Finite Group Databasebeta

← #14682557

Subgroups — #14682557

Order 2816.

2134 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66928C211yesmaximal, characteristic
2C2×#10622278C212yesmaximal
3#13066886C212yesmaximal, complemented
4#13066864C212yesmaximal, complemented
5#13066864C212yesmaximal, complemented
6#13066843C211yesmaximal, characteristic, complemented
7(C2×D11)⋊#95C212yesmaximal, complemented
8(C2×D11)⋊#95C212yesmaximal, complemented
9C11×#1434C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C23×C4×D11C2212yes—
12C23×Dic22C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×(C2×D11)⋊C4C2212yes—
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C2×#66928—28no—
20C2×#66928C418yescomplemented
21C2×C11×#95C2212yes—
22C2×C11×#95C2212yes—
23C2×C11×#95C2211yescharacteristic
24C2×C11×#95C2211yescharacteristic
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33#10622278—28no—
34C24×D11C2312yes—
35C23×C4×C11C2312yes—
36C23×C4×C11C2311yescharacteristic
37C23×C4×C11C2311yescharacteristic
38C23×C4×C11C2312yes—
39C23×C4×C11C2311yescharacteristic
40C23×Dic11C2312yes—
41C23×Dic11C2312yes—
42C23×Dic11C2312yes—
43C22×D44—41no—
44C22×D44—42no—
45C22×D44—41no—
46C22×D44C2×C414yes—
47C22×D44D418yes—
48C22×C4×D11—24no—
49C22×C4×D11—24no—
50C22×C4×D11—24no—
51C22×C4×D11—42no—
52C22×C4×D11—42no—
53C22×C4×D11—42no—
54C22×C4×D11—42no—
55C22×Dic22—24no—
56C22×Dic22—42no—
57C22×Dic22—41no—
58C22×Dic22—41no—
59C22×Dic22C2×C414yescomplemented
60C2×C42×C11—24no—
61C2×C42×C11C2×C414yescomplemented
62C2×(C2×D11)⋊C4—24no—
63C2×(C2×D11)⋊C4—24no—
64C2×(C2×D11)⋊C4—24no—
65C2×(C2×D11)⋊C4—24no—
66C2×(C2×D11)⋊C4—24no—
67C2×(C2×D11)⋊C4—24no—
68C2×(C2×D11)⋊C4—24no—
69C2×(C2×D11)⋊C4—24no—
70C2×(C2×D11)⋊C4—24no—
71C2×(C2×D11)⋊C4—42no—
72C2×(C2×D11)⋊C4—42no—
73C2×(C2×D11)⋊C4—42no—
74C2×(C2×D11)⋊C4—42no—
75C2×(C2×D11)⋊C4C2×C418yescomplemented
76C2×(C2×D11)⋊C4C2×C418yescomplemented
77#66928—232no—
78C11×#95—24no—
79C11×#95—24no—
80C11×#95—41no—
81C11×#95—41no—
82C11⋊#95—24no—
83C11⋊#95—24no—
84C11⋊#95—42no—
85C11⋊#95—42no—
86C11⋊#95—42no—
87C11⋊#95—42no—
88C11⋊#95—41no—
89C11⋊#95—41no—
90#14473—111nomaximal, Sylow
91C24×C11C2411yescharacteristic
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×D11—22no—
103C23×D11—22no—
104C23×D11C22×C414yes—
105C23×D11C2×D414yes—
106C23×D11C2×D414yes—
107C22×C4×C11—22no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11C22×C412yes—
132C22×C4×C11C22×C412yes—
133C22×C4×C11C22×C412yes—
134C22×C4×C11C2×D414yes—
135C22×C4×C11#4114yes—
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×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11C22×C414yes—
156C22×Dic11#4114yes—
157C2×D44—44no—
158C2×D44—44no—
159C2×D44—48no—
160C2×D44—48no—
161C2×D44C22⋊C4116yes—
162C2×C4×D11—48no—
163C2×C4×D11—48no—
164C2×C4×D11—48no—
165C2×C4×D11—48no—
166C2×C4×D11—48no—
167C2×C4×D11—48no—
168C2×C4×D11—48no—
169C2×Dic22—28no—
170C2×Dic22—44no—
171C2×Dic22—44no—
172C2×Dic22—48no—
173C2×Dic22—48no—
174C42×C11—28no—
175(C2×D11)⋊C4—216no—
