Finite Group Databasebeta

← SD32×C22⋊D43 #25253265

Subgroups — SD32×C22⋊D43 #25253265

Order 11008.

738 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD32×D43C211yesmaximal, characteristic, complemented
2Q16×C22⋊D43C211yesmaximal, characteristic, complemented
3D8×C22⋊D43C211yesmaximal, characteristic
4#19136849C211yesmaximal, characteristic, complemented
5#19136691C211yesmaximal, characteristic, complemented
6#19136688C211yesmaximal, characteristic, complemented
7#19136638C211yesmaximal, characteristic, complemented
8#19136633C211yesmaximal, characteristic, complemented
9#19136524C211yesmaximal, characteristic, complemented
10#19136522C211yesmaximal, characteristic, complemented
11#19136512C211yesmaximal, characteristic, complemented
12#19136510C211yesmaximal, characteristic, complemented
13SD32×Dic43C211yesmaximal, characteristic, complemented
14C16×C22⋊D43C211yesmaximal, characteristic, complemented
15C22×SD32×C43C211yesmaximal, characteristic, complemented
16C2×Q16×D43C2211yescharacteristic, complemented
17C2×D8×D43C2211yescharacteristic
18Q8×C22⋊D43—21no—
19D4×C22⋊D43—21no—
20C2×#13063270C2211yescharacteristic, complemented
21C2×#13063269C2211yescharacteristic
22C2×#13063269C2211yescharacteristic, complemented
23C2×#13063268C2211yescharacteristic, complemented
24C2×#13063268C2211yescharacteristic, complemented
25SD32×D43—24no—
26C2×C16×D43C2211yescharacteristic, complemented
27#14583277C2211yescharacteristic, complemented
28#14583274C2211yescharacteristic
29#14583140C2211yescharacteristic, complemented
30#14583137C2211yescharacteristic, complemented
31#14583135C2211yescharacteristic
32#14583132C2211yescharacteristic
33#14583107—21no—
34#14583092—21no—
35#14583055—21no—
36#14583053—21no—
37#14583033—21no—
38#14583031—21no—
39Q16×Dic43C2211yescharacteristic, complemented
40D8×Dic43C2211yescharacteristic
41C8×C22⋊D43C2211yescharacteristic
42#14582727C2211yescharacteristic, complemented
43Dic43⋊C16C2211yescharacteristic, complemented
44#14582704C2211yescharacteristic, complemented
45#14582703C2211yescharacteristic, complemented
46#14582703C2211yescharacteristic, complemented
47#14582701C2211yescharacteristic, complemented
48#14582700C2211yescharacteristic
49#14582700C2211yescharacteristic, complemented
50C22⋊(C43⋊C16)C2211yescharacteristic, complemented
51(C2×D43)⋊C16C2211yescharacteristic, complemented
52C16×Dic43C2211yescharacteristic, complemented
53C22×Q16×C43C2211yescharacteristic, complemented
54C22×D8×C43C2211yescharacteristic
55C2×SD32×C43—24no—
56C2×SD32×C43C2211yescharacteristic
57C2×SD32×C43C2211yescharacteristic
58C2×SD32×C43C2211yescharacteristic, complemented
59C2×SD32×C43C2211yescharacteristic, complemented
60C22×C16×C43C2211yescharacteristic, complemented
61C2×Q8×D43—21no—
62C22×C22⋊D43—41no—
63C2×D4×D43—21no—
64C2×Dic172C2311yescharacteristic
65C2×#10621885—21no—
66C2×#10621885—21no—
67Q16×D43—22no—
68Q16×D43—41no—
69C2×D344C2311yescharacteristic
70C2×#10621882—21no—
71C2×#10621882—21no—
72D8×D43—22no—
73D8×D43—41no—
74C2×C8×D43C2311yescharacteristic
75#13063323—21no—
76#13063323—41no—
77#13063321—21no—
78#13063304—21no—
79#13063304—41no—
80#13063301—21no—
81#13063301—41no—
82#13063299—21no—
83#13063297—41no—
84#13063296—21no—
85#13063294—41no—
86#13063293—41no—
87Q8×Dic43—21no—
88D4×Dic43—21no—
89C4×C22⋊D43—41no—
90C4×C22⋊D43D411yescharacteristic
91#13063270—22no—
92#13063269—22no—
93#13063269—41no—
94#13063268—22no—
95#13063268—41no—
96C2×C43⋊C16C2311yescharacteristic
97C2×C43⋊C16C2311yescharacteristic
98C16×D43—22no—
99#13063259C2311yescharacteristic
100#13063259C2311yescharacteristic
101Dic43⋊C8D411yescharacteristic
102#13063250—21no—
103#13063249—21no—
104#13063249—21no—
105#13063247—21no—
106#13063246—21no—
107#13063246—21no—
108C22⋊(C43⋊C8)D411yescharacteristic
109(C2×D43)⋊C8D411yescharacteristic
110C8×Dic43C2311yescharacteristic
111C22×Q8×C43—21no—
112C22×D4×C43—21no—
113C2×Q16×C43—22no—
114C2×Q16×C43—21no—
115C2×Q16×C43—41no—
