Finite Group Databasebeta

← #14725629

Subgroups — #14725629

Order 2816.

656 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077621C211yesmaximal, characteristic, complemented
2#13077360C211yesmaximal, characteristic, complemented
3#13067530C211yesmaximal, characteristic, complemented
4#13067507C211yesmaximal, characteristic, complemented
5#13067495C211yesmaximal, characteristic, complemented
6#13067481C211yesmaximal, characteristic, complemented
7#13067453C211yesmaximal, characteristic, complemented
8#13067446C211yesmaximal, characteristic, complemented
9SD16⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
10D8×C11⋊C8C211yesmaximal, characteristic, complemented
11#13067368C211yesmaximal, characteristic, complemented
12#13067033C211yesmaximal, characteristic, complemented
13#13067029C211yesmaximal, characteristic, complemented
14#13066919C211yesmaximal, characteristic, complemented
15C11×#3171C211yesmaximal, characteristic
16C11×#532C2211yescharacteristic
17C11×#529C2211yescharacteristic
18C2×#67001—21no—
19C11×#501C411yescharacteristic
20C11×#496C411yescharacteristic
21C11×#490C411yescharacteristic
22C11×#489C411yescharacteristic
23C11×#469C411yescharacteristic
24C11×#469C411yescharacteristic
25C11×#468C411yescharacteristic
26C11×#468C411yescharacteristic
27C4×C11×SD16C2211yescharacteristic
28C4×C11×SD16C2211yescharacteristic
29C4×C11×D8C2211yescharacteristic
30C4×C11×D8C2211yescharacteristic
31C4×C11×M16C2211yescharacteristic
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#10622610—21no—
47#10622538C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49C4×#4318C2211yescharacteristic
50C4×#4318C2211yescharacteristic
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#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
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
94#67001—44no—
95C2×#4318—21no—
96C2×#4318—21no—
97C2×#4318—21no—
98C2×#4318—21no—
99C2×#4318D411yescharacteristic
100C2×#4318D411yescharacteristic
101C22×C11⋊C8—21no—
102C22×C11⋊C8—21no—
103C22×C11⋊C8—21no—
104C22×C11⋊C8—21no—
105C11×#107C2×C411yescharacteristic
106C11×#107C2×C411yescharacteristic
107C11×#106C2×C411yescharacteristic
108C11×#106C2×C411yescharacteristic
109C11×#103C2×C411yescharacteristic
110C11×#103C2×C411yescharacteristic
111C11×#102C2×C411yescharacteristic
112C11×#102C2×C411yescharacteristic
113C11×#102C2×C411yescharacteristic
114C11×#102C2×C411yescharacteristic
115C11×#102C2×C411yescharacteristic
116C11×#102C2×C411yescharacteristic
117C11×#97C2×C411yescharacteristic
118C11×#97C2×C411yescharacteristic
119C4×C8×C11C2311yescharacteristic
120C4×C8×C11C2311yescharacteristic
121C22⋊(C11⋊C8)—21no—
122C22⋊(C11⋊C8)—21no—
123C22⋊(C11⋊C8)—21no—
124C22⋊(C11⋊C8)—21no—
125C22⋊(C11⋊C8)—21no—
126C22⋊(C11⋊C8)—21no—
127C22⋊(C11⋊C8)—21no—
128C4⋊(C11⋊C8)—21no—
129C4⋊(C11⋊C8)—21no—
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)C2311yescharacteristic
132C4⋊(C11⋊C8)C2311yescharacteristic
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135#66867—21no—
136#66867—21no—
137#66867D411yescharacteristic
138#66867D411yescharacteristic
139C4×C11⋊C8—21no—
140C4×C11⋊C8—21no—
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#18076—111nomaximal, Sylow
