Finite Group Databasebeta

← #14721563

Subgroups — #14721563

Order 2816.

1014 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#13082450C211yesmaximal, characteristic
2#13077655C211yesmaximal, characteristic, complemented
3#13071553C211yesmaximal, characteristic, complemented
4#13067190C212yesmaximal, complemented
5#13067156C212yesmaximal, complemented
6#13067148C211yesmaximal, characteristic, complemented
7#13067137C211yesmaximal, characteristic, complemented
8#13067132C211yesmaximal, characteristic, complemented
9#13067117C212yesmaximal, complemented
10#13067099C212yesmaximal, complemented
11C11×#1510C211yesmaximal, characteristic, complemented
12C2×C11×#121C2211yescharacteristic
13#10623337C412yescomplemented
14#10623335—21no—
15#10623329—21no—
16C2×C4×C22⋊D11C2211yescharacteristic
17C2×#66977C2211yescharacteristic
18#10623149C412yescomplemented
19#10623148—21no—
20#10623137C2212yes—
21#10623133—21no—
22#10623132—22no—
23#10623131C2212yes—
24#10623129C412yescomplemented
25#10623044C412yescomplemented
26#10623026—22no—
27C11×#407C2211yescharacteristic
28C11×#381C2211yescharacteristic
29C4×C22⋊Dic11C2211yescharacteristic
30#10622820C2211yescharacteristic
31#10622741—22no—
32#10622569—21no—
33#10622558—21no—
34#10622342—22no—
35#10622339C2212yescomplemented
36#10622331C2212yescomplemented
37#10622280C2211yescharacteristic, complemented
38#10622279—21no—
39D11×#95C2211yescharacteristic, complemented
40#10622265—21no—
41#10622264C2211yescharacteristic, complemented
42#10622261C2211yescharacteristic, complemented
43C11×#327C2212yes—
44C11×#327C2212yes—
45#10622175C2212yes—
46#10622175C2212yes—
47#10622105C2212yescomplemented
48#10622105C2212yescomplemented
49#10622090C2212yescomplemented
50#10622090C2212yescomplemented
51C22×D4×C11—21no—
52C22×D4×C11C2×C411yescharacteristic, complemented
53C23×C4×C11C2311yescharacteristic
54C22×C22⋊D11D411yescharacteristic
55C2×#4341C2×C412yes—
56C22×C4×D11—21no—
57C22×C4×D11C2311yescharacteristic
58C22×Dic22C2×C411yescharacteristic, complemented
59C2×C11×M16—21no—
60C11×#121—21no—
61C11×#121—21no—
62C11×#121C2×C412yescomplemented
63C11×#121C2312yes—
64C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4—21no—
67#67006—22no—
68C2×C22⋊Dic11—21no—
69C2×C22⋊Dic11—22no—
70C2×C22⋊Dic11—21no—
71C2×C22⋊Dic11D411yescharacteristic
72#66992—22no—
73#66992—22no—
74#66992—22no—
75#66991C2×C412yes—
76#66990—22no—
77#66989C2×C412yescomplemented
78#66988—22no—
79#66988—22no—
80D4×Dic11—22no—
81D4×Dic11—22no—
82D4×Dic11—22no—
83D4×Dic11—22no—
84D4×Dic11C2×C412yescomplemented
85#66982—22no—
86C4×C22⋊D11C2×C412yes—
87C4×C22⋊D11C2×C412yes—
88C4×C22⋊D11D412yes—
89C4×C22⋊D11D412yes—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4D411yescharacteristic
92#66979—22no—
93C2×C4⋊Dic11C2×C411yescharacteristic, complemented
94#66977—21no—
95#66977—21no—
96#66977C2×C412yescomplemented
97#66977C2312yes—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4D411yescharacteristic
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11C2311yescharacteristic
104C2×#4318—21no—
105C2×#4313—22no—
106#66951—22no—
107#66950C2×C412yes—
108#66945C2×C412yes—
109#66943C2×C412yescomplemented
110#66942—22no—
111#66940C2×C412yescomplemented
112#66939—22no—
113#66938—22no—
114#66936—22no—
115(C22⋊D11)⋊C4—22no—
116#66932—22no—
117#66932—22no—
118#66931—22no—
119#66930—22no—
120C11×C22⋊C8—21no—
121C11×C22⋊C8C2312yes—
122C11×#95—21no—
123C11×#95C2311yescharacteristic
124C11×#95C2311yescharacteristic
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#17623—111nomaximal, Sylow
137C24×C11—21no—
138C24×C11C2×D411yescharacteristic
139C23×D11C2×D411yescharacteristic
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—21no—
143C2×D4×C11—42no—
144C2×D4×C11—42no—
145C2×D4×C11—81no—
146C2×D4×C11C22×C412yes—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—81no—
