Finite Group Databasebeta

← #14769663

Subgroups — #14769663

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×#10623299C211yesmaximal, characteristic
2C2×#10622330C211yesmaximal, characteristic, complemented
3C2×#10622508C211yesmaximal, characteristic, complemented
4#13077064C212yesmaximal, complemented
5#13069505C211yesmaximal, characteristic, complemented
6#13068946C212yesmaximal, complemented
7#13068940C212yesmaximal, complemented
8#13068655C211yesmaximal, characteristic, complemented
9#13068558C212yesmaximal, complemented
10#13068401C211yesmaximal, characteristic, complemented
11C11×#1975C211yesmaximal, characteristic, complemented
12C2×#41×D11C2212yes—
13C2×C11×#135C2211yescharacteristic
14C2×#67003C2212yes—
15#10623299—24no—
16#10623299—24no—
17C2×#66971C412yescomplemented
18C2×#66968C412yescomplemented
19C2×#66967C412yescomplemented
20C2×#66964C412yescomplemented
21C2×#66960C2212yescomplemented
22C2×#66957C2211yescharacteristic
23C2×#66954C2212yescomplemented
24C22×#4313C2211yescharacteristic
25C2×C11×#108C2211yescharacteristic, complemented
26C2×C11×#104C2212yescomplemented
27C11×#408C2212yescomplemented
28C2×C11×#97C2211yescharacteristic, complemented
29C2×#66901C2212yescomplemented
30#10622847C2212yescomplemented
31C2×#66889C2212yescomplemented
32#10622739C2212yes—
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×#66883C2211yescharacteristic, complemented
35C2×C8×Dic11C2211yescharacteristic, complemented
36C4×(C2×D11)⋊C4C2211yescharacteristic
37C2×#66869C2212yescomplemented
38#10622508—24no—
39#10622340—22no—
40#10622340—22no—
41#10622339—22no—
42D11×C22⋊C8—22no—
43#10622330—24no—
44#10622196C2212yescomplemented
45#10622188C2211yescharacteristic, complemented
46#10622162C2211yescharacteristic, complemented
47C2×C11×#41C2312yes—
48#41×D11—24no—
49#41×D11—24no—
50#41×D11—42no—
51#41×D11—42no—
52C2×#4343C2×C412yes—
53C2×Q8×D11C2×C412yes—
54C2×#4341—22no—
55C2×#4341C2×C412yes—
56C2×D4×D11—22no—
57C2×D4×D11C2×C412yes—
58C2×#4339—22no—
59C2×#4339C2312yes—
60C22×C4×D11—22no—
61C22×C4×D11C2311yescharacteristic
62C11×#135—22no—
63C11×#135—22no—
64C2×C11×Q16C2×C411yescharacteristic
65C2×C11×SD16C2×C412yes—
66C2×C11×D8C2×C411yescharacteristic
67C2×C11×M16C2312yes—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71#67003—24no—
72#67003—24no—
73C2×#4326C2×C412yes—
74C2×#4325C2×C412yes—
75C2×#4324C2×C412yes—
76C2×#4323C2×C412yes—
77C2×(C2×D11)⋊C4—21no—
78C2×C4×Dic11C2311yescharacteristic
79C2×#4318C2312yes—
80C22×C11⋊C8C2311yescharacteristic
81C22×C11⋊C8C2311yescharacteristic
82#66971—28no—
83#66968—28no—
84#66967—28no—
85#66964—28no—
86#66960—24no—
87#66960—42no—
88C2×Dic44C2×C411yescharacteristic
89#66957D414yes—
90#66957D414yes—
91C2×D88C2×C411yescharacteristic
92C2×#4314C2×C412yes—
93#66954—24no—
94#66954—42no—
95C2×#4313—22no—
96C2×#4313—22no—
97C2×#4313—22no—
98C2×#4313—22no—
99C2×#4313C2×C412yes—
100C2×#4313C2×C412yes—
101C2×C8×D11—22no—
102C2×C8×D11—22no—
103C11×#108—22no—
104C11×#104—42no—
105C11×C22⋊C8—22no—
106C11×C22⋊C8—22no—
107C11×#97—22no—
108#66901—42no—
109C11⋊#95—21no—
110C22⋊(C11⋊C8)—22no—
111C22⋊(C11⋊C8)—22no—
112#66889—24no—
113(C2×D11)⋊C8—22no—
114(C2×D11)⋊C8—22no—
115(C2×D11)⋊C8D412yes—
116(C2×D11)⋊C8D412yes—
117#66883—22no—
118C8×Dic11—22no—
119#66869—24no—
120#22453—111nomaximal, Sylow
121C23×D11—22no—
122C23×D11#4111yescharacteristic
123C11×#41—22no—
