Finite Group Databasebeta

← SD16×#6094 #15834352

Subgroups — SD16×#6094 #15834352

Order 3328.

716 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#6094C211yesmaximal, characteristic, complemented
2C4×SD16×D13C211yesmaximal, characteristic
3D4×#6094C211yesmaximal, characteristic
4#13113728C211yesmaximal, characteristic, complemented
5#13113725C211yesmaximal, characteristic, complemented
6#13113679C211yesmaximal, characteristic, complemented
7#13113676C211yesmaximal, characteristic, complemented
8#13113672C211yesmaximal, characteristic, complemented
9#13113669C211yesmaximal, characteristic, complemented
10SD16×#1055C211yesmaximal, characteristic, complemented
11#13113590C211yesmaximal, characteristic, complemented
12#13113263C211yesmaximal, characteristic, complemented
13#13113259C211yesmaximal, characteristic
14C8×#6094C211yesmaximal, characteristic, complemented
15C8×C13×SD16C211yesmaximal, characteristic, complemented
16C2×SD16×D13C411yescharacteristic
17C22×#6094—21no—
18C4×Q8×D13C2211yescharacteristic
19C4×D4×D13C2211yescharacteristic
20C8×Q8×C13C2211yescharacteristic, complemented
21C4×C13×SD16C2211yescharacteristic
22C8×D4×C13C2211yescharacteristic
23SD16×Dic13C411yescharacteristic
24#11718772—21no—
25C4×#6106C2211yescharacteristic
26Q8×#1055C2211yescharacteristic, complemented
27C4×#6105C2211yescharacteristic
28D4×#1055C2211yescharacteristic
29D13×#106C411yescharacteristic
30#11718513C411yescharacteristic
31#11718499C2211yescharacteristic
32#11718498—21no—
33#11718498C2211yescharacteristic
34#11718498C2211yescharacteristic
35#11718492—21no—
36#11718492C2211yescharacteristic, complemented
37D13×#103C411yescharacteristic
38#11718449C411yescharacteristic
39D13×#102C411yescharacteristic
40#11718419C411yescharacteristic
41#11718391—21no—
42#11718387—21no—
43C4×#6095C2211yescharacteristic
44#11718349C2211yescharacteristic
45C4×#6094—21no—
46C4×#6094C2211yescharacteristic
47#11718346C2211yescharacteristic
48C4×C8×D13C2211yescharacteristic
49#11718340—21no—
50#11718340C2211yescharacteristic, complemented
51C13×#334C2211yescharacteristic, complemented
52C13×Q8⋊C8C2211yescharacteristic, complemented
53C13×D4⋊C8C2211yescharacteristic
54C82×C13C2211yescharacteristic, complemented
55Q8⋊#1055C2211yescharacteristic, complemented
56D4⋊#1055C2211yescharacteristic
57#11718076C2211yescharacteristic, complemented
58#11718075C2211yescharacteristic
59#11718072C2211yescharacteristic, complemented
60#11718072C2211yescharacteristic, complemented
61#11718051C2211yescharacteristic
62#11718049C2211yescharacteristic, complemented
63#11718048C2211yescharacteristic, complemented
64#11718047C2211yescharacteristic, complemented
65#11718046C2211yescharacteristic, complemented
66C8×#1055C2211yescharacteristic, complemented
67C2×Q8×D13C2×C411yescharacteristic
68C2×D4×D13C2×C411yescharacteristic
69C22×C4×D13—21no—
70C2×C13×SD16C2×C411yescharacteristic
71C22×C8×C13—21no—
72C4×Q8×C13C2311yescharacteristic
73C4×D4×C13C2311yescharacteristic
74Q8×Dic13C2×C411yescharacteristic
75C2×#6106C2×C411yescharacteristic
76D4×Dic13C2×C411yescharacteristic
77C2×#6105C2×C411yescharacteristic
78C4×C22⋊D13—21no—
79C22×#1055—21no—
80SD16×D13—24no—
81C2×#6095C2×C411yescharacteristic
82C2×#6094—21no—
83C2×#6094—21no—
84C2×#6094—21no—
85C2×#6094—21no—
86C2×#6094—44no—
87C2×#6094D411yescharacteristic
88C2×#6094D411yescharacteristic
89C2×C8×D13C2×C411yescharacteristic
90C2×C8×D13C2×C411yescharacteristic
91#88147C2×C411yescharacteristic
92C4⋊C4×D13—21no—
93C4⋊C4×D13C2×C411yescharacteristic
94C4⋊C4×D13C2×C411yescharacteristic
95#88141—21no—
96#88141C2×C411yescharacteristic
