Finite Group Databasebeta

← #14763473

Subgroups — #14763473

Order 2816.

1138 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623111C211yesmaximal, characteristic
2C2×#10622446C211yesmaximal, characteristic, complemented
3#13071021C211yesmaximal, characteristic, complemented
4#13069579C212yesmaximal, complemented
5#13069424C212yesmaximal, complemented
6#13068937C212yesmaximal
7#13068925C212yesmaximal, complemented
8#13068621C211yesmaximal, characteristic, complemented
9#13068617C211yesmaximal, characteristic, complemented
10#13068613C211yesmaximal, characteristic, complemented
11C11×#1803C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#67000C2211yescharacteristic
14C2×#66999C2211yescharacteristic
15#10623111—24no—
16#10623111C418yescomplemented
17C2×#66951—21no—
18C2×#66948C2211yescharacteristic
19C2×#66947—21no—
20C2×#66945C2212yes—
21C2×#66943C2211yescharacteristic
22C2×C4×D44—21no—
23C2×C4×D44C2211yescharacteristic
24C2×#66925—21no—
25C2×C42×D11C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×#103C2212yes—
28C11×#384C2211yescharacteristic
29C2×#66899C2212yes—
30C2×#66885C2212yes—
31C2×(C2×D11)⋊C8C2212yes—
32C2×C8×Dic11C2212yes—
33#10622600—21no—
34#10622600—21no—
35#10622590C2212yes—
36C4⋊C4×Dic11—21no—
37C4⋊C4×Dic11—21no—
38C2×#66873C2212yes—
39#10622548C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41#10622446—24no—
42C11×#340C2212yes—
43#10622189C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C22×Q8×C11C2311yescharacteristic
47C22×D44—21no—
48C22×D44C2311yescharacteristic
49C22×C4×D11—21no—
50C22×C4×D11D411yescharacteristic
51C22×C4×D11D411yescharacteristic
52C22×C4×D11C2311yescharacteristic
53C22×C8×C11C2312yes—
54C4×Q8×C11—22no—
55C4×Q8×C11C2×C414yes—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C42×C11—21no—
62C2×C42×C11C2311yescharacteristic
63#67000—22no—
64#67000C2×C414yes—
65#66999—22no—
66#66999C2×C414yes—
67C2×(C2×D11)⋊C4—21no—
68C2×(C2×D11)⋊C4—21no—
69C2×(C2×D11)⋊C4—21no—
70C2×(C2×D11)⋊C4—21no—
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—22no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11C2312yes—
77C2×C4⋊Dic11C2311yescharacteristic
78C2×Dic11⋊C4—21no—
79C2×Dic11⋊C4—21no—
80C2×C4×Dic11—22no—
81C2×C4×Dic11D411yescharacteristic
82C2×C4×Dic11D411yescharacteristic
83C2×C4×Dic11C2311yescharacteristic
84C22×C11⋊C8C2312yes—
85#66951—28no—
86#66948—22no—
87#66948C2×C414yes—
88#66947—28no—
89#66945—42no—
90#66945—42no—
91#66943—22no—
92#66943C2×C414yes—
93C4×D44—28no—
94C4×D44—22no—
95C4×D44C2×C414yes—
96#66925—28no—
97C42×D11C2×C414yes—
98C42×D11D414yes—
99C11×C4⋊C8—22no—
100C11×#103—42no—
101#66899—42no—
102C11⋊#95—22no—
103C11⋊#95—22no—
104#66885—42no—
105(C2×D11)⋊C8—24no—
106C8×Dic11—24no—
107#66873—42no—
108C4⋊(C11⋊C8)—22no—
109#21862—111nomaximal, Sylow
110C23×D11—21no—
111C23×D11C2×D411yescharacteristic
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11C22×C412yes—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2411yescharacteristic
124C22×Dic11—21no—
125C22×Dic11—22no—
126C22×Dic11C2×D411yescharacteristic
127C22×Dic11C2×D411yescharacteristic
