Finite Group Databasebeta

← #15638618

Subgroups — #15638618

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×D4×C22⋊D11C211yesmaximal, characteristic, complemented
3#13080761C214yesmaximal, complemented
4#13080633C214yesmaximal, complemented
5#13080115C214yesmaximal, complemented
6#13080096C214yesmaximal, complemented
7#13079632C212yesmaximal, complemented
8#13079427C212yesmaximal, complemented
9#13079374C211yesmaximal, characteristic, complemented
10#13079364C211yesmaximal, characteristic, complemented
11#13078749C212yesmaximal, complemented
12#13077840C212yesmaximal, complemented
13C2×#10622831C211yesmaximal, characteristic, complemented
14#13077642C211yesmaximal, characteristic, complemented
15C2×C11×#447C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C23×C22⋊D11—21no—
18C22×D4×D11C2211yescharacteristic, complemented
19C22×C11×D8C2212yescomplemented
20C2×C11×#121C2211yescharacteristic, complemented
21C2×#67006—21no—
22#10623337C2212yescomplemented
23#10623335—21no—
24C2×#66993C2211yescharacteristic, complemented
25C2×#66992—21no—
26D4×C22⋊D11—22no—
27D4×C22⋊D11—22no—
28D4×C22⋊D11C2214yes—
29D4×C22⋊D11C2214yescomplemented
30C2×#66991C2211yescharacteristic, complemented
31C2×#66990—21no—
32#10623329—21no—
33C2×D4×Dic11C2211yescharacteristic, complemented
34C22×#4324C2212yescomplemented
35C2×#66983C2211yescharacteristic
36C2×C4×C22⋊D11C2211yescharacteristic
37C2×#66977C2211yescharacteristic, complemented
38C2×#66964C2214yescomplemented
39#10623149C2212yescomplemented
40#10623148—21no—
41#10623137C2212yescomplemented
42#10623133—21no—
43#10623132—22no—
44#10623131C2212yescomplemented
45#10623129C2212yescomplemented
46#10623044C2212yescomplemented
47#10623026—22no—
48C11×#447C2212yes—
49C11×#447C2212yescomplemented
50C11×#447C2214yescomplemented
51C2×C11×#102C2212yescomplemented
52C2×C11×C22⋊C8C2211yescharacteristic, complemented
53#10622831C2212yescomplemented
54#10622831C2212yescomplemented
55#10622831C2214yescomplemented
56#10622830C2212yescomplemented
57C2×#66896C2212yescomplemented
58C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
59#10622772C2214yescomplemented
60#10622771C2214yescomplemented
61#10622769C2214yescomplemented
62#10622767C2214yescomplemented
63#10622766C2214yescomplemented
64#10622765C2214yescomplemented
65#10622763C2214yescomplemented
66#10622727C2214yescomplemented
67#10622724C2214yescomplemented
68#10622651C2214yescomplemented
69#10622649C2212yescomplemented
70#10622646C2212yescomplemented
71#10622580C2212yescomplemented
72#10622393C2214yescomplemented
73#10622392C2214yescomplemented
74#10622389C2214yescomplemented
75#10622383C2214yescomplemented
76#10622377C2214yescomplemented
77#10622376C2214yescomplemented
78#10622375C2214yescomplemented
79#10622370C2214yescomplemented
80#10622351C2212yescomplemented
81#10622348C2212yescomplemented
82#10622344C2212yescomplemented
83#10622343C2214yescomplemented
84#10622339C2212yescomplemented
85#10622334C2212yescomplemented