97#88135—21no—
98C22⋊C4×D13—21no—
99C4×D52C2311yescharacteristic
100C42×D13—21no—
101C42×D13C2311yescharacteristic
102C4×Dic26—21no—
103C4×Dic26C2311yescharacteristic
104C13×#106C2×C411yescharacteristic
105C13×C4⋊C8—21no—
106C13×C4⋊C8C2311yescharacteristic
107C13×C4⋊C8C2311yescharacteristic
108C13×#103C2×C411yescharacteristic
109C13×#102C2×C411yescharacteristic
110C13×C22⋊C8—21no—
111C4×C8×C13—21no—
112C4×C8×C13C2311yescharacteristic
113C4×C8×C13C2311yescharacteristic
114C4×C8×C13C2311yescharacteristic
115#88075C2×C411yescharacteristic
116#88072C2×C411yescharacteristic
117C22⋊#1055—21no—
118#88061C2×C411yescharacteristic
119#88060—21no—
120#88060—21no—
121#88060—21no—
122#88057C2×C411yescharacteristic
123#88056C2×C411yescharacteristic
124#88055—21no—
125#88055—21no—
126#88055D411yescharacteristic
127#88055D411yescharacteristic
128#88054—21no—
129#88054—21no—
130#88054—21no—
131#88054—21no—
132#88054—21no—
133C8×Dic13C2×C411yescharacteristic
134C8×Dic13C2×C411yescharacteristic
135#88050C2×C411yescharacteristic
136#88049C2×C411yescharacteristic
137#88048C2×C411yescharacteristic
138#88048C2×C411yescharacteristic
139C4⋊#1055—21no—
140C4⋊#1055C2311yescharacteristic
141C4⋊#1055C2311yescharacteristic
142C4×#1055—21no—
143C4×#1055C2311yescharacteristic
144C4×#1055C2311yescharacteristic
145C4×#1055C2311yescharacteristic
146M16×SD16—131nomaximal, Sylow
147C23×D13—21no—
148C2×Q8×C13C22×C411yescharacteristic
149C2×D4×C13C22×C411yescharacteristic
150C22×C4×C13—21no—
151C2×C22⋊D13—21no—
152C22×Dic13—21no—
153Q8×D13—22no—
154Q8×D13—41no—
155D4×D13—22no—
156D4×D13—41no—
157C2×D52C22×C411yescharacteristic
158C2×C4×D13—21no—
159C2×C4×D13—21no—
160C2×C4×D13—21no—
161C2×C4×D13—21no—
162C2×C4×D13—21no—
163C2×C4×D13—42no—
164C2×C4×D13—42no—
165C2×C4×D13C22×C411yescharacteristic
166C2×C4×D13C2×D411yescharacteristic
167C2×C4×D13#4111yescharacteristic
168C2×Dic26—21no—
169C2×Dic26C22×C411yescharacteristic
170C13×SD16M1614yescomplemented
171C2×C8×C13—21no—
172C2×C8×C13—21no—
173C2×C8×C13—21no—
174C2×C8×C13—42no—
175C2×C8×C13C22×C411yescharacteristic
176C2×C8×C13C22×C411yescharacteristic
177C2×C8×C13C2×D411yescharacteristic
178C2×C8×C13C2×D411yescharacteristic
179C13×C4⋊C4—21no—
180C13×C4⋊C4C22×C411yescharacteristic
181C13×C4⋊C4C22×C411yescharacteristic
182C13×C22⋊C4—21no—
183C42×C13—21no—
184C42×C13C2411yescharacteristic
185C22⋊Dic13—21no—
186#6106—22no—
187#6105—22no—
188#6103—21no—
189#6103—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13C22×C411yescharacteristic
192C4⋊Dic13C22×C411yescharacteristic
193#6101—21no—
194#6101—21no—
195#6101—21no—
196#6101—21no—
197C4×Dic13—21no—
198C4×Dic13—21no—
199C4×Dic13—21no—
200C4×Dic13C22×C411yescharacteristic
201C4×Dic13C2×D411yescharacteristic
202C4×Dic13#4111yescharacteristic
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—42no—
207C2×#1055C22×C411yescharacteristic
208C2×#1055C22×C411yescharacteristic
209C2×#1055C2×D411yescharacteristic
210C2×#1055C2×D411yescharacteristic
211#6095—22no—
212#6094—22no—
213#6094—42no—
214#6094—42no—
215#6094—42no—
216#6094—42no—
217#6094SD1614yesdirect product factor
218C8×D13—22no—
219C8×D13—41no—
220Q8×M16—131no—
221C2×C4×SD16—131no—
222D4×M16—131no—
223#1590—131no—
224#1590—131no—
225#1583—131no—
226#1583—131no—
227#1582—131no—
228#1582—131no—
229C8×SD16—131no—
230C8×SD16D1311yescharacteristic, complemented
231#1566—131no—
232#1487—131no—
233#1486—131no—
234C8×M16—131no—
235C23×C13—21no—
236C22×D13—21no—
237C22×D13—42no—
238C22×D13—42no—
239C22×D13—81no—
240C22×D13C4×D411yescharacteristic
241Q8×C13—21no—
242Q8×C13C2×M1612yescomplemented
