Finite Group Databasebeta

← #15638621

Subgroups — #15638621

Order 2816.

2578 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082450C211yesmaximal, characteristic, complemented
2C2×#10623140C211yesmaximal, characteristic, complemented
3#13080763C214yesmaximal, complemented
4#13080635C214yesmaximal, complemented
5#13080108C214yesmaximal, complemented
6#13080089C214yesmaximal, complemented
7#13079632C212yesmaximal, complemented
8#13079429C212yesmaximal, complemented
9#13079373C211yesmaximal, characteristic, complemented
10#13078751C212yesmaximal, complemented
11#13077840C212yesmaximal, complemented
12C2×#10622344C211yesmaximal, characteristic, complemented
13C2×#10622649C211yesmaximal, characteristic, complemented
14#13077642C211yesmaximal, characteristic, complemented
15C11×#3186C211yesmaximal, characteristic, complemented
16C22×D4×D11—21no—
17C22×D4×D11C2211yescharacteristic, complemented
18C23×D44C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic, complemented
21#10623337C2212yescomplemented
22#10623335—21no—
23C2×#66993C2211yescharacteristic, complemented
24C2×#66990—21no—
25#10623329—21no—
26C22×#4323C2212yescomplemented
27C2×C4×C22⋊D11C2211yescharacteristic
28C2×#66977C2211yescharacteristic, complemented
29C2×#66964C2214yescomplemented
30C22×#4314C2212yescomplemented
31#10623149C2212yescomplemented
32#10623148—21no—
33#10623140—22no—
34#10623140—22no—
35#10623140C2214yes—
36#10623140C2214yescomplemented
37#10623137C2212yescomplemented
38#10623133—21no—
39#10623132—22no—
40#10623131C2212yescomplemented
41#10623129C2212yescomplemented
42#10623044C2212yescomplemented
43C2×#66948C2211yescharacteristic, complemented
44C2×#66946C2211yescharacteristic, complemented
45#10623026—22no—
46C2×#66937—21no—
47C2×#66935—21no—
48C11×#480C2212yescomplemented
49C11×#480C2212yescomplemented
50C11×#466C2214yescomplemented
51C11×#447C2212yescomplemented
52C11×#447C2212yescomplemented
53C2×C11×C22⋊C8C2211yescharacteristic, complemented
54#10622831C2212yescomplemented
55C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
56#10622769C2214yescomplemented
57#10622767C2214yescomplemented
58#10622763C2214yescomplemented
59C2×#66885C2212yescomplemented
60#10622724C2214yescomplemented
61#10622654C2214yescomplemented
62#10622653C2212yescomplemented
63#10622649C2212yes—
64#10622649C2214yescomplemented
65#10622649C2212yescomplemented
66#10622647C2212yescomplemented
67#10622584C2212yescomplemented
68C2×#66873C2212yescomplemented
69#10622504C2214yescomplemented
70#10622502C2214yescomplemented
71#10622499C2214yescomplemented
72#10622498C2214yescomplemented
73#10622400C2214yescomplemented
74#10622398C2214yescomplemented
75#10622395C2214yescomplemented
76#10622394C2214yescomplemented
77#10622389C2214yescomplemented
78#10622383C2214yescomplemented
79#10622377C2214yescomplemented
80#10622375C2214yescomplemented
81#10622344C2212yescomplemented
82#10622344C2214yescomplemented
83#10622344C2212yescomplemented