86#10622332C2212yescomplemented
87C25×C11—21no—
88C24×D11—21no—
89C22×D4×C11—21no—
90C22×D4×C11—21no—
91C22×D4×C11—21no—
92C22×D4×C11—21no—
93C22×D4×C11—44no—
94C22×D4×C11C2311yescharacteristic
95C22×D4×C11C2312yes—
96C22×D4×C11C2312yes—
97C22×D4×C11C2311yescharacteristic
98C22×D4×C11C2311yescharacteristic, complemented
99C23×C4×C11C2311yescharacteristic
100C22×C22⋊D11—21no—
101C22×C22⋊D11—21no—
102C22×C22⋊D11—24no—
103C22×C22⋊D11—24no—
104C22×C22⋊D11—21no—
105C22×C22⋊D11—21no—
106C22×C22⋊D11—21no—
107C22×C22⋊D11—48no—
108C22×C22⋊D11D411yescharacteristic
109C23×Dic11—21no—
110C2×#4341C2312yescomplemented
111C2×D4×D11—22no—
112C2×D4×D11—44no—
113C2×D4×D11C2314yes—
114C22×D44C2311yescharacteristic
115C22×C4×D11C2311yescharacteristic
116C22×Dic22C2311yescharacteristic, complemented
117C2×C11×D8—44no—
118C2×C11×D8C2314yes—
119C2×C11×D8C2314yescomplemented
120C22×C8×C11C2312yescomplemented
121C11×#121—21no—
122C11×#121—21no—
123C11×#121C2312yes—
124C11×#121C2312yescomplemented
125C2×C11×C4⋊C4C2311yescharacteristic, complemented
126C2×C11×C22⋊C4—21no—
127#67006—22no—
128#67006—24no—
129#67006—24no—
130C2×C22⋊Dic11—21no—
131C2×C22⋊Dic11—21no—
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#66992—24no—
141#66992—24no—
142#66991—22no—
143#66991C2314yes—
144#66991C2312yescomplemented
145#66990—22no—
146#66990—24no—
147#66990—24no—
148#66989C2312yescomplemented
149#66988—22no—
150#66988—22no—
151D4×Dic11—22no—
152D4×Dic11—22no—
153D4×Dic11—22no—
154D4×Dic11—22no—
155D4×Dic11—22no—
156D4×Dic11C2314yes—
157D4×Dic11C2312yescomplemented
158C2×#4324—44no—
159C2×#4324C2314yes—
160C2×#4324C2314yescomplemented
161C2×#4323C2314yescomplemented
162#66983—21no—
163#66983—21no—
164#66983C2312yes—
165#66983C2312yes—
166#66982—22no—
167C4×C22⋊D11D412yes—
168C4×C22⋊D11D412yes—
169C4×C22⋊D11C2312yes—
170C4×C22⋊D11C2312yes—
171C2×(C2×D11)⋊C4—21no—
172C2×(C2×D11)⋊C4D411yescharacteristic
173#66979—22no—
174C2×C4⋊Dic11C2311yescharacteristic
175C2×C4⋊Dic11C2311yescharacteristic, complemented
176#66977—21no—
177#66977—21no—
178#66977C2312yes—
179#66977C2312yescomplemented
180C2×Dic11⋊C4—21no—
181C2×Dic11⋊C4D411yescharacteristic
182C2×C4×Dic11C2311yescharacteristic
183C22×C11⋊C8C2312yescomplemented
184#66964—48no—
185C2×#4314C2314yescomplemented
186C2×#4313C2314yescomplemented
187#66951—22no—
188#66950C2312yescomplemented
189#66945C2312yescomplemented
190#66943C2312yescomplemented
191#66942—22no—
192#66940C2312yescomplemented
193#66939—22no—
194#66938—22no—
195#66936—22no—
196(C22⋊D11)⋊C4—22no—
197#66932—22no—
198#66932—22no—
199#66931—22no—
200#66930—22no—
201C11×#102C2314yes—
202C11×#102C2314yescomplemented
203C11×C22⋊C8C2312yes—
204C11×C22⋊C8C2312yescomplemented
205#66896C2314yes—
206#66896C2314yescomplemented
207#66896C2314yescomplemented
208C22⋊(C11⋊C8)C2312yes—
209C22⋊(C11⋊C8)C2312yescomplemented
210#66885C2314yescomplemented
211(C2×D11)⋊C8C2314yescomplemented
212#66881C2314yescomplemented
213#66880C2314yescomplemented
214#66879C2314yescomplemented
