Finite Group Databasebeta

← #14675639

Subgroups — #14675639

Order 2816.

7150 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C22⋊D11C211yesmaximal, characteristic
2C2×#10622826C214yesmaximal, complemented
3C2×#10622860C211yesmaximal, characteristic, complemented
4C2×#10622568C212yesmaximal, complemented
5#13066855C214yesmaximal, complemented
6#13066838C212yesmaximal, complemented
7C23×C11×C22⋊C4C211yesmaximal, characteristic, complemented
8C26×C11C2211yescharacteristic
9C25×D11C2211yescharacteristic
10C24×C4×C11C2212yescomplemented
11C23×C22⋊D11—24no—
12C23×C22⋊D11—24no—
13C23×C22⋊D11—216no—
14C23×C22⋊D11C418yescomplemented
15C23×C22⋊D11C2212yes—
16C23×C22⋊D11C2212yes—
17C24×Dic11C2211yescharacteristic
18C22×C11×C22⋊C4—24no—
19C22×C11×C22⋊C4—28no—
20C22×C11×C22⋊C4C2212yes—
21C22×C11×C22⋊C4C2212yescomplemented
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yescomplemented
24C22×C22⋊Dic11C2212yescomplemented
25C22×(C2×D11)⋊C4C2218yescomplemented
26#10622860—24no—
27#10622826—216no—
28C2×C11⋊#95C2218yescomplemented
29#10622568—28no—
30C25×C11—24no—
31C25×C11—28no—
32C25×C11—24no—
33C25×C11—44no—
34C25×C11C2×C414yes—
35C25×C11D414yes—
36C25×C11D414yes—
37C25×C11C2311yescharacteristic
38C25×C11C2311yescharacteristic
39C25×C11C2311yescharacteristic
40C24×D11—22no—
41C24×D11—22no—
42C24×D11—28no—
43C24×D11—24no—
44C24×D11—24no—
45C24×D11—44no—
46C24×D11C2×C414yescomplemented
47C24×D11C2312yes—
48C23×C4×C11—24no—
49C23×C4×C11—28no—
50C23×C4×C11—28no—
51C23×C4×C11—44no—
52C23×C4×C11C2314yes—
53C22×C22⋊D11—264no—
54C22×C22⋊D11—264no—
55C22×C22⋊D11—232no—
56C22×C22⋊D11—24no—
57C22×C22⋊D11—24no—
58C22×C22⋊D11—28no—
59C22×C22⋊D11—24no—
60C22×C22⋊D11—24no—
61C22×C22⋊D11—28no—
62C22×C22⋊D11—264no—
63C22×C22⋊D11—28no—
64C22×C22⋊D11C2×C418yes—
65C22×C22⋊D11C2×C418yescomplemented
66C22×C22⋊D11D4116yes—
67C23×Dic11—22no—
68C23×Dic11—22no—
69C23×Dic11—28no—
70C23×Dic11C2×C414yescomplemented
71C23×Dic11C2314yes—
72C23×Dic11C2312yes—
73C2×C11×C22⋊C4—232no—
74C2×C11×C22⋊C4—24no—
75C2×C11×C22⋊C4—24no—
76C2×C11×C22⋊C4—24no—
77C2×C11×C22⋊C4—28no—
78C2×C11×C22⋊C4D418yescomplemented
79C2×C22⋊Dic11—24no—
80C2×C22⋊Dic11—28no—
81C2×C22⋊Dic11—24no—
82C2×C22⋊Dic11—24no—
83C2×C22⋊Dic11—24no—
84C2×C22⋊Dic11—24no—
85C2×C22⋊Dic11—44no—
86C2×(C2×D11)⋊C4—216no—
87C2×(C2×D11)⋊C4—216no—
88C2×(C2×D11)⋊C4—48no—
89C11⋊#95—216no—
90#13867—111nomaximal, Sylow
91C24×C11—24no—
92C24×C11—22no—
93C24×C11—22no—
94C24×C11—24no—
95C24×C11—24no—
