Finite Group Databasebeta

← #14769657

Subgroups — #14769657

Order 2816.

1362 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623279C211yesmaximal, characteristic
2C2×#10622507C211yesmaximal, characteristic, complemented
3C2×#10622508C211yesmaximal, characteristic, complemented
4#13077066C212yesmaximal, complemented
5#13069507C211yesmaximal, characteristic, complemented
6#13069502C211yesmaximal, characteristic, complemented
7#13068944C212yesmaximal, complemented
8#13068944C212yesmaximal, complemented
9#13068559C212yesmaximal, complemented
10#13068397C211yesmaximal, characteristic, complemented
11C11×#1811C211yesmaximal, characteristic, complemented
12C22×#4339C2212yes—
13C22×C11×M16C2211yescharacteristic
14#10623279—24no—
15#10623279—24no—
16C2×#66962C412yescomplemented
17C2×#66962C412yescomplemented
18C2×#66961C412yescomplemented
19C2×#66961C412yescomplemented
20C2×#66960C2212yescomplemented
21C2×#66960C2212yescomplemented
22C2×#66957C2212yes—
23C2×#66957C2211yescharacteristic
24C2×#66957C2211yescharacteristic
25C2×C11×#108C2211yescharacteristic, complemented
26C2×C11×#108C2211yescharacteristic, complemented
27C11×#407C2212yes—
28C4×C22⋊Dic11C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×#66889C2212yescomplemented
31C2×#66889C2212yescomplemented
32C2×#66889C2212yescomplemented
33C2×#66889C2212yescomplemented
34#10622742C2212yescomplemented
35#10622742C2212yescomplemented
36C2×#66879C2211yescharacteristic, complemented
37C2×C8×Dic11C2211yescharacteristic, complemented
38#10622508—24no—
39#10622507—24no—
40#10622340—22no—
41#10622340—22no—
42#10622339—22no—
43D11×C22⋊C8—22no—
44C11×#341C2212yescomplemented
45#10622188C2211yescharacteristic, complemented
46#10622188C2211yescharacteristic, complemented
47C23×C4×C11C2311yescharacteristic
48C22×C22⋊D11—22no—
49C2×#4339—22no—
50C2×#4339—22no—
51C2×#4339—24no—
52C2×#4339—24no—
53C2×#4339—42no—
54C2×#4339—42no—
55C2×#4339C2×C412yes—
56C2×#4339C2×C412yes—
57C2×#4339C2312yes—
58C2×#4339C2312yes—
59C22×D44C2×C412yes—
60C22×C4×D11—22no—
61C22×Dic22C2×C412yes—
62C2×C11×M16—22no—
63C2×C11×M16—22no—
64C2×C11×M16C2×C412yes—
65C2×C11×M16C2×C412yes—
66C2×C11×M16C2312yes—
67C2×C11×M16C2312yes—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C2×C22⋊Dic11—21no—
71C2×C4×Dic11C2311yescharacteristic
72C2×C4×Dic11C2311yescharacteristic
73C22×C11⋊C8C2311yescharacteristic
74C22×C11⋊C8C2311yescharacteristic
75#66962—28no—
76#66962—28no—
77#66961—28no—
78#66961—28no—
79#66960—24no—
80#66960—24no—
81#66960—42no—
82#66960—42no—
83C2×Dic44C2×C412yes—
84C2×Dic44C2×C411yescharacteristic
85C2×Dic44C2×C411yescharacteristic
86#66957—24no—
87#66957—24no—
88#66957—22no—
89#66957—22no—
90#66957D414yes—
91#66957D414yes—
92C2×D88C2×C412yes—
93C2×D88C2×C411yescharacteristic
94C2×D88C2×C411yescharacteristic
95C2×#4314C2×C412yes—
96C2×#4314C2×C412yes—
97C2×#4314C2×C412yes—
98C2×#4314C2×C412yes—
99C2×#4313—22no—
100C2×#4313—22no—
101C2×C8×D11—22no—
102C2×C8×D11—22no—
103C11×#108—22no—
104C11×#108—22no—
105C11×C22⋊C8—22no—
106C11×C22⋊C8—22no—
107C11⋊#95—21no—
108C22⋊(C11⋊C8)D412yes—
109C22⋊(C11⋊C8)D412yes—
110#66889—24no—
111#66889—24no—
112#66889—42no—
113#66889—42no—
114(C2×D11)⋊C8—22no—
115(C2×D11)⋊C8—22no—
116(C2×D11)⋊C8—22no—
117(C2×D11)⋊C8—22no—
118#66879—22no—
119C8×Dic11—22no—
120#22453—111nomaximal, Sylow
121C24×C11#4111yescharacteristic
122C23×D11—22no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11C22×C412yes—
128C22×C4×C11C2×D412yes—
129C22×C4×C11#4111yescharacteristic
130C22×C4×C11C2411yescharacteristic
131C2×C22⋊D11—22no—
132C2×C22⋊D11—22no—
133C2×C22⋊D11—22no—
134C2×C22⋊D11—22no—
135C2×C22⋊D11—44no—
136C2×C22⋊D11—44no—
137C22×Dic11—22no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140#4339—24no—
141#4339—24no—
142#4339—22no—
143#4339—22no—
144#4339—22no—
145#4339—22no—
146#4339—22no—
147#4339—22no—
148#4339—42no—
149#4339—42no—
150#4339—44no—
151#4339—44no—
152#4339—44no—
153#4339—44no—
154#4339C2×D414yes—
155#4339C2×D414yes—
156C2×D44—24no—
157C2×D44—22no—
158C2×D44—42no—
159C2×D44C22×C412yes—
160C2×D44C22×C412yes—
161C2×C4×D11—22no—
162C2×C4×D11—22no—
163C2×C4×D11—22no—
164C2×C4×D11—22no—
165C2×C4×D11—44no—