243D4×C13—21no—
244D4×C13C2×M1612yes—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13C23×C411yescharacteristic
251C2×C4×C13C22×D411yescharacteristic
252C2×C4×C13C2×#4111yescharacteristic
253C22⋊D13—42no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—42no—
258C2×Dic13C4×D411yescharacteristic
259C2×Dic13C4×D411yescharacteristic
260C2×Dic13C4×D411yescharacteristic
261D52—21no—
262D52—21no—
263C4×D13—21no—
264C4×D13—21no—
265C4×D13—41no—
266C4×D13—42no—
267C4×D13—42no—
268C4×D13—41no—
269C4×D13—41no—
270C4×D13—42no—
271C4×D13—81no—
272C4×D13C2×SD1612yes—
273C4×D13#13512yes—
274Dic26—21no—
275Dic26—21no—
276Dic26—42no—
277C8×C13—21no—
278C8×C13—21no—
279C8×C13—41no—
280C8×C13—41no—
281C8×C13—41no—
282C8×C13C2×M1612yescomplemented
283C8×C13C2×SD1612yescomplemented
284#1055—21no—
285#1055—21no—
286#1055—21no—
287#1055—41no—
288#1055—41no—
289#1055—41no—
290#1055C2×SD1612yescomplemented
291C22×SD16—131no—
292C22×M16—261no—
293C2×C4×Q8—131no—
294C2×C4×D4—131no—
295#446—131no—
296#446—131no—
297#446—261no—
298#446—261no—
299C8×Q8—131no—
300C8×Q8C2×D1311yescharacteristic, complemented
301C4×SD16—131no—
302C4×SD16—131no—
303C4×SD16—131no—
304C4×SD16—131no—
305C4×SD16—131no—
306C4×SD16—131no—
307C4×SD16—131no—
308C4×SD16C2×D1311yescharacteristic
309#436—131no—
310#436—131no—
311#435—261no—
312#435—261no—
313C8×D4—131no—
314C8×D4C2×D1311yescharacteristic
315#431—131no—
316C2×#106—131no—
317#423—131no—
318#423—131no—
319#423—261no—
320C2×#103—131no—
321C2×#102—131no—
322#407—261no—
323C4×M16—131no—
324C4×M16—261no—
325C2×C4×C8—131no—
326#334—131no—
327#334—131no—
328#334—131no—
329#334C2×D1311yescharacteristic, complemented
330Q8⋊C8—131no—
331Q8⋊C8—131no—
332Q8⋊C8—131no—
333Q8⋊C8C2×D1311yescharacteristic, complemented
334D4⋊C8—131no—
335D4⋊C8—131no—
336D4⋊C8—131no—
337D4⋊C8C2×D1311yescharacteristic
338#322—131no—
339#322—131no—
340C82—131no—
341C82C2×D1311yescharacteristic, complemented
342C22×C13—22no—
343C22×C13—41no—
344C22×C13—41no—
345C22×C13C2×C4×D411yescharacteristic
346C2×D13—21no—
347C2×D13—21no—
348C2×D13—41no—
349C2×D13—41no—
350C2×D13—41no—
351C2×D13—84no—
352C2×D13C4×SD1612yes—
353C4×C13—22no—
354C4×C13—21no—
355C4×C13—41no—
356C4×C13—41no—
357C4×C13C22×M1611yescharacteristic
358C4×C13#56811yescharacteristic
359C4×C13C22×SD1611yescharacteristic
360C4×C13C2×#13511yescharacteristic
361Dic13—21no—
362Dic13—21no—
363Dic13—41no—
364Dic13—41no—
365Dic13—41no—
366Dic13C4×SD1612yes—
367C22×Q8—131no—
368C22×D4—131no—
369C23×C4—261no—
370C2×SD16—131no—
371C2×SD16—131no—
372C2×SD16—131no—
373C2×SD16—264no—
374C2×SD16C4×D1311yescharacteristic
375C2×M16—131no—
376C2×M16—131no—
377C2×M16—261no—
378C2×M16—261no—
379C2×M16—261no—
380C2×M16—261no—
381C2×M16—524no—
382C22×C8—21no—
383C22×C8—131no—
384C22×C8—131no—
385C22×C8—261no—
386C4×Q8—131no—
387C4×Q8—131no—
388C4×Q8—131no—
389C4×Q8—261no—
390C4×Q8—261no—
391C4×Q8C22×D1311yescharacteristic
392C4×D4—131no—
393C4×D4—131no—
394C4×D4—131no—
395C4×D4—261no—
396C4×D4—261no—
397C4×D4C22×D1311yescharacteristic
398C2×C4⋊C4—131no—
399C2×C4⋊C4—131no—
400C2×C4⋊C4—261no—
401C2×C22⋊C4—261no—
402C2×C42—131no—
403C2×C42—261no—
404#106—131no—
405#106—131no—
406#106—131no—
407#106C4×D1311yescharacteristic
408C4⋊C8—21no—
409C4⋊C8—131no—
410C4⋊C8—131no—
411C4⋊C8—261no—
412C4⋊C8—261no—
413C4⋊C8—261no—
414C4⋊C8—261no—
415C4⋊C8—261no—
416C4⋊C8—261no—
417C4⋊C8C22×D1311yescharacteristic
418C4⋊C8C22×D1311yescharacteristic
419#103—131no—
420#103—131no—
421#103—131no—
422#103C4×D1311yescharacteristic
423#102—131no—
424#102—131no—
425#102—131no—
426#102C4×D1311yescharacteristic
427C22⋊C8—21no—
