Finite Group Databasebeta

← #14746133

Subgroups — #14746133

Order 2816.

798 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#4323C211yesmaximal, characteristic, complemented
2D4×#4325C211yesmaximal, characteristic, complemented
3#13080307C211yesmaximal, characteristic, complemented
4#13080288C211yesmaximal, characteristic
5#13068207C211yesmaximal, characteristic, complemented
6#13068004C211yesmaximal, characteristic, complemented
7#13067974C211yesmaximal, characteristic, complemented
8#13067960C211yesmaximal, characteristic, complemented
9#13067955C211yesmaximal, characteristic, complemented
10#13067798C211yesmaximal, characteristic, complemented
11#13067792C211yesmaximal, characteristic, complemented
12#13067721C211yesmaximal, characteristic, complemented
13#13067413C211yesmaximal, characteristic, complemented
14#13067408C211yesmaximal, characteristic, complemented
15C11×#1627C211yesmaximal, characteristic, complemented
16D4×Q8×C11C2211yescharacteristic, complemented
17C22×#4325—21no—
18C2×SD16×D11—21no—
19C2×D8×D11—21no—
20#10623248C2211yescharacteristic
21Q8×D44C2211yescharacteristic, complemented
22D4×D44C2211yescharacteristic
23C11×#486C2211yescharacteristic, complemented
24C11×#460C2211yescharacteristic, complemented
25C11×#459C2211yescharacteristic
26#10622840—21no—
27#10622783—21no—
28#10622769—21no—
29#10622700—21no—
30#10622700C2211yescharacteristic, complemented
31#10622698C2211yescharacteristic, complemented
32#10622696C2211yescharacteristic
33#10622691—21no—
34#10622691C2211yescharacteristic, complemented
35#10622689C2211yescharacteristic, complemented
36#10622686C2211yescharacteristic
37#10622661—21no—
38#10622659—21no—
39#10622640C2211yescharacteristic, complemented
40C4×#4325C2211yescharacteristic
41Q8×C11⋊C8C2211yescharacteristic, complemented
42C4×#4323—21no—
43C4×#4323C2211yescharacteristic
44D4×C11⋊C8C2211yescharacteristic, complemented
45#10622620—21no—
46#10622620C2211yescharacteristic, complemented
47#10622456C2211yescharacteristic
48#10622454C2211yescharacteristic
49#10622447C2211yescharacteristic
50#10622447C2211yescharacteristic, complemented
51#10622391—21no—
52#10622389—21no—
53#10622388—21no—
54#10622386—21no—
55#10622307C2211yescharacteristic, complemented
56C11×#332C2211yescharacteristic, complemented
57C11×Q8⋊C8C2211yescharacteristic, complemented
58C11×D4⋊C8C2211yescharacteristic, complemented
59#10622182C2211yescharacteristic, complemented
60#10622124C2211yescharacteristic, complemented
61#10622123C2211yescharacteristic, complemented
62#10622118C2211yescharacteristic, complemented
63#10622117C2211yescharacteristic, complemented
64#10622097C2211yescharacteristic
65#10622097C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C22×Q8×C11—21no—
68C2×Q8×D11—21no—
69C2×D4×D11—21no—
70C2×D4×D11—21no—
71C2×D4×D11—21no—
72C22×D44—21no—
73C2×C11×SD16—21no—
74C2×C11×D8—21no—
75C11×C4⋊Q8—21no—
76C11×C4⋊Q8C2311yescharacteristic
77C11×#127C2311yescharacteristic
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—41no—
80C4×Q8×C11C2311yescharacteristic
81C4×D4×C11—21no—
82C4×D4×C11C2311yescharacteristic
83C2×#4325—21no—
84C2×#4325—21no—
85C2×#4325—21no—
86C2×#4325—21no—
87C2×#4325—44no—
88C2×#4325D411yescharacteristic
89#66991—21no—
90#66991—21no—
91#66990—41no—
92C2×#4324—21no—
93C2×#4324—21no—
94C2×#4323—21no—
95C2×#4323—21no—
96C2×#4323D411yescharacteristic
97#66983—21no—
98C22×C11⋊C8—21no—
99SD16×D11—44no—
100D8×D11—44no—
101C2×D88—21no—
102C2×#4314—21no—
103C2×C8×D11—21no—
104C2×C8×D11—21no—
