Finite Group Databasebeta

← #14816713

Subgroups — #14816713

Order 2816.

804 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622409C211yesmaximal, characteristic, complemented
2C2×#10622577C211yesmaximal, characteristic
3#13072334C211yesmaximal, characteristic
4#13071647C211yesmaximal, characteristic
5#13070166C211yesmaximal, characteristic, complemented
6#13070113C211yesmaximal, characteristic, complemented
7#13070007C211yesmaximal, characteristic, complemented
8#13069953C211yesmaximal, characteristic, complemented
9#13069387C211yesmaximal, characteristic, complemented
10#13069197C211yesmaximal, characteristic, complemented
11#13069050C211yesmaximal, characteristic
12#13068882C211yesmaximal, characteristic, complemented
13#13068817C211yesmaximal, characteristic
14#13068798C211yesmaximal, characteristic
15C11×#1872C211yesmaximal, characteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C2×#66943C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25#10622843C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28#10622825—21no—
29#10622825C2211yescharacteristic
30#10622823—21no—
31C4×C22⋊Dic11C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36#10622599—21no—
37#10622598C2211yescharacteristic
38#10622598C2211yescharacteristic
39#10622597—21no—
40#10622594—21no—
41#10622590C2211yescharacteristic
42C4⋊C4×Dic11—21no—
43C4⋊C4×Dic11C2211yescharacteristic
44#10622586C2211yescharacteristic
45#10622577—24no—
46C2×#66872C2211yescharacteristic
47C2×#66872C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49C2×#66871C2211yescharacteristic
50#10622564—21no—
51#10622564—21no—
52#10622409—24no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C11×C22⋊Q8—22no—
67C11×C22⋊Q8Q814yes—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—41no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11D411yescharacteristic
79C2×C22⋊Dic11D411yescharacteristic
80Q8×Dic11—22no—
81Q8×Dic11—41no—
82#66979—22no—
83#66979—41no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11C2311yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C2×#4318—22no—
100C2×#4318—22no—
101C2×#4318—22no—
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104#66943—22no—
105#66943—41no—
106C11×#103—22no—
107C11×#103—41no—
108C11×C22⋊C8—22no—
109#66899—22no—
110#66899—22no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95D411yescharacteristic
121C11⋊#95D411yescharacteristic
122#66882—22no—
123#66881—41no—
124Dic11⋊C8—22no—
125Dic11⋊C8—22no—
126#66872—22no—
127#66872D414yes—
128#66871—22no—
129#66871—22no—
130#26367—111nomaximal, Sylow
131C24×C11C2×D411yescharacteristic
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11C2×Q812yes—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—42no—
147C22×C4×C11—42no—
148C22×C4×C11—81no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×Q812yes—
151C22×C4×C11#4112yes—
152C22×C4×C11C2411yescharacteristic
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—42no—
173C11×C4⋊C4C2×D412yes—
174C11×C4⋊C4C2×Q812yes—
175C11×C22⋊C4—24no—
176C22⋊Dic11—41no—
177C22⋊Dic11—41no—
178C22⋊Dic11—42no—
179C22⋊Dic11—42no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—42no—
188C4⋊Dic11—42no—
189C4⋊Dic11—42no—
190C4⋊Dic11—81no—
191C4⋊Dic11C2×D412yes—
192Dic11⋊C4—42no—
193Dic11⋊C4—81no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—42no—
199C4×Dic11—42no—
200C4×Dic11—42no—
201#4318—28no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8C2×D412yes—
207C2×C11⋊C8#4112yes—
208C2×#479—111no—
209C2×#428—111no—
210#2442—111no—