428C22⋊C8—261no—
429C22⋊C8—261no—
430C22⋊C8—261no—
431C22⋊C8—261no—
432#97—131no—
433#97—131no—
434#97—261no—
435#97—261no—
436C4×C8—21no—
437C4×C8—131no—
438C4×C8—131no—
439C4×C8—131no—
440C4×C8—131no—
441C4×C8—131no—
442C4×C8—261no—
443C4×C8C22×D1311yescharacteristic
444C4×C8C22×D1311yescharacteristic
445C4×C8C22×D1311yescharacteristic
446C2×C13—42no—
447C2×C13D4×M1611yescharacteristic
448C2×C13C2×C4×SD1611yescharacteristic
449C2×C13#295711yescharacteristic
450D13—22no—
451D13—81no—
452C24—261no—
453C2×Q8—131no—
454C2×Q8—261no—
455C2×Q8—262no—
456C2×Q8—521no—
457C2×Q8C2×C4×D1311yescharacteristic
458C2×D4—131no—
459C2×D4—261no—
460C2×D4—262no—
461C2×D4—521no—
462C2×D4C2×C4×D1311yescharacteristic
463C22×C4—21no—
464C22×C4—131no—
465C22×C4—131no—
466C22×C4—131no—
467C22×C4—261no—
468C22×C4—261no—
469C22×C4—261no—
470C22×C4—261no—
471C22×C4—261no—
472C22×C4—261no—
473C22×C4—522no—
474C22×C4—522no—
475SD16—262no—
476SD16—262no—
477SD16—262no—
478SD16#609414yesdirect product factor
479M16—134no—
480M16—262no—
481M16—522no—
482M16—522no—
483M16—522no—
484M16—522no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—42no—
489C2×C8—131no—
490C2×C8—131no—
491C2×C8—131no—
492C2×C8—131no—
493C2×C8—262no—
494C2×C8—261no—
495C2×C8—261no—
496C2×C8—261no—
497C2×C8—521no—
498C2×C8—522no—
499C2×C8C2×C4×D1311yescharacteristic
500C2×C8C2×C4×D1311yescharacteristic
501C2×C8D4×D1311yescharacteristic
502C2×C8D4×D1311yescharacteristic
503C4⋊C4—21no—
504C4⋊C4—131no—
505C4⋊C4—131no—
506C4⋊C4—261no—
507C4⋊C4—261no—
508C4⋊C4—261no—
509C4⋊C4—261no—
510C4⋊C4—261no—
511C4⋊C4C2×C4×D1311yescharacteristic
512C4⋊C4C2×C4×D1311yescharacteristic
513C22⋊C4—21no—
514C22⋊C4—261no—
515C22⋊C4—261no—
516C22⋊C4—261no—
517C42—21no—
518C42—131no—
519C42—131no—
520C42—131no—
521C42—261no—
522C42—261no—
523C42—261no—
524C42C23×D1311yescharacteristic
525C13M16×SD1611yescharacteristic, complemented, Sylow
526C23—21no—
527C23—131no—
528C23—261no—
529C23—522no—
530C23—522no—
531C23—1041no—
532Q8—21no—
533Q8—261no—
534Q8—261no—
535Q8—522no—
536Q8C2×#609412yescomplemented
537D4—21no—
538D4—261no—
539D4—261no—
540D4—522no—
541D4C2×#609412yes—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—131no—
548C2×C4—132no—
549C2×C4—132no—
550C2×C4—131no—
551C2×C4—131no—
552C2×C4—261no—
553C2×C4—261no—
554C2×C4—261no—
555C2×C4—261no—
556C2×C4—261no—
557C2×C4—521no—
558C2×C4—522no—
559C2×C4—522no—
560C2×C4—522no—
561C2×C4—522no—
562C2×C4—521no—
563C2×C4—521no—
564C2×C4—1041no—
565C2×C4C22×C4×D1311yescharacteristic
566C2×C4C2×D4×D1311yescharacteristic
567C2×C4#41×D1311yescharacteristic
568C8—21no—
569C8—21no—
570C8—41no—
571C8—41no—
572C8—41no—
573C8—132no—
574C8—261no—
575C8—261no—
576C8—261no—
577C8—521no—
578C8—521no—
579C8—521no—
580C8C2×#609412yescomplemented
581C8SD16×D1312yescomplemented
582C22—22no—
583C22—41no—
584C22—41no—
585C22—132no—
586C22—261no—
587C22—261no—
588C22—521no—
589C22—521no—
590C22—521no—
591C22—1044no—
592C22C4×D4×D1311yescharacteristic
593C4—21no—
594C4—22no—
595C4—41no—
596C4—41no—
597C4—132no—
598C4—261no—
599C4—261no—
600C4—521no—
601C4—521no—
602C4—521no—
603C4C22×#609411yescharacteristic
604C4#1171945511yescharacteristic
605C4C2×SD16×D1311yescharacteristic
606C4D13×#13511yescharacteristic
607C2—42no—
608C2—262no—
609C2—1041no—
610C2D4×#609411yescharacteristic
611C2C4×SD16×D1311yescharacteristic
612C2#1312374811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC8×C13×SD16C2
socleC22×C13C2×C4×D4
prime radicalC2×D4×D13C2×C4
cosocleC42×C13C24
hypercenterC8×SD16D13
hypocenterC13M16×SD16
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×SD16

