Finite Group Databasebeta

← #14721616

Subgroups — #14721616

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082468C211yesmaximal, characteristic
2#13077645C211yesmaximal, characteristic, complemented
3#13067170C212yesmaximal, complemented
4#13067166C211yesmaximal, characteristic, complemented
5#13067162C211yesmaximal, characteristic, complemented
6#13067157C212yesmaximal, complemented
7#13067127C211yesmaximal, characteristic, complemented
8#13067123C211yesmaximal, characteristic, complemented
9#13067118C212yesmaximal, complemented
10#13067105C212yesmaximal, complemented
11C11×#2353C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2211yescharacteristic
13#10623336—21no—
14#10623322C2212yes—
15#10623322C2212yes—
16#10623094C412yescomplemented
17#10623090—22no—
18#10623089—22no—
19#10623084C412yescomplemented
20#10623082C412yescomplemented
21#10623073C412yescomplemented
22#10623035—21no—
23#10623025—21no—
24#10623025—21no—
25#10623008C2211yescharacteristic
26#10623001C2211yescharacteristic
27C11×#388—21no—
28C11×#387—21no—
29C11×#386—21no—
30C11×#383C2211yescharacteristic
31C11×#381C2211yescharacteristic
32C11×#380C2211yescharacteristic
33C4×C11×C22⋊C4—21no—
34C4×C11×C22⋊C4C2211yescharacteristic
35C11×#376C2211yescharacteristic
36C2×C11×#95C2211yescharacteristic
37#10622820C2212yes—
38C2×C22⋊(C11⋊C8)C2212yes—
39#10622624—22no—
40#10622624—22no—
41#10622539C2211yescharacteristic
42#10622539C2211yescharacteristic
43#10622090C2212yes—
44#10622090C2212yes—
45#10622090C2212yes—
46#10622090C2212yes—
47#10622089C2212yes—
48#10622089C2212yes—
49#10622089C2212yes—
50#10622089C2212yes—
51C22×D4×C11D411yescharacteristic
52C23×C4×C11—21no—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C2×#4339—21no—
56C2×#4339C2×C412yes—
57C2×#4339C2×C412yescomplemented
58C4×D4×C11C2×C412yes—
59C4×D4×C11C2×C412yes—
60C4×D4×C11D412yes—
61C4×D4×C11D412yes—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C22⋊C4—21no—
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4D411yescharacteristic
68C2×C11×C22⋊C4D411yescharacteristic
69C2×C42×C11—21no—
70C2×C42×C11—21no—
71C2×C42×C11C2311yescharacteristic
72#67006—22no—
73#67006—22no—
74#66993—22no—
75#66991—22no—
76#66991—22no—
77#66989—22no—
78#66983—21no—
79#66983C2×C412yes—
80#66983C2×C412yescomplemented
81#66983C2312yes—
82#66982—22no—
83#66982—22no—
84C4×C22⋊D11—22no—
85C4×C22⋊D11—22no—
86C4×C22⋊D11—22no—
87C4×C22⋊D11—22no—
88#66979—21no—
89#66979C2×C412yes—
90#66979C2×C412yescomplemented
91#66977—21no—
92#66977C2×C412yes—
93#66977C2×C412yescomplemented
94#66977C2312yes—
95C2×#4318—22no—
96C22×C11⋊C8—22no—
97#66946—22no—
98#66945—22no—
99C4⋊C4×D11—22no—
100#66940—22no—
101#66938—22no—
102#66938—22no—
103#66937—22no—
104#66937—22no—
105#66936—22no—
106#66936—22no—
