Finite Group Databasebeta

← #14721499

Subgroups — #14721499

Order 2816.

1038 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
1#13082457C211yesmaximal, characteristic
2#13077638C211yesmaximal, characteristic, complemented
3#13071558C211yesmaximal, characteristic, complemented
4#13067192C212yesmaximal, complemented
5#13067183C211yesmaximal, characteristic, complemented
6#13067171C212yesmaximal, complemented
7#13067106C212yesmaximal, complemented
8#13067101C212yesmaximal, complemented
9C2×#10622176C211yesmaximal, characteristic, complemented
10C2×#10622108C211yesmaximal, characteristic, complemented
11C11×#1520C211yesmaximal, characteristic, complemented
12C2×C11×C22⋊Q8C2211yescharacteristic
13#10623348C412yescomplemented
14C2×#66983C2211yescharacteristic
15C2×C4×C22⋊D11C2211yescharacteristic
16#10623176—21no—
17#10623175—21no—
18#10623173C412yescomplemented
19#10623168—22no—
20#10623161C412yescomplemented
21#10623158C2212yes—
22#10623155C2212yes—
23#10623045—22no—
24#10623045C412yescomplemented
25#10623024—21no—
26#10623017—21no—
27C2×C11×C22⋊C8C2211yescharacteristic
28C11×#380C2211yescharacteristic
29C2×C11⋊#95C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C8×C22⋊D11—22no—
32#10622603—21no—
33#10622591—21no—
34#10622571—21no—
35C22⋊C4×Dic11—21no—
36(C22⋊D11)⋊C8—22no—
37D11×C22⋊C8C2212yescomplemented
38#10622331C2212yescomplemented
39#10622279C2211yescharacteristic, complemented
40#10622277C2211yescharacteristic, complemented
41#10622264C2211yescharacteristic, complemented
42#10622261C2211yescharacteristic, complemented
43C11×#328C2212yescomplemented
44C11×#328C2212yescomplemented
45#10622176C2212yescomplemented
46#10622176C2212yescomplemented
47#10622108C2212yes—
48#10622108C2212yes—
49#10622089C2212yes—
50#10622089C2212yes—
51C22×Q8×C11C2×C411yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C22×C22⋊D11—21no—
54C22×C22⋊D11D411yescharacteristic
55C23×Dic11—21no—
56C2×#4343C2×C412yescomplemented
57C22×D44C2×C411yescharacteristic
58C22×C4×D11C2311yescharacteristic
59C22×C8×C11—21no—
60C11×C22⋊Q8—21no—
61C11×C22⋊Q8—21no—
62C11×C22⋊Q8C2×C412yes—
63C11×C22⋊Q8C2312yes—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4C2×C411yescharacteristic
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—21no—
69C2×C22⋊Dic11D411yescharacteristic
70#67000—22no—
71#67000C2×C412yescomplemented
72#66999—22no—
73#66999C2×C412yescomplemented
74Q8×Dic11C2×C412yescomplemented
75#66983—21no—
76#66983—21no—
77#66983—22no—
78#66983—22no—
79#66983C2×C412yes—
80#66983C2312yes—
81C4×C22⋊D11—22no—
82C4×C22⋊D11—22no—
83C4×C22⋊D11C2×C412yes—
84C4×C22⋊D11C2×C412yes—
85C4×C22⋊D11D412yes—
86C4×C22⋊D11D412yes—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4D411yescharacteristic
91C2×C4⋊Dic11C2×C411yescharacteristic
92C2×Dic11⋊C4D411yescharacteristic
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11C2311yescharacteristic
96C22×C11⋊C8—21no—
97C2×C8×D11—22no—
98#66951—22no—
99#66951—22no—
100#66951—22no—
101#66948—22no—
102#66948C2×C412yescomplemented
103#66947—22no—
104#66947—22no—
105#66947—22no—
106#66946—22no—
107#66946C2×C412yescomplemented
108#66945—22no—
109#66945C2×C412yescomplemented
110#66943—22no—
111#66943C2×C412yescomplemented
112#66939—22no—
113#66939—22no—
114#66935—22no—
115#66935—22no—
116(C22⋊D11)⋊C4—22no—
117(C22⋊D11)⋊C4—22no—
118C22⋊C4×D11—22no—
