Finite Group Databasebeta

← #14719921

Subgroups — #14719921

Order 2816.

952 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623046C211yesmaximal, characteristic
2#13077655C211yesmaximal, characteristic, complemented
3#13077643C211yesmaximal, characteristic, complemented
4#13066984C212yesmaximal, complemented
5#13066978C212yesmaximal, complemented
6#13066970C212yesmaximal, complemented
7#13066963C212yesmaximal, complemented
8#13066952C211yesmaximal, characteristic, complemented
9#13066952C211yesmaximal, characteristic, complemented
10#13066946C211yesmaximal, characteristic, complemented
11C11×#1463C211yesmaximal, characteristic, complemented
12C22×C11×C4⋊C4C2211yescharacteristic
13C2×#66983C411yescharacteristic
14C2×#66982C411yescharacteristic
15C2×#66982C411yescharacteristic
16C2×C4×C22⋊D11C2211yescharacteristic
17C2×C4×C22⋊D11C2211yescharacteristic
18C2×#66977C411yescharacteristic
19#10623046—22no—
20#10623046—22no—
21#10623046—22no—
22#10623046—22no—
23C2×#66951C411yescharacteristic
24C2×#66951C2211yescharacteristic
25C2×#66949C411yescharacteristic
26C2×#66949C2211yescharacteristic
27C2×#66947C411yescharacteristic
28C2×#66947C2211yescharacteristic
29C2×#66942C411yescharacteristic
30C2×#66942C2211yescharacteristic
31C11×#407C2211yescharacteristic
32C11×#407C2211yescharacteristic
33#10622820C2211yescharacteristic
34#10622820C2211yescharacteristic
35#10622741—22no—
36#10622740—22no—
37#10622342—22no—
38#10622341—22no—
39#10622339C2212yes—
40D11×C22⋊C8C2212yes—
41#10622332C2212yes—
42#10622331C2212yes—
43C11×#324C2212yes—
44C11×#324C2212yes—
45#10622166C2212yes—
46#10622166C2212yes—
47#10622107C2212yes—
48#10622107C2212yes—
49#10622106C2212yes—
50#10622106C2212yes—
51C23×C4×C11C2×C411yescharacteristic
52C23×C4×C11C2×C411yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C22×C22⋊D11C2×C411yescharacteristic
55C22×C22⋊D11C2×C411yescharacteristic
56C22×D44C2×C411yescharacteristic
57C22×C4×D11C2×C411yescharacteristic
58C22×C4×D11C2311yescharacteristic
59C22×Dic22C2×C411yescharacteristic
60C2×C11×M16—21no—
61C2×C11×M16—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4C2×C411yescharacteristic
67C2×C11×C4⋊C4C2×C411yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C22⋊Dic11C2×C411yescharacteristic
71C2×C22⋊Dic11C2×C411yescharacteristic
72#66983—22no—
73#66983—22no—
74#66982—22no—
75#66982—22no—
76#66982—22no—
77#66982—22no—
78C4×C22⋊D11—21no—
79C4×C22⋊D11—21no—
80C4×C22⋊D11—21no—
81C4×C22⋊D11—21no—
82C4×C22⋊D11D412yes—
83C4×C22⋊D11D412yes—
84C4×C22⋊D11D412yes—
85C4×C22⋊D11D412yes—
86C2×(C2×D11)⋊C4C2×C411yescharacteristic
87C2×(C2×D11)⋊C4C2×C411yescharacteristic
88C2×(C2×D11)⋊C4C2×C411yescharacteristic
89C2×(C2×D11)⋊C4C2×C411yescharacteristic
90C2×(C2×D11)⋊C4C2×C411yescharacteristic
91C2×(C2×D11)⋊C4C2×C411yescharacteristic
92C2×(C2×D11)⋊C4C2×C411yescharacteristic
