Finite Group Databasebeta

← #14757481

Subgroups — #14757481

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×#10623336C211yesmaximal, characteristic
2C2×#10622579C211yesmaximal, characteristic, complemented
3C2×#10622828C211yesmaximal, characteristic, complemented
4C2×#10622726C211yesmaximal, characteristic, complemented
5C2×#10622714C211yesmaximal, characteristic, complemented
6#13071240C211yesmaximal, characteristic, complemented
7#13069438C212yesmaximal, complemented
8#13069431C212yesmaximal, complemented
9#13069426C212yesmaximal, complemented
10#13069420C212yesmaximal, complemented
11C22×C11×#102C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C22×#4339C2211yescharacteristic
14C23×C8×C11C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C2×#67006—22no—
17#10623336—24no—
18#10623336C418yescomplemented
19C2×#66993C2212yes—
20C2×#66991—22no—
21C2×#66989C2212yes—
22C2×#66979C2211yescharacteristic
23C2×#66979C2211yescharacteristic
24C22×#4318C2211yescharacteristic
25C2×C11×#102—24no—
26C2×C11×#102C2212yes—
27C2×C11×#102C2212yes—
28#10622828—24no—
29C2×#66896C2212yes—
30C2×#66896C2212yes—
31#10622823—22no—
32#10622726—24no—
33C2×#66885C2211yescharacteristic, complemented
34C2×#66885C2211yescharacteristic, complemented
35C2×#66880C2211yescharacteristic, complemented
36C2×#66880C2211yescharacteristic, complemented
37#10622714—24no—
38C2×#66879C2212yescomplemented
39C2×C8×Dic11C2212yescomplemented
40#10622590C2212yescomplemented
41#10622589C2212yescomplemented
42#10622586—22no—
43C2×#66874C2212yescomplemented
44#10622579—24no—
45C2×#66873C2212yescomplemented
46C25×C11—21no—
47C22×D4×C11—22no—
48C22×D4×C11—22no—
49C22×D4×C11—21no—
50C22×D4×C11—22no—
51C22×D4×C11—22no—
52C22×D4×C11—22no—
53C22×D4×C11C2×C414yes—
54C22×D4×C11C2312yes—
55C23×C4×C11—21no—
56C23×C4×C11C2311yescharacteristic
57C22×C22⋊D11—21no—
58C22×C22⋊D11—24no—
59C2×#4339—22no—
60C2×#4339—22no—
61C2×#4339—22no—
62C2×#4339—22no—
63C2×#4339—22no—
64C2×#4339C2×C414yes—
65C22×D44C2311yescharacteristic
66C22×C4×D11—21no—
67C22×Dic22C2311yescharacteristic
68C22×C8×C11—22no—
69C22×C8×C11—22no—
70C22×C8×C11D414yescomplemented
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4C2312yes—
77#67006—216no—
78C2×C22⋊Dic11—24no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11D412yes—
81#66993—24no—
82#66993C2×C418yescomplemented
83#66991—216no—
84#66989—24no—
85#66989C2×C418yescomplemented
86#66979—22no—
87#66979—22no—
88#66979C2×C414yes—
89#66979D414yes—
90C2×C4⋊Dic11D412yes—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×Dic11⋊C4—24no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11C2312yes—
96C2×#4318—22no—
97C2×#4318—22no—
98C2×#4318D414yescomplemented
99C22×C11⋊C8C2312yes—
100C11×#102—24no—
101C11×#102—24no—
102#66896—24no—
103#66896—24no—
104C11⋊#95—24no—
105#66885—22no—
106#66885—22no—
107#66880—22no—
108#66880—22no—
109#66879—24no—
110C8×Dic11—24no—
111#66874—24no—
112#66873—24no—
113#21206—111nomaximal, Sylow
114C24×C11—22no—
115C24×C11—24no—
116C24×C11—42no—
117C24×C11—42no—
118C24×C11—82no—
119C24×C11—82no—
120C24×C11C2×D411yescharacteristic
121C23×D11—21no—
122C2×D4×C11—24no—
123C2×D4×C11—28no—
124C2×D4×C11—28no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—44no—
