Finite Group Databasebeta

← #14724886

Subgroups — #14724886

Order 2816.

660 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077636C211yesmaximal, characteristic, complemented
2#13077360C211yesmaximal, characteristic, complemented
3#13067530C211yesmaximal, characteristic, complemented
4#13067501C211yesmaximal, characteristic, complemented
5#13067495C211yesmaximal, characteristic, complemented
6#13067481C211yesmaximal, characteristic, complemented
7#13067460C211yesmaximal, characteristic, complemented
8#13067446C211yesmaximal, characteristic, complemented
9SD16⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
10SD16×C11⋊C8C211yesmaximal, characteristic, complemented
11#13067401C211yesmaximal, characteristic, complemented
12#13067085C211yesmaximal, characteristic, complemented
13#13067003C211yesmaximal, characteristic, complemented
14#13066911C211yesmaximal, characteristic, complemented
15C11×#3106C211yesmaximal, characteristic
16C11×#532C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18C2×#67001—21no—
19C11×#482C411yescharacteristic
20C11×#482C411yescharacteristic
21C11×#477C411yescharacteristic
22C11×#476C411yescharacteristic
23C11×#460C411yescharacteristic
24C11×#459C411yescharacteristic
25C11×#449C411yescharacteristic
26C11×#449C411yescharacteristic
27C4×C11×SD16C2211yescharacteristic
28C4×C11×SD16C2211yescharacteristic
29C4×C11×D8C2211yescharacteristic
30C4×C11×D8C2211yescharacteristic
31C11×#431C2211yescharacteristic
32#10622847—21no—
33Q8×C11⋊C8C2211yescharacteristic
34Q8×C11⋊C8C2211yescharacteristic
35#10622625—21no—
36#10622625—21no—
37#10622625C2211yescharacteristic
38#10622625C2211yescharacteristic
39#10622625C2211yescharacteristic
40#10622625C2211yescharacteristic
41#10622624—21no—
42#10622624—21no—
43D4×C11⋊C8C2211yescharacteristic
44D4×C11⋊C8C2211yescharacteristic
45#10622539—21no—
46#10622539C2211yescharacteristic
47#10622538C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49C4×#4318—21no—
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×#41C2×C411yescharacteristic
69C2×C11×SD16C2×C411yescharacteristic
70C2×C11×SD16C2×C411yescharacteristic
71C2×C11×D8C2×C411yescharacteristic
72C2×C11×D8C2×C411yescharacteristic
73C11×C4⋊Q8C2×C411yescharacteristic
74C11×#127C2×C411yescharacteristic
75C11×#124—21no—
76C11×#121—21no—
77C11×#121C2×C411yescharacteristic
78C11×#121C2×C411yescharacteristic
79C4×Q8×C11C2×C411yescharacteristic
80C4×Q8×C11C2311yescharacteristic
81C4×D4×C11—21no—
82C4×D4×C11—21no—
83C4×D4×C11—21no—
84C4×D4×C11C2×C411yescharacteristic
85C4×D4×C11C2311yescharacteristic
86C4×D4×C11C2311yescharacteristic
87C4×D4×C11C2311yescharacteristic
88C11×#117—21no—
89C11×#117C2×C411yescharacteristic
90C2×C42×C11—21no—
91C2×C42×C11C2311yescharacteristic
92#67001—44no—
93C2×#4318—21no—
94C2×#4318—21no—
95C2×#4318—21no—
96C2×#4318—21no—
97C2×#4318D411yescharacteristic
98C2×#4318D411yescharacteristic
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×C4⋊C8C2×C411yescharacteristic
107C11×C4⋊C8C2×C411yescharacteristic
108C11×#103C2×C411yescharacteristic
109C11×#103C2×C411yescharacteristic
110C11×#102C2×C411yescharacteristic
111C11×#102C2×C411yescharacteristic
112C11×#102C2×C411yescharacteristic