151C22×C4×C11C22×C411yescharacteristic
152C22×C4×C11C22×C411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C2×C22⋊D11—22no—
158C2×C22⋊D11—22no—
159C2×C22⋊D11—41no—
160C2×C22⋊D11—41no—
161C2×C22⋊D11C22⋊C412yes—
162C2×C22⋊D11C22⋊C412yes—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11C2×D411yescharacteristic
170C22×Dic11C2×D411yescharacteristic
171C22×Dic11C2×D411yescharacteristic
172#4341—82no—
173C2×C4×D11—42no—
174C2×C4×D11—42no—
175C2×C4×D11—81no—
176C2×C4×D11—81no—
177C2×C4×D11C22×C412yes—
178C2×C4×D11C2×D412yes—
179C2×Dic22—21no—
180C2×Dic22—81no—
181C2×Dic22C22×C412yes—
182C11×M16—81no—
183C2×C8×C11—22no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4C22×C412yes—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—81no—
189C22⋊Dic11—22no—
190C22⋊Dic11—22no—
191C22⋊Dic11—22no—
192C22⋊Dic11—22no—
193C22⋊Dic11—22no—
194C22⋊Dic11—22no—
195C22⋊Dic11—42no—
196C22⋊Dic11C22⋊C412yes—
197C22⋊Dic11C22⋊C412yes—
198(C2×D11)⋊C4—22no—
199(C2×D11)⋊C4—22no—
200(C2×D11)⋊C4—42no—
201(C2×D11)⋊C4C22⋊C412yes—
202(C2×D11)⋊C4C22⋊C412yes—
203C4⋊Dic11—22no—
204C4⋊Dic11—22no—
205C4⋊Dic11—21no—
206C4⋊Dic11C22×C412yes—
207Dic11⋊C4—22no—
208Dic11⋊C4—22no—
209Dic11⋊C4—22no—
210Dic11⋊C4—22no—
211Dic11⋊C4—81no—
212Dic11⋊C4C22⋊C412yes—
213Dic11⋊C4C22⋊C412yes—
214C4×Dic11—22no—
215C4×Dic11—22no—
216C4×Dic11—42no—
217C4×Dic11—81no—
218C4×Dic11C22×C412yes—
219C4×Dic11C2×D412yes—
220#4318—81no—
221C2×C11⋊C8—22no—
222#4313—82no—
223#3505—111no—
224#2975—111no—
225#2353—111no—
226#1521—112no—
227#1513—112no—
228#1511—111no—
229#1510D1111yescharacteristic, complemented
230#1508—111no—
231#1507—111no—
232#1504—112no—
233#1500—112no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—22no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—42no—
240C23×C11—81no—
241C23×C11—81no—
242C23×C11C2×C22⋊C411yescharacteristic
243C23×C11C2×C22⋊C411yescharacteristic
244C23×C11C22×D411yescharacteristic
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—41no—
248C22×D11—41no—
249C22×D11C2×C22⋊C412yes—
250D4×C11—42no—
251D4×C11—44no—
252D4×C11—42no—
253D4×C11—42no—
254D4×C11—81no—
255C2×C4×C11—22no—
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—42no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11C2×C22⋊C411yescharacteristic
270C2×C4×C11C2×C22⋊C411yescharacteristic
271C2×C4×C11C23×C411yescharacteristic
272C2×C4×C11C22×D411yescharacteristic
273C22⋊D11—42no—
274C22⋊D11—42no—
275C22⋊D11—82no—
276C22⋊D11—82no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—82no—
290C2×Dic11—82no—
291C2×Dic11—81no—
292C2×Dic11—81no—
293C2×Dic11C2×C22⋊C412yes—
294C2×Dic11C2×C22⋊C412yes—
295C2×Dic11C2×C22⋊C412yes—
296C4×D11—42no—
297C4×D11—42no—
298C4×D11—84no—
299Dic22—42no—
300Dic22—81no—
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⋊Q8—111no—
315C2×#121C2×D1111yescharacteristic
316#518—221no—
317C2×C4×D4—111no—
318#436—222no—
319#436—222no—
320#431—112no—
321#407—111no—
322#407—112no—
323#407C2×D1111yescharacteristic
324#388—221no—
325#387—221no—
326#386—221no—
327#383—111no—
328#381C2×D1111yescharacteristic
329#380—111no—
330C4×C22⋊C4—111no—
331C4×C22⋊C4—221no—
332#376—111no—
333C2×#95—111no—
334#328—112no—
335#328—112no—
336#328—112no—
337#328—112no—
338#327—112no—
339#327—112no—
340#327C2×D1112yes—
341#327C2×D1112yes—
342C22×C11—21no—
343C22×C11—21no—
344C22×C11—21no—
345C22×C11—21no—
346C22×C11—21no—
347C22×C11—21no—
348C22×C11—21no—
349C22×C11—21no—
350C22×C11—42no—
351C22×C11—42no—
352C22×C11—42no—
353C22×C11—81no—
354C22×C11—81no—
355C22×C11—162no—
356C22×C11C22×C22⋊C411yescharacteristic
357C22×C11#57511yescharacteristic
358C22×C11#57511yescharacteristic
359C2×D11—22no—
360C2×D11—22no—
361C2×D11—22no—
362C2×D11—42no—
363C2×D11—42no—
364C4×C11—21no—
365C4×C11—21no—
366C4×C11—21no—
367C4×C11—21no—
368C4×C11—42no—
369C4×C11—81no—
370C4×C11—81no—
371Dic11—22no—
372Dic11—22no—
373Dic11—22no—