96C24×C11—216no—
97C24×C11—216no—
98C24×C11—28no—
99C24×C11—216no—
100C24×C11—216no—
101C24×C11—216no—
102C24×C11—28no—
103C24×C11—22no—
104C24×C11—24no—
105C24×C11—22no—
106C24×C11—24no—
107C24×C11—48no—
108C24×C11—48no—
109C24×C11—48no—
110C24×C11—432no—
111C24×C11—432no—
112C24×C11C22⋊C4116yescomplemented
113C24×C11C22×C412yes—
114C24×C11C22×C412yes—
115C24×C11C22×C412yes—
116C24×C11C2×D412yes—
117C24×C11C2×D412yes—
118C24×C11C2×D412yes—
119C24×C11C2×D418yes—
120C24×C11C2×D412yes—
121C24×C11C2×D412yes—
122C24×C11C2×D412yes—
123C24×C11C2×D414yes—
124C24×C11#4114yes—
125C24×C11C2411yescharacteristic
126C23×D11—216no—
127C23×D11—216no—
128C23×D11—28no—
129C23×D11—24no—
130C23×D11—22no—
131C23×D11—22no—
132C23×D11—24no—
133C23×D11—24no—
134C23×D11—28no—
135C23×D11—216no—
136C23×D11—216no—
137C23×D11—48no—
138C23×D11—432no—
139C23×D11—432no—
140C23×D11—48no—
141C23×D11—48no—
142C23×D11—44no—
143C23×D11—48no—
144C23×D11—44no—
145C23×D11C22×C414yes—
146C23×D11C2×D418yes—
147C22×C4×C11—216no—
148C22×C4×C11—28no—
149C22×C4×C11—24no—
150C22×C4×C11—24no—
151C22×C4×C11—28no—
152C22×C4×C11—432no—
153C22×C4×C11—48no—
154C22×C4×C11—48no—
155C22×C4×C11C2×D418yescomplemented
156C2×C22⋊D11—2256no—
157C2×C22⋊D11—232no—
158C2×C22⋊D11—232no—
159C2×C22⋊D11—216no—
160C2×C22⋊D11—216no—
161C2×C22⋊D11—216no—
162C2×C22⋊D11—216no—
163C2×C22⋊D11—232no—
164C2×C22⋊D11—232no—
165C2×C22⋊D11—216no—
166C2×C22⋊D11C22⋊C4132yescomplemented
167C22×Dic11—216no—
168C22×Dic11—216no—
169C22×Dic11—216no—
170C22×Dic11—28no—
171C22×Dic11—22no—
172C22×Dic11—24no—
173C22×Dic11—22no—
174C22×Dic11—28no—
175C22×Dic11—24no—
176C22×Dic11—24no—
177C22×Dic11—24no—
178C22×Dic11—28no—
179C22×Dic11C22×C414yes—
180C22×Dic11C2×D418yes—
181C11×C22⋊C4—216no—
182C11×C22⋊C4—216no—
183C22⋊Dic11—48no—
184C22⋊Dic11—48no—
185C22⋊Dic11—48no—
186(C2×D11)⋊C4—432no—
187C24×D4—111no—
188C23×C22⋊C4D1111yescharacteristic, complemented
189C2×#386—114no—
190C2×#379—111no—
191C2×#379—112no—
192#1438—114no—
193C22⋊#95—112no—
194C23×C11—24no—
195C23×C11—24no—
196C23×C11—24no—
197C23×C11—24no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—22no—
201C23×C11—24no—
202C23×C11—22no—
203C23×C11—24no—
204C23×C11—24no—
205C23×C11—24no—
206C23×C11—24no—
207C23×C11—216no—
208C23×C11—216no—
209C23×C11—216no—
210C23×C11—216no—
211C23×C11—24no—
212C23×C11—24no—
213C23×C11—24no—
214C23×C11—22no—
215C23×C11—24no—
216C23×C11—24no—
217C23×C11—24no—
218C23×C11—22no—
219C23×C11—24no—
