Finite Group Databasebeta

← #14801943

Subgroups — #14801943

Order 2816.

806 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622336C211yesmaximal, characteristic
2C2×#10622664C211yesmaximal, characteristic
3#13073070C211yesmaximal, characteristic
4#13071643C211yesmaximal, characteristic
5#13070091C211yesmaximal, characteristic, complemented
6#13070038C211yesmaximal, characteristic, complemented
7#13069995C211yesmaximal, characteristic, complemented
8#13069937C211yesmaximal, characteristic, complemented
9#13069383C211yesmaximal, characteristic, complemented
10#13069259C211yesmaximal, characteristic, complemented
11#13068954C211yesmaximal, characteristic, complemented
12#13068793C211yesmaximal, characteristic
13#13068620C211yesmaximal, characteristic, complemented
14#13068332C211yesmaximal, characteristic
15C11×#1873C211yesmaximal, characteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×#4326C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C2×#66977C2211yescharacteristic
21C23×C11⋊C8C2211yescharacteristic
22C2×#66940C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26#10622843C2211yescharacteristic
27#10622843C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C4×C22⋊Dic11C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31C2×#66881C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36#10622664—24no—
37#10622591—21no—
38#10622591—21no—
39#10622590C2211yescharacteristic
40#10622589C2211yescharacteristic
41C4⋊C4×Dic11C2211yescharacteristic
42#10622587C2211yescharacteristic
43#10622586C2211yescharacteristic
44C2×#66874C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622565—21no—
47#10622565—21no—
48#10622558—21no—
49#10622557—21no—
50#10622546—21no—
51C4×Dic11⋊C4—21no—
52#10622336—24no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C11×C22⋊Q8—22no—
67C11×C22⋊Q8—22no—
68C11×#117—22no—
69C11×#117—41no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C42×C11—21no—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11D411yescharacteristic
80C2×C22⋊Dic11D411yescharacteristic
81C2×#4326—22no—
82C2×#4326—22no—
83C2×#4326—41no—
84#66979—22no—
85#66979—22no—
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89#66977—22no—
90#66977D414yes—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11C2311yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C22×C11⋊C8—22no—
102C22×C11⋊C8—22no—
103C22×C11⋊C8—41no—
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106#66940—22no—
107#66940—41no—
108C11×#103—22no—
109C11×#103—41no—
110C11×C22⋊C8—22no—
111#66899—22no—
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⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95D411yescharacteristic
123C11⋊#95D411yescharacteristic
124#66882—22no—
125#66881—22no—
126#66880—22no—
127#66880—22no—
128Dic11⋊C8—22no—
129Dic11⋊C8—41no—
130#66874—22no—
131#66871—22no—
132#25201—111nomaximal, Sylow
133C24×C11C2×D411yescharacteristic
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×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—21no—
147C22×C4×C11—21no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D412yes—
150C22×C4×C11#4112yes—
151C22×C4×C11C2411yescharacteristic
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22C2×D412yes—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—42no—
178C11×C4⋊C4#4112yes—
179C11×C22⋊C4—42no—
180C11×C22⋊C4—42no—
181C42×C11—42no—
182C22⋊Dic11—22no—
183C22⋊Dic11—24no—
184C22⋊Dic11—41no—
185C22⋊Dic11—42no—
186#4326—44no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11C2×D412yes—
193Dic11⋊C4—24no—
194Dic11⋊C4—42no—
195Dic11⋊C4—42no—
196Dic11⋊C4—42no—
197Dic11⋊C4—42no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201C4×Dic11—21no—