119#66930—22no—
120C11×C22⋊C8—21no—
121C11×C22⋊C8C2312yes—
122C11×#95C2311yescharacteristic
123C11×#95C2311yescharacteristic
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95C2311yescharacteristic
130C11⋊#95C2311yescharacteristic
131C22⋊(C11⋊C8)—21no—
132C22⋊(C11⋊C8)C2312yes—
133(C2×D11)⋊C8—22no—
134Dic11⋊C8—22no—
135C8×Dic11—22no—
136#17615—111nomaximal, Sylow
137C24×C11C2×D411yescharacteristic
138C23×D11—21no—
139C23×D11C2×D411yescharacteristic
140C2×Q8×C11—21no—
141C2×Q8×C11—81no—
142C2×Q8×C11C22×C412yes—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—81no—
148C22×C4×C11C22×C411yescharacteristic
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2411yescharacteristic
154C2×C22⋊D11—22no—
155C2×C22⋊D11—22no—
156C2×C22⋊D11—22no—
157C2×C22⋊D11—22no—
158C2×C22⋊D11—42no—
159C2×C22⋊D11—42no—
160C2×C22⋊D11C22⋊C412yes—
161C2×C22⋊D11C22⋊C412yes—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—42no—
166C22×Dic11—42no—
167C22×Dic11—81no—
168C22×Dic11C2×D411yescharacteristic
169C22×Dic11C2×D411yescharacteristic
170C22×Dic11C2×D411yescharacteristic
171#4343—82no—
172C2×D44—22no—
173C2×D44—22no—
174C2×D44—21no—
175C2×D44—81no—
176C2×D44C22×C412yes—
177C2×C4×D11—22no—
178C2×C4×D11—22no—
179C2×C4×D11—81no—
180C2×C4×D11C22×C412yes—
181C2×C4×D11C2×D412yes—
182C2×C8×C11—22no—
183C2×C8×C11—81no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—81no—
188C11×C4⋊C4C22×C412yes—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—42no—
192C22⋊Dic11C22⋊C412yes—
193C22⋊Dic11C22⋊C412yes—
194(C2×D11)⋊C4—22no—
195(C2×D11)⋊C4—22no—
196(C2×D11)⋊C4—22no—
197(C2×D11)⋊C4—22no—
198(C2×D11)⋊C4—22no—
199(C2×D11)⋊C4—22no—
200(C2×D11)⋊C4—22no—
201(C2×D11)⋊C4—22no—
202(C2×D11)⋊C4—42no—
203(C2×D11)⋊C4—81no—
204(C2×D11)⋊C4C22⋊C412yes—
205(C2×D11)⋊C4C22⋊C412yes—
206C4⋊Dic11—22no—
207C4⋊Dic11—22no—
208C4⋊Dic11—21no—
209C4⋊Dic11C22×C412yes—
210Dic11⋊C4—22no—
211Dic11⋊C4—22no—
212Dic11⋊C4C22⋊C412yes—
213Dic11⋊C4C22⋊C412yes—
214C4×Dic11—22no—
215C4×Dic11—22no—
216C4×Dic11—42no—
217C4×Dic11—81no—
218C4×Dic11C22×C412yes—
219C4×Dic11C2×D412yes—
220C2×C11⋊C8—22no—
221C2×C11⋊C8—81no—
222C8×D11—82no—
223#3505—111no—
224#2972—111no—
225#2353—111no—
226#1521—112no—
227#1520D1111yescharacteristic, complemented
228#1519—111no—
229#1516—112no—
230#1501—112no—
231#1500—112no—
232C2×#328—111no—
233C2×#327—111no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11C2×C22⋊C411yescharacteristic
237C23×C11C2×C22⋊C411yescharacteristic
238C23×C11#13512yes—
239C23×C11#13512yes—
240C23×C11C22×D411yescharacteristic
241C22×D11—21no—
242C22×D11—21no—
243C22×D11—22no—
244C22×D11—41no—
245C22×D11—41no—
246C22×D11—42no—
247C22×D11—81no—
248C22×D11—81no—
249C22×D11C2×C22⋊C412yes—
250Q8×C11—42no—
251Q8×C11—81no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—81no—
267C2×C4×C11—81no—
268C2×C4×C11C2×C22⋊C411yescharacteristic
269C2×C4×C11C2×C22⋊C411yescharacteristic
270C2×C4×C11C23×C411yescharacteristic
271C2×C4×C11C22×D411yescharacteristic
272C22⋊D11—24no—
273C22⋊D11—24no—
274C22⋊D11—42no—
275C22⋊D11—42no—
276C22⋊D11—44no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—42no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—84no—
290C2×Dic11C2×C22⋊C412yes—
291C2×Dic11C2×C22⋊C412yes—
292C2×Dic11C2×C22⋊C412yes—
293D44—42no—
294D44—81no—
295D44—82no—
296D44—82no—
297C4×D11—42no—
