Finite Group Databasebeta

← #14743236

Subgroups — #14743236

Order 2816.

756 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081511C211yesmaximal, characteristic, complemented
2#13080442C211yesmaximal, characteristic, complemented
3D4×#4323C211yesmaximal, characteristic
4#13068243C211yesmaximal, characteristic, complemented
5#13068098C211yesmaximal, characteristic, complemented
6#13068025C211yesmaximal, characteristic, complemented
7#13067989C211yesmaximal, characteristic, complemented
8#13067954C211yesmaximal, characteristic, complemented
9#13067793C211yesmaximal, characteristic, complemented
10#13067732C211yesmaximal, characteristic, complemented
11#13067719C211yesmaximal, characteristic, complemented
12#13067687C211yesmaximal, characteristic, complemented
13#13067453C211yesmaximal, characteristic, complemented
14#13067438C211yesmaximal, characteristic, complemented
15D4×C11×SD16C211yesmaximal, characteristic, complemented
16C22×C11×SD16—21no—
17D4×Q8×C11C2211yescharacteristic, complemented
18D42×C11C2211yescharacteristic
19C22×#4323—21no—
20#10623110C2211yescharacteristic, complemented
21D4×D44C2211yescharacteristic
22C11×#492C2211yescharacteristic, complemented
23C11×#465—21no—
24C11×#461C2211yescharacteristic
25C11×#460C2211yescharacteristic, complemented
26C11×#450—21no—
27C11×#448—21no—
28C4×C11×SD16C2211yescharacteristic
29C8×D4×C11C2211yescharacteristic, complemented
30#10622830—21no—
31#10622782—21no—
32#10622701C2211yescharacteristic, complemented
33#10622700C2211yescharacteristic, complemented
34#10622697—21no—
35#10622693—21no—
36#10622692C2211yescharacteristic, complemented
37#10622689C2211yescharacteristic, complemented
38#10622686C2211yescharacteristic
39#10622685C2211yescharacteristic
40#10622651—21no—
41#10622649—21no—
42#10622640C2211yescharacteristic, complemented
43#10622637C2211yescharacteristic, complemented
44#10622628C2211yescharacteristic
45#10622627—21no—
46C4×#4323C2211yescharacteristic
47D4×C11⋊C8C2211yescharacteristic
48#10622622—21no—
49#10622621C2211yescharacteristic
50#10622621C2211yescharacteristic, complemented
51#10622476—21no—
52#10622420—21no—
53D11×#102—21no—
54#10622307C2211yescharacteristic, complemented
55C8×D44C2211yescharacteristic, complemented
56#10622185C2211yescharacteristic, complemented
57#10622182C2211yescharacteristic, complemented
58Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
59D4⋊(C11⋊C8)C2211yescharacteristic
60D4⋊(C11⋊C8)C2211yescharacteristic, complemented
61#10622123C2211yescharacteristic, complemented
62#10622121C2211yescharacteristic, complemented
63#10622119C2211yescharacteristic, complemented
64#10622118C2211yescharacteristic, complemented
65#10622095C2211yescharacteristic, complemented
66#10622092C2211yescharacteristic, complemented
67C22×Q8×C11—21no—
68C22×D4×C11—21no—
69C22×D4×C11—21no—
70C2×D4×D11—21no—
71C22×D44—21no—
72C2×C11×SD16—21no—
73C2×C11×SD16—21no—
74C2×C11×SD16—21no—
75C2×C11×SD16—21no—
76C2×C11×SD16—44no—
77C2×C11×SD16D411yescharacteristic
78C22×C8×C11—21no—
79C11×C4⋊Q8—21no—
80C11×C4⋊Q8C2311yescharacteristic
81C11×#127C2311yescharacteristic
82C11×C22⋊Q8—21no—
83C11×C22⋊Q8—41no—
84C11×#121—21no—
85C11×#121—21no—
86C11×#120—41no—
87C4×Q8×C11C2311yescharacteristic
88C4×D4×C11—21no—
89C4×D4×C11C2311yescharacteristic
90C4×D4×C11C2311yescharacteristic
91#66999—21no—
92C2×#4325—21no—
93C2×#4324—41no—
94C2×#4323—21no—
95C2×#4323—21no—
96C2×#4323—21no—
97C2×#4323—21no—
98C2×#4323—44no—