128C22×Dic11C2×D411yescharacteristic
129C2×D44—24no—
130C2×D44—21no—
131C2×D44—21no—
132C2×D44—21no—
133C2×D44—21no—
134C2×D44—21no—
135C2×D44—42no—
136C2×D44—42no—
137C2×D44C22×C412yes—
138C2×C4×D11—24no—
139C2×C4×D11—22no—
140C2×C4×D11—22no—
141C2×C4×D11—21no—
142C2×C4×D11—21no—
143C2×C4×D11—21no—
144C2×C4×D11—21no—
145C2×C4×D11—41no—
146C2×C4×D11—41no—
147C2×C4×D11—42no—
148C2×C4×D11—42no—
149C2×C4×D11C22⋊C414yes—
150C2×C4×D11C22⋊C414yes—
151C2×C4×D11C22×C412yes—
152C2×C4×D11C2×D412yes—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—42no—
161C11×C4⋊C4—42no—
162C11×C4⋊C4C22×C412yes—
163C42×C11—24no—
164C42×C11C22×C412yes—
165C42×C11C2×D412yes—
166(C2×D11)⋊C4—24no—
167(C2×D11)⋊C4—24no—
168(C2×D11)⋊C4—24no—
169(C2×D11)⋊C4—24no—
170(C2×D11)⋊C4—24no—
171(C2×D11)⋊C4—44no—
172C4⋊Dic11—24no—
173C4⋊Dic11—21no—
174C4⋊Dic11—22no—
175C4⋊Dic11—22no—
176C4⋊Dic11—42no—
177C4⋊Dic11—42no—
178C4⋊Dic11C22×C412yes—
179Dic11⋊C4—24no—
180Dic11⋊C4—24no—
181C4×Dic11—44no—
182C4×Dic11C22⋊C414yes—
183C4×Dic11C22⋊C414yes—
184C4×Dic11C22×C412yes—
185C4×Dic11C2×D412yes—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—22no—
189C2×#529—111no—
190C2×#431—111no—
191#2285—111no—
192#1991—112no—
193#1958—112no—
194#1875—112no—
195#1873—112no—
196#1803—111no—
197#1803D1111yescharacteristic, complemented
198#1802—111no—
199#1802—111no—
200C23×C11C22×D411yescharacteristic
201C22×D11—21no—
202C22×D11—21no—
203C22×D11—21no—
204C22×D11—21no—
205C22×D11—21no—
206C22×D11—21no—
207C22×D11—22no—
208C22×D11—41no—
209C22×D11—41no—
210C22×D11—41no—
211C22×D11—41no—
212C22×D11—41no—
213C22×D11—41no—
214C22×D11C2×C22⋊C412yes—
215Q8×C11—22no—
216Q8×C11—22no—
217Q8×C11—41no—
218Q8×C11—41no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11C2×C22⋊C412yes—
231C2×C4×C11C2×C22⋊C412yes—
232C2×C4×C11#13512yes—
233C2×C4×C11#13512yes—
234C2×C4×C11C23×C411yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11H(5,𝔽2)11yescharacteristic
237C2×C4×C11H(5,𝔽2)11yescharacteristic
238C2×C4×C112−1+411yescharacteristic
239C2×C4×C112−1+411yescharacteristic
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—22no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11C2×C22⋊C412yes—
253C2×Dic11C2×C22⋊C412yes—
254C2×Dic11C2×C22⋊C412yes—
255D44—22no—
256D44—22no—
257D44—48no—
258D44—41no—
259D44—41no—
260C4×D11—22no—
261C4×D11—22no—
262C4×D11—22no—
263C4×D11—22no—
264C4×D11—28no—
265C4×D11—44no—
266C4×D11—48no—
267C8×C11—42no—
268C11⋊C8—42no—
269#529—118no—
270#529—224no—
271C2×#126—221no—
272C2×#125—111no—
273C2×#124—111no—
274C2×#123—221no—
275C2×C22⋊Q8—111no—
276C2×#121—111no—
277C2×C4×Q8C2×D1111yescharacteristic
278C2×C4×D4—111no—
279C2×C4×D4—221no—
280C2×#117—112no—
281C2×#117—221no—
282C22×C42—111no—
283#431—224no—
284C2×C4⋊C8—111no—
285C2×C4⋊C8C2×D1111yescharacteristic
286C2×#103—112no—
287C2×#103C2×D1112yes—
288C2×#102—112no—
289C2×#102—112no—
290C2×C22⋊C8—112no—
291C2×C4×C8—112no—
292#384—111no—
293#384C2×D1111yescharacteristic
294#382—112no—
295#380—221no—
296#380—221no—
297C4×C4⋊C4—221no—
298C4×C4⋊C4—221no—
299#340—112no—
300#340—112no—
301#340—112no—
302#340C2×D1112yes—
303C22×C11C22×C22⋊C411yescharacteristic
