Finite Group Databasebeta

← #14765586

Subgroups — #14765586

Order 2816.

780 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071300C211yesmaximal, characteristic
2#13071239C211yesmaximal, characteristic
3#13069355C211yesmaximal, characteristic, complemented
4#13069345C211yesmaximal, characteristic, complemented
5#13069308C211yesmaximal, characteristic, complemented
6#13069294C211yesmaximal, characteristic, complemented
7#13069210C211yesmaximal, characteristic, complemented
8#13069203C211yesmaximal, characteristic, complemented
9#13068924C211yesmaximal, characteristic
10#13068886C211yesmaximal, characteristic, complemented
11#13068886C211yesmaximal, characteristic, complemented
12#13068811C211yesmaximal, characteristic
13#13068711C211yesmaximal, characteristic
14#13068384C211yesmaximal, characteristic
15C2×C11×#485C211yesmaximal, characteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C11×#485C418yescomplemented
22C2×C11×#107C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27#10622843C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30#10622825C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×#66879C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36#10622598—21no—
37#10622598C2211yescharacteristic
38#10622598C2211yescharacteristic
39#10622598C2211yescharacteristic
40#10622598C2211yescharacteristic
41#10622598C2211yescharacteristic
42#10622594—21no—
43C4⋊C4×Dic11C2211yescharacteristic
44#10622564—21no—
45#10622564—21no—
46#10622563—21no—
47#10622563—21no—
48#10622549—21no—
49#10622548—21no—
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11—21no—
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C11×C22⋊Q8—22no—
66C11×C22⋊Q8C2×C414yes—
67C11×#117—22no—
68C11×#117C2×C414yes—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C42×C11—21no—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11D411yescharacteristic
78C2×C22⋊Dic11D411yescharacteristic
79Q8×Dic11—41no—
80Q8×Dic11—41no—
81#66979—41no—
82#66979—41no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—41no—
91C2×C4⋊Dic11—41no—
92C2×C4⋊Dic11D411yescharacteristic
93C2×C4⋊Dic11D411yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11C2311yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C11×#107C2×C414yescomplemented
105C11×#106C2×C414yescomplemented
106C11×#103C2×C414yescomplemented
107C11×#103C2×C414yescomplemented
108C11×C22⋊C8C2×C414yes—
109#66899—41no—
110#66899—41no—
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—
120C22⋊(C11⋊C8)—22no—
121#66881—41no—
122#66881—41no—
123#66879—41no—
124C8×Dic11—41no—
125#22092—111nomaximal, Sylow
126C24×C11C2×D411yescharacteristic
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11C22×C412yes—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11C22×C412yes—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11#4112yes—
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—42no—
150C22×Dic11—81no—
151C22×Dic11—81no—
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11C22×C412yes—
161C2×C8×C11C22×C412yes—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4C22×C412yes—
167C11×C4⋊C4C22×C412yes—
168C11×C4⋊C4C22×C412yes—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—24no—
171C42×C11—24no—
172C22⋊Dic11—41no—
173C22⋊Dic11—41no—
174C22⋊Dic11—81no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—41no—
184C4⋊Dic11—41no—
185C4⋊Dic11—42no—
186C4⋊Dic11—42no—
187C4⋊Dic11—81no—
188C4⋊Dic11—81no—
189C4⋊Dic11—81no—
190C4⋊Dic11—81no—
191C4⋊Dic11—81no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—42no—
