Finite Group Databasebeta

← SD16×C22⋊Dic11 #14769606

Subgroups — SD16×C22⋊Dic11 #14769606

Order 2816.

1614 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×Dic11C212yesmaximal, complemented
2Q8×C22⋊Dic11C211yesmaximal, characteristic, complemented
3D4×C22⋊Dic11C211yesmaximal, characteristic
4#13069472C212yesmaximal, complemented
5#13068973C212yesmaximal, complemented
6#13068952C212yesmaximal, complemented
7#13068641C211yesmaximal, characteristic, complemented
8#13068551C211yesmaximal, characteristic, complemented
9#13068547C211yesmaximal, characteristic
10C8×C22⋊Dic11C211yesmaximal, characteristic, complemented
11C23×C11×SD16C211yesmaximal, characteristic
12C23×Q8×C11C2211yescharacteristic
13C23×D4×C11C2211yescharacteristic
14C22×C11×SD16—28no—
15C22×C11×SD16C418yescomplemented
16C22×C11×SD16C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C23×C8×C11C2211yescharacteristic
21C22×C22⋊Dic11—21no—
22C2×Q8×Dic11C2212yescomplemented
23C2×D4×Dic11C2212yes—
24#10622860—21no—
25#10622843—22no—
26#10622843C2212yescomplemented
27C2×#66899C2212yescomplemented
28C2×#66899C2212yescomplemented
29#10622834C2212yes—
30#10622833—22no—
31C2×#66896C2212yes—
32C2×#66896C2212yes—
33#10622825—21no—
34#10622825C2211yescharacteristic
35#10622825C2211yescharacteristic
36C4×C22⋊Dic11—21no—
37C4×C22⋊Dic11C2211yescharacteristic
38C2×C22⋊(C11⋊C8)C2211yescharacteristic
39SD16×Dic11—28no—
40C2×#66881C2212yescomplemented
41C2×C8×Dic11C2212yescomplemented
42#10622189C2212yescomplemented
43#10622188C2212yescomplemented
44C25×C11—21no—
45C22×Q8×C11—21no—
46C22×Q8×C11—22no—
47C22×Q8×C11—24no—
48C22×Q8×C11—42no—
49C22×Q8×C11C2×C414yescomplemented
50C22×Q8×C11C2311yescharacteristic
51C22×Q8×C11C2311yescharacteristic
52C22×D4×C11—24no—
53C22×D4×C11—21no—
54C22×D4×C11—22no—
55C22×D4×C11—42no—
56C22×D4×C11C2×C414yes—
57C22×D4×C11C2311yescharacteristic
58C22×D4×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11C2311yescharacteristic
61C23×Dic11—22no—
62C2×C11×SD16—24no—
63C2×C11×SD16—24no—
64C2×C11×SD16—232no—
65C2×C11×SD16—24no—
66C2×C11×SD16C2×C414yes—
67C2×C11×SD16C2×C414yes—
68C2×C11×SD16C2×C414yescomplemented
69C2×C11×SD16C2×C414yescomplemented
70C2×C11×SD16D418yes—
71C22×C8×C11—24no—
72C22×C8×C11C2×C414yescomplemented
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—22no—
78C2×C22⋊Dic11—22no—
79C2×C22⋊Dic11—22no—
80C2×C22⋊Dic11—44no—
81C2×C22⋊Dic11D411yescharacteristic
82C2×C22⋊Dic11D411yescharacteristic
83Q8×Dic11—24no—
84Q8×Dic11—42no—
85D4×Dic11—24no—
86D4×Dic11—42no—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11C2312yes—
89C2×C4⋊Dic11C2312yes—
90C2×C4×Dic11—22no—
91C2×C4×Dic11C2312yes—
92C22×C11⋊C8C2312yes—
93#66899—24no—
94#66899—42no—
95#66896—24no—
96#66896—42no—
97C11⋊#95—21no—
98C11⋊#95—21no—
99C11⋊#95—22no—
100C11⋊#95—22no—
101C11⋊#95D412yes—
102C22⋊(C11⋊C8)—22no—
103#66881—24no—
104C8×Dic11—24no—
105C22⋊C4×SD16—111nomaximal, Sylow
106C24×C11—21no—
107C24×C11—21no—
108C24×C11—24no—
109C24×C11—44no—
110C24×C11—42no—
111C24×C11—42no—
112C24×C11—82no—
113C24×C11C2×D411yescharacteristic
114C2×Q8×C11—24no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—22no—
118C2×Q8×C11—28no—
119C2×Q8×C11—22no—
120C2×Q8×C11—22no—
121C2×Q8×C11—44no—
122C2×Q8×C11—44no—
123C2×Q8×C11—48no—
124C2×Q8×C11C22×C412yes—
125C2×Q8×C11C22×C412yes—
126C2×Q8×C11C2×D414yes—
127C2×D4×C11—28no—
128C2×D4×C11—24no—
129C2×D4×C11—22no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—44no—
135C2×D4×C11—48no—
136C2×D4×C11—44no—
137C2×D4×C11C22×C412yes—
138C2×D4×C11C22×C412yes—
139C2×D4×C11C2×D414yes—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—24no—
144C22×C4×C11—21no—
145C22×C4×C11—44no—
146C22×C4×C11C22×C412yes—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11#4112yes—
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—44no—
153C22×Dic11—44no—
154C22×Dic11—82no—
155C22×Dic11C2×D412yes—
156C22×Dic11C2×D412yes—
157C11×SD16—28no—
158C11×SD16—28no—
159C11×SD16—28no—
160C11×SD16C22⋊C4116yescomplemented
161C2×C8×C11—28no—
