Finite Group Databasebeta

← #14680336

Subgroups — #14680336

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×#10622564C212yesmaximal, complemented
2#13066869C212yesmaximal, complemented
3#13066865C212yesmaximal, complemented
4#13066861C212yesmaximal, complemented
5#13066857C212yesmaximal
6#13066853C212yesmaximal, complemented
7#13066843C211yesmaximal, characteristic, complemented
8C4×C11⋊#95C211yesmaximal, characteristic, complemented
9C2×C11×#390C211yesmaximal, characteristic
10C23×D4×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C11×C22⋊C4C2212yes—
13C22×C11×C22⋊C4C2212yes—
14C22×C42×C11C2211yescharacteristic
15C22×C22⋊Dic11C2212yes—
16C22×C22⋊Dic11C2212yes—
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×C4⋊Dic11C2212yes—
20C22×C4×Dic11C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C11×#390C418yescomplemented
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32#10622564—28no—
33C25×C11C2312yes—
34C22×D4×C11—24no—
35C22×D4×C11—41no—
36C22×D4×C11—41no—
37C22×D4×C11—42no—
38C22×D4×C11C2×C414yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×Dic11C2312yes—
44C23×Dic11C2312yes—
45C23×Dic11C2312yes—
46C23×Dic11C2312yes—
47C2×C11×C4⋊C4—42no—
48C2×C11×C4⋊C4C2×C414yes—
49C2×C11×C22⋊C4—24no—
50C2×C11×C22⋊C4—24no—
51C2×C11×C22⋊C4—42no—
52C2×C11×C22⋊C4—42no—
53C2×C11×C22⋊C4C2×C418yes—
54C2×C11×C22⋊C4C2×C418yes—
55C2×C42×C11—41no—
56C2×C42×C11—41no—
57C2×C42×C11C2×C414yes—
58C2×C22⋊Dic11—24no—
59C2×C22⋊Dic11—24no—
60C2×C22⋊Dic11—24no—
61C2×C22⋊Dic11—24no—
62C2×C22⋊Dic11—42no—
63C2×C22⋊Dic11—42no—
64C2×C22⋊Dic11—42no—
65C2×C22⋊Dic11—42no—
66C2×C22⋊Dic11—42no—
67C2×C22⋊Dic11—42no—
68C2×C22⋊Dic11—42no—
69C2×C22⋊Dic11—42no—
70C2×C4⋊Dic11—24no—
71C2×C4⋊Dic11—42no—
72C2×C4⋊Dic11—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—24no—
82C11⋊#95—24no—
83C11⋊#95—24no—
84C11⋊#95—42no—
85C11⋊#95—42no—
86C11⋊#95—41no—
87C11⋊#95—41no—
88#14278—111nomaximal, Sylow
89C24×C11—22no—
90C24×C11—22no—
91C24×C11—22no—
92C24×C11—22no—
93C24×C11—22no—
94C24×C11—22no—
95C24×C11—22no—
96C24×C11—22no—
97C24×C11—22no—
98C24×C11—22no—
99C24×C11—22no—
100C24×C11—22no—
101C24×C11—22no—
102C24×C11—22no—
103C24×C11C22×C414yes—
104C24×C11C2411yescharacteristic
105C2×D4×C11—28no—
106C2×D4×C11—44no—
107C2×D4×C11—44no—
108C2×D4×C11—48no—
109C2×D4×C11—48no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11C22×C412yes—
128C22×C4×C11C22×C414yes—
129C22×C4×C11C22×C412yes—
130C22×C4×C11C22×C412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11#4114yes—
133C22×C4×C11#4112yes—
134C22×Dic11—22no—
135C22×Dic11—22no—
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×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11C2×D414yes—
161C22×Dic11#4114yes—
162C11×C4⋊C4—44no—
163C11×C22⋊C4—216no—
164C11×C22⋊C4—48no—
165C42×C11—44no—
166C22⋊Dic11—48no—
167C22⋊Dic11—48no—
168C22⋊Dic11—48no—
169C22⋊Dic11—48no—
170C4⋊Dic11—48no—
171C4×Dic11—44no—
172C4×Dic11—44no—
173C2×#390D1111yescharacteristic
174C2×#388—112no—
175#1441—112no—
176#1440—112no—
177#1439—112no—
178#1438—112no—
179#1437—112no—
180#1434—111no—
181C4×#95—111no—
182C23×C11—24no—
183C23×C11—24no—
184C23×C11—24no—
185C23×C11—24no—
186C23×C11—24no—
187C23×C11—24no—
188C23×C11—24no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11C23×C411yescharacteristic
218C23×C11C22×D411yescharacteristic
219C23×C11C2×#4112yes—
220C23×C11C2×#4111yescharacteristic
221C23×C11C2×#4112yes—
222C23×C11H(5,𝔽2)11yescharacteristic
