Finite Group Databasebeta

← #14676397

Subgroups — #14676397

Order 2816.

1630 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622282C212yesmaximal
2C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
3#13066871C212yesmaximal, complemented
4#13066860C212yesmaximal
5#13066847C212yesmaximal, complemented
6Dic11⋊#95C211yesmaximal, characteristic, complemented
7Dic11⋊#95C211yesmaximal, characteristic, complemented
8(C2×D11)⋊#95C211yesmaximal, characteristic
9(C2×D11)⋊#95C211yesmaximal, characteristic
10C4×C11⋊#95C211yesmaximal, characteristic, complemented
11C11×#1434C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×(C2×D11)⋊C4C2212yes—
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2211yescharacteristic
17C22×(C2×D11)⋊C4C2211yescharacteristic
18C22×Dic11⋊C4C2212yes—
19C22×Dic11⋊C4C2212yes—
20C22×C4×Dic11C2212yes—
21C22×C4×Dic11C2211yescharacteristic
22C2×C11×#95C2211yescharacteristic
23C2×C11×#95C2211yescharacteristic
24C2×C11×#95C2212yes—
25C2×C11×#95C2212yes—
26C2×C11⋊#95C2211yescharacteristic
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2211yescharacteristic
35C4×(C2×D11)⋊C4C418yescomplemented
36#10622282—28no—
37C24×D11C2311yescharacteristic
38C23×C4×C11C2312yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×Dic11C2311yescharacteristic
44C23×Dic11C2312yes—
45C23×Dic11C2312yes—
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2311yescharacteristic
48C22×C4×D11—22no—
49C22×C4×D11—22no—
50C22×C4×D11—42no—
51C22×C4×D11—42no—
52C22×C4×D11C2×C414yes—
53C2×C42×C11—42no—
54C2×C42×C11C2×C414yes—
55C2×(C2×D11)⋊C4—22no—
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4—24no—
58C2×(C2×D11)⋊C4—24no—
59C2×(C2×D11)⋊C4—24no—
60C2×(C2×D11)⋊C4—24no—
61C2×(C2×D11)⋊C4—42no—
62C2×(C2×D11)⋊C4—42no—
63C2×(C2×D11)⋊C4C2×C414yes—
64C2×(C2×D11)⋊C4C2×C414yes—
65C2×(C2×D11)⋊C4D414yes—
66C2×(C2×D11)⋊C4Q814yes—
67C2×Dic11⋊C4—24no—
68C2×Dic11⋊C4—24no—
69C2×Dic11⋊C4—24no—
70C2×Dic11⋊C4—24no—
71C2×Dic11⋊C4—42no—
72C2×Dic11⋊C4—42no—
73C2×C4×Dic11—24no—
74C2×C4×Dic11—24no—
75C2×C4×Dic11—42no—
76C2×C4×Dic11—42no—
77C2×C4×Dic11C2×C414yes—
78C11×#95—24no—
79C11×#95—22no—
80C11×#95—22no—
81C11×#95—42no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84C11⋊#95—24no—
85C11⋊#95—24no—
86C11⋊#95—24no—
87C11⋊#95—42no—
88C11⋊#95—42no—
89C11⋊#95C2×C414yes—
90C11⋊#95C2×C414yes—
91#13948—111nomaximal, Sylow
92C24×C11C2411yescharacteristic
93C23×D11—21no—
94C23×D11—21no—
95C23×D11—22no—
96C23×D11—22no—
97C23×D11—21no—
98C23×D11—21no—
99C23×D11—22no—
100C23×D11—22no—
101C23×D11C22×C412yes—
102C23×D11C2×D412yes—
103C23×D11C2×Q812yes—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
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×C11—22no—
126C22×C4×C11C22×C412yes—
127C22×C4×C11C22×C412yes—
128C22×C4×C11C22×C412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×Q812yes—
131C22×C4×C11#4112yes—
132C22×C4×C11#4112yes—
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—21no—