162C2×C8×C11—22no—
163C2×C8×C11C22×C412yes—
164C2×C8×C11C22×C412yes—
165C2×C8×C11C2×D414yes—
166C22⋊Dic11—22no—
167C22⋊Dic11—44no—
168C22⋊Dic11—44no—
169C22⋊Dic11—42no—
170C22⋊Dic11—42no—
171C22⋊Dic11—82no—
172C22⋊Dic11SD1614yesdirect product factor
173C4⋊Dic11—22no—
174C4⋊Dic11—22no—
175C4⋊Dic11—22no—
176C4⋊Dic11—22no—
177C4⋊Dic11—44no—
178C4×Dic11—22no—
179C4×Dic11—22no—
180C4×Dic11—44no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—22no—
184C23×SD16D1111yescharacteristic
185C2×C4×SD16—112no—
186Q8×C22⋊C4—111no—
187D4×C22⋊C4—111no—
188#1968—112no—
189#1880—112no—
190#1877—112no—
191#1807—111no—
192#1787—111no—
193#1786—111no—
194C8×C22⋊C4—111no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—24no—
199C23×C11—22no—
200C23×C11—48no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11—42no—
208C23×C11—48no—
209C23×C11—84no—
210C23×C11—88no—
211C23×C11—88no—
212C23×C11C4×D412yes—
213C23×C11C2×SD1612yes—
214C23×C11#13512yes—
215C23×C11C22×D411yescharacteristic
216Q8×C11—22no—
217Q8×C11—24no—
218Q8×C11—22no—
219Q8×C11—22no—
220Q8×C11—48no—
221Q8×C11—42no—
222Q8×C11C2×C22⋊C414yescomplemented
223D4×C11—22no—
224D4×C11—22no—
225D4×C11—22no—
226D4×C11—24no—
227D4×C11—48no—
228D4×C11—42no—
229D4×C11C2×C22⋊C414yes—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—22no—
237C2×C4×C11—48no—
238C2×C4×C11—42no—
239C2×C4×C11C4×D412yes—
240C2×C4×C11C23×C411yescharacteristic
241C2×C4×C11C22×D412yes—
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11H(5,𝔽2)12yes—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255C2×Dic11—88no—
256C2×Dic11C2×SD1614yescomplemented
257C8×C11—22no—
258C8×C11C2×C22⋊C414yescomplemented
259C11⋊C8—42no—
260C23×Q8C2×D1111yescharacteristic
261C23×D4C2×D1111yescharacteristic
262C22×SD16—28no—
263C22×SD16Dic1118yescomplemented
264C22×SD16C2×D1111yescharacteristic
265C22×SD16C2×D1111yescharacteristic
266C22×SD16C2×D1111yescharacteristic
267C22×SD16C2×D1111yescharacteristic
268C23×C8C2×D1111yescharacteristic
269C2×C4×Q8—112no—
270C2×C4×D4—112no—
271C22×C22⋊C4—221no—
272C4×SD16—228no—
273C2×#106—112no—
274C2×#103—112no—
275C2×#103—112no—
276C2×#102—112no—
277C2×#102—112no—
278C2×C22⋊C8—111no—
279C2×C4×C8—112no—
280#391—112no—
281#391—222no—
282#390—112no—
283#386—222no—
284#380—111no—
285#380—111no—
286#380—221no—
287#379—221no—
288C4×C22⋊C4—111no—
289C4×C22⋊C4—221no—
290#340—112no—
291#336—112no—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11—24no—
295C22×C11—24no—
296C22×C11—24no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—44no—
300C22×C11—44no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—816no—
305C22×C11—82no—
306C22×C11—82no—
307C22×C11C4×SD1614yescomplemented
308C22×C11C2×C4×D411yescharacteristic
309C22×C11D4212yes—
310C22×C11C22×SD1611yescharacteristic
311C22×C11C2×#13511yescharacteristic
312C22×C11#57712yes—
313C4×C11—22no—
314C4×C11—24no—
315C4×C11—42no—
316C4×C11C22×C22⋊C411yescharacteristic
317C4×C11#51811yescharacteristic
318C4×C11#54612yes—
319Dic11—24no—
320Dic11—42no—
321Dic11—82no—
322Dic11—82no—
323C25—21no—
324C22×Q8—21no—
325C22×Q8—22no—
326C22×Q8—24no—
327C22×Q8—42no—
328C22×Q8C2×Dic1114yescomplemented
329C22×Q8C22×D1111yescharacteristic
330C22×Q8C22×D1111yescharacteristic
331C22×D4—24no—
332C22×D4—21no—
333C22×D4—22no—
334C22×D4—42no—
335C22×D4C2×Dic1114yes—
336C22×D4C22×D1111yescharacteristic
337C22×D4C22×D1111yescharacteristic
338C23×C4—21no—
339C23×C4—222no—
340C23×C4C22×D1111yescharacteristic
341C2×SD16—24no—
342C2×SD16—24no—
343C2×SD16—232no—
344C2×SD16—24no—
345C2×SD16C2×Dic1114yes—
346C2×SD16C2×Dic1114yes—
347C2×SD16C2×Dic1114yescomplemented
348C2×SD16C2×Dic1114yescomplemented
349C2×SD16C22⋊D1118yes—
350C22×C8—24no—
351C22×C8—112no—
352C22×C8C2×Dic1114yescomplemented
353C22×C8C22×D1111yescharacteristic
354C22×C8C22×D1111yescharacteristic
355C4×Q8—224no—
356C4×Q8—442no—
357C4×D4—224no—
358C4×D4—442no—
359C2×C4⋊C4—112no—
360C2×C4⋊C4—112no—
361C2×C4⋊C4—222no—
362C2×C22⋊C4—111no—
363C2×C22⋊C4—111no—
364C2×C22⋊C4—222no—