197C4×Dic11—81no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×#485D1111yescharacteristic
205#2323—111no—
206#2317—111no—
207#1943—111no—
208#1941—111no—
209#1935—111no—
210#1933—111no—
211#1921—111no—
212#1920—111no—
213#1872—111no—
214#1865—111no—
215#1865—111no—
216#1853—111no—
217#1825—111no—
218#1750—111no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11C4×D412yes—
226C23×C11C22×D411yescharacteristic
227Q8×C11—22no—
228Q8×C11—22no—
229Q8×C11—41no—
230Q8×C11—41no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11C4×D412yes—
250C2×C4×C11C23×C411yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11H(5,𝔽2)11yescharacteristic
253C2×C4×C11H(5,𝔽2)11yescharacteristic
254C2×C4×C112−1+411yescharacteristic
255C2×C4×C112−1+411yescharacteristic
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—84no—
281C8×C11—22no—
282C8×C11—22no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285C2×C22⋊Q8C2×D1111yescharacteristic
286C2×C4×Q8—111no—
287C2×#117—111no—
288C2×#117C2×D1111yescharacteristic
289C22×C4⋊C4—111no—
290#485Dic1118yescomplemented
291C2×#107C2×D1111yescharacteristic
292C2×#106—111no—
293C2×#106—111no—
294C2×#106C2×D1111yescharacteristic
295C2×#103—111no—
296C2×#103—111no—
297C2×#103C2×D1111yescharacteristic
298C2×#103C2×D1111yescharacteristic
299C2×C22⋊C8—111no—
300C2×C22⋊C8C2×D1111yescharacteristic
301C2×#97—111no—
302C2×C4×C8—111no—
303#391—111no—
304#389—111no—
305#389—111no—
306#389—111no—
307#389—111no—
308#389—111no—
309#389—221no—
310#388—221no—
311#388—221no—
312#387—221no—
313#385—221no—
314#385—221no—
315#384—221no—
316#382—221no—
317#380—111no—
318C4×C4⋊C4—111no—
319#340—111no—
320#340—111no—
321#340—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#336—111no—
328#336—111no—
329C22×C11—22no—
330C22×C11—22no—
331C22×C11—22no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11C2×C4×D411yescharacteristic
337C22×C11#53411yescharacteristic
338C22×C11#53611yescharacteristic
339C22×C11#57711yescharacteristic
340C22×C11#57711yescharacteristic
341C22×C11#57711yescharacteristic
342C22×C11#57811yescharacteristic
343C4×C11—22no—
344C4×C11—42no—
345C4×C11—42no—
346C4×C11—42no—
347C4×C11—42no—
348C4×C11#52011yescharacteristic
349C4×C11#52011yescharacteristic
350C4×C11#53911yescharacteristic
351C4×C11#53911yescharacteristic
352Dic11—41no—
353Dic11—41no—
354Dic11—41no—
355Dic11—41no—
356Dic11—81no—
357Dic11—81no—
358Dic11—81no—
359Dic11—81no—
360C22×Q8C22×D1111yescharacteristic
361C23×C4—221no—
362C23×C4C22×D1111yescharacteristic
363C22×C8—111no—
364C22×C8—111no—
365C22×C8C22×D1111yescharacteristic
366C22×C8C22×D1111yescharacteristic
367C22⋊Q8—22no—
368C22⋊Q8C2×Dic1114yes—
369C4×Q8—441no—
370C4×Q8—441no—
371#117—22no—
372#117—441no—
373#117—441no—
374#117C2×Dic1114yes—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—441no—
390C2×C4⋊C4—441no—
391C2×C4⋊C4C22×D1111yescharacteristic
392C2×C4⋊C4C22×D1111yescharacteristic
393C2×C4⋊C4C22×D1111yescharacteristic
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—111no—
397C2×C22⋊C4—111no—
398C2×C22⋊C4—221no—
399C2×C42—21no—
400C2×C42—111no—
401C2×C42—111no—
402C2×C42—221no—
403C2×C42—221no—
404#107C2×Dic1114yescomplemented
405#106—441no—
406#106—441no—
407#106C2×Dic1114yescomplemented
408#103—441no—
409#103—441no—
410#103C2×Dic1114yescomplemented
411#103C2×Dic1114yescomplemented
412C22⋊C8—222no—
413C22⋊C8C2×Dic1114yes—
414#97—441no—
415C4×C8—441no—
416#95—221no—
417#95—221no—
418#95—221no—
419#95—221no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425C2×C11—42no—
426C2×C11#232211yescharacteristic