215Dic11⋊C8C2314yescomplemented
216#66873C2314yescomplemented
217#66871C2314yescomplemented
218#61571—111nomaximal, Sylow
219C24×C11—21no—
220C24×C11—21no—
221C24×C11—22no—
222C24×C11—22no—
223C24×C11—21no—
224C24×C11—44no—
225C24×C11—44no—
226C24×C11—82no—
227C24×C11C2×D411yescharacteristic
228C23×D11—21no—
229C23×D11—24no—
230C23×D11—44no—
231C23×D11—44no—
232C23×D11—82no—
233C23×D11C2×D411yescharacteristic
234C2×D4×C11—24no—
235C2×D4×C11—24no—
236C2×D4×C11—24no—
237C2×D4×C11—22no—
238C2×D4×C11—22no—
239C2×D4×C11—21no—
240C2×D4×C11—22no—
241C2×D4×C11—22no—
242C2×D4×C11—21no—
243C2×D4×C11—21no—
244C2×D4×C11—42no—
245C2×D4×C11—42no—
246C2×D4×C11—42no—
247C2×D4×C11—42no—
248C2×D4×C11—44no—
249C2×D4×C11—44no—
250C2×D4×C11—44no—
251C2×D4×C11—44no—
252C2×D4×C11C2412yes—
253C2×D4×C11C2412yes—
254C2×D4×C11C2412yes—
255C22×C4×C11—21no—
256C22×C4×C11—42no—
257C22×C4×C11C2×D411yescharacteristic
258C22×C4×C11C2×D411yescharacteristic
259C22×C4×C11C2×D411yescharacteristic
260C22×C4×C11C2411yescharacteristic
261C22×C4×C11C2411yescharacteristic
262C22×C4×C11C2411yescharacteristic
263C2×C22⋊D11—24no—
264C2×C22⋊D11—24no—
265C2×C22⋊D11—24no—
266C2×C22⋊D11—24no—
267C2×C22⋊D11—22no—
268C2×C22⋊D11—22no—
269C2×C22⋊D11—24no—
270C2×C22⋊D11—22no—
271C2×C22⋊D11—22no—
272C2×C22⋊D11—44no—
273C2×C22⋊D11—44no—
274C2×C22⋊D11—44no—
275C2×C22⋊D11—416no—
276C2×C22⋊D11—416no—
277C2×C22⋊D11—44no—
278C2×C22⋊D11—82no—
279C2×C22⋊D11C2×D412yes—
280C2×C22⋊D11C2×D412yes—
281C22×Dic11—24no—
282C22×Dic11—22no—
283C22×Dic11—22no—
284C22×Dic11—21no—
285C22×Dic11—21no—
286C22×Dic11—21no—
287C22×Dic11—44no—
288C22×Dic11C2×D411yescharacteristic
289C22×Dic11C2×D411yescharacteristic
290C22×Dic11C2×D411yescharacteristic
291#4341—44no—
292D4×D11—28no—
293D4×D11—44no—
294D4×D11—48no—
295C2×D44—21no—
296C2×D44—42no—
297C2×D44C2412yes—
298C2×C4×D11—42no—
299C2×C4×D11C2×D412yes—
300C2×C4×D11C2412yes—
301C2×Dic22—21no—
302C2×Dic22—42no—
303C2×Dic22C2412yes—
304C11×D8—28no—
305C11×D8—44no—
306C2×C8×C11—42no—
307C2×C8×C11C2414yes—
308C11×C4⋊C4—21no—
309C11×C4⋊C4C2412yes—
310C11×C22⋊C4—22no—
311C11×C22⋊C4—22no—
312C22⋊Dic11—22no—
313C22⋊Dic11—22no—
314C22⋊Dic11—22no—
315C22⋊Dic11—22no—
316C22⋊Dic11—24no—
317C22⋊Dic11—24no—
318C22⋊Dic11—22no—
319C22⋊Dic11—22no—
320C22⋊Dic11C2×D412yes—
321C22⋊Dic11C2×D412yes—
322#4324—28no—
323#4324—44no—
324#4323—44no—
325(C2×D11)⋊C4—22no—
326(C2×D11)⋊C4—22no—
327(C2×D11)⋊C4—22no—
328(C2×D11)⋊C4—22no—
329(C2×D11)⋊C4C2×D412yes—
330(C2×D11)⋊C4C2×D412yes—
331C4⋊Dic11—22no—
332C4⋊Dic11—22no—
333C4⋊Dic11—21no—
334C4⋊Dic11—21no—
335C4⋊Dic11C2412yes—
336C4⋊Dic11C2412yes—
337Dic11⋊C4—22no—
338Dic11⋊C4—22no—
339Dic11⋊C4—22no—
340Dic11⋊C4—22no—
341Dic11⋊C4C2×D412yes—
342Dic11⋊C4C2×D412yes—
343C4×Dic11—22no—
344C4×Dic11—22no—
345C4×Dic11C2×D412yes—
346C4×Dic11C2412yes—
347C2×C11⋊C8—42no—
348C2×C11⋊C8C2414yes—
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#3186—111no—
361#3114—112no—
362#3003—112no—
363C2×#450—111no—
364C2×#447D1111yescharacteristic, complemented