146C11×#41—42no—
147C11×#41—42no—
148C2×Q8×C11—21no—
149C2×Q8×C11C22×C411yescharacteristic
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11C22×C411yescharacteristic
156C2×D4×C11C22×C411yescharacteristic
157C2×D4×C11C22×C411yescharacteristic
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11C22×C411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11#4111yescharacteristic
164C11×SD16—22no—
165C11×SD16—41no—
166C11×D8—22no—
167C11×D8—41no—
168C11×M16—22no—
169C11×M16—41no—
170C2×C8×C11C22×C411yescharacteristic
171C2×C8×C11C22×C411yescharacteristic
172C2×C8×C11C22×C411yescharacteristic
173C2×C8×C11C22×C411yescharacteristic
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4C22×C411yescharacteristic
180C11×C4⋊C4C22×C411yescharacteristic
181C11×C4⋊C4C22×C411yescharacteristic
182C11×C4⋊C4C22×C411yescharacteristic
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—
191C11×C22⋊C4—21no—
192C42×C11—21no—
193C42×C11C22×C411yescharacteristic
194C42×C11C2×D411yescharacteristic
195C42×C11#4111yescharacteristic
196C42×C11C2411yescharacteristic
197#4318—22no—
198#4318—41no—
199#4318—42no—
200#4318—42no—
201#4318—42no—
202#4318—42no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—42no—
210C2×C11⋊C8—42no—
211C2×C11⋊C8—42no—
212C2×C11⋊C8—42no—
213C2×C11⋊C8C2×D411yescharacteristic
214C2×C11⋊C8C2×D411yescharacteristic
215C2×C11⋊C8C2×D411yescharacteristic
216C2×C11⋊C8C2×D411yescharacteristic
217#3171D1111yescharacteristic
218#2969—111no—
219#2935—111no—
220#1594—111no—
221#1590—111no—
222#1588—111no—
223#1586—111no—
224#1582—111no—
225#1581—111no—
226SD16⋊C8—111no—
227C8×D8—111no—
228#1565—111no—
229#1484—111no—
230#1483—111no—
231#1455—111no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11C4×D411yescharacteristic
236Q8×C11—21no—
237Q8×C11—21no—
238Q8×C11—42no—
239D4×C11—21no—
240D4×C11—21no—
241D4×C11—21no—
242D4×C11—21no—
243D4×C11—21no—
244D4×C11—21no—
245D4×C11—42no—
246D4×C11—42no—
247D4×C11—42no—
248D4×C11—81no—
249D4×C11—81no—
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—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
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×C11C4×D411yescharacteristic
267C2×C4×C11C4×D411yescharacteristic
268C2×C4×C11C4×D411yescharacteristic
269C2×C4×C11C23×C411yescharacteristic
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C8×C11—21no—
273C8×C11—21no—
274C8×C11—21no—
275C8×C11#13112yescomplemented
276C11⋊C8—22no—
277C11⋊C8—21no—
278C11⋊C8—21no—
279C11⋊C8—21no—
280C11⋊C8—41no—
281C11⋊C8—41no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285C11⋊C8AGL(1,ℤ/8)12yes—
286C2×#131—221no—
287#532C2×D1111yescharacteristic
288#529C2×D1111yescharacteristic
289#501Dic1111yescharacteristic
290#496Dic1111yescharacteristic
291#490Dic1111yescharacteristic
292#489Dic1111yescharacteristic
293#469Dic1111yescharacteristic
294#469Dic1111yescharacteristic
295#468Dic1111yescharacteristic
296#468Dic1111yescharacteristic
297#446—111no—
298C8×Q8—111no—
299C4×SD16C2×D1111yescharacteristic
300C4×SD16C2×D1111yescharacteristic
301C4×D8C2×D1111yescharacteristic
302C4×D8C2×D1111yescharacteristic
303#436—111no—
304#436—111no—
305#436—111no—
