Finite Group Databasebeta

← #14682920

Subgroups — #14682920

Order 2816.

1558 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622552C211yesmaximal, characteristic
2#13066864C212yesmaximal, complemented
3#13066864C212yesmaximal, complemented
4#13066856C212yesmaximal
5#13066852C212yesmaximal, complemented
6#13066852C212yesmaximal, complemented
7#13066850C212yesmaximal, complemented
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×C4×Dic11C2212yes—
20C2×C11×#95C2212yes—
21C2×C11×#95C2212yes—
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—
31#10622552C418yescomplemented
32C24×D11C2312yes—
33C23×C4×C11C2312yes—
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C23×C4×C11C2312yes—
37C23×C4×C11C2311yescharacteristic
38C23×Dic11C2312yes—
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C22×D44—22no—
42C22×D44—22no—
43C22×D44—41no—
44C22×D44—41no—
45C22×D44—41no—
46C22×D44—41no—
47C22×D44C2×C414yes—
48C2×C42×C11—41no—
49C2×C42×C11—41no—
50C2×C42×C11C2×C414yes—
51C2×(C2×D11)⋊C4—24no—
52C2×(C2×D11)⋊C4—24no—
53C2×(C2×D11)⋊C4—24no—
54C2×(C2×D11)⋊C4—24no—
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)⋊C4—42no—
65C2×(C2×D11)⋊C4—42no—
66C2×(C2×D11)⋊C4—42no—
67C2×(C2×D11)⋊C4C2×C418yes—
68C2×(C2×D11)⋊C4C2×C418yes—
69C2×C4⋊Dic11—41no—
70C2×C4⋊Dic11—41no—
71C2×C4⋊Dic11C2×C414yes—
72C2×C4×Dic11—42no—
73C2×C4×Dic11—42no—
74C2×C4×Dic11—42no—
75C11×#95—24no—
76C11×#95—24no—
77C11×#95—41no—
78C11×#95—41no—
79C11⋊#95—24no—
80C11⋊#95—24no—
81C11⋊#95—42no—
82C11⋊#95—42no—
83C11⋊#95—41no—
84C11⋊#95—42no—
85C11⋊#95—41no—
86#14503—111nomaximal, Sylow
87C24×C11C2411yescharacteristic
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×D11—22no—
100C23×D11—22no—
101C23×D11—22no—
102C23×D11C22×C414yes—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
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×C11C22×C412yes—
129C22×C4×C11C22×C412yes—
130C22×C4×C11C22×C412yes—
131C22×C4×C11#4114yes—
132C22×C4×C11#4112yes—
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×Dic11C22×C414yes—
154C22×Dic11#4114yes—
155C2×D44—28no—
156C2×D44—44no—
157C2×D44—44no—
158C2×D44—44no—
159C2×D44—44no—
160C2×D44—44no—
161C2×D44—44no—
162C42×C11—44no—
163(C2×D11)⋊C4—48no—
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—
170C4×Dic11—48no—
171C2×#390—111no—
172#1440—112no—
173#1440—112no—
174#1438—112no—
175#1437—112no—
176#1437—112no—
177#1436—112no—
178#1434—111no—
179#1434D1111yescharacteristic, complemented
180C23×C11C23×C411yescharacteristic
181C23×C11C2×#4112yes—
182C23×C11C2×#4111yescharacteristic
183C23×C11C2×#4111yescharacteristic
184C23×C11C2×#4112yes—
185C23×C11H(5,𝔽2)11yescharacteristic
186C23×C11H(5,𝔽2)11yescharacteristic
187C23×C11H(5,𝔽2)11yescharacteristic
188C23×C11H(5,𝔽2)11yescharacteristic
189C23×C11H(5,𝔽2)12yes—
190C23×C11H(5,𝔽2)12yes—
191C22×D11—24no—
192C22×D11—24no—
193C22×D11—24no—
194C22×D11—24no—
195C22×D11—24no—
196C22×D11—24no—
197C22×D11—24no—
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—
219C22×D11—42no—
220C22×D11—42no—
221C22×D11—42no—
222C22×D11—42no—
223C22×D11—42no—
224C22×D11—42no—
225C22×D11—42no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
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—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
