Finite Group Databasebeta

← #14676343

Subgroups — #14676343

Order 2816.

1846 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66979C211yesmaximal, characteristic
2C2×#10622557C212yesmaximal
3#13066868C212yesmaximal, complemented
4#13066863C212yesmaximal
5#13066850C212yesmaximal, complemented
6Dic11⋊#95C211yesmaximal, characteristic, complemented
7#13066842C211yesmaximal, characteristic, complemented
8#13066841C211yesmaximal, characteristic, complemented
9#13066839C211yesmaximal, characteristic
10#95×Dic11C211yesmaximal, characteristic, complemented
11C11×C22⋊#95C211yesmaximal, characteristic
12C24×C4×C11C2211yescharacteristic
13C22×C11×C22⋊C4C2212yes—
14C22×C22⋊Dic11C2212yes—
15C22×C22⋊Dic11C2211yescharacteristic
16C22×C22⋊Dic11C2211yescharacteristic
17C2×#66979—28no—
18C2×#66979C418yescomplemented
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C22×Dic11⋊C4C2212yes—
22C22×C4×Dic11C2212yes—
23C22×C4×Dic11C2211yescharacteristic
24C22×C4×Dic11C2211yescharacteristic
25C2×C11×#95C2211yescharacteristic
26C2×C11×#95C2211yescharacteristic
27C2×C11×#95C2212yes—
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37#10622557—28no—
38C25×C11C2311yescharacteristic
39C23×C4×C11—24no—
40C23×C4×C11—22no—
41C23×C4×C11—22no—
42C23×C4×C11—24no—
43C23×C4×C11C2×C414yes—
44C23×C4×C11C2312yes—
45C23×C4×C11C2312yes—
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×Dic11C2312yes—
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2311yescharacteristic
51C23×Dic11C2312yes—
52C23×Dic11C2311yescharacteristic
53C23×Dic11C2311yescharacteristic
54C2×C11×C22⋊C4—24no—
55C2×C11×C22⋊C4—24no—
56C2×C11×C22⋊C4—42no—
57C2×C22⋊Dic11—24no—
58C2×C22⋊Dic11—24no—
59C2×C22⋊Dic11—24no—
60C2×C22⋊Dic11—42no—
61C2×C22⋊Dic11C2×C414yes—
62C2×C22⋊Dic11C2×C414yes—
63C2×C22⋊Dic11D418yes—
64#66979—232no—
65C2×C4⋊Dic11—24no—
66C2×C4⋊Dic11—24no—
67C2×C4⋊Dic11C2×C414yes—
68C2×C4⋊Dic11C2×C414yes—
69C2×Dic11⋊C4—24no—
70C2×Dic11⋊C4—24no—
71C2×Dic11⋊C4—42no—
72C2×C4×Dic11—24no—
73C2×C4×Dic11—24no—
74C2×C4×Dic11—24no—
75C2×C4×Dic11—24no—
76C2×C4×Dic11—42no—
77C2×C4×Dic11C2×C414yes—
78C2×C4×Dic11C2×C414yes—
79C11×#95—22no—
80C11×#95—24no—
81C11×#95—22no—
82C11⋊#95—24no—
83C11⋊#95—22no—
84C11⋊#95—24no—
85C11⋊#95—22no—
86C11⋊#95—24no—
87C11⋊#95—24no—
88C11⋊#95—24no—
89C11⋊#95—42no—
90C11⋊#95—42no—
91#13943—111nomaximal, Sylow
92C24×C11—22no—
93C24×C11—22no—
94C24×C11—21no—
95C24×C11—21no—
96C24×C11—22no—
97C24×C11—21no—
98C24×C11—21no—
99C24×C11—21no—
100C24×C11—21no—
101C24×C11C22×C412yes—
102C24×C11C2×D414yes—
103C24×C11C2411yescharacteristic
104C22×C4×C11—216no—
105C22×C4×C11—216no—
106C22×C4×C11—28no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—28no—
113C22×C4×C11—28no—
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×C11—22no—
127C22×C4×C11C22×C412yes—
128C22×C4×C11C22×C412yes—
129C22×C4×C11#4114yes—
130C22×C4×C11#4112yes—
131C22×C4×C11#4112yes—
132C22×C4×C11#4114yes—