166C2×C4×D11—44no—
167C2×Dic22—24no—
168C2×Dic22—22no—
169C2×Dic22—42no—
170C2×Dic22C22×C412yes—
171C2×Dic22C22×C412yes—
172C11×M16—24no—
173C11×M16—24no—
174C11×M16—22no—
175C11×M16—22no—
176C11×M16—22no—
177C11×M16—22no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—22no—
181C2×C8×C11—22no—
182C2×C8×C11C22×C412yes—
183C2×C8×C11C22×C411yescharacteristic
184C2×C8×C11C22×C411yescharacteristic
185C2×C8×C11C2×D412yes—
186C2×C8×C11C2×D412yes—
187C22⋊Dic11—42no—
188C4×Dic11—21no—
189C4×Dic11—21no—
190C4×Dic11—21no—
191C4×Dic11—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8C2×D411yescharacteristic
197C2×C11⋊C8C2×D412yes—
198C2×C11⋊C8C2×D411yescharacteristic
199Dic44—24no—
200Dic44—22no—
201Dic44C22⋊C414yescomplemented
202D88—24no—
203D88—22no—
204D88C22⋊C414yescomplemented
205#4314—24no—
206#4314—24no—
207#4314—24no—
208#4314C22⋊C418yescomplemented
209#4313—44no—
210#4313—44no—
211C8×D11—44no—
212C8×D11—44no—
213C2×#575—111no—
214C2×#444—111no—
215C2×#443—111no—
216#2880—112no—
217#1975—111no—
218#1974—111no—
219#1876—112no—
220#1876—112no—
221#1811D1111yescharacteristic, complemented
222#1789—112no—
223#1753—111no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11C4×D412yes—
229C23×C11C2×#4111yescharacteristic
230C22×D11—22no—
231C22×D11—22no—
232C22×D11—44no—
233C22×D11—44no—
234C22×D11—82no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11C4×D412yes—
242C2×C4×C11C23×C411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11H(5,𝔽2)11yescharacteristic
247C2×C4×C11H(5,𝔽2)11yescharacteristic
248C22⋊D11—24no—
249C22⋊D11—24no—
250C22⋊D11—44no—
251C22⋊D11—44no—
252C22⋊D11—42no—
253C22⋊D11—42no—
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—44no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263D44—22no—
264D44—22no—
265D44—22no—
266D44—44no—
267D44C2×C22⋊C414yes—
268C4×D11—24no—
269C4×D11—24no—
270C4×D11—44no—
271C4×D11—44no—
272C4×D11—42no—
273C4×D11—42no—
274Dic22—22no—
275Dic22—22no—
276Dic22—22no—
277Dic22—44no—
278Dic22C2×C22⋊C414yes—
279C8×C11—22no—
280C8×C11—42no—
281C8×C11—42no—
282C8×C11C2×C22⋊C412yes—
283C8×C11C2×C22⋊C412yes—
284C11⋊C8—21no—
285C11⋊C8—22no—
286C11⋊C8—21no—
287C22×#41—112no—
288#575—224no—
289#575—224no—
290C2×#137—112no—
291C2×#137—112no—
292C2×AGL(1,ℤ/8)—112no—
293C2×AGL(1,ℤ/8)—112no—
294C2×#135—111no—
295C2×#135—112no—
296C2×#135—111no—
297C2×#131—112no—
298C2×#131—112no—
299C22×M16C2×D1111yescharacteristic
300#444—224no—
301#443—224no—
302C2×#108C2×D1111yescharacteristic, complemented
303C2×#108C2×D1111yescharacteristic, complemented
304C2×#104—112no—
305C2×#104—112no—
306C2×#104—112no—
307C2×#104—112no—
308#408—112no—
309#408—112no—
310#408—222no—
311#408—222no—
312#407—222no—
313#407C2×D1112yes—
314C2×C22⋊C8—111no—
315C2×C22⋊C8—222no—
316C2×#97—111no—
317C2×C4×C8—111no—
318C4×C22⋊C4—111no—
319#341C2×D1112yescomplemented
320#336—111no—
321#336—111no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—22no—
325C22×C11—22no—
326C22×C11—22no—
327C22×C11—81no—
328C22×C11—81no—
329C22×C11C2×C4×D411yescharacteristic
330C22×C11#54611yescharacteristic
331C22×C11#54611yescharacteristic
332C2×D11—24no—
333C2×D11—42no—
334C2×D11—42no—
335C2×D11—42no—
336C2×D11—42no—
337C2×D11—42no—
338C2×D11—88no—
339C4×C11—22no—
340C4×C11C22×C22⋊C411yescharacteristic
341C4×C11#51811yescharacteristic
342C4×C11D4211yescharacteristic
343C4×C11D4211yescharacteristic
344Dic11—24no—
345Dic11—42no—
346Dic11—42no—
347Dic11—81no—
348C2×#41—112no—
349C2×#41—112no—
350C2×#41—112no—
351C2×#41—112no—
352C2×#41—224no—
353C2×#41—224no—
354C2×#41—222no—
355C2×#41—222no—
356C2×#41—442no—
357C2×#41—442no—
358C22×Q8—112no—
359C22×D4—112no—
360C22×D4—222no—
361C23×C4—222no—
362C23×C4C22×D1111yescharacteristic
363#137—228no—
364#137—228no—
365AGL(1,ℤ/8)—228no—
366AGL(1,ℤ/8)—228no—
367#135—114no—
368#135—114no—
369#135—224no—
370#135—224no—
371#135—222no—
372#135—222no—
373C2×Q16—111no—
374C2×Q16—112no—
375C2×Q16—111no—
376C2×SD16—112no—
377C2×SD16—112no—
378C2×SD16—112no—
379C2×SD16—112no—
380C2×D8—111no—
381C2×D8—112no—
382C2×D8—111no—
383#131—224no—
384#131—224no—
385#131—442no—
386#131—442no—
387C2×M16—22no—
388C2×M16—22no—
389C2×M16—222no—