220C23×C11—24no—
221C23×C11—232no—
222C23×C11—232no—
223C23×C11—416no—
224C23×C11—464no—
225C23×C11—432no—
226C23×C11—432no—
227C23×C11—464no—
228C23×C11—48no—
229C23×C11—48no—
230C23×C11C2×C22⋊C418yes—
231C23×C11C2×C22⋊C414yes—
232C23×C11C2×C22⋊C414yes—
233C23×C11C2×C22⋊C414yes—
234C23×C11C4×D418yes—
235C23×C11#12018yes—
236C23×C11#12018yes—
237C23×C11#12014yes—
238C23×C11#12118yes—
239C23×C11#12314yes—
240C23×C11C23×C411yescharacteristic
241C23×C11C22×D411yescharacteristic
242C23×C11C22×D414yes—
243C23×C11C22×D411yescharacteristic
244C23×C11C22×D412yes—
245C23×C11C2×#4112yes—
246C23×C11H(5,𝔽2)14yes—
247C22×D11—232no—
248C22×D11—24no—
249C22×D11—24no—
250C22×D11—28no—
251C22×D11—28no—
252C22×D11—28no—
253C22×D11—28no—
254C22×D11—216no—
255C22×D11—216no—
256C22×D11—464no—
257C22×D11—416no—
258C22×D11—432no—
259C22×D11—432no—
260C22×D11—464no—
261C22×D11—42no—
262C22×D11—44no—
263C22×D11—42no—
264C22×D11—44no—
265C22×D11—44no—
266C22×D11—48no—
267C22×D11—48no—
268C22×D11—416no—
269C22×D11C2×C22⋊C418yescomplemented
270C2×C4×C11—28no—
271C2×C4×C11—216no—
272C2×C4×C11—432no—
273C2×C4×C11—44no—
274C2×C4×C11—44no—
275C2×C4×C11—48no—
276C22⋊D11—264no—
277C22⋊D11—264no—
278C2×Dic11—232no—
279C2×Dic11—24no—
280C2×Dic11—24no—
281C2×Dic11—28no—
282C2×Dic11—28no—
283C2×Dic11—44no—
284C2×Dic11—44no—
285C2×Dic11—44no—
286C2×Dic11—48no—
287C2×Dic11—48no—
288C2×Dic11C2×C22⋊C418yescomplemented
289C26—111no—
290C26C2×D1111yescharacteristic
291C23×D4—112no—
292C23×D4—112no—
293C23×D4—118no—
294C23×D4—2216no—
295C23×D4—224no—
296C23×D4—224no—
297C24×C4—111no—
298C24×C4C2×D1112yescomplemented
299C22×C22⋊C4—24no—
300C22×C22⋊C4—28no—
301C22×C22⋊C4—112no—
302C22×C22⋊C4—112no—
303C22×C22⋊C4—118no—
304C22×C22⋊C4—112no—
305C22×C22⋊C4C2×D1112yes—
306C22×C22⋊C4C2×D1112yescomplemented
307#386—2216no—
308#379—224no—
309#379—228no—
310C2×#95—118no—
311C22×C11—24no—
312C22×C11—24no—
313C22×C11—216no—
314C22×C11—216no—
315C22×C11—28no—
316C22×C11—28no—
317C22×C11—28no—
318C22×C11—28no—
319C22×C11—216no—
320C22×C11—216no—
321C22×C11—24no—
322C22×C11—24no—
323C22×C11—24no—
324C22×C11—24no—
325C22×C11—24no—
326C22×C11—464no—
327C22×C11—48no—
328C22×C11—44no—
329C22×C11—44no—
330C22×C11—48no—
331C22×C11#37918yescomplemented
332C22×C11#38618yescomplemented
333C22×C11C22×C22⋊C412yes—
334C22×C11C22×C22⋊C411yescharacteristic
335C22×C11C2×C4×D412yes—
336C22×C11#51812yes—
337C22×C11C2×#12012yes—
338C22×C11C2×#12012yes—
339C22×C11C2×#12011yescharacteristic