113C11×#102C2×C411yescharacteristic
114C11×#102C2×C411yescharacteristic
115C11×#102C2×C411yescharacteristic
116C11×C22⋊C8C2×C411yescharacteristic
117C11×C22⋊C8C2×C411yescharacteristic
118C4×C8×C11C2311yescharacteristic
119C4×C8×C11C2311yescharacteristic
120C22⋊(C11⋊C8)—21no—
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)—21no—
132C4⋊(C11⋊C8)C2311yescharacteristic
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
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#18011—111nomaximal, Sylow
146C11×#41—22no—
147C11×#41—41no—
148C11×#41—42no—
149C11×#41—42no—
150C2×Q8×C11—21no—
151C2×Q8×C11C22×C411yescharacteristic
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11C22×C411yescharacteristic
158C2×D4×C11C22×C411yescharacteristic
159C2×D4×C11C22×C411yescharacteristic
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11C22×C411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11#4111yescharacteristic
168C11×SD16—22no—
169C11×SD16—22no—
170C11×D8—41no—
171C11×D8—41no—
172C2×C8×C11C22×C411yescharacteristic
173C2×C8×C11C22×C411yescharacteristic
174C2×C8×C11C22×C411yescharacteristic
175C2×C8×C11C22×C411yescharacteristic
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—
190C42×C11—21no—
191C42×C11—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⋊C8C2×D411yescharacteristic
213C2×C11⋊C8C2×D411yescharacteristic
214C2×C11⋊C8C2×D411yescharacteristic
215C2×C11⋊C8C2×D411yescharacteristic
216#3106D1111yescharacteristic
217#2971—111no—
218#2935—111no—
219#1594—111no—
220#1589—111no—
221#1588—111no—
222#1586—111no—
223#1583—111no—
224#1581—111no—
225SD16⋊C8—111no—
226C8×SD16—111no—
227#1573—111no—
228#1496—111no—
229#1477—111no—
230#1453—111no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11C4×D411yescharacteristic
235Q8×C11—21no—
236Q8×C11—42no—
237Q8×C11#13112yescomplemented
238D4×C11—21no—
239D4×C11—21no—
240D4×C11—21no—
241D4×C11—21no—
242D4×C11—21no—
243D4×C11—21no—
244D4×C11—42no—
245D4×C11—42no—
246D4×C11—42no—
247D4×C11—42no—
248D4×C11—81no—
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—21no—
257C2×C4×C11—21no—
258C2×C4×C11—41no—
259C2×C4×C11—42no—
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—81no—
267C2×C4×C11C4×D411yescharacteristic
268C2×C4×C11C4×D411yescharacteristic
269C2×C4×C11C4×D411yescharacteristic
270C2×C4×C11C23×C411yescharacteristic
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C8×C11—21no—
274C8×C11—21no—
275C8×C11—21no—
276C8×C11—21no—
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⋊C8—41no—
286C11⋊C8AGL(1,ℤ/8)12yes—
287C2×#131—221no—
288#532C2×D1111yescharacteristic
289C4×#41C2×D1111yescharacteristic
290#482Dic1111yescharacteristic
291#482Dic1111yescharacteristic
292#477Dic1111yescharacteristic
293#476Dic1111yescharacteristic
294#460Dic1111yescharacteristic
295#459Dic1111yescharacteristic
296#449Dic1111yescharacteristic
297#449Dic1111yescharacteristic
298C8×Q8—111no—
299C8×Q8—111no—
300C4×SD16C2×D1111yescharacteristic
301C4×SD16C2×D1111yescharacteristic
302C4×D8C2×D1111yescharacteristic
303C4×D8C2×D1111yescharacteristic
304#436—111no—
305#436—111no—
306#436—111no—
307#436—111no—
308#436—221no—
309#436—221no—
310#435—221no—
311#435—221no—
312C8×D4—111no—
313C8×D4—111no—