298C4×D11—42no—
299C4×D11—82no—
300C4×D11—82no—
301C8×C11—42no—
302C11⋊C8—42no—
303#553—112no—
304#553—222no—
305#552—112no—
306#551—222no—
307#548—112no—
308#546—112no—
309#539—221no—
310#538—221no—
311#534—221no—
312#529—112no—
313#525—112no—
314C2×C22⋊Q8C2×D1111yescharacteristic
315C2×#121—111no—
316#518—221no—
317C2×C4×D4—111no—
318C8×D4—222no—
319C8×D4—222no—
320#431—112no—
321C2×C22⋊C8—111no—
322C2×C22⋊C8—112no—
323C2×C22⋊C8C2×D1111yescharacteristic
324#388—221no—
325#387—221no—
326#386—221no—
327#383—111no—
328#381—111no—
329#380C2×D1111yescharacteristic
330C4×C22⋊C4—111no—
331C4×C22⋊C4—221no—
332#376—111no—
333C2×#95—111no—
334#328—112no—
335#328—112no—
336#328C2×D1112yescomplemented
337#328C2×D1112yescomplemented
338#327—112no—
339#327—112no—
340#327—112no—
341#327—112no—
342C22×C11—21no—
343C22×C11—21no—
344C22×C11—21no—
345C22×C11—21no—
346C22×C11—21no—
347C22×C11—21no—
348C22×C11—42no—
349C22×C11—42no—
350C22×C11#41612yes—
351C22×C11#41612yes—
352C22×C11C22×C22⋊C411yescharacteristic
353C22×C11C2×#13511yescharacteristic
354C22×C11C2×#13511yescharacteristic
355C2×D11—22no—
356C2×D11—22no—
357C2×D11—22no—
358C2×D11—42no—
359C2×D11—42no—
360C2×D11—42no—
361C2×D11—81no—
362C2×D11—81no—
363C2×D11—162no—
364C4×C11—21no—
365C4×C11—21no—
366C4×C11—21no—
367C4×C11—21no—
368C4×C11—42no—
369C4×C11—42no—
370C4×C11—81no—
371C4×C11—81no—
372Dic11—22no—
373Dic11—22no—
374Dic11—22no—
375Dic11—42no—
376Dic11—42no—
377Dic11—81no—
378C2×#41—112no—
379C22×Q8C4×D1111yescharacteristic
380C22×D4—111no—
381C22×D4—111no—
382C22×D4—221no—
383C23×C4—111no—
384C23×C4—221no—
385C23×C4C22×D1111yescharacteristic
386C22×C8—21no—
387C22×C8—222no—
388C22×C8—221no—
389#126—222no—
390#126—222no—
391#126—222no—
392#125—112no—
393#125—222no—
394#124—112no—
395#124—222no—
396#123—222no—
397#123—222no—
398#123—222no—
399#123—222no—
400#123—222no—
401C22⋊Q8—21no—
402C22⋊Q8—21no—
403C22⋊Q8—112no—
404C22⋊Q8—222no—
405C22⋊Q8C4×D1112yes—
406C22⋊Q8C22×D1112yes—
407#121—112no—
408#121—112no—
409#121—112no—
410#121—222no—
411#121—222no—
412#121—222no—
413#121—221no—
414#121—221no—
415#120—222no—
416#120—222no—
417C4×Q8—112no—
418C4×D4—112no—
419C4×D4—112no—
420C4×D4—112no—
421C4×D4—112no—
422C4×D4—112no—
423C4×D4—222no—
424C4×D4—222no—
425C4×D4—222no—
426C4×D4—222no—
427C4×D4—222no—
428#117—112no—
429#117—222no—
430#117—222no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—111no—
434C2×C4⋊C4—111no—
435C2×C4⋊C4C4×D1111yescharacteristic
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—111no—
439C2×C22⋊C4—111no—
440C2×C22⋊C4—222no—
441C2×C22⋊C4—221no—
442C2×C22⋊C4—221no—
443C2×C22⋊C4—221no—
444C2×C42—111no—
445C2×C42—221no—
446C2×C42—221no—
447C4⋊C8—222no—
448C22⋊C8—21no—
449C22⋊C8—112no—
450C22⋊C8—222no—
451C22⋊C8—221no—
452C22⋊C8C22×D1112yes—
453C4×C8—222no—
454#95—111no—
455#95—111no—
456#95—221no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461#95C22×D1111yescharacteristic
462#95C22×D1111yescharacteristic
463C2×C11—21no—
464C2×C11—21no—
465C2×C11—22no—
466C2×C11—22no—
467C2×C11#288311yescharacteristic
468C2×C11C2×#41611yescharacteristic
469C2×C11#290111yescharacteristic
470D11—42no—
471D11—82no—
472C24—111no—
473C24—221no—
474C24D4×D1111yescharacteristic
475#41—882no—
476C2×Q8—21no—
477C2×Q8—81no—
478C2×Q8C2×C4×D1112yes—
479C2×D4—112no—
480C2×D4—112no—
481C2×D4—112no—
482C2×D4—222no—
