112no—
794C22⋊C4—112no—
795C22⋊C4—112no—
796C22⋊C4—224no—
797C22⋊C4—224no—
798C22⋊C4—222no—
799C22⋊C4—222no—
800C22⋊C4—224no—
801C22⋊C4—224no—
802C22⋊C4—222no—
803C22⋊C4—222no—
804C42—112no—
805C42—112no—
806C42—222no—
807C42—222no—
808C11#6157011yescharacteristic, complemented, Sylow
809C23—22no—
810C23—22no—
811C23—41no—
812C23—41no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—112no—
817C23—114no—
818C23—224no—
819C23—222no—
820C23—441no—
821C23—441no—
822C23—442no—
823C23—448no—
824C23—448no—
825C23—442no—
826C23—884no—
827C23—8816no—
828C23C2×D4×D1111yescharacteristic
829C23C2×D4×D1111yescharacteristic
830C23C2×D4×D1111yescharacteristic
831Q8—24no—
832Q8—81no—
833Q8—224no—
834Q8—222no—
835Q8—222no—
836Q8—442no—
837Q8—881no—
838Q8—882no—
839Q8—882no—
840D4—24no—
841D4—42no—
842D4—82no—
843D4—82no—
844D4—114no—
845D4—224no—
846D4—224no—
847D4—224no—
848D4—222no—
849D4—448no—
850D4—444no—
851D4—444no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—81no—
863C2×C4—81no—
864C2×C4—112no—
865C2×C4—112no—
866C2×C4—112no—
867C2×C4—222no—
868C2×C4—224no—
869C2×C4—222no—
870C2×C4—222no—
871C2×C4—222no—
872C2×C4—442no—
873C2×C4—444no—
874C2×C4—444no—
875C2×C4—441no—
876C2×C4—441no—
877C2×C4—442no—
878C2×C4—884no—
879C2×C4—882no—
880C2×C4—882no—
881C2×C4—881no—
882C2×C4—881no—
883C2×C4C2×D4×D1111yescharacteristic
884C2×C4C2×D4×D1111yescharacteristic
885C2×C4C2×D4×D1111yescharacteristic
886C2×C4C24×D1111yescharacteristic
887C8—24no—
888C8—224no—
889C22—21no—
890C22—21no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—82no—
901C22—84no—
902C22—114no—
903C22—222no—
904C22—222no—
905C22—224no—
906C22—444no—
907C22—448no—
908C22—442no—
909C22—442no—
910C22—8816no—
911C22D11×#13712yes—
912C22C22×D4×D1111yescharacteristic
913C4—21no—
914C4—21no—
915C4—21no—
916C4—42no—
917C4—42no—
918C4—42no—
919C4—222no—
920C4—222no—
921C4—222no—
922C4—442no—
923C4—442no—
924C4—442no—
925C4D11×H(5,𝔽2)12yes—
926C2—22no—
927C2—41no—
928C2—41no—
929C2—82no—
930C2—224no—
931C2—444no—
932C2#1308224811yescharacteristic
933C2C2×D11×#13711yescharacteristic
934C2#1308339211yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3193C2
socleC22×C11C23×D4
prime radicalC2×#10623143C2
hypercenter#3193D11
hypocenterC11#61570
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3193

Complements

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

NH ≅ G/Ntype
1. #13082412C2semidirect
3. #13080700C2semidirect
4. #13080692C2semidirect
5. #13080133C2semidirect
6. #13080129C2semidirect
7. #13079616C2semidirect
8. #13079422C2semidirect
9. #13079390C2semidirect
10. #13078712C2semidirect
11. #13077878C2semidirect
12. #13077874C2semidirect
13. D11×#450C2semidirect
14. #13077643C2semidirect
15. C11×#3193C2semidirect
18. C2×C11×C22⋊Q8C22semidirect
20. Q8×C22⋊D11C22semidirect
21. C2×#66995C22semidirect
26. C2×#66977C22semidirect
27. C2×SD16×D11C22semidirect
28. C2×#66962C22semidirect
30. #10623166C22semidirect
32. #10623163C22semidirect
35. #10623153C22semidirect
41. #10623042C22semidirect
48. C11×#484C22semidirect
49. C11×#480C22semidirect
50. C11×#468C22semidirect
52. C11×#448C22semidirect
53. C11×#407C22semidirect
55. #10622820C22semidirect
56. #10622782C22semidirect
57. #10622780C22semidirect
58. #10622779C22semidirect
59. #10622746C22semidirect
60. #10622740C22semidirect
61. #10622663C22semidirect
62. #10622660C22semidirect
64. #10622655C22semidirect
65. #10622653C22semidirect
66. #10622646C22semidirect
67. #10622583C22semidirect
68. #10622579C22semidirect
69. #10622503C22semidirect
70. #10622502C22semidirect
71. #10622500C22semidirect
72. #10622497C22semidirect
73. #10622431C22semidirect
74. #10622430C22semidirect
75. #10622426C22semidirect
76. #10622421C22semidirect
77. #10622389C22semidirect
78. D11×#102C22semidirect
79. #10622380C22semidirect
80. #10622378C22semidirect
81. #10622352C22semidirect
82. #10622346C22semidirect
84. #10622341C22semidirect
86. #10622332C22semidirect
88. C22×Q8×C11C23semidirect
109. C22×Dic22C23semidirect
111. C2×C11×M16C23semidirect
115. C11×C22⋊Q8C23semidirect
122. C2×C11×C4⋊C4C23semidirect
131. Q8×Dic11C23semidirect
133. #66997C23semidirect
134. C2×#4326C23semidirect
154. C2×C4⋊Dic11C23semidirect
160. #66977C23semidirect
164. C2×#4318C23semidirect
167. C2×Dic44C23semidirect
185. #66941C23semidirect
187. #66940C23semidirect
200. C11×#107C23semidirect
201. C11×#103C23semidirect
204. C11×C22⋊C8C23semidirect
207. C22⋊(C11⋊C8)C23semidirect
210. #66880C23semidirect
211. #66879C23semidirect
212. Dic11⋊C8C23semidirect
213. #66874C23semidirect
214. #66874C23semidirect
216. #66871C23semidirect
350. #3193D11semidirect
377. C22×D11#137semidirect
461. C2×C22⋊Q8C2×D11semidirect
473. #484C2×D11semidirect
475. #480C2×D11semidirect
478. #468C2×D11semidirect
496. #448C2×D11semidirect
506. #407C2×D11semidirect
554. C22×Q8C22×D11semidirect
578. C2×M16C22×D11semidirect
613. C22⋊Q8C22×D11semidirect
644. C2×C4⋊C4C22×D11semidirect
659. #107C22×D11semidirect
664. #103C22×D11semidirect
673. C22⋊C8C22×D11semidirect
808. C11#61570semidirect

Maximal subgroups

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

subgroupindex
#130824122
C2×#106231432
#130807002
#130806922
#130801332
#130801292
#130796162
#130794222
#130793902
#130787122
#130778782
#130778742
D11×#4502
#130776432
C11×#31932
#6157011