Finite Group Databasebeta

← #14680331

Subgroups — #14680331

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×#10622553C212yesmaximal, complemented
3#13066868C212yesmaximal, complemented
4#13066864C212yesmaximal, complemented
5#13066860C212yesmaximal, complemented
6#13066856C212yesmaximal
7#13066854C212yesmaximal, complemented
8#13066843C211yesmaximal, characteristic, complemented
9C4×C11×#95C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C22×C42×C11C2211yescharacteristic
12C22×C42×C11C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×(C2×D11)⋊C4C2212yes—
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2212yes—
20C22×C4⋊Dic11C2211yescharacteristic
21C22×Dic11⋊C4C2212yes—
22C2×C11×#95C2212yes—
23C2×C11×#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31#10622553—28no—
32#10622552C418yescomplemented
33C24×D11C2312yes—
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2312yes—
36C23×C4×C11C2312yes—
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—22no—
48C2×C42×C11—41no—
49C2×C42×C11—41no—
50C2×C42×C11—41no—
51C2×C42×C11—41no—
52C2×C42×C11—41no—
53C2×C42×C11—41no—
54C2×C42×C11C2×C414yes—
55C2×C42×C11D414yescomplemented
56C2×(C2×D11)⋊C4—24no—
57C2×(C2×D11)⋊C4—24no—
58C2×(C2×D11)⋊C4—24no—
59C2×(C2×D11)⋊C4—24no—
60C2×(C2×D11)⋊C4—24no—
61C2×(C2×D11)⋊C4—24no—
62C2×(C2×D11)⋊C4—42no—
63C2×(C2×D11)⋊C4—42no—
64C2×(C2×D11)⋊C4—42no—
65C2×(C2×D11)⋊C4—42no—
66C2×(C2×D11)⋊C4—42no—
67C2×(C2×D11)⋊C4—42no—
68C2×(C2×D11)⋊C4—42no—
69C2×(C2×D11)⋊C4—42no—
70C2×(C2×D11)⋊C4—42no—
71C2×(C2×D11)⋊C4—42no—
72C2×(C2×D11)⋊C4C2×C418yes—
73C2×(C2×D11)⋊C4C2×C418yes—
74C2×C4⋊Dic11—42no—
75C2×C4⋊Dic11C2×C414yes—
76C2×Dic11⋊C4—24no—
77C2×Dic11⋊C4—42no—
78C2×Dic11⋊C4—42no—
79C11×#95—24no—
80C11×#95—24no—
81C11⋊#95—24no—
82C11⋊#95—24no—
83C11⋊#95—24no—
84C11⋊#95—42no—
85C11⋊#95—42no—
86C11⋊#95—41no—
87C11⋊#95—41no—
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—22no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
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×C11C22×C412yes—
129C22×C4×C11C22×C412yes—
130C22×C4×C11C22×C412yes—
131C22×C4×C11C2×D414yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11#4114yes—
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×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11C22×C414yes—
157C2×D44—28no—
158C2×D44—44no—
159C2×D44—44no—
160C2×D44—48no—
161C2×D44—48no—
162C42×C11—44no—
163C42×C11—44no—
164C42×C11—44no—
165(C2×D11)⋊C4—216no—
166(C2×D11)⋊C4—48no—
167(C2×D11)⋊C4—48no—
168(C2×D11)⋊C4—48no—
169(C2×D11)⋊C4—48no—
170(C2×D11)⋊C4—48no—
171C4⋊Dic11—44no—
172Dic11⋊C4—48no—
173C2×#390—111no—
174C2×#388—112no—
175#1441—112no—
176#1440—112no—
177#1439—112no—
178#1438—112no—
179#1437—112no—
180#1434—111no—
181C4×#95D1111yescharacteristic, complemented
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)11yescharacteristic
190C23×C11H(5,𝔽2)12yes—
191C23×C11H(5,𝔽2)12yes—
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—24no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
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—42no—
263C2×Dic11—42no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—42no—
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×C42C2×D1111yescharacteristic
291C22×C42C2×D1111yescharacteristic
292C22×C42C2×D1111yescharacteristic
293#390—118no—
294#388—228no—
295C2×#95—112no—
296C2×#95—112no—
297C2×#95—112no—
298C2×#95—111no—
299C2×#95—111no—
300C2×#95—112no—
301C2×#95—112no—
302C2×#95C2×D1112yes—
303C2×#95C2×D1112yes—
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#53811yescharacteristic