390C2×M16—222no—
391C2×M16C4×D1112yes—
392C2×M16C4×D1112yes—
393C2×M16C22×D1112yes—
394C2×M16C22×D1112yes—
395C22×C8—111no—
396C22×C8—111no—
397C22×C8—222no—
398C22×C8—222no—
399C22×C8C22×D1111yescharacteristic
400C22×C8C22×D1111yescharacteristic
401C2×C22⋊C4—221no—
402C2×C42—111no—
403C2×C42—111no—
404#108—22no—
405#108—22no—
406#104—224no—
407#104—224no—
408#104—442no—
409#104—442no—
410C22⋊C8—22no—
411C22⋊C8—22no—
412C22⋊C8—112no—
413C22⋊C8—112no—
414C22⋊C8—222no—
415C22⋊C8—222no—
416C22⋊C8—222no—
417C22⋊C8—222no—
418#97—222no—
419C4×C8—222no—
420#95—221no—
421C2×C11—21no—
422C2×C11—21no—
423C2×C11—42no—
424C2×C11D4×C22⋊C411yescharacteristic
425C2×C11#295511yescharacteristic
426C2×C11#295611yescharacteristic
427D11—44no—
428D11—82no—
429C24—222no—
430C24#434311yescharacteristic
431#41—114no—
432#41—114no—
433#41—224no—
434#41—224no—
435#41—222no—
436#41—222no—
437#41—222no—
438#41—222no—
439#41—222no—
440#41—222no—
441#41—444no—
442#41—444no—
443#41—442no—
444#41—442no—
445#41—444no—
446#41—444no—
447C2×Q8—112no—
448C2×Q8—112no—
449C2×Q8—224no—
450C2×Q8—222no—
451C2×Q8—442no—
452C2×D4—112no—
453C2×D4—112no—
454C2×D4—224no—
455C2×D4—222no—
456C2×D4—222no—
457C2×D4—222no—
458C2×D4—222no—
459C2×D4—222no—
460C2×D4—442no—
461C2×D4—444no—
462C2×D4—444no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—221no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4—221no—
474C22×C4—444no—
475C22×C4—444no—
476C22×C4C2×C4×D1112yes—
477C22×C4D4×D1112yes—
478C22×C4#434311yescharacteristic
479C22×C4C23×D1111yescharacteristic
480Q16—114no—
481Q16—224no—
482Q16—222no—
483SD16—118no—
484SD16—224no—
485SD16—224no—
486SD16—224no—
487D8—114no—
488D8—224no—
489D8—222no—
490M16—24no—
491M16—24no—
492M16—22no—
493M16—22no—
494M16—22no—
495M16—22no—
496M16—444no—
497M16—444no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—111no—
503C2×C8—112no—
504C2×C8—111no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—444no—
510C2×C8—444no—
511C2×C8C2×C4×D1112yes—
512C2×C8C2×C4×D1111yescharacteristic
513C2×C8C2×C4×D1111yescharacteristic
514C2×C8D4×D1112yes—
515C2×C8D4×D1112yes—
516C22⋊C4—442no—
517C42—221no—
518C42—221no—
519C42—221no—
520C42—221no—
521C11#2245311yescharacteristic, complemented, Sylow
522C23—21no—
523C23—21no—
524C23—41no—
525C23—41no—
526C23—222no—
527C23—222no—
528C23—444no—
529C23—444no—
530C23—882no—
531C23#6694612yes—
532C23C2×#434311yescharacteristic
533Q8—114no—
534Q8—222no—
535Q8—222no—
536Q8—222no—
537Q8—444no—
538D4—114no—
539D4—224no—
540D4—224no—
541D4—222no—
542D4—222no—
543D4—222no—
544D4—444no—
545D4—444no—
546D4—444no—
547D4—442no—
548D4—442no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—222no—
556C2×C4—224no—
557C2×C4—224no—
558C2×C4—222no—
559C2×C4—222no—
560C2×C4—444no—
561C2×C4—444no—
562C2×C4—444no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—442no—
566C2×C4—442no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4#6694612yes—
571C2×C4C22×C4×D1111yescharacteristic
572C2×C4C2×D4×D1111yescharacteristic
573C2×C4C2×D4×D1111yescharacteristic
574C2×C4C2×D4×D1111yescharacteristic
575C2×C4#6704211yescharacteristic
576C2×C4#6704211yescharacteristic
577C8—22no—
578C8—42no—
579C8—42no—
580C8—221no—
581C8—222no—
582C8—221no—
583C8C22⋊C4×D1112yes—
584C8C22⋊C4×D1112yes—
585C22—21no—
586C22—21no—
587C22—22no—
588C22—22no—
589C22—22no—
590C22—81no—
591C22—81no—
592C22—224no—
593C22—442no—
594C22—442no—
595C22—442no—
596C22—442no—
597C22—442no—
598C22—888no—
599C22C2×#6694611yescharacteristic
600C22#1062316111yescharacteristic
601C22#1062316111yescharacteristic
602C4—22no—
603C4—224no—
604C4—442no—
605C4—442no—
606C4—881no—
607C4C2×C22⋊C4×D1111yescharacteristic
608C4#1062305211yescharacteristic
609C4#1062314011yescharacteristic
610C4#1062314011yescharacteristic
611C2—21no—
612C2—21no—
613C2—42no—
614C2—444no—
615C2—882no—
616C2#1307143611yescharacteristic
617C2#1307751811yescharacteristic
618C2#1307752511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1811C2
socleC22×C11C2×C4×D4
prime radicalC2×#10623279C2
cosocleC22×C4×C11C24
hypercenter#1811D11
hypocenterC11#22453
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1811

