Finite Group Databasebeta

← #14680337

Subgroups — #14680337

Order 2816.

1658 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622552C211yesmaximal, characteristic
2C2×#10622282C212yesmaximal, complemented
3#13066868C212yesmaximal, complemented
4#13066864C212yesmaximal, complemented
5#13066860C212yesmaximal, complemented
6#13066856C212yesmaximal
7#13066852C212yesmaximal, complemented
8C4×C11⋊#95C211yesmaximal, characteristic, complemented
9C11×#1434C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C22×C42×C11C2211yescharacteristic
12C22×(C2×D11)⋊C4C2212yes—
13C22×(C2×D11)⋊C4C2212yes—
14C22×(C2×D11)⋊C4C2212yes—
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×C4⋊Dic11C2211yescharacteristic
19C22×Dic11⋊C4C2212yes—
20C22×C4×Dic11C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C2×C11×#95C2212yes—
23C2×C11×#95C2212yes—
24C2×C11×#95C2211yescharacteristic
25C2×C11×#95C2211yescharacteristic
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31#10622552C418yescomplemented
32#10622282—28no—
33C24×D11C2312yes—
34C23×C4×C11C2312yes—
35C23×C4×C11C2312yes—
36C23×C4×C11C2311yescharacteristic
37C23×C4×C11C2311yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C23×Dic11C2312yes—
42C22×D44—24no—
43C22×D44—42no—
44C22×D44—41no—
45C22×D44—41no—
46C22×D44C2×C414yes—
47C2×C42×C11—41no—
48C2×C42×C11—41no—
49C2×C42×C11C2×C414yes—
50C2×(C2×D11)⋊C4—24no—
51C2×(C2×D11)⋊C4—24no—
52C2×(C2×D11)⋊C4—24no—
53C2×(C2×D11)⋊C4—24no—
54C2×(C2×D11)⋊C4—24no—
55C2×(C2×D11)⋊C4—24no—
56C2×(C2×D11)⋊C4—42no—
57C2×(C2×D11)⋊C4—42no—
58C2×(C2×D11)⋊C4—42no—
59C2×(C2×D11)⋊C4—42no—
60C2×(C2×D11)⋊C4—42no—
61C2×(C2×D11)⋊C4—42no—
62C2×(C2×D11)⋊C4—42no—
63C2×(C2×D11)⋊C4—42no—
64C2×(C2×D11)⋊C4—42no—
65C2×(C2×D11)⋊C4—42no—
66C2×(C2×D11)⋊C4C2×C418yes—
67C2×(C2×D11)⋊C4C2×C418yes—
68C2×C4⋊Dic11—42no—
69C2×C4⋊Dic11C2×C414yes—
70C2×Dic11⋊C4—24no—
71C2×Dic11⋊C4—42no—
72C2×Dic11⋊C4—42no—
73C2×C4×Dic11—22no—
74C2×C4×Dic11—41no—
75C2×C4×Dic11—41no—
76C2×C4×Dic11—41no—
77C2×C4×Dic11—41no—
78C2×C4×Dic11D414yescomplemented
79C11×#95—24no—
80C11×#95—24no—
81C11×#95—41no—
82C11×#95—41no—
83C11⋊#95—24no—
84C11⋊#95—24no—
85C11⋊#95—24no—
86C11⋊#95—42no—
87C11⋊#95—42no—
88#14278—111nomaximal, Sylow
89C24×C11C2411yescharacteristic
90C23×D11—22no—
91C23×D11—22no—
92C23×D11—22no—
93C23×D11—22no—
94C23×D11—22no—
95C23×D11—22no—
96C23×D11—22no—
97C23×D11—22no—
98C23×D11—22no—
99C23×D11—22no—
100C23×D11—22no—
101C23×D11—22no—
102C23×D11—22no—
103C23×D11—22no—
104C23×D11C22×C414yes—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—22no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11C22×C412yes—
131C22×C4×C11C22×C412yes—
132C22×C4×C11C22×C412yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11#4114yes—
135C22×C4×C11#4112yes—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11C22×C414yes—
155C22×Dic11C2×D414yes—
156C22×Dic11#4114yes—
157C2×D44—28no—
158C2×D44—44no—
159C2×D44—44no—
