Finite Group Databasebeta

← #14721987

Subgroups — #14721987

Order 2816.

1152 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082409C211yesmaximal, characteristic
2#13077630C211yesmaximal, characteristic, complemented
3#13067250C211yesmaximal, characteristic, complemented
4#13067239C212yesmaximal, complemented
5#13067228C212yesmaximal, complemented
6#13067226C212yesmaximal, complemented
7#13067215C211yesmaximal, characteristic, complemented
8#13067213C211yesmaximal, characteristic, complemented
9#13067207C211yesmaximal, characteristic, complemented
10C2×#10622102C212yesmaximal, complemented
11C11×#2970C211yesmaximal, characteristic, complemented
12C2×#67043C411yescharacteristic
13C2×#67042C411yescharacteristic
14C4×C11×#41C2211yescharacteristic
15#10623107—21no—
16#10623107—21no—
17#10623085—21no—
18#10623085—22no—
19#10623085—21no—
20#10623085—22no—
21#10623057C412yes—
22#10623057C411yescharacteristic
23#10623056C412yes—
24#10623056C411yescharacteristic
25#10623008C2211yescharacteristic
26#10623008C2212yes—
27C2×#66928C2212yes—
28C2×#66928C2211yescharacteristic
29C11×#446—21no—
30C11×#435—22no—
31C8×D4×C11—21no—
32C11×#432C2211yescharacteristic, complemented
33C11×#432C2212yescomplemented
34C4×C11×M16C2211yescharacteristic, complemented
35C2×C11×#97C2212yescomplemented
36#10622637—21no—
37#10622624—22no—
38D4×C11⋊C8—21no—
39#10622539C2211yescharacteristic, complemented
40#10622539C2212yescomplemented
41C4×#4318C2211yescharacteristic, complemented
42C2×#66867C2212yescomplemented
43#10622102C2211yescharacteristic, complemented
44#10622102C2212yescomplemented
45#10622102C2212yescomplemented
46#10622102C2212yescomplemented
47#10622102C2211yescharacteristic, complemented
48#10622102C2211yescharacteristic, complemented
49#10622102C2211yescharacteristic, complemented
50#10622102C2212yescomplemented
51#10622102C2212yescomplemented
52#10622102C2212yescomplemented
53C2×C11×#41C2×C411yescharacteristic
54#67043—44no—
55#67042—44no—
56C2×#4343—21no—
57C2×Q8×D11—21no—
58C2×#4341—22no—
59C2×#4341—21no—
60C2×D4×D11—22no—
61C2×D4×D11—21no—
62C2×#4339C2×C412yes—
63C2×#4339C2×C411yescharacteristic
64C2×#4339C2×C412yes—
65C2×#4339C2×C411yescharacteristic
66C22×D44C2×C411yescharacteristic
67C22×D44C2×C412yes—
68C22×Dic22C2×C412yes—
69C22×Dic22C2×C411yescharacteristic
70C2×C11×M16—21no—
71C22×C8×C11—22no—
72C4×Q8×C11D411yescharacteristic
73C4×Q8×C11D411yescharacteristic
74C4×D4×C11D411yescharacteristic
75C4×D4×C11D412yes—
76C4×D4×C11D411yescharacteristic
77C4×D4×C11D412yes—
78C11×#117C2×C411yescharacteristic
79C11×#117C2×C412yes—
80C2×C42×C11C2312yes—
81C2×C42×C11C2311yescharacteristic
82#66983—22no—
83#66983—21no—
84#66983—22no—
85#66983—21no—
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—22no—
89C2×(C2×D11)⋊C4—21no—
90C2×#4318—21no—
91C22×C11⋊C8—22no—
92#66950—22no—
93#66950—21no—
94#66950—22no—
95#66950—21no—
96#66948—22no—
97#66948—21no—
98#66948—22no—
99#66948—21no—
100#66939—22no—
101#66939—22no—
102#66939—22no—
103#66935—22no—
104#66935—22no—
105#66935—22no—
106#66928—21no—
107#66928—22no—
108#66928—21no—
109#66928—22no—
110#66928C2×C412yes—
111#66928C2×C412yes—
112#66928C2×C412yes—
113#66928C2311yescharacteristic
114#66928C2312yes—
115#66928C2311yescharacteristic
116#66927C2×C411yescharacteristic
117#66927C2×C412yes—
118C4×D44—21no—
119C4×D44—22no—
120C4×D44—21no—
121C4×D44—22no—
122#66922C2×C411yescharacteristic
123#66922C2×C412yes—
124C11×C4⋊C8—21no—
125C11×C4⋊C8—22no—
126C11×C22⋊C8—22no—
127C11×C22⋊C8—21no—
128C11×#97—22no—