99C2×#4323D411yescharacteristic
100#66983—21no—
101C22×C11⋊C8—21no—
102C2×C8×D11—21no—
103#66949—41no—
104#66948—21no—
105C4⋊C4×D11—21no—
106#66935—41no—
107#66927C2311yescharacteristic
108C4×D44—21no—
109C4×D44C2311yescharacteristic
110#66923—21no—
111#66922C2311yescharacteristic
112C11×#106D411yescharacteristic
113C11×C4⋊C8C2311yescharacteristic
114C11×#103—21no—
115C11×#103D411yescharacteristic
116C11×#102—21no—
117C11×#102D411yescharacteristic
118C11×C22⋊C8—21no—
119C4×C8×C11C2311yescharacteristic
120#66896—21no—
121#66896—21no—
122#66896—21no—
123#66896D411yescharacteristic
124C22⋊(C11⋊C8)—21no—
125#66885—21no—
126#66885—21no—
127(C2×D11)⋊C8—21no—
128#66873—21no—
129#66873—21no—
130#66873—21no—
131#66873—41no—
132#66873D411yescharacteristic
133#66872—21no—
134#66872—21no—
135#66872—21no—
136#66872—21no—
137#66871—21no—
138#66871D411yescharacteristic
139C4⋊(C11⋊C8)—21no—
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143#66867—21no—
144C4×C11⋊C8C2311yescharacteristic
145C4×C11⋊C8C2311yescharacteristic
146#19763—111nomaximal, Sylow
147C24×C11—41no—
148C23×D11—41no—
149C2×Q8×C11—21no—
150C2×Q8×C11—41no—
151C2×Q8×C11—42no—
152C2×Q8×C11—81no—
153C2×Q8×C11C2×D411yescharacteristic
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—41no—
158C2×D4×C11—41no—
159C2×D4×C11—42no—
160C2×D4×C11—42no—
161C2×D4×C11—81no—
162C2×D4×C11—81no—
163C2×D4×C11C2×D411yescharacteristic
164C2×D4×C11C2×D411yescharacteristic
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—41no—
168C2×C22⋊D11—41no—
169D4×D11—42no—
170D4×D11—81no—
171C2×D44—21no—
172C2×D44—21no—
173C2×D44—21no—
174C2×D44—41no—
175C2×D44—42no—
176C2×D44—81no—
177C2×D44C2×D411yescharacteristic
178C2×C4×D11—21no—
179C2×C4×D11—41no—
180C2×Dic22—21no—
181C11×SD16—22no—
182C11×SD16—42no—
183C11×SD16—42no—
184C11×SD16—42no—
185C11×SD16—81no—
186C2×C8×C11—21no—
187C2×C8×C11—42no—
188C2×C8×C11C2×D411yescharacteristic
189C2×C8×C11C2×D411yescharacteristic
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—41no—
194C11×C4⋊C4C2×D411yescharacteristic
195C11×C4⋊C4C2×D411yescharacteristic
196C11×C4⋊C4C2×D411yescharacteristic
197C11×C22⋊C4—21no—
198C11×C22⋊C4—21no—
199C11×C22⋊C4—41no—
200C11×C22⋊C4—41no—
201C42×C11—21no—
202C42×C11C2411yescharacteristic
203#4325—81no—
204#4324—82no—
205#4323—42no—
206#4323—42no—
207#4323—42no—
208#4323—81no—
209#4323SD1614yescomplemented
210(C2×D11)⋊C4—21no—
211(C2×D11)⋊C4—41no—
212(C2×D11)⋊C4—41no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11C2×D411yescharacteristic
216Dic11⋊C4—41no—
217Dic11⋊C4—41no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—42no—
223C2×C11⋊C8C2×D411yescharacteristic
224C2×C11⋊C8C2×D411yescharacteristic
225C8×D11—81no—
226#3384—111no—
227#3295—111no—
228D4×SD16D1111yescharacteristic, complemented
229D4×D8—111no—
230#1715—111no—
231#1688—111no—
232#1677—111no—
233#1671—111no—
234#1665—111no—
235#1639—111no—
236#1629—111no—
237#1627—111no—
238#1622—111no—
239#1582—111no—
240#1580—111no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—41no—
244C23×C11—82no—
245C23×C11—82no—
246C23×C11—161no—
247C22×D11—21no—
248C22×D11—41no—
249C22×D11—82no—
250C22×D11—82no—
251C22×D11—161no—
252Q8×C11—21no—
253Q8×C11—21no—
254Q8×C11—41no—
255Q8×C11—41no—
256Q8×C11—82no—
257D4×C11—21no—
258D4×C11—21no—
259D4×C11—41no—
260D4×C11—41no—
261D4×C11—41no—
262D4×C11—41no—
263D4×C11—81no—
264D4×C11—82no—
265D4×C11—82no—
266D4×C11C2×SD1612yes—