483C2×D4—222no—
484C2×D4—222no—
485C2×D4—222no—
486C2×D4—222no—
487C2×D4—222no—
488C2×D4—221no—
489C2×D4—442no—
490C2×D4—442no—
491C2×D4—881no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—81no—
497C22×C4—111no—
498C22×C4—111no—
499C22×C4—111no—
500C22×C4—112no—
501C22×C4—112no—
502C22×C4—222no—
503C22×C4—222no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—442no—
508C22×C4—442no—
509C22×C4—881no—
510C22×C4—881no—
511C22×C4C2×C4×D1111yescharacteristic
512C22×C4C2×C4×D1111yescharacteristic
513C22×C4D4×D1111yescharacteristic
514C22×C4D4×D1111yescharacteristic
515C22×C4D4×D1111yescharacteristic
516C22×C4C23×D1111yescharacteristic
517C2×C8—22no—
518C2×C8—81no—
519C2×C8—222no—
520C2×C8—882no—
521C2×C8—881no—
522C4⋊C4—22no—
523C4⋊C4—21no—
524C4⋊C4—22no—
525C4⋊C4—81no—
526C4⋊C4—112no—
527C4⋊C4—112no—
528C4⋊C4—112no—
529C4⋊C4—222no—
530C4⋊C4—222no—
531C4⋊C4—222no—
532C4⋊C4—222no—
533C4⋊C4—221no—
534C4⋊C4C2×C4×D1112yes—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—42no—
538C22⋊C4—112no—
539C22⋊C4—112no—
540C22⋊C4—112no—
541C22⋊C4—112no—
542C22⋊C4—222no—
543C22⋊C4—222no—
544C22⋊C4—222no—
545C22⋊C4—222no—
546C22⋊C4—222no—
547C22⋊C4—222no—
548C22⋊C4—222no—
549C22⋊C4—222no—
550C22⋊C4—442no—
551C22⋊C4—881no—
552C42—112no—
553C42—112no—
554C42—222no—
555C42—222no—
556C42—442no—
557C42—881no—
558C11#1761511yescharacteristic, complemented, Sylow
559C23—41no—
560C23—41no—
561C23—112no—
562C23—221no—
563C23—221no—
564C23—222no—
565C23—441no—
566C23—441no—
567C23—442no—
568C23—881no—
569C23—881no—
570C23C22⋊C4×D1111yescharacteristic
571C23C22⋊C4×D1111yescharacteristic
572C23#6696912yes—
573C23#6697212yes—
574C23C2×D4×D1111yescharacteristic
575Q8—42no—
576Q8—81no—
577D4—224no—
578D4—224no—
579D4—442no—
580D4—442no—
581D4—442no—
582D4—444no—
583D4—881no—
584D4—882no—
585D4—882no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—81no—
601C2×C4—81no—
602C2×C4—112no—
603C2×C4—112no—
604C2×C4—112no—
605C2×C4—221no—
606C2×C4—221no—
607C2×C4—222no—
608C2×C4—222no—
609C2×C4—442no—
610C2×C4—442no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—442no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—882no—
620C2×C4—882no—
621C2×C4—884no—
622C2×C4C22⋊C4×D1111yescharacteristic
623C2×C4C22⋊C4×D1111yescharacteristic
624C2×C4C22×C4×D1111yescharacteristic
625C2×C4C2×D4×D1111yescharacteristic
626C8—42no—
627C8—442no—
628C22—21no—
629C22—21no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—21no—
634C22—42no—
635C22—42no—
636C22—222no—
637C22—222no—
638C22—222no—
639C22—442no—
640C22—442no—
641C22—442no—
642C22—881no—
643C22—881no—
644C22—1762no—
645C22#1062241712yes—
646C22#1062241712yes—
647C22C2×C22⋊C4×D1111yescharacteristic
648C22C2×#6696911yescharacteristic
649C22C2×#6697211yescharacteristic
650C4—21no—
651C4—21no—
652C4—21no—
653C4—21no—
654C4—42no—
655C4—42no—
656C4—81no—
657C4—81no—
658C4—222no—
659C4—222no—
660C4—222no—
661C4—442no—
662C4—442no—
663C4—881no—
664C2—21no—
665C2—21no—
666C2—22no—
667C2—22no—
668C2—442no—
669C2—882no—
670C2#1307707411yescharacteristic
671C2C2×#1062241711yescharacteristic
672C2#1307716211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1520C2
socleC22×C11C22×C22⋊C4
prime radical#13082457C2
cosocleC22×C4×C11C24
hypercenter#1520D11
hypocenterC11#17615
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1520