176(C2×D11)⋊C4—216no—
177(C2×D11)⋊C4—48no—
178(C2×D11)⋊C4—48no—
179(C2×D11)⋊C4—48no—
180C22×#124—111no—
181C2×#386—112no—
182#1446—112no—
183#1440—112no—
184#1440—112no—
185#1434—111no—
186#1434D1111yescharacteristic, complemented
187C22⋊#95—112no—
188C22⋊#95—112no—
189C23×C11C23×C411yescharacteristic
190C23×C11C22×D412yes—
191C23×C11C2×#4112yes—
192C23×C11C2×#4112yes—
193C23×C11H(5,𝔽2)11yescharacteristic
194C23×C11H(5,𝔽2)12yes—
195C23×C11H(5,𝔽2)11yescharacteristic
196C23×C11H(5,𝔽2)11yescharacteristic
197C23×C11H(5,𝔽2)11yescharacteristic
198C23×C112−1+411yescharacteristic
199C23×C112−1+411yescharacteristic
200C22×D11—24no—
201C22×D11—24no—
202C22×D11—24no—
203C22×D11—24no—
204C22×D11—24no—
205C22×D11—24no—
206C22×D11—24no—
207C22×D11—24no—
208C22×D11—24no—
209C22×D11—24no—
210C22×D11—24no—
211C22×D11—24no—
212C22×D11—24no—
213C22×D11—24no—
214C22×D11—24no—
215C22×D11—24no—
216C22×D11—24no—
217C22×D11—24no—
218C22×D11—42no—
219C22×D11—42no—
220C22×D11—42no—
221C22×D11—42no—
222C22×D11—42no—
223C22×D11—42no—
224C22×D11—42no—
225C22×D11—42no—
226C22×D11—42no—
227C22×D11—42no—
228C22×D11—42no—
229C22×D11—42no—
230C22×D11—42no—
231C22×D11—42no—
232C22×D11—42no—
233C22×D11—42no—
234C22×D11C2×C22⋊C418yes—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
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—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11C2×C22⋊C414yes—
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—24no—
269C2×Dic11—24no—
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×Dic11—42no—
280C2×Dic11—42no—
281C2×Dic11—42no—
282C2×Dic11—42no—
283C2×Dic11—42no—
284C2×Dic11—42no—
285D44—416no—
286C4×D11—432no—
287Dic22—416no—
288C23×Q8—111no—
289C23×D4—111no—
290C24×C4—112no—
291C2×#124—118no—
292C2×#124—228no—
293C22×C22⋊C4—112no—
294C22×C22⋊C4—112no—
295C22×C22⋊C4—112no—
296C22×C22⋊C4—112no—
297C22×C22⋊C4—112no—
298C22×C42C2×D1111yescharacteristic
299#386—228no—
300C2×#95—112no—
301C2×#95—112no—
302C2×#95—111no—
303C2×#95—112no—
304C2×#95—112no—
305C2×#95—112no—
306C2×#95—111no—
307C2×#95—112no—
308C2×#95C2×D1112yes—
309C2×#95C2×D1112yes—
310C2×#95C2×D1111yescharacteristic
311C2×#95C2×D1111yescharacteristic
312C22×C11C22×C22⋊C411yescharacteristic
313C22×C11C4×#4111yescharacteristic
314C22×C11C4×#4111yescharacteristic
315C22×C11#51811yescharacteristic
316C22×C11#51811yescharacteristic
317C22×C11#52011yescharacteristic
318C22×C11#52011yescharacteristic
319C22×C11#53412yes—
320C22×C11#53412yes—
321C22×C11#53812yes—
322C22×C11#53812yes—
323C22×C11#54212yes—
324C22×C11#54212yes—
325C22×C11#54612yes—
326C22×C11#54612yes—
327C22×C11#54712yes—
328C22×C11#54712yes—
329C22×C11#55112yes—
330C22×C11#55512yes—
331C22×C11H(3,𝔽4)11yescharacteristic
332C22×C11#56211yescharacteristic
333C22×C11#56211yescharacteristic
334C22×C11#56311yescharacteristic
335C2×D11—28no—
336C2×D11—28no—
337C2×D11—28no—
338C2×D11—44no—
339C2×D11—44no—
340C2×D11—44no—
341C2×D11—44no—
342C2×D11—44no—
343C2×D11—44no—
344C2×D11—44no—
345C2×D11—44no—
346C2×D11—44no—