144C22×Dic11—21no—
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×Dic11C22×C412yes—
154C22×Dic11C22×C412yes—
155C22×Dic11C22×C412yes—
156C22×Dic11C2×D412yes—
157C22×Dic11C2×Q812yes—
158C22×Dic11#4114yes—
159C22×Dic11#4114yes—
160C22×Dic11#4112yes—
161C22×Dic11#4112yes—
162C2×C4×D11—28no—
163C2×C4×D11—44no—
164C2×C4×D11—44no—
165C2×C4×D11—48no—
166C2×C4×D11—48no—
167C42×C11—44no—
168(C2×D11)⋊C4—28no—
169(C2×D11)⋊C4—48no—
170(C2×D11)⋊C4—48no—
171(C2×D11)⋊C4C4⋊C4116yescomplemented
172Dic11⋊C4—48no—
173Dic11⋊C4—48no—
174C4×Dic11—44no—
175C4×Dic11—48no—
176C2×#388—112no—
177C2×C4×C22⋊C4—111no—
178#1442—112no—
179#1439—112no—
180#1436—112no—
181C4⋊#95—111no—
182C4⋊#95—111no—
183#1434D1111yescharacteristic, complemented
184C22⋊#95—111no—
185C22⋊#95—111no—
186C4×#95—111no—
187C23×C11C23×C411yescharacteristic
188C23×C11C22×D411yescharacteristic
189C23×C11C22×Q811yescharacteristic
190C23×C11C2×#4111yescharacteristic
191C23×C11C2×#4111yescharacteristic
192C23×C11C2×#4111yescharacteristic
193C23×C11C2×#4111yescharacteristic
194C23×C11C2×#4112yes—
195C23×C11C2×#4112yes—
196C23×C11H(5,𝔽2)12yes—
197C23×C11H(5,𝔽2)12yes—
198C22×D11—22no—
199C22×D11—22no—
200C22×D11—22no—
201C22×D11—22no—
202C22×D11—22no—
203C22×D11—22no—
204C22×D11—22no—
205C22×D11—22no—
206C22×D11—22no—
207C22×D11—22no—
208C22×D11—24no—
209C22×D11—24no—
210C22×D11—24no—
211C22×D11—24no—
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×D11C2×C4⋊C414yes—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
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—42no—
248C2×C4×C11C2×C4⋊C414yes—
249C2×C4×C11#11714yes—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—24no—
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×Dic11C2×C4⋊C414yes—
278C2×Dic11#11714yes—
279C4×D11—416no—
280C24×C4—111no—
281C22×C4⋊C4—112no—
282C22×C4⋊C4—112no—
283C22×C22⋊C4—111no—
284C22×C22⋊C4—111no—
285C22×C22⋊C4—112no—
286C22×C22⋊C4—112no—
287C22×C42—111no—
288C22×C42—112no—
289C22×C42C2×D1111yescharacteristic
290#388—228no—
291C4×C22⋊C4—118no—
292C2×#95—111no—
293C2×#95—111no—
294C2×#95—111no—
295C2×#95—111no—
296C2×#95—112no—
297C2×#95—112no—
298C2×#95—112no—
299C2×#95—112no—
300C2×#95—112no—
301C2×#95C2×D1111yescharacteristic
302C2×#95C2×D1111yescharacteristic
303C2×#95C2×D1112yes—
304C2×#95C2×D1112yes—
305C22×C11C22×C4⋊C411yescharacteristic
306C22×C11C2×#11711yescharacteristic
307C22×C11C2×#11711yescharacteristic
308C22×C11C4×#4111yescharacteristic
309C22×C11C4×#4111yescharacteristic
310C22×C11#51811yescharacteristic
311C22×C11#51811yescharacteristic
312C22×C11#52912yes—
313C22×C11#52912yes—
314C22×C11#53211yescharacteristic
315C22×C11#53211yescharacteristic
316C22×C11#53311yescharacteristic
317C22×C11#53311yescharacteristic
318C22×C11#53812yes—
319C22×C11#53812yes—
320C22×C11#54612yes—
321C22×C11#54612yes—
322C22×C11#55112yes—
323C22×C11#55312yes—
324C22×C11#55312yes—
325C22×C11#55412yes—
326C22×C11#55412yes—
327C22×C11#55912yes—
328C2×D11—24no—