131C2×D4×C11—44no—
132C2×D4×C11—42no—
133C2×D4×C11—42no—
134C2×D4×C11C22×C414yes—
135C22×C4×C11—22no—
136C22×C4×C11—42no—
137C22×C4×C11—82no—
138C22×C4×C11C22×C412yes—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D412yes—
143C22×C4×C11#4112yes—
144C22×C4×C11#4112yes—
145C22×C4×C11C2411yescharacteristic
146C2×C22⋊D11—216no—
147C2×C22⋊D11—24no—
148C2×C22⋊D11—42no—
149C2×C22⋊D11—42no—
150C2×C22⋊D11—84no—
151C2×C22⋊D11—84no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11C2×D414yes—
156#4339—28no—
157#4339—28no—
158#4339—44no—
159#4339—44no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44C22×C412yes—
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—
175C2×C8×C11—28no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11C2×D412yes—
181C2×C8×C11C2×D412yes—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—42no—
185C22⋊Dic11—216no—
186C22⋊Dic11—42no—
187C22⋊Dic11C22⋊C418yes—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11C22⋊C418yes—
193Dic11⋊C4—84no—
194C4×Dic11—42no—
195C4×Dic11C22×C414yes—
196C4×Dic11C2×D414yes—
197#4318—28no—
198C2×C11⋊C8—22no—
199C2×C11⋊C8—22no—
200C2×C11⋊C8C2×D414yes—
201C2×#535—111no—
202C2×#417—111no—
203C2×#418—111no—
204C2×#416—111no—
205C22×#102D1111yescharacteristic, complemented
206C2×#405—111no—
207#2317—111no—
208#1961—112no—
209#1959—112no—
210#1958—112no—
211#1957—112no—
212C23×C11—22no—
213C23×C11—22no—
214C23×C11—24no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11—44no—
218C23×C11—44no—
219C23×C11—48no—
220C23×C11—88no—
221C23×C11—88no—
222C23×C11—84no—
223C23×C11—84no—
224C23×C11C2×C22⋊C412yes—
225C23×C11#12412yes—
226C23×C11#12712yes—
227C23×C11C22×D411yescharacteristic
228C22×D11—22no—
229C22×D11—41no—
230C22×D11—41no—
231C22×D11—42no—
232C22×D11—42no—
233D4×C11—24no—
234D4×C11—24no—
235D4×C11—42no—
236D4×C11—42no—
237D4×C11—48no—
238C2×C4×C11—42no—
239C2×C4×C11—44no—
240C2×C4×C11—84no—
241C2×C4×C11C2×C22⋊C412yes—
242C2×C4×C11C4×D414yes—
243C2×C4×C11C4×D414yes—
244C2×C4×C11#12114yes—
245C2×C4×C11#12114yes—
246C2×C4×C11#12412yes—
247C2×C4×C11#12712yes—
248C2×C4×C11C23×C411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C22⋊D11—48no—
255C22⋊D11—816no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—22no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—42no—
264C2×Dic11—42no—
265C2×Dic11C2×C22⋊C418yes—
266D44—22no—
267D44—22no—
268D44—41no—
269D44—41no—
270C4×D11—48no—
271Dic22—22no—
272Dic22—22no—
273Dic22—41no—
274Dic22—41no—
275C8×C11—22no—
276C8×C11—22no—
277C11⋊C8—24no—
278C22×#41—111no—
279C23×D4C2×D1111yescharacteristic
280C22×M16—111no—
281C23×C8C2×D1111yescharacteristic
282#535—118no—
283#535—224no—
284C2×#127—112no—
285C2×#124—112no—
286C2×#121—222no—
287C2×#120—222no—
288C2×#117—111no—
289C2×#117—111no—
290C22×C4⋊C4C2×D1111yescharacteristic
291#418—224no—
292#417—224no—
293#416—224no—
294C2×#103—111no—
295C2×#103—111no—
296C2×#103—112no—
297C2×#102—24no—
298C2×#102—112no—
299C2×#102—112no—
300C2×#102—111no—
301C2×#102—111no—
302C2×#102—112no—
303C2×#102C2×D1112yes—
304C2×#102C2×D1112yes—
305#405—224no—
306C2×#97—112no—
307C2×C4×C8—112no—
308#389—222no—
309#385—222no—
310#384—112no—
311#382—112no—
312C22×C11—24no—
313C22×C11—24no—
314C22×C11—22no—