267D4×C11AGL(1,ℤ/8)12yes—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—82no—
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11H(5,𝔽2)11yescharacteristic
281C22⋊D11—82no—
282C2×Dic11—21no—
283C2×Dic11—41no—
284D44—21no—
285D44—41no—
286D44—41no—
287D44—41no—
288D44—41no—
289D44—81no—
290D44—82no—
291D44C2×SD1612yescomplemented
292C4×D11—41no—
293C4×D11—41no—
294C4×D11—161no—
295Dic22—81no—
296C8×C11—21no—
297C8×C11—21no—
298C8×C11—41no—
299C11⋊C8—21no—
300C11⋊C8—41no—
301C11⋊C8—41no—
302C11⋊C8—41no—
303C11⋊C8—41no—
304C11⋊C8C2×SD1612yescomplemented
305C22×SD16—21no—
306C22×D8—221no—
307#554—111no—
308D4×Q8C2×D1111yescharacteristic, complemented
309D42—111no—
310D42C2×D1111yescharacteristic
311#501—221no—
312#498—111no—
313#493—111no—
314#492—111no—
315#492C2×D1111yescharacteristic, complemented
316#486—111no—
317#486—111no—
318#481—221no—
319#478—221no—
320#476—111no—
321#476—111no—
322#476—221no—
323#474—111no—
324#466—221no—
325#465—21no—
326#465—221no—
327#461C2×D1111yescharacteristic
328#460—111no—
329#460C2×D1111yescharacteristic, complemented
330#459—111no—
331#459—111no—
332#450—21no—
333#450—221no—
334#448—21no—
335#447—221no—
336#447—221no—
337#446—111no—
338#442—221no—
339C4×SD16C2×D1111yescharacteristic
340C4×D8—111no—
341C8×D4—111no—
342C8×D4—111no—
343C8×D4C2×D1111yescharacteristic, complemented
344C2×#102—221no—
345#334—111no—
346#334—111no—
347#333—111no—
348#332—111no—
349#331—111no—
350#331—111no—
351Q8⋊C8—111no—
352D4⋊C8—111no—
353D4⋊C8—111no—
354D4⋊C8—111no—
355#322—111no—
356C22×C11—22no—
357C22×C11—22no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11—81no—
363C22×C11—81no—
364C22×C11—81no—
365C22×C11—164no—
366C22×C11D4211yescharacteristic
367C2×D11—22no—
368C2×D11—41no—
369C2×D11—41no—
370C2×D11—81no—
371C2×D11—81no—
372C2×D11—81no—
373C2×D11—164no—
374C4×C11—21no—
375C4×C11—41no—
376C4×C11—41no—
377C4×C11—41no—
378C4×C11—41no—
379C4×C11—81no—
380C4×C11C22×SD1611yescharacteristic
381C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
382C4×C11#57611yescharacteristic
383C4×C11#57711yescharacteristic
384Dic11—41no—
385Dic11—81no—
386C22×Q8—21no—
387C22×D4—21no—
388C22×D4—21no—
389C22×D4—221no—
390C22×D4—221no—
391C2×SD16—21no—
392C2×SD16—21no—
393C2×SD16—21no—
394C2×SD16—21no—
395C2×SD16—44no—
396C2×SD16—221no—
397C2×SD16—441no—
398C2×SD16C22⋊D1111yescharacteristic
399C2×D8—111no—
400C2×D8—221no—
401C2×D8—221no—
402C2×D8—221no—
403C2×D8—221no—
404C2×D8—444no—
405C22×C8—21no—
406C22×C8—221no—
407C22×C8—221no—
408C4⋊Q8—21no—
409C4⋊Q8—111no—
410C4⋊Q8C22×D1111yescharacteristic
411#127—111no—
412#127C22×D1111yescharacteristic
413#125—221no—
414C22⋊Q8—21no—
415C22⋊Q8—41no—
416C22⋊Q8—221no—
417C22⋊Q8—441no—
418#121—21no—
419#121—21no—
420#121—221no—
421#121—221no—
422#120—41no—
423#120—441no—
424C4×Q8C22×D1111yescharacteristic
425C4×D4—21no—
426C4×D4—111no—
427C4×D4—221no—
428C4×D4C22×D1111yescharacteristic
429C4×D4C22×D1111yescharacteristic
430C2×C4⋊C4—221no—
431#107—111no—
432#107—221no—
433#106—221no—
434#106—221no—
435#106—221no—
436#106—221no—
437#106C22⋊D1111yescharacteristic
438C4⋊C8—111no—
439C4⋊C8—111no—
440C4⋊C8—111no—
441C4⋊C8—221no—
442C4⋊C8C22×D1111yescharacteristic
443#103—21no—
444#103C22⋊D1111yescharacteristic
445#102—21no—
446#102—111no—
447#102—111no—
448#102—221no—
449#102—221no—
450#102—221no—
451#102—221no—
452#102—221no—
453#102—221no—
454#102—221no—
455#102—221no—
456#102—441no—
457#102C22⋊D1111yescharacteristic
458C22⋊C8—21no—
459C22⋊C8—221no—