374Dic11—42no—
375Dic11—42no—
376Dic11—42no—
377Dic11—81no—
378C2×#41—112no—
379C22×Q8—111no—
380C22×D4—21no—
381C22×D4—111no—
382C22×D4C4×D1111yescharacteristic, complemented
383C23×C4—111no—
384C23×C4—221no—
385C23×C4C22×D1111yescharacteristic
386C2×M16—21no—
387C2×M16—222no—
388C2×M16—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—112no—
402C22⋊Q8—112no—
403C22⋊Q8—112no—
404C22⋊Q8—222no—
405C22⋊Q8—221no—
406C22⋊Q8—221no—
407#121—21no—
408#121—21no—
409#121—112no—
410#121—222no—
411#121—222no—
412#121—222no—
413#121C4×D1112yescomplemented
414#121C22×D1112yes—
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—111no—
432C2×C4⋊C4—111no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4C4×D1111yescharacteristic, complemented
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—21no—
455#95—111no—
456#95—111no—
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—41no—
466C2×C11—41no—
467C2×C11—82no—
468C2×C11#288311yescharacteristic
469C2×C11#289611yescharacteristic
470C2×C11#290111yescharacteristic
471D11—42no—
472C24—21no—
473C24—111no—
474C24D4×D1111yescharacteristic
475#41—882no—
476C2×Q8—112no—
477C2×Q8—221no—
478C2×Q8—881no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—21no—
482C2×D4—42no—
483C2×D4—42no—
484C2×D4—81no—
485C2×D4—112no—
486C2×D4—112no—
487C2×D4—222no—
488C2×D4—222no—
489C2×D4—441no—
490C2×D4—441no—
491C2×D4C2×C4×D1112yes—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—81no—
496C22×C4—111no—
497C22×C4—111no—
498C22×C4—111no—
499C22×C4—112no—
500C22×C4—112no—
501C22×C4—222no—
502C22×C4—222no—
503C22×C4—221no—
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
517M16—81no—
518M16—882no—
519M16—881no—
520C2×C8—22no—
521C2×C8—222no—
522C4⋊C4—21no—
523C4⋊C4—112no—
524C4⋊C4—112no—
525C4⋊C4—112no—
526C4⋊C4—222no—
527C4⋊C4—222no—
528C4⋊C4—222no—
529C4⋊C4—222no—
530C4⋊C4—221no—
531C4⋊C4—222no—
532C4⋊C4—222no—
533C4⋊C4—881no—
534C4⋊C4C2×C4×D1112yes—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—81no—
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—442no—
552C42—112no—
553C42—112no—
554C42—222no—
555C42—222no—
556C42—442no—
557C42—881no—
558C11#1762311yescharacteristic, complemented, Sylow
559C23—21no—
560C23—21no—
561C23—22no—
562C23—41no—
563C23—41no—
564C23—42no—
565C23—81no—
566C23—81no—
567C23—112no—
568C23—221no—
569C23—221no—
570C23—441no—
571C23—441no—
572C23C22⋊C4×D1111yescharacteristic
573C23C22⋊C4×D1111yescharacteristic
574C23C2×D4×D1111yescharacteristic
575Q8—442no—
576Q8—881no—
577D4—42no—
578D4—44no—
579D4—42no—
580D4—42no—
581D4—81no—
582D4—442no—
583D4—442no—
584D4—882no—
585D4—882no—
586C2×C4—22no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—112no—
601C2×C4—112no—
602C2×C4—112no—
603C2×C4—221no—
604C2×C4—221no—
605C2×C4—222no—
606C2×C4—222no—
607C2×C4—222no—
608C2×C4—442no—
609C2×C4—442no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—884no—
618C2×C4—882no—
619C2×C4—882no—
620C2×C4—881no—
621C2×C4—881no—
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—21no—
635C22—21no—
636C22—42no—
637C22—42no—
638C22—42no—
639C22—81no—
640C22—81no—
641C22—162no—
642C22—222no—
643C22—222no—
644C22—222no—
645C22—442no—
646C22—442no—
647C22C2×C22⋊C4×D1111yescharacteristic
648C22#1062330411yescharacteristic
649C22#1062330411yescharacteristic
650C4—21no—
651C4—21no—
652C4—21no—
653C4—21no—
654C4—42no—
655C4—81no—
656C4—81no—
657C4—222no—
658C4—222no—
659C4—222no—
660C4—442no—
661C4—442no—
662C4—442no—
663C4—881no—
664C2—21no—
665C2—21no—
666C2—41no—
667C2—41no—
668C2—82no—
669C2—442no—
670C2#1307707411yescharacteristic
671C2#1307713011yescharacteristic
672C2#1307716211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1510C2
socleC22×C11C22×C22⋊C4
prime radical#13082450C2
cosocleC22×C4×C11C24
hypercenter#1510D11
hypocenterC11#17623
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1510