314#432—111no—
315#432—221no—
316#431—111no—
317#431C2×D1111yescharacteristic
318C2×C4⋊C8—111no—
319#408—221no—
320C4×M16—111no—
321C4×M16—221no—
322#335—111no—
323#335—111no—
324#334—111no—
325#334—111no—
326Q8⋊C8—111no—
327Q8⋊C8—111no—
328D4⋊C8—111no—
329D4⋊C8—111no—
330D4⋊C8—111no—
331D4⋊C8—111no—
332D4⋊C8—111no—
333D4⋊C8—111no—
334#322—111no—
335#322—111no—
336#322—111no—
337C82—111no—
338C22×C11—21no—
339C22×C11—21no—
340C22×C11—21no—
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×C11—41no—
350C22×C11C2×C4×D411yescharacteristic
351C4×C11—21no—
352C4×C11—22no—
353C4×C11—21no—
354C4×C11—21no—
355C4×C11—21no—
356C4×C11—41no—
357C4×C11—41no—
358C4×C11—41no—
359C4×C11—41no—
360C4×C11C2×#13111yescharacteristic
361C4×C11#56811yescharacteristic
362C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
363C4×C11#57511yescharacteristic
364C2×#41—21no—
365C2×#41C2×Dic1111yescharacteristic
366C2×SD16C2×Dic1111yescharacteristic
367C2×SD16C2×Dic1111yescharacteristic
368C2×D8C2×Dic1111yescharacteristic
369C2×D8C2×Dic1111yescharacteristic
370#131—444no—
371C2×M16—111no—
372C2×M16—111no—
373C2×M16—221no—
374C2×M16—221no—
375C2×M16—221no—
376C2×M16—221no—
377C22×C8—221no—
378C22×C8—221no—
379C22×C8—221no—
380C4⋊Q8C2×Dic1111yescharacteristic
381#127C2×Dic1111yescharacteristic
382#124—21no—
383#121—21no—
384#121C2×Dic1111yescharacteristic
385#121C2×Dic1111yescharacteristic
386C4×Q8C2×Dic1111yescharacteristic
387C4×Q8C22×D1111yescharacteristic
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4C2×Dic1111yescharacteristic
392C4×D4C22×D1111yescharacteristic
393C4×D4C22×D1111yescharacteristic
394C4×D4C22×D1111yescharacteristic
395#117—21no—
396#117C2×Dic1111yescharacteristic
397C2×C42—21no—
398C2×C42C22×D1111yescharacteristic
399#107C2×Dic1111yescharacteristic
400#107C2×Dic1111yescharacteristic
401#106C2×Dic1111yescharacteristic
402#106C2×Dic1111yescharacteristic
403C4⋊C8—111no—
404C4⋊C8—111no—
405C4⋊C8—111no—
406C4⋊C8—111no—
407C4⋊C8—221no—
408C4⋊C8—221no—
409C4⋊C8—221no—
410C4⋊C8—221no—
411C4⋊C8C2×Dic1111yescharacteristic
412C4⋊C8C2×Dic1111yescharacteristic
413#103C2×Dic1111yescharacteristic
414#103C2×Dic1111yescharacteristic
415#102C2×Dic1111yescharacteristic
416#102C2×Dic1111yescharacteristic
417#102C2×Dic1111yescharacteristic
418#102C2×Dic1111yescharacteristic
419#102C2×Dic1111yescharacteristic
420#102C2×Dic1111yescharacteristic
421C22⋊C8—221no—
422C22⋊C8—221no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425C22⋊C8—221no—
426C22⋊C8—221no—
427C22⋊C8—221no—
428C22⋊C8—221no—
429C22⋊C8C2×Dic1111yescharacteristic
430C22⋊C8C2×Dic1111yescharacteristic
431#97—111no—
432#97—111no—
433#97—221no—
434C4×C8—111no—
435C4×C8—111no—
436C4×C8—111no—
437C4×C8—111no—
438C4×C8—221no—
439C4×C8—221no—
440C4×C8C22×D1111yescharacteristic
441C4×C8C22×D1111yescharacteristic
442C2×C11—41no—
443C2×C11—81no—
444C2×C11—81no—
445C2×C11—81no—
446C2×C11#293311yescharacteristic
447C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
448C2×C11#295711yescharacteristic
449#41—22no—
450#41—41no—
451#41—42no—
452#41—42no—
453C2×Q8—21no—
454C2×Q8C22×Dic1111yescharacteristic
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4C22×Dic1111yescharacteristic