Complements

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

NH ≅ G/Ntype
1. Q8×#6094C2semidirect
4. #13113728C2semidirect
5. #13113725C2semidirect
6. #13113679C2semidirect
7. #13113676C2semidirect
8. #13113672C2semidirect
9. #13113669C2semidirect
10. SD16×#1055C2semidirect
11. #13113590C2semidirect
12. #13113263C2semidirect
14. C8×#6094C2semidirect
15. C8×C13×SD16C2semidirect
20. C8×Q8×C13C22semidirect
26. Q8×#1055C22semidirect
36. #11718492C22semidirect
50. #11718340C22semidirect
51. C13×#334C22semidirect
52. C13×Q8⋊C8C22semidirect
54. C82×C13C22semidirect
55. Q8⋊#1055C22semidirect
57. #11718076C22semidirect
59. #11718072C22semidirect
60. #11718072C22semidirect
62. #11718049C22semidirect
63. #11718048C22semidirect
64. #11718047C22semidirect
65. #11718046C22semidirect
66. C8×#1055C22semidirect
170. C13×SD16M16semidirect
217. #6094SD16direct (N × H)
230. C8×SD16D13semidirect
242. Q8×C13C2×M16semidirect
282. C8×C13C2×M16semidirect
283. C8×C13C2×SD16semidirect
290. #1055C2×SD16semidirect
300. C8×Q8C2×D13semidirect
329. #334C2×D13semidirect
333. Q8⋊C8C2×D13semidirect
341. C82C2×D13semidirect
478. SD16#6094direct (N × H)
525. C13M16×SD16semidirect
536. Q8C2×#6094semidirect
580. C8C2×#6094semidirect
581. C8SD16×D13semidirect

Maximal subgroups

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

subgroupindex
Q8×#60942
C4×SD16×D132
D4×#60942
#131137282
#131137252
#131136792
#131136762
#131136722
#131136692
SD16×#10552
#131135902
#131132632
#131132592
C8×#60942
C8×C13×SD162
M16×SD1613