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#11714yes—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—24no—
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—
278D44—416no—
279C23×D4—111no—
280C22×C4⋊C4—111no—
281C22×C22⋊C4—112no—
282C22×C22⋊C4—112no—
283C22×C22⋊C4—112no—
284C22×C22⋊C4—112no—
285C22×C22⋊C4—112no—
286C22×C22⋊C4—112no—
287C22×C42—112no—
288C22×C42C2×D1111yescharacteristic
289#390—118no—
290C2×#95—112no—
291C2×#95—112no—
292C2×#95—111no—
293C2×#95—111no—
294C2×#95—112no—
295C2×#95—112no—
296C2×#95—112no—
297C2×#95C2×D1112yes—
298C2×#95C2×D1112yes—
299C2×#95C2×D1111yescharacteristic
300C2×#95C2×D1111yescharacteristic
301C22×C11C2×#11711yescharacteristic
302C22×C11C4×#4111yescharacteristic
303C22×C11C4×#4111yescharacteristic
304C22×C11#51811yescharacteristic
305C22×C11#51811yescharacteristic
306C22×C11#51811yescharacteristic
307C22×C11#51811yescharacteristic
308C22×C11#53812yes—
309C22×C11#53811yescharacteristic
310C22×C11#53811yescharacteristic
311C22×C11#53811yescharacteristic
312C22×C11#53811yescharacteristic
313C22×C11#53812yes—
314C22×C11#54012yes—
315C22×C11#54012yes—
316C22×C11#55112yes—
317C22×C11#55312yes—
318C22×C11#55312yes—
319C22×C11#55512yes—
320C22×C11#55912yes—
321C22×C11#55912yes—
322C22×C11#56012yes—
323C22×C11#56012yes—
324C2×D11—44no—
325C2×D11—44no—
326C2×D11—44no—
327C2×D11—44no—
328C2×D11—44no—
329C2×D11—44no—
330C2×D11—44no—
331C2×D11—82no—
332C2×D11—82no—
333C2×D11—82no—
334C2×D11—82no—
335C2×D11—82no—
336C2×D11—82no—
337C2×D11—82no—
338C2×D11—82no—
339C4×C11—24no—
340C4×C11—42no—
341C4×C11—42no—
342C4×C11—44no—
343C4×C11—82no—
344Dic11—44no—
345Dic11—44no—
346Dic11—82no—
347C25—112no—
348C22×D4—114no—
349C22×D4—222no—
350C22×D4—222no—
351C22×D4—441no—
352C22×D4—441no—
353C22×D4—441no—
354C22×D4—441no—
355C23×C4—112no—
356C23×C4—112no—
357C23×C4—112no—
358C23×C4C22×D1112yes—
359C23×C4C22×D1111yescharacteristic
360C23×C4C22×D1111yescharacteristic
361C23×C4C22×D1112yes—
362C23×C4C22×D1111yescharacteristic
363C2×C4⋊C4—114no—
364C2×C4⋊C4—441no—
365C2×C4⋊C4—441no—
366C2×C22⋊C4—118no—
367C2×C22⋊C4—118no—
368C2×C22⋊C4—224no—
369C2×C22⋊C4—224no—
370C2×C22⋊C4—224no—
371C2×C22⋊C4—224no—
372C2×C22⋊C4—442no—
373C2×C22⋊C4—442no—
374C2×C22⋊C4—442no—
375C2×C22⋊C4—442no—
376C2×C22⋊C4—442no—
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×C42—41no—
385C2×C42—41no—
386C2×C42—442no—
387C2×C42—442no—
388C2×C42—442no—
389C2×C42C4×D1114yes—
390#95—24no—
391#95—24no—
392#95—41no—
393#95—41no—
394#95—224no—
395#95—224no—
396#95—441no—
397#95—441no—
398#95—442no—
399#95—442no—
400#95—442no—
401C2×C11#231211yescharacteristic
402C2×C11#233311yescharacteristic
403C2×C11#233311yescharacteristic
404C2×C11#235711yescharacteristic
405C2×C11#235711yescharacteristic
406C2×C11#237211yescharacteristic
407C2×C11#238011yescharacteristic
408C2×C11#279712yes—
409C2×C11#279712yes—
410C2×C11#280312yes—
411C2×C11#280312yes—
412D11—84no—
413C24—114no—
414C24—222no—
415C24—222no—
416C24—222no—
417C24—222no—
418C24—222no—
419C24—222no—
420C24—222no—
421C24—222no—
422C24—222no—
423C24—222no—
424C24—222no—
425C24—222no—
426C24—222no—
427C24—222no—
428C24C23×D1111yescharacteristic
429C2×D4—228no—
430C2×D4—444no—
431C2×D4—444no—
432C2×D4—444no—