461C2×D4C22×Dic1111yescharacteristic
462C2×D4C22×Dic1111yescharacteristic
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4D4×D1111yescharacteristic
469C22×C4#434111yescharacteristic
470C22×C4C22×Dic1111yescharacteristic
471SD16—22no—
472SD16—22no—
473D8—41no—
474D8—41no—
475M16—222no—
476M16—442no—
477M16—442no—
478M16—441no—
479M16—442no—
480M16—442no—
481C2×C8—111no—
482C2×C8—111no—
483C2×C8—111no—
484C2×C8—111no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8—442no—
492C2×C8—442no—
493C2×C8—442no—
494C2×C8C22×Dic1111yescharacteristic
495C2×C8C22×Dic1111yescharacteristic
496C2×C8C22×Dic1111yescharacteristic
497C2×C8C22×Dic1111yescharacteristic
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—
512C42—21no—
513C42—21no—
514C42—21no—
515C42D4×D1111yescharacteristic
516C42#434111yescharacteristic
517C42C22×Dic1111yescharacteristic
518C42C23×D1111yescharacteristic
519C11#1801111yescharacteristic, complemented, Sylow
520C23—21no—
521C23—21no—
522C23—21no—
523C23D4×Dic1111yescharacteristic
524Q8—21no—
525Q8—42no—
526Q8#6700112yescomplemented
527D4—21no—
528D4—21no—
529D4—21no—
530D4—21no—
531D4—21no—
532D4—21no—
533D4—42no—
534D4—42no—
535D4—42no—
536D4—42no—
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—42no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—81no—
556C2×C4D4×Dic1111yescharacteristic
557C2×C4D4×Dic1111yescharacteristic
558C2×C4D4×Dic1111yescharacteristic
559C2×C4C2×D4×D1111yescharacteristic
560C2×C4C2×#434111yescharacteristic
561C2×C4C23×Dic1111yescharacteristic
562C8—21no—
563C8—21no—
564C8—21no—
565C8—21no—
566C8—112no—
567C8—221no—
568C8—221no—
569C8—221no—
570C8—441no—
571C8—441no—
572C8—441no—
573C8—441no—
574C8—441no—
575C8—441no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22C2×D4×Dic1111yescharacteristic
589C4—21no—
590C4—21no—
591C4—21no—
592C4—22no—
593C4—21no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4D11×AGL(1,ℤ/8)11yescharacteristic
599C4#1062330411yescharacteristic
600C4C2×#6700111yescharacteristic
601C4#1062335011yescharacteristic
602C2—41no—
603C2—81no—
604C2—81no—
605C2—81no—
606C2#1307734311yescharacteristic
607C2AGL(1,ℤ/8)×Dic1111yescharacteristic
608C2#1307753311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
Fitting, prime radicalC11×#3106C2
socleC22×C11C2×C4×D4
cosocleC42×C11C24
hypercenter#3106D11
hypocenterC11#18011
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3106

Complements

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

NH ≅ G/Ntype
1. #13077636C2semidirect
2. #13077360C2semidirect
3. #13067530C2semidirect
4. #13067501C2semidirect
5. #13067495C2semidirect
6. #13067481C2semidirect
7. #13067460C2semidirect
8. #13067446C2semidirect
9. SD16⋊(C11⋊C8)C2semidirect
10. SD16×C11⋊C8C2semidirect
11. #13067401C2semidirect
12. #13067085C2semidirect
13. #13067003C2semidirect
14. #13066911C2semidirect
237. Q8×C11#131semidirect
519. C11#18011semidirect
526. Q8#67001semidirect

Maximal subgroups

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

subgroupindex
#130776362
#130773602
#130675302
#130675012
#130674952
#130674812
#130674602
#130674462
SD16⋊(C11⋊C8)2
SD16×C11⋊C82
#130674012
#130670852
#130670032
#130669112
C11×#31062
#1801111