Finite Group Databasebeta

← #14684841

Subgroups — #14684841

Order 2816.

1494 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622552C211yesmaximal, characteristic
2#13066868C212yesmaximal, complemented
3#13066864C212yesmaximal, complemented
4#13066864C212yesmaximal, complemented
5#13066860C212yesmaximal, complemented
6#13066860C212yesmaximal, complemented
7#13066856C212yesmaximal
8#13066843C211yesmaximal, 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—
20C2×C11×#95C2212yes—
21C2×C11×#95C2211yescharacteristic
22C2×C11×#95C2212yes—
23C2×C11×#95C2211yescharacteristic
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2211yescharacteristic
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31#10622552C418yescomplemented
32C24×D11C2312yes—
33C23×C4×C11C2312yes—
34C23×C4×C11C2312yes—
35C23×C4×C11C2311yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C23×C4×C11C2311yescharacteristic
38C23×Dic11C2312yes—
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C22×D44—24no—
42C22×D44—41no—
43C22×D44—41no—
44C22×D44—42no—
45C22×D44C2×C414yes—
46C2×C42×C11—42no—
47C2×C42×C11C2×C414yes—
48C2×(C2×D11)⋊C4—42no—
49C2×(C2×D11)⋊C4—42no—
50C2×(C2×D11)⋊C4—42no—
51C2×(C2×D11)⋊C4—42no—
52C2×(C2×D11)⋊C4—42no—
53C2×(C2×D11)⋊C4—42no—
54C2×(C2×D11)⋊C4—42no—
55C2×(C2×D11)⋊C4—42no—
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)⋊C4C2×C418yes—
65C2×(C2×D11)⋊C4C2×C418yes—
66C2×C4⋊Dic11—41no—
67C2×C4⋊Dic11—41no—
68C2×C4⋊Dic11C2×C414yes—
69C2×Dic11⋊C4—42no—
70C2×Dic11⋊C4—42no—
71C2×Dic11⋊C4—42no—
72C11×#95—24no—
73C11×#95—41no—
74C11×#95—41no—
75C11×#95—42no—
76C11⋊#95—24no—
77C11⋊#95—42no—
78C11⋊#95—42no—
79C11⋊#95—42no—
80C11⋊#95—41no—
81C11⋊#95—41no—
82C11⋊#95—42no—
83#14667—111nomaximal, Sylow
84C24×C11C2411yescharacteristic
85C23×D11—22no—
86C23×D11—22no—
87C23×D11—22no—
88C23×D11—22no—
89C23×D11—22no—
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×D11C22×C414yes—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—22no—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
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—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11C22×C412yes—
126C22×C4×C11C22×C412yes—
127C22×C4×C11C22×C412yes—
128C22×C4×C11#4114yes—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
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×Dic11C22×C414yes—
150C2×D44—28no—
151C2×D44—44no—
152C2×D44—44no—
153C2×D44—48no—
154C2×D44—48no—
155C42×C11—44no—
156(C2×D11)⋊C4—48no—
157(C2×D11)⋊C4—48no—
158(C2×D11)⋊C4—48no—
159(C2×D11)⋊C4—48no—
160(C2×D11)⋊C4—48no—
161(C2×D11)⋊C4—48no—
162C4⋊Dic11—44no—
163Dic11⋊C4—48no—
164C2×#390—111no—
165#1441—112no—
166#1440—112no—
167#1440—112no—
168#1439—112no—
169#1439—112no—
170#1438—112no—
171#1434—111no—
172#1434D1111yescharacteristic, complemented
173C23×C11C23×C411yescharacteristic
174C23×C11C2×#4112yes—
175C23×C11H(5,𝔽2)12yes—
176C23×C11H(5,𝔽2)11yescharacteristic
177C23×C11H(5,𝔽2)11yescharacteristic
178C23×C11H(5,𝔽2)11yescharacteristic
179C23×C11H(5,𝔽2)12yes—
180C23×C11H(5,𝔽2)12yes—
181C23×C11H(5,𝔽2)11yescharacteristic
182C23×C112−1+411yescharacteristic
183C23×C112−1+411yescharacteristic
184C22×D11—24no—
185C22×D11—24no—
186C22×D11—24no—
187C22×D11—24no—
188C22×D11—24no—
189C22×D11—24no—
190C22×D11—24no—
191C22×D11—42no—
192C22×D11—42no—
193C22×D11—42no—
194C22×D11—42no—
195C22×D11—42no—
196C22×D11—42no—
197C22×D11—42no—
198C22×D11—42no—
199C22×D11—42no—
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—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