84#10622343C2214yescomplemented
85#10622339C2212yescomplemented
86#10622332C2212yescomplemented
87C24×D11—21no—
88C24×D11—21no—
89C22×D4×C11—21no—
90C22×D4×C11—21no—
91C22×D4×C11C2311yescharacteristic
92C22×D4×C11C2311yescharacteristic, complemented
93C23×C4×C11C2311yescharacteristic
94C22×C22⋊D11—21no—
95C22×C22⋊D11—21no—
96C22×C22⋊D11—21no—
97C22×C22⋊D11D411yescharacteristic
98C2×#4341C2312yescomplemented
99C2×D4×D11—24no—
100C2×D4×D11—24no—
101C2×D4×D11—22no—
102C2×D4×D11—44no—
103C2×D4×D11—48no—
104C2×D4×D11C2314yes—
105C22×D44—21no—
106C22×D44—21no—
107C22×D44—21no—
108C22×D44—21no—
109C22×D44—44no—
110C22×D44C2311yescharacteristic
111C22×D44C2312yes—
112C22×D44C2312yes—
113C22×D44C2311yescharacteristic
114C22×C4×D11—21no—
115C22×C4×D11C2311yescharacteristic
116C22×Dic22C2311yescharacteristic, complemented
117C2×C11×D8C2314yescomplemented
118C22×C8×C11C2312yescomplemented
119C11×#121—21no—
120C11×#121—21no—
121C11×#121—21no—
122C11×#121—21no—
123C11×#121C2312yes—
124C11×#121C2312yes—
125C11×#121C2312yes—
126C11×#121C2312yescomplemented
127C2×C11×C4⋊C4C2311yescharacteristic
128C2×C11×C4⋊C4C2311yescharacteristic, complemented
129C2×C11×C22⋊C4—21no—
130C2×C11×C22⋊C4—21no—
131#67006—22no—
132C2×C22⋊Dic11—21no—
133C2×C22⋊Dic11—22no—
134C2×C22⋊Dic11D411yescharacteristic
135#66993—22no—
136#66993C2314yes—
137#66992—22no—
138#66992—22no—
139#66992—22no—
140#66991C2312yescomplemented
141#66990—22no—
142#66990—24no—
143#66990—24no—
144#66989C2312yescomplemented
145#66988—22no—
146#66988—22no—
147D4×Dic11—22no—
148D4×Dic11—22no—
149D4×Dic11—22no—
150D4×Dic11—22no—
151D4×Dic11C2312yescomplemented
152C2×#4324C2314yescomplemented
153C2×#4323—44no—
154C2×#4323C2314yes—
155C2×#4323C2314yescomplemented
156#66982—22no—
157C4×C22⋊D11D412yes—
158C4×C22⋊D11D412yes—
159C4×C22⋊D11C2312yes—
160C4×C22⋊D11C2312yes—
161C2×(C2×D11)⋊C4—21no—
162C2×(C2×D11)⋊C4—21no—
163C2×(C2×D11)⋊C4D411yescharacteristic
164#66979—22no—
165C2×C4⋊Dic11C2311yescharacteristic, complemented
166#66977—21no—
167#66977—21no—
168#66977C2312yes—
169#66977C2312yescomplemented
170C2×Dic11⋊C4—21no—
171C2×Dic11⋊C4D411yescharacteristic
172C2×C4×Dic11C2311yescharacteristic
173C22×C11⋊C8C2312yescomplemented
174#66964—48no—
175C2×#4314—44no—
176C2×#4314C2314yes—
177C2×#4314C2314yescomplemented
178C2×#4313C2314yescomplemented
179#66951—22no—
180#66950C2312yescomplemented
181#66948—22no—
182#66948C2314yes—
183#66946—22no—
184#66946C2314yes—
185#66945C2312yescomplemented
186#66943C2312yescomplemented
187#66942—22no—
188#66940C2312yescomplemented
189#66939—22no—
190#66938—22no—
191#66937—24no—
192#66937—24no—
193#66936—22no—
194#66935—24no—
195#66935—24no—
196(C22⋊D11)⋊C4—22no—
197#66932—22no—
198#66932—22no—
199#66931—22no—
200#66930—22no—
201C11×#107C2314yescomplemented
202C11×#102C2314yescomplemented
203C11×#102C2314yescomplemented
204C11×C22⋊C8C2312yes—
205C11×C22⋊C8C2312yescomplemented
206#66896C2314yescomplemented
207C22⋊(C11⋊C8)C2312yes—
208C22⋊(C11⋊C8)C2312yescomplemented