202C4×Dic11—42no—
203C4×Dic11—42no—
204C4×Dic11—42no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—44no—
211C2×C11⋊C8#4112yes—
212C2×#485—111no—
213C2×#467—111no—
214#2499—111no—
215#2362—111no—
216#2083—111no—
217#2074—111no—
218#2066—111no—
219#2056—111no—
220#1949—111no—
221#1928—111no—
222#1878—111no—
223#1873D1111yescharacteristic
224#1850—111no—
225#1803—111no—
226#1735—111no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11#12112yes—
234C23×C11C22×D411yescharacteristic
235Q8×C11—41no—
236Q8×C11—41no—
237Q8×C11—41no—
238Q8×C11—41no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
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—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11#12112yes—
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11H(5,𝔽2)11yescharacteristic
263C2×C4×C112−1+411yescharacteristic
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11#13512yes—
288Dic22—22no—
289Dic22—22no—
290Dic22—41no—
291Dic22—41no—
292C8×C11—41no—
293C8×C11—41no—
294C11⋊C8—22no—
295C11⋊C8—41no—
296C22×Q16—111no—
297C23×C8—111no—
298C2×C22⋊Q8—111no—
299C2×C22⋊Q8C2×D1111yescharacteristic
300C2×C4×Q8—111no—
301C2×#117—111no—
302C2×#117C2×D1111yescharacteristic
303#485—224no—
304#467—224no—
305C2×#107—111no—
306C2×#107—111no—
307C2×#106—111no—
308C2×C4⋊C8—111no—
309C2×C4⋊C8—111no—
310C2×#103—111no—
311C2×#103—111no—
312C2×#103—111no—
313C2×#103—111no—
314C2×#103C2×D1111yescharacteristic
315C2×#103C2×D1111yescharacteristic
316C2×C22⋊C8C2×D1111yescharacteristic
317#397—221no—
318#397—221no—
319#391—111no—
320#391—111no—
321#391—111no—
322#389—111no—
323#388—221no—
324#388—221no—
325#387—221no—
326#387—221no—
327#387—221no—
328#384—111no—
329#382—111no—
330C4×C4⋊C4—111no—
331C4×C4⋊C4—221no—
332C4×C22⋊C4—111no—
333#340—111no—
334#340—111no—
335#340—111no—
336#340—111no—
337#340C2×D1111yescharacteristic
338#340C2×D1111yescharacteristic
339#336—111no—
340#336—111no—
341C22×C11—22no—
342C22×C11—22no—
343C22×C11—22no—
344C22×C11—41no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11C2×#12111yescharacteristic
349C22×C11#54611yescharacteristic
350C22×C11#54711yescharacteristic
351C22×C11C2×#13511yescharacteristic
352C22×C11#57511yescharacteristic
353C22×C11#57811yescharacteristic
354C22×C11#57811yescharacteristic
355C4×C11—22no—
356C4×C11—42no—
357C4×C11—81no—
358C4×C11—81no—
359C4×C11—81no—
360C4×C11#52911yescharacteristic
361C4×C11#53911yescharacteristic
362C4×C11#54611yescharacteristic
363C4×C11#54711yescharacteristic
364Dic11—22no—
365Dic11—41no—
366Dic11—41no—
367Dic11—42no—
368Dic11—42no—
369Dic11—41no—
370Dic11—81no—
371Dic11—81no—
372C22×Q8—111no—
373C22×Q8C22×D1111yescharacteristic
374C23×C4C22×D1111yescharacteristic
375C2×Q16—222no—
376C2×Q16—222no—
377C2×Q16—441no—
378C22×C8—111no—
379C22×C8—111no—
380C22×C8—222no—
381C22×C8—222no—
382C22×C8—441no—
383C22×C8C22×D1111yescharacteristic
384C22×C8C22×D1111yescharacteristic
385C22⋊Q8—22no—
386C22⋊Q8—22no—
387C22⋊Q8—114no—
388C22⋊Q8—222no—
389C4×Q8—222no—
390C4×Q8—441no—
391#117—22no—
392#117—41no—
393#117—222no—
394#117—222no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4C22×D1111yescharacteristic
405C2×C4⋊C4C22×D1111yescharacteristic
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—111no—
410C2×C22⋊C4—111no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C42—21no—
414C2×C42—111no—
415C2×C42—111no—
416C2×C42—221no—
417C2×C42—221no—
418C2×C42—221no—
419#107—222no—
420#107—222no—
421#106—222no—
422C4⋊C8—222no—
423C4⋊C8—441no—
424#103—22no—
425#103—41no—
426#103—222no—
427#103—222no—
428#103—222no—
429#103—222no—
430C22⋊C8—22no—
431#95—111no—
432#95—111no—
433#95—221no—
434#95—221no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95—221no—