105#66950—21no—
106#66950—41no—
107#66948—21no—
108#66935—41no—
109#66927C2311yescharacteristic
110C4×D44—21no—
111C4×D44C2311yescharacteristic
112C4×D44C2311yescharacteristic
113#66922—21no—
114#66922C2311yescharacteristic
115C11×C4⋊C8C2311yescharacteristic
116C11×C4⋊C8C2311yescharacteristic
117C11×#102—21no—
118C11×#102—21no—
119C11×#102—41no—
120C4×C8×C11C2311yescharacteristic
121#66899—21no—
122#66899D411yescharacteristic
123#66896—21no—
124#66896D411yescharacteristic
125C22⋊(C11⋊C8)—21no—
126#66885—21no—
127#66885—41no—
128(C2×D11)⋊C8—21no—
129(C2×D11)⋊C8—21no—
130#66880—21no—
131#66873—21no—
132#66873—21no—
133#66873D411yescharacteristic
134#66873D411yescharacteristic
135#66872D411yescharacteristic
136#66871—21no—
137#66871—21no—
138#66871—21no—
139#66871—21no—
140#66871D411yescharacteristic
141C4⋊(C11⋊C8)—21no—
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4⋊(C11⋊C8)C2311yescharacteristic
144C4×C11⋊C8—21no—
145C4×C11⋊C8C2311yescharacteristic
146C4×C11⋊C8C2311yescharacteristic
147D8×SD16—111nomaximal, Sylow
148C23×D11—41no—
149C23×D11—41no—
150C2×Q8×C11—21no—
151C2×Q8×C11—41no—
152C2×Q8×C11—42no—
153C2×Q8×C11—81no—
154C2×Q8×C11C2×D411yescharacteristic
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11C2×D411yescharacteristic
159C22×C4×C11—21no—
160C22×C4×C11—41no—
161C2×C22⋊D11—41no—
162C2×C22⋊D11—41no—
163C2×C22⋊D11—41no—
164Q8×D11—42no—
165Q8×D11—81no—
166D4×D11—42no—
167D4×D11—42no—
168D4×D11—42no—
169D4×D11—81no—
170D4×D11—81no—
171D4×D11—81no—
172C2×D44—21no—
173C2×D44—21no—
174C2×D44—21no—
175C2×D44—41no—
176C2×D44—42no—
177C2×D44—81no—
178C2×D44C2×D411yescharacteristic
179C2×D44C2×D411yescharacteristic
180C2×C4×D11—21no—
181C2×C4×D11—21no—
182C2×C4×D11—41no—
183C2×Dic22—21no—
184C2×Dic22—41no—
185C11×SD16—42no—
186C11×D8—42no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
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×C22⋊C4—21no—
197C11×C22⋊C4—41no—
198C42×C11—21no—
199C42×C11C2411yescharacteristic
200C22⋊Dic11—41no—
201#4325—42no—
202#4325—42no—
203#4325—42no—
204#4325—81no—
205#4325D814yescomplemented
206#4324—42no—
207#4324—81no—
208#4323—42no—
209#4323—81no—
210#4323SD1614yescomplemented
211(C2×D11)⋊C4—21no—
212(C2×D11)⋊C4—21no—
213(C2×D11)⋊C4—41no—
214(C2×D11)⋊C4—41no—
215C4⋊Dic11—21no—
216C4⋊Dic11—21no—
217C4⋊Dic11—41no—
218C4⋊Dic11C2×D411yescharacteristic
219C4⋊Dic11C2×D411yescharacteristic
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—42no—
223C2×C11⋊C8C2×D411yescharacteristic
224C2×C11⋊C8C2×D411yescharacteristic
225C2×C11⋊C8C2×D411yescharacteristic
226C2×C11⋊C8C2×D411yescharacteristic
227D88—42no—
228#4314—42no—
229C8×D11—42no—
230C8×D11—42no—
231Q8×D8—111no—
232D4×SD16—111no—
233D4×SD16—111no—
234D4×D8—111no—
235#1706—111no—
236#1673—111no—
237#1668—111no—
238#1665—111no—
239#1665—111no—
240#1639—111no—
241#1639—111no—
242#1627—111no—
243#1627D1111yescharacteristic, complemented
244C8×SD16—111no—
245C8×D8—111no—
246C23×C11—21no—
247C23×C11—41no—
248C22×D11—21no—
249C22×D11—21no—
250C22×D11—41no—
251C22×D11—82no—
252C22×D11—82no—
253C22×D11—82no—
254C22×D11—82no—
255C22×D11—161no—
256C22×D11—161no—
257Q8×C11—21no—
258Q8×C11—41no—
259Q8×C11—41no—
260Q8×C11—82no—
261Q8×C11C2×D812yescomplemented
262D4×C11—21no—
263D4×C11—41no—
264D4×C11—41no—
265D4×C11—41no—
266D4×C11—41no—
267D4×C11—81no—
268D4×C11C2×SD1612yescomplemented
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—82no—
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C22×D411yescharacteristic
278C2×C4×C11H(5,𝔽2)11yescharacteristic