209#66885C2314yes—
210#66885C2314yescomplemented
211(C2×D11)⋊C8C2314yescomplemented
212#66879C2314yescomplemented
213Dic11⋊C8C2314yescomplemented
214#66874C2314yescomplemented
215#66873C2314yes—
216#66873C2314yescomplemented
217#66872C2314yescomplemented
218#61571—111nomaximal, Sylow
219C24×C11—21no—
220C24×C11—21no—
221C24×C11C2×D411yescharacteristic
222C23×D11—21no—
223C23×D11—21no—
224C23×D11—22no—
225C23×D11—22no—
226C23×D11—24no—
227C23×D11—44no—
228C23×D11—44no—
229C23×D11—44no—
230C23×D11—44no—
231C23×D11—82no—
232C23×D11—82no—
233C23×D11C2×D411yescharacteristic
234C2×D4×C11—22no—
235C2×D4×C11—22no—
236C2×D4×C11—22no—
237C2×D4×C11—22no—
238C2×D4×C11—21no—
239C2×D4×C11—21no—
240C2×D4×C11—42no—
241C2×D4×C11—42no—
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—24no—
257C2×C22⋊D11—24no—
258C2×C22⋊D11—24no—
259C2×C22⋊D11—22no—
260C2×C22⋊D11—22no—
261C2×C22⋊D11—44no—
262C2×C22⋊D11—44no—
263C2×C22⋊D11—82no—
264C2×C22⋊D11C2×D412yes—
265C2×C22⋊D11C2×D412yes—
266C22×Dic11—22no—
267C22×Dic11—22no—
268C22×Dic11—21no—
269C22×Dic11—21no—
270C22×Dic11C2×D411yescharacteristic
271C22×Dic11C2×D411yescharacteristic
272C22×Dic11C2×D411yescharacteristic
273#4341—44no—
274D4×D11—28no—
275D4×D11—44no—
276D4×D11—48no—
277D4×D11—416no—
278D4×D11—416no—
279C2×D44—24no—
280C2×D44—24no—
281C2×D44—24no—
282C2×D44—24no—
283C2×D44—21no—
284C2×D44—22no—
285C2×D44—22no—
286C2×D44—21no—
287C2×D44—42no—
288C2×D44—42no—
289C2×D44—42no—
290C2×D44—44no—
291C2×D44—44no—
292C2×D44—44no—
293C2×D44—44no—
294C2×D44C2412yes—
295C2×D44C2412yes—
296C2×C4×D11—24no—
297C2×C4×D11—42no—
298C2×C4×D11—44no—
299C2×C4×D11C2×D412yes—
300C2×C4×D11C2412yes—
301C2×Dic22—21no—
302C2×Dic22—42no—
303C2×Dic22C2412yes—
304C11×D8—44no—
305C2×C8×C11—42no—
306C2×C8×C11C2414yes—
307C11×C4⋊C4—21no—
308C11×C4⋊C4—21no—
309C11×C4⋊C4C2412yes—
310C11×C4⋊C4C2412yes—
311C11×C22⋊C4—22no—
312C11×C22⋊C4—22no—
313C11×C22⋊C4—22no—
314C11×C22⋊C4—22no—
315C22⋊Dic11—22no—
316C22⋊Dic11—22no—
317C22⋊Dic11—22no—
318C22⋊Dic11—22no—
319C22⋊Dic11—22no—
320C22⋊Dic11—22no—
321C22⋊Dic11C2×D412yes—
322C22⋊Dic11C2×D412yes—
323#4324—44no—
324#4323—28no—
325#4323—44no—
326(C2×D11)⋊C4—24no—
327(C2×D11)⋊C4—24no—
328(C2×D11)⋊C4—22no—
329(C2×D11)⋊C4—22no—
330(C2×D11)⋊C4C2×D412yes—
331(C2×D11)⋊C4C2×D412yes—
332C4⋊Dic11—22no—
333C4⋊Dic11—22no—
334C4⋊Dic11—21no—
335C4⋊Dic11C2412yes—
336Dic11⋊C4—22no—
337Dic11⋊C4—22no—
338Dic11⋊C4—22no—
339Dic11⋊C4—22no—
340Dic11⋊C4C2×D412yes—
341Dic11⋊C4C2×D412yes—
342C4×Dic11—22no—
343C4×Dic11—22no—
344C4×Dic11C2×D412yes—
345C4×Dic11C2412yes—
346C2×C11⋊C8—42no—
347C2×C11⋊C8C2414yes—
348#4314—28no—
349#4314—44no—
350#4313—44no—
351#3505—111no—
352C2×D42—111no—
353#3318—114no—
354#3310—114no—
355#3265—114no—
356#3264—114no—
357#3217—112no—
358#3194—112no—
359#3187—111no—
360#3186D1111yescharacteristic, complemented
361#3114—112no—
362#3003—112no—
363C2×#450—111no—
364C2×#447—111no—
365#2973—111no—
366C23×C11—22no—
367C23×C11—22no—
368C23×C11—41no—
