Finite Group Databasebeta

← #14757483

Subgroups — #14757483

Order 2816.

1718 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623056C211yesmaximal, characteristic
2C2×#10622579C211yesmaximal, characteristic, complemented
3C2×#10622614C211yesmaximal, characteristic, complemented
4C2×#10622615C211yesmaximal, characteristic, complemented
5C22×#66873C211yesmaximal, characteristic, complemented
6C2×#10622610C211yesmaximal, characteristic, complemented
7#13069439C212yesmaximal, complemented
8#13069430C212yesmaximal, complemented
9#13069425C212yesmaximal, complemented
10#13069421C212yesmaximal, complemented
11C11×#2317C211yesmaximal, characteristic, complemented
12C22×#4339C2211yescharacteristic
13C23×D44C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×#4318C2211yescharacteristic
18C23×C11⋊C8C2211yescharacteristic
19#10623056—24no—
20#10623056C418yescomplemented
21C2×#66948—22no—
22C2×#66935—22no—
23C2×#66928C2212yes—
24C2×#66927C2212yes—
25C11×#389—22no—
26C11×#385—22no—
27C11×#384C2212yescomplemented
28C11×#382C2212yescomplemented
29#10622615—24no—
30#10622614—24no—
31#10622610—24no—
32C2×#66874C2211yescharacteristic, complemented
33C2×#66874C2212yescomplemented
34C2×#66874C2211yescharacteristic, complemented
35#10622579—24no—
36C2×#66873—24no—
37C2×#66873C2212yes—
38C2×#66873C2212yes—
39C2×#66873C2212yes—
40C2×#66873C2212yes—
41C2×#66873C2211yescharacteristic, complemented
42C2×#66873C2212yescomplemented
43C2×#66873C2211yescharacteristic, complemented
44C2×#66867C2212yescomplemented
45C2×C4×C11⋊C8C2212yescomplemented
46C24×D11—21no—
47C23×C4×C11—21no—
48C23×C4×C11C2311yescharacteristic
49C22×C22⋊D11—21no—
50C2×#4339—22no—
51C2×#4339—22no—
52C2×#4339—22no—
53C2×#4339—22no—
54C2×#4339—22no—
55C2×#4339C2×C414yes—
56C22×D44—22no—
57C22×D44—22no—
58C22×D44—22no—
59C22×D44—22no—
60C22×D44—21no—
61C22×D44—22no—
62C22×D44—24no—
63C22×D44C2×C414yes—
64C22×D44C2311yescharacteristic
65C22×D44C2312yes—
66C22×C4×D11—21no—
67C22×Dic22C2311yescharacteristic
68C11×#117—22no—
69C11×#117—22no—
70C11×#117C2×C414yes—
71C11×#117D414yes—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—24no—
76C2×C11×C4⋊C4D412yes—
77C2×C11×C4⋊C4C2312yes—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4D412yes—
82C2×C42×C11—21no—
83C2×C42×C11C2312yes—
84C2×(C2×D11)⋊C4—24no—
85C2×#4318—22no—
86C2×#4318—22no—
87C2×#4318D414yescomplemented
88C22×C11⋊C8—22no—
89C22×C11⋊C8—22no—
90C22×C11⋊C8D414yescomplemented
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2312yes—
93C22×C11⋊C8C2311yescharacteristic
94#66948—216no—
95#66935—216no—
96#66928—24no—
97#66928C2×C418yescomplemented
98#66927—24no—
99#66927C2×C418yescomplemented
100C11×#95—24no—
101#66874—24no—
102#66874—22no—
103#66874—22no—
104#66873—24no—
105#66873—24no—
106#66873—24no—
107#66873—24no—
108#66873—24no—
109#66873—22no—
110#66873—22no—
111#66867—24no—
112C4×C11⋊C8—24no—
113#21206—111nomaximal, Sylow
114C24×C11C2×D411yescharacteristic
115C23×D11—22no—
116C23×D11—21no—
117C23×D11—24no—
118C23×D11—42no—
119C23×D11—42no—
120C23×D11—82no—
121C23×D11—82no—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—21no—
125C22×C4×C11—42no—
126C22×C4×C11—82no—
127C22×C4×C11C22×C412yes—
128C22×C4×C11C2×D414yes—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11#4112yes—
134C22×C4×C11#4112yes—
135C22×C4×C11C2411yescharacteristic
136C2×C22⋊D11—24no—
137C2×C22⋊D11—42no—
138C2×C22⋊D11—42no—
139C22×Dic11—21no—
140#4339—28no—
141#4339—28no—
142#4339—44no—
143#4339—44no—
144C2×D44—24no—
145C2×D44—216no—
146C2×D44—28no—
147C2×D44—28no—
148C2×D44—21no—
149C2×D44—22no—
150C2×D44—22no—
151C2×D44—22no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—22no—
155C2×D44—22no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—44no—
159C2×D44—44no—
160C2×D44—42no—
161C2×D44—42no—
162C2×D44—84no—
163C2×D44—84no—
164C2×D44C22×C412yes—
165C2×D44C22×C414yes—
166C2×C4×D11—24no—
167C2×C4×D11—42no—
168C2×C4×D11—42no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22C22×C412yes—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—42no—