340C22×C11C2×#12112yes—
341C22×C11C2×#12311yescharacteristic
342C22×C11#53412yes—
343C22×C11#53412yes—
344C22×C11D4218yes—
345C22×C11#54618yes—
346C2×D11—216no—
347C2×D11—28no—
348C2×D11—464no—
349C2×D11—44no—
350C2×D11—48no—
351C2×D11—48no—
352C2×D11—48no—
353C2×D11—416no—
354C2×D11—44no—
355C4×C11—48no—
356Dic11—28no—
357Dic11—84no—
358C25—24no—
359C25—28no—
360C25—24no—
361C25—44no—
362C25—112no—
363C25—114no—
364C25—228no—
365C25—222no—
366C25—222no—
367C25—224no—
368C25—224no—
369C25—444no—
370C25C4×D1114yes—
371C25D4414yes—
372C25C22⋊D1114yes—
373C25C22×D1111yescharacteristic
374C25C22×D1111yescharacteristic
375C25C22×D1111yescharacteristic
376C22×D4—118no—
377C22×D4—1116no—
378C22×D4—118no—
379C22×D4—228no—
380C22×D4—2264no—
381C22×D4—228no—
382C22×D4—2264no—
383C22×D4—2264no—
384C22×D4—2232no—
385C22×D4—224no—
386C22×D4—224no—
387C22×D4—228no—
388C22×D4—224no—
389C22×D4—224no—
390C23×C4—24no—
391C23×C4—28no—
392C23×C4—28no—
393C23×C4—44no—
394C23×C4—112no—
395C23×C4—114no—
396C23×C4—114no—
397C23×C4—228no—
398C23×C4—222no—
399C23×C4—222no—
400C23×C4C22×D1114yes—
401C2×C22⋊C4—232no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—24no—
405C2×C22⋊C4—28no—
406C2×C22⋊C4—2216no—
407C2×C22⋊C4—224no—
408C2×C22⋊C4—224no—
409C2×C22⋊C4—224no—
410C2×C22⋊C4—224no—
411C2×C22⋊C4—228no—
412C2×C22⋊C4—224no—
413C2×C22⋊C4—2216no—
414C2×C22⋊C4—448no—
415C2×C22⋊C4—444no—
416C2×C22⋊C4C22⋊D1118yescomplemented
417#95—2216no—
418C2×C11—28no—
419C2×C11—28no—
420C2×C11—44no—
421C2×C11C2×#37911yescharacteristic
422C2×C11C2×#38611yescharacteristic
423C2×C11#230811yescharacteristic
424C2×C11D4×C22⋊C414yes—
425C2×C11#240312yes—
426C2×C11#240512yes—
427C2×C11#241014yes—
428D11—48no—
429C24—22no—
430C24—24no—
431C24—24no—
432C24—24no—
433C24—22no—
434C24—216no—
435C24—216no—
436C24—216no—
437C24—28no—
438C24—216no—
439C24—216no—
440C24—28no—
441C24—22no—
442C24—24no—
443C24—24no—
444C24—22no—
445C24—48no—
446C24—48no—
447C24—48no—
448C24—432no—
449C24—432no—
450C24—114no—
451C24—118no—
452C24—2216no—
453C24—2216no—
454C24—2216no—
455C24—228no—
456C24—222no—
457C24—224no—
458C24—224no—
459C24—228no—
460C24—224no—
461C24—222no—
462C24—2216no—
463C24—448no—
464C24—4432no—
465C24—4432no—
466C24—448no—
467C24—448no—
468C24—444no—
469C24—448no—
470C24—444no—
471C24(C2×D11)⋊C4116yescomplemented
472C24C2×C4×D1112yes—
473C24C2×C4×D1112yes—
474C24C2×C4×D1112yes—
475C24C2×D4412yes—
476C24C2×D4412yes—
477C24C2×D4412yes—