365#2973—111no—
366C23×C11—24no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11—41no—
371C23×C11—41no—
372C23×C11—44no—
373C23×C11—44no—
374C23×C11—42no—
375C23×C11—42no—
376C23×C11—42no—
377C23×C11—42no—
378C23×C11—44no—
379C23×C11—44no—
380C23×C11—42no—
381C23×C11—42no—
382C23×C11—82no—
383C23×C11—82no—
384C23×C11—81no—
385C23×C11—81no—
386C23×C11—816no—
387C23×C11AGL(1,ℤ/8)14yescomplemented
388C23×C11C22×D411yescharacteristic
389C23×C11C22×D411yescharacteristic
390C23×C11C22×D411yescharacteristic
391C22×D11—22no—
392C22×D11—22no—
393C22×D11—41no—
394C22×D11—41no—
395C22×D11—48no—
396C22×D11—48no—
397C22×D11—42no—
398C22×D11—42no—
399C22×D11—42no—
400C22×D11—84no—
401C22×D11—816no—
402C22×D11C22×D412yes—
403D4×C11—24no—
404D4×C11—22no—
405D4×C11—24no—
406D4×C11—22no—
407D4×C11—22no—
408D4×C11—44no—
409D4×C11—44no—
410D4×C11—42no—
411D4×C11—44no—
412D4×C11—44no—
413D4×C11—81no—
414D4×C11H(5,𝔽2)14yes—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
419C2×C4×C11—41no—
420C2×C4×C11—41no—
421C2×C4×C11—41no—
422C2×C4×C11—42no—
423C2×C4×C11C22×D411yescharacteristic
424C2×C4×C11C22×D411yescharacteristic
425C2×C4×C11C22×D411yescharacteristic
426C2×C4×C11C2511yescharacteristic
427C22⋊D11—24no—
428C22⋊D11—24no—
429C22⋊D11—48no—
430C22⋊D11—48no—
431C22⋊D11—48no—
432C22⋊D11—44no—
433C22⋊D11—44no—
434C22⋊D11—84no—
435C22⋊D11—82no—
436C22⋊D11—82no—
437C2×Dic11—22no—
438C2×Dic11—22no—
439C2×Dic11—22no—
440C2×Dic11—22no—
441C2×Dic11—41no—
442C2×Dic11—41no—
443C2×Dic11—48no—
444C2×Dic11—42no—
445C2×Dic11—82no—
446C2×Dic11—82no—
447C2×Dic11—81no—
448C2×Dic11—81no—
449C2×Dic11C22×D412yes—
450C2×Dic11C22×D412yes—
451C2×Dic11C22×D412yes—
452D44—24no—
453D44—42no—
454C4×D11—24no—
455C4×D11—42no—
456Dic22—24no—
457Dic22—81no—
458C8×C11—24no—
459C11⋊C8—24no—
460C23×D4—111no—
461C23×D4—221no—
462C23×D4C2×D1111yescharacteristic
463C2×AGL(1,ℤ/8)—114no—
464C22×SD16—112no—
465C22×D8C2×D1112yescomplemented
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—111no—
485C2×#121—221no—
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#480—112no—
498#480—112no—
499#478—114no—
500#469—114no—
501#468—114no—
502#466—114no—
503#465—114no—
504#463—114no—
505#460—114no—
506#459—114no—
507#450—112no—
508#450—112no—
509#450—114no—
510#450—114no—
511#450—112no—
512#449—114no—
513#448—112no—
514#447—112no—
515#447—114no—
516#447—112no—
517#447C2×D1112yes—
518#447C2×D1112yescomplemented
519#447C2×D1114yescomplemented
520#442—114no—
521#440—114no—
522#435—114no—
523#435—114no—
524#432—112no—
525#418—114no—
526C2×#102—112no—
527C2×#102C2×D1112yescomplemented
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—24no—
538C22×C11—44no—
539C22×C11—48no—
540C22×C11—42no—
541C22×C11—42no—
542C22×C11—42no—
543C22×C11—42no—
544C22×C11—42no—
545C22×C11—42no—
546C22×C11—42no—
547C22×C11—42no—
548C22×C11—88no—
549C22×C11—88no—
550C22×C11—84no—
551C22×C11—162no—
552C22×C11C2×AGL(1,ℤ/8)12yes—
553C22×C11C2×AGL(1,ℤ/8)12yes—
554C22×C11C2×AGL(1,ℤ/8)12yes—