Complements

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

NH ≅ G/Ntype
2. #13077638C2semidirect
3. #13071558C2semidirect
4. #13067192C2semidirect
5. #13067183C2semidirect
6. #13067171C2semidirect
7. #13067106C2semidirect
8. #13067101C2semidirect
9. C2×#10622176C2semidirect
10. C2×#10622108C2semidirect
11. C11×#1520C2semidirect
13. #10623348C4semidirect
18. #10623173C4semidirect
20. #10623161C4semidirect
24. #10623045C4semidirect
37. D11×C22⋊C8C22semidirect
38. #10622331C22semidirect
39. #10622279C22semidirect
40. #10622277C22semidirect
41. #10622264C22semidirect
42. #10622261C22semidirect
43. C11×#328C22semidirect
44. C11×#328C22semidirect
45. #10622176C22semidirect
46. #10622176C22semidirect
56. C2×#4343C2×C4semidirect
71. #67000C2×C4semidirect
73. #66999C2×C4semidirect
74. Q8×Dic11C2×C4semidirect
102. #66948C2×C4semidirect
107. #66946C2×C4semidirect
109. #66945C2×C4semidirect
111. #66943C2×C4semidirect
227. #1520D11semidirect
336. #328C2×D11semidirect
337. #328C2×D11semidirect
558. C11#17615semidirect

Maximal subgroups

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

subgroupindex
#130824572
#130776382
#130715582
#130671922
#130671832
#130671712
#130671062
#130671012
C2×#106221762
C2×#106221082
C11×#15202
#1761511