478C24#433914yes—
479C24D4×D1118yes—
480C24C2×C22⋊D1112yes—
481C24C2×C22⋊D1112yes—
482C24C2×C22⋊D1112yes—
483C24C2×C22⋊D1114yes—
484C24C23×D1111yescharacteristic
485C2×D4—1132no—
486C2×D4—2216no—
487C2×D4—2216no—
488C2×D4—22256no—
489C2×D4—2232no—
490C2×D4—2232no—
491C2×D4—2216no—
492C2×D4—2232no—
493C2×D4—2216no—
494C2×D4—2216no—
495C2×D4—2232no—
496C22×C4—216no—
497C22×C4—28no—
498C22×C4—28no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—432no—
502C22×C4—48no—
503C22×C4—48no—
504C22×C4—114no—
505C22×C4—118no—
506C22×C4—2216no—
507C22×C4—2216no—
508C22×C4—2216no—
509C22×C4—228no—
510C22×C4—222no—
511C22×C4—224no—
512C22×C4—222no—
513C22×C4—224no—
514C22×C4—224no—
515C22×C4—228no—
516C22×C4—228no—
517C22×C4—224no—
518C22×C4C2×C22⋊D1118yescomplemented
519C22⋊C4—216no—
520C22⋊C4—216no—
521C22⋊C4—4432no—
522C22⋊C4—448no—
523C22⋊C4—448no—
524C22⋊C4—448no—
525C11#1386711yescharacteristic, complemented, Sylow
526C23—24no—
527C23—24no—
528C23—24no—
529C23—24no—
530C23—216no—
531C23—216no—
532C23—24no—
533C23—24no—
534C23—24no—
535C23—22no—
536C23—24no—
537C23—24no—
538C23—216no—
539C23—216no—
540C23—24no—
541C23—24no—
542C23—22no—
543C23—24no—
544C23—24no—
545C23—24no—
546C23—24no—
547C23—24no—
548C23—22no—
549C23—24no—
550C23—24no—
551C23—24no—
552C23—232no—
553C23—232no—
554C23—22no—
555C23—416no—
556C23—432no—
557C23—432no—
558C23—464no—
559C23—464no—
560C23—48no—
561C23—48no—
562C23—118no—
563C23—2232no—
564C23—224no—
565C23—228no—
566C23—228no—
567C23—2216no—
568C23—224no—
569C23—228no—
570C23—228no—
571C23—2216no—
572C23—4464no—
573C23—4432no—
574C23—4432no—
575C23—4416no—
576C23—4464no—
577C23—448no—
578C23—444no—
579C23—442no—
580C23—444no—
581C23—448no—
582C23—444no—
583C23—4416no—
584C23—442no—
585C23C22⋊C4×D1118yes—
586C23#6693518yes—
587C23C2×(C2×D11)⋊C414yes—
588C23C2×(C2×D11)⋊C414yes—
589C23C2×(C2×D11)⋊C414yes—
590C23C4×C22⋊D1118yes—
591C23#6698214yes—
592C23#6698318yes—
593C23#6699018yes—
594C23#6700614yes—
595C23C22×C4×D1111yescharacteristic
596C23C22×D4411yescharacteristic
597C23C2×#433912yes—
598C23C2×D4×D1114yes—
599C23#6703714yes—
600C23C22×C22⋊D1111yescharacteristic
601C23C22×C22⋊D1112yes—
602D4—2264no—
603D4—2264no—
604C2×C4—216no—
605C2×C4—28no—
606C2×C4—432no—
607C2×C4—44no—
608C2×C4—48no—
609C2×C4—44no—
610C2×C4—118no—
611C2×C4—2232no—
612C2×C4—224no—
613C2×C4—228no—
614C2×C4—224no—
615C2×C4—228no—
616C2×C4—444no—
617C2×C4—448no—
618C2×C4—444no—
619C2×C4—444no—
620C2×C4—448no—
621C22—28no—