369C23×C11—41no—
370C23×C11—42no—
371C23×C11—42no—
372C23×C11—42no—
373C23×C11—42no—
374C23×C11—81no—
375C23×C11—81no—
376C23×C11AGL(1,ℤ/8)14yescomplemented
377C23×C11C22×D411yescharacteristic
378C23×C11C22×D411yescharacteristic
379C23×C11C22×D411yescharacteristic
380C22×D11—24no—
381C22×D11—22no—
382C22×D11—22no—
383C22×D11—22no—
384C22×D11—41no—
385C22×D11—41no—
386C22×D11—48no—
387C22×D11—44no—
388C22×D11—44no—
389C22×D11—48no—
390C22×D11—42no—
391C22×D11—42no—
392C22×D11—42no—
393C22×D11—42no—
394C22×D11—42no—
395C22×D11—44no—
396C22×D11—44no—
397C22×D11—84no—
398C22×D11—82no—
399C22×D11—82no—
400C22×D11—816no—
401C22×D11—816no—
402C22×D11C22×D412yes—
403D4×C11—24no—
404D4×C11—24no—
405D4×C11—42no—
406D4×C11—44no—
407D4×C11—44no—
408D4×C11—44no—
409D4×C11—44no—
410D4×C11—81no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—41no—
417C2×C4×C11—41no—
418C2×C4×C11—41no—
419C2×C4×C11—42no—
420C2×C4×C11—42no—
421C2×C4×C11C22×D411yescharacteristic
422C2×C4×C11C22×D411yescharacteristic
423C2×C4×C11C22×D411yescharacteristic
424C2×C4×C11C2511yescharacteristic
425C22⋊D11—24no—
426C22⋊D11—24no—
427C22⋊D11—48no—
428C22⋊D11—48no—
429C22⋊D11—84no—
430C22⋊D11—82no—
431C22⋊D11—82no—
432C2×Dic11—22no—
433C2×Dic11—22no—
434C2×Dic11—22no—
435C2×Dic11—41no—
436C2×Dic11—41no—
437C2×Dic11—82no—
438C2×Dic11—82no—
439C2×Dic11—81no—
440C2×Dic11—81no—
441C2×Dic11C22×D412yes—
442C2×Dic11C22×D412yes—
443C2×Dic11C22×D412yes—
444D44—24no—
445D44—22no—
446D44—22no—
447D44—22no—
448D44—44no—
449D44—44no—
450D44—42no—
451D44—48no—
452D44H(5,𝔽2)14yes—
453C4×D11—24no—
454C4×D11—42no—
455C4×D11—48no—
456Dic22—24no—
457Dic22—81no—
458C8×C11—24no—
459C11⋊C8—24no—
460C23×D4—111no—
461C23×D4—111no—
462C23×D4—221no—
463C2×AGL(1,ℤ/8)—114no—
464C22×SD16—112no—
465C22×D8—112no—
466#553—112no—
467#553—222no—
468#552—112no—
469#551—222no—
470#548—112no—
471#546—112no—
472D42—114no—
473D42—114no—
474D42—222no—
475D42—222no—
476#539—221no—
477#538—221no—
478#534—221no—
479C2×#127—111no—
480#529—112no—
481#525—112no—
482C2×C22⋊Q8—111no—
483C2×#121—111no—
484C2×#121—221no—
485C2×#121C2×D1111yescharacteristic
486C2×#121C2×D1111yescharacteristic, complemented
487C2×#120—221no—
488C2×#120—221no—
489#518—221no—
490C2×C4×D4—111no—
491C2×C4×D4—111no—
492#496—114no—
493#490—114no—
494#483—112no—
495#482—114no—
496#481—112no—
497#480C2×D1112yescomplemented
498#480C2×D1112yescomplemented
499#478—114no—
500#469—114no—
501#468—114no—
502#466C2×D1114yescomplemented
503#465—114no—
504#463—114no—
505#460—114no—
506#459—114no—
507#450—112no—
508#450—114no—
509#450—112no—
510#450—112no—
511#450—114no—
512#449—114no—
513#448—112no—
514#447—114no—
515#447—112no—
516#447—112no—
517#447—114no—
518#447C2×D1112yescomplemented
519#447C2×D1112yescomplemented
520#442—114no—
521#440—114no—
522#435—114no—
523#435—114no—
524#432—112no—
525#418—114no—
526C2×#102—112no—
527C2×#102—112no—
528#407—112no—
529C2×C22⋊C8—111no—
530C2×C22⋊C8C2×D1111yescharacteristic, complemented
