Finite Group Databasebeta

← #14724405

Subgroups — #14724405

Order 2816.

622 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077765C211yesmaximal, characteristic, complemented
2#13077692C211yesmaximal, characteristic, complemented
3#13067530C211yesmaximal, characteristic, complemented
4#13067519C211yesmaximal, characteristic, complemented
5#13067507C211yesmaximal, characteristic, complemented
6#13067501C211yesmaximal, characteristic, complemented
7#13067440C211yesmaximal, characteristic, complemented
8SD16⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
9SD16×C11⋊C8C211yesmaximal, characteristic, complemented
10D8×C11⋊C8C211yesmaximal, characteristic, complemented
11#13067383C211yesmaximal, characteristic, complemented
12#13067076C211yesmaximal, characteristic, complemented
13#13067067C211yesmaximal, characteristic, complemented
14M16×C11⋊C8C211yesmaximal, characteristic, complemented
15C11×#3171C211yesmaximal, characteristic
16C11×#532C2211yescharacteristic
17C11×#529C2211yescharacteristic
18C11×#501C411yescharacteristic
19C11×#496C411yescharacteristic
20C11×#490C411yescharacteristic
21C11×#489C411yescharacteristic
22C11×#469C411yescharacteristic
23C11×#469C411yescharacteristic
24C11×#468C411yescharacteristic
25C11×#468C411yescharacteristic
26C4×C11×SD16C2211yescharacteristic
27C4×C11×SD16C2211yescharacteristic
28C4×C11×D8C2211yescharacteristic
29C4×C11×D8C2211yescharacteristic
30C4×C11×M16C2211yescharacteristic
31#10622847—21no—
32#10622847—21no—
33#10622637C2211yescharacteristic
34Q8×C11⋊C8C2211yescharacteristic
35#10622625—21no—
36#10622625C2211yescharacteristic
37#10622625C2211yescharacteristic
38#10622625C2211yescharacteristic
39#10622624—21no—
40#10622624—21no—
41#10622624—21no—
42D4×C11⋊C8C2211yescharacteristic
43D4×C11⋊C8C2211yescharacteristic
44D4×C11⋊C8C2211yescharacteristic
45#10622613—21no—
46#10622612—21no—
47#10622539C2211yescharacteristic
48#10622538C2211yescharacteristic
49#10622537C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51Q8⋊(C11⋊C8)C2211yescharacteristic
52Q8⋊(C11⋊C8)C2211yescharacteristic
53D4⋊(C11⋊C8)C2211yescharacteristic
54D4⋊(C11⋊C8)C2211yescharacteristic
55D4⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57D4⋊(C11⋊C8)C2211yescharacteristic
58D4⋊(C11⋊C8)C2211yescharacteristic
59#10622096C2211yescharacteristic
60#10622096C2211yescharacteristic
61#10622095C2211yescharacteristic
62#10622095C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622093C2211yescharacteristic
65C8×C11⋊C8C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×SD16C2×C411yescharacteristic
69C2×C11×SD16C2×C411yescharacteristic
70C2×C11×D8C2×C411yescharacteristic
71C2×C11×D8C2×C411yescharacteristic
72C2×C11×M16C2×C411yescharacteristic
73C2×C11×M16C2×C411yescharacteristic
74C11×C4⋊Q8C2×C411yescharacteristic
75C11×#127C2×C411yescharacteristic
76C11×#126—21no—
77C11×#125C2×C411yescharacteristic
78C11×#124—21no—
79C11×#124C2×C411yescharacteristic
80C11×#123—21no—
81C11×C22⋊Q8C2×C411yescharacteristic
82C11×#121—21no—
83C11×#121C2×C411yescharacteristic
84C11×#121C2×C411yescharacteristic
85C11×#121C2×C411yescharacteristic
86C4×Q8×C11C2311yescharacteristic
87C4×D4×C11—21no—
88C4×D4×C11—21no—
89C4×D4×C11C2311yescharacteristic
90C4×D4×C11C2311yescharacteristic
91C4×D4×C11C2311yescharacteristic
92C11×#117—21no—
93C2×C42×C11C2311yescharacteristic
94C2×#4318—21no—
95C2×#4318—21no—
96C2×#4318—21no—
97C2×#4318—21no—
98C22×C11⋊C8—21no—
99C22×C11⋊C8—21no—
100C22×C11⋊C8—21no—
101C22×C11⋊C8—21no—
102C11×#107C2×C411yescharacteristic
103C11×#107C2×C411yescharacteristic
