Finite Group Databasebeta

← #14724929

Subgroups — #14724929

Order 2816.

650 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#13078663C211yesmaximal, characteristic
2#13077778C211yesmaximal, characteristic, complemented
3#13067504C211yesmaximal, characteristic, complemented
4#13067499C211yesmaximal, characteristic, complemented
5#13067492C211yesmaximal, characteristic, complemented
6#13067480C211yesmaximal, characteristic, complemented
7#13067478C211yesmaximal, characteristic, complemented
8#13067473C211yesmaximal, characteristic, complemented
9C8×#4324C211yesmaximal, characteristic, complemented
10C8×#4323C211yesmaximal, characteristic, complemented
11#13067402C211yesmaximal, characteristic, complemented
12#13067074C211yesmaximal, characteristic, complemented
13C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
14#13066900C211yesmaximal, characteristic, complemented
15C11×#2974C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17#10623010C2211yescharacteristic
18C11×#436C2211yescharacteristic
19C11×#436C2211yescharacteristic
20C11×#435—21no—
21C11×#435—21no—
22C8×D4×C11C2211yescharacteristic
23C8×D4×C11C2211yescharacteristic
24C11×#432C2211yescharacteristic
25C11×#431C2211yescharacteristic
26C11×#407—21no—
27C2×C11×C22⋊C8—21no—
28#10622831C411yescharacteristic
29#10622830C411yescharacteristic
30C4×#4324C2211yescharacteristic
31C4×#4324C2211yescharacteristic
32#10622629C411yescharacteristic
33#10622629C411yescharacteristic
34C4×#4323C2211yescharacteristic
35C4×#4323C2211yescharacteristic
36#10622622C411yescharacteristic
37#10622622C411yescharacteristic
38#10622583C411yescharacteristic
39#10622581C411yescharacteristic
40#10622538C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622453—21no—
44#10622452—21no—
45#10622343—21no—
46(C22⋊D11)⋊C8—21no—
47#10622301C2211yescharacteristic, complemented
48C8×D44C2211yescharacteristic, complemented
49#10622292C2211yescharacteristic, complemented
50C8×Dic22C2211yescharacteristic, complemented
51D4⋊(C11⋊C8)C2211yescharacteristic
52D4⋊(C11⋊C8)C2211yescharacteristic
53D4⋊(C11⋊C8)C2211yescharacteristic
54D4⋊(C11⋊C8)C2211yescharacteristic
55#10622122C2211yescharacteristic, complemented
56#10622122C2211yescharacteristic, complemented
57#10622121C2211yescharacteristic, complemented
58#10622121C2211yescharacteristic, complemented
59#10622118C2211yescharacteristic, complemented
60#10622118C2211yescharacteristic, complemented
61#10622117C2211yescharacteristic, complemented
62#10622117C2211yescharacteristic, complemented
63#10622092C2211yescharacteristic, complemented
64#10622092C2211yescharacteristic, complemented
65C8×C11⋊C8C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C22×D4×C11C2×C411yescharacteristic
68C23×C4×C11—21no—
69C2×C11×M16—21no—
70C2×C11×M16—21no—
71C22×C8×C11—21no—
72C22×C8×C11—21no—
73C4×D4×C11—21no—
74C4×D4×C11—21no—
75C4×D4×C11C2×C411yescharacteristic
76C4×D4×C11C2×C411yescharacteristic
77C4×D4×C11C2311yescharacteristic
78C4×D4×C11C2311yescharacteristic
79C2×C11×C4⋊C4C2×C411yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C42×C11C2311yescharacteristic
82C2×#4324C2×C411yescharacteristic
83C2×#4324C2×C411yescharacteristic
84C2×#4323C2×C411yescharacteristic
85C2×#4323C2×C411yescharacteristic
86#66983C2×C411yescharacteristic
87#66982—21no—
88C4×C22⋊D11—21no—
89#66977C2×C411yescharacteristic
90C22×C11⋊C8—21no—
91C22×C11⋊C8—21no—
92C2×#4313—21no—
93C2×C8×D11—21no—
94#66929—21no—
95#66928C2×C411yescharacteristic
96C4×D44C2311yescharacteristic
97#66925—21no—
98#66923C2×C411yescharacteristic
99C4×Dic22C2311yescharacteristic
100C11×C4⋊C8D411yescharacteristic
101C11×C4⋊C8D411yescharacteristic
102C11×C4⋊C8C2311yescharacteristic
103C11×C4⋊C8C2311yescharacteristic
104C11×C22⋊C8—21no—
105C11×C22⋊C8—21no—
106C11×C22⋊C8—21no—
107C11×C22⋊C8—21no—
108C11×C22⋊C8—21no—
109C11×C22⋊C8D411yescharacteristic
110C11×C22⋊C8D411yescharacteristic
111C11×#97—21no—
112C4×C8×C11C2311yescharacteristic
113C4×C8×C11C2311yescharacteristic
114#66896C2×C411yescharacteristic
115#66896C2×C411yescharacteristic
116#66896C2×C411yescharacteristic
117#66896C2×C411yescharacteristic
118C22⋊(C11⋊C8)C2×C411yescharacteristic
119C22⋊(C11⋊C8)C2×C411yescharacteristic
120(C2×D11)⋊C8—21no—
121(C2×D11)⋊C8—21no—
122#66879—21no—
123Dic11⋊C8—21no—
124Dic11⋊C8—21no—
125C8×Dic11—21no—
126#66874C2×C411yescharacteristic
127#66874C2×C411yescharacteristic
128#66873C2×C411yescharacteristic
129#66873C2×C411yescharacteristic
130#66872C2×C411yescharacteristic
131#66872C2×C411yescharacteristic
132#66871C2×C411yescharacteristic