Complements

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

NH ≅ G/Ntype
2. C2×#10622507C2semidirect
3. C2×#10622508C2semidirect
4. #13077066C2semidirect
5. #13069507C2semidirect
6. #13069502C2semidirect
7. #13068944C2semidirect
8. #13068944C2semidirect
9. #13068559C2semidirect
10. #13068397C2semidirect
11. C11×#1811C2semidirect
16. C2×#66962C4semidirect
17. C2×#66962C4semidirect
18. C2×#66961C4semidirect
19. C2×#66961C4semidirect
20. C2×#66960C22semidirect
21. C2×#66960C22semidirect
25. C2×C11×#108C22semidirect
26. C2×C11×#108C22semidirect
30. C2×#66889C22semidirect
31. C2×#66889C22semidirect
32. C2×#66889C22semidirect
33. C2×#66889C22semidirect
34. #10622742C22semidirect
35. #10622742C22semidirect
36. C2×#66879C22semidirect
37. C2×C8×Dic11C22semidirect
44. C11×#341C22semidirect
45. #10622188C22semidirect
46. #10622188C22semidirect
201. Dic44C22⋊C4semidirect
204. D88C22⋊C4semidirect
208. #4314C22⋊C4semidirect
221. #1811D11semidirect
302. C2×#108C2×D11semidirect
303. C2×#108C2×D11semidirect
319. #341C2×D11semidirect
521. C11#22453semidirect

Maximal subgroups

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

subgroupindex
C2×#106232792
C2×#106225072
C2×#106225082
#130770662
#130695072
#130695022
#130689442
#130685592
#130683972
C11×#18112
#2245311