104C11×#106C2×C411yescharacteristic
105C11×#106C2×C411yescharacteristic
106C11×#103C2×C411yescharacteristic
107C11×#103C2×C411yescharacteristic
108C11×#102C2×C411yescharacteristic
109C11×#102C2×C411yescharacteristic
110C11×#102C2×C411yescharacteristic
111C11×#102C2×C411yescharacteristic
112C11×#102C2×C411yescharacteristic
113C11×#102C2×C411yescharacteristic
114C11×#97C2×C411yescharacteristic
115C11×#97C2×C411yescharacteristic
116C4×C8×C11C2311yescharacteristic
117C4×C8×C11C2311yescharacteristic
118C22⋊(C11⋊C8)—21no—
119C22⋊(C11⋊C8)—21no—
120C22⋊(C11⋊C8)—21no—
121C22⋊(C11⋊C8)—21no—
122C22⋊(C11⋊C8)—21no—
123C22⋊(C11⋊C8)—21no—
124C22⋊(C11⋊C8)—21no—
125C22⋊(C11⋊C8)D411yescharacteristic
126C22⋊(C11⋊C8)D411yescharacteristic
127C4⋊(C11⋊C8)—21no—
128C4⋊(C11⋊C8)—21no—
129C4⋊(C11⋊C8)—21no—
130C4⋊(C11⋊C8)D411yescharacteristic
131C4⋊(C11⋊C8)D411yescharacteristic
132C4⋊(C11⋊C8)C2311yescharacteristic
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136#66867—21no—
137#66867—21no—
138C4×C11⋊C8—21no—
139C4×C11⋊C8—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17968—111nomaximal, Sylow
145C11×#41—81no—
146C11×#41—81no—
147C2×Q8×C11—21no—
148C2×Q8×C11C22×C411yescharacteristic
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11C22×C411yescharacteristic
155C2×D4×C11C22×C411yescharacteristic
156C2×D4×C11C22×C411yescharacteristic
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11C22×C411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11#4111yescharacteristic
163C11×SD16—22no—
164C11×SD16—22no—
165C11×D8—22no—
166C11×D8—22no—
167C11×M16—22no—
168C11×M16—22no—
169C2×C8×C11C22×C411yescharacteristic
170C2×C8×C11C22×C411yescharacteristic
171C2×C8×C11C22×C411yescharacteristic
172C2×C8×C11C22×C411yescharacteristic
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4C22×C411yescharacteristic
179C11×C4⋊C4C22×C411yescharacteristic
180C11×C4⋊C4C22×C411yescharacteristic
181C11×C4⋊C4C22×C411yescharacteristic
182C11×C22⋊C4—21no—
183C11×C22⋊C4—21no—
184C11×C22⋊C4—21no—
185C11×C22⋊C4—21no—
186C11×C22⋊C4—21no—
187C11×C22⋊C4—21no—
188C11×C22⋊C4—21no—
189C11×C22⋊C4—21no—
190C11×C22⋊C4—21no—
191C42×C11—21no—
192C42×C11C22×C411yescharacteristic
193C42×C11C2×D411yescharacteristic
194C42×C11#4111yescharacteristic
195C42×C11C2411yescharacteristic
196#4318—81no—
197#4318—81no—
198#4318—81no—
199#4318—81no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—42no—
207C2×C11⋊C8—81no—
208C2×C11⋊C8—81no—
209C2×C11⋊C8—81no—
210C2×C11⋊C8C2×D411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212C2×C11⋊C8C2×D411yescharacteristic
213C2×C11⋊C8C2×D411yescharacteristic
214#3171D1111yescharacteristic
215#2993—111no—
216#2981—111no—
217#1594—111no—
218#1592—111no—
219#1590—111no—
220#1589—111no—
221#1580—111no—
222SD16⋊C8—111no—
223C8×SD16—111no—
224C8×D8—111no—
225#1569—111no—
226#1494—111no—
227#1492—111no—
228C8×M16—111no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11C4×D411yescharacteristic
233Q8×C11—21no—
234Q8×C11—21no—
235Q8×C11—81no—
236D4×C11—21no—
237D4×C11—21no—
238D4×C11—21no—
239D4×C11—21no—
240D4×C11—21no—
241D4×C11—21no—
242D4×C11—81no—
243D4×C11—81no—
244D4×C11—81no—
245D4×C11—81no—
246D4×C11—81no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
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×C11C4×D411yescharacteristic
264C2×C4×C11C4×D411yescharacteristic
265C2×C4×C11C4×D411yescharacteristic
266C2×C4×C11C23×C411yescharacteristic
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C8×C11—21no—
270C8×C11—21no—
271C8×C11#13112yes—
272C8×C11#13112yes—