304C22×C11#53511yescharacteristic
305C22×C11#53611yescharacteristic
306C22×C11C2×#13511yescharacteristic
307C22×C11C2×#13511yescharacteristic
308C22×C11#57511yescharacteristic
309C22×C11#57511yescharacteristic
310C2×D11—22no—
311C2×D11—22no—
312C2×D11—22no—
313C2×D11—41no—
314C2×D11—41no—
315C2×D11—41no—
316C2×D11—41no—
317C2×D11—42no—
318C2×D11—42no—
319C2×D11—42no—
320C2×D11—81no—
321C2×D11—81no—
322C2×D11—81no—
323C2×D11—81no—
324C4×C11—22no—
325C4×C11—42no—
326C4×C11—42no—
327C4×C11—82no—
328C4×C11#41614yes—
329C4×C11#52011yescharacteristic
330C4×C11#52011yescharacteristic
331C4×C11#53711yescharacteristic
332C4×C11#53711yescharacteristic
333Dic11—22no—
334Dic11—22no—
335Dic11—22no—
336Dic11—42no—
337Dic11—82no—
338C22×Q8C22×D1111yescharacteristic
339C22×D4—111no—
340C22×D4—221no—
341C23×C4—111no—
342C23×C4—111no—
343C23×C4—111no—
344C23×C4—221no—
345C22×C8—112no—
346C22×C8C22×D1112yes—
347#126—228no—
348#125—114no—
349#125—222no—
350#124—114no—
351#124—222no—
352#123—228no—
353C22⋊Q8—114no—
354C22⋊Q8—222no—
355#121—114no—
356#121—222no—
357C4×Q8—22no—
358C4×Q8C4×D1114yes—
359C4×D4—114no—
360C4×D4—228no—
361C4×D4—222no—
362#117—228no—
363#117—442no—
364#117—442no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—112no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4C22×D1112yes—
376C2×C4⋊C4C22×D1111yescharacteristic
377C2×C22⋊C4—221no—
378C2×C22⋊C4—221no—
379C2×C22⋊C4—221no—
380C2×C22⋊C4—221no—
381C2×C22⋊C4—221no—
382C2×C22⋊C4—222no—
383C2×C42—21no—
384C2×C42—111no—
385C2×C42—111no—
386C2×C42—111no—
387C2×C42—114no—
388C2×C42—114no—
389C2×C42—222no—
390C2×C42C22×D1111yescharacteristic
391C4⋊C8—22no—
392C4⋊C8—222no—
393#103—42no—
394#103—442no—
395#102—442no—
396#102—442no—
397C22⋊C8—224no—
398C4×C8—224no—
399#95—222no—
400#95—222no—
401C2×C11#231111yescharacteristic
402C2×C11C2×#41611yescharacteristic
403C2×C11#289611yescharacteristic
404C2×C11#321211yescharacteristic
405C2×C11#321211yescharacteristic
406C2×C11#323311yescharacteristic
407C2×C11#323311yescharacteristic
408D11—42no—
409D11—82no—
410C24—111no—
411C24—221no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8C2×C4×D1112yes—
418C2×D4—112no—
419C2×D4—224no—
420C2×D4—221no—
421C2×D4—221no—
422C2×D4—221no—
423C2×D4—221no—
424C2×D4—221no—
425C2×D4—442no—
426C2×D4—442no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—111no—
431C22×C4—111no—
432C22×C4—111no—
433C22×C4—114no—
434C22×C4—112no—
435C22×C4—112no—
436C22×C4—114no—
437C22×C4—222no—
438C22×C4—222no—
439C22×C4—221no—
440C22×C4—221no—
441C22×C4—221no—
442C22×C4—221no—
443C22×C4—221no—
444C22×C4—224no—
445C22×C4—222no—
446C22×C4—441no—
447C22×C4—441no—
448C22×C4—442no—
449C22×C4—442no—
450C22×C4D4×D1111yescharacteristic
451C22×C4D4×D1111yescharacteristic
452C22×C4C23×D1111yescharacteristic
453C2×C8—22no—
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—222no—
457C2×C8—222no—
458C2×C8—222no—
459C4⋊C4—24no—
460C4⋊C4—21no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—42no—
464C4⋊C4—42no—
465C4⋊C4—112no—
466C4⋊C4—224no—
467C4⋊C4—224no—
468C4⋊C4—224no—
469C4⋊C4—221no—
470C4⋊C4—222no—