160C2×D44—48no—
161C2×D44—48no—
162C42×C11—44no—
163(C2×D11)⋊C4—216no—
164(C2×D11)⋊C4—48no—
165(C2×D11)⋊C4—48no—
166(C2×D11)⋊C4—48no—
167(C2×D11)⋊C4—48no—
168(C2×D11)⋊C4—48no—
169C4⋊Dic11—44no—
170Dic11⋊C4—48no—
171C4×Dic11—44no—
172C4×Dic11—44no—
173C2×#390—111no—
174C2×#388—112no—
175#1441—112no—
176#1440—112no—
177#1439—112no—
178#1438—112no—
179#1437—112no—
180#1434D1111yescharacteristic, complemented
181C4×#95—111no—
182C23×C11C23×C411yescharacteristic
183C23×C11C22×D411yescharacteristic
184C23×C11C2×#4112yes—
185C23×C11C2×#4111yescharacteristic
186C23×C11C2×#4112yes—
187C23×C11H(5,𝔽2)11yescharacteristic
188C23×C11H(5,𝔽2)11yescharacteristic
189C23×C11H(5,𝔽2)12yes—
190C23×C11H(5,𝔽2)12yes—
191C23×C11H(5,𝔽2)11yescharacteristic
192C23×C112−1+411yescharacteristic
193C22×D11—24no—
194C22×D11—24no—
195C22×D11—24no—
196C22×D11—24no—
197C22×D11—24no—
198C22×D11—24no—
199C22×D11—24no—
200C22×D11—42no—
201C22×D11—42no—
202C22×D11—42no—
203C22×D11—42no—
204C22×D11—42no—
205C22×D11—42no—
206C22×D11—42no—
207C22×D11—42no—
208C22×D11—42no—
209C22×D11—42no—
210C22×D11—42no—
211C22×D11—42no—
212C22×D11—42no—
213C22×D11—42no—
214C22×D11—42no—
215C22×D11—42no—
216C22×D11—42no—
217C22×D11—42no—
218C22×D11—42no—
219C22×D11—42no—
220C22×D11—42no—
221C22×D11—42no—
222C22×D11—42no—
223C22×D11—42no—
224C22×D11—42no—
225C22×D11—42no—
226C22×D11—42no—
227C22×D11—42no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11#11714yes—
258C2×C4×C11C4×D414yes—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—42no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11—42no—
273C2×Dic11—42no—
274C2×Dic11—42no—
275C2×Dic11—42no—
276C2×Dic11—42no—
277C2×Dic11—42no—
278C2×Dic11—42no—
279C2×Dic11—42no—
280D44—416no—
281C23×D4—111no—
282C22×C4⋊C4—111no—
283C22×C4⋊C4—112no—
284C22×C22⋊C4—112no—
285C22×C22⋊C4—112no—
286C22×C22⋊C4—112no—
287C22×C22⋊C4—112no—
288C22×C22⋊C4—112no—
289C22×C22⋊C4—112no—
290C22×C42—111no—
291C22×C42—111no—
292C22×C42C2×D1111yescharacteristic
293#390—118no—
294#388—228no—
295C2×#95—112no—
296C2×#95—112no—
297C2×#95—112no—
298C2×#95—112no—
299C2×#95—112no—
300C2×#95C2×D1112yes—
301C2×#95C2×D1112yes—
302C2×#95C2×D1111yescharacteristic
303C2×#95C2×D1111yescharacteristic
304C22×C11C2×#11711yescharacteristic
305C22×C11C2×C4×D411yescharacteristic
306C22×C11C4×#4111yescharacteristic
307C22×C11#51811yescharacteristic
308C22×C11#51811yescharacteristic
309C22×C11#51811yescharacteristic
310C22×C11#52011yescharacteristic
311C22×C11#52912yes—
312C22×C11#53212yes—
313C22×C11#53411yescharacteristic
314C22×C11#53512yes—
315C22×C11#53711yescharacteristic
316C22×C11#53812yes—
317C22×C11#53812yes—
318C22×C11#53812yes—
319C22×C11#53811yescharacteristic
320C22×C11#53812yes—
321C22×C11#53911yescharacteristic
322C22×C11#54012yes—
323C22×C11#54012yes—
324C22×C11#54012yes—
325C22×C11#54212yes—
326C22×C11#54212yes—
327C2×D11—44no—
328C2×D11—44no—
329C2×D11—44no—