133#66871C2×C411yescharacteristic
134C4⋊(C11⋊C8)—21no—
135C4⋊(C11⋊C8)C2×C411yescharacteristic
136C4⋊(C11⋊C8)C2×C411yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4×C11⋊C8—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18014—111nomaximal, Sylow
145C24×C11—21no—
146C2×D4×C11—22no—
147C2×D4×C11—21no—
148C2×D4×C11—41no—
149C2×D4×C11C22×C411yescharacteristic
150C2×D4×C11C22×C411yescharacteristic
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—81no—
157C22×C4×C11—81no—
158C22×C4×C11C22×C411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11#4111yescharacteristic
161C2×C22⋊D11—21no—
162C2×D44C22×C411yescharacteristic
163C2×C4×D11—21no—
164C2×Dic22C22×C411yescharacteristic
165C11×M16—81no—
166C11×M16—81no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—81no—
170C2×C8×C11—81no—
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C11×C4⋊C4—21no—
176C11×C4⋊C4C22×C411yescharacteristic
177C11×C4⋊C4C22×C411yescharacteristic
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C42×C11C22×C411yescharacteristic
183C42×C11C2×D411yescharacteristic
184C42×C11#4111yescharacteristic
185C42×C11C2411yescharacteristic
186C22⋊Dic11—21no—
187#4324—22no—
188#4324—41no—
189#4323—22no—
190#4323—41no—
191(C2×D11)⋊C4—21no—
192(C2×D11)⋊C4—21no—
193(C2×D11)⋊C4—21no—
194(C2×D11)⋊C4—21no—
195C4⋊Dic11C22×C411yescharacteristic
196C4⋊Dic11C22×C411yescharacteristic
197Dic11⋊C4—21no—
198Dic11⋊C4—21no—
199Dic11⋊C4—21no—
200Dic11⋊C4—21no—
201C4×Dic11—21no—
202C2×C11⋊C8—24no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—81no—
208C2×C11⋊C8C22×C411yescharacteristic
209C2×C11⋊C8C22×C411yescharacteristic
210C2×C11⋊C8C22×C411yescharacteristic
211C2×C11⋊C8C22×C411yescharacteristic
212#4313—81no—
213C8×D11—81no—
214#3105—111no—
215#2994—111no—
216#2974D1111yescharacteristic, complemented
217#1590—111no—
218#1589—111no—
219#1588—111no—
220#1586—111no—
221#1586—111no—
222#1585—111no—
223C8×SD16—111no—
224C8×D8—111no—
225#1573—111no—
226#1494—111no—
227C2×D4⋊C8—111no—
228#1450—111no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—42no—
232C23×C11—42no—
233C23×C11—81no—
234C23×C11C4×D411yescharacteristic
235C22×D11—21no—
236D4×C11—21no—
237D4×C11—21no—
238D4×C11—21no—
239D4×C11—42no—
240D4×C11#13112yes—
241C2×C4×C11—22no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—81no—
253C2×C4×C11—81no—
254C2×C4×C11—81no—
255C2×C4×C11C4×D411yescharacteristic
256C2×C4×C11C4×D411yescharacteristic
257C2×C4×C11C4×D411yescharacteristic
258C2×C4×C11C23×C411yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C22⋊D11—42no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265D44—21no—
266D44—21no—
267C4×D11—41no—
268C4×D11—41no—
269Dic22—21no—
270Dic22—21no—
271C8×C11—21no—
272C8×C11—21no—
273C8×C11—21no—
274C8×C11—21no—
275C8×C11—41no—
276C8×C11—41no—
277C11⋊C8—22no—
278C11⋊C8—22no—
279C11⋊C8—21no—
280C11⋊C8—21no—
281C11⋊C8—21no—
282C11⋊C8—21no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285#529—111no—
286C2×C4×D4C2×D1111yescharacteristic
287#484—111no—
288#481—111no—
289#478—111no—
290#478—111no—
291#463—111no—
292#463—111no—
293#450—111no—
294#447—111no—
295#446—111no—
296C8×Q8—111no—
297C4×SD16—111no—
298C4×SD16—111no—
299C4×D8—111no—
300C4×D8—111no—
301#436—111no—
302#436C2×D1111yescharacteristic
303#436C2×D1111yescharacteristic
304#435—21no—
305#435—21no—
306#435—221no—
307C8×D4—111no—
308C8×D4—221no—
309C8×D4C2×D1111yescharacteristic
310C8×D4C2×D1111yescharacteristic
311#433—221no—
312#432C2×D1111yescharacteristic
313#431—111no—
314#431C2×D1111yescharacteristic
315#424—221no—
316C2×C4⋊C8—111no—
317#407—21no—
318C2×C22⋊C8—21no—
319C2×C4×C8—111no—
320#335—111no—
321#335—111no—
322#334—111no—
323#334—111no—
324Q8⋊C8—111no—
325Q8⋊C8—111no—
326D4⋊C8—111no—
327D4⋊C8—111no—
328D4⋊C8—111no—
329D4⋊C8—111no—
330D4⋊C8—111no—
331D4⋊C8—111no—
332#322—111no—
333#322—111no—
334C82—111no—
335C82—111no—
336C22×C11—21no—
337C22×C11—21no—
338C22×C11—22no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11—84no—
345C22×C11#44312yes—
346C22×C11C2×C4×D411yescharacteristic
347C2×D11—41no—
348C2×D11—41no—
349C2×D11—41no—
350C4×C11—21no—
351C4×C11—21no—
352C4×C11—21no—
353C4×C11—21no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11C2×#13111yescharacteristic
357C4×C11#56811yescharacteristic
358C4×C11#57611yescharacteristic
359C4×C11#57711yescharacteristic
360Dic11—41no—
361Dic11—41no—
362Dic11—41no—
363C22×D4C4×D1111yescharacteristic
364C23×C4—21no—
365C2×SD16—111no—
366C2×SD16—111no—
367C2×D8—111no—