471C4⋊C4—222no—
472C4⋊C4—442no—
473C4⋊C4—442no—
474C4⋊C4C2×C4×D1112yes—
475C22⋊C4—224no—
476C22⋊C4—224no—
477C22⋊C4—224no—
478C22⋊C4—224no—
479C22⋊C4—224no—
480C22⋊C4—444no—
481C42—24no—
482C42—114no—
483C42—114no—
484C42—112no—
485C42—112no—
486C42—444no—
487C42C2×C4×D1112yes—
488C42D4×D1112yes—
489C11#2186211yescharacteristic, complemented, Sylow
490C23—112no—
491C23—221no—
492C23—221no—
493C23—221no—
494C23—221no—
495C23—221no—
496C23—221no—
497C23—222no—
498C23—441no—
499C23—441no—
500C23—441no—
501C23—441no—
502C23—441no—
503C23—441no—
504C23C2×D4×D1111yescharacteristic
505Q8—22no—
506Q8—22no—
507Q8—41no—
508Q8—41no—
509D4—222no—
510D4—222no—
511D4—448no—
512D4—441no—
513D4—441no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—112no—
526C2×C4—112no—
527C2×C4—112no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—222no—
535C2×C4—222no—
536C2×C4—222no—
537C2×C4—222no—
538C2×C4—228no—
539C2×C4—222no—
540C2×C4—444no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—448no—
544C2×C4—442no—
545C2×C4—442no—
546C2×C4—442no—
547C2×C4C22⋊C4×D1112yes—
548C2×C4C22⋊C4×D1112yes—
549C2×C4#6696912yes—
550C2×C4#6697212yes—
551C2×C4C22×C4×D1111yescharacteristic
552C2×C4C2×D4×D1111yescharacteristic
553C2×C4#6703711yescharacteristic
554C2×C4#6704011yescharacteristic
555C2×C4#6704211yescharacteristic
556C2×C4#6704311yescharacteristic
557C8—42no—
558C8—442no—
559C22—222no—
560C22—222no—
561C22—222no—
562C22—441no—
563C22—441no—
564C22—441no—
565C22—441no—
566C22—442no—
567C22—442no—
568C22—442no—
569C22—881no—
570C22—881no—
571C22—881no—
572C22—881no—
573C22C2×C22⋊C4×D1111yescharacteristic
574C22#1062313811yescharacteristic
575C22#1062315911yescharacteristic
576C22C2×#6696911yescharacteristic
577C22C2×#6697211yescharacteristic
578C22#1062330411yescharacteristic
579C22#1062330811yescharacteristic
580C4—22no—
581C4—42no—
582C4—42no—
583C4—82no—
584C4—222no—
585C4—222no—
586C4—222no—
587C4—442no—
588C4—882no—
589C4#1062241714yes—
590C4#1062303511yescharacteristic
591C4#1062305411yescharacteristic
592C4#1062313911yescharacteristic
593C4#1062316011yescharacteristic
594C2—442no—
595C2—882no—
596C2#1307120511yescharacteristic
597C2C2×#1062241711yescharacteristic
598C2#1307713211yescharacteristic
599C2#1307959611yescharacteristic
600C2#1307959711yescharacteristic
601C2#1307979911yescharacteristic
602C2#1307980011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1803C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
cosocleC22×C4×C11C24
hypercenter#1803D11
hypocenterC11#21862
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
2. C2×#10622446C2semidirect
3. #13071021C2semidirect
4. #13069579C2semidirect
5. #13069424C2semidirect
7. #13068925C2semidirect
8. #13068621C2semidirect
9. #13068617C2semidirect
10. #13068613C2semidirect
11. C11×#1803C2semidirect
16. #10623111C4semidirect
197. #1803D11semidirect
489. C11#21862semidirect

Maximal subgroups

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

subgroupindex
C2×#106231112
C2×#106224462
#130710212
#130695792
#130694242
#130689372
#130689252
#130686212
#130686172
#130686132
C11×#18032
#2186211