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—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—22no—
160C22×Dic11C22×C412yes—
161C22×Dic11C22×C412yes—
162C22×Dic11C22×C412yes—
163C22×Dic11C22×C412yes—
164C22×Dic11C2×D414yes—
165C22×Dic11C2×D414yes—
166C22×Dic11#4114yes—
167C11×C22⋊C4—48no—
168C22⋊Dic11—28no—
169C22⋊Dic11—48no—
170C22⋊Dic11C22⋊C4116yes—
171C4⋊Dic11—28no—
172C4⋊Dic11—28no—
173Dic11⋊C4—48no—
174C4×Dic11—28no—
175C4×Dic11—28no—
176C4×Dic11—48no—
177C22×#117—111no—
178C2×#388—112no—
179#1441—112no—
180#1440—112no—
181#1436—112no—
182C4⋊#95—111no—
183#1434—111no—
184#1434—111no—
185C22⋊#95—111no—
186C22⋊#95D1111yescharacteristic
187C4×#95—111no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—24no—
195C23×C11—24no—
196C23×C11—24no—
197C23×C11—24no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11—41no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11C2×C22⋊C414yes—
211C23×C11C23×C411yescharacteristic
212C23×C11C22×D412yes—
213C23×C11C2×#4112yes—
214C23×C11C2×#4111yescharacteristic
215C23×C11C2×#4111yescharacteristic
216C23×C11C2×#4112yes—
217C23×C11C2×#4112yes—
218C23×C11H(5,𝔽2)11yescharacteristic
219C23×C11H(5,𝔽2)11yescharacteristic
220C23×C112−1+411yescharacteristic
221C23×C112−1+411yescharacteristic
222C2×C4×C11—232no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
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#11714yes—
246C2×C4×C11#11714yes—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—24no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—24no—
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×Dic11C2×C22⋊C414yes—
280C2×Dic11C2×C22⋊C414yes—
281C24×C4C2×D1111yescharacteristic
282C2×#117—118no—
283C2×#117—228no—
284C22×C4⋊C4—111no—
285C22×C4⋊C4—111no—
286C22×C4⋊C4—112no—
287C22×C22⋊C4—111no—
288C22×C22⋊C4—111no—
289C22×C22⋊C4—112no—
290C22×C22⋊C4C2×D1112yes—
291C22×C42—111no—
292C22×C42—111no—
293C22×C42—112no—
294#388—228no—
295C2×#95—111no—
296C2×#95—112no—
297C2×#95—111no—
298C2×#95—112no—
299C2×#95—112no—
300C2×#95—112no—
301C2×#95—112no—
302C2×#95—112no—
303C2×#95—112no—
304C2×#95C2×D1111yescharacteristic
305C2×#95C2×D1111yescharacteristic
306C2×#95C2×D1112yes—
307C22×C11—24no—
308C22×C11—24no—
309C22×C11—24no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11—42no—
313C22×C11—44no—
314C22×C11—44no—
315C22×C11—44no—
316C22×C11—44no—
317C22×C11—42no—
318C22×C11C22×C22⋊C411yescharacteristic
319C22×C11C2×#11711yescharacteristic
320C22×C11C2×#11711yescharacteristic
321C22×C11C4×#4111yescharacteristic
322C22×C11C4×#4111yescharacteristic
323C22×C11#52011yescharacteristic
324C22×C11#52011yescharacteristic
325C22×C11#52512yes—
326C22×C11#52512yes—
327C22×C11#52912yes—
328C22×C11#52912yes—
329C22×C11#54011yescharacteristic
330C22×C11#54111yescharacteristic
331C22×C11#54211yescharacteristic
332C22×C11#54211yescharacteristic
333C22×C11#54612yes—
334C22×C11#54612yes—