368C2×D8—111no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—221no—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—221no—
375C22×C8—221no—
376C22×C8—221no—
377#126—221no—
378#125—111no—
379#124—111no—
380#123—221no—
381C22⋊Q8—111no—
382#121—111no—
383C4×Q8—111no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—111no—
387C4×D4—221no—
388C4×D4C4×D1111yescharacteristic
389C4×D4C4×D1111yescharacteristic
390C4×D4C22×D1111yescharacteristic
391C4×D4C22×D1111yescharacteristic
392#117—221no—
393C2×C4⋊C4C4×D1111yescharacteristic
394C2×C22⋊C4—21no—
395C2×C42C22×D1111yescharacteristic
396#107—111no—
397#107—111no—
398#106—111no—
399#106—111no—
400C4⋊C8—111no—
401C4⋊C8—111no—
402C4⋊C8—111no—
403C4⋊C8—111no—
404C4⋊C8—221no—
405C4⋊C8—221no—
406C4⋊C8—221no—
407C4⋊C8C22⋊D1111yescharacteristic
408C4⋊C8C22⋊D1111yescharacteristic
409C4⋊C8C22×D1111yescharacteristic
410C4⋊C8C22×D1111yescharacteristic
411#103—111no—
412#103—111no—
413#102—111no—
414#102—111no—
415#102—111no—
416#102—111no—
417#102—111no—
418#102—111no—
419C22⋊C8—21no—
420C22⋊C8—21no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424C22⋊C8—111no—
425C22⋊C8—111no—
426C22⋊C8—221no—
427C22⋊C8—221no—
428C22⋊C8C22⋊D1111yescharacteristic
429C22⋊C8C22⋊D1111yescharacteristic
430#97—21no—
431#97—221no—
432C4×C8—111no—
433C4×C8—111no—
434C4×C8—111no—
435C4×C8—111no—
436C4×C8—221no—
437C4×C8—221no—
438C4×C8C22×D1111yescharacteristic
439C4×C8C22×D1111yescharacteristic
440C2×C11—22no—
441C2×C11—42no—
442C2×C11—81no—
443C2×C11#293311yescharacteristic
444C2×C11#294611yescharacteristic
445C2×C11C2×#44311yescharacteristic
446D11—81no—
447C24—21no—
448C2×Q8—111no—
449C2×D4—22no—
450C2×D4—21no—
451C2×D4—41no—
452C2×D4—111no—
453C2×D4—221no—
454C2×D4C2×C4×D1111yescharacteristic
455C2×D4C2×C4×D1111yescharacteristic
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—81no—
462C22×C4—81no—
463C22×C4—221no—
464C22×C4C2×C4×D1111yescharacteristic
465C22×C4#433911yescharacteristic
466C22×C4C2×C22⋊D1111yescharacteristic
467SD16—222no—
468SD16—441no—
469D8—222no—
470D8—441no—
471M16—81no—
472M16—81no—
473M16—881no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—81no—
477C2×C8—81no—
478C2×C8—111no—
479C2×C8—111no—
480C2×C8—111no—
481C2×C8—111no—
482C2×C8—224no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—881no—
488C2×C8—881no—
489C2×C8C2×C22⋊D1111yescharacteristic
490C2×C8C2×C22⋊D1111yescharacteristic
491C2×C8C2×C22⋊D1111yescharacteristic
492C2×C8C2×C22⋊D1111yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—111no—
495C4⋊C4—111no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4C2×C4×D1111yescharacteristic
501C4⋊C4C2×C4×D1111yescharacteristic
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—221no—
507C22⋊C4—221no—
508C22⋊C4—221no—
509C22⋊C4—221no—
510C22⋊C4—221no—
511C42—221no—
512C42C2×C4×D1111yescharacteristic
513C42#433911yescharacteristic
514C42C2×C22⋊D1111yescharacteristic
515C42C23×D1111yescharacteristic
516C11#1801411yescharacteristic, complemented, Sylow
517C23—21no—
518C23—21no—
519C23—42no—
520C23—42no—
521C23—81no—
522C23—221no—
523C23C4×C22⋊D1111yescharacteristic
524Q8—221no—
525Q8—221no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—42no—
530D4—221no—
531D4—221no—
532D4—442no—
533D4#6696012yes—
534C2×C4—22no—
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—81no—
546C2×C4—81no—
547C2×C4—81no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4C4×C22⋊D1111yescharacteristic
554C2×C4C4×C22⋊D1111yescharacteristic
555C2×C4C4×C22⋊D1111yescharacteristic
556C2×C4C22×C4×D1111yescharacteristic
557C2×C4C2×#433911yescharacteristic
558C2×C4C22×C22⋊D1111yescharacteristic
559C8—21no—
560C8—21no—
561C8—21no—
562C8—21no—
563C8—41no—
564C8—41no—
565C8—222no—
566C8—222no—
567C8—221no—
568C8—221no—
569C8—221no—
570C8—221no—
571C8—441no—
572C8—441no—
573C22—21no—
574C22—21no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—84no—
582C22—441no—
583C22—441no—
584C22—441no—
585C22#1062275712yes—
586C22C2×C4×C22⋊D1111yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—441no—
594C4—441no—
595C4—441no—
596C4C2×#6696011yescharacteristic
597C4#1062327611yescharacteristic
598C4#1062336611yescharacteristic
599C4#1062336711yescharacteristic
600C2—22no—
601C2—42no—
602C2—81no—
603C2—881no—
604C2#1307734111yescharacteristic
605C2#1307744811yescharacteristic
606C2C2×#1062275711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2974C2
socleC22×C11C2×C4×D4
prime radical#10622830C4
cosocleC42×C11C24
hypercenter#2974D11
hypocenterC11#18014
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2974

