Finite Group Databasebeta

← SD16×#4323 #14746134

Subgroups — SD16×#4323 #14746134

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
2SD16×D44C211yesmaximal, characteristic, complemented
3D4×#4323C211yesmaximal, characteristic
4#13068206C211yesmaximal, characteristic, complemented
5#13068003C211yesmaximal, characteristic, complemented
6#13067974C211yesmaximal, characteristic, complemented
7#13067957C211yesmaximal, characteristic, complemented
8#13067954C211yesmaximal, characteristic, complemented
9#13067795C211yesmaximal, characteristic, complemented
10#13067793C211yesmaximal, characteristic, complemented
11#13067719C211yesmaximal, characteristic, complemented
12#13067717C211yesmaximal, characteristic, complemented
13SD16×C11⋊C8C211yesmaximal, characteristic, complemented
14C8×#4323C211yesmaximal, characteristic, complemented
15D4×C11×SD16C211yesmaximal, characteristic, complemented
16C22×C11×SD16—21no—
17D4×Q8×C11C2211yescharacteristic, complemented
18D42×C11C2211yescharacteristic
19C22×#4323—21no—
20C2×SD16×D11—21no—
21Q8×D44C2211yescharacteristic, complemented
22D4×D44C2211yescharacteristic
23C11×#492C2211yescharacteristic, complemented
24C11×#465—21no—
25C11×#461C2211yescharacteristic
26C11×#460C2211yescharacteristic, complemented
27C11×#450—21no—
28C11×#448—21no—
29C4×C11×SD16C2211yescharacteristic
30C8×D4×C11C2211yescharacteristic, complemented
31#10622830—21no—
32#10622701C2211yescharacteristic, complemented
33#10622700—21no—
34#10622700C2211yescharacteristic, complemented
35#10622691—21no—
36#10622691C2211yescharacteristic, complemented
37#10622686C2211yescharacteristic
38#10622685C2211yescharacteristic
39#10622683C2211yescharacteristic, complemented
40#10622651—21no—
41#10622649—21no—
42#10622640C2211yescharacteristic, complemented
43Q8×C11⋊C8C2211yescharacteristic, complemented
44#10622632C2211yescharacteristic
45#10622628C2211yescharacteristic
46C4×#4323—21no—
47C4×#4323C2211yescharacteristic
48D4×C11⋊C8C2211yescharacteristic
49#10622620—21no—
50#10622620C2211yescharacteristic, complemented
51#10622477—21no—
52#10622419—21no—
53#10622389—21no—
54#10622306C2211yescharacteristic, 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#10622120C2211yescharacteristic, complemented
64#10622117C2211yescharacteristic, complemented
65#10622095C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C22×Q8×C11—21no—
68C22×D4×C11—21no—
69C22×D4×C11—21no—
70C2×Q8×D11—21no—
71C2×D4×D11—21no—
72C22×D44—21no—
73C2×C11×SD16—21no—
74C2×C11×SD16—21no—
75C2×C11×SD16—21no—
76C2×C11×SD16—21no—
77C2×C11×SD16—44no—
78C2×C11×SD16D411yescharacteristic
79C22×C8×C11—21no—
80C11×C4⋊Q8—21no—
81C11×C4⋊Q8C2311yescharacteristic
82C11×#127C2311yescharacteristic
83C11×C22⋊Q8—21no—
84C11×C22⋊Q8—41no—
85C11×#121—21no—
86C11×#121—21no—
87C11×#120—41no—
88C4×Q8×C11C2311yescharacteristic
89C4×D4×C11—21no—
90C4×D4×C11C2311yescharacteristic
91C4×D4×C11C2311yescharacteristic
92C2×#4325—21no—
93C2×#4324—21no—
94C2×#4323—21no—
95C2×#4323—21no—
96C2×#4323—21no—