441#95—221no—
442#95—221no—
443C2×C11—42no—
444C2×C11#242511yescharacteristic
445C2×C11#303511yescharacteristic
446C2×C11#304411yescharacteristic
447C2×C11#330011yescharacteristic
448C2×C11#331511yescharacteristic
449C2×C11#334211yescharacteristic
450C2×C11#334911yescharacteristic
451C24D4×D1111yescharacteristic
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—112no—
459C2×Q8—221no—
460C2×Q8—221no—
461C2×Q8—221no—
462C2×Q8—221no—
463C2×Q8—221no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—111no—
475C22×C4—111no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4#433912yes—
481C22×C4D4×D1111yescharacteristic
482C22×C4D4×D1112yes—
483C22×C4C23×D1111yescharacteristic
484Q16—444no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—112no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—444no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—42no—
504C4⋊C4—112no—
505C4⋊C4—224no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—442no—
512C4⋊C4—442no—
513C4⋊C4—442no—
514C4⋊C4—442no—
515C4⋊C4#434112yes—
516C22⋊C4—42no—
517C22⋊C4—42no—
518C22⋊C4—222no—
519C22⋊C4—224no—
520C22⋊C4—441no—
521C22⋊C4—442no—
522C42—42no—
523C42—221no—
524C42—221no—
525C42—221no—
526C42—221no—
527C42—442no—
528C42—442no—
529C42—442no—
530C11#2520111yescharacteristic, complemented, Sylow
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23#6693712yes—
538C23C2×D4×D1111yescharacteristic
539Q8—41no—
540Q8—41no—
541Q8—41no—
542Q8—41no—
543Q8—222no—
544Q8—222no—
545Q8—441no—
546Q8—441no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—112no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—222no—
569C2×C4—222no—
570C2×C4—221no—
571C2×C4—221no—
572C2×C4—221no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4#6693712yes—
590C2×C4C2×#433911yescharacteristic
591C2×C4C2×D4×D1111yescharacteristic
592C2×C4C2×#434111yescharacteristic
593C2×C4#6703711yescharacteristic
594C2×C4#41×D1111yescharacteristic
595C2×C4#6704311yescharacteristic
596C8—41no—
597C8—41no—
598C8—222no—
599C8—441no—
600C22—22no—
601C22—22no—
602C22—22no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22C2×#6693711yescharacteristic
608C22#1062312211yescharacteristic
609C22#1062318611yescharacteristic
610C22D11×#13511yescharacteristic
611C22#1062329911yescharacteristic
612C22#1062331011yescharacteristic
613C22#1062331011yescharacteristic
614C4—22no—
615C4—42no—
616C4—81no—
617C4—81no—
618C4—81no—
619C4—222no—
620C4—442no—
621C4—442no—
622C4—441no—
623C4—441no—
624C4—441no—
625C4—881no—
626C4—881no—
627C4#1062306911yescharacteristic
628C4#1062309511yescharacteristic
629C4#1062314111yescharacteristic
630C4#1062314211yescharacteristic
631C2—42no—
632C2#1307216911yescharacteristic
633C2#1307806911yescharacteristic
634C2#1307814511yescharacteristic
635C2#1308049611yescharacteristic
636C2#1308071611yescharacteristic
637C2#1308104111yescharacteristic
638C2#1308115011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1873C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1873D11
hypocenterC11#25201
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1873

Complements

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

NH ≅ G/Ntype
5. #13070091C2semidirect
6. #13070038C2semidirect
7. #13069995C2semidirect
8. #13069937C2semidirect
9. #13069383C2semidirect
10. #13069259C2semidirect
11. #13068954C2semidirect
13. #13068620C2semidirect
530. C11#25201semidirect

Maximal subgroups

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

subgroupindex
C2×#106223362
C2×#106226642
#130730702
#130716432
#130700912
#130700382
#130699952
#130699372
#130693832
#130692592
#130689542
#130687932
#130686202
#130683322
C11×#18732
#2520111