Finite Group Databasebeta

← #14802151

Subgroups — #14802151

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×#10622609C211yesmaximal, characteristic
2C2×#10622729C211yesmaximal, characteristic
3#13073065C211yesmaximal, characteristic
4#13071643C211yesmaximal, characteristic
5#13070103C211yesmaximal, characteristic, complemented
6#13070028C211yesmaximal, characteristic, complemented
7#13070012C211yesmaximal, characteristic, complemented
8#13069940C211yesmaximal, characteristic, complemented
9#13069373C211yesmaximal, characteristic, complemented
10#13069248C211yesmaximal, characteristic, complemented
11#13068958C211yesmaximal, characteristic, complemented
12#13068928C211yesmaximal, characteristic
13#13068794C211yesmaximal, characteristic
14#13068630C211yesmaximal, characteristic, complemented
15C11×#1735C211yesmaximal, characteristic
16C23×C8×C11C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C2×#66977C2211yescharacteristic
20C2×#66977C2211yescharacteristic
21C22×Dic44C2211yescharacteristic
22C2×#66940C2211yescharacteristic
23C4×C22⋊Dic11C2211yescharacteristic
24C2×C22⋊(C11⋊C8)C2211yescharacteristic
25#10622729—24no—
26C2×#66882C2211yescharacteristic
27C2×#66880C2211yescharacteristic
28C2×#66880C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31#10622609—24no—
32#10622590C2211yescharacteristic
33#10622589C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35#10622587C2211yescharacteristic
36#10622587C2211yescharacteristic
37#10622587C2211yescharacteristic
38#10622586C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622565—21no—
46#10622565—21no—
47#10622558—21no—
48#10622557—21no—
49#10622546—21no—
50#10622546—21no—
51#10622546—21no—
52C4×Dic11⋊C4—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×Dic22C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C22×C8×C11—22no—
65C22×C8×C11—22no—
66C22×C8×C11—41no—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×#117—22no—
70C11×#117—22no—
71C11×#117—22no—
72C11×#117—41no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C42×C11—21no—
80C2×C42×C11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11D411yescharacteristic
84C2×C22⋊Dic11D411yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87#66977—22no—
88#66977—22no—
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×Dic11⋊C4—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11C2311yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C2×Dic44—22no—
104C2×Dic44—22no—
105C2×Dic44—41no—
106#66940—22no—
107#66940—41no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95D411yescharacteristic
119C11⋊#95D411yescharacteristic
120C22⋊(C11⋊C8)—22no—
121#66882—22no—
122#66880—22no—
123#66880—22no—
124Dic11⋊C8—22no—
125Dic11⋊C8—41no—
126#66874—22no—
127#66874—22no—
128#66874—22no—
129#66874—41no—
130#66872—22no—
131#66871—22no—
132#25215—111nomaximal, Sylow
133C24×C11C2×D411yescharacteristic
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×C11—21no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D412yes—
144C22×C4×C11#4112yes—
145C22×C4×C11C2411yescharacteristic
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
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—44no—
172C2×C8×C11#4112yes—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4#4112yes—
181C11×C22⋊C4—42no—
182C11×C22⋊C4—42no—
183C42×C11—42no—
184C42×C11—42no—
185C22⋊Dic11—22no—
186C22⋊Dic11—24no—
187C22⋊Dic11—41no—
188C22⋊Dic11—42no—
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—
198Dic11⋊C4—42no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201C4×Dic11—21no—
202C4×Dic11—21no—
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—21no—
211Dic44—44no—
212C2×#485—111no—
213C2×#467—111no—
214#2499—111no—
215#2362—111no—
216#2085—111no—
217#2072—111no—
218#2068—111no—
219#2056—111no—
220#1947—111no—
221#1927—111no—
222#1878—111no—
223#1873—111no—
224#1850—111no—
225#1805—111no—
226#1735D1111yescharacteristic
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11#12112yes—
234C23×C11C22×D411yescharacteristic
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—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×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11#12112yes—
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11H(5,𝔽2)11yescharacteristic
259C2×C4×C112−1+411yescharacteristic
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—22no—
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—41no—