97C2×#4323—21no—
98C2×#4323—44no—
99C2×#4323D411yescharacteristic
100#66983—21no—
101C22×C11⋊C8—21no—
102SD16×D11—44no—
103C2×#4314—21no—
104C2×#4314—21no—
105C2×C8×D11—21no—
106#66950—21no—
107#66950—41no—
108#66948—21no—
109#66935—41no—
110#66927C2311yescharacteristic
111C4×D44—21no—
112C4×D44C2311yescharacteristic
113#66922—21no—
114#66922C2311yescharacteristic
115C11×#106D411yescharacteristic
116C11×C4⋊C8C2311yescharacteristic
117C11×#103—21no—
118C11×#103D411yescharacteristic
119C11×#102—21no—
120C11×#102D411yescharacteristic
121C11×C22⋊C8—21no—
122C4×C8×C11C2311yescharacteristic
123#66896—21no—
124#66896—21no—
125#66896—41no—
126#66896D411yescharacteristic
127C22⋊(C11⋊C8)—21no—
128(C2×D11)⋊C8—21no—
129#66874—21no—
130#66873—21no—
131#66873—21no—
132#66873—21no—
133#66873—41no—
134#66873D411yescharacteristic
135#66871—21no—
136#66871—21no—
137#66871—21no—
138#66871—21no—
139#66871D411yescharacteristic
140C4⋊(C11⋊C8)—21no—
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4⋊(C11⋊C8)C2311yescharacteristic
144C4×C11⋊C8—21no—
145C4×C11⋊C8C2311yescharacteristic
146C4×C11⋊C8C2311yescharacteristic
147D8×SD16—111nomaximal, Sylow
148C24×C11—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×C11—41no—
159C2×D4×C11—41no—
160C2×D4×C11—42no—
161C2×D4×C11—42no—
162C2×D4×C11—81no—
163C2×D4×C11—81no—
164C2×D4×C11C2×D411yescharacteristic
165C2×D4×C11C2×D411yescharacteristic
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—41no—
169C2×C22⋊D11—41no—
170Q8×D11—42no—
171Q8×D11—81no—
172D4×D11—42no—
173D4×D11—81no—
174C2×D44—21no—
175C2×D44—21no—
176C2×D44—21no—
177C2×D44—41no—
178C2×D44—42no—
179C2×D44—81no—
180C2×D44C2×D411yescharacteristic
181C2×C4×D11—21no—
182C2×C4×D11—41no—
183C2×Dic22—21no—
184C2×Dic22—41no—
185C11×SD16—42no—
186C11×SD16—42no—
187C11×SD16—42no—
188C11×SD16—81no—
189C11×SD16D814yescomplemented
190C2×C8×C11—21no—
191C2×C8×C11—42no—
192C2×C8×C11C2×D411yescharacteristic
193C2×C8×C11C2×D411yescharacteristic
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—41no—
198C11×C4⋊C4C2×D411yescharacteristic
199C11×C4⋊C4C2×D411yescharacteristic
200C11×C4⋊C4C2×D411yescharacteristic
201C11×C22⋊C4—21no—
202C11×C22⋊C4—21no—
203C11×C22⋊C4—41no—
204C11×C22⋊C4—41no—
205C42×C11—21no—
206C42×C11C2411yescharacteristic
207#4325—42no—
208#4324—42no—
209#4323—42no—
210#4323—42no—
211#4323—42no—
212#4323—81no—
213#4323SD1614yesdirect product factor
214(C2×D11)⋊C4—21no—
215(C2×D11)⋊C4—41no—
216(C2×D11)⋊C4—41no—
217C4⋊Dic11—21no—
218C4⋊Dic11—21no—
219C4⋊Dic11—41no—
220C4⋊Dic11C2×D411yescharacteristic
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—42no—
226C2×C11⋊C8C2×D411yescharacteristic
227C2×C11⋊C8C2×D411yescharacteristic
228#4314—42no—
229#4314—81no—
230C8×D11—42no—
231Q8×D8—111no—
232D4×SD16—111no—
233D4×SD16D1111yescharacteristic, complemented
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#1627—111no—
244C8×SD16—111no—
245C8×D8—111no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—41no—
249C23×C11—82no—
250C23×C11—82no—