555C22×C11C23×D411yescharacteristic
556C2×D11—22no—
557C2×D11—22no—
558C2×D11—22no—
559C2×D11—44no—
560C2×D11—42no—
561C2×D11—42no—
562C2×D11—42no—
563C2×D11—816no—
564C2×D11—84no—
565C4×C11—21no—
566C4×C11—21no—
567C4×C11—21no—
568C4×C11—42no—
569C4×C11C2×H(5,𝔽2)12yes—
570Dic11—22no—
571Dic11—22no—
572Dic11—22no—
573Dic11—42no—
574Dic11—42no—
575Dic11—42no—
576C25—21no—
577C25—221no—
578C2×#41—112no—
579C22×Q8—111no—
580C22×D4—21no—
581C22×D4—21no—
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—44no—
585C22×D4—111no—
586C22×D4—114no—
587C22×D4—111no—
588C22×D4—222no—
589C22×D4—221no—
590C22×D4—221no—
591C22×D4—221no—
592C22×D4—224no—
593C22×D4—224no—
594C22×D4—221no—
595C22×D4—221no—
596C22×D4—444no—
597C22×D4—448no—
598C22×D4C22×D1111yescharacteristic
599C22×D4C22×D1112yes—
600C22×D4C22×D1112yes—
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—44no—
612C2×D8—114no—
613C2×D8C22×D1114yes—
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—114no—
641#121—112no—
642#121—112no—
643#121—112no—
644#121—222no—
645#121—224no—
646#121—224no—
647#121—222no—
648#121—222no—
649#121—222no—
650#121—221no—
651#121—221no—
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—114no—
666C4×D4—112no—
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—111no—
679C2×C4⋊C4—221no—
680C2×C4⋊C4C22×D1111yescharacteristic, complemented
681C2×C22⋊C4—21no—
682C2×C22⋊C4—111no—
683C2×C22⋊C4—111no—
684C2×C22⋊C4—222no—
685C2×C22⋊C4—221no—
686C2×C22⋊C4—221no—
687C2×C22⋊C4—221no—
688C2×C22⋊C4—221no—
689C2×C42—111no—
690#107—114no—
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×D1114yes—
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—44no—
711C2×C11—82no—
712C2×C11—82no—
713C2×C11#348411yescharacteristic
714C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
715C2×C11#358511yescharacteristic
716D11—42no—
717D11—82no—
718C24—21no—
719C24—21no—
720C24—22no—
721C24—22no—
722C24—21no—
723C24—44no—
724C24—44no—
725C24—82no—
726C24—111no—
727C24—224no—
728C24—221no—
729C24—444no—
730C24—444no—
731C24—882no—
732C24D4×D1111yescharacteristic
733#41—444no—
734C2×Q8—112no—
735C2×Q8—221no—
736C2×Q8—442no—
737C2×D4—24no—
738C2×D4—24no—
739C2×D4—24no—
740C2×D4—22no—
741C2×D4—22no—
742C2×D4—21no—
743C2×D4—22no—
744C2×D4—22no—
745C2×D4—21no—
746C2×D4—21no—
747C2×D4—42no—
748C2×D4—42no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—44no—
755C2×D4—112no—
756C2×D4—112no—
757C2×D4—112no—
758C2×D4—224no—
759C2×D4—224no—
760C2×D4—224no—
761C2×D4—224no—
762C2×D4—228no—
763C2×D4—224no—
764C2×D4—222no—
765C2×D4—222no—
766C2×D4—222no—
767C2×D4—222no—
768C2×D4—221no—
769C2×D4—442no—
770C2×D4—444no—
771C2×D4—444no—
772C2×D4—448no—
773C2×D4—4416no—
774C2×D4—4416no—
775C2×D4—444no—
776C2×D4—444no—
777C2×D4—444no—
778C2×D4—882no—
779C2×D4C23×D1112yes—
780C2×D4C23×D1112yes—
781C2×D4C23×D1112yes—
782C22×C4—21no—
783C22×C4—42no—
784C22×C4—111no—
785C22×C4—111no—
786C22×C4—111no—
787C22×C4—112no—
788C22×C4—112no—
789C22×C4—224no—
790C22×C4—222no—
