Finite Group Databasebeta

← #14801939

Subgroups — #14801939

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×#10622729C211yesmaximal, characteristic
3#13073069C211yesmaximal, characteristic
4#13071641C211yesmaximal, characteristic
5#13070089C211yesmaximal, characteristic, complemented
6#13070036C211yesmaximal, characteristic, complemented
7#13069996C211yesmaximal, characteristic, complemented
8#13069939C211yesmaximal, characteristic, complemented
9#13069386C211yesmaximal, characteristic, complemented
10#13069258C211yesmaximal, characteristic, complemented
11#13068956C211yesmaximal, characteristic, complemented
12#13068926C211yesmaximal, characteristic
13#13068622C211yesmaximal, characteristic, complemented
14#13068333C211yesmaximal, characteristic
15C11×#1850C211yesmaximal, characteristic
16C23×C8×C11C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C2×#66977C2211yescharacteristic
20C2×#66977C2211yescharacteristic
21C22×Dic44C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C4×C11×C22⋊C4C2211yescharacteristic
27#10622729—24no—
28C2×#66882C2211yescharacteristic
29C2×#66882C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37#10622566—21no—
38#10622566—21no—
39#10622558—21no—
40#10622557—21no—
41#10622549C2211yescharacteristic
42#10622548C2211yescharacteristic
43C4×C4⋊Dic11C2211yescharacteristic
44#10622542C2211yescharacteristic
45#10622542C2211yescharacteristic
46#10622542C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622336—24no—
49#10622266—21no—
50#10622266—21no—
51#10622265—21no—
52#10622262—21no—
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
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
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C2×C11×C22⋊C4D411yescharacteristic
72C2×C11×C22⋊C4D411yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79#66979—22no—
80#66979—22no—
81#66979—22no—
82#66979—41no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91#66977—22no—
92#66977—22no—
93#66977—22no—
94#66977D414yes—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×Dic44—22no—
104C2×Dic44—22no—
105C2×Dic44—41no—
106C4×Dic22—22no—
107C4×Dic22—41no—
108C11×C4⋊C8—22no—
109C11×C4⋊C8—41no—
110C11×C22⋊C8—22no—
111C11×#95D411yescharacteristic
112C11×#95D411yescharacteristic
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⋊#95—21no—
123#66882—22no—
124#66882—22no—
125#66881—22no—
126#66880—22no—
127#66880—22no—
128#66880—22no—
129#66880—22no—
130#66880—22no—
131#66880—41no—
132#25201—111nomaximal, Sylow
133C24×C11C2×D411yescharacteristic
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11#4112yes—
145C22×C4×C11C2411yescharacteristic
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
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—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—44no—
178C2×C8×C11#4112yes—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—41no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—21no—
185C22⋊Dic11—24no—
186C22⋊Dic11—42no—
187C22⋊Dic11—42no—
188C22⋊Dic11—42no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—42no—
200C4⋊Dic11—42no—
201C4⋊Dic11C2×D412yes—
202C4⋊Dic11#4112yes—
203Dic11⋊C4—24no—
204Dic11⋊C4—42no—
205Dic11⋊C4—42no—
206Dic11⋊C4—42no—
207C4×Dic11—42no—
208C4×Dic11—42no—
209C4×Dic11—42no—
210C4×Dic11—42no—
211Dic44—44no—
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#1873—111no—
224#1850D1111yescharacteristic
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
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11#12112yes—
253C2×C4×C11#13512yes—
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—22no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
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—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284Dic22—22no—
285Dic22—22no—
286Dic22—41no—
287Dic22—41no—
288Dic22—41no—
289Dic22—41no—
290Dic22—41no—
291Dic22—41no—
292C8×C11—22no—
293C8×C11—41no—
294C8×C11—41no—
295C8×C11—41no—
296C22×Q16—111no—
297C23×C8C2×D1111yescharacteristic
298C2×C22⋊Q8—111no—
299C2×C22⋊Q8—111no—
300C2×C4×Q8—111no—
301C2×#117—111no—
302C2×#117—111no—
303#485—224no—
304#467—224no—
305C2×#107—111no—
306C2×#107—111no—
307C2×#106—111no—
308C2×C4⋊C8C2×D1111yescharacteristic
309C2×C4⋊C8C2×D1111yescharacteristic
310C2×#103—111no—
311C2×#103—111no—
312C2×#103—111no—
313C2×#103—111no—
314C2×#103—111no—
315C2×#103—111no—
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⋊C4C2×D1111yescharacteristic
333#340—111no—
334#340—111no—
335#340—111no—
336#340—111no—
337#340—111no—
338#340—111no—
339#336C2×D1111yescharacteristic
340#336C2×D1111yescharacteristic