107#66932—22no—
108#66932—22no—
109#66928—21no—
110#66927C2×C411yescharacteristic, complemented
111C4×D44—21no—
112C4×D44C2×C412yescomplemented
113#66923—21no—
114#66922C2×C411yescharacteristic, complemented
115#66922C2×C411yescharacteristic, complemented
116#66922C2×C411yescharacteristic, complemented
117C4×Dic22—21no—
118C4×Dic22C2×C412yescomplemented
119C11×#95—21no—
120C11×#95—21no—
121C11×#95—21no—
122C11×#95—21no—
123C11×#95—21no—
124C11×#95C2311yescharacteristic
125C11×#95C2311yescharacteristic
126C11×#95C2311yescharacteristic
127C11×#95C2311yescharacteristic
128C22⋊(C11⋊C8)—22no—
129C22⋊(C11⋊C8)—22no—
130C22⋊(C11⋊C8)C2312yes—
131C22⋊(C11⋊C8)C2312yes—
132C4⋊(C11⋊C8)—21no—
133C4⋊(C11⋊C8)—21no—
134#66867—21no—
135#66867—21no—
136#17629—111nomaximal, Sylow
137C24×C11C2×D411yescharacteristic
138C24×C11C2×D411yescharacteristic
139C2×D4×C11—41no—
140C2×D4×C11—41no—
141C2×D4×C11C22⋊C412yes—
142C2×D4×C11C22⋊C412yes—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11—81no—
150C22×C4×C11—81no—
151C22×C4×C11—81no—
152C22×C4×C11C22×C412yes—
153C22×C4×C11C22×C412yes—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2411yescharacteristic
161C2×C22⋊D11—22no—
162C2×C22⋊D11—22no—
163C2×C22⋊D11—22no—
164C2×C22⋊D11—22no—
165C2×C22⋊D11—22no—
166#4339—42no—
167#4339—42no—
168#4339—82no—
169#4339—82no—
170C2×D44—21no—
171C2×D44—21no—
172C2×D44C22×C412yes—
173C2×C4×D11—22no—
174C2×C4×D11—22no—
175C2×C4×D11—22no—
176C2×Dic22—21no—
177C2×Dic22—21no—
178C2×Dic22C22×C412yes—
179C11×C4⋊C4—81no—
180C11×C4⋊C4C22⋊C412yes—
181C11×C4⋊C4C22⋊C412yes—
182C11×C22⋊C4—42no—
183C11×C22⋊C4—42no—
184C11×C22⋊C4—81no—
185C11×C22⋊C4C22⋊C412yes—
186C11×C22⋊C4C22⋊C412yes—
187C11×C22⋊C4C22⋊C412yes—
188C11×C22⋊C4C22⋊C412yes—
189C42×C11—42no—
190C42×C11—81no—
191C42×C11C22×C411yescharacteristic
192C42×C11C22×C411yescharacteristic
193C42×C11C2×D411yescharacteristic
194C42×C11C2×D411yescharacteristic
195C22⋊Dic11—22no—
196C22⋊Dic11—22no—
197C22⋊Dic11—22no—
198C22⋊Dic11—22no—
199C22⋊Dic11—22no—
200(C2×D11)⋊C4—22no—
201(C2×D11)⋊C4—22no—
202(C2×D11)⋊C4—22no—
203(C2×D11)⋊C4—22no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11C22×C412yes—
209C4⋊Dic11C22×C412yes—
210Dic11⋊C4—22no—
211Dic11⋊C4—22no—
212Dic11⋊C4—22no—
213Dic11⋊C4—22no—
214C4×Dic11—22no—
215C4×Dic11—22no—
216C4×Dic11—22no—
217#4318—82no—
218C2×C11⋊C8—22no—
219C2×C11⋊C8—22no—
220C2×C11⋊C8—82no—
221#3506—111no—
222#2973—111no—
223#2353D1111yescharacteristic, complemented
224#1516—112no—
225#1515—111no—
226#1514—111no—
227#1513—112no—
228#1506—111no—
229#1505—111no—
230#1504—112no—
231#1501—112no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11C2×C22⋊C412yes—
241C23×C11C2×C22⋊C412yes—
242C23×C11C22×D411yescharacteristic
243C22×D11—22no—
244D4×C11—42no—