330C2×D11—44no—
331C2×D11—44no—
332C2×D11—44no—
333C2×D11—44no—
334C2×D11—82no—
335C2×D11—82no—
336C2×D11—82no—
337C2×D11—82no—
338C2×D11—82no—
339C2×D11—82no—
340C2×D11—82no—
341C2×D11—82no—
342C4×C11—24no—
343C4×C11—24no—
344C4×C11—42no—
345C4×C11—82no—
346C4×C11—82no—
347Dic11—44no—
348Dic11—44no—
349Dic11—44no—
350C25—112no—
351C22×D4—114no—
352C22×D4—224no—
353C22×D4—441no—
354C22×D4—441no—
355C22×D4—442no—
356C23×C4—112no—
357C23×C4—112no—
358C23×C4—112no—
359C23×C4C22×D1112yes—
360C23×C4C22×D1112yes—
361C23×C4C22×D1111yescharacteristic
362C23×C4C22×D1111yescharacteristic
363C23×C4C22×D1111yescharacteristic
364C2×C4⋊C4—114no—
365C2×C4⋊C4—224no—
366C2×C4⋊C4—442no—
367C2×C4⋊C4—442no—
368C2×C4⋊C4—442no—
369C2×C22⋊C4—118no—
370C2×C22⋊C4—118no—
371C2×C22⋊C4—224no—
372C2×C22⋊C4—224no—
373C2×C22⋊C4—224no—
374C2×C22⋊C4—224no—
375C2×C22⋊C4—224no—
376C2×C22⋊C4—224no—
377C2×C22⋊C4—442no—
378C2×C22⋊C4—442no—
379C2×C22⋊C4—442no—
380C2×C22⋊C4—442no—
381C2×C22⋊C4—442no—
382C2×C22⋊C4—442no—
383C2×C22⋊C4—442no—
384C2×C22⋊C4—442no—
385C2×C22⋊C4—442no—
386C2×C22⋊C4—442no—
387C2×C42—41no—
388C2×C42—41no—
389C2×C42—114no—
390C2×C42—222no—
391C2×C42—441no—
392C2×C42—441no—
393C2×C42—441no—
394C2×C42—441no—
395C2×C42C4×D1114yes—
396#95—24no—
397#95—24no—
398#95—41no—
399#95—41no—
400#95—224no—
401#95—224no—
402#95—224no—
403#95—442no—
404#95—442no—
405C2×C11#229311yescharacteristic
406C2×C11#231211yescharacteristic
407C2×C11#231911yescharacteristic
408C2×C11#232511yescharacteristic
409C2×C11#232811yescharacteristic
410C2×C11#233311yescharacteristic
411C2×C11#233711yescharacteristic
412C2×C11#264812yes—
413C2×C11#265112yes—
414C2×C11#266112yes—
415C2×C11#266212yes—
416D11—84no—
417C24—114no—
418C24—222no—
419C24—222no—
420C24—222no—
421C24—222no—
422C24—222no—
423C24—222no—
424C24—222no—
425C24—222no—
426C24—222no—
427C24—222no—
428C24—222no—
429C24—222no—
430C24—222no—
431C24—222no—
432C24C23×D1111yescharacteristic
433C2×D4—228no—
434C2×D4—444no—
435C2×D4—444no—
436C2×D4—448no—
437C2×D4—448no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—114no—
464C22×C4—114no—
465C22×C4—114no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4—222no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—222no—
484C22×C4C2×C4×D1112yes—
485C22×C4C2×C4×D1112yes—
486C22×C4C2×C4×D1112yes—
487C22×C4#433914yes—
488C22×C4D4×D1112yes—
489C22×C4#434312yes—
490C4⋊C4—444no—
491C4⋊C4—448no—
492C22⋊C4—2216no—
493C22⋊C4—448no—
494C22⋊C4—448no—
495C22⋊C4—448no—
496C22⋊C4—448no—
497C22⋊C4—448no—
498C42—44no—
499C42—444no—
500C42—444no—
501C11#1427811yescharacteristic, complemented, Sylow
502C23—224no—
503C23—224no—
504C23—224no—
505C23—224no—
506C23—224no—
507C23—224no—
508C23—224no—
509C23—442no—
510C23—442no—
511C23—442no—
512C23—442no—
513C23—442no—
514C23—442no—
515C23—442no—
516C23—442no—
517C23—442no—
518C23—442no—
519C23—442no—
520C23—442no—
521C23—442no—
522C23—442no—
523C23—442no—