460C22⋊C8—221no—
461#97—221no—
462C4×C8—111no—
463C4×C8—111no—
464C4×C8C22×D1111yescharacteristic
465C2×C11—42no—
466C2×C11—42no—
467C2×C11—161no—
468C2×C11#326411yescharacteristic
469C2×C11D4×SD1611yescharacteristic
470C2×C11#328811yescharacteristic
471D11—42no—
472D11—161no—
473C24—41no—
474C24—441no—
475C2×Q8—21no—
476C2×Q8—41no—
477C2×Q8—42no—
478C2×Q8—81no—
479C2×Q8—221no—
480C2×Q8C2×C22⋊D1111yescharacteristic
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4—42no—
487C2×D4—42no—
488C2×D4—81no—
489C2×D4—81no—
490C2×D4—111no—
491C2×D4—221no—
492C2×D4—221no—
493C2×D4—221no—
494C2×D4—441no—
495C2×D4—442no—
496C2×D4—441no—
497C2×D4—442no—
498C2×D4—881no—
499C2×D4—881no—
500C2×D4D4×D1111yescharacteristic
501C2×D4C2×C22⋊D1111yescharacteristic
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—41no—
505C22×C4—221no—
506C22×C4—441no—
507SD16—22no—
508SD16—42no—
509SD16—42no—
510SD16—42no—
511SD16—81no—
512SD16—882no—
513SD16—881no—
514D8—114no—
515D8—442no—
516D8—442no—
517D8—442no—
518D8—881no—
519C2×C8—21no—
520C2×C8—42no—
521C2×C8—111no—
522C2×C8—111no—
523C2×C8—221no—
524C2×C8—221no—
525C2×C8—221no—
526C2×C8—221no—
527C2×C8—442no—
528C2×C8—881no—
529C2×C8C2×C22⋊D1111yescharacteristic
530C2×C8C2×C22⋊D1111yescharacteristic
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—41no—
535C4⋊C4—111no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—441no—
539C4⋊C4—441no—
540C4⋊C4D4×D1111yescharacteristic
541C4⋊C4C2×C22⋊D1111yescharacteristic
542C4⋊C4C2×C22⋊D1111yescharacteristic
543C22⋊C4—21no—
544C22⋊C4—21no—
545C22⋊C4—41no—
546C22⋊C4—41no—
547C22⋊C4—221no—
548C22⋊C4—441no—
549C22⋊C4—441no—
550C42—21no—
551C42C23×D1111yescharacteristic
552C11#1976311yescharacteristic, complemented, Sylow
553C23—21no—
554C23—21no—
555C23—41no—
556C23—82no—
557C23—82no—
558C23—161no—
559C23—221no—
560C23—441no—
561C23—882no—
562C23—882no—
563C23—1761no—
564Q8—21no—
565Q8—21no—
566Q8—41no—
567Q8—41no—
568Q8—82no—
569Q8—881no—
570D4—21no—
571D4—21no—
572D4—41no—
573D4—41no—
574D4—41no—
575D4—41no—
576D4—81no—
577D4—82no—
578D4—82no—
579D4—112no—
580D4—221no—
581D4—441no—
582D4—441no—
583D4—441no—
584D4—441no—
585D4—881no—
586D4—882no—
587D4—882no—
588D4SD16×D1112yes—
589D4#6698512yes—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—82no—
600C2×C4—221no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—1761no—
605C2×C4C2×D4×D1111yescharacteristic
606C2×C4#6703711yescharacteristic
607C2×C4C22×C22⋊D1111yescharacteristic
608C8—21no—
609C8—21no—
610C8—41no—
611C8—112no—
612C8—221no—
613C8—441no—
614C8—441no—
615C8—441no—
616C8—441no—
617C22—22no—
618C22—22no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—81no—
624C22—81no—
625C22—81no—
626C22—164no—
627C22—222no—
628C22—441no—
629C22—441no—
630C22—881no—
631C22—881no—
632C22—881no—
633C22—1764no—
634C22D4×C22⋊D1111yescharacteristic
635C4—21no—
636C4—41no—
637C4—41no—
638C4—41no—
639C4—41no—
640C4—81no—
641C4—441no—
642C4—881no—
643C4C2×SD16×D1111yescharacteristic
644C4#1062329311yescharacteristic
645C4C2×#6698511yescharacteristic
646C4#1062336611yescharacteristic
647C2—42no—
648C2—42no—
649C2—161no—
650C2—442no—
651C2—1761no—
652C2#1308009211yescharacteristic
653C2SD16×C22⋊D1111yescharacteristic
654C2#1308037811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingD4×C11×SD16C2
socleC22×C11D42
prime radicalD4×#4323C2
hypercenterD4×SD16D11
hypocenterC11#19763
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ D4×SD16