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—22no—
357C4×C11—41no—
358C4×C11—41no—
359C4×C11—41no—
360C4×C11#52911yescharacteristic
361C4×C11#53911yescharacteristic
362C4×C11#54611yescharacteristic
363C4×C11#54711yescharacteristic
364Dic11—42no—
365Dic11—42no—
366Dic11—42no—
367Dic11—81no—
368Dic11—81no—
369Dic11—81no—
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×C8C22×D1111yescharacteristic
382C22×C8C22×D1111yescharacteristic
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—222no—
392#117—222no—
393#117—222no—
394#117—441no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—221no—
407C2×C22⋊C4—221no—
408C2×C22⋊C4—221no—
409C2×C22⋊C4—221no—
410C2×C22⋊C4—221no—
411C2×C22⋊C4D4411yescharacteristic
412C2×C22⋊C4D4411yescharacteristic
413C2×C42—221no—
414C2×C42—221no—
415C2×C42—221no—
416C2×C42—221no—
417C2×C42C22×D1111yescharacteristic
418C2×C42C22×D1111yescharacteristic
419#107—222no—
420#107—222no—
421#106—222no—
422C4⋊C8—22no—
423C4⋊C8—41no—
424#103—222no—
425#103—222no—
426#103—222no—
427#103—222no—
428#103—222no—
429#103—441no—
430C22⋊C8—22no—
431#95—221no—
432#95—221no—
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#95D4411yescharacteristic
442#95D4411yescharacteristic
443C2×C11—42no—
444C2×C11#242511yescharacteristic
445C2×C11#303511yescharacteristic
446C2×C11#304411yescharacteristic
447C2×C11#330011yescharacteristic
448C2×C11#331511yescharacteristic
449C2×C11#334211yescharacteristic
450C2×C11#334911yescharacteristic
451C24C2×D4411yescharacteristic
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—221no—
469C22×C4—221no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4C2×D4411yescharacteristic
477C22×C4C2×D4411yescharacteristic
478C22×C4C2×D4411yescharacteristic
479C22×C4C2×D4411yescharacteristic
480C22×C4C2×D4411yescharacteristic
481C22×C4D4×D1112yes—
482C22×C4#434312yes—
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—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—44no—
497C2×C8#434112yes—
498C4⋊C4—112no—
499C4⋊C4—112no—
500C4⋊C4—224no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4—221no—
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—442no—
516C22⋊C4—22no—
517C22⋊C4—41no—
518C22⋊C4—224no—
519C22⋊C4—442no—
520C22⋊C4—442no—
521C22⋊C4—442no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42—442no—
527C42—442no—
528C42—442no—
529C42—442no—
530C11#2520111yescharacteristic, complemented, Sylow
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23#6694812yes—
538C23C22×D4411yescharacteristic
539Q8—222no—
540Q8—222no—
541Q8—441no—
542Q8—441no—
543Q8—441no—
544Q8—441no—
545Q8—441no—
546Q8—441no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—222no—
565C2×C4—222no—
566C2×C4—222no—
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—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
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#6694812yes—
589C2×C4#6695712yes—
590C2×C4C2×D4×D1111yescharacteristic
591C2×C4C2×#434111yescharacteristic
592C2×C4#6703711yescharacteristic
593C2×C4C2×#434311yescharacteristic
594C2×C4#41×D1111yescharacteristic
595C2×C4#6704311yescharacteristic
596C8—22no—
597C8—41no—
598C8—41no—
599C8—41no—
600C22—22no—
601C22—22no—
602C22—22no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22C2×#6694811yescharacteristic
608C22#1062308511yescharacteristic
609C22#1062308611yescharacteristic
610C22C2×#6695711yescharacteristic
611C22#1062327911yescharacteristic
612C22#1062328411yescharacteristic
613C22#1062328411yescharacteristic
614C4—22no—
615C4—22no—
616C4—41no—
617C4—41no—
618C4—41no—
619C4—442no—
620C4—442no—
621C4—442no—
622C4—881no—
623C4—881no—
624C4—881no—
625C4—881no—
626C4—881no—
627C4#1062312211yescharacteristic
628C4#1062315511yescharacteristic
629C4#1062317611yescharacteristic
630C4#1062318611yescharacteristic
631C2—42no—
632C2#1307216511yescharacteristic
633C2#1307807311yescharacteristic
634C2#1307814711yescharacteristic
635C2#1308050511yescharacteristic
636C2#1308071411yescharacteristic
637C2#1308104711yescharacteristic
638C2#1308114811yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1850C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1850D11
hypocenterC11#25201
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
5. #13070089C2semidirect
6. #13070036C2semidirect
7. #13069996C2semidirect
8. #13069939C2semidirect
9. #13069386C2semidirect
10. #13069258C2semidirect
11. #13068956C2semidirect
13. #13068622C2semidirect
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×#106227292
#130730692
#130716412
#130700892
#130700362
#130699962
#130699392
#130693862
#130692582
#130689562
#130689262
#130686222
#130683332
C11×#18502
#2520111