279C22⋊D11—82no—
280C22⋊D11—82no—
281C22⋊D11—82no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—41no—
285D44—21no—
286D44—21no—
287D44—41no—
288D44—41no—
289D44—41no—
290D44—41no—
291D44—81no—
292D44—82no—
293D44C2×D812yes—
294D44C2×SD1612yescomplemented
295C4×D11—41no—
296C4×D11—41no—
297C4×D11—41no—
298C4×D11—41no—
299C4×D11—82no—
300Dic22—41no—
301Dic22—41no—
302Dic22—82no—
303C8×C11—41no—
304C8×C11—41no—
305C8×C11—41no—
306C11⋊C8—21no—
307C11⋊C8—21no—
308C11⋊C8—41no—
309C11⋊C8—41no—
310C11⋊C8C2×D812yescomplemented
311C11⋊C8C2×SD1612yescomplemented
312C22×SD16—221no—
313C22×SD16—221no—
314C22×D8—221no—
315D4×Q8—111no—
316D4×Q8C2×D1111yescharacteristic, complemented
317D42—111no—
318D42—111no—
319#500—111no—
320#500—221no—
321#493—111no—
322#492—111no—
323#492—111no—
324#486—111no—
325#486C2×D1111yescharacteristic, complemented
326#474—111no—
327#474—111no—
328#474—221no—
329#474—221no—
330#466—221no—
331#465—221no—
332#465—221no—
333#461—111no—
334#461—111no—
335#460—111no—
336#460C2×D1111yescharacteristic, complemented
337#459—111no—
338#459C2×D1111yescharacteristic
339#450—221no—
340#450—221no—
341#448—221no—
342#448—221no—
343#447—221no—
344#447—221no—
345C8×Q8—111no—
346C4×SD16—111no—
347C4×D8—111no—
348C4×D8—221no—
349C8×D4—111no—
350C8×D4—111no—
351C8×D4—111no—
352#335—111no—
353#334—111no—
354#332—111no—
355#332C2×D1111yescharacteristic, complemented
356#331—111no—
357#331—111no—
358Q8⋊C8C2×D1111yescharacteristic, complemented
359D4⋊C8—111no—
360D4⋊C8—111no—
361D4⋊C8C2×D1111yescharacteristic, complemented
362C82—111no—
363C22×C11—22no—
364C22×C11—41no—
365C22×C11—41no—
366C22×C11—81no—
367C22×C11—81no—
368C22×C11—81no—
369C22×C11D4211yescharacteristic
370C2×D11—22no—
371C2×D11—22no—
372C2×D11—41no—
373C2×D11—41no—
374C2×D11—41no—
375C2×D11—41no—
376C2×D11—81no—
377C2×D11—81no—
378C2×D11—81no—
379C2×D11—164no—
380C2×D11—164no—
381C4×C11—22no—
382C4×C11—21no—
383C4×C11—41no—
384C4×C11—41no—
385C4×C11—81no—
386C4×C11C22×D811yescharacteristic
387C4×C11C22×SD1611yescharacteristic
388C4×C11#57611yescharacteristic
389C4×C11#57711yescharacteristic
390Dic11—41no—
391Dic11—41no—
392Dic11—81no—
393C22×Q8—21no—
394C22×Q8—221no—
395C22×D4—221no—
396C22×D4—221no—
397C22×D4—221no—
398C22×D4—221no—
399C2×SD16—21no—
400C2×SD16—111no—
401C2×SD16—221no—
402C2×SD16—221no—
403C2×SD16—221no—
404C2×SD16—221no—
405C2×SD16—221no—
406C2×SD16—221no—
407C2×SD16—221no—
408C2×SD16—444no—
409C2×SD16—444no—
410C2×D8—21no—
411C2×D8—111no—
412C2×D8—221no—
413C2×D8—221no—
414C2×D8—221no—
415C2×D8—444no—
416C22×C8—221no—
417C22×C8—221no—
418C22×C8—221no—
419C4⋊Q8—21no—
420C4⋊Q8—111no—
421C4⋊Q8—221no—
422C4⋊Q8C22×D1111yescharacteristic
423#127—111no—
424#127C22×D1111yescharacteristic
425C22⋊Q8—21no—
426C22⋊Q8—41no—
427C22⋊Q8—221no—
428C22⋊Q8—441no—
429#121—221no—
430#121—221no—
431#121—221no—
432#121—221no—
433#120—441no—
434#120—441no—
435C4×Q8C22×D1111yescharacteristic
436C4×D4—21no—
437C4×D4—111no—
438C4×D4—111no—
439C4×D4—221no—
440C4×D4C22×D1111yescharacteristic
441#107—111no—
442#107—221no—
443#107—221no—
444#107—221no—
445#107—221no—
446#106—111no—
447C4⋊C8—111no—
448C4⋊C8—111no—
449C4⋊C8—221no—
450C4⋊C8C22×D1111yescharacteristic
451C4⋊C8C22×D1111yescharacteristic
452#103—111no—
453#103—221no—
454#103—221no—
455#102—21no—
456#102—21no—
457#102—41no—
458#102—111no—
459#102—111no—
460#102—111no—
461#102—221no—
462#102—221no—
463#102—221no—
464#102—221no—
465#102—441no—
466C22⋊C8—221no—
467C22⋊C8—221no—
468C22⋊C8—221no—
469C4×C8—111no—