93C2×(C2×D11)⋊C4C2311yescharacteristic
94C2×C4⋊Dic11C2×C411yescharacteristic
95C2×C4⋊Dic11C2×C411yescharacteristic
96#66977—22no—
97#66977—22no—
98C2×Dic11⋊C4C2×C411yescharacteristic
99C2×Dic11⋊C4C2×C411yescharacteristic
100C2×Dic11⋊C4C2×C411yescharacteristic
101C2×Dic11⋊C4C2×C411yescharacteristic
102C2×Dic11⋊C4C2×C411yescharacteristic
103C2×Dic11⋊C4C2×C411yescharacteristic
104C2×Dic11⋊C4C2×C411yescharacteristic
105C2×Dic11⋊C4C2311yescharacteristic
106C2×C4×Dic11C2×C411yescharacteristic
107C2×C4×Dic11C2311yescharacteristic
108C2×#4318—21no—
109C2×#4318—21no—
110C2×#4313—22no—
111C2×C8×D11—22no—
112#66951—22no—
113#66951—22no—
114#66951—22no—
115#66951—22no—
116#66949—22no—
117#66949—22no—
118#66949—22no—
119#66949—22no—
120#66947—22no—
121#66947—22no—
122#66947—22no—
123#66947—22no—
124#66942—22no—
125#66942—22no—
126#66942—22no—
127#66942—22no—
128C11×C22⋊C8—21no—
129C11×C22⋊C8—21no—
130C11×C22⋊C8C2312yes—
131C11×C22⋊C8C2312yes—
132C22⋊(C11⋊C8)—21no—
133C22⋊(C11⋊C8)—21no—
134C22⋊(C11⋊C8)C2312yes—
135C22⋊(C11⋊C8)C2312yes—
136(C2×D11)⋊C8—22no—
137(C2×D11)⋊C8—22no—
138#66879—22no—
139Dic11⋊C8—22no—
140Dic11⋊C8—22no—
141C8×Dic11—22no—
142#17406—111nomaximal, Sylow
143C24×C11C22×C411yescharacteristic
144C23×D11C22×C411yescharacteristic
145C23×D11C22×C411yescharacteristic
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—42no—
151C22×C4×C11—81no—
152C22×C4×C11—81no—
153C22×C4×C11C22×C411yescharacteristic
154C22×C4×C11C22×C411yescharacteristic
155C22×C4×C11C22×C411yescharacteristic
156C22×C4×C11C22×C411yescharacteristic
157C22×C4×C11C22×C411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2411yescharacteristic
163C2×C22⋊D11—21no—
164C2×C22⋊D11—21no—
165C2×C22⋊D11—42no—
166C2×C22⋊D11—42no—
167C2×C22⋊D11C22⋊C412yes—
168C2×C22⋊D11C22⋊C412yes—
169C22×Dic11C22×C411yescharacteristic
170C22×Dic11C22×C411yescharacteristic
171C22×Dic11C22×C411yescharacteristic
172C22×Dic11C22×C411yescharacteristic
173C22×Dic11C22×C411yescharacteristic
174C22×Dic11C22×C411yescharacteristic
175C2×D44—22no—
176C2×D44—81no—
177C2×C4×D11—21no—
178C2×C4×D11—21no—
179C2×C4×D11—81no—
180C2×C4×D11—81no—
181C2×C4×D11C2×D412yes—
182C2×C4×D11C2×D412yes—
183C2×Dic22—22no—
184C2×Dic22—81no—
185C11×M16—81no—
186C11×M16—81no—
187C2×C8×C11—22no—
188C2×C8×C11—22no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C22⋊Dic11—21no—
198C22⋊Dic11—21no—
199C22⋊Dic11C22⋊C412yes—
200C22⋊Dic11C22⋊C412yes—
201(C2×D11)⋊C4—22no—
202(C2×D11)⋊C4—22no—
203(C2×D11)⋊C4—22no—
204(C2×D11)⋊C4—22no—
205(C2×D11)⋊C4—22no—
206(C2×D11)⋊C4—22no—
207(C2×D11)⋊C4—21no—
208(C2×D11)⋊C4—21no—
209(C2×D11)⋊C4C22⋊C412yes—
210(C2×D11)⋊C4C22⋊C412yes—
211C4⋊Dic11—22no—
212C4⋊Dic11—22no—
213Dic11⋊C4—22no—
214Dic11⋊C4—22no—
215Dic11⋊C4—22no—
216Dic11⋊C4—22no—
217Dic11⋊C4—22no—
218Dic11⋊C4—22no—
219Dic11⋊C4—21no—
220Dic11⋊C4—21no—