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#13512yes—
284Dic22—22no—
285Dic22—22no—
286Dic22—41no—
287Dic22—41no—
288Dic22—41no—
289Dic22—41no—
290Dic22—41no—
291Dic22—41no—
292C8×C11—22no—
293C8×C11—41no—
294C11⋊C8—41no—
295C11⋊C8—41no—
296C22×Q16—111no—
297C23×C8C2×D1111yescharacteristic
298C2×C22⋊Q8—111no—
299C2×C22⋊Q8—111no—
300C2×C4×Q8—111no—
301C2×#117C2×D1111yescharacteristic
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×#103—111no—
315C2×#103—111no—
316C2×C22⋊C8—111no—
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#340C2×D1111yescharacteristic
336#340C2×D1111yescharacteristic
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—42no—
367Dic11—42no—
368Dic11—41no—
369Dic11—41no—
370Dic11—81no—
371Dic11—81no—
372C22×Q8—111no—
373C22×Q8—111no—
374C23×C4C22×D1111yescharacteristic
375C2×Q16—222no—
376C2×Q16—222no—
377C2×Q16—441no—
378C22×C8—22no—
379C22×C8—22no—
380C22×C8—41no—
381C22×C8—111no—
382C22×C8—111no—
383C22×C8C22×D1111yescharacteristic
384C22×C8C22×D1111yescharacteristic
385C22⋊Q8—114no—
386C22⋊Q8—222no—
387C22⋊Q8—222no—
388C22⋊Q8—222no—
389C4×Q8—222no—
390C4×Q8—441no—
391#117—22no—
392#117—22no—
393#117—22no—
394#117—41no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4C22×D1111yescharacteristic
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—21no—
415C2×C42—111no—
416C2×C42—111no—
417C2×C42—221no—
418C2×C42—221no—
419#107—222no—
420#107—222no—
421#106—222no—
422C4⋊C8—222no—
423C4⋊C8—441no—
424#103—222no—
425#103—222no—
426#103—222no—
427#103—222no—
428#103—222no—
429#103—441no—
430C22⋊C8—222no—
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#330211yescharacteristic
448C2×C11#331311yescharacteristic
449C2×C11#333611yescharacteristic
450C2×C11#334911yescharacteristic
451C24D4×D1111yescharacteristic
452C2×Q8—112no—
453C2×Q8—221no—
454C2×Q8—221no—
455C2×Q8—221no—
456C2×Q8—221no—
457C2×Q8—221no—
458C2×Q8—221no—
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—44no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8#433912yes—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—112no—
506C4⋊C4—224no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—442no—
511C4⋊C4—442no—
512C4⋊C4—442no—
513C4⋊C4—442no—
514C4⋊C4—442no—
515C4⋊C4#433912yes—
516C22⋊C4—42no—
517C22⋊C4—42no—
518C22⋊C4—222no—
519C22⋊C4—224no—
520C22⋊C4—441no—
521C22⋊C4—442no—
522C42—42no—
523C42—42no—
524C42—221no—
525C42—221no—
526C42—221no—
527C42—221no—
528C42—442no—
529C42—442no—
530C11#2521511yescharacteristic, complemented, Sylow
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23#6693712yes—
538C23C2×D4×D1111yescharacteristic
539Q8—222no—
540Q8—222no—
541Q8—441no—
542Q8—441no—
543Q8—441no—
544Q8—441no—
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×#433911yescharacteristic
592C2×C4C2×#433911yescharacteristic
593C2×C4C2×D4×D1111yescharacteristic
594C2×C4#6703711yescharacteristic
595C2×C4#6704011yescharacteristic
596C8—22no—
597C8—41no—
598C8—441no—
599C8—441no—
600C22—22no—
601C22—22no—
602C22—22no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22C2×#6693711yescharacteristic
608C22#1062302111yescharacteristic
609C22#1062303811yescharacteristic
610C22D11×#13511yescharacteristic
611C22#1062329911yescharacteristic
612C22#1062330211yescharacteristic
613C22#1062330211yescharacteristic
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#1062301011yescharacteristic
628C4#1062302111yescharacteristic
629C4#1062303811yescharacteristic
630C4#1062304611yescharacteristic
631C2—42no—
632C2#1307216711yescharacteristic
633C2#1307806911yescharacteristic
634C2#1307814911yescharacteristic
635C2#1308052911yescharacteristic
636C2#1308067811yescharacteristic
637C2#1308098411yescharacteristic
638C2#1308114211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1735C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1735D11
hypocenterC11#25215
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1735

Complements

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

NH ≅ G/Ntype
5. #13070103C2semidirect
6. #13070028C2semidirect
7. #13070012C2semidirect
8. #13069940C2semidirect
9. #13069373C2semidirect
10. #13069248C2semidirect
11. #13068958C2semidirect
14. #13068630C2semidirect
530. C11#25215semidirect

Maximal subgroups

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

subgroupindex
C2×#106226092
C2×#106227292
#130730652
#130716432
#130701032
#130700282
#130700122
#130699402
#130693732
#130692482
#130689582
#130689282
#130687942
#130686302
C11×#17352
#2521511