470C4×C8—111no—
471C4×C8—221no—
472C4×C8C22×D1111yescharacteristic
473C2×C11—42no—
474C2×C11—161no—
475C2×C11D4×D811yescharacteristic
476C2×C11D4×SD1611yescharacteristic
477C2×C11#329011yescharacteristic
478D11—42no—
479D11—42no—
480D11—161no—
481C24—441no—
482C24—441no—
483C2×Q8—21no—
484C2×Q8—41no—
485C2×Q8—42no—
486C2×Q8—81no—
487C2×Q8—221no—
488C2×Q8—441no—
489C2×Q8—442no—
490C2×Q8—881no—
491C2×Q8D4×D1111yescharacteristic
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—111no—
496C2×D4—111no—
497C2×D4—221no—
498C2×D4—221no—
499C2×D4—221no—
500C2×D4—441no—
501C2×D4—442no—
502C2×D4—441no—
503C2×D4—441no—
504C2×D4—441no—
505C2×D4—442no—
506C2×D4—442no—
507C2×D4—442no—
508C2×D4—881no—
509C2×D4—881no—
510C2×D4—881no—
511C2×D4—881no—
512C2×D4D4×D1111yescharacteristic
513C22×C4—21no—
514C22×C4—41no—
515C22×C4—221no—
516C22×C4—221no—
517C22×C4—441no—
518SD16—42no—
519SD16—114no—
520SD16—442no—
521SD16—442no—
522SD16—442no—
523SD16—442no—
524SD16—442no—
525SD16—881no—
526SD16—881no—
527D8—42no—
528D8—114no—
529D8—442no—
530D8—442no—
531D8—881no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—111no—
536C2×C8—111no—
537C2×C8—111no—
538C2×C8—111no—
539C2×C8—221no—
540C2×C8—221no—
541C2×C8—442no—
542C2×C8—442no—
543C2×C8—442no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—41no—
548C4⋊C4—111no—
549C4⋊C4—111no—
550C4⋊C4—221no—
551C4⋊C4—221no—
552C4⋊C4—441no—
553C4⋊C4D4×D1111yescharacteristic
554C4⋊C4D4×D1111yescharacteristic
555C22⋊C4—21no—
556C22⋊C4—41no—
557C22⋊C4—221no—
558C22⋊C4—221no—
559C22⋊C4—441no—
560C22⋊C4—441no—
561C22⋊C4—441no—
562C42—21no—
563C42C23×D1111yescharacteristic
564C11D8×SD1611yescharacteristic, complemented, Sylow
565C23—21no—
566C23—41no—
567C23—221no—
568C23—221no—
569C23—441no—
570C23—882no—
571C23—882no—
572C23—882no—
573C23—882no—
574C23—1761no—
575C23—1761no—
576Q8—21no—
577Q8—41no—
578Q8—41no—
579Q8—82no—
580Q8—441no—
581Q8—441no—
582Q8—882no—
583Q8D8×D1112yescomplemented
584D4—21no—
585D4—41no—
586D4—41no—
587D4—41no—
588D4—41no—
589D4—81no—
590D4—112no—
591D4—112no—
592D4—221no—
593D4—221no—
594D4—441no—
595D4—441no—
596D4—441no—
597D4—441no—
598D4—881no—
599D4—882no—
600D4—882no—
601D4—882no—
602D4—882no—
603D4SD16×D1112yescomplemented
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—82no—
611C2×C4—221no—
612C2×C4—221no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—882no—
619C2×C4C2×D4×D1111yescharacteristic
620C2×C4C2×D4×D1111yescharacteristic
621C2×C4#6703711yescharacteristic
622C8—41no—
623C8—41no—
624C8—41no—
625C8—112no—
626C8—112no—
627C8—221no—
628C8—221no—
629C8—441no—
630C8—441no—
631C22—22no—
632C22—41no—
633C22—41no—
634C22—81no—
635C22—81no—
636C22—81no—
637C22—222no—
638C22—222no—
639C22—441no—
640C22—441no—
641C22—441no—
642C22—441no—
643C22—881no—
644C22—881no—
645C22—881no—
646C22—1764no—
647C22—1764no—
648C22#1062312111yescharacteristic
649C4—21no—
650C4—22no—
651C4—41no—
652C4—41no—
653C4—81no—
654C4—441no—
655C4—441no—
656C4—881no—
657C4C2×D8×D1111yescharacteristic
658C4C2×SD16×D1111yescharacteristic
659C4#1062330511yescharacteristic
660C4#1062330911yescharacteristic
661C2—42no—
662C2—161no—
663C2—442no—
664C2—442no—
665C2—1761no—
666C2#1308028611yescharacteristic
667C2#1308030511yescharacteristic
668C2#1308039511yescharacteristic
subgroupG/H
centerC22#10623121
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1627C2
socleC22×C11D42
prime radical#13080288C2
hypercenter#1627D11
hypocenterC11D8×SD16
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #1627