335C22×C11#54712yes—
336C22×C11#54712yes—
337C22×C11#55212yes—
338C22×C11#55312yes—
339C22×C11#55512yes—
340C22×C11#55612yes—
341C4×C11—24no—
342C4×C11—24no—
343C4×C11—44no—
344C4×C11—82no—
345Dic11—24no—
346Dic11—24no—
347Dic11—42no—
348Dic11—42no—
349Dic11—44no—
350Dic11—82no—
351C25C22×D1111yescharacteristic
352C23×C4—24no—
353C23×C4—22no—
354C23×C4—24no—
355C23×C4—22no—
356C23×C4—111no—
357C23×C4—111no—
358C23×C4—111no—
359C23×C4—111no—
360C23×C4—112no—
361C23×C4—112no—
362C23×C4C4×D1114yes—
363C23×C4C22×D1112yes—
364C23×C4C22×D1112yes—
365C23×C4C22×D1111yescharacteristic
366C23×C4C22×D1111yescharacteristic
367#117—2232no—
368C2×C4⋊C4—114no—
369C2×C4⋊C4—114no—
370C2×C4⋊C4—224no—
371C2×C4⋊C4—224no—
372C2×C4⋊C4—224no—
373C2×C4⋊C4—224no—
374C2×C4⋊C4—442no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—114no—
379C2×C22⋊C4—118no—
380C2×C22⋊C4—114no—
381C2×C22⋊C4—224no—
382C2×C22⋊C4—224no—
383C2×C22⋊C4—224no—
384C2×C22⋊C4—442no—
385C2×C42—114no—
386C2×C42—114no—
387C2×C42—224no—
388C2×C42—224no—
389C2×C42—224no—
390C2×C42—224no—
391C2×C42—442no—
392#95—22no—
393#95—24no—
394#95—22no—
395#95—224no—
396#95—224no—
397#95—224no—
398#95—224no—
399#95—222no—
400#95—224no—
401#95—222no—
402#95—442no—
403#95—442no—
404C2×C11—44no—
405C2×C11#228011yescharacteristic
406C2×C11#229811yescharacteristic
407C2×C11#231411yescharacteristic
408C2×C11#233911yescharacteristic
409C2×C11#233911yescharacteristic
410C2×C11#234611yescharacteristic
411C2×C11#234711yescharacteristic
412C2×C11#247012yes—
413C2×C11#247412yes—
414C2×C11#247612yes—
415C2×C11#247812yes—
416C24—22no—
417C24—21no—
418C24—22no—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—22no—
423C24—21no—
424C24—21no—
425C24C2×C4×D1112yes—
426C24D4×D1114yes—
427C24C23×D1111yescharacteristic
428C22×C4—216no—
429C22×C4—216no—
430C22×C4—28no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—28no—
437C22×C4—28no—
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—22no—
450C22×C4—22no—
451C22×C4—112no—
452C22×C4—112no—
453C22×C4—114no—
454C22×C4—114no—
455C22×C4—112no—
456C22×C4—112no—
457C22×C4—114no—
458C22×C4—222no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—222no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—222no—
465C22×C4—222no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—221no—
472C22×C4—222no—
473C22×C4—221no—
474C22×C4—222no—
475C22×C4—221no—
476C22×C4—222no—
477C22×C4—221no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—222no—
484C22×C4—222no—
485C22×C4C2×C4×D1112yes—
486C22×C4C2×C4×D1112yes—
487C22×C4#433914yes—
488C22×C4#434112yes—
489C22×C4#434114yes—
490C22×C4#434112yes—
491C4⋊C4—228no—
492C4⋊C4—228no—
493C4⋊C4—448no—
494C22⋊C4—48no—
495C22⋊C4—1116no—
496C22⋊C4—228no—
497C22⋊C4—448no—
498C42—228no—
499C42—228no—
500C42—448no—
501C11#1394311yescharacteristic, complemented, Sylow
502C23—22no—
503C23—22no—
504C23—22no—
505C23—24no—