273C11⋊C8—22no—
274C11⋊C8—21no—
275C11⋊C8—21no—
276C11⋊C8—21no—
277C11⋊C8—21no—
278C11⋊C8—41no—
279C11⋊C8—41no—
280C11⋊C8—41no—
281C11⋊C8—41no—
282C11⋊C8—41no—
283#532C2×D1111yescharacteristic
284#529C2×D1111yescharacteristic
285#501Dic1111yescharacteristic
286#496Dic1111yescharacteristic
287#490Dic1111yescharacteristic
288#489Dic1111yescharacteristic
289#469Dic1111yescharacteristic
290#469Dic1111yescharacteristic
291#468Dic1111yescharacteristic
292#468Dic1111yescharacteristic
293#446—111no—
294C8×Q8—111no—
295C4×SD16C2×D1111yescharacteristic
296C4×SD16C2×D1111yescharacteristic
297C4×D8C2×D1111yescharacteristic
298C4×D8C2×D1111yescharacteristic
299#436—111no—
300#436—111no—
301#436—111no—
302#436—221no—
303#435—221no—
304#435—221no—
305#435—221no—
306C8×D4—111no—
307C8×D4—111no—
308C8×D4—111no—
309#433—221no—
310#432—111no—
311#431—111no—
312#424—221no—
313#423—111no—
314#408—221no—
315#408—221no—
316C4×M16C2×D1111yescharacteristic
317C2×C4×C8—111no—
318#335—111no—
319#335—111no—
320#334—111no—
321#334—111no—
322Q8⋊C8—111no—
323Q8⋊C8—111no—
324D4⋊C8—111no—
325D4⋊C8—111no—
326D4⋊C8—111no—
327D4⋊C8—111no—
328D4⋊C8—111no—
329D4⋊C8—111no—
330#322—111no—
331#322—111no—
332C82—111no—
333C82—111no—
334C22×C11—21no—
335C22×C11—21no—
336C22×C11—21no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11—41no—
346C22×C11C2×C4×D411yescharacteristic
347C4×C11—21no—
348C4×C11—21no—
349C4×C11—21no—
350C4×C11—21no—
351C4×C11—41no—
352C4×C11—41no—
353C4×C11—41no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11C2×#13111yescharacteristic
357C4×C11C2×#13111yescharacteristic
358C4×C11#57611yescharacteristic
359C4×C11#57711yescharacteristic
360C2×#41—21no—
361C2×SD16C2×Dic1111yescharacteristic
362C2×SD16C2×Dic1111yescharacteristic
363C2×D8C2×Dic1111yescharacteristic
364C2×D8C2×Dic1111yescharacteristic
365C2×M16—221no—
366C2×M16—221no—
367C2×M16—221no—
368C2×M16—221no—
369C2×M16C2×Dic1111yescharacteristic
370C2×M16C2×Dic1111yescharacteristic
371C22×C8—221no—
372C22×C8—221no—
373C22×C8—221no—
374C22×C8—221no—
375C4⋊Q8C2×Dic1111yescharacteristic
376#127C2×Dic1111yescharacteristic
377#126—21no—
378#125C2×Dic1111yescharacteristic
379#124—21no—
380#124C2×Dic1111yescharacteristic
381#123—21no—
382C22⋊Q8C2×Dic1111yescharacteristic
383#121—21no—
384#121C2×Dic1111yescharacteristic
385#121C2×Dic1111yescharacteristic
386#121C2×Dic1111yescharacteristic
387C4×Q8C22×D1111yescharacteristic
388C4×D4—21no—
389C4×D4—21no—
390C4×D4C22×D1111yescharacteristic
391C4×D4C22×D1111yescharacteristic
392C4×D4C22×D1111yescharacteristic
393#117—21no—
394C2×C42C22×D1111yescharacteristic
395#107C2×Dic1111yescharacteristic
396#107C2×Dic1111yescharacteristic
397#106C2×Dic1111yescharacteristic
398#106C2×Dic1111yescharacteristic
399C4⋊C8—111no—
400C4⋊C8—111no—
401C4⋊C8—111no—
402C4⋊C8—111no—
403C4⋊C8—111no—
404C4⋊C8—111no—
405C4⋊C8—221no—
406C4⋊C8—221no—
407C4⋊C8—221no—
408#103C2×Dic1111yescharacteristic
409#103C2×Dic1111yescharacteristic
410#102C2×Dic1111yescharacteristic
411#102C2×Dic1111yescharacteristic
412#102C2×Dic1111yescharacteristic
413#102C2×Dic1111yescharacteristic
414#102C2×Dic1111yescharacteristic
415#102C2×Dic1111yescharacteristic
416C22⋊C8—111no—
417C22⋊C8—111no—
418C22⋊C8—221no—
419C22⋊C8—221no—
420C22⋊C8—221no—
421C22⋊C8—221no—
422C22⋊C8—221no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425#97—221no—
426#97—221no—
427#97C2×Dic1111yescharacteristic
428#97C2×Dic1111yescharacteristic
429C4×C8—111no—
430C4×C8—111no—
431C4×C8—111no—
432C4×C8—111no—
433C4×C8—221no—
434C4×C8—221no—