Complements

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

NH ≅ G/Ntype
1. Q8×#4323C2semidirect
2. D4×#4325C2semidirect
3. #13080307C2semidirect
5. #13068207C2semidirect
6. #13068004C2semidirect
7. #13067974C2semidirect
8. #13067960C2semidirect
9. #13067955C2semidirect
10. #13067798C2semidirect
11. #13067792C2semidirect
12. #13067721C2semidirect
13. #13067413C2semidirect
14. #13067408C2semidirect
15. C11×#1627C2semidirect
16. D4×Q8×C11C22semidirect
21. Q8×D44C22semidirect
23. C11×#486C22semidirect
24. C11×#460C22semidirect
30. #10622700C22semidirect
31. #10622698C22semidirect
34. #10622691C22semidirect
35. #10622689C22semidirect
39. #10622640C22semidirect
41. Q8×C11⋊C8C22semidirect
44. D4×C11⋊C8C22semidirect
46. #10622620C22semidirect
50. #10622447C22semidirect
55. #10622307C22semidirect
56. C11×#332C22semidirect
57. C11×Q8⋊C8C22semidirect
58. C11×D4⋊C8C22semidirect
59. #10622182C22semidirect
60. #10622124C22semidirect
61. #10622123C22semidirect
62. #10622118C22semidirect
63. #10622117C22semidirect
65. #10622097C22semidirect
66. C8×C11⋊C8C22semidirect
205. #4325D8semidirect
210. #4323SD16semidirect
243. #1627D11semidirect
261. Q8×C11C2×D8semidirect
268. D4×C11C2×SD16semidirect
294. D44C2×SD16semidirect
310. C11⋊C8C2×D8semidirect
311. C11⋊C8C2×SD16semidirect
316. D4×Q8C2×D11semidirect
325. #486C2×D11semidirect
336. #460C2×D11semidirect
355. #332C2×D11semidirect
358. Q8⋊C8C2×D11semidirect
361. D4⋊C8C2×D11semidirect
564. C11D8×SD16semidirect
583. Q8D8×D11semidirect
603. D4SD16×D11semidirect

Maximal subgroups

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

subgroupindex
Q8×#43232
D4×#43252
#130803072
#130802882
#130682072
#130680042
#130679742
#130679602
#130679552
#130677982
#130677922
#130677212
#130674132
#130674082
C11×#16272
D8×SD1611