245D4×C11—42no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—22no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
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—41no—
267C2×C4×C11—41no—
268C2×C4×C11—84no—
269C2×C4×C11C2×C22⋊C411yescharacteristic
270C2×C4×C11C2×C22⋊C412yes—
271C2×C4×C11C2×C22⋊C412yes—
272C2×C4×C11C2×C22⋊C411yescharacteristic
273C2×C4×C11C2×C22⋊C411yescharacteristic
274C2×C4×C11C2×C22⋊C411yescharacteristic
275C2×C4×C11C23×C411yescharacteristic
276C2×C4×C11C22×D411yescharacteristic
277C22⋊D11—42no—
278C22⋊D11—42no—
279C22⋊D11—82no—
280C22⋊D11—82no—
281C22⋊D11—82no—
282C22⋊D11—82no—
283C2×Dic11—22no—
284C2×Dic11—22no—
285C2×Dic11—22no—
286D44—42no—
287D44—42no—
288D44—81no—
289C4×D11—44no—
290C4×D11—82no—
291C4×D11—82no—
292Dic22—42no—
293Dic22—42no—
294Dic22—81no—
295C11⋊C8—42no—
296C11⋊C8—42no—
297#559—222no—
298#556—112no—
299#555—112no—
300#553—222no—
301#550—112no—
302#547—112no—
303#538—221no—
304#538—221no—
305#535—221no—
306#533—111no—
307#532—111no—
308#525—112no—
309#525—112no—
310#520—221no—
311C2×C4×D4C2×D1111yescharacteristic
312#435—222no—
313#435—222no—
314#432—111no—
315#432—111no—
316#407—112no—
317C2×C22⋊C8—112no—
318#388—21no—
319#387—21no—
320#386—21no—
321#383C2×D1111yescharacteristic
322#381C2×D1111yescharacteristic
323#380C2×D1111yescharacteristic
324C4×C22⋊C4—21no—
325C4×C22⋊C4C2×D1111yescharacteristic
326#376C2×D1111yescharacteristic
327C2×#95C2×D1111yescharacteristic
328#328—112no—
329#328—112no—
330#328—112no—
331#328—112no—
332#327—112no—
333#327—112no—
334#327—112no—
335#327—112no—
336C22×C11—21no—
337C22×C11—21no—
338C22×C11—22no—
339C22×C11—22no—
340C22×C11—22no—
341C22×C11—22no—
342C22×C11—22no—
343C22×C11—22no—
344C22×C11—42no—
345C22×C11—42no—
346C22×C11—81no—
347C22×C11—81no—
348C22×C11C22×C22⋊C411yescharacteristic
349C22×C11#57511yescharacteristic
350C22×C11#57511yescharacteristic
351C2×D11—42no—
352C2×D11—42no—
353C2×D11—42no—
354C4×C11—21no—
355C4×C11—21no—
356C4×C11—22no—
357C4×C11—22no—
358C4×C11—21no—
359C4×C11—21no—
360C4×C11—21no—
361C4×C11—21no—
362C4×C11—42no—
363C4×C11—81no—
364C4×C11—81no—
365C4×C11—81no—
366Dic11—42no—
367Dic11—42no—
368Dic11—42no—
369C2×#41—112no—
370C2×#41—112no—
371C2×#41—221no—
372C22×D4C22⋊D1111yescharacteristic
373C23×C4—21no—
374C23×C4C22×D1111yescharacteristic
375C23×C4C22×D1111yescharacteristic
376C2×M16—222no—
377C22×C8—222no—
378C4⋊Q8—111no—
379C4⋊Q8—111no—
380C4⋊Q8—111no—
381#127—111no—
382#127—222no—
383#126—222no—
384#126—222no—
385#125—221no—
386#124—222no—
387#124—222no—
388#124—222no—
389#124—221no—
390#123—222no—
391#123—222no—
392#123—222no—
393#123—222no—
394C22⋊Q8—112no—
395C22⋊Q8—112no—
396C22⋊Q8—112no—
397C22⋊Q8—221no—
398#121—112no—
399#121—112no—
400#121—112no—
401#121—222no—
402#121—222no—
403#121—221no—
404#121—222no—
