Finite Group Databasebeta

← #14645809

Subgroups — #14645809

Order 2816.

792 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068636C211yesmaximal, characteristic, complemented
2C4×#66896C211yesmaximal, characteristic, complemented
3#13067115C211yesmaximal, characteristic, complemented
4#13067071C211yesmaximal, characteristic, complemented
5#13067041C211yesmaximal, characteristic, complemented
6#13066998C211yesmaximal, characteristic, complemented
7C11×#3475C211yesmaximal, characteristic
8C11×#556C411yescharacteristic, complemented
9C11×#555C411yescharacteristic, complemented
10C11×#554C411yescharacteristic, complemented
11C11×#553—21no—
12C11×#552—21no—
13C11×#552—21no—
14C11×#551—22no—
15C11×#547C411yescharacteristic, complemented
16C11×#546—21no—
17C11×#533C2211yescharacteristic
18C11×#529—22no—
19C11×#529—21no—
20C11×#525—21no—
21C4×C11×#41—21no—
22C4×C11×#41C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C2×C11×#117—21no—
25C2×#66901—21no—
26C2×#66896—21no—
27C4×C4⋊Dic11C2211yescharacteristic
28#10622538C2211yescharacteristic
29#10622537C2211yescharacteristic
30C2×C4×C11⋊C8C2211yescharacteristic
31#10622176—22no—
32Q8⋊(C11⋊C8)—22no—
33Q8⋊(C11⋊C8)—21no—
34D4⋊(C11⋊C8)—21no—
35D4⋊(C11⋊C8)—21no—
36D4⋊(C11⋊C8)—21no—
37#10622170—21no—
38#10622167—21no—
39C2×C11×#41—21no—
40C2×C11×#41D411yescharacteristic
41C22×D4×C11D411yescharacteristic
42C23×C4×C11—21no—
43C11×C4⋊Q8C2×C411yescharacteristic
44C11×C4⋊Q8C2×C411yescharacteristic
45C11×#126—22no—
46C11×#126—22no—
47C11×#126—22no—
48C11×#125—22no—
49C11×#125—21no—
50C11×#125—21no—
51C11×#124—22no—
52C11×#124—21no—
53C11×#123—22no—
54C11×#123—22no—
55C11×#123—22no—
56C11×#123—22no—
57C11×C22⋊Q8—21no—
58C11×C22⋊Q8—21no—
59C11×C22⋊Q8—22no—
60C11×C22⋊Q8—21no—
61C11×C22⋊Q8—21no—
62C11×C22⋊Q8D412yes—
63C11×#121—22no—
64C11×#121—21no—
65C11×#121—21no—
66C11×#121—21no—
67C11×#120—22no—
68C4×Q8×C11—21no—
69C4×Q8×C11—21no—
70C4×Q8×C11C2×C411yescharacteristic
71C4×Q8×C11D411yescharacteristic
72C4×Q8×C11D412yes—
73C4×D4×C11—22no—
74C4×D4×C11—22no—
75C4×D4×C11—22no—
76C4×D4×C11—21no—
77C4×D4×C11—21no—
78C4×D4×C11—21no—
79C4×D4×C11—21no—
80C4×D4×C11—21no—
81C4×D4×C11C2×C411yescharacteristic
82C4×D4×C11C2×C411yescharacteristic
83C4×D4×C11C2×C411yescharacteristic
84C4×D4×C11D411yescharacteristic
85C4×D4×C11D411yescharacteristic
86C4×D4×C11D411yescharacteristic
87C11×#117—22no—
88C11×#117—22no—
89C11×#117—22no—
90C11×#117—21no—
91C11×#117—21no—
92C11×#117—21no—
93C11×#117—21no—
94C11×#117—21no—
95C11×#117D411yescharacteristic
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4D411yescharacteristic
99C2×C11×C22⋊C4—22no—
100C2×C11×C22⋊C4—21no—
101C2×C42×C11—22no—
102C2×C42×C11—21no—
103C2×C42×C11C2311yescharacteristic
104C2×C4⋊Dic11—21no—
105C2×C4×Dic11—21no—
106C2×#4318—21no—
107C22×C11⋊C8—21no—
108#66901—42no—
109#66896—24no—
110C11⋊#95—21no—
111C22⋊(C11⋊C8)—21no—
112C4⋊(C11⋊C8)—21no—
113C4⋊(C11⋊C8)—21no—
114C4⋊(C11⋊C8)—21no—
115C4×C11⋊C8—21no—
116C4×C11⋊C8—21no—
117C4×C11⋊C8—21no—
118#8438—111nomaximal, Sylow
119C24×C11—21no—
120C11×#41—21no—
121C11×#41—21no—
122C11×#41—21no—
123C11×#41—21no—
124C11×#41—42no—
125C11×#41—42no—
126C2×Q8×C11—21no—
127C2×Q8×C11C22⋊C411yescharacteristic
128C2×Q8×C11C22⋊C412yes—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—21no—