365C2×C22⋊C4—222no—
366C2×C22⋊C4—221no—
367C2×C22⋊C4—221no—
368C2×C22⋊C4—222no—
369C2×C22⋊C4—444no—
370C2×C42—112no—
371C2×C42—222no—
372#106—224no—
373#103—224no—
374#103—442no—
375#102—224no—
376#102—442no—
377C22⋊C8—222no—
378C4×C8—224no—
379#95—112no—
380#95—222no—
381#95—222no—
382#95—221no—
383#95—221no—
384C2×C11—24no—
385C2×C11—44no—
386C2×C11—82no—
387C2×C11D4×C22⋊C411yescharacteristic
388C2×C11C2×C4×SD1611yescharacteristic
389C2×C11#294911yescharacteristic
390C2×C11D4×SD1612yes—
391C2×C11#328212yes—
392C24—21no—
393C24—21no—
394C24—24no—
395C24—44no—
396C24—42no—
397C24—42no—
398C24—82no—
399C24D4×D1111yescharacteristic
400C2×Q8—24no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—22no—
404C2×Q8—28no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—44no—
408C2×Q8—44no—
409C2×Q8—48no—
410C2×Q8C22×Dic1112yes—
411C2×Q8C22×Dic1112yes—
412C2×Q8C2×C22⋊D1114yes—
413C2×D4—28no—
414C2×D4—24no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—44no—
421C2×D4—48no—
422C2×D4—44no—
423C2×D4C22×Dic1112yes—
424C2×D4C22×Dic1112yes—
425C2×D4C2×C22⋊D1114yes—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—21no—
431C22×C4—44no—
432C22×C4—112no—
433C22×C4—112no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4—444no—
437C22×C4—444no—
438C22×C4—882no—
439C22×C4D4×D1111yescharacteristic
440C22×C4#434112yes—
441C22×C4C22×Dic1112yes—
442C22×C4C23×D1111yescharacteristic
443SD16—28no—
444SD16—28no—
445SD16—28no—
446SD16C22⋊Dic11116yesdirect product factor
447C2×C8—22no—
448C2×C8—28no—
449C2×C8—222no—
450C2×C8—222no—
451C2×C8—222no—
452C2×C8C22×Dic1112yes—
453C2×C8C22×Dic1112yes—
454C2×C8C2×C22⋊D1114yes—
455C4⋊C4—222no—
456C4⋊C4—222no—
457C4⋊C4—222no—
458C4⋊C4—222no—
459C4⋊C4—444no—
460C22⋊C4—114no—
461C22⋊C4—222no—
462C22⋊C4—444no—
463C22⋊C4—444no—
464C22⋊C4—442no—
465C22⋊C4—442no—
466C22⋊C4—882no—
467C42—222no—
468C42—222no—
469C42—444no—
470C11C22⋊C4×SD1611yescharacteristic, complemented, Sylow
471C23—22no—
472C23—22no—
473C23—22no—
474C23—24no—
475C23—22no—
476C23—48no—
477C23—41no—
478C23—41no—
479C23—42no—
480C23—48no—
481C23—41no—
482C23—41no—
483C23—42no—
484C23—42no—
485C23—84no—
486C23—88no—
487C23—88no—
488C23SD16×D1112yes—
489C23#6696912yes—
490C23D4×Dic1112yes—
491C23C2×D4×D1111yescharacteristic
492Q8—22no—
493Q8—24no—
494Q8—22no—
495Q8—22no—
496Q8—48no—
497Q8—42no—
498Q8C2×C22⋊Dic1114yescomplemented
499D4—22no—
500D4—22no—
501D4—24no—
502D4—22no—
503D4—48no—
504D4—42no—
505D4C2×C22⋊Dic1114yes—
506C2×C4—22no—
507C2×C4—24no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—48no—
514C2×C4—42no—
515C2×C4—114no—
516C2×C4—222no—
517C2×C4—222no—
518C2×C4—222no—
519C2×C4—222no—
520C2×C4—222no—
521C2×C4—442no—
522C2×C4—442no—
523C2×C4—442no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4—442no—
527C2×C4—888no—
528C2×C4D4×Dic1112yes—
529C2×C4C2×#434111yescharacteristic
530C2×C4#6703712yes—
531C2×C4C23×Dic1111yescharacteristic
532C2×C4C22×C22⋊D1112yes—
533C8—22no—
534C8—442no—
535C8C2×C22⋊Dic1114yescomplemented
536C22—24no—
537C22—22no—
538C22—22no—
539C22—24no—
540C22—24no—
541C22—44no—
542C22—42no—
543C22—42no—
544C22—44no—
545C22—42no—
546C22—42no—
547C22—42no—
548C22—816no—
549C22—82no—
550C22—82no—
551C22SD16×Dic1114yescomplemented
552C22C2×SD16×D1111yescharacteristic
553C22C2×#6696911yescharacteristic
554C22#1062329312yes—
555C22C2×D4×Dic1111yescharacteristic
556C22D4×C22⋊D1112yes—
557C4—22no—
558C4—24no—
559C4—42no—
560C4—224no—
561C4—442no—
562C4—882no—
563C4—882no—
564C4#1062332911yescharacteristic
565C4#1062333712yes—
566C4C22×C22⋊Dic1111yescharacteristic
567C2—24no—
568C2—44no—
569C2—82no—
570C2D4×C22⋊Dic1111yescharacteristic
571C2C2×SD16×Dic1111yescharacteristic
572C2#1307747611yescharacteristic
573C2SD16×C22⋊D1112yes—
574C2#1308032312yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC23×C11×SD16C2
socleC23×C11C22×D4
prime radicalC23×D4×C11C22
cosocleC22×C4×C11C24
hypercenterC23×SD16D11
hypocenterC11C22⋊C4×SD16
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×SD16