531C22×C11—21no—
532C22×C11—21no—
533C22×C11—21no—
534C22×C11—21no—
535C22×C11—21no—
536C22×C11—21no—
537C22×C11—44no—
538C22×C11—42no—
539C22×C11—42no—
540C22×C11—42no—
541C22×C11—42no—
542C22×C11—42no—
543C22×C11—42no—
544C22×C11—84no—
545C22×C11—162no—
546C22×C11C2×AGL(1,ℤ/8)12yes—
547C22×C11C2×AGL(1,ℤ/8)12yes—
548C22×C11C2×AGL(1,ℤ/8)12yes—
549C22×C11C23×D411yescharacteristic
550C2×D11—22no—
551C2×D11—24no—
552C2×D11—22no—
553C2×D11—22no—
554C2×D11—44no—
555C2×D11—48no—
556C2×D11—42no—
557C2×D11—42no—
558C2×D11—42no—
559C2×D11—42no—
560C2×D11—42no—
561C2×D11—816no—
562C2×D11—88no—
563C2×D11—88no—
564C2×D11—84no—
565C4×C11—21no—
566C4×C11—21no—
567C4×C11—21no—
568C4×C11—42no—
569C4×C11—42no—
570C4×C11C2×H(5,𝔽2)12yes—
571Dic11—22no—
572Dic11—22no—
573Dic11—22no—
574Dic11—42no—
575Dic11—42no—
576C25—221no—
577C25—221no—
578C2×#41—112no—
579C22×Q8—111no—
580C22×D4—21no—
581C22×D4—21no—
582C22×D4—111no—
583C22×D4—114no—
584C22×D4—111no—
585C22×D4—112no—
586C22×D4—112no—
587C22×D4—111no—
588C22×D4—221no—
589C22×D4—222no—
590C22×D4—221no—
591C22×D4—221no—
592C22×D4—221no—
593C22×D4—224no—
594C22×D4—224no—
595C22×D4—221no—
596C22×D4—221no—
597C22×D4—221no—
598C22×D4—444no—
599C22×D4—444no—
600C22×D4—448no—
601C22×D4C22×D1111yescharacteristic
602C22×D4C22×D1111yescharacteristic, complemented
603C23×C4—111no—
604C23×C4—221no—
605C23×C4C22×D1111yescharacteristic
606AGL(1,ℤ/8)—448no—
607C2×SD16—114no—
608C2×SD16—114no—
609C2×SD16—114no—
610C2×SD16—444no—
611C2×D8—114no—
612C2×D8—114no—
613C2×D8—444no—
614C2×D8C22×D1114yescomplemented
615C2×M16—114no—
616C22×C8—112no—
617C22×C8C22×D1112yescomplemented
618#127—114no—
619#127—222no—
620#126—222no—
621#126—222no—
622#126—222no—
623#125—112no—
624#125—222no—
625#124—112no—
626#124—222no—
627#123—222no—
628#123—222no—
629#123—222no—
630#123—222no—
631#123—222no—
632C22⋊Q8—112no—
633C22⋊Q8—112no—
634C22⋊Q8—112no—
635C22⋊Q8—222no—
636C22⋊Q8—221no—
637C22⋊Q8—221no—
638#121—21no—
639#121—21no—
640#121—21no—
641#121—21no—
642#121—112no—
643#121—114no—
644#121—224no—
645#121—224no—
646#121—222no—
647#121—222no—
648#121—222no—
649#121—222no—
650#121C22×D1112yes—
651#121C22×D1112yes—
652#121C22×D1112yes—
653#121C22×D1112yescomplemented
654#120—224no—
655#120—224no—
656#120—224no—
657#120—224no—
658#120—222no—
659#120—222no—
660C4×Q8—112no—
661C4×D4—112no—
662C4×D4—112no—
663C4×D4—112no—
664C4×D4—112no—
665C4×D4—112no—
666C4×D4—114no—
667C4×D4—222no—
668C4×D4—222no—
669C4×D4—222no—
670C4×D4—222no—
671C4×D4—222no—
672C4×D4—222no—
673#117—112no—
674#117—222no—
675#117—222no—
676C2×C4⋊C4—111no—
677C2×C4⋊C4—111no—
678C2×C4⋊C4—221no—
679C2×C4⋊C4C22×D1111yescharacteristic
680C2×C4⋊C4C22×D1111yescharacteristic, complemented
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—111no—
684C2×C22⋊C4—111no—
685C2×C22⋊C4—222no—
686C2×C22⋊C4—221no—
687C2×C22⋊C4—221no—
688C2×C22⋊C4—221no—
689C2×C42—111no—
690#107C22×D1114yescomplemented
691#106—114no—
692C4⋊C8—114no—
693#103—114no—