132C2×D4×C11—22no—
133C2×D4×C11—21no—
134C2×D4×C11—41no—
135C2×D4×C11C22⋊C411yescharacteristic
136C2×D4×C11C22⋊C411yescharacteristic
137C2×D4×C11C22⋊C411yescharacteristic
138C22×C4×C11—22no—
139C22×C4×C11—21no—
140C22×C4×C11—22no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—41no—
149C22×C4×C11—41no—
150C22×C4×C11—41no—
151C22×C4×C11—41no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×Dic11—41no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4C22⋊C411yescharacteristic
169C11×C4⋊C4C22⋊C411yescharacteristic
170C11×C4⋊C4C22⋊C411yescharacteristic
171C11×C4⋊C4C22⋊C411yescharacteristic
172C11×C4⋊C4C22⋊C412yes—
173C11×C22⋊C4—22no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—21no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C11×C22⋊C4—21no—
184C11×C22⋊C4—21no—
185C11×C22⋊C4—21no—
186C11×C22⋊C4—21no—
187C42×C11—22no—
188C42×C11—22no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—22no—
192C42×C11—21no—
193C42×C11C22×C411yescharacteristic
194C42×C11C2×D411yescharacteristic
195C42×C11C2×D411yescharacteristic
196C42×C11C2×D411yescharacteristic
197C4⋊Dic11—22no—
198C4⋊Dic11—41no—
199C4×Dic11—41no—
200C4×Dic11—41no—
201#4318—41no—
202#4318—41no—
203C2×C11⋊C8—22no—
204C2×C11⋊C8—41no—
205C2×C11⋊C8—41no—
206C2×C11⋊C8—41no—
207C2×C11⋊C8—41no—
208#3475D1111yescharacteristic
209#1806—111no—
210C4×#102—111no—
211#1503—111no—
212#1493—111no—
213#1486—111no—
214#1476—111no—
215C23×C11—21no—
216C23×C11—21no—
217C23×C11—21no—
218C23×C11—42no—
219C23×C11—41no—
220C23×C11—41no—
221C23×C11—81no—
222C23×C11#12011yescharacteristic
223Q8×C11—21no—
224Q8×C11—21no—
225Q8×C11—42no—
226Q8×C11—41no—
227Q8×C11—41no—
228D4×C11—21no—
229D4×C11—21no—
230D4×C11—21no—
231D4×C11—21no—
232D4×C11—21no—
233D4×C11—42no—
234D4×C11—44no—
235D4×C11—41no—
236D4×C11—41no—
237D4×C11—82no—
238D4×C11#10412yescomplemented
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—22no—
245C2×C4×C11—21no—
246C2×C4×C11—22no—
247C2×C4×C11—21no—
248C2×C4×C11—41no—
249C2×C4×C11—44no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
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×C11—41no—
264C2×C4×C11—81no—
265C2×C4×C11—82no—
266C2×C4×C11C2×C22⋊C411yescharacteristic
267C2×C4×C11C2×C22⋊C411yescharacteristic
268C2×C4×C11C2×C22⋊C411yescharacteristic
269C2×C4×C11#12011yescharacteristic
270C2×C4×C11#12011yescharacteristic
271C2×C4×C11#12011yescharacteristic
272C2×C4×C11#13511yescharacteristic
273C2×C4×C11#13511yescharacteristic
274C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
275C2×C4×C11#13711yescharacteristic
276C2×Dic11—42no—
277C2×Dic11—81no—
278C2×Dic11—81no—
279C11⋊C8—42no—
280C11⋊C8—81no—
281C11⋊C8—81no—
282#556Dic1111yescharacteristic, complemented
283#555Dic1111yescharacteristic, complemented
284#554Dic1111yescharacteristic, complemented
285#553—21no—
286#552—21no—
287#552—21no—
288#551—22no—
289#547Dic1111yescharacteristic, complemented
290#546—21no—
291#533C2×D1111yescharacteristic
292#529—22no—
293#529—21no—
294#525—21no—
295C4×#41—21no—
296C4×#41C2×D1111yescharacteristic
297C2×C4×D4C2×D1111yescharacteristic
298C2×#117—21no—
299#431—111no—
300#423—111no—
301C2×#104—221no—
302C2×#102—221no—
303C2×C4×C8—111no—
304C4×C4⋊C4—111no—
305#340—221no—