347C2×D11—44no—
348C2×D11—44no—
349C2×D11—44no—
350C4×C11—24no—
351C4×C11—42no—
352C4×C11—42no—
353C4×C11—44no—
354C4×C11—82no—
355Dic11—44no—
356Dic11—44no—
357Dic11—82no—
358C25—112no—
359C22×Q8—114no—
360C22×Q8—224no—
361C22×Q8—442no—
362C22×Q8—441no—
363C22×Q8—441no—
364C22×D4—114no—
365C22×D4—118no—
366C22×D4—441no—
367C22×D4—442no—
368C22×D4—441no—
369C23×C4—112no—
370C23×C4—112no—
371C23×C4—112no—
372C23×C4—224no—
373C23×C4—224no—
374C23×C4—224no—
375C23×C4—442no—
376C23×C4—442no—
377C23×C4—442no—
378C23×C4—442no—
379C23×C4C22×D1112yes—
380C23×C4C22×D1111yescharacteristic
381C23×C4C22×D1111yescharacteristic
382C23×C4C22×D1112yes—
383C23×C4C22×D1111yescharacteristic
384#124—2232no—
385C2×C22⋊C4—118no—
386C2×C22⋊C4—118no—
387C2×C22⋊C4—224no—
388C2×C22⋊C4—224no—
389C2×C22⋊C4—224no—
390C2×C22⋊C4—224no—
391C2×C22⋊C4—224no—
392C2×C22⋊C4—224no—
393C2×C22⋊C4—224no—
394C2×C22⋊C4—224no—
395C2×C22⋊C4—224no—
396C2×C22⋊C4—442no—
397C2×C22⋊C4—442no—
398C2×C22⋊C4—442no—
399C2×C22⋊C4—442no—
400C2×C42—24no—
401C2×C42C4×D1114yescomplemented
402#95—24no—
403#95—24no—
404#95—41no—
405#95—41no—
406#95—224no—
407#95—224no—
408#95—441no—
409#95—441no—
410#95—442no—
411#95—442no—
412#95—442no—
413#95—442no—
414C2×C11#230811yescharacteristic
415C2×C11#233711yescharacteristic
416C2×C11#233711yescharacteristic
417C2×C11#233911yescharacteristic
418C2×C11#233911yescharacteristic
419C2×C11#237211yescharacteristic
420C2×C11#237911yescharacteristic
421C2×C11#268412yes—
422C2×C11#268612yes—
423C2×C11#268612yes—
424C2×C11#271712yes—
425D11—48no—
426C24—114no—
427C24—114no—
428C24—114no—
429C24—222no—
430C24—222no—
431C24—222no—
432C24—222no—
433C24—222no—
434C24—222no—
435C24—222no—
436C24—222no—
437C24—222no—
438C24—222no—
439C24—222no—
440C24—222no—
441C24C23×D1111yescharacteristic
442C2×Q8—228no—
443C2×Q8—444no—
444C2×Q8—444no—
445C2×Q8—448no—
446C2×Q8—448no—
447C2×D4—1116no—
448C2×D4—444no—
449C2×D4—444no—
450C2×D4—448no—
451C2×D4—448no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—114no—
477C22×C4—114no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—222no—
484C22×C4—222no—
485C22×C4—222no—
486C22×C4—222no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—222no—
492C22×C4—222no—
493C22×C4—222no—
494C22×C4—222no—
495C22×C4—222no—
496C22×C4—222no—
497C22×C4—448no—
498C22×C4—448no—
499C22×C4—448no—
500C22×C4—448no—
501C22×C4—448no—
502C22×C4—448no—
503C22×C4—448no—
504C22×C4C2×C4×D1112yes—
505C22×C4C2×C4×D1112yes—
506C22×C4C2×C4×D1112yes—
507C22×C4#433914yes—
508C22×C4D4×D1114yes—
509C22⋊C4—2216no—
510C22⋊C4—2216no—
511C22⋊C4—448no—
512C22⋊C4—448no—
513C22⋊C4—448no—
514C42—28no—
515C11#1447311yescharacteristic, complemented, Sylow
516C23—118no—
517C23—224no—
518C23—224no—
519C23—224no—
520C23—224no—
521C23—224no—
522C23—224no—
523C23—224no—
524C23—224no—
525C23—224no—
526C23—224no—
527C23—224no—
528C23—224no—
529C23—224no—
530C23—224no—
531C23—224no—
532C23—224no—
533C23—224no—
534C23—224no—
535C23—442no—
536C23—442no—
537C23—442no—
538C23—442no—