427C2×C11#294711yescharacteristic
428C2×C11#295211yescharacteristic
429C2×C11#320011yescharacteristic
430C2×C11#320111yescharacteristic
431C2×C11#324211yescharacteristic
432C2×C11#324411yescharacteristic
433C24D4×D1111yescharacteristic
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8C22×Dic1112yes—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—111no—
449C22×C4—111no—
450C22×C4—111no—
451C22×C4—111no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4—221no—
456C22×C4—442no—
457C22×C4—881no—
458C22×C4—881no—
459C22×C4D4×D1111yescharacteristic
460C22×C4#434112yes—
461C22×C4C22×Dic1112yes—
462C22×C4C23×D1111yescharacteristic
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8C22×Dic1112yes—
474C2×C8C22×Dic1112yes—
475C4⋊C4—24no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—441no—
488C4⋊C4—441no—
489C4⋊C4—442no—
490C4⋊C4—442no—
491C4⋊C4—881no—
492C4⋊C4—881no—
493C4⋊C4—881no—
494C4⋊C4—881no—
495C4⋊C4—881no—
496C4⋊C4C22×Dic1112yes—
497C4⋊C4C22×Dic1112yes—
498C4⋊C4C22×Dic1112yes—
499C22⋊C4—24no—
500C22⋊C4—24no—
501C22⋊C4—441no—
502C22⋊C4—441no—
503C22⋊C4—881no—
504C42—24no—
505C42—221no—
506C42—221no—
507C42—221no—
508C42—221no—
509C42—442no—
510C42—881no—
511C11#2209211yescharacteristic, complemented, Sylow
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23D4×Dic1112yes—
519C23C2×D4×D1111yescharacteristic
520Q8—22no—
521Q8—22no—
522Q8—41no—
523Q8—41no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—884no—
567C2×C4D4×Dic1112yes—
568C2×C4C2×#434111yescharacteristic
569C2×C4#6704211yescharacteristic
570C2×C4#6704211yescharacteristic
571C2×C4#6704311yescharacteristic
572C2×C4#6704311yescharacteristic
573C2×C4C23×Dic1111yescharacteristic
574C8—22no—
575C8—22no—
576C8—441no—
577C8—441no—
578C22—22no—
579C22—22no—
580C22—22no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22#1062317911yescharacteristic
586C22#1062318411yescharacteristic
587C22#1062330111yescharacteristic
588C22#1062330111yescharacteristic
589C22#1062330911yescharacteristic
590C22#1062331011yescharacteristic
591C22C2×D4×Dic1111yescharacteristic
592C4—22no—
593C4—42no—
594C4—42no—
595C4—42no—
596C4—42no—
597C4—441no—
598C4—441no—
599C4—441no—
600C4—441no—
601C4—881no—
602C4—881no—
603C4—881no—
604C4—881no—
605C4#1062319611yescharacteristic
606C4#1062319611yescharacteristic
607C4#1062335811yescharacteristic
608C4#1062335811yescharacteristic
609C2—42no—
610C2#1307128811yescharacteristic
611C2#1307746011yescharacteristic
612C2#1307750011yescharacteristic
613C2#1307948711yescharacteristic
614C2#1307950411yescharacteristic
615C2#1307989011yescharacteristic
616C2#1307992011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#485C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×#485D11
hypocenterC11#22092
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
3. #13069355C2semidirect
4. #13069345C2semidirect
5. #13069308C2semidirect
6. #13069294C2semidirect
7. #13069210C2semidirect
8. #13069203C2semidirect
10. #13068886C2semidirect
11. #13068886C2semidirect
21. C11×#485C4semidirect
104. C11×#107C2×C4semidirect
105. C11×#106C2×C4semidirect
106. C11×#103C2×C4semidirect
107. C11×#103C2×C4semidirect
290. #485Dic11semidirect
404. #107C2×Dic11semidirect
407. #106C2×Dic11semidirect
410. #103C2×Dic11semidirect
411. #103C2×Dic11semidirect
511. C11#22092semidirect

Maximal subgroups

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

subgroupindex
#130713002
#130712392
#130693552
#130693452
#130693082
#130692942
#130692102
#130692032
#130689242
#130688862
#130688112
#130687112
#130683842
C2×C11×#4852
#2209211