129C11×#97C2311yescharacteristic
130C11×#97C2312yes—
131C11×#97C2311yescharacteristic
132C4×C8×C11—21no—
133C22⋊(C11⋊C8)—22no—
134C22⋊(C11⋊C8)—21no—
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)—22no—
137#66867—22no—
138#66867C2311yescharacteristic
139#66867C2312yes—
140#66867C2311yescharacteristic
141C4×C11⋊C8—21no—
142#17685—111nomaximal, Sylow
143C23×D11—21no—
144C23×D11—22no—
145C11×#41—24no—
146C2×Q8×C11C22⋊C411yescharacteristic
147C2×D4×C11C22⋊C412yes—
148C2×D4×C11C22⋊C411yescharacteristic
149C22×C4×C11C22×C412yes—
150C22×C4×C11C22×C411yescharacteristic
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2×D411yescharacteristic
155C2×C22⋊D11—21no—
156C2×C22⋊D11—22no—
157C2×C22⋊D11—21no—
158C2×C22⋊D11—22no—
159C22×Dic11—21no—
160C22×Dic11—22no—
161#4343—44no—
162Q8×D11—44no—
163#4341—48no—
164#4341—44no—
165D4×D11—48no—
166D4×D11—44no—
167#4339—44no—
168#4339—44no—
169#4339—42no—
170#4339—42no—
171C2×D44—22no—
172C2×D44—21no—
173C2×D44—21no—
174C2×D44—22no—
175C2×D44—21no—
176C2×D44—22no—
177C2×D44—42no—
178C2×D44—44no—
179C2×D44C22×C411yescharacteristic
180C2×D44C22×C412yes—
181C2×D44C22×C411yescharacteristic
182C2×C4×D11—22no—
183C2×C4×D11—21no—
184C2×C4×D11—22no—
185C2×C4×D11—21no—
186C2×Dic22—22no—
187C2×Dic22—21no—
188C2×Dic22—44no—
189C2×Dic22—42no—
190C2×Dic22C22×C411yescharacteristic
191C2×Dic22C22×C411yescharacteristic
192C2×Dic22C22×C412yes—
193C11×M16—42no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—22no—
197C2×C8×C11—44no—
198C11×C4⋊C4C22⋊C412yes—
199C11×C4⋊C4C22⋊C412yes—
200C11×C4⋊C4C22⋊C411yescharacteristic
201C11×C4⋊C4C22⋊C411yescharacteristic
202C11×C22⋊C4C22⋊C412yes—
203C11×C22⋊C4C22⋊C412yes—
204C11×C22⋊C4C22⋊C412yes—
205C42×C11C22×C412yes—
206C42×C11C22×C411yescharacteristic
207C42×C11C2×D411yescharacteristic
208C42×C11C2×D412yes—
209C42×C11C2×D411yescharacteristic
210C42×C11C2×D412yes—
211C42×C11C2411yescharacteristic
212(C2×D11)⋊C4—22no—
213(C2×D11)⋊C4—22no—
214(C2×D11)⋊C4—22no—
215(C2×D11)⋊C4—22no—
216(C2×D11)⋊C4—22no—
217(C2×D11)⋊C4—22no—
218(C2×D11)⋊C4—21no—
219(C2×D11)⋊C4—21no—
220(C2×D11)⋊C4—21no—
221(C2×D11)⋊C4—22no—
222(C2×D11)⋊C4—21no—
223(C2×D11)⋊C4—22no—
224C4⋊Dic11—21no—
225C4⋊Dic11—22no—
226C4⋊Dic11—21no—
227C4⋊Dic11—22no—
228#4318—42no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—22no—
232C2×C11⋊C8—44no—
233#3500—111no—
234#2970—111no—
235#2970D1111yescharacteristic, complemented
236#1536—111no—
237#1533—112no—
238#1530—112no—
239#1530—112no—
240#1527—111no—
241#1527—111no—
242#1525—111no—
243C2×#329—112no—
244C23×C11C2×C22⋊C411yescharacteristic
245C23×C11C2×C22⋊C412yes—
246C22×D11—22no—
247C22×D11—21no—
248C22×D11—21no—
249C22×D11—42no—
250C22×D11—44no—
251C22×D11—82no—
252C22×D11—82no—
253C22×D11—81no—
254C22×D11—81no—
255Q8×C11—22no—
256D4×C11—24no—
257D4×C11#10014yes—
258C2×C4×C11—24no—
259C2×C4×C11—22no—
260C2×C4×C11—42no—
261C2×C4×C11—41no—
262C2×C4×C11—42no—
263C2×C4×C11—41no—
264C2×C4×C11C2×C22⋊C411yescharacteristic
265C2×C4×C11C2×C22⋊C412yes—
266C2×C4×C11C2×C22⋊C411yescharacteristic
267C2×C4×C11C2×C22⋊C412yes—
268C2×C4×C11C2×C22⋊C412yes—
269C2×C4×C11C2×C22⋊C411yescharacteristic
270C2×C4×C11C23×C411yescharacteristic
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C22×D411yescharacteristic
273C22⋊D11—42no—
274C22⋊D11—42no—
275C22⋊D11—44no—
276C22⋊D11—44no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—22no—
280C2×Dic11—42no—
281C2×Dic11—44no—
282D44—42no—
283D44—41no—
284D44—41no—
285D44—44no—
286D44—42no—
287D44—82no—
288D44—81no—
289D44—82no—
290D44—81no—
291C4×D11—44no—