182C11×C4⋊C4—84no—
183C11×C4⋊C4C22⋊C418yes—
184C11×C22⋊C4—42no—
185C11×C22⋊C4C22⋊C418yes—
186C42×C11—42no—
187C42×C11C22×C414yes—
188C42×C11C2×D414yes—
189(C2×D11)⋊C4—216no—
190#4318—28no—
191C2×C11⋊C8—28no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8C2×D412yes—
199C2×C11⋊C8C2×D412yes—
200C2×C11⋊C8C2×D414yes—
201C2×#535—111no—
202C2×#417—111no—
203C2×#418—111no—
204C2×#416—111no—
205C22×#102—111no—
206C2×#405—111no—
207#2317D1111yescharacteristic, complemented
208#1961—112no—
209#1959—112no—
210#1958—112no—
211#1957—112no—
212C23×C11—22no—
213C23×C11—22no—
214C23×C11C2×C22⋊C412yes—
215C23×C11#12412yes—
216C23×C11#12712yes—
217C23×C11C22×D411yescharacteristic
218C22×D11—24no—
219C22×D11—22no—
220C22×D11—41no—
221C22×D11—42no—
222C22×D11—41no—
223C22×D11—42no—
224C22×D11—42no—
225C22×D11—44no—
226C22×D11—42no—
227C22×D11—44no—
228C22×D11—48no—
229C22×D11—88no—
230C22×D11—88no—
231C22×D11—84no—
232C22×D11—84no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—44no—
240C2×C4×C11—42no—
241C2×C4×C11—84no—
242C2×C4×C11C2×C22⋊C418yes—
243C2×C4×C11C2×C22⋊C412yes—
244C2×C4×C11C4×D414yes—
245C2×C4×C11C4×D414yes—
246C2×C4×C11#12114yes—
247C2×C4×C11#12114yes—
248C2×C4×C11#12412yes—
249C2×C4×C11#12712yes—
250C2×C4×C11C23×C411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C22⋊D11—48no—
257C2×Dic11—22no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260D44—24no—
261D44—24no—
262D44—22no—
263D44—22no—
264D44—42no—
265D44—42no—
266D44—41no—
267D44—41no—
268D44—48no—
269D44—816no—
270C4×D11—48no—
271Dic22—22no—
272Dic22—22no—
273Dic22—41no—
274Dic22—41no—
275C11⋊C8—22no—
276C11⋊C8—22no—
277C11⋊C8—24no—
278C22×#41—111no—
279C23×D4—111no—
280C22×M16—111no—
281C23×C8—111no—
282#535—118no—
283#535—224no—
284C2×#127—112no—
285C2×#124—112no—
286C2×#121—222no—
287C2×#120—222no—
288C2×#117C2×D1111yescharacteristic
289C2×#117C2×D1111yescharacteristic
290C22×C4⋊C4C2×D1111yescharacteristic
291#418—224no—
292#417—224no—
293#416—224no—
294C2×#103—111no—
295C2×#103—111no—
296C2×#103—112no—
297C2×#102—112no—
298C2×#102—112no—
299C2×#102—111no—
300C2×#102—111no—
301C2×#102—112no—
302C2×#102—112no—
303C2×#102—112no—
304C2×#102—224no—
305#405—224no—
306C2×#97—112no—
307C2×C4×C8—112no—
308#389—22no—
309#385—22no—
310#384C2×D1112yescomplemented
311#382C2×D1112yescomplemented
312C22×C11—24no—
313C22×C11—24no—
314C22×C11—22no—
315C22×C11—22no—
316C22×C11#39014yes—
317C22×C11C22×C22⋊C411yescharacteristic
318C22×C11C2×#12411yescharacteristic
319C22×C11C2×#12711yescharacteristic
320C22×C11#57612yes—
321C22×C11#57712yes—
322C2×D11—48no—
323C2×D11—44no—
324C2×D11—44no—
325C2×D11—42no—
326C2×D11—816no—
327C2×D11—82no—
328C2×D11—84no—
329C2×D11—81no—
330C2×D11—82no—
331C2×D11—81no—
332C2×D11—82no—
333C4×C11—28no—
334C4×C11—81no—
335C4×C11—81no—
336C4×C11—82no—
337C4×C11#39014yes—
338C4×C11C2×C4×D411yescharacteristic
339C4×C11C2×C4×D411yescharacteristic
340C4×C11C2×#12111yescharacteristic
341C4×C11C2×#12111yescharacteristic
342Dic11—42no—
343C25—221no—
344C2×#41—114no—
345C2×#41—222no—
346C2×#41—222no—
347C2×#41—222no—
348C2×#41—222no—
349C2×#41—222no—
350C22×Q8—111no—
351C22×D4—114no—
352C22×D4—112no—
353C22×D4—111no—
354C22×D4—221no—
355C22×D4—222no—
356C22×D4—222no—
357C22×D4—222no—
358C22×D4—222no—
359C22×D4—222no—
360C22×D4—221no—
361C22×D4—224no—
362C23×C4—21no—
363C23×C4—221no—
364C23×C4C22×D1111yescharacteristic
365C2×M16—114no—
366C2×M16—222no—
367C2×M16—222no—
368C22×C8—114no—
369C22×C8—111no—
370C22×C8—111no—
371C22×C8—112no—
372C22×C8—222no—
373C22×C8—222no—
374#127—118no—
375#127—224no—
376#124—118no—
377#124—224no—
378#121—2216no—
379#120—2216no—
380#117—22no—
381#117—22no—
382#117C4×D1114yes—
383#117D4414yes—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4C22⋊D1112yes—
389C2×C4⋊C4C22×D1112yes—
390C2×C4⋊C4C22×D1111yescharacteristic
391C2×C4⋊C4C22×D1111yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—224no—
394C2×C22⋊C4C22⋊D1112yes—
395C2×C42—21no—
396C2×C42C22×D1112yes—
397#103—222no—
398#103—222no—
399#103—224no—
400#102—224no—
401#102—224no—