433C2×D4—444no—
434C2×D4—444no—
435C2×D4—444no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
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—114no—
462C22×C4—114no—
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×C4#433914yes—
486C22×C4#434112yes—
487C22×C4#434312yes—
488C4⋊C4—444no—
489C22⋊C4—448no—
490C22⋊C4—448no—
491C22⋊C4—448no—
492C22⋊C4—448no—
493C22⋊C4—448no—
494C22⋊C4—448no—
495C42—44no—
496C42—448no—
497C11#1450311yescharacteristic, complemented, Sylow
498C23—224no—
499C23—224no—
500C23—224no—
501C23—224no—
502C23—224no—
503C23—224no—
504C23—224no—
505C23—442no—
506C23—442no—
507C23—442no—
508C23—442no—
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—
533C23C22×C4×D1111yescharacteristic
534C23C2×#433912yes—
535C23C2×#434111yescharacteristic
536C23#6703711yescharacteristic
537C23#6703711yescharacteristic
538C23C2×#434311yescharacteristic
539C23#41×D1112yes—
540C23#6704211yescharacteristic
541C23#6704211yescharacteristic
542C23#6704212yes—
543C23#6704212yes—
544D4—4416no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
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—24no—
560C2×C4—42no—
561C2×C4—42no—
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—224no—
576C2×C4—224no—
577C2×C4—224no—
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#6694514yes—
597C22—444no—
598C22—444no—
599C22—444no—
600C22—444no—
601C22—444no—
602C22—444no—
603C22—444no—
604C22—882no—
605C22—882no—
606C22—882no—
607C22—882no—
608C22—882no—
609C22—882no—
610C22—882no—
611C22—882no—
612C22C4×#433911yescharacteristic
613C22#1062301711yescharacteristic
614C22C2×#6694511yescharacteristic
615C22#1062305211yescharacteristic
616C22#1062305211yescharacteristic
617C22#1062305211yescharacteristic
618C22#1062305311yescharacteristic
619C22#1062305812yes—
620C22#1062306312yes—
621C22#1062309112yes—
622C22#1062309312yes—
623C22#1062309612yes—
624C22#1062311612yes—
625C22#1062314811yescharacteristic
626C22#1062314811yescharacteristic
627C22#1062317511yescharacteristic
628C22#1062317511yescharacteristic
629C22#1062318812yes—
630C22#1062319412yes—
631C22#1062321212yes—
632C22#1062322612yes—
633C22#1062324212yes—
634C22#1062324212yes—
635C4—24no—
636C4—42no—
637C4—42no—
638C4—44no—
639C4—82no—
640C4—444no—
641C4—444no—
642C4—882no—
643C2—884no—
644C2#1307121311yescharacteristic
645C2#1307137811yescharacteristic
646C2#1307138111yescharacteristic
647C2#1307158711yescharacteristic
648C2#1307159111yescharacteristic
649C2#1307172611yescharacteristic
650C2#1307179211yescharacteristic
651C2#1307646812yes—
652C2#1307647112yes—
653C2#1307654912yes—
654C2#1307655312yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1434C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1434D11
hypocenterC11#14503
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. #13066864C2semidirect
3. #13066864C2semidirect
5. #13066852C2semidirect
6. #13066852C2semidirect
7. #13066850C2semidirect
8. #13066843C2semidirect
9. C11×#1434C2semidirect
31. #10622552C4semidirect
179. #1434D11semidirect
497. C11#14503semidirect

Maximal subgroups

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

subgroupindex
C2×#106225522
#130668642
#130668562
#130668522
#130668502
#130668432
C11×#14342
#1450311