292C4×D11—44no—
293C4×D11—42no—
294C4×D11—42no—
295Dic22—44no—
296Dic22—42no—
297Dic22—41no—
298Dic22—42no—
299Dic22—41no—
300C8×C11—22no—
301C8×C11—42no—
302C8×C11—41no—
303C11⋊C8—22no—
304C11⋊C8—42no—
305C11⋊C8—41no—
306C2×2−1+4—111no—
307C2×H(5,𝔽2)—111no—
308#548—221no—
309#548—221no—
310#546—221no—
311#546—222no—
312#546—221no—
313#546—222no—
314#536—111no—
315#536—112no—
316#535—111no—
317#535—112no—
318#532—111no—
319#532—112no—
320C2×#124—112no—
321C2×#124—111no—
322C4×#41C2×D1111yescharacteristic
323#446—21no—
324#446—221no—
325#435—22no—
326#435—222no—
327C8×D4—21no—
328C8×D4—221no—
329#432—111no—
330#432—112no—
331#432C2×D1111yescharacteristic, complemented
332#432C2×D1112yescomplemented
333C4×M16—111no—
334C4×M16C2×D1111yescharacteristic, complemented
335C2×#97—112no—
336C2×#97C2×D1112yescomplemented
337#329—112no—
338#329—112no—
339#329—111no—
340#329—112no—
341#329—112no—
342#329—111no—
343#329—111no—
344#329—111no—
345#329—112no—
346#329—112no—
347C22×C11—22no—
348C22×C11—22no—
349C22×C11—21no—
350C22×C11—21no—
351C22×C11—21no—
352C22×C11C2×#10014yes—
353C22×C11C22×C22⋊C411yescharacteristic
354C2×D11—42no—
355C2×D11—41no—
356C2×D11—41no—
357C2×D11—41no—
358C2×D11—42no—
359C2×D11—41no—
360C2×D11—42no—
361C2×D11—41no—
362C2×D11—41no—
363C2×D11—164no—
364C2×D11—162no—
365C4×C11—21no—
366C4×C11—22no—
367C4×C11—21no—
368C4×C11—21no—
369C4×C11—22no—
370C4×C11—21no—
371C4×C11—22no—
372C4×C11—21no—
373C4×C11C2×#10012yes—
374Dic11—41no—
375Dic11—42no—
376Dic11—41no—
3772−1+4—444no—
378H(5,𝔽2)—444no—
379C2×#41—112no—
380C2×#41—111no—
381C2×#41—112no—
382C2×#41—111no—
383C2×#41—221no—
384C2×#41—222no—
385C2×#41—221no—
386C2×#41C4×D1111yescharacteristic
387C22×Q8—111no—
388C22×Q8—112no—
389C22×Q8—221no—
390C22×D4—112no—
391C22×D4—111no—
392C22×D4—222no—
393C22×D4—221no—
394C2×M16—21no—
395C2×M16—221no—
396C22×C8—22no—
397C22×C8—222no—
398C4⋊Q8—111no—
399C4⋊Q8—112no—
400#127—111no—
401#127—112no—
402#124—112no—
403#124—112no—
404#124—112no—
405#124—111no—
406#124—112no—
407#124—111no—
408#124—221no—
409#124—222no—
410#124—221no—
411#124—222no—
412#123—222no—
413#123—222no—
414#123—222no—
415C22⋊Q8—222no—
416C22⋊Q8—221no—
417C22⋊Q8—222no—
418C22⋊Q8—221no—
419#121—222no—
420#121—221no—
421#121—222no—
422#121—221no—
423#121—222no—
424#121—221no—
425#121—222no—
426#121—221no—
427#120—222no—
428#120—222no—
429#120—222no—
430C4×Q8D4411yescharacteristic
431C4×Q8C22⋊D1111yescharacteristic
432C4×D4—221no—
433C4×D4—222no—
434C4×D4—221no—
435C4×D4—222no—
436C4×D4D4411yescharacteristic
437C4×D4D4412yes—
438C4×D4C22⋊D1111yescharacteristic
439C4×D4C22⋊D1112yes—
440#117C4×D1111yescharacteristic
441#117C4×D1112yes—
442C2×C22⋊C4—222no—
443C2×C22⋊C4—221no—
444C2×C22⋊C4—222no—
445C2×C22⋊C4—221no—
446C2×C42C22×D1112yes—
447C2×C42C22×D1111yescharacteristic
448C4⋊C8—21no—
449C4⋊C8—22no—
450C4⋊C8—221no—
451C4⋊C8—222no—
452C22⋊C8—22no—
453C22⋊C8—21no—
454C22⋊C8—222no—
455C22⋊C8—221no—
456#97—22no—
457#97—111no—
458#97—112no—
459#97—111no—
460#97—222no—
461#97C22×D1111yescharacteristic
462#97C22×D1112yes—
463#97C22×D1111yescharacteristic
464C4×C8—21no—
465C4×C8—221no—
466C2×C11—24no—
467C2×C11—41no—
468C2×C11C22×#10011yescharacteristic
469C2×C11#290111yescharacteristic
470C2×C11#290111yescharacteristic
471D11—81no—
472D11—81no—
473D11—82no—
474C24—221no—
475C24—222no—
476#41—24no—
477#41—444no—
478#41—444no—
479#41—442no—
480#41—442no—
481#41—448no—
482#41—444no—
483#41—444no—
484C2×Q8—112no—
485C2×Q8—111no—
486C2×Q8—111no—
487C2×Q8—222no—
488C2×Q8—221no—