329C2×D11—24no—
330C2×D11—24no—
331C2×D11—42no—
332C2×D11—44no—
333C2×D11—44no—
334C2×D11—42no—
335C2×D11—42no—
336C2×D11—42no—
337C2×D11—44no—
338C2×D11—44no—
339C4×C11—24no—
340C4×C11—24no—
341C4×C11—42no—
342C4×C11—82no—
343C4×C11—82no—
344Dic11—24no—
345Dic11—24no—
346Dic11—42no—
347Dic11—44no—
348Dic11—44no—
349C25—111no—
350C23×C4—111no—
351C23×C4—111no—
352C23×C4—112no—
353C23×C4—112no—
354C23×C4—111no—
355C23×C4—114no—
356C23×C4—222no—
357C23×C4—222no—
358C23×C4—442no—
359C23×C4—442no—
360C23×C4C22×D1112yes—
361C23×C4C22×D1112yes—
362C23×C4C22×D1111yescharacteristic
363C23×C4C22×D1111yescharacteristic
364C23×C4C22×D1111yescharacteristic
365C2×C4⋊C4—224no—
366C2×C4⋊C4—224no—
367C2×C4⋊C4—224no—
368C2×C4⋊C4—224no—
369C2×C4⋊C4—442no—
370C2×C4⋊C4—442no—
371C2×C22⋊C4—114no—
372C2×C22⋊C4—114no—
373C2×C22⋊C4—114no—
374C2×C22⋊C4—114no—
375C2×C22⋊C4—222no—
376C2×C22⋊C4—222no—
377C2×C22⋊C4—224no—
378C2×C22⋊C4—224no—
379C2×C22⋊C4—224no—
380C2×C22⋊C4—224no—
381C2×C22⋊C4—442no—
382C2×C22⋊C4—442no—
383C2×C42—42no—
384C2×C42—114no—
385C2×C42—224no—
386C2×C42—224no—
387C2×C42—442no—
388C2×C42—442no—
389C2×C42C4×D1114yes—
390#95—22no—
391#95—22no—
392#95—24no—
393#95—42no—
394#95—114no—
395#95—114no—
396#95—224no—
397#95—224no—
398#95—224no—
399#95—222no—
400#95—222no—
401#95—442no—
402#95—442no—
403C2×C11#228511yescharacteristic
404C2×C11#229811yescharacteristic
405C2×C11#231211yescharacteristic
406C2×C11#234911yescharacteristic
407C2×C11#234911yescharacteristic
408C2×C11#235311yescharacteristic
409C2×C11#235711yescharacteristic
410C2×C11#255712yes—
411C2×C11#255912yes—
412C2×C11#258712yes—
413C2×C11#258912yes—
414D11—44no—
415C24—112no—
416C24—112no—
417C24—112no—
418C24—221no—
419C24—221no—
420C24—222no—
421C24—221no—
422C24—221no—
423C24—222no—
424C24—222no—
425C24—222no—
426C24C23×D1111yescharacteristic
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—21no—
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—22no—
448C22×C4—22no—
449C22×C4—112no—
450C22×C4—112no—
451C22×C4—112no—
452C22×C4—112no—
453C22×C4—112no—
454C22×C4—112no—
455C22×C4—112no—
456C22×C4—114no—
457C22×C4—114no—
458C22×C4—222no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4—222no—
463C22×C4—222no—
464C22×C4—221no—
465C22×C4—221no—
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—228no—
479C22×C4—444no—
480C22×C4—444no—
481C22×C4—448no—
482C22×C4—448no—
483C22×C4C2×C4×D1112yes—
484C22×C4C2×C4×D1112yes—
485C22×C4C2×C4×D1112yes—
486C22×C4#433912yes—
487C22×C4#433912yes—
488C22×C4D4×D1112yes—
489C22×C4Q8×D1112yes—
490C4⋊C4—448no—
491C4⋊C4—448no—
492C22⋊C4—1116no—
493C22⋊C4—228no—
494C22⋊C4—448no—
495C22⋊C4—448no—
496C42—44no—
497C42—444no—
498C42—448no—
499C11#1394811yescharacteristic, complemented, Sylow
500C23—114no—
501C23—222no—
502C23—222no—
503C23—222no—
504C23—222no—
505C23—222no—
506C23—222no—
507C23—222no—
508C23—222no—
509C23—222no—
510C23—222no—
511C23—224no—
512C23—224no—
513C23—224no—