524C23—442no—
525C23—442no—
526C23—442no—
527C23—442no—
528C23—442no—
529C23—442no—
530C23—442no—
531C23—442no—
532C23—442no—
533C23—442no—
534C23—442no—
535C23—442no—
536C23—442no—
537C23C22×C4×D1111yescharacteristic
538C23C2×#433912yes—
539C23C2×D4×D1111yescharacteristic
540C23#6703711yescharacteristic
541C23#6703711yescharacteristic
542C23C2×#434311yescharacteristic
543C23#41×D1112yes—
544C23#6704211yescharacteristic
545C23#6704212yes—
546C23#6704212yes—
547C23#6704311yescharacteristic
548D4—4416no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—224no—
579C2×C4—224no—
580C2×C4—224no—
581C2×C4—224no—
582C2×C4—224no—
583C2×C4—224no—
584C2×C4—224no—
585C2×C4—224no—
586C2×C4—224no—
587C2×C4—442no—
588C2×C4—442no—
589C2×C4—442no—
590C2×C4—442no—
591C2×C4—442no—
592C2×C4—442no—
593C2×C4—442no—
594C2×C4—442no—
595C2×C4—442no—
596C2×C4—442no—
597C2×C4—442no—
598C2×C4—442no—
599C2×C4#6692514yes—
600C2×C4#6694614yes—
601C22—444no—
602C22—444no—
603C22—444no—
604C22—444no—
605C22—444no—
606C22—444no—
607C22—444no—
608C22—882no—
609C22—882no—
610C22—882no—
611C22—882no—
612C22—882no—
613C22—882no—
614C22—882no—
615C22—882no—
616C22C2×#6692511yescharacteristic
617C22#1062301711yescharacteristic
618C22C2×#6694611yescharacteristic
619C22#1062305211yescharacteristic
620C22#1062305211yescharacteristic
621C22#1062305311yescharacteristic
622C22#1062305411yescharacteristic
623C22#1062306512yes—
624C22#1062306612yes—
625C22#1062307912yes—
626C22#1062309112yes—
627C22#1062309112yes—
628C22#1062311112yes—
629C22#1062312811yescharacteristic
630C22#1062313611yescharacteristic
631C22#1062317511yescharacteristic
632C22#1062317611yescharacteristic
633C22#1062318812yes—
634C22#1062319412yes—
635C22#1062320512yes—
636C22#1062322912yes—
637C22#1062323512yes—
638C22#1062324112yes—
639C4—24no—
640C4—24no—
641C4—42no—
642C4—82no—
643C4—82no—
644C4—444no—
645C4—444no—
646C4—444no—
647C2—884no—
648C2#1307107711yescharacteristic
649C2#1307121111yescharacteristic
650C2#1307126011yescharacteristic
651C2#1307131611yescharacteristic
652C2#1307133911yescharacteristic
653C2#1307137811yescharacteristic
654C2#1307142611yescharacteristic
655C2#1307461012yes—
656C2#1307465512yes—
657C2#1307474812yes—
658C2#1307475912yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1434C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1434D11
hypocenterC11#14278
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. C2×#10622282C2semidirect
3. #13066868C2semidirect
4. #13066864C2semidirect
5. #13066860C2semidirect
7. #13066852C2semidirect
8. C4×C11⋊#95C2semidirect
9. C11×#1434C2semidirect
31. #10622552C4semidirect
78. C2×C4×Dic11D4semidirect
180. #1434D11semidirect
501. C11#14278semidirect

Maximal subgroups

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

subgroupindex
C2×#106225522
C2×#106222822
#130668682
#130668642
#130668602
#130668562
#130668522
C4×C11⋊#952
C11×#14342
#1427811