Complements

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

NH ≅ G/Ntype
1. #13081511C2semidirect
2. #13080442C2semidirect
4. #13068243C2semidirect
5. #13068098C2semidirect
6. #13068025C2semidirect
7. #13067989C2semidirect
8. #13067954C2semidirect
9. #13067793C2semidirect
10. #13067732C2semidirect
11. #13067719C2semidirect
12. #13067687C2semidirect
13. #13067453C2semidirect
14. #13067438C2semidirect
15. D4×C11×SD16C2semidirect
17. D4×Q8×C11C22semidirect
20. #10623110C22semidirect
22. C11×#492C22semidirect
25. C11×#460C22semidirect
29. C8×D4×C11C22semidirect
32. #10622701C22semidirect
33. #10622700C22semidirect
36. #10622692C22semidirect
37. #10622689C22semidirect
42. #10622640C22semidirect
43. #10622637C22semidirect
50. #10622621C22semidirect
54. #10622307C22semidirect
55. C8×D44C22semidirect
56. #10622185C22semidirect
57. #10622182C22semidirect
58. Q8⋊(C11⋊C8)C22semidirect
60. D4⋊(C11⋊C8)C22semidirect
61. #10622123C22semidirect
62. #10622121C22semidirect
63. #10622119C22semidirect
64. #10622118C22semidirect
65. #10622095C22semidirect
66. #10622092C22semidirect
209. #4323SD16semidirect
228. D4×SD16D11semidirect
291. D44C2×SD16semidirect
304. C11⋊C8C2×SD16semidirect
308. D4×Q8C2×D11semidirect
315. #492C2×D11semidirect
329. #460C2×D11semidirect
343. C8×D4C2×D11semidirect
552. C11#19763semidirect

Maximal subgroups

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

subgroupindex
#130815112
#130804422
D4×#43232
#130682432
#130680982
#130680252
#130679892
#130679542
#130677932
#130677322
#130677192
#130676872
#130674532
#130674382
D4×C11×SD162
#1976311