317C22×C11#53812yes—
318C22×C11#53812yes—
319C22×C11#53812yes—
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—44no—
346C4×C11—44no—
347Dic11—44no—
348Dic11—82no—
349Dic11—82no—
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×D1111yescharacteristic
360C23×C4C22×D1112yes—
361C23×C4C22×D1112yes—
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—22no—
388C2×C42—41no—
389C2×C42—41no—
390C2×C42—41no—
391C2×C42—41no—
392C2×C42—41no—
393C2×C42—41no—
394C2×C42C4×D1114yes—
395C2×C42D4414yescomplemented
396#95—24no—
397#95—24no—
398#95—224no—
399#95—224no—
400#95—224no—
401#95—441no—
402#95—441no—
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—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
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—114no—
462C22×C4—222no—
463C22×C4—222no—
464C22×C4—222no—
465C22×C4—222no—
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×C4C2×C4×D1112yes—
483C22×C4C2×C4×D1112yes—
484C22×C4C2×C4×D1112yes—
485C22×C4C2×D4414yes—
486C22×C4C2×D4412yes—
487C22×C4#433914yes—
488C22×C4#433914yes—
489C22×C4#433912yes—
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—44no—
500C42—44no—
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
538C23C22×D4411yescharacteristic
539C23C2×#433912yes—
540C23C2×#433911yescharacteristic
541C23C2×#433912yes—
542C23#6703711yescharacteristic
543C23#6703711yescharacteristic
544C23#6703711yescharacteristic
545C23#6704011yescharacteristic
546C23#6704212yes—
547C23#6704212yes—
548D4—4416no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
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—442no—
582C2×C4—442no—
583C2×C4—442no—
584C2×C4—442no—
585C2×C4—442no—
586C2×C4—442no—
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×C4C4×D4414yes—
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
617C22C2×C4×D4411yescharacteristic
618C22C4×#433911yescharacteristic
619C22#1062300812yes—
620C22#1062301012yes—
621C22#1062301711yescharacteristic
622C22#1062302411yescharacteristic
623C22#1062302511yescharacteristic
624C22#1062303511yescharacteristic
625C22#1062304111yescharacteristic
626C22#1062304611yescharacteristic
627C22#1062305211yescharacteristic
628C22#1062305211yescharacteristic
629C22#1062305612yes—
630C22#1062306612yes—
631C22#1062309112yes—
632C22#1062309112yes—
633C22#1062309112yes—
634C22#1062309112yes—
635C22#1062309312yes—
636C22#1062309312yes—
637C22#1062311312yes—
638C22#1062311312yes—
639C4—24no—
640C4—24no—
641C4—42no—
642C4—44no—
643C4—44no—
644C4—444no—
645C4—882no—
646C4—882no—
647C2—884no—
648C2#1307108011yescharacteristic
649C2#1307121111yescharacteristic
650C2#1307125411yescharacteristic
651C2#1307131911yescharacteristic
652C2#1307134111yescharacteristic
653C2#1307138111yescharacteristic
654C2#1307142911yescharacteristic
655C2#1307459812yes—
656C2#1307464312yes—
657C2#1307474212yes—
658C2#1307475312yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC4×C11×#95C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenterC4×#95D11
hypocenterC11#14278
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
2. C2×#10622553C2semidirect
3. #13066868C2semidirect
4. #13066864C2semidirect
5. #13066860C2semidirect
7. #13066854C2semidirect
8. #13066843C2semidirect
9. C4×C11×#95C2semidirect
32. #10622552C4semidirect
55. C2×C42×C11D4semidirect
181. C4×#95D11semidirect
395. C2×C42D44semidirect
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×#106225532
#130668682
#130668642
#130668602
#130668562
#130668542
#130668432
C4×C11×#952
#1427811