221Dic11⋊C4C22⋊C412yes—
222Dic11⋊C4C22⋊C412yes—
223C4×Dic11—21no—
224C4×Dic11—21no—
225C4×Dic11C2×D412yes—
226C4×Dic11C2×D412yes—
227#4318—81no—
228#4318—81no—
229C2×C11⋊C8—22no—
230C2×C11⋊C8—22no—
231#4313—82no—
232C8×D11—82no—
233C2×#539—111no—
234#2975—111no—
235#2973—111no—
236#1473—112no—
237#1472—112no—
238#1470—112no—
239#1468—112no—
240#1465—111no—
241#1465—111no—
242#1463—111no—
243#1463D1111yescharacteristic, complemented
244C23×C11—22no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11C2×C22⋊C411yescharacteristic
248C23×C11C2×C22⋊C411yescharacteristic
249C23×C11C23×C411yescharacteristic
250C22×D11—22no—
251C22×D11—21no—
252C22×D11—22no—
253C22×D11—41no—
254C22×D11—41no—
255C22×D11—41no—
256C22×D11—41no—
257C22×D11C2×C22⋊C412yes—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—42no—
271C2×C4×C11—42no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—81no—
275C2×C4×C11—81no—
276C2×C4×C11C2×C22⋊C411yescharacteristic
277C2×C4×C11C2×C22⋊C411yescharacteristic
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11C22×D411yescharacteristic
280C22⋊D11—42no—
281C22⋊D11—42no—
282C22⋊D11—42no—
283C22⋊D11—42no—
284C2×Dic11—22no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—22no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11C2×C22⋊C412yes—
294C2×Dic11C2×C22⋊C412yes—
295C2×Dic11C2×C22⋊C412yes—
296D44—82no—
297C4×D11—42no—
298C4×D11—42no—
299C4×D11—81no—
300C4×D11—81no—
301Dic22—82no—
302C8×C11—42no—
303C8×C11—42no—
304C11⋊C8—42no—
305C11⋊C8—42no—
306#539—222no—
307#539—222no—
308#539—222no—
309#539—222no—
310C2×#126—111no—
311C2×#126—111no—
312C2×#125—111no—
313C2×#125—111no—
314C2×#123—111no—
315C2×#123—111no—
316C2×#123—111no—
317C2×#123—111no—
318C2×C22⋊Q8—111no—
319C2×C22⋊Q8—111no—
320C2×C22⋊Q8—111no—
321C2×#121—111no—
322C2×C4×D4—111no—
323C2×C4×D4—111no—
324C22×C4⋊C4C2×D1111yescharacteristic
325#436—222no—
326#436—222no—
327#435—222no—
328#435—222no—
329#432—112no—
330#431—112no—
331#407—111no—
332#407—111no—
333#407—112no—
334#407C2×D1111yescharacteristic
335#407C2×D1111yescharacteristic
336C2×C22⋊C8—112no—
337#324—112no—
338#324—112no—
339#324—112no—
340#324—112no—
341#324C2×D1112yes—
342#324C2×D1112yes—
343#323—112no—
344#323—112no—
345C22×C11—21no—
346C22×C11—21no—
347C22×C11—21no—
348C22×C11—21no—
349C22×C11—21no—
350C22×C11—21no—
351C22×C11—21no—
352C22×C11—21no—
353C22×C11—44no—
354C22×C11C22×C22⋊C411yescharacteristic
355C22×C11#56812yes—
356C2×D11—22no—
357C2×D11—22no—
358C2×D11—22no—
359C2×D11—41no—
360C2×D11—41no—
361C2×D11—41no—
362C2×D11—82no—
363C2×D11—82no—
364C4×C11—21no—
365C4×C11—21no—
366C4×C11—21no—
367C4×C11—21no—
368C4×C11—41no—
369C4×C11—41no—
370C4×C11—41no—
371C4×C11—41no—
372Dic11—22no—
373Dic11—22no—
374Dic11—22no—
375Dic11—41no—
376Dic11—41no—
377Dic11—41no—
378C22×Q8—111no—
379C22×D4—111no—
380C22×D4—111no—