Complements

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

NH ≅ G/Ntype
1. C2×SD16×Dic11C2semidirect
2. Q8×C22⋊Dic11C2semidirect
4. #13069472C2semidirect
5. #13068973C2semidirect
6. #13068952C2semidirect
7. #13068641C2semidirect
8. #13068551C2semidirect
10. C8×C22⋊Dic11C2semidirect
15. C22×C11×SD16C4semidirect
22. C2×Q8×Dic11C22semidirect
26. #10622843C22semidirect
27. C2×#66899C22semidirect
28. C2×#66899C22semidirect
40. C2×#66881C22semidirect
41. C2×C8×Dic11C22semidirect
42. #10622189C22semidirect
43. #10622188C22semidirect
49. C22×Q8×C11C2×C4semidirect
68. C2×C11×SD16C2×C4semidirect
69. C2×C11×SD16C2×C4semidirect
72. C22×C8×C11C2×C4semidirect
160. C11×SD16C22⋊C4semidirect
172. C22⋊Dic11SD16direct (N × H)
222. Q8×C11C2×C22⋊C4semidirect
256. C2×Dic11C2×SD16semidirect
258. C8×C11C2×C22⋊C4semidirect
263. C22×SD16Dic11semidirect
307. C22×C11C4×SD16semidirect
328. C22×Q8C2×Dic11semidirect
347. C2×SD16C2×Dic11semidirect
348. C2×SD16C2×Dic11semidirect
352. C22×C8C2×Dic11semidirect
446. SD16C22⋊Dic11direct (N × H)
470. C11C22⋊C4×SD16semidirect
498. Q8C2×C22⋊Dic11semidirect
535. C8C2×C22⋊Dic11semidirect
551. C22SD16×Dic11semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×Dic112
Q8×C22⋊Dic112
D4×C22⋊Dic112
#130694722
#130689732
#130689522
#130686412
#130685512
#130685472
C8×C22⋊Dic112
C23×C11×SD162
C22⋊C4×SD1611