694#102—114no—
695#102—114no—
696#102—114no—
697#102—114no—
698#102—114no—
699#102C22×D1114yescomplemented
700#102C22×D1114yescomplemented
701C22⋊C8—112no—
702C22⋊C8—112no—
703C22⋊C8—114no—
704C22⋊C8C22×D1112yes—
705C22⋊C8C22×D1112yescomplemented
706#97—114no—
707C2×C11—22no—
708C2×C11—22no—
709C2×C11—22no—
710C2×C11—82no—
711C2×C11—82no—
712C2×C11#348411yescharacteristic
713C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
714C2×C11#358511yescharacteristic
715D11—42no—
716D11—44no—
717D11—82no—
718C24—21no—
719C24—21no—
720C24—111no—
721C24—224no—
722C24—221no—
723C24—221no—
724C24—222no—
725C24—222no—
726C24—444no—
727C24—444no—
728C24—444no—
729C24—444no—
730C24—882no—
731C24—882no—
732C24D4×D1111yescharacteristic
733#41—444no—
734C2×Q8—112no—
735C2×Q8—221no—
736C2×Q8—442no—
737C2×D4—22no—
738C2×D4—22no—
739C2×D4—22no—
740C2×D4—22no—
741C2×D4—21no—
742C2×D4—21no—
743C2×D4—42no—
744C2×D4—42no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—112no—
748C2×D4—112no—
749C2×D4—112no—
750C2×D4—112no—
751C2×D4—224no—
752C2×D4—224no—
753C2×D4—224no—
754C2×D4—224no—
755C2×D4—224no—
756C2×D4—224no—
757C2×D4—224no—
758C2×D4—228no—
759C2×D4—224no—
760C2×D4—222no—
761C2×D4—222no—
762C2×D4—221no—
763C2×D4—222no—
764C2×D4—222no—
765C2×D4—221no—
766C2×D4—442no—
767C2×D4—442no—
768C2×D4—442no—
769C2×D4—444no—
770C2×D4—444no—
771C2×D4—444no—
772C2×D4—444no—
773C2×D4—444no—
774C2×D4—444no—
775C2×D4—448no—
776C2×D4—4416no—
777C2×D4—4416no—
778C2×D4—444no—
779C2×D4—882no—
780C2×D4C23×D1112yes—
781C2×D4C23×D1112yes—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—42no—
785C22×C4—111no—
786C22×C4—111no—
787C22×C4—111no—
788C22×C4—112no—
789C22×C4—112no—
790C22×C4—224no—
791C22×C4—222no—
792C22×C4—222no—
793C22×C4—221no—
794C22×C4—221no—
795C22×C4—442no—
796C22×C4—444no—
797C22×C4D4×D1111yescharacteristic
798C22×C4D4×D1111yescharacteristic
799C22×C4D4×D1111yescharacteristic
800C22×C4C23×D1111yescharacteristic
801C22×C4C23×D1111yescharacteristic
802C22×C4C23×D1111yescharacteristic
803SD16—228no—
804SD16—444no—
805SD16—444no—
806D8—44no—
807D8—228no—
808D8—444no—
809M16—444no—
810C2×C8—42no—
811C2×C8—114no—
812C2×C8—442no—
813C2×C8C23×D1114yes—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—112no—
817C4⋊C4—112no—
818C4⋊C4—112no—
819C4⋊C4—222no—
820C4⋊C4—222no—
821C4⋊C4—222no—
822C4⋊C4—222no—
823C4⋊C4—221no—
824C4⋊C4—222no—
825C4⋊C4—222no—
826C4⋊C4C23×D1112yes—
827C4⋊C4C23×D1112yes—
828C22⋊C4—22no—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—22no—
832C22⋊C4—112no—
833C22⋊C4—112no—
834C22⋊C4—112no—
835C22⋊C4—112no—
836C22⋊C4—224no—
837C22⋊C4—224no—
838C22⋊C4—222no—
839C22⋊C4—222no—
840C22⋊C4—222no—
841C22⋊C4—222no—
842C22⋊C4—222no—
843C22⋊C4—222no—
844C22⋊C4—222no—
845C22⋊C4—222no—
846C42—112no—
847C42—112no—
848C42—222no—
849C42—222no—
850C11#6157111yescharacteristic, complemented, Sylow
851C23—22no—
852C23—22no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—81no—
860C23—81no—
861C23—112no—