306#339—221no—
307#328—222no—
308Q8⋊C8—221no—
309Q8⋊C8—222no—
310D4⋊C8—221no—
311D4⋊C8—221no—
312D4⋊C8—221no—
313C22×C11—21no—
314C22×C11—21no—
315C22×C11—22no—
316C22×C11—41no—
317C22×C11—41no—
318C22×C11—41no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11—41no—
322C22×C11—41no—
323C22×C11—41no—
324C22×C11—82no—
325C22×C11—82no—
326C22×C11#37911yescharacteristic
327C22×C11#44911yescharacteristic
328C22×C11#45211yescharacteristic
329C4×C11—21no—
330C4×C11—21no—
331C4×C11—21no—
332C4×C11—41no—
333C4×C11—42no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11—41no—
338C4×C11—42no—
339C4×C11#41611yescharacteristic
340C4×C11#41711yescharacteristic
341C4×C11C2×#10411yescharacteristic
342C4×C11#42111yescharacteristic
343C4×C11#44911yescharacteristic
344C4×C11#45211yescharacteristic
345Dic11—82no—
346C2×#41—21no—
347C2×#41C22⋊D1111yescharacteristic
348C22×D4C22⋊D1111yescharacteristic
349C23×C4—21no—
350C2×M16—221no—
351C22×C8—221no—
352C4⋊Q8C2×Dic1111yescharacteristic
353C4⋊Q8C2×Dic1111yescharacteristic
354#126—22no—
355#126—22no—
356#126—22no—
357#125—22no—
358#125—21no—
359#125—21no—
360#124—22no—
361#124—21no—
362#123—22no—
363#123—22no—
364#123—22no—
365#123—22no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368C22⋊Q8—22no—
369C22⋊Q8—21no—
370C22⋊Q8—21no—
371C22⋊Q8C22⋊D1112yes—
372#121—22no—
373#121—21no—
374#121—21no—
375#121—21no—
376#120—22no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8C2×Dic1111yescharacteristic
380C4×Q8C22⋊D1111yescharacteristic
381C4×Q8C22⋊D1112yes—
382C4×D4—22no—
383C4×D4—22no—
384C4×D4—22no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—21no—
388C4×D4—21no—
389C4×D4—21no—
390C4×D4C2×Dic1111yescharacteristic
391C4×D4C2×Dic1111yescharacteristic
392C4×D4C2×Dic1111yescharacteristic
393C4×D4C22⋊D1111yescharacteristic
394C4×D4C22⋊D1111yescharacteristic
395C4×D4C22⋊D1111yescharacteristic
396#117—22no—
397#117—22no—
398#117—22no—
399#117—21no—
400#117—21no—
401#117—21no—
402#117—21no—
403#117—21no—
404#117C22⋊D1111yescharacteristic
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4C22⋊D1111yescharacteristic
409C2×C22⋊C4—22no—
410C2×C22⋊C4—21no—
411C2×C42—22no—
412C2×C42—21no—
413C2×C42—221no—
414C2×C42C22×D1111yescharacteristic
415C4⋊C8—221no—
416C4⋊C8—221no—
417C4⋊C8—221no—
418#104—442no—
419#102—224no—
420C22⋊C8—221no—
421C4×C8—221no—
422C4×C8—221no—
423C4×C8—221no—
424#95—221no—
425C2×C11—21no—
426C2×C11—21no—
427C2×C11—42no—
428C2×C11—81no—
429C2×C11—81no—
430C2×C11#178811yescharacteristic
431C2×C11#178911yescharacteristic
432C2×C11#179411yescharacteristic
433C24—21no—
434#41—21no—
435#41—21no—
436#41—21no—
437#41—21no—
438#41—42no—
439#41—42no—
440C2×Q8—21no—
441C2×Q8C22⋊Dic1111yescharacteristic
442C2×Q8C22⋊Dic1112yes—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—21no—
446C2×D4—22no—
447C2×D4—21no—
448C2×D4—41no—
449C2×D4C22⋊Dic1111yescharacteristic
450C2×D4C22⋊Dic1111yescharacteristic
451C2×D4C22⋊Dic1111yescharacteristic
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—441no—
467C22×C4C2×C22⋊D1111yescharacteristic
468C22×C4C2×C22⋊D1111yescharacteristic
469C22×C4C2×C22⋊D1111yescharacteristic
470M16—441no—
471M16—441no—
472C2×C8—222no—
473C2×C8—441no—
474C2×C8—441no—
475C2×C8—441no—