124C11×#41—22no—
125C11×#41—22no—
126C11×#41—22no—
127C2×Q8×C11C22×C412yes—
128C2×D4×C11—22no—
129C2×D4×C11C22×C412yes—
130C22×C4×C11—22no—
131C22×C4×C11—21no—
132C22×C4×C11C2411yescharacteristic
133C2×C22⋊D11—22no—
134C2×C22⋊D11—22no—
135C2×C22⋊D11—22no—
136C22×Dic11—22no—
137C22×Dic11—21no—
138C22×Dic11#4111yescharacteristic
139#4343—24no—
140#4343—42no—
141Q8×D11—24no—
142Q8×D11—42no—
143#4341—24no—
144#4341—42no—
145#4341—44no—
146#4341—44no—
147D4×D11—24no—
148D4×D11—42no—
149D4×D11—44no—
150D4×D11—44no—
151#4339—22no—
152#4339—22no—
153#4339—44no—
154#4339—44no—
155#4339C2×D414yes—
156#4339C2×D414yes—
157C2×D44—22no—
158C2×D44C22×C412yes—
159C2×C4×D11—22no—
160C2×C4×D11—22no—
161C2×C4×D11—22no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—44no—
167C2×C4×D11—44no—
168C2×C4×D11C22×C412yes—
169C2×C4×D11C2×D412yes—
170C2×Dic22—22no—
171C2×Dic22C22×C412yes—
172C11×Q16—22no—
173C11×SD16—24no—
174C11×D8—22no—
175C11×M16—22no—
176C11×M16—22no—
177C2×C8×C11—21no—
178C2×C8×C11—22no—
179C2×C8×C11—21no—
180C2×C8×C11C22×C411yescharacteristic
181C2×C8×C11C22×C411yescharacteristic
182C2×C8×C11C2×D412yes—
183C2×C8×C11C2×D412yes—
184C2×C8×C11C2×D412yes—
185C42×C11—21no—
186C42×C11—21no—
187#4326—24no—
188#4325—24no—
189#4324—24no—
190#4323—24no—
191(C2×D11)⋊C4—42no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194#4318—22no—
195#4318—22no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—22no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8C22×C412yes—
202C2×C11⋊C8C2×D411yescharacteristic
203C2×C11⋊C8C2×D411yescharacteristic
204Dic44C22⋊C414yescomplemented
205D88C22⋊C414yescomplemented
206#4314C22⋊C418yescomplemented
207#4313—24no—
208#4313—24no—
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#1975D1111yescharacteristic, complemented
218#1974—111no—
219#1876—112no—
220#1876—112no—
221#1811—111no—
222#1789—112no—
223#1753—111no—
224C23×C11—22no—
225C23×C11C2×#4111yescharacteristic
226C22×D11—22no—
227C22×D11—21no—
228C22×D11—21no—
229C22×D11—41no—
230C22×D11—41no—
231C22×D11—44no—
232C22×D11—44no—
233C22×D11—82no—
234C22×D11C4×D412yes—
235Q8×C11—22no—
236Q8×C11—22no—
237D4×C11—22no—
238D4×C11—22no—
239D4×C11—42no—
240D4×C11—42no—
241C2×C4×C11—22no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11C23×C411yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11H(5,𝔽2)11yescharacteristic
252C2×C4×C11H(5,𝔽2)11yescharacteristic
253C22⋊D11—24no—
254C22⋊D11—24no—
255C22⋊D11—44no—
256C22⋊D11—44no—
257C2×Dic11—22no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—22no—
261C2×Dic11—44no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11C4×D412yes—
265D44—22no—
266D44—44no—
267D44C2×C22⋊C414yes—
268C4×D11—22no—
269C4×D11—22no—
270C4×D11—24no—
271C4×D11—24no—
272C4×D11—22no—
273C4×D11—22no—
274C4×D11—44no—
275C4×D11—44no—
276Dic22—22no—
277Dic22—44no—
278Dic22C2×C22⋊C414yes—
279C8×C11—22no—
280C8×C11—42no—
281C8×C11C2×C22⋊C412yes—
282C8×C11C2×C22⋊C412yes—
283C11⋊C8—22no—
284C11⋊C8—21no—
285C11⋊C8—21no—
286C11⋊C8—42no—
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—112no—
295C2×#135—111no—
296C2×#135C2×D1111yescharacteristic
297C2×#131—112no—
298C2×#131—112no—
299C22×M16—111no—
300#444—224no—
301#443—224no—
302C2×#108—111no—
303C2×#108C2×D1111yescharacteristic, complemented
304C2×#104—112no—
305C2×#104—112no—
306C2×#104—112no—
307C2×#104C2×D1112yescomplemented
308#408—112no—