402#102—222no—
403#102—222no—
404#102—224no—
405#102—224no—
406#102—224no—
407#97—224no—
408C4×C8—224no—
409#95—24no—
410C2×C11—24no—
411C2×C11C2×#39011yescharacteristic
412C2×C11#289712yes—
413C2×C11#313612yes—
414C2×C11#315411yescharacteristic
415C2×C11#315511yescharacteristic
416D11—82no—
417D11—84no—
418C24—222no—
419C24—221no—
420C24—224no—
421C24—442no—
422C24—442no—
423C24—882no—
424C24—882no—
425C24C2×C22⋊D1111yescharacteristic
426#41—228no—
427#41—228no—
428#41—444no—
429#41—444no—
430C2×Q8—112no—
431C2×Q8—221no—
432C2×Q8—221no—
433C2×Q8—221no—
434C2×Q8—221no—
435C2×Q8—221no—
436C2×D4—114no—
437C2×D4—112no—
438C2×D4—224no—
439C2×D4—228no—
440C2×D4—228no—
441C2×D4—224no—
442C2×D4—2216no—
443C2×D4—222no—
444C2×D4—221no—
445C2×D4—222no—
446C2×D4—222no—
447C2×D4—221no—
448C2×D4—221no—
449C2×D4—222no—
450C2×D4—222no—
451C2×D4—221no—
452C2×D4—221no—
453C2×D4—442no—
454C2×D4—442no—
455C2×D4—444no—
456C2×D4—444no—
457C2×D4—442no—
458C2×D4—442no—
459C2×D4—884no—
460C2×D4—884no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—42no—
465C22×C4—82no—
466C22×C4—221no—
467C22×C4—224no—
468C22×C4—442no—
469C22×C4—442no—
470C22×C4C2×C4×D1112yes—
471C22×C4C2×D4412yes—
472C22×C4D4×D1112yes—
473C22×C4D4×D1112yes—
474C22×C4#434312yes—
475C22×C4#434312yes—
476C22×C4C2×C22⋊D1114yes—
477C22×C4C2×C22⋊D1111yescharacteristic
478C22×C4C23×D1111yescharacteristic
479M16—228no—
480C2×C8—112no—
481C2×C8—112no—
482C2×C8—114no—
483C2×C8—228no—
484C2×C8—221no—
485C2×C8—222no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—222no—
490C4⋊C4—22no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—22no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—42no—
497C4⋊C4—84no—
498C4⋊C4(C2×D11)⋊C418yes—
499C22⋊C4—42no—
500C22⋊C4—2216no—
501C22⋊C4(C2×D11)⋊C418yes—
502C42—42no—
503C42C2×C4×D1114yes—
504C42C2×D4414yes—
505C11#2120611yescharacteristic, complemented, Sylow
506C23—22no—
507C23—22no—
508C23—224no—
509C23—222no—
510C23—441no—
511C23—442no—
512C23—441no—
513C23—442no—
514C23—442no—
515C23—444no—
516C23—442no—
517C23—444no—
518C23—448no—
519C23—888no—
520C23—884no—
521C23—884no—
522C23—888no—
523C23C2×(C2×D11)⋊C412yes—
524C23#6699312yes—
525C23#6700012yes—
526C23C22×C22⋊D1111yescharacteristic
527Q8—222no—
528Q8—222no—
529Q8—441no—
530Q8—441no—
531D4—224no—
532D4—224no—
533D4—222no—
534D4—222no—
535D4—448no—
536D4—442no—
537D4—442no—
538D4—441no—
539D4—441no—
540D4—448no—
541D4—8816no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—44no—
549C2×C4—42no—
550C2×C4—84no—
551C2×C4—222no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—448no—
555C2×C4#6694614yes—
556C2×C4#6694614yes—
557C2×C4#6694814yes—
558C2×C4#6694814yes—
559C2×C4C2×(C2×D11)⋊C418yes—
560C2×C4C2×(C2×D11)⋊C412yes—
561C2×C4#6699312yes—
562C2×C4#6700012yes—
563C2×C4C22×C4×D1111yescharacteristic
564C2×C4C22×D4411yescharacteristic
565C2×C4C2×D4×D1111yescharacteristic
566C2×C4C2×D4×D1111yescharacteristic
567C2×C4C2×#434311yescharacteristic
568C2×C4C2×#434311yescharacteristic
569C8—222no—
570C8—222no—
571C8—224no—
572C22—22no—
573C22—22no—
574C22—24no—
575C22—24no—
576C22—444no—
577C22—448no—
578C22—442no—
579C22—444no—
580C22—8816no—
581C22—882no—
582C22—881no—
583C22—882no—
584C22—881no—
585C22—884no—
586C22—882no—
587C22#1062260114yes—
588C22C22×(C2×D11)⋊C411yescharacteristic
589C22C2×#6699311yescharacteristic
590C22C2×#6700011yescharacteristic
591C22#1062336612yes—
592C22#1062336812yes—
593C4—28no—
594C4—81no—
595C4—82no—
596C4—81no—
597C4—442no—
598C4#1062260114yes—
599C4C2×#6694611yescharacteristic
600C4C2×#6694611yescharacteristic
601C4C2×#6694811yescharacteristic
602C4C2×#6694811yescharacteristic
603C2—24no—
604C2—884no—
605C2—882no—
606C2C2×#1062260111yescharacteristic
607C2#1307713912yes—
608C2#1307897512yes—
609C2#1307909411yescharacteristic
610C2#1307909911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2317C2
socleC23×C11C22×D4
prime radicalC2×#10623056C2
cosocleC22×C4×C11C24
hypercenter#2317D11
hypocenterC11#21206
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2317