862C23—224no—
863C23—222no—
864C23—222no—
865C23—222no—
866C23—441no—
867C23—441no—
868C23—444no—
869C23—444no—
870C23—442no—
871C23—442no—
872C23—442no—
873C23—448no—
874C23—448no—
875C23—442no—
876C23—444no—
877C23—444no—
878C23—442no—
879C23—882no—
880C23—882no—
881C23—884no—
882C23—8816no—
883C23—8816no—
884C23#6696414yescomplemented
885C23C2×D4×D1111yescharacteristic
886C23C2×D4×D1111yescharacteristic
887C23C2×D4×D1111yescharacteristic
888Q8—224no—
889Q8—881no—
890D4—24no—
891D4—24no—
892D4—42no—
893D4—44no—
894D4—44no—
895D4—44no—
896D4—44no—
897D4—81no—
898D4—114no—
899D4—224no—
900D4—224no—
901D4—224no—
902D4—222no—
903D4—222no—
904D4—222no—
905D4—444no—
906D4—444no—
907D4—442no—
908D4—448no—
909D4—448no—
910D4—448no—
911D4—884no—
912D4—882no—
913D4—882no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—42no—
923C2×C4—42no—
924C2×C4—112no—
925C2×C4—112no—
926C2×C4—112no—
927C2×C4—222no—
928C2×C4—224no—
929C2×C4—222no—
930C2×C4—222no—
931C2×C4—442no—
932C2×C4—448no—
933C2×C4—441no—
934C2×C4—441no—
935C2×C4—882no—
936C2×C4—882no—
937C2×C4—881no—
938C2×C4—881no—
939C2×C4C2×D4×D1111yescharacteristic
940C2×C4C2×D4×D1111yescharacteristic
941C2×C4C2×D4×D1111yescharacteristic
942C2×C4C24×D1111yescharacteristic
943C8—24no—
944C8—224no—
945C22—21no—
946C22—21no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—44no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—84no—
959C22—162no—
960C22—222no—
961C22—222no—
962C22—224no—
963C22—222no—
964C22—444no—
965C22—448no—
966C22—442no—
967C22—442no—
968C22—442no—
969C22—442no—
970C22—442no—
971C22—888no—
972C22—888no—
973C22—884no—
974C22—8816no—
975C22C2×#6696412yes—
976C22C2×#6696412yes—
977C22C2×#6696412yes—
978C22C22×D4×D1111yescharacteristic
979C4—21no—
980C4—21no—
981C4—21no—
982C4—42no—
983C4—42no—
984C4—222no—
985C4—222no—
986C4—222no—
987C4—442no—
988C4—442no—
989C4D11×H(5,𝔽2)12yes—
990C2—22no—
991C2—22no—
992C2—22no—
993C2—82no—
994C2—82no—
995C2—442no—
996C2—444no—
997C2—882no—
998C2#1308224811yescharacteristic
999C2C22×#6696411yescharacteristic
1000C2#1308339311yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3186C2
socleC22×C11C23×D4
hypercenter#3186D11
hypocenterC11#61571
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3186

Complements

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

NH ≅ G/Ntype
1. #13082450C2semidirect
2. C2×#10623140C2semidirect
3. #13080763C2semidirect
4. #13080635C2semidirect
5. #13080108C2semidirect
6. #13080089C2semidirect
7. #13079632C2semidirect
8. #13079429C2semidirect
9. #13079373C2semidirect
10. #13078751C2semidirect
11. #13077840C2semidirect
12. C2×#10622344C2semidirect
13. C2×#10622649C2semidirect
14. #13077642C2semidirect
15. C11×#3186C2semidirect
17. C22×D4×D11C22semidirect
20. C2×C11×#121C22semidirect
21. #10623337C22semidirect
23. C2×#66993C22semidirect
26. C22×#4323C22semidirect
28. C2×#66977C22semidirect
29. C2×#66964C22semidirect
30. C22×#4314C22semidirect
31. #10623149C22semidirect