251C23×C11—161no—
252C22×D11—21no—
253C22×D11—41no—
254C22×D11—82no—
255C22×D11—82no—
256C22×D11—161no—
257Q8×C11—21no—
258Q8×C11—41no—
259Q8×C11—41no—
260Q8×C11—82no—
261Q8×C11C2×D812yescomplemented
262D4×C11—21no—
263D4×C11—21no—
264D4×C11—41no—
265D4×C11—41no—
266D4×C11—41no—
267D4×C11—41no—
268D4×C11—81no—
269D4×C11—82no—
270D4×C11—82no—
271D4×C11C2×D812yes—
272D4×C11C2×SD1612yescomplemented
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—82no—
283C2×C4×C11C22×D411yescharacteristic
284C2×C4×C11C22×D411yescharacteristic
285C2×C4×C11H(5,𝔽2)11yescharacteristic
286C22⋊D11—82no—
287C2×Dic11—21no—
288C2×Dic11—41no—
289D44—21no—
290D44—41no—
291D44—41no—
292D44—41no—
293D44—41no—
294D44—81no—
295D44—82no—
296D44C2×SD1612yescomplemented
297C4×D11—41no—
298C4×D11—41no—
299C4×D11—82no—
300Dic22—41no—
301Dic22—41no—
302Dic22—82no—
303C8×C11—21no—
304C8×C11—41no—
305C8×C11C2×D812yescomplemented
306C11⋊C8—21no—
307C11⋊C8—41no—
308C11⋊C8—41no—
309C11⋊C8—41no—
310C11⋊C8—41no—
311C11⋊C8C2×SD1612yescomplemented
312C22×SD16—21no—
313C22×SD16—221no—
314C22×D8—221no—
315D4×Q8—111no—
316D4×Q8C2×D1111yescharacteristic, complemented
317D42—111no—
318D42C2×D1111yescharacteristic
319#500—111no—
320#500—221no—
321#493—111no—
322#492—111no—
323#492C2×D1111yescharacteristic, complemented
324#486—111no—
325#486—111no—
326#474—111no—
327#474—111no—
328#474—221no—
329#474—221no—
330#466—221no—
331#465—21no—
332#465—221no—
333#461—111no—
334#461C2×D1111yescharacteristic
335#460—111no—
336#460C2×D1111yescharacteristic, complemented
337#459—111no—
338#459—111no—
339#450—21no—
340#450—221no—
341#448—21no—
342#448—221no—
343#447—221no—
344#447—221no—
345C8×Q8—111no—
346C4×SD16C2×D1111yescharacteristic
347C4×D8—111no—
348C4×D8—221no—
349C8×D4—111no—
350C8×D4—111no—
351C8×D4C2×D1111yescharacteristic, complemented
352#335—111no—
353#334—111no—
354#332—111no—
355#332—111no—
356#331—111no—
357#331—111no—
358Q8⋊C8—111no—
359D4⋊C8—111no—
360D4⋊C8—111no—
361D4⋊C8—111no—
362C82—111no—
363C22×C11—22no—
364C22×C11—22no—
365C22×C11—41no—
366C22×C11—41no—
367C22×C11—41no—
368C22×C11—41no—
369C22×C11—81no—
370C22×C11—81no—
371C22×C11—81no—
372C22×C11—164no—
373C22×C11D4211yescharacteristic
374C2×D11—22no—
375C2×D11—41no—
376C2×D11—41no—
377C2×D11—81no—
378C2×D11—81no—
379C2×D11—81no—
380C2×D11—164no—
381C4×C11—22no—
382C4×C11—21no—
383C4×C11—41no—
384C4×C11—41no—
385C4×C11—41no—
386C4×C11—81no—
387C4×C11C22×D811yescharacteristic
388C4×C11C22×SD1611yescharacteristic
389C4×C11#57611yescharacteristic
390C4×C11#57711yescharacteristic
391Dic11—41no—
392Dic11—81no—
393C22×Q8—21no—
394C22×Q8—221no—
395C22×D4—21no—
396C22×D4—21no—
397C22×D4—221no—
398C22×D4—221no—
399C2×SD16—21no—
400C2×SD16—21no—
401C2×SD16—21no—
402C2×SD16—21no—
403C2×SD16—44no—
404C2×SD16—221no—
405C2×SD16—221no—
406C2×SD16—221no—
407C2×SD16—221no—
408C2×SD16—444no—
409C2×SD16C22⋊D1111yescharacteristic
410C2×D8—111no—
411C2×D8—221no—
412C2×D8—221no—
413C2×D8—221no—
414C2×D8—221no—
415C2×D8—444no—
416C22×C8—21no—