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#11714yes—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258C2×Dic11—42no—
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—
269D44—416no—
270C23×D4—111no—
271C22×C4⋊C4—111no—
272C22×C4⋊C4—112no—
273C22×C22⋊C4—112no—
274C22×C22⋊C4—112no—
275C22×C22⋊C4—112no—
276C22×C22⋊C4—112no—
277C22×C22⋊C4—112no—
278C22×C22⋊C4—112no—
279C22×C42C2×D1111yescharacteristic
280#390—118no—
281C2×#95—112no—
282C2×#95—111no—
283C2×#95—112no—
284C2×#95—111no—
285C2×#95—112no—
286C2×#95—112no—
287C2×#95—112no—
288C2×#95C2×D1112yes—
289C2×#95C2×D1111yescharacteristic
290C2×#95C2×D1112yes—
291C2×#95C2×D1111yescharacteristic
292C22×C11C2×#11711yescharacteristic
293C22×C11#51811yescharacteristic
294C22×C11#51811yescharacteristic
295C22×C11#51811yescharacteristic
296C22×C11#51811yescharacteristic
297C22×C11#52011yescharacteristic
298C22×C11#52011yescharacteristic
299C22×C11#53812yes—
300C22×C11#53812yes—
301C22×C11#54012yes—
302C22×C11#54012yes—
303C22×C11#54212yes—
304C22×C11#54212yes—
305C22×C11#56012yes—
306C22×C11#56012yes—
307C22×C11#56012yes—
308C22×C11#56012yes—
309C22×C11H(3,𝔽4)11yescharacteristic
310C22×C11#56212yes—
311C22×C11#56212yes—
312C22×C11#56211yescharacteristic
313C22×C11#56211yescharacteristic
314C22×C11#56311yescharacteristic
315C2×D11—44no—
316C2×D11—44no—
317C2×D11—44no—
318C2×D11—44no—
319C2×D11—44no—
320C2×D11—44no—
321C2×D11—44no—
322C2×D11—82no—
323C2×D11—82no—
324C2×D11—82no—
325C2×D11—82no—
326C2×D11—82no—
327C2×D11—82no—
328C2×D11—82no—
329C2×D11—82no—
330C4×C11—24no—
331C4×C11—42no—
332C4×C11—42no—
333C4×C11—82no—
334C4×C11—82no—
335Dic11—44no—
336Dic11—82no—
337Dic11—82no—
338C25—112no—
339C22×D4—114no—
340C22×D4—224no—
341C22×D4—442no—
342C22×D4—441no—
343C22×D4—441no—
344C23×C4—112no—
345C23×C4—112no—
346C23×C4—112no—
347C23×C4C22×D1112yes—
348C23×C4C22×D1112yes—
349C23×C4C22×D1111yescharacteristic
350C23×C4C22×D1111yescharacteristic
351C23×C4C22×D1111yescharacteristic
352C2×C4⋊C4—114no—
353C2×C4⋊C4—442no—
354C2×C4⋊C4—442no—
355C2×C4⋊C4—442no—
356C2×C4⋊C4—441no—
357C2×C4⋊C4—441no—
358C2×C22⋊C4—118no—
359C2×C22⋊C4—118no—
360C2×C22⋊C4—442no—
361C2×C22⋊C4—442no—
362C2×C22⋊C4—442no—
363C2×C22⋊C4—442no—
364C2×C22⋊C4—442no—
365C2×C22⋊C4—442no—
366C2×C22⋊C4—442no—
367C2×C22⋊C4—442no—
368C2×C22⋊C4—442no—
369C2×C22⋊C4—442no—
370C2×C22⋊C4—442no—
371C2×C22⋊C4—442no—
372C2×C22⋊C4—442no—
373C2×C22⋊C4—442no—
374C2×C22⋊C4—442no—
375C2×C22⋊C4—442no—
376C2×C42—42no—
377C2×C42C4×D1114yes—
378#95—24no—
379#95—41no—
380#95—41no—
381#95—42no—
382#95—224no—
383#95—442no—
384#95—441no—
385#95—441no—
386#95—442no—
387#95—442no—
388#95—442no—
389C2×C11#231211yescharacteristic
390C2×C11#231911yescharacteristic
391C2×C11#231911yescharacteristic
392C2×C11#237711yescharacteristic
393C2×C11#237711yescharacteristic
394C2×C11#237911yescharacteristic
395C2×C11#238011yescharacteristic
396C2×C11#282812yes—
397C2×C11#282912yes—
398C2×C11#282912yes—
399C2×C11#283012yes—
400D11—84no—
401C24—114no—
402C24—222no—
403C24—222no—
404C24—222no—
405C24—222no—
406C24—222no—
407C24—222no—
408C24—222no—
409C24—222no—
410C24—222no—
411C24—222no—
412C24—222no—
413C24—222no—
414C24—222no—
415C24—222no—
416C24C23×D1111yescharacteristic
417C2×D4—228no—
418C2×D4—444no—
419C2×D4—444no—
420C2×D4—448no—
421C2×D4—448no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—114no—
448C22×C4—222no—
449C22×C4—222no—
450C22×C4—222no—
451C22×C4—222no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4—222no—