405#121—222no—
406#120—222no—
407#120—222no—
408C4×Q8—112no—
409C4×Q8—222no—
410C4×Q8—221no—
411C4×D4—112no—
412C4×D4—222no—
413C4×D4—222no—
414C4×D4—222no—
415C4×D4—222no—
416C4×D4—222no—
417C4×D4—221no—
418C4×D4C4×D1112yes—
419C4×D4C4×D1112yes—
420C4×D4D4412yes—
421C4×D4D4412yes—
422#117—112no—
423#117—112no—
424#117—221no—
425#117—222no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—222no—
428C2×C4⋊C4C22⋊D1111yescharacteristic
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4C22⋊D1111yescharacteristic
433C2×C22⋊C4C22⋊D1111yescharacteristic
434C2×C42—21no—
435C2×C42—21no—
436C2×C42C22×D1111yescharacteristic
437C4⋊C8—221no—
438C4⋊C8—221no—
439C22⋊C8—112no—
440C22⋊C8—112no—
441C22⋊C8—222no—
442C22⋊C8—222no—
443#97—221no—
444#97—221no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—21no—
450#95C22×D1111yescharacteristic
451#95C22×D1111yescharacteristic
452#95C22×D1111yescharacteristic
453#95C22×D1111yescharacteristic
454C2×C11—21no—
455C2×C11—21no—
456C2×C11—42no—
457C2×C11—42no—
458C2×C11#288311yescharacteristic
459C2×C11#289611yescharacteristic
460C2×C11#290111yescharacteristic
461D11—82no—
462C24C2×C22⋊D1111yescharacteristic
463C24C2×C22⋊D1111yescharacteristic
464#41—442no—
465#41—442no—
466#41—882no—
467#41—882no—
468C2×Q8—112no—
469C2×Q8—221no—
470C2×Q8—221no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—112no—
474C2×D4—222no—
475C2×D4—222no—
476C2×D4—222no—
477C2×D4—222no—
478C2×D4—222no—
479C2×D4—221no—
480C2×D4—221no—
481C2×D4(C2×D11)⋊C412yes—
482C2×D4(C2×D11)⋊C412yes—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—81no—
490C22×C4—81no—
491C22×C4—81no—
492C22×C4—222no—
493C22×C4—222no—
494C22×C4—222no—
495C22×C4C2×C4×D1112yes—
496C22×C4C2×C4×D1112yes—
497C22×C4C2×D4412yes—
498C22×C4C2×D4412yes—
499C22×C4C2×C22⋊D1111yescharacteristic
500C22×C4C2×C22⋊D1111yescharacteristic
501C22×C4C2×C22⋊D1111yescharacteristic
502C22×C4C2×C22⋊D1111yescharacteristic
503C22×C4C23×D1111yescharacteristic
504M16—882no—
505C2×C8—222no—
506C2×C8—222no—
507C2×C8—882no—
508C4⋊C4—81no—
509C4⋊C4—112no—
510C4⋊C4—112no—
511C4⋊C4—221no—
512C4⋊C4—222no—
513C4⋊C4—222no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—222no—
517C4⋊C4—221no—
518C4⋊C4—222no—
519C4⋊C4(C2×D11)⋊C412yes—
520C4⋊C4(C2×D11)⋊C412yes—
521C22⋊C4—42no—
522C22⋊C4—42no—
523C22⋊C4—81no—
524C22⋊C4—222no—
525C22⋊C4—222no—
526C22⋊C4—222no—
527C22⋊C4—222no—
528C22⋊C4—222no—
529C22⋊C4—222no—
530C22⋊C4—222no—
531C22⋊C4—222no—
532C22⋊C4—222no—
533C22⋊C4(C2×D11)⋊C412yes—
534C22⋊C4(C2×D11)⋊C412yes—
535C22⋊C4(C2×D11)⋊C412yes—
536C22⋊C4(C2×D11)⋊C412yes—
537C42—42no—
538C42—81no—
539C42—222no—
540C42—222no—
541C42—222no—
542C42C2×C4×D1111yescharacteristic
543C42C2×C4×D1111yescharacteristic
544C42C2×D4411yescharacteristic
545C42C2×D4411yescharacteristic