Complements

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

NH ≅ G/Ntype
2. C2×#10622579C2semidirect
3. C2×#10622614C2semidirect
4. C2×#10622615C2semidirect
5. C22×#66873C2semidirect
6. C2×#10622610C2semidirect
7. #13069439C2semidirect
8. #13069430C2semidirect
9. #13069425C2semidirect
10. #13069421C2semidirect
11. C11×#2317C2semidirect
20. #10623056C4semidirect
27. C11×#384C22semidirect
28. C11×#382C22semidirect
32. C2×#66874C22semidirect
33. C2×#66874C22semidirect
34. C2×#66874C22semidirect
41. C2×#66873C22semidirect
42. C2×#66873C22semidirect
43. C2×#66873C22semidirect
44. C2×#66867C22semidirect
45. C2×C4×C11⋊C8C22semidirect
87. C2×#4318D4semidirect
90. C22×C11⋊C8D4semidirect
97. #66928C2×C4semidirect
99. #66927C2×C4semidirect
207. #2317D11semidirect
310. #384C2×D11semidirect
311. #382C2×D11semidirect
505. C11#21206semidirect

Maximal subgroups

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

subgroupindex
C2×#106230562
C2×#106225792
C2×#106226142
C2×#106226152
C22×#668732
C2×#106226102
#130694392
#130694302
#130694252
#130694212
C11×#23172
#2120611