211#2362—111no—
212#2097—111no—
213#2087—111no—
214#2068—111no—
215#2059—111no—
216#1949—111no—
217#1919—111no—
218#1894—111no—
219#1872D1111yescharacteristic
220#1865—111no—
221#1854—111no—
222#1851—111no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11C22⋊Q812yes—
230C23×C11C22×D411yescharacteristic
231Q8×C11—22no—
232Q8×C11—22no—
233Q8×C11—41no—
234Q8×C11—41no—
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×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—84no—
254C2×C4×C11C22⋊Q812yes—
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×Q811yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11H(5,𝔽2)11yescharacteristic
260C2×C4×C112−1+411yescharacteristic
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—22no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C8×C11—41no—
286C8×C11—41no—
287C11⋊C8—22no—
288C11⋊C8—22no—
289C22×M16—111no—
290C2×#125—111no—
291C2×C22⋊Q8C2×D1111yescharacteristic
292C2×C4×Q8—111no—
293C2×#117—111no—
294C22×C4⋊C4C2×D1111yescharacteristic
295#479—224no—
296#428—224no—
297C2×#107—111no—
298C2×#107—111no—
299C2×#107—111no—
300C2×#106—111no—
301C2×#106—111no—
302C2×#106—111no—
303C2×C4⋊C8—111no—
304C2×C4⋊C8—111no—
305C2×#103—111no—
306C2×#103—111no—
307C2×#103C2×D1111yescharacteristic
308C2×#103C2×D1111yescharacteristic
309C2×C22⋊C8C2×D1111yescharacteristic
310#400—221no—
311#398—221no—
312#391—111no—
313#389—111no—
314#389—111no—
315#389—111no—
316#388—221no—
317#388—221no—
318#387—221no—
319#385—221no—
320#382—111no—
321#380—111no—
322#380—221no—
323C4×C4⋊C4—111no—
324C4×C4⋊C4—221no—
325C4×C22⋊C4—111no—
326#340—111no—
327#340—111no—
328#340—111no—
329#340—111no—
330#340C2×D1111yescharacteristic
331#340C2×D1111yescharacteristic
332#336—111no—
333#336—111no—
334C22×C11—22no—
335C22×C11—22no—
336C22×C11—22no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11C2×C22⋊Q811yescharacteristic
342C22×C11D4211yescharacteristic
343C22×C11#54711yescharacteristic
344C22×C11#57511yescharacteristic
345C22×C11#57511yescharacteristic
346C22×C11#57711yescharacteristic
347C22×C11#57811yescharacteristic
348C4×C11—22no—
349C4×C11—42no—
350C4×C11—42no—
351C4×C11—42no—
352C4×C11—81no—
353C4×C11#52511yescharacteristic
354C4×C11#53911yescharacteristic
355C4×C11D4×Q811yescharacteristic
356C4×C11#55411yescharacteristic
357Dic11—41no—
358Dic11—41no—
359Dic11—41no—
360Dic11—42no—
361Dic11—41no—
362Dic11—81no—
363Dic11—81no—
364Dic11—81no—
365C22×Q8C22×D1111yescharacteristic
366C23×C4—21no—
367C23×C4C22×D1111yescharacteristic
368C2×M16—222no—
369C2×M16—222no—
370C2×M16—222no—
371C22×C8—111no—
372C22×C8—111no—
373C22×C8C22×D1111yescharacteristic
374C22×C8C22×D1111yescharacteristic
375#125—222no—
376#125—441no—
377C22⋊Q8—22no—
378C22⋊Q8Dic2214yes—
379C4×Q8—222no—
380C4×Q8—441no—
381#117—222no—
382#117—441no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—41no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4C22×D1111yescharacteristic
398C2×C4⋊C4C22×D1111yescharacteristic
399C2×C4⋊C4C22×D1111yescharacteristic
400C2×C22⋊C4—21no—
401C2×C22⋊C4—111no—
402C2×C22⋊C4—111no—
403C2×C22⋊C4—221no—
404C2×C22⋊C4—221no—
405C2×C42—111no—
406C2×C42—111no—
407C2×C42—221no—
408C2×C42—221no—
409C2×C42—221no—
410#107—222no—
411#107—222no—
412#107—222no—
413#106—114no—
414#106—222no—
415#106—441no—
416C4⋊C8—222no—
417C4⋊C8—222no—
418#103—22no—
419#103—41no—
420#103—222no—
421#103—222no—
422C22⋊C8—22no—
423#95—111no—
424#95—111no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95—221no—
429#95—221no—
430#95—221no—