489C2×Q8—442no—
490C2×Q8—444no—
491C2×Q8—444no—
492C2×Q8(C2×D11)⋊C411yescharacteristic
493C2×D4—111no—
494C2×D4—112no—
495C2×D4—111no—
496C2×D4—221no—
497C2×D4—222no—
498C2×D4—221no—
499C2×D4—222no—
500C2×D4—222no—
501C2×D4—221no—
502C2×D4—221no—
503C2×D4—222no—
504C2×D4—221no—
505C2×D4—222no—
506C2×D4—444no—
507C2×D4—442no—
508C2×D4—448no—
509C2×D4—444no—
510C2×D4(C2×D11)⋊C412yes—
511C2×D4(C2×D11)⋊C411yescharacteristic
512C22×C4—221no—
513C22×C4—222no—
514C22×C4—222no—
515C22×C4—221no—
516C22×C4—222no—
517C22×C4—221no—
518C22×C4C2×C4×D1112yes—
519C22×C4C2×C4×D1111yescharacteristic
520C22×C4C2×D4412yes—
521C22×C4C2×D4411yescharacteristic
522C22×C4C2×C22⋊D1112yes—
523C22×C4C2×C22⋊D1111yescharacteristic
524M16—42no—
525M16—442no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—22no—
529C2×C8—44no—
530C2×C8—221no—
531C2×C8—221no—
532C2×C8—222no—
533C2×C8—444no—
534C4⋊C4—221no—
535C4⋊C4—222no—
536C4⋊C4—221no—
537C4⋊C4—222no—
538C4⋊C4(C2×D11)⋊C412yes—
539C4⋊C4(C2×D11)⋊C411yescharacteristic
540C4⋊C4(C2×D11)⋊C412yes—
541C4⋊C4(C2×D11)⋊C411yescharacteristic
542C22⋊C4—222no—
543C22⋊C4—222no—
544C22⋊C4—222no—
545C22⋊C4—222no—
546C22⋊C4—222no—
547C22⋊C4—222no—
548C22⋊C4—221no—
549C22⋊C4—222no—
550C22⋊C4—221no—
551C22⋊C4—221no—
552C22⋊C4—222no—
553C22⋊C4—221no—
554C22⋊C4(C2×D11)⋊C412yes—
555C22⋊C4(C2×D11)⋊C412yes—
556C22⋊C4(C2×D11)⋊C412yes—
557C42C2×C4×D1112yes—
558C42C2×C4×D1111yescharacteristic
559C42C2×D4411yescharacteristic
560C42C2×D4412yes—
561C42C2×C22⋊D1111yescharacteristic
562C42C2×C22⋊D1112yes—
563C42C23×D1111yescharacteristic
564C11#1768511yescharacteristic, complemented, Sylow
565C23—222no—
566C23—221no—
567C23—221no—
568C23—442no—
569C23—444no—
570C23—882no—
571C23—882no—
572C23—881no—
573C23—881no—
574C23C2×(C2×D11)⋊C411yescharacteristic
575C23C2×(C2×D11)⋊C412yes—
576Q8—22no—
577Q8—442no—
578Q8—441no—
579Q8—441no—
580Q8—444no—
581Q8—442no—
582D4—24no—
583D4—441no—
584D4—442no—
585D4—441no—
586D4—444no—
587D4—442no—
588D4—442no—
589D4—444no—
590D4—444no—
591D4—442no—
592D4—882no—
593D4—881no—
594D4—882no—
595D4—881no—
596D4#6688714yes—
597C2×C4—24no—
598C2×C4—22no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—222no—
604C2×C4—221no—
605C2×C4—221no—
606C2×C4—444no—
607C2×C4—444no—
608C2×C4—442no—
609C2×C4—444no—
610C2×C4—442no—
611C2×C4—442no—
612C2×C4C2×(C2×D11)⋊C411yescharacteristic
613C2×C4C2×(C2×D11)⋊C412yes—
614C2×C4C2×(C2×D11)⋊C411yescharacteristic
615C2×C4C2×(C2×D11)⋊C412yes—
616C2×C4C2×(C2×D11)⋊C412yes—
617C2×C4C2×(C2×D11)⋊C411yescharacteristic
618C2×C4C22×C4×D1111yescharacteristic
619C2×C4C22×D4411yescharacteristic
620C2×C4C22×C22⋊D1111yescharacteristic
621C8—22no—
622C8—42no—
623C8—41no—
624C8—222no—
625C8—442no—
626C8—441no—
627C22—22no—
628C22—22no—
629C22—21no—
630C22—21no—
631C22—21no—
632C22—441no—
633C22—442no—
634C22—441no—
635C22—441no—
636C22—441no—
637C22—442no—
638C22—441no—
639C22—441no—
640C22—442no—
641C22—1764no—
642C22—1762no—
643C22C2×#6688714yes—
644C22C22×(C2×D11)⋊C411yescharacteristic
645C4—21no—
646C4—22no—
647C4—21no—
648C4—22no—
649C4—21no—
650C4—21no—
651C4—22no—
652C4—21no—
653C4—441no—
654C4—442no—
655C4—441no—
656C4C2×#6688712yes—
657C2—24no—
658C2—41no—
659C2—881no—
660C2—882no—
661C2—881no—
662C2C22×#6688711yescharacteristic
663C2#1307716111yescharacteristic
664C2#1307716411yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2970C2
socleC22×C11C22×C22⋊C4
prime radical#13082409C2
cosocleC42×C11C24
hypercenter#2970D11
hypocenterC11#17685
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2970