539C23—442no—
540C23—442no—
541C23—442no—
542C23—442no—
543C23—442no—
544C23—442no—
545C23—442no—
546C23—442no—
547C23—442no—
548C23—442no—
549C23—442no—
550C23—442no—
551C23C22×C4×D1111yescharacteristic
552C23C2×#433912yes—
553C23C2×D4×D1112yes—
554C23#6703711yescharacteristic
555C23#6704011yescharacteristic
556C23#41×D1112yes—
557C23#6704211yescharacteristic
558C23#6704212yes—
559C23#6704211yescharacteristic
560C23#6704211yescharacteristic
561C23#6704311yescharacteristic
562Q8—4416no—
563D4—4416no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—224no—
593C2×C4—224no—
594C2×C4—224no—
595C2×C4—224no—
596C2×C4—224no—
597C2×C4—224no—
598C2×C4—4432no—
599C2×C4—442no—
600C2×C4—442no—
601C2×C4—442no—
602C2×C4—442no—
603C2×C4—442no—
604C2×C4—442no—
605C2×C4—442no—
606C2×C4—442no—
607C2×C4—442no—
608C2×C4—442no—
609C2×C4—442no—
610C2×C4—442no—
611C2×C4—442no—
612C2×C4—442no—
613C2×C4—442no—
614C2×C4C22⋊C4×D1114yes—
615C22—228no—
616C22—228no—
617C22—228no—
618C22—444no—
619C22—444no—
620C22—444no—
621C22—444no—
622C22—444no—
623C22—444no—
624C22—444no—
625C22—444no—
626C22—444no—
627C22—444no—
628C22—444no—
629C22—444no—
630C22C4×#433911yescharacteristic
631C22C2×C22⋊C4×D1111yescharacteristic
632C22#1062303511yescharacteristic
633C22#1062305211yescharacteristic
634C22#1062305211yescharacteristic
635C22#1062305311yescharacteristic
636C22#1062305411yescharacteristic
637C22#1062305812yes—
638C22#1062306312yes—
639C22#1062308112yes—
640C22#1062308212yes—
641C22#1062309112yes—
642C22#1062311312yes—
643C22#1062314312yes—
644C22#1062316212yes—
645C22#1062318412yes—
646C22#1062318412yes—
647C22#1062321411yescharacteristic
648C22#1062321511yescharacteristic
649C22#1062323011yescharacteristic
650C22#1062323111yescharacteristic
651C22#1062323512yes—
652C22#1062324112yes—
653C4—24no—
654C4—44no—
655C4—42no—
656C4—42no—
657C4—82no—
658C4—444no—
659C4—444no—
660C4—882no—
661C2—448no—
662C2#1307119311yescharacteristic
663C2#1307142611yescharacteristic
664C2#1307142911yescharacteristic
665C2#1307144411yescharacteristic
666C2#1307144711yescharacteristic
667C2#1307172611yescharacteristic
668C2#1307178711yescharacteristic
669C2#1307499712yes—
670C2#1307502312yes—
671C2#1307502512yes—
672C2#1307545612yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1434C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1434D11
hypocenterC11#14473
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
3. #13066886C2semidirect
4. #13066864C2semidirect
5. #13066864C2semidirect
6. #13066843C2semidirect
7. (C2×D11)⋊#95C2semidirect
8. (C2×D11)⋊#95C2semidirect
9. C11×#1434C2semidirect
20. C2×#66928C4semidirect
59. C22×Dic22C2×C4semidirect
61. C2×C42×C11C2×C4semidirect
75. C2×(C2×D11)⋊C4C2×C4semidirect
76. C2×(C2×D11)⋊C4C2×C4semidirect
186. #1434D11semidirect
401. C2×C42C4×D11semidirect
515. C11#14473semidirect

Maximal subgroups

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

subgroupindex
C22×#669282
C2×#106222782
#130668862
#130668642
#130668432
(C2×D11)⋊#952
C11×#14342
#1447311