Complements

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

NH ≅ G/Ntype
2. #13077655C2semidirect
3. #13071553C2semidirect
4. #13067190C2semidirect
5. #13067156C2semidirect
6. #13067148C2semidirect
7. #13067137C2semidirect
8. #13067132C2semidirect
9. #13067117C2semidirect
10. #13067099C2semidirect
11. C11×#1510C2semidirect
13. #10623337C4semidirect
18. #10623149C4semidirect
24. #10623129C4semidirect
25. #10623044C4semidirect
35. #10622339C22semidirect
36. #10622331C22semidirect
37. #10622280C22semidirect
39. D11×#95C22semidirect
41. #10622264C22semidirect
42. #10622261C22semidirect
47. #10622105C22semidirect
48. #10622105C22semidirect
49. #10622090C22semidirect
50. #10622090C22semidirect
52. C22×D4×C11C2×C4semidirect
58. C22×Dic22C2×C4semidirect
62. C11×#121C2×C4semidirect
64. C2×C11×C4⋊C4C2×C4semidirect
77. #66989C2×C4semidirect
84. D4×Dic11C2×C4semidirect
93. C2×C4⋊Dic11C2×C4semidirect
96. #66977C2×C4semidirect
109. #66943C2×C4semidirect
111. #66940C2×C4semidirect
229. #1510D11semidirect
382. C22×D4C4×D11semidirect
413. #121C4×D11semidirect
435. C2×C4⋊C4C4×D11semidirect
558. C11#17623semidirect

Maximal subgroups

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

subgroupindex
#130824502
#130776552
#130715532
#130671902
#130671562
#130671482
#130671372
#130671322
#130671172
#130670992
C11×#15102
#1762311