Complements

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

NH ≅ G/Ntype
2. #13077778C2semidirect
3. #13067504C2semidirect
4. #13067499C2semidirect
5. #13067492C2semidirect
6. #13067480C2semidirect
7. #13067478C2semidirect
8. #13067473C2semidirect
9. C8×#4324C2semidirect
10. C8×#4323C2semidirect
11. #13067402C2semidirect
12. #13067074C2semidirect
13. C2×D4⋊(C11⋊C8)C2semidirect
14. #13066900C2semidirect
15. C11×#2974C2semidirect
47. #10622301C22semidirect
48. C8×D44C22semidirect
49. #10622292C22semidirect
50. C8×Dic22C22semidirect
55. #10622122C22semidirect
56. #10622122C22semidirect
57. #10622121C22semidirect
58. #10622121C22semidirect
59. #10622118C22semidirect
60. #10622118C22semidirect
61. #10622117C22semidirect
62. #10622117C22semidirect
63. #10622092C22semidirect
64. #10622092C22semidirect
65. C8×C11⋊C8C22semidirect
66. C8×C11⋊C8C22semidirect
216. #2974D11semidirect
516. C11#18014semidirect

Maximal subgroups

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

subgroupindex
#130786632
#130777782
#130675042
#130674992
#130674922
#130674802
#130674782
#130674732
C8×#43242
C8×#43232
#130674022
#130670742
C2×D4⋊(C11⋊C8)2
#130669002
C11×#29742
#1801411