223C23×C11H(5,𝔽2)12yes—
224C23×C11H(5,𝔽2)12yes—
225C23×C11H(5,𝔽2)11yescharacteristic
226C23×C11H(5,𝔽2)11yescharacteristic
227C23×C112−1+411yescharacteristic
228D4×C11—416no—
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—22no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—22no—
239C2×C4×C11—24no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
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#11714yes—
252C2×C4×C11C4×D414yes—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—42no—
260C2×Dic11—42no—
261C2×Dic11—42no—
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—
280C2×Dic11—42no—
281C23×D4C2×D1111yescharacteristic
282C22×C4⋊C4—112no—
283C22×C4⋊C4C2×D1111yescharacteristic
284C22×C22⋊C4—112no—
285C22×C22⋊C4—112no—
286C22×C22⋊C4—112no—
287C22×C22⋊C4—112no—
288C22×C22⋊C4C2×D1112yes—
289C22×C22⋊C4C2×D1112yes—
290C22×C42—111no—
291C22×C42—111no—
292C22×C42C2×D1111yescharacteristic
293#390Dic1118yescomplemented
294#388—228no—
295C2×#95—112no—
296C2×#95—112no—
297C2×#95—112no—
298C2×#95—112no—
299C2×#95—112no—
300C2×#95—111no—
301C2×#95—111no—
302C2×#95—112no—
303C2×#95—112no—
304C22×C11—44no—
305C22×C11—44no—
306C22×C11—44no—
307C22×C11—44no—
308C22×C11—44no—
309C22×C11—44no—
310C22×C11—44no—
311C22×C11—82no—
312C22×C11—82no—
313C22×C11—82no—
314C22×C11—82no—
315C22×C11—82no—
316C22×C11—82no—
317C22×C11—82no—
318C22×C11—82no—
319C22×C11C2×#11711yescharacteristic
320C22×C11C2×C4×D411yescharacteristic
321C22×C11C4×#4111yescharacteristic
322C22×C11#51811yescharacteristic
323C22×C11#51811yescharacteristic
324C22×C11#51811yescharacteristic
325C22×C11#52011yescharacteristic
326C22×C11#52912yes—
327C22×C11#53212yes—
328C22×C11#53411yescharacteristic
329C22×C11#53512yes—
330C22×C11#53711yescharacteristic
331C22×C11#53812yes—
332C22×C11#53812yes—
333C22×C11#53812yes—
334C22×C11#53811yescharacteristic
335C22×C11#53812yes—
336C22×C11#53911yescharacteristic
337C22×C11#54012yes—
338C22×C11#54012yes—
339C22×C11#54012yes—
340C22×C11#54212yes—
341C22×C11#54212yes—
342C4×C11—24no—
343C4×C11—24no—
344C4×C11—44no—
345C4×C11—42no—
346Dic11—44no—
347Dic11—44no—
348Dic11—82no—
349Dic11—82no—
350C25C22×D1112yes—
351C22×D4—24no—
352C22×D4—41no—
353C22×D4—41no—
354C22×D4—42no—
355C22×D4C2×Dic1114yes—
356C23×C4—112no—
357C23×C4—112no—
358C23×C4—112no—
359C23×C4—112no—
360C23×C4C22×D1112yes—
361C23×C4C22×D1111yescharacteristic
362C23×C4C22×D1111yescharacteristic
363C23×C4C22×D1111yescharacteristic
364C2×C4⋊C4—42no—
365C2×C4⋊C4—224no—
366C2×C4⋊C4—442no—
367C2×C4⋊C4—442no—
368C2×C4⋊C4C2×Dic1114yes—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
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⋊C4C2×Dic1118yes—
386C2×C22⋊C4C2×Dic1118yes—
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×C42C2×Dic1114yes—
396#95—224no—
397#95—224no—
398#95—224no—
399#95—224no—
400#95—224no—
401#95—441no—
402#95—441no—
403#95—442no—
404#95—442no—
405C2×C11—84no—
406C2×C11#229311yescharacteristic
407C2×C11#231211yescharacteristic
408C2×C11#231911yescharacteristic
409C2×C11#232511yescharacteristic
410C2×C11#232811yescharacteristic
411C2×C11#233311yescharacteristic
412C2×C11#233711yescharacteristic
413C2×C11#264812yes—
414C2×C11#265112yes—
415C2×C11#266112yes—
416C2×C11#266212yes—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24C22×Dic1114yes—
432C24C23×D1111yescharacteristic
433C2×D4—28no—
434C2×D4—44no—
435C2×D4—44no—
436C2×D4—48no—