791C22×C4—222no—
792C22×C4—221no—
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—28no—
807D8—44no—
808D8—444no—
809M16—444no—
810C2×C8—42no—
811C2×C8—114no—
812C2×C8—442no—
813C2×C8C23×D1114yes—
814C4⋊C4—21no—
815C4⋊C4—112no—
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—221no—
825C4⋊C4—222no—
826C4⋊C4—222no—
827C4⋊C4C23×D1112yes—
828C22⋊C4—22no—
829C22⋊C4—22no—
830C22⋊C4—112no—
831C22⋊C4—112no—
832C22⋊C4—112no—
833C22⋊C4—112no—
834C22⋊C4—222no—
835C22⋊C4—222no—
836C22⋊C4—224no—
837C22⋊C4—222no—
838C22⋊C4—222no—
839C22⋊C4—224no—
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—24no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—41no—
856C23—41no—
857C23—44no—
858C23—44no—
859C23—42no—
860C23—42no—
861C23—42no—
862C23—42no—
863C23—44no—
864C23—44no—
865C23—42no—
866C23—42no—
867C23—82no—
868C23—82no—
869C23—81no—
870C23—81no—
871C23—816no—
872C23—112no—
873C23—222no—
874C23—222no—
875C23—441no—
876C23—441no—
877C23—448no—
878C23—442no—
879C23—442no—
880C23—448no—
881C23—442no—
882C23—884no—
883C23—8816no—
884C23#6696414yescomplemented
885C23C2×D4×D1111yescharacteristic
886C23C2×D4×D1111yescharacteristic
887C23C2×D4×D1111yescharacteristic
888Q8—224no—
889Q8—881no—
890D4—24no—
891D4—22no—
892D4—24no—
893D4—22no—
894D4—22no—
895D4—44no—
896D4—44no—
897D4—42no—
898D4—44no—
899D4—44no—
900D4—81no—
901D4—224no—
902D4—224no—
903D4—224no—
904D4—442no—
905D4—448no—
906D4—448no—
907D4—448no—
908D4—444no—
909D4—444no—
910D4—884no—
911D4—882no—
912D4—882no—
913D4#6703714yes—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—42no—
922C2×C4—112no—
923C2×C4—112no—
924C2×C4—112no—
925C2×C4—222no—
926C2×C4—224no—
927C2×C4—222no—
928C2×C4—222no—
929C2×C4—222no—
930C2×C4—442no—
931C2×C4—441no—
932C2×C4—441no—
933C2×C4—448no—
934C2×C4—442no—
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—24no—
952C22—44no—
953C22—48no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—88no—
963C22—88no—
964C22—84no—
965C22—162no—
966C22—222no—
967C22—222no—
968C22—222no—
969C22—444no—
970C22—442no—
971C22—442no—
972C22—442no—
973C22—884no—
974C22—8816no—
975C22C2×#6696412yes—
976C22C2×#6696412yes—
977C22C2×#6696412yes—
978C22C22×D4×D1111yescharacteristic
979C4—21no—
980C4—21no—
981C4—21no—
982C4—42no—
983C4—222no—
984C4—222no—
985C4—222no—
986C4—442no—
987C4—442no—
988C4—442no—
989C4C2×#6703712yes—
990C2—22no—
991C2—22no—
992C2—22no—
993C2—44no—
994C2—82no—
995C2—82no—
996C2—442no—
997C2—882no—
998C2#1308224511yescharacteristic
999C2C22×#6696411yescharacteristic
1000C2#1308339211yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#447C2
socleC22×C11C23×D4
hypercenterC2×#447D11
hypocenterC11#61571
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. #13082450C2semidirect
2. C2×D4×C22⋊D11C2semidirect
3. #13080761C2semidirect
4. #13080633C2semidirect
5. #13080115C2semidirect
6. #13080096C2semidirect
7. #13079632C2semidirect
8. #13079427C2semidirect
9. #13079374C2semidirect
10. #13079364C2semidirect