431#95—221no—
432#95—221no—
433#95—221no—
434C2×C11—42no—
435C2×C11#244911yescharacteristic
436C2×C11#308011yescharacteristic
437C2×C11#308211yescharacteristic
438C2×C11#326911yescharacteristic
439C2×C11#327511yescharacteristic
440C2×C11#334911yescharacteristic
441C2×C11#335111yescharacteristic
442C24D4×D1111yescharacteristic
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8C2×Dic2212yes—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—42no—
458C22×C4—42no—
459C22×C4—81no—
460C22×C4—111no—
461C22×C4—111no—
462C22×C4—111no—
463C22×C4—111no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4C2×Dic2212yes—
469C22×C4D4×D1111yescharacteristic
470C22×C4#434112yes—
471C22×C4C23×D1111yescharacteristic
472M16—228no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—112no—
480C2×C8—112no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C4⋊C4—24no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—42no—
491C4⋊C4—112no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—442no—
500C4⋊C4—442no—
501C4⋊C4—442no—
502C4⋊C4—442no—
503C4⋊C4—881no—
504C4⋊C4—881no—
505C4⋊C4C2×Dic2212yes—
506C4⋊C4D4×D1112yes—
507C22⋊C4—24no—
508C22⋊C4—441no—
509C22⋊C4—441no—
510C22⋊C4—442no—
511C22⋊C4—442no—
512C42—221no—
513C42—221no—
514C42—221no—
515C42—221no—
516C42—442no—
517C42—442no—
518C42—442no—
519C11#2636711yescharacteristic, complemented, Sylow
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23#6693112yes—
527C23C2×D4×D1111yescharacteristic
528Q8—22no—
529Q8—22no—
530Q8—41no—
531Q8—41no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—84no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—222no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4#6693112yes—
576C2×C4C22×Dic2211yescharacteristic
577C2×C4C2×D4×D1111yescharacteristic
578C2×C4C2×#434111yescharacteristic
579C2×C4#6703711yescharacteristic
580C2×C4#41×D1111yescharacteristic
581C2×C4#6704311yescharacteristic
582C8—41no—
583C8—41no—
584C8—222no—
585C8—222no—
586C22—22no—
587C22—22no—
588C22—22no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22C2×#6693111yescharacteristic
594C22#1062312111yescharacteristic
595C22#1062318611yescharacteristic
596C22#1062329311yescharacteristic
597C22#1062329711yescharacteristic
598C22#1062330411yescharacteristic
599C22#1062330811yescharacteristic
600C4—22no—
601C4—42no—
602C4—42no—
603C4—42no—
604C4—81no—
605C4—441no—
606C4—441no—
607C4—441no—
608C4—442no—
609C4—441no—
610C4—881no—
611C4—881no—
612C4—881no—
613C4D4×Dic2211yescharacteristic
614C4#1062307011yescharacteristic
615C4#1062313311yescharacteristic
616C4#1062313711yescharacteristic
617C2—42no—
618C2#1307242911yescharacteristic
619C2#1307843611yescharacteristic
620C2#1307845411yescharacteristic
621C2#1308017411yescharacteristic
622C2#1308025111yescharacteristic
623C2#1308113911yescharacteristic
624C2#1308117911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1872C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1872D11
hypocenterC11#26367
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
1. C2×#10622409C2semidirect
5. #13070166C2semidirect
6. #13070113C2semidirect
7. #13070007C2semidirect
8. #13069953C2semidirect
9. #13069387C2semidirect
10. #13069197C2semidirect
12. #13068882C2semidirect
519. C11#26367semidirect

Maximal subgroups

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

subgroupindex
C2×#106224092
C2×#106225772
#130723342
#130716472
#130701662
#130701132
#130700072
#130699532
#130693872
#130691972
#130690502
#130688822
#130688172
#130687982
C11×#18722
#2636711