456C22×C4—222no—
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×C4C2×C4×D1112yes—
469C22×C4C2×C4×D1112yes—
470C22×C4C2×C4×D1112yes—
471C22×C4#433914yes—
472C4⋊C4—444no—
473C4⋊C4—448no—
474C22⋊C4—448no—
475C22⋊C4—448no—
476C22⋊C4—448no—
477C22⋊C4—448no—
478C22⋊C4—448no—
479C22⋊C4—448no—
480C42—44no—
481C11#1466711yescharacteristic, complemented, Sylow
482C23—224no—
483C23—224no—
484C23—224no—
485C23—224no—
486C23—224no—
487C23—224no—
488C23—224no—
489C23—442no—
490C23—442no—
491C23—442no—
492C23—442no—
493C23—442no—
494C23—442no—
495C23—442no—
496C23—442no—
497C23—442no—
498C23—442no—
499C23—442no—
500C23—442no—
501C23—442no—
502C23—442no—
503C23—442no—
504C23—442no—
505C23—442no—
506C23—442no—
507C23—442no—
508C23—442no—
509C23—442no—
510C23—442no—
511C23—442no—
512C23—442no—
513C23—442no—
514C23—442no—
515C23—442no—
516C23—442no—
517C23C22×C4×D1111yescharacteristic
518C23C2×#433912yes—
519C23#6703712yes—
520C23#6703711yescharacteristic
521C23#6704011yescharacteristic
522C23#6704212yes—
523C23#6704211yescharacteristic
524C23#6704211yescharacteristic
525C23#6704212yes—
526C23#6704211yescharacteristic
527C23#6704311yescharacteristic
528D4—4416no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—224no—
558C2×C4—224no—
559C2×C4—224no—
560C2×C4—442no—
561C2×C4—442no—
562C2×C4—442no—
563C2×C4—442no—
564C2×C4—442no—
565C2×C4—442no—
566C2×C4—442no—
567C2×C4—442no—
568C2×C4—442no—
569C2×C4—442no—
570C2×C4—442no—
571C2×C4—442no—
572C2×C4—442no—
573C2×C4—442no—
574C2×C4—442no—
575C2×C4—442no—
576C2×C4—442no—
577C2×C4—442no—
578C2×C4#6692514yes—
579C22—444no—
580C22—444no—
581C22—444no—
582C22—444no—
583C22—444no—
584C22—444no—
585C22—444no—
586C22—882no—
587C22—882no—
588C22—882no—
589C22—882no—
590C22—882no—
591C22—882no—
592C22—882no—
593C22—882no—
594C22C2×#6692511yescharacteristic
595C22#1062301711yescharacteristic
596C22#1062303511yescharacteristic
597C22#1062305211yescharacteristic
598C22#1062305211yescharacteristic
599C22#1062305211yescharacteristic
600C22#1062305411yescharacteristic
601C22#1062306512yes—
602C22#1062306612yes—
603C22#1062309112yes—
604C22#1062309112yes—
605C22#1062309312yes—
606C22#1062311312yes—
607C22#1062315112yes—
608C22#1062317812yes—
609C22#1062319712yes—
610C22#1062319812yes—
611C22#1062321411yescharacteristic
612C22#1062321511yescharacteristic
613C22#1062323011yescharacteristic
614C22#1062323111yescharacteristic
615C22#1062324212yes—
616C22#1062324212yes—
617C4—24no—
618C4—42no—
619C4—42no—
620C4—82no—
621C4—82no—
622C4—444no—
623C4—882no—
624C4—882no—
625C2—884no—
626C2#1307121111yescharacteristic
627C2#1307125411yescharacteristic
628C2#1307126011yescharacteristic
629C2#1307177011yescharacteristic
630C2#1307177511yescharacteristic
631C2#1307178711yescharacteristic
632C2#1307179211yescharacteristic
633C2#1307673312yes—
634C2#1307674212yes—
635C2#1307674612yes—
636C2#1307675712yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1434C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1434D11
hypocenterC11#14667
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. #13066868C2semidirect
3. #13066864C2semidirect
4. #13066864C2semidirect
5. #13066860C2semidirect
6. #13066860C2semidirect
8. #13066843C2semidirect
9. C11×#1434C2semidirect
31. #10622552C4semidirect
172. #1434D11semidirect
481. C11#14667semidirect

Maximal subgroups

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

subgroupindex
C2×#106225522
#130668682
#130668642
#130668602
#130668562
#130668432
C11×#14342
#1466711