309#408—222no—
310#408—222no—
311#408C2×D1112yescomplemented
312#407—112no—
313#407—222no—
314C2×C22⋊C8—111no—
315C2×C22⋊C8—222no—
316C2×#97C2×D1111yescharacteristic, complemented
317C2×C4×C8—111no—
318C4×C22⋊C4—111no—
319#341—112no—
320#336—111no—
321#336—111no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—42no—
325C22×C11—42no—
326C22×C11—42no—
327C22×C11C2×C4×D411yescharacteristic
328C22×C11#54611yescharacteristic
329C22×C11#54611yescharacteristic
330C2×D11—22no—
331C2×D11—24no—
332C2×D11—22no—
333C2×D11—22no—
334C2×D11—42no—
335C2×D11—42no—
336C2×D11—81no—
337C2×D11—81no—
338C2×D11—88no—
339C4×C11—42no—
340C4×C11—81no—
341C4×C11C22×C22⋊C411yescharacteristic
342C4×C11#51811yescharacteristic
343C4×C11D4211yescharacteristic
344C4×C11D4211yescharacteristic
345Dic11—24no—
346Dic11—22no—
347Dic11—42no—
348C2×#41—112no—
349C2×#41—112no—
350C2×#41—112no—
351C2×#41—222no—
352C2×#41—222no—
353C2×#41—224no—
354C2×#41—224no—
355C2×#41—442no—
356C2×#41—442no—
357C2×#41C22×D1112yes—
358C22×Q8—112no—
359C22×D4—112no—
360C22×D4—222no—
361C23×C4—111no—
362C23×C4—222no—
363#137—228no—
364#137—228no—
365AGL(1,ℤ/8)—228no—
366AGL(1,ℤ/8)—228no—
367#135—22no—
368#135—22no—
369#135—114no—
370#135—114no—
371#135—224no—
372#135—224no—
373C2×Q16—112no—
374C2×Q16—111no—
375C2×Q16C4×D1111yescharacteristic
376C2×SD16—112no—
377C2×SD16—112no—
378C2×SD16—112no—
379C2×SD16C4×D1112yes—
380C2×D8—112no—
381C2×D8—111no—
382C2×D8C4×D1111yescharacteristic
383#131—224no—
384#131—224no—
385#131—442no—
386#131—442no—
387C2×M16—112no—
388C2×M16—112no—
389C2×M16—112no—
390C2×M16—222no—
391C2×M16—222no—
392C2×M16—222no—
393C2×M16—222no—
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×C42C22×D1111yescharacteristic
404#108—22no—
405#108—222no—
406#104—42no—
407#104—224no—
408#104—224no—
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—22no—
419C4×C8—222no—
420#95—221no—
421C2×C11—21no—
422C2×C11—21no—
423C2×C11—82no—
424C2×C11D4×C22⋊C411yescharacteristic
425C2×C11#295511yescharacteristic
426C2×C11#295611yescharacteristic
427D11—42no—
428D11—44no—
429C24—111no—
430C24—222no—
431#41—22no—
432#41—22no—
433#41—22no—
434#41—22no—
435#41—114no—
436#41—114no—
437#41—222no—
438#41—222no—
439#41—224no—
440#41—224no—
441#41—444no—
442#41—444no—
443#41—442no—
444#41—444no—
445#41—444no—
446#41—442no—
447C2×Q8—112no—
448C2×Q8—222no—
449C2×Q8—224no—
450C2×Q8—442no—
451C2×Q8C2×C4×D1112yes—
452C2×D4—22no—
453C2×D4—112no—
454C2×D4—222no—
455C2×D4—222no—
456C2×D4—224no—
457C2×D4—222no—
458C2×D4—222no—
459C2×D4—442no—
460C2×D4—444no—
461C2×D4—444no—
462C2×D4C2×C4×D1112yes—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—111no—
466C22×C4—112no—
467C22×C4—112no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—222no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—444no—
478C22×C4—444no—
479C22×C4C23×D1111yescharacteristic
480Q16—22no—
481Q16—114no—
482Q16—224no—
483SD16—24no—
484SD16—118no—
485SD16—224no—
486SD16—224no—
487D8—22no—
488D8—114no—
489D8—224no—
490M16—22no—
491M16—22no—
492M16—224no—
493M16—224no—
494M16—222no—
495M16—222no—
496M16—444no—
497M16—444no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—22no—
501C2×C8—112no—
502C2×C8—111no—
503C2×C8—111no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—222no—
509C2×C8—444no—
510C2×C8—444no—
511C2×C8C2×C4×D1111yescharacteristic
512C2×C8C2×C4×D1111yescharacteristic