36. #10623140C22semidirect
37. #10623137C22semidirect
40. #10623131C22semidirect
41. #10623129C22semidirect
42. #10623044C22semidirect
43. C2×#66948C22semidirect
44. C2×#66946C22semidirect
48. C11×#480C22semidirect
49. C11×#480C22semidirect
50. C11×#466C22semidirect
51. C11×#447C22semidirect
52. C11×#447C22semidirect
53. C2×C11×C22⋊C8C22semidirect
54. #10622831C22semidirect
55. C2×C22⋊(C11⋊C8)C22semidirect
56. #10622769C22semidirect
57. #10622767C22semidirect
58. #10622763C22semidirect
59. C2×#66885C22semidirect
60. #10622724C22semidirect
61. #10622654C22semidirect
62. #10622653C22semidirect
64. #10622649C22semidirect
65. #10622649C22semidirect
66. #10622647C22semidirect
67. #10622584C22semidirect
68. C2×#66873C22semidirect
69. #10622504C22semidirect
70. #10622502C22semidirect
71. #10622499C22semidirect
72. #10622498C22semidirect
73. #10622400C22semidirect
74. #10622398C22semidirect
75. #10622395C22semidirect
76. #10622394C22semidirect
77. #10622389C22semidirect
78. #10622383C22semidirect
79. #10622377C22semidirect
80. #10622375C22semidirect
81. #10622344C22semidirect
82. #10622344C22semidirect
83. #10622344C22semidirect
84. #10622343C22semidirect
85. #10622339C22semidirect
86. #10622332C22semidirect
92. C22×D4×C11C23semidirect
98. C2×#4341C23semidirect
116. C22×Dic22C23semidirect
117. C2×C11×D8C23semidirect
118. C22×C8×C11C23semidirect
126. C11×#121C23semidirect
128. C2×C11×C4⋊C4C23semidirect
140. #66991C23semidirect
144. #66989C23semidirect
151. D4×Dic11C23semidirect
152. C2×#4324C23semidirect
155. C2×#4323C23semidirect
165. C2×C4⋊Dic11C23semidirect
169. #66977C23semidirect
173. C22×C11⋊C8C23semidirect
177. C2×#4314C23semidirect
178. C2×#4313C23semidirect
180. #66950C23semidirect
185. #66945C23semidirect
186. #66943C23semidirect
188. #66940C23semidirect
201. C11×#107C23semidirect
202. C11×#102C23semidirect
203. C11×#102C23semidirect
205. C11×C22⋊C8C23semidirect
206. #66896C23semidirect
208. C22⋊(C11⋊C8)C23semidirect
210. #66885C23semidirect
211. (C2×D11)⋊C8C23semidirect
212. #66879C23semidirect
213. Dic11⋊C8C23semidirect
214. #66874C23semidirect
216. #66873C23semidirect
217. #66872C23semidirect
360. #3186D11semidirect
376. C23×C11AGL(1,ℤ/8)semidirect
486. C2×#121C2×D11semidirect
497. #480C2×D11semidirect
498. #480C2×D11semidirect
502. #466C2×D11semidirect
518. #447C2×D11semidirect
519. #447C2×D11semidirect
530. C2×C22⋊C8C2×D11semidirect
602. C22×D4C22×D11semidirect
614. C2×D8C22×D11semidirect
617. C22×C8C22×D11semidirect
653. #121C22×D11semidirect
680. C2×C4⋊C4C22×D11semidirect
690. #107C22×D11semidirect
699. #102C22×D11semidirect
700. #102C22×D11semidirect
705. C22⋊C8C22×D11semidirect
850. C11#61571semidirect
884. C23#66964semidirect

Maximal subgroups

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

subgroupindex
#130824502
C2×#106231402
#130807632
#130806352
#130801082
#130800892
#130796322
#130794292
#130793732
#130787512
#130778402
C2×#106223442
C2×#106226492
#130776422
C11×#31862
#6157111