315C22×C11—22no—
316C22×C11—48no—
317C22×C11—44no—
318C22×C11—816no—
319C22×C11—84no—
320C22×C11—82no—
321C22×C11—82no—
322C22×C11#39014yes—
323C22×C11C22×C22⋊C411yescharacteristic
324C22×C11C2×#12411yescharacteristic
325C22×C11C2×#12711yescharacteristic
326C22×C11#57612yes—
327C22×C11#57712yes—
328C2×D11—44no—
329C2×D11—42no—
330C2×D11—82no—
331C2×D11—81no—
332C2×D11—81no—
333C4×C11—82no—
334C4×C11#39014yes—
335C4×C11C2×C4×D411yescharacteristic
336C4×C11C2×C4×D411yescharacteristic
337C4×C11C2×#12111yescharacteristic
338C4×C11C2×#12111yescharacteristic
339Dic11—28no—
340Dic11—42no—
341Dic11—81no—
342Dic11—81no—
343C25—21no—
344C2×#41—114no—
345C2×#41—222no—
346C2×#41—222no—
347C2×#41—222no—
348C2×#41—222no—
349C2×#41—222no—
350C22×Q8—111no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—21no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—111no—
358C22×D4—224no—
359C22×D4—221no—
360C22×D4C4×D1114yes—
361C22×D4C22×D1112yes—
362C23×C4—21no—
363C23×C4—221no—
364C23×C4C22×D1111yescharacteristic
365C2×M16—114no—
366C2×M16—222no—
367C2×M16—222no—
368C22×C8—22no—
369C22×C8—22no—
370C22×C8—112no—
371C22×C8C22⋊D1114yescomplemented
372C22×C8C22×D1111yescharacteristic
373C22×C8C22×D1111yescharacteristic
374#127—118no—
375#127—224no—
376#124—118no—
377#124—224no—
378#121—2216no—
379#120—2216no—
380#117—114no—
381#117—114no—
382#117—222no—
383#117—222no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—112no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—224no—
391C2×C4⋊C4C22×D1112yes—
392C2×C22⋊C4—112no—
393C2×C22⋊C4—224no—
394C2×C22⋊C4—221no—
395C2×C42—112no—
396C2×C42—221no—
397#103—224no—
398#103—222no—
399#103—222no—
400#102—24no—
401#102—24no—
402#102—224no—
403#102—224no—
404#102—224no—
405#102—222no—
406#102—222no—
407#97—224no—
408C4×C8—224no—
409#95—224no—
410C2×C11—24no—
411C2×C11—84no—
412C2×C11C2×#39011yescharacteristic
413C2×C11#289712yes—
414C2×C11#313612yes—
415C2×C11#315411yescharacteristic
416C2×C11#315511yescharacteristic
417D11—82no—
418C24—22no—
419C24—24no—
420C24—42no—
421C24—42no—
422C24—82no—
423C24—82no—
424C24—221no—
425C24D4×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—24no—
437C2×D4—28no—
438C2×D4—28no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—44no—
445C2×D4—42no—
446C2×D4—44no—
447C2×D4—42no—
448C2×D4—112no—
449C2×D4—2216no—
450C2×D4—224no—
451C2×D4—221no—
452C2×D4—221no—
453C2×D4—221no—
454C2×D4—221no—
455C2×D4—221no—
456C2×D4—442no—
457C2×D4—442no—
458C2×D4—884no—
459C2×D4—884no—
460C2×D4C2×C4×D1114yes—
461C22×C4—22no—
462C22×C4—42no—
463C22×C4—82no—
464C22×C4—114no—
465C22×C4—221no—
466C22×C4—224no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—442no—
470C22×C4—442no—
471C22×C4C2×C4×D1112yes—
472C22×C4#433912yes—
473C22×C4D4×D1111yescharacteristic
474C22×C4D4×D1112yes—
475C22×C4D4×D1112yes—
476C22×C4#434112yes—
477C22×C4C2×C22⋊D1112yes—
478C22×C4C23×D1111yescharacteristic
479M16—228no—
480C2×C8—28no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—114no—
486C2×C8—222no—
487C2×C8—222no—
488C2×C8C2×C22⋊D1112yes—
489C2×C8C2×C22⋊D1112yes—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—42no—
493C4⋊C4—118no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—884no—
499C22⋊C4—118no—