506C23—22no—
507C23—24no—
508C23—22no—
509C23—22no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—24no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—41no—
519C23—42no—
520C23—41no—
521C23—41no—
522C23—42no—
523C23—41no—
524C23C22⋊C4×D1114yes—
525C23C22×C4×D1111yescharacteristic
526C23C2×#433912yes—
527C23C2×D4×D1112yes—
528C23C2×#434111yescharacteristic
529C23C2×#434112yes—
530C23C2×#434111yescharacteristic
531C23#6703711yescharacteristic
532C23#6704011yescharacteristic
533C23#41×D1112yes—
534C23#6704211yescharacteristic
535C23#6704311yescharacteristic
536C2×C4—232no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
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—114no—
560C2×C4—114no—
561C2×C4—222no—
562C2×C4—224no—
563C2×C4—222no—
564C2×C4—224no—
565C2×C4—222no—
566C2×C4—222no—
567C2×C4—224no—
568C2×C4—224no—
569C2×C4—222no—
570C2×C4—222no—
571C2×C4—222no—
572C2×C4—222no—
573C2×C4—222no—
574C2×C4—222no—
575C2×C4—224no—
576C2×C4—224no—
577C2×C4—224no—
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#6693014yes—
594C2×C4#6693014yes—
595C22—24no—
596C22—24no—
597C22—24no—
598C22—42no—
599C22—44no—
600C22—42no—
601C22—44no—
602C22—42no—
603C22—42no—
604C22—44no—
605C22—44no—
606C22C4×#433911yescharacteristic
607C22C2×#6693011yescharacteristic
608C22C2×#6693011yescharacteristic
609C22C2×C22⋊C4×D1111yescharacteristic
610C22#1062302112yes—
611C22#1062303511yescharacteristic
612C22#1062303812yes—
613C22#1062305311yescharacteristic
614C22#1062305411yescharacteristic
615C22#1062306912yes—
616C22#1062307212yes—
617C22#1062308812yes—
618C22#1062309412yes—
619C22#1062311712yes—
620C22#1062311712yes—
621C22#1062313411yescharacteristic
622C22#1062314512yes—
623C22#1062315011yescharacteristic
624C22#1062315611yescharacteristic
625C22#1062317212yes—
626C22#1062317411yescharacteristic
627C22#1062318512yes—
628C22#1062318612yes—
629C4—24no—
630C4—24no—
631C4—44no—
632C4—82no—
633C4—224no—
634C4—224no—
635C4—442no—
636C4—442no—
637C4—444no—
638C4—882no—
639C2—44no—
640C2#1307099411yescharacteristic
641C2#1307111211yescharacteristic
642C2#1307122311yescharacteristic
643C2#1307144011yescharacteristic
644C2#1307144311yescharacteristic
645C2#1307149911yescharacteristic
646C2#1307151111yescharacteristic
647C2#1307270912yes—
648C2#1307276912yes—
649C2#1307280112yes—
650C2#1307283112yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC22⋊#95D11
hypocenterC11#13943
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. #13066868C2semidirect
5. #13066850C2semidirect
6. Dic11⋊#95C2semidirect
7. #13066842C2semidirect
8. #13066841C2semidirect
10. #95×Dic11C2semidirect
18. C2×#66979C4semidirect
501. C11#13943semidirect

Maximal subgroups

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

subgroupindex
C22×#669792
C2×#106225572
#130668682
#130668632
#130668502
Dic11⋊#952
#130668422
#130668412
#130668392
#95×Dic112
C11×C22⋊#952
#1394311