622C22—28no—
623C22—28no—
624C22—28no—
625C22—216no—
626C22—216no—
627C22—24no—
628C22—24no—
629C22—216no—
630C22—216no—
631C22—24no—
632C22—24no—
633C22—24no—
634C22—24no—
635C22—24no—
636C22—464no—
637C22—44no—
638C22—44no—
639C22—48no—
640C22—48no—
641C22—2216no—
642C22—228no—
643C22—4464no—
644C22—448no—
645C22—448no—
646C22—448no—
647C22—444no—
648C22—4416no—
649C22—444no—
650C22#1062256818yescomplemented
651C22#1062282618yescomplemented
652C22C2×C22⋊C4×D1112yes—
653C22#1062301712yes—
654C22C2×#6693512yes—
655C22#1062302118yes—
656C22#1062302412yes—
657C22C22×(C2×D11)⋊C411yescharacteristic
658C22C2×C4×C22⋊D1112yes—
659C22C2×#6698211yescharacteristic
660C22C2×#6698312yes—
661C22C2×#6699012yes—
662C22D4×C22⋊D1118yes—
663C22#1062333512yes—
664C22C2×#6700611yescharacteristic
665C4—48no—
666C4—228no—
667C4—884no—
668C2—28no—
669C2—28no—
670C2—44no—
671C2—448no—
672C2C2×#1062256811yescharacteristic
673C2C2×#1062282611yescharacteristic
674C2#1307119111yescharacteristic
675C2C22⋊C4×C22⋊D1114yes—
676C2#1307192612yes—
677C2#1307194312yes—
678C2#1307198414yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC23×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC24×C22⋊D11C2
hypercenterC23×C22⋊C4D11
hypocenterC11#13867
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#10622826C2semidirect
3. C2×#10622860C2semidirect
4. C2×#10622568C2semidirect
5. #13066855C2semidirect
6. #13066838C2semidirect
7. C23×C11×C22⋊C4C2semidirect
10. C24×C4×C11C22semidirect
14. C23×C22⋊D11C4semidirect
21. C22×C11×C22⋊C4C22semidirect
23. C22×C22⋊Dic11C22semidirect
24. C22×C22⋊Dic11C22semidirect
25. C22×(C2×D11)⋊C4C22semidirect
28. C2×C11⋊#95C22semidirect
46. C24×D11C2×C4semidirect
65. C22×C22⋊D11C2×C4semidirect
70. C23×Dic11C2×C4semidirect
78. C2×C11×C22⋊C4D4semidirect
112. C24×C11C22⋊C4semidirect
155. C22×C4×C11C2×D4semidirect
166. C2×C22⋊D11C22⋊C4semidirect
188. C23×C22⋊C4D11semidirect
269. C22×D11C2×C22⋊C4semidirect
288. C2×Dic11C2×C22⋊C4semidirect
298. C24×C4C2×D11semidirect
306. C22×C22⋊C4C2×D11semidirect
331. C22×C11#379semidirect
332. C22×C11#386semidirect
416. C2×C22⋊C4C22⋊D11semidirect
471. C24(C2×D11)⋊C4semidirect
518. C22×C4C2×C22⋊D11semidirect
525. C11#13867semidirect
650. C22#10622568semidirect
651. C22#10622826semidirect

Maximal subgroups

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

subgroupindex
C24×C22⋊D112
C2×#106228262
C2×#106228602
C2×#106225682
#130668552
#130668382
C23×C11×C22⋊C42
#1386711