Complements

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

NH ≅ G/Ntype
2. #13077630C2semidirect
3. #13067250C2semidirect
4. #13067239C2semidirect
5. #13067228C2semidirect
6. #13067226C2semidirect
7. #13067215C2semidirect
8. #13067213C2semidirect
9. #13067207C2semidirect
10. C2×#10622102C2semidirect
11. C11×#2970C2semidirect
32. C11×#432C22semidirect
33. C11×#432C22semidirect
34. C4×C11×M16C22semidirect
35. C2×C11×#97C22semidirect
39. #10622539C22semidirect
40. #10622539C22semidirect
41. C4×#4318C22semidirect
42. C2×#66867C22semidirect
43. #10622102C22semidirect
44. #10622102C22semidirect
45. #10622102C22semidirect
46. #10622102C22semidirect
47. #10622102C22semidirect
48. #10622102C22semidirect
49. #10622102C22semidirect
50. #10622102C22semidirect
51. #10622102C22semidirect
52. #10622102C22semidirect
235. #2970D11semidirect
331. #432C2×D11semidirect
332. #432C2×D11semidirect
334. C4×M16C2×D11semidirect
336. C2×#97C2×D11semidirect
564. C11#17685semidirect

Maximal subgroups

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

subgroupindex
#130824092
#130776302
#130672502
#130672392
#130672282
#130672262
#130672152
#130672132
#130672072
C2×#106221022
C11×#29702
#1768511