476C2×C8—441no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—22no—
487C4⋊C4—21no—
488C4⋊C4—22no—
489C4⋊C4—222no—
490C4⋊C4—441no—
491C4⋊C4C22⋊Dic1111yescharacteristic
492C4⋊C4C22⋊Dic1111yescharacteristic
493C4⋊C4C22⋊Dic1111yescharacteristic
494C4⋊C4C22⋊Dic1111yescharacteristic
495C4⋊C4C22⋊Dic1112yes—
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—21no—
503C22⋊C4—22no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C42—22no—
511C42—22no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—22no—
516C42—441no—
517C42—441no—
518C42C22×Dic1111yescharacteristic
519C42C2×C22⋊D1111yescharacteristic
520C42C2×C22⋊D1111yescharacteristic
521C42C2×C22⋊D1111yescharacteristic
522C11#843811yescharacteristic, complemented, Sylow
523C23—21no—
524C23—21no—
525C23—21no—
526C23—42no—
527C23—41no—
528C23—41no—
529C23—81no—
530C23#6700611yescharacteristic
531Q8—21no—
532Q8—21no—
533Q8—42no—
534Q8—41no—
535Q8—41no—
536D4—21no—
537D4—21no—
538D4—21no—
539D4—21no—
540D4—21no—
541D4—42no—
542D4—44no—
543D4—41no—
544D4—41no—
545D4—82no—
546D4#6690112yescomplemented
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—44no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—81no—
573C2×C4—82no—
574C2×C4—442no—
575C2×C4—881no—
576C2×C4—881no—
577C2×C4#6700211yescharacteristic
578C2×C4#6700311yescharacteristic
579C2×C4#6700311yescharacteristic
580C2×C4#6700411yescharacteristic
581C2×C4C2×C22⋊Dic1111yescharacteristic
582C2×C4C2×C22⋊Dic1111yescharacteristic
583C2×C4C2×C22⋊Dic1111yescharacteristic
584C2×C4#6700611yescharacteristic
585C2×C4#6700611yescharacteristic
586C2×C4#6700611yescharacteristic
587C8—442no—
588C8—881no—
589C8—881no—
590C22—21no—
591C22—21no—
592C22—22no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—82no—
602C22—82no—
603C22#1062285111yescharacteristic
604C22#1062285211yescharacteristic
605C22#1062286011yescharacteristic
606C4—21no—
607C4—21no—
608C4—21no—
609C4—41no—
610C4—41no—
611C4—41no—
612C4—41no—
613C4—42no—
614C4—41no—
615C4—42no—
616C4—882no—
617C4#1062284511yescharacteristic
618C4#1062284611yescharacteristic
619C4C2×#6690111yescharacteristic
620C4#1062284911yescharacteristic
621C4#1062285111yescharacteristic
622C4#1062285211yescharacteristic
623C2—21no—
624C2—21no—
625C2—42no—
626C2—81no—
627C2—81no—
628C2#1306855611yescharacteristic
629C2#1306856011yescharacteristic
630C2#1306858011yescharacteristic
subgroupG/H
centerC2×C4#67006
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#3475C2
socleC22×C11#379
cosocleC2×C42×C11C23
hypercenter#3475D11
hypocenterC11#8438
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3475

Complements

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

NH ≅ G/Ntype
1. #13068636C2semidirect
2. C4×#66896C2semidirect
3. #13067115C2semidirect
4. #13067071C2semidirect
5. #13067041C2semidirect
6. #13066998C2semidirect
8. C11×#556C4semidirect
9. C11×#555C4semidirect
10. C11×#554C4semidirect
15. C11×#547C4semidirect
238. D4×C11#104semidirect
282. #556Dic11semidirect
283. #555Dic11semidirect
284. #554Dic11semidirect
289. #547Dic11semidirect
522. C11#8438semidirect
546. D4#66901semidirect

Maximal subgroups

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

subgroupindex
#130686362
C4×#668962
#130671152
#130670712
#130670412
#130669982
C11×#34752
#843811