435C4×C8C22×D1111yescharacteristic
436C4×C8C22×D1111yescharacteristic
437C2×C11—41no—
438C2×C11—81no—
439C2×C11—81no—
440C2×C11—81no—
441C2×C11#293111yescharacteristic
442C2×C11#294611yescharacteristic
443C2×C11#295611yescharacteristic
444#41—81no—
445#41—81no—
446C2×Q8—21no—
447C2×Q8C22×Dic1111yescharacteristic
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4C22×Dic1111yescharacteristic
454C2×D4C22×Dic1111yescharacteristic
455C2×D4C22×Dic1111yescharacteristic
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4D4×D1111yescharacteristic
460C22×C4#434111yescharacteristic
461C22×C4C22×Dic1111yescharacteristic
462SD16—22no—
463SD16—22no—
464D8—22no—
465D8—22no—
466M16—22no—
467M16—22no—
468M16—881no—
469M16—881no—
470M16—881no—
471M16—881no—
472C2×C8—111no—
473C2×C8—111no—
474C2×C8—111no—
475C2×C8—111no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—442no—
483C2×C8—881no—
484C2×C8—881no—
485C2×C8—881no—
486C2×C8C22×Dic1111yescharacteristic
487C2×C8C22×Dic1111yescharacteristic
488C2×C8C22×Dic1111yescharacteristic
489C2×C8C22×Dic1111yescharacteristic
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4C22×Dic1111yescharacteristic
496C4⋊C4C22×Dic1111yescharacteristic
497C4⋊C4C22×Dic1111yescharacteristic
498C4⋊C4C22×Dic1111yescharacteristic
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C42—21no—
509C42D4×D1111yescharacteristic
510C42#434111yescharacteristic
511C42C22×Dic1111yescharacteristic
512C42C23×D1111yescharacteristic
513C11#1796811yescharacteristic, complemented, Sylow
514C23—21no—
515C23—21no—
516C23—21no—
517C23D4×Dic1111yescharacteristic
518Q8—21no—
519Q8—21no—
520Q8—81no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—81no—
528D4—81no—
529D4—81no—
530D4—81no—
531D4—81no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4D4×Dic1111yescharacteristic
549C2×C4D4×Dic1111yescharacteristic
550C2×C4D4×Dic1111yescharacteristic
551C2×C4C2×D4×D1111yescharacteristic
552C2×C4C2×#434111yescharacteristic
553C2×C4C23×Dic1111yescharacteristic
554C8—21no—
555C8—21no—
556C8—222no—
557C8—221no—
558C8—221no—
559C8—221no—
560C8—221no—
561C8—441no—
562C8—441no—
563C8—441no—
564C8—441no—
565C8—441no—
566C8#6700112yes—
567C8#6700112yes—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22C2×D4×Dic1111yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—41no—
590C4#1062330511yescharacteristic
591C4#1062330611yescharacteristic
592C4C2×#6700111yescharacteristic
593C4C2×#6700111yescharacteristic
594C2—41no—
595C2—81no—
596C2—81no—
597C2—81no—
598C2#1307732811yescharacteristic
599C2#1307744911yescharacteristic
600C2#1307752611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
Fitting, prime radicalC11×#3171C2
socleC22×C11C2×C4×D4
cosocleC42×C11C24
hypercenter#3171D11
hypocenterC11#17968
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3171

Complements

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

NH ≅ G/Ntype
1. #13077765C2semidirect
2. #13077692C2semidirect
3. #13067530C2semidirect
4. #13067519C2semidirect
5. #13067507C2semidirect
6. #13067501C2semidirect
7. #13067440C2semidirect
8. SD16⋊(C11⋊C8)C2semidirect
9. SD16×C11⋊C8C2semidirect
10. D8×C11⋊C8C2semidirect
11. #13067383C2semidirect
12. #13067076C2semidirect
13. #13067067C2semidirect
14. M16×C11⋊C8C2semidirect
513. C11#17968semidirect

Maximal subgroups

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

subgroupindex
#130777652
#130776922
#130675302
#130675192
#130675072
#130675012
#130674402
SD16⋊(C11⋊C8)2
SD16×C11⋊C82
D8×C11⋊C82
#130673832
#130670762
#130670672
M16×C11⋊C82
C11×#31712
#1796811