306#436—221no—
307#435—221no—
308#435—221no—
309#435—221no—
310C8×D4—111no—
311C8×D4—111no—
312C8×D4—111no—
313#433—221no—
314#431—111no—
315C2×C4⋊C8—111no—
316#408—221no—
317#405—221no—
318C4×M16—111no—
319C4×M16—111no—
320C4×M16C2×D1111yescharacteristic
321#335—111no—
322#335—111no—
323#334—111no—
324#334—111no—
325Q8⋊C8—111no—
326Q8⋊C8—111no—
327D4⋊C8—111no—
328D4⋊C8—111no—
329D4⋊C8—111no—
330D4⋊C8—111no—
331D4⋊C8—111no—
332D4⋊C8—111no—
333#322—111no—
334#322—111no—
335#322—111no—
336C82—111no—
337C22×C11—21no—
338C22×C11—21no—
339C22×C11—21no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11C2×C4×D411yescharacteristic
350C4×C11—21no—
351C4×C11—21no—
352C4×C11—21no—
353C4×C11—21no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11—41no—
357C4×C11—41no—
358C4×C11—41no—
359C4×C11C2×#13111yescharacteristic
360C4×C11#56811yescharacteristic
361C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
362C4×C11#57511yescharacteristic
363C2×#41—21no—
364C2×SD16C2×Dic1111yescharacteristic
365C2×SD16C2×Dic1111yescharacteristic
366C2×D8C2×Dic1111yescharacteristic
367C2×D8C2×Dic1111yescharacteristic
368#131—444no—
369C2×M16—111no—
370C2×M16—111no—
371C2×M16—221no—
372C2×M16—221no—
373C2×M16—221no—
374C2×M16—221no—
375C2×M16C2×Dic1111yescharacteristic
376C2×M16C2×Dic1111yescharacteristic
377C22×C8—221no—
378C22×C8—221no—
379C22×C8—221no—
380C22×C8—221no—
381C4⋊Q8C2×Dic1111yescharacteristic
382#127C2×Dic1111yescharacteristic
383#126—21no—
384#125C2×Dic1111yescharacteristic
385#124—21no—
386#124C2×Dic1111yescharacteristic
387#123—21no—
388C22⋊Q8C2×Dic1111yescharacteristic
389#121—21no—
390#121C2×Dic1111yescharacteristic
391#121C2×Dic1111yescharacteristic
392#121C2×Dic1111yescharacteristic
393C4×Q8C22×D1111yescharacteristic
394C4×D4—21no—
395C4×D4—21no—
396C4×D4C22×D1111yescharacteristic
397C4×D4C22×D1111yescharacteristic
398C4×D4C22×D1111yescharacteristic
399#117—21no—
400C2×C42C22×D1111yescharacteristic
401#107C2×Dic1111yescharacteristic
402#107C2×Dic1111yescharacteristic
403#106C2×Dic1111yescharacteristic
404#106C2×Dic1111yescharacteristic
405C4⋊C8—111no—
406C4⋊C8—111no—
407C4⋊C8—111no—
408C4⋊C8—111no—
409C4⋊C8—221no—
410C4⋊C8—221no—
411C4⋊C8—221no—
412#103C2×Dic1111yescharacteristic
413#103C2×Dic1111yescharacteristic
414#102C2×Dic1111yescharacteristic
415#102C2×Dic1111yescharacteristic
416#102C2×Dic1111yescharacteristic
417#102C2×Dic1111yescharacteristic
418#102C2×Dic1111yescharacteristic
419#102C2×Dic1111yescharacteristic
420C22⋊C8—221no—
421C22⋊C8—221no—
422C22⋊C8—221no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425C22⋊C8—221no—
426C22⋊C8—221no—
427#97—111no—
428#97—111no—
429#97—221no—
430#97—221no—
431#97C2×Dic1111yescharacteristic
432#97C2×Dic1111yescharacteristic
433C4×C8—111no—
434C4×C8—111no—
435C4×C8—111no—
436C4×C8—111no—
437C4×C8—221no—
438C4×C8—221no—
439C4×C8C22×D1111yescharacteristic
440C4×C8C22×D1111yescharacteristic
441C2×C11—41no—
442C2×C11—81no—
443C2×C11—81no—
444C2×C11—81no—
445C2×C11#293511yescharacteristic
446C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
447C2×C11#295611yescharacteristic
448#41—42no—
449#41—42no—
450C2×Q8—21no—
451C2×Q8C22×Dic1111yescharacteristic