381C22×D4—111no—
382C23×C4—111no—
383C23×C4—111no—
384C23×C4C4×D1111yescharacteristic
385C23×C4C4×D1111yescharacteristic
386C23×C4C22×D1111yescharacteristic
387C2×M16—21no—
388C2×M16—21no—
389C2×M16—222no—
390C2×M16—221no—
391C2×M16—221no—
392C22×C8—222no—
393#126—222no—
394#126—222no—
395#126—222no—
396#126—222no—
397#125—222no—
398#125—222no—
399#125—222no—
400#125—222no—
401#123—222no—
402#123—222no—
403#123—222no—
404#123—222no—
405#123—222no—
406#123—222no—
407#123—222no—
408#123—222no—
409C22⋊Q8—222no—
410C22⋊Q8—222no—
411C22⋊Q8—222no—
412C22⋊Q8—222no—
413C22⋊Q8—222no—
414C22⋊Q8—222no—
415#121—222no—
416#121—222no—
417C4×D4—112no—
418C4×D4—112no—
419C4×D4—112no—
420C4×D4—112no—
421C4×D4—221no—
422C4×D4—221no—
423C4×D4—221no—
424C4×D4—221no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—111no—
430C2×C4⋊C4—111no—
431C2×C4⋊C4—111no—
432C2×C4⋊C4—111no—
433C2×C4⋊C4—111no—
434C2×C4⋊C4—111no—
435C2×C4⋊C4—111no—
436C2×C4⋊C4—111no—
437C2×C4⋊C4—111no—
438C2×C4⋊C4—111no—
439C2×C4⋊C4C4×D1111yescharacteristic
440C2×C4⋊C4C4×D1111yescharacteristic
441C2×C4⋊C4C22×D1111yescharacteristic
442C2×C4⋊C4C22×D1111yescharacteristic
443C2×C22⋊C4—111no—
444C2×C22⋊C4—111no—
445C2×C22⋊C4—111no—
446C2×C22⋊C4—111no—
447C2×C22⋊C4—111no—
448C2×C22⋊C4—111no—
449C2×C22⋊C4—111no—
450C2×C22⋊C4—111no—
451C2×C22⋊C4—111no—
452C2×C22⋊C4—111no—
453C2×C42—111no—
454C2×C42—111no—
455C4⋊C8—222no—
456C4⋊C8—222no—
457C22⋊C8—21no—
458C22⋊C8—21no—
459C22⋊C8—112no—
460C22⋊C8—112no—
461C22⋊C8—222no—
462C22⋊C8—222no—
463C22⋊C8—221no—
464C22⋊C8—221no—
465C22⋊C8C22×D1112yes—
466C22⋊C8C22×D1112yes—
467#97—222no—
468C4×C8—222no—
469C2×C11—22no—
470C2×C11—41no—
471C2×C11—41no—
472C2×C11#287911yescharacteristic
473C2×C11#288311yescharacteristic
474C2×C11#288911yescharacteristic
475D11—42no—
476D11—81no—
477C24—111no—
478C24—111no—
479C24C2×C4×D1111yescharacteristic
480C2×Q8—222no—
481C2×Q8—881no—
482C2×D4—112no—
483C2×D4—112no—
484C2×D4—222no—
485C2×D4—221no—
486C2×D4—221no—
487C2×D4—442no—
488C2×D4—442no—
489C2×D4—881no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—42no—
495C22×C4—81no—
496C22×C4—81no—
497C22×C4—111no—
498C22×C4—111no—
499C22×C4—111no—
500C22×C4—112no—
501C22×C4—112no—
502C22×C4—111no—
503C22×C4—111no—
504C22×C4—111no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—881no—
508C22×C4—881no—
509C22×C4C2×C4×D1111yescharacteristic
510C22×C4C2×C4×D1111yescharacteristic
511C22×C4C2×C4×D1111yescharacteristic
512C22×C4C2×C4×D1111yescharacteristic
513C22×C4C2×C4×D1111yescharacteristic
514C22×C4D4×D1111yescharacteristic
515C22×C4D4×D1111yescharacteristic
516C22×C4D4×D1111yescharacteristic
517C22×C4D4×D1111yescharacteristic
518C22×C4C23×D1111yescharacteristic
519M16—81no—
520M16—81no—
521M16—882no—
522M16—881no—
523M16—881no—
524C2×C8—22no—
525C2×C8—22no—
526C2×C8—222no—
527C2×C8—222no—