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—21no—
430#121—21no—
431#121—221no—
432#121—221no—
433#120—41no—
434#120—441no—
435C4×Q8C22×D1111yescharacteristic
436C4×D4—21no—
437C4×D4—111no—
438C4×D4—221no—
439C4×D4C22×D1111yescharacteristic
440C4×D4C22×D1111yescharacteristic
441#107—111no—
442#107—221no—
443#107—221no—
444#107—221no—
445#107—221no—
446#106C22⋊D1111yescharacteristic
447C4⋊C8—111no—
448C4⋊C8—111no—
449C4⋊C8—111no—
450C4⋊C8—221no—
451C4⋊C8C22×D1111yescharacteristic
452#103—21no—
453#103—221no—
454#103C22⋊D1111yescharacteristic
455#102—21no—
456#102—111no—
457#102—111no—
458#102—221no—
459#102—221no—
460#102—221no—
461#102—221no—
462#102—221no—
463#102—441no—
464#102—441no—
465#102C22⋊D1111yescharacteristic
466C22⋊C8—21no—
467C22⋊C8—221no—
468C22⋊C8—221no—
469C4×C8—111no—
470C4×C8—111no—
471C4×C8—221no—
472C4×C8C22×D1111yescharacteristic
473C2×C11—42no—
474C2×C11—42no—
475C2×C11—161no—
476C2×C11D4×D811yescharacteristic
477C2×C11D4×SD1611yescharacteristic
478C2×C11#329011yescharacteristic
479D11—42no—
480D11—161no—
481C24—41no—
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×Q8C2×C22⋊D1111yescharacteristic
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—41no—
496C2×D4—41no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—81no—
500C2×D4—81no—
501C2×D4—111no—
502C2×D4—221no—
503C2×D4—221no—
504C2×D4—221no—
505C2×D4—441no—
506C2×D4—442no—
507C2×D4—441no—
508C2×D4—442no—
509C2×D4—881no—
510C2×D4—881no—
511C2×D4D4×D1111yescharacteristic
512C2×D4C2×C22⋊D1111yescharacteristic
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—41no—
516C22×C4—221no—
517C22×C4—441no—
518SD16—42no—
519SD16—42no—
520SD16—42no—
521SD16—81no—
522SD16—442no—
523SD16—442no—
524SD16—442no—
525SD16—881no—
526SD16#432314yesdirect product factor
527D8—114no—
528D8—442no—
529D8—442no—
530D8—442no—
531D8—881no—
532C2×C8—21no—
533C2×C8—42no—
534C2×C8—111no—
535C2×C8—111no—
536C2×C8—221no—
537C2×C8—221no—
538C2×C8—221no—
539C2×C8—221no—
540C2×C8—442no—
541C2×C8—442no—
542C2×C8C2×C22⋊D1111yescharacteristic
543C2×C8C2×C22⋊D1111yescharacteristic
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—41no—
548C4⋊C4—111no—
549C4⋊C4—221no—
550C4⋊C4—221no—
551C4⋊C4—441no—
552C4⋊C4D4×D1111yescharacteristic
553C4⋊C4C2×C22⋊D1111yescharacteristic
554C4⋊C4C2×C22⋊D1111yescharacteristic
555C22⋊C4—21no—
556C22⋊C4—21no—
557C22⋊C4—41no—
558C22⋊C4—41no—
559C22⋊C4—221no—
560C22⋊C4—441no—
561C22⋊C4—441no—
562C42—21no—
563C42C23×D1111yescharacteristic
564C11D8×SD1611yescharacteristic, complemented, Sylow
565C23—21no—
566C23—21no—
567C23—41no—
568C23—82no—
569C23—82no—
570C23—161no—
571C23—221no—
572C23—441no—
573C23—882no—
574C23—882no—
575C23—1761no—
576Q8—21no—
577Q8—41no—
578Q8—41no—
579Q8—82no—
580Q8—441no—
581Q8—441no—
582Q8—882no—
583Q8C2×#432312yescomplemented
584D4—21no—
585D4—21no—
586D4—41no—
587D4—41no—
588D4—41no—
589D4—41no—
590D4—81no—
591D4—82no—
592D4—82no—
593D4—112no—
594D4—221no—
595D4—441no—
596D4—441no—
597D4—441no—
598D4—441no—
599D4—881no—