513C2×C8D4×D1112yes—
514C2×C8D4×D1112yes—
515C2×C8D4×D1112yes—
516C22⋊C4—442no—
517C42—21no—
518C42—21no—
519C42—221no—
520C42—221no—
521C11#2245311yescharacteristic, complemented, Sylow
522C23—22no—
523C23—112no—
524C23—222no—
525C23—221no—
526C23—221no—
527C23—441no—
528C23—441no—
529C23—444no—
530C23—444no—
531C23—882no—
532C23#41×D1111yescharacteristic
533Q8—22no—
534Q8—22no—
535Q8—114no—
536Q8—222no—
537Q8—444no—
538D4—22no—
539D4—22no—
540D4—42no—
541D4—42no—
542D4—114no—
543D4—224no—
544D4—224no—
545D4—222no—
546D4—444no—
547D4—444no—
548D4—444no—
549C2×C4—22no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—112no—
556C2×C4—222no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—224no—
560C2×C4—222no—
561C2×C4—222no—
562C2×C4—222no—
563C2×C4—224no—
564C2×C4—222no—
565C2×C4—222no—
566C2×C4—444no—
567C2×C4—444no—
568C2×C4—444no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4C22×C4×D1111yescharacteristic
572C2×C4C2×D4×D1111yescharacteristic
573C2×C4C2×D4×D1111yescharacteristic
574C2×C4C2×D4×D1111yescharacteristic
575C2×C4#6703711yescharacteristic
576C2×C4#6704211yescharacteristic
577C8—22no—
578C8—42no—
579C8—221no—
580C8—221no—
581C8—222no—
582C8—442no—
583C8C22⋊C4×D1112yes—
584C8C22⋊C4×D1112yes—
585C22—21no—
586C22—21no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—222no—
591C22—222no—
592C22—222no—
593C22—224no—
594C22—442no—
595C22—442no—
596C22—881no—
597C22—881no—
598C22—888no—
599C22C4×D4×D1111yescharacteristic
600C22#1062314311yescharacteristic
601C22#1062320711yescharacteristic
602C4—42no—
603C4—81no—
604C4—222no—
605C4—224no—
606C4—442no—
607C4C2×C22⋊C4×D1111yescharacteristic
608C4#1062307611yescharacteristic
609C4#1062314011yescharacteristic
610C4#1062324811yescharacteristic
611C2—21no—
612C2—21no—
613C2—82no—
614C2—442no—
615C2—444no—
616C2#1307143711yescharacteristic
617C2#1307751611yescharacteristic
618C2#1307752411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1975C2
socleC22×C11C2×C4×D4
prime radicalC2×#10623299C2
cosocleC22×C4×C11C24
hypercenter#1975D11
hypocenterC11#22453
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1975

Complements

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

NH ≅ G/Ntype
2. C2×#10622330C2semidirect
3. C2×#10622508C2semidirect
4. #13077064C2semidirect
5. #13069505C2semidirect
6. #13068946C2semidirect
7. #13068940C2semidirect
8. #13068655C2semidirect
9. #13068558C2semidirect
10. #13068401C2semidirect
11. C11×#1975C2semidirect
17. C2×#66971C4semidirect
18. C2×#66968C4semidirect
19. C2×#66967C4semidirect
20. C2×#66964C4semidirect
21. C2×#66960C22semidirect
23. C2×#66954C22semidirect
25. C2×C11×#108C22semidirect
26. C2×C11×#104C22semidirect
27. C11×#408C22semidirect
28. C2×C11×#97C22semidirect
29. C2×#66901C22semidirect
30. #10622847C22semidirect
31. C2×#66889C22semidirect
34. C2×#66883C22semidirect
35. C2×C8×Dic11C22semidirect
37. C2×#66869C22semidirect
44. #10622196C22semidirect
45. #10622188C22semidirect
46. #10622162C22semidirect
204. Dic44C22⋊C4semidirect
205. D88C22⋊C4semidirect
206. #4314C22⋊C4semidirect
217. #1975D11semidirect
303. C2×#108C2×D11semidirect
307. C2×#104C2×D11semidirect
311. #408C2×D11semidirect
316. C2×#97C2×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×#106232992
C2×#106223302
C2×#106225082
#130770642
#130695052
#130689462
#130689402
#130686552
#130685582
#130684012
C11×#19752
#2245311