514C23—224no—
515C23—442no—
516C23—442no—
517C23—442no—
518C23—442no—
519C23—442no—
520C23—442no—
521C23—442no—
522C23—442no—
523C23C22×C4×D1111yescharacteristic
524C23C2×#433911yescharacteristic
525C23C2×#433911yescharacteristic
526C23C2×D4×D1111yescharacteristic
527C23#6703712yes—
528C23C2×Q8×D1111yescharacteristic
529C23#41×D1111yescharacteristic
530C23#41×D1112yes—
531C23#41×D1111yescharacteristic
532C23#41×D1112yes—
533C23#6704212yes—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
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—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—114no—
562C2×C4—114no—
563C2×C4—224no—
564C2×C4—224no—
565C2×C4—222no—
566C2×C4—222no—
567C2×C4—222no—
568C2×C4—222no—
569C2×C4—224no—
570C2×C4—224no—
571C2×C4—224no—
572C2×C4—222no—
573C2×C4—222no—
574C2×C4—222no—
575C2×C4—224no—
576C2×C4—224no—
577C2×C4—224no—
578C2×C4—224no—
579C2×C4—224no—
580C2×C4—4416no—
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#6692514yes—
592C2×C4C4⋊C4×D1114yes—
593C22—224no—
594C22—224no—
595C22—224no—
596C22—442no—
597C22—444no—
598C22—444no—
599C22—442no—
600C22—444no—
601C22—444no—
602C22—442no—
603C22—442no—
604C22C2×#6692511yescharacteristic
605C22#1062301711yescharacteristic
606C22C2×C4⋊C4×D1111yescharacteristic
607C22D11×#11711yescharacteristic
608C22#1062305211yescharacteristic
609C22#1062305311yescharacteristic
610C22#1062305311yescharacteristic
611C22#1062305912yes—
612C22#1062305912yes—
613C22#1062307911yescharacteristic
614C22#1062307911yescharacteristic
615C22#1062309112yes—
616C22#1062309112yes—
617C22#1062310911yescharacteristic
618C22#1062310911yescharacteristic
619C22#1062314112yes—
620C22#1062316712yes—
621C22#1062319212yes—
622C22#1062319512yes—
623C22#1062320712yes—
624C22#1062322112yes—
625C22#1062323612yes—
626C22#1062324012yes—
627C4—24no—
628C4—24no—
629C4—42no—
630C4—82no—
631C4—82no—
632C4—224no—
633C4—224no—
634C4—444no—
635C4—444no—
636C4—442no—
637C2—444no—
638C2#1307102011yescharacteristic
639C2#1307111111yescharacteristic
640C2#1307121111yescharacteristic
641C2#1307152011yescharacteristic
642C2#1307152411yescharacteristic
643C2#1307154911yescharacteristic
644C2#1307158411yescharacteristic
645C2#1307371712yes—
646C2#1307374712yes—
647C2#1307403912yes—
648C2#1307406912yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1434C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1434D11
hypocenterC11#13948
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
3. #13066871C2semidirect
5. #13066847C2semidirect
6. Dic11⋊#95C2semidirect
7. Dic11⋊#95C2semidirect
10. C4×C11⋊#95C2semidirect
11. C11×#1434C2semidirect
35. C4×(C2×D11)⋊C4C4semidirect
171. (C2×D11)⋊C4C4⋊C4semidirect
183. #1434D11semidirect
499. C11#13948semidirect

Maximal subgroups

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

subgroupindex
C2×#106222822
C2×C4×(C2×D11)⋊C42
#130668712
#130668602
#130668472
Dic11⋊#952
(C2×D11)⋊#952
C4×C11⋊#952
C11×#14342
#1394811