600D4—882no—
601D4—882no—
602D4SD16×D1112yescomplemented
603D4C2×#432312yes—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—82no—
614C2×C4—221no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—882no—
619C2×C4C2×D4×D1111yescharacteristic
620C2×C4#6703711yescharacteristic
621C2×C4C22×C22⋊D1111yescharacteristic
622C8—21no—
623C8—41no—
624C8—112no—
625C8—221no—
626C8—441no—
627C8—441no—
628C8—441no—
629C8—441no—
630C8C2×#432312yescomplemented
631C22—22no—
632C22—22no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22—164no—
641C22—222no—
642C22—441no—
643C22—441no—
644C22—881no—
645C22—881no—
646C22—881no—
647C22—1764no—
648C22D4×C22⋊D1111yescharacteristic
649C4—21no—
650C4—22no—
651C4—41no—
652C4—41no—
653C4—41no—
654C4—81no—
655C4—441no—
656C4—881no—
657C4C2×SD16×D1111yescharacteristic
658C4#1062329311yescharacteristic
659C4C22×#432311yescharacteristic
660C4#1062336611yescharacteristic
661C2—42no—
662C2—42no—
663C2—161no—
664C2—442no—
665C2—1761no—
666C2D4×#432311yescharacteristic
667C2SD16×C22⋊D1111yescharacteristic
668C2#1308039611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingD4×C11×SD16C2
socleC22×C11D42
prime radicalD4×#4323C2
hypercenterD4×SD16D11
hypocenterC11D8×SD16
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. Q8×#4323C2semidirect
2. SD16×D44C2semidirect
4. #13068206C2semidirect
5. #13068003C2semidirect
6. #13067974C2semidirect
7. #13067957C2semidirect
8. #13067954C2semidirect
9. #13067795C2semidirect
10. #13067793C2semidirect
11. #13067719C2semidirect
12. #13067717C2semidirect
13. SD16×C11⋊C8C2semidirect
14. C8×#4323C2semidirect
15. D4×C11×SD16C2semidirect
17. D4×Q8×C11C22semidirect
21. Q8×D44C22semidirect
23. C11×#492C22semidirect
26. C11×#460C22semidirect
30. C8×D4×C11C22semidirect
32. #10622701C22semidirect
34. #10622700C22semidirect
36. #10622691C22semidirect
39. #10622683C22semidirect
42. #10622640C22semidirect
43. Q8×C11⋊C8C22semidirect
50. #10622620C22semidirect
54. #10622306C22semidirect
55. C8×D44C22semidirect
56. #10622185C22semidirect
57. #10622182C22semidirect
58. Q8⋊(C11⋊C8)C22semidirect
60. D4⋊(C11⋊C8)C22semidirect
61. #10622123C22semidirect
62. #10622121C22semidirect
63. #10622120C22semidirect
64. #10622117C22semidirect
65. #10622095C22semidirect
66. C8×C11⋊C8C22semidirect
189. C11×SD16D8semidirect
213. #4323SD16direct (N × H)
233. D4×SD16D11semidirect
261. Q8×C11C2×D8semidirect
272. D4×C11C2×SD16semidirect
296. D44C2×SD16semidirect
305. C8×C11C2×D8semidirect
311. C11⋊C8C2×SD16semidirect
316. D4×Q8C2×D11semidirect
323. #492C2×D11semidirect
336. #460C2×D11semidirect
351. C8×D4C2×D11semidirect
526. SD16#4323direct (N × H)
564. C11D8×SD16semidirect
583. Q8C2×#4323semidirect
602. D4SD16×D11semidirect
630. C8C2×#4323semidirect

Maximal subgroups

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

subgroupindex
Q8×#43232
SD16×D442
D4×#43232
#130682062
#130680032
#130679742
#130679572
#130679542
#130677952
#130677932
#130677192
#130677172
SD16×C11⋊C82
C8×#43232
D4×C11×SD162
D8×SD1611