437C2×D4—48no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—114no—
456C22×C4—114no—
457C22×C4—222no—
458C22×C4—222no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—222no—
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×C4—222no—
483C22×C4#433914yes—
484C22×C4D4×D1112yes—
485C22×C4#434112yes—
486C22×C4C22×Dic1112yes—
487C22×C4C22×Dic1114yes—
488C22×C4C22×Dic1112yes—
489C22×C4C22×Dic1112yes—
490C4⋊C4—44no—
491C4⋊C4—448no—
492C22⋊C4—216no—
493C22⋊C4—48no—
494C22⋊C4—448no—
495C22⋊C4—448no—
496C22⋊C4—448no—
497C22⋊C4—448no—
498C42—44no—
499C42—444no—
500C42—444no—
501C11#1427811yescharacteristic, complemented, Sylow
502C23—24no—
503C23—24no—
504C23—24no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—24no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23C2×#433912yes—
538C23C2×D4×D1111yescharacteristic
539C23C2×#434111yescharacteristic
540C23#6703712yes—
541C23#6703712yes—
542C23#6703711yescharacteristic
543C23#6703711yescharacteristic
544C23#41×D1112yes—
545C23#6704211yescharacteristic
546C23#6704311yescharacteristic
547C23C23×Dic1111yescharacteristic
548D4—416no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—22no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—224no—
572C2×C4—224no—
573C2×C4—224no—
574C2×C4—224no—
575C2×C4—224no—
576C2×C4—224no—
577C2×C4—442no—
578C2×C4—442no—
579C2×C4—442no—
580C2×C4—442no—
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#6697914yes—
600C2×C4D4×Dic1114yes—
601C22—44no—
602C22—44no—
603C22—44no—
604C22—44no—
605C22—44no—
606C22—44no—
607C22—44no—
608C22—82no—
609C22—82no—
610C22—82no—
611C22—82no—
612C22—82no—
613C22—82no—
614C22—82no—
615C22—82no—
616C22#1062302512yes—
617C22#1062302512yes—
618C22#1062307912yes—
619C22#1062308812yes—
620C22#1062309212yes—
621C22#1062309312yes—
622C22#1062312811yescharacteristic
623C22#1062313311yescharacteristic
624C22#1062313611yescharacteristic
625C22#1062314412yes—
626C22#1062314612yes—
627C22#1062314811yescharacteristic
628C22#1062320012yes—
629C22#1062320912yes—
630C22#1062324612yes—
631C22#1062325012yes—
632C22C2×#6697911yescharacteristic
633C22C2×D4×Dic1111yescharacteristic
634C22#1062332911yescharacteristic
635C22#1062332911yescharacteristic
636C22#1062332911yescharacteristic
637C22#41×Dic1111yescharacteristic
638C22#1062335811yescharacteristic
639C4—24no—
640C4—24no—
641C4—42no—
642C4—44no—
643C4—444no—
644C4—444no—
645C4—882no—
646C4—882no—
647C2—84no—
648C2#1307108111yescharacteristic
649C2#1307121411yescharacteristic
650C2#1307125911yescharacteristic
651C2#1307132111yescharacteristic
652C2#1307134211yescharacteristic
653C2#1307138311yescharacteristic
654C2#1307143111yescharacteristic
655C2#1307460812yes—
656C2#1307465312yes—
657C2#1307474612yes—
658C2#1307475712yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#390C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#390D11
hypocenterC11#14278
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C2×#10622564C2semidirect
2. #13066869C2semidirect
3. #13066865C2semidirect
4. #13066861C2semidirect
6. #13066853C2semidirect
7. #13066843C2semidirect
8. C4×C11⋊#95C2semidirect
22. C11×#390C4semidirect
78. C2×C4×Dic11D4semidirect
293. #390Dic11semidirect
501. C11#14278semidirect

Maximal subgroups

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

subgroupindex
C2×#106225642
#130668692
#130668652
#130668612
#130668572
#130668532
#130668432
C4×C11⋊#952
C2×C11×#3902
#1427811