500C22⋊C4—2216no—
501C22⋊C4—442no—
502C42—114no—
503C42—114no—
504C42—442no—
505C11#2120611yescharacteristic, complemented, Sylow
506C23—22no—
507C23—22no—
508C23—24no—
509C23—42no—
510C23—44no—
511C23—44no—
512C23—42no—
513C23—48no—
514C23—88no—
515C23—84no—
516C23—84no—
517C23—88no—
518C23—222no—
519C23—441no—
520C23—442no—
521C23—442no—
522C23—441no—
523C23C22⋊C4×D1112yes—
524C23#6693812yes—
525C23#6699312yes—
526C23C2×D4×D1111yescharacteristic
527Q8—222no—
528Q8—222no—
529Q8—441no—
530Q8—441no—
531D4—24no—
532D4—24no—
533D4—42no—
534D4—42no—
535D4—48no—
536D4—222no—
537D4—222no—
538D4—448no—
539D4—441no—
540D4—441no—
541D4—8816no—
542C2×C4—44no—
543C2×C4—42no—
544C2×C4—84no—
545C2×C4—118no—
546C2×C4—224no—
547C2×C4—224no—
548C2×C4—222no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—448no—
552C2×C4—442no—
553C2×C4—442no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4C22⋊C4×D1112yes—
557C2×C4(C22⋊D11)⋊C414yes—
558C2×C4#6693714yes—
559C2×C4#6693812yes—
560C2×C4C4×C22⋊D1114yes—
561C2×C4#6699214yes—
562C2×C4#6699312yes—
563C2×C4C22×C4×D1111yescharacteristic
564C2×C4C2×#433911yescharacteristic
565C2×C4C2×D4×D1111yescharacteristic
566C2×C4C2×D4×D1111yescharacteristic
567C2×C4C2×#434111yescharacteristic
568C2×C4C22×C22⋊D1111yescharacteristic
569C8—22no—
570C8—22no—
571C8—224no—
572C22—22no—
573C22—22no—
574C22—24no—
575C22—24no—
576C22—48no—
577C22—44no—
578C22—816no—
579C22—82no—
580C22—82no—
581C22—84no—
582C22—444no—
583C22—442no—
584C22—881no—
585C22—881no—
586C22—882no—
587C22#1062257014yes—
588C22C2×C22⋊C4×D1111yescharacteristic
589C22C2×#6693811yescharacteristic
590C22#1062328812yes—
591C22#1062329312yes—
592C22C2×#6699311yescharacteristic
593C4—82no—
594C4—228no—
595C4—442no—
596C4—881no—
597C4—881no—
598C4#1062257014yes—
599C4C2×(C22⋊D11)⋊C411yescharacteristic
600C4C2×#6693711yescharacteristic
601C4C2×C4×C22⋊D1111yescharacteristic
602C4C2×#6699211yescharacteristic
603C2—24no—
604C2—84no—
605C2—882no—
606C2C2×#1062257011yescharacteristic
607C2#1307713712yes—
608C2#1307896812yes—
609C2#1307908611yescharacteristic
610C2#1307909711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#102C2
socleC23×C11C22×D4
prime radicalC2×#10623336C2
cosocleC22×C4×C11C24
hypercenterC22×#102D11
hypocenterC11#21206
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C2×#10622579C2semidirect
3. C2×#10622828C2semidirect
4. C2×#10622726C2semidirect
5. C2×#10622714C2semidirect
6. #13071240C2semidirect
7. #13069438C2semidirect
8. #13069431C2semidirect
9. #13069426C2semidirect
10. #13069420C2semidirect
11. C22×C11×#102C2semidirect
18. #10623336C4semidirect
33. C2×#66885C22semidirect
34. C2×#66885C22semidirect
35. C2×#66880C22semidirect
36. C2×#66880C22semidirect
38. C2×#66879C22semidirect
39. C2×C8×Dic11C22semidirect
40. #10622590C22semidirect
41. #10622589C22semidirect
43. C2×#66874C22semidirect
45. C2×#66873C22semidirect
70. C22×C8×C11D4semidirect
82. #66993C2×C4semidirect
85. #66989C2×C4semidirect
98. C2×#4318D4semidirect
205. C22×#102D11semidirect
371. C22×C8C22⋊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×#106233362
C2×#106225792
C2×#106228282
C2×#106227262
C2×#106227142
#130712402
#130694382
#130694312
#130694262
#130694202
C22×C11×#1022
#2120611