546C11#1762911yescharacteristic, complemented, Sylow
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—222no—
556C23C2×(C2×D11)⋊C412yes—
557C23C2×(C2×D11)⋊C412yes—
558C23C22×C22⋊D1111yescharacteristic
559Q8—442no—
560Q8—442no—
561Q8—881no—
562D4—42no—
563D4—42no—
564D4—442no—
565D4—442no—
566D4—442no—
567D4—442no—
568D4—881no—
569D4—882no—
570D4—882no—
571D4—882no—
572D4—882no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—41no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—84no—
596C2×C4—222no—
597C2×C4—222no—
598C2×C4—222no—
599C2×C4—444no—
600C2×C4—882no—
601C2×C4—882no—
602C2×C4C2×(C2×D11)⋊C411yescharacteristic
603C2×C4C2×(C2×D11)⋊C412yes—
604C2×C4C2×(C2×D11)⋊C412yes—
605C2×C4C2×(C2×D11)⋊C411yescharacteristic
606C2×C4C2×(C2×D11)⋊C411yescharacteristic
607C2×C4C2×(C2×D11)⋊C411yescharacteristic
608C2×C4C22×C4×D1111yescharacteristic
609C2×C4C22×D4411yescharacteristic
610C8—442no—
611C8—442no—
612C22—21no—
613C22—21no—
614C22—22no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—42no—
621C22—42no—
622C22—81no—
623C22—81no—
624C22—442no—
625C22—442no—
626C22—442no—
627C22C22×(C2×D11)⋊C411yescharacteristic
628C22#1062335311yescharacteristic
629C22#1062335311yescharacteristic
630C4—21no—
631C4—21no—
632C4—22no—
633C4—22no—
634C4—21no—
635C4—21no—
636C4—21no—
637C4—21no—
638C4—42no—
639C4—81no—
640C4—81no—
641C4—81no—
642C4—442no—
643C4—442no—
644C4—442no—
645C2—21no—
646C2—21no—
647C2—42no—
648C2—42no—
649C2—882no—
650C2#1307707611yescharacteristic
651C2#1307713311yescharacteristic
652C2#1307716411yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2353C2
socleC22×C11C22×C22⋊C4
prime radical#13082468C2
cosocleC22×C4×C11C24
hypercenter#2353D11
hypocenterC11#17629
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2353

Complements

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

NH ≅ G/Ntype
2. #13077645C2semidirect
3. #13067170C2semidirect
4. #13067166C2semidirect
5. #13067162C2semidirect
6. #13067157C2semidirect
7. #13067127C2semidirect
8. #13067123C2semidirect
9. #13067118C2semidirect
10. #13067105C2semidirect
11. C11×#2353C2semidirect
16. #10623094C4semidirect
19. #10623084C4semidirect
20. #10623082C4semidirect
21. #10623073C4semidirect
57. C2×#4339C2×C4semidirect
80. #66983C2×C4semidirect
90. #66979C2×C4semidirect
93. #66977C2×C4semidirect
110. #66927C2×C4semidirect
112. C4×D44C2×C4semidirect
114. #66922C2×C4semidirect
115. #66922C2×C4semidirect
116. #66922C2×C4semidirect
118. C4×Dic22C2×C4semidirect
223. #2353D11semidirect
546. C11#17629semidirect

Maximal subgroups

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

subgroupindex
#130824682
#130776452
#130671702
#130671662
#130671622
#130671572
#130671272
#130671232
#130671182
#130671052
C11×#23532
#1762911