11. #13078749C2semidirect
12. #13077840C2semidirect
13. C2×#10622831C2semidirect
14. #13077642C2semidirect
15. C2×C11×#447C2semidirect
18. C22×D4×D11C22semidirect
19. C22×C11×D8C22semidirect
20. C2×C11×#121C22semidirect
22. #10623337C22semidirect
24. C2×#66993C22semidirect
29. D4×C22⋊D11C22semidirect
30. C2×#66991C22semidirect
33. C2×D4×Dic11C22semidirect
34. C22×#4324C22semidirect
37. C2×#66977C22semidirect
38. C2×#66964C22semidirect
39. #10623149C22semidirect
41. #10623137C22semidirect
44. #10623131C22semidirect
45. #10623129C22semidirect
46. #10623044C22semidirect
49. C11×#447C22semidirect
50. C11×#447C22semidirect
51. C2×C11×#102C22semidirect
52. C2×C11×C22⋊C8C22semidirect
53. #10622831C22semidirect
54. #10622831C22semidirect
55. #10622831C22semidirect
56. #10622830C22semidirect
57. C2×#66896C22semidirect
58. C2×C22⋊(C11⋊C8)C22semidirect
59. #10622772C22semidirect
60. #10622771C22semidirect
61. #10622769C22semidirect
62. #10622767C22semidirect
63. #10622766C22semidirect
64. #10622765C22semidirect
65. #10622763C22semidirect
66. #10622727C22semidirect
67. #10622724C22semidirect
68. #10622651C22semidirect
69. #10622649C22semidirect
70. #10622646C22semidirect
71. #10622580C22semidirect
72. #10622393C22semidirect
73. #10622392C22semidirect
74. #10622389C22semidirect
75. #10622383C22semidirect
76. #10622377C22semidirect
77. #10622376C22semidirect
78. #10622375C22semidirect
79. #10622370C22semidirect
80. #10622351C22semidirect
81. #10622348C22semidirect
82. #10622344C22semidirect
83. #10622343C22semidirect
84. #10622339C22semidirect
85. #10622334C22semidirect
86. #10622332C22semidirect
98. C22×D4×C11C23semidirect
110. C2×#4341C23semidirect
116. C22×Dic22C23semidirect
119. C2×C11×D8C23semidirect
120. C22×C8×C11C23semidirect
124. C11×#121C23semidirect
125. C2×C11×C4⋊C4C23semidirect
144. #66991C23semidirect
148. #66989C23semidirect
157. D4×Dic11C23semidirect
160. C2×#4324C23semidirect
161. C2×#4323C23semidirect
175. C2×C4⋊Dic11C23semidirect
179. #66977C23semidirect
183. C22×C11⋊C8C23semidirect
185. C2×#4314C23semidirect
186. C2×#4313C23semidirect
188. #66950C23semidirect
189. #66945C23semidirect
190. #66943C23semidirect
192. #66940C23semidirect
202. C11×#102C23semidirect
204. C11×C22⋊C8C23semidirect
206. #66896C23semidirect
207. #66896C23semidirect
209. C22⋊(C11⋊C8)C23semidirect
210. #66885C23semidirect
211. (C2×D11)⋊C8C23semidirect
212. #66881C23semidirect
213. #66880C23semidirect
214. #66879C23semidirect
215. Dic11⋊C8C23semidirect
216. #66873C23semidirect
217. #66871C23semidirect
364. C2×#447D11semidirect
387. C23×C11AGL(1,ℤ/8)semidirect
465. C22×D8C2×D11semidirect
486. C2×#121C2×D11semidirect
518. #447C2×D11semidirect
519. #447C2×D11semidirect
527. C2×#102C2×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
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×D4×C22⋊D112
#130807612
#130806332
#130801152
#130800962
#130796322
#130794272
#130793742
#130793642
#130787492
#130778402
C2×#106228312
#130776422
C2×C11×#4472
#6157111