528C2×C8—882no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—112no—
538C4⋊C4—112no—
539C4⋊C4—222no—
540C4⋊C4—222no—
541C4⋊C4—222no—
542C4⋊C4—222no—
543C4⋊C4—222no—
544C4⋊C4—222no—
545C4⋊C4—222no—
546C4⋊C4—222no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C22⋊C4—112no—
550C22⋊C4—112no—
551C22⋊C4—112no—
552C22⋊C4—112no—
553C22⋊C4—222no—
554C22⋊C4—222no—
555C22⋊C4—222no—
556C22⋊C4—222no—
557C22⋊C4—222no—
558C22⋊C4—222no—
559C22⋊C4—221no—
560C22⋊C4—221no—
561C22⋊C4—221no—
562C22⋊C4—221no—
563C42—112no—
564C42—112no—
565C42—221no—
566C42—221no—
567C11#1740611yescharacteristic, complemented, Sylow
568C23—22no—
569C23—41no—
570C23—41no—
571C23—112no—
572C23—222no—
573C23—221no—
574C23—222no—
575C23—441no—
576C23—441no—
577C23—441no—
578C23—441no—
579C23C22⋊C4×D1111yescharacteristic
580C23C22⋊C4×D1111yescharacteristic
581C23C22×C4×D1111yescharacteristic
582Q8—882no—
583D4—442no—
584D4—442no—
585D4—442no—
586D4—442no—
587D4—882no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—81no—
605C2×C4—81no—
606C2×C4—112no—
607C2×C4—112no—
608C2×C4—112no—
609C2×C4—222no—
610C2×C4—221no—
611C2×C4—221no—
612C2×C4—221no—
613C2×C4—222no—
614C2×C4—442no—
615C2×C4—442no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—881no—
621C2×C4—881no—
622C2×C4C22⋊C4×D1111yescharacteristic
623C2×C4C22⋊C4×D1111yescharacteristic
624C2×C4C2×D4×D1111yescharacteristic
625C2×C4C2×D4×D1111yescharacteristic
626C8—42no—
627C8—42no—
628C8—442no—
629C8—442no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—21no—
634C22—21no—
635C22—21no—
636C22—21no—
637C22—21no—
638C22—44no—
639C22—222no—
640C22—222no—
641C22—222no—
642C22—441no—
643C22—441no—
644C22—441no—
645C22—882no—
646C22—882no—
647C22C2×C22⋊C4×D1111yescharacteristic
648C22#1062327612yes—
649C4—21no—
650C4—21no—
651C4—21no—
652C4—21no—
653C4—41no—
654C4—41no—
655C4—41no—
656C4—41no—
657C4—222no—
658C4—222no—
659C4—222no—
660C4—441no—
661C4—441no—
662C4—441no—
663C2—22no—
664C2—41no—
665C2—41no—
666C2—442no—
667C2—881no—
668C2#1307705911yescharacteristic
669C2#1307707411yescharacteristic
670C2#1307709611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1463C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#66983C4
cosocleC22×C4×C11C24
hypercenter#1463D11
hypocenterC11#17406
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
2. #13077655C2semidirect
3. #13077643C2semidirect
4. #13066984C2semidirect
5. #13066978C2semidirect
6. #13066970C2semidirect
7. #13066963C2semidirect
8. #13066952C2semidirect
9. #13066952C2semidirect
10. #13066946C2semidirect
11. C11×#1463C2semidirect
243. #1463D11semidirect
567. C11#17406semidirect

Maximal subgroups

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

subgroupindex
C2×#106230462
#130776552
#130776432
#130669842
#130669782
#130669702
#130669632
#130669522
#130669462
C11×#14632
#1740611