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4C22×Dic1111yescharacteristic
458C2×D4C22×Dic1111yescharacteristic
459C2×D4C22×Dic1111yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4D4×D1111yescharacteristic
464C22×C4#434111yescharacteristic
465C22×C4C22×Dic1111yescharacteristic
466SD16—22no—
467SD16—41no—
468D8—22no—
469D8—41no—
470M16—22no—
471M16—41no—
472M16—222no—
473M16—442no—
474M16—441no—
475M16—442no—
476M16—442no—
477M16—442no—
478C2×C8—111no—
479C2×C8—111no—
480C2×C8—111no—
481C2×C8—111no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—442no—
489C2×C8—442no—
490C2×C8—442no—
491C2×C8—442no—
492C2×C8C22×Dic1111yescharacteristic
493C2×C8C22×Dic1111yescharacteristic
494C2×C8C22×Dic1111yescharacteristic
495C2×C8C22×Dic1111yescharacteristic
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4C22×Dic1111yescharacteristic
502C4⋊C4C22×Dic1111yescharacteristic
503C4⋊C4C22×Dic1111yescharacteristic
504C4⋊C4C22×Dic1111yescharacteristic
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—21no—
514C42—21no—
515C42D4×D1111yescharacteristic
516C42#434111yescharacteristic
517C42C22×Dic1111yescharacteristic
518C42C23×D1111yescharacteristic
519C11#1807611yescharacteristic, complemented, Sylow
520C23—21no—
521C23—21no—
522C23—21no—
523C23D4×Dic1111yescharacteristic
524Q8—21no—
525Q8—21no—
526Q8—42no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—21no—
531D4—21no—
532D4—21no—
533D4—42no—
534D4—42no—
535D4—42no—
536D4—81no—
537D4—81no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4D4×Dic1111yescharacteristic
555C2×C4D4×Dic1111yescharacteristic
556C2×C4D4×Dic1111yescharacteristic
557C2×C4C2×D4×D1111yescharacteristic
558C2×C4C2×#434111yescharacteristic
559C2×C4C23×Dic1111yescharacteristic
560C8—21no—
561C8—21no—
562C8—21no—
563C8—112no—
564C8—222no—
565C8—221no—
566C8—221no—
567C8—221no—
568C8—441no—
569C8—441no—
570C8—441no—
571C8—441no—
572C8—441no—
573C8#6700112yescomplemented
574C22—21no—
575C22—21no—
576C22—21no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22C2×D4×Dic1111yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4D11×AGL(1,ℤ/8)11yescharacteristic
597C4#1062330411yescharacteristic
598C4C2×#6700111yescharacteristic
599C4#1062335011yescharacteristic
600C2—41no—
601C2—81no—
602C2—81no—
603C2—81no—
604C2#1307736011yescharacteristic
605C2AGL(1,ℤ/8)×Dic1111yescharacteristic
606C2#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#18076
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. #13077621C2semidirect
2. #13077360C2semidirect
3. #13067530C2semidirect
4. #13067507C2semidirect
5. #13067495C2semidirect
6. #13067481C2semidirect
7. #13067453C2semidirect
8. #13067446C2semidirect
9. SD16⋊(C11⋊C8)C2semidirect
10. D8×C11⋊C8C2semidirect
11. #13067368C2semidirect
12. #13067033C2semidirect
13. #13067029C2semidirect
14. #13066919C2semidirect
275. C8×C11#131semidirect
519. C11#18076semidirect
573. C8#67001semidirect

Maximal subgroups

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

subgroupindex
#130776212
#130773602
#130675302
#130675072
#130674952
#130674812
#130674532
#130674462
SD16⋊(C11⋊C8)2
D8×C11⋊C82
#130673682
#130670332
#130670292
#130669192
C11×#31712
#1807611