116C2×Q16×C43C2311yescharacteristic
117C2×Q16×C43C2311yescharacteristic
118C2×D8×C43—22no—
119C2×D8×C43—21no—
120C2×D8×C43—41no—
121C2×D8×C43C2311yescharacteristic
122C2×D8×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124SD32×C43—22no—
125SD32×C43—22no—
126SD32×C43—22no—
127SD32×C43D414yescomplemented
128C2×C16×C43—22no—
129C2×C16×C43C2311yescharacteristic
130C2×C16×C43C2311yescharacteristic
131C24×C43—41no—
132C23×D43—41no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—42no—
136C2×Q8×C43—41no—
137C2×Q8×C43—81no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43—41no—
141C2×D4×C43—42no—
142C2×D4×C43—81no—
143C22×C4×C43—41no—
144C22×C4×C43C2×D411yescharacteristic
145C2×C22⋊D43—41no—
146C2×C22⋊D43—41no—
147C2×C22⋊D43—41no—
148C2×C22⋊D43—41no—
149C2×C22⋊D43—41no—
150C2×C22⋊D43—84no—
151C2×C22⋊D43D811yescharacteristic
152C22×Dic43—41no—
153Q8×D43—42no—
154Q8×D43—81no—
155D4×D43—42no—
156D4×D43—81no—
157C2×D172—21no—
158C2×C4×D43—41no—
159C2×C4×D43C2×D411yescharacteristic
160C2×Dic86—21no—
161C2×Dic86—41no—
162Q16×C43—21no—
163Q16×C43—21no—
164Q16×C43—21no—
165Q16×C43—42no—
166Q16×C43C2×D412yescomplemented
167D8×C43—21no—
168D8×C43—21no—
169D8×C43—21no—
170D8×C43—42no—
171D8×C43C2×D412yes—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43C2×D411yescharacteristic
175C2×C8×C43C2411yescharacteristic
176C22⋊Dic43—41no—
177C22⋊Dic43—41no—
178C22⋊Dic43—41no—
179C22⋊Dic43D811yescharacteristic
180#10621885—42no—
181#10621885—81no—
182#10621882—42no—
183#10621882—81no—
184(C2×D43)⋊C4—41no—
185(C2×D43)⋊C4—41no—
186(C2×D43)⋊C4D811yescharacteristic
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—41no—
190Dic43⋊C4—41no—
191Dic43⋊C4—41no—
192Dic43⋊C4—41no—
193Dic43⋊C4—41no—
194Dic43⋊C4D811yescharacteristic
195C4×Dic43—41no—
196C4×Dic43C2×D411yescharacteristic
197C2×C43⋊C8C2×D411yescharacteristic
198C2×C43⋊C8C2×D411yescharacteristic
199Dic172—21no—
200Dic172—21no—
201D344—21no—
202D344—21no—
203C8×D43—21no—
204C8×D43—21no—
205C16×C43—21no—
206C16×C43C2×D412yescomplemented
207C43⋊C16—21no—
208C43⋊C16—21no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—82no—
212C23×C43—82no—
213C23×C43—161no—
214C23×C43C2×D811yescharacteristic
215C22×D43—41no—
216C22×D43—82no—
217C22×D43—82no—
218C22×D43—161no—
219C22×D43C2×D811yescharacteristic
220Q8×C43—22no—
221Q8×C43—41no—
222Q8×C43—41no—
223Q8×C43—41no—
224Q8×C43—82no—
225D4×C43—22no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—41no—
229D4×C43—82no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—82no—
235C2×C4×C43C2×D811yescharacteristic
236C2×C4×C43C22×D411yescharacteristic
237C22⋊D43—82no—
238C22⋊D43—82no—
239C22⋊D43—82no—
240C22⋊D43—82no—
241C22⋊D43—161no—
242C22⋊D43SD3214yesdirect product factor
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—82no—
247C2×Dic43C2×D811yescharacteristic
248C2×Dic43C2×D811yescharacteristic
249C2×Dic43C2×D811yescharacteristic
250D172—41no—
251D172—41no—
252C4×D43—21no—
253C4×D43—21no—
254C4×D43—82no—
255Dic86—41no—
256Dic86—41no—
257Dic86—82no—
258C8×C43—21no—
259C8×C43C22×D411yescharacteristic
260C8×C43H(5,𝔽2)11yescharacteristic
261C43⋊C8—21no—
262C43⋊C8—21no—
263D4×SD32—431nomaximal, Sylow
264C22×C43—21no—
265C22×C43—21no—
266C22×C43—42no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43—81no—
272C22×C43—164no—
273C22×C43C2×SD3212yescomplemented
274C22×C43C22×D811yescharacteristic
275C2×D43—21no—
276C2×D43—21no—
277C2×D43—81no—
278C2×D43—81no—
279C2×D43—81no—
280C2×D43—164no—
281C2×D43C2×SD3212yescomplemented
282C4×C43—21no—
283C4×C43—42no—
284C4×C43—81no—
285C4×C43D4211yescharacteristic
286C4×C43#57611yescharacteristic
287Dic43—21no—
288Dic43—21no—
289Dic43—81no—
290Dic43—81no—
291Dic43—81no—
292Dic43C2×SD3212yescomplemented
293C22×SD32—431no—
294C22×SD32D4311yescharacteristic, complemented
295D4×Q16—431no—
296D4×D8—431no—
297#2248—431no—
298#2217—431no—
299#2217—431no—
300#2208—431no—
301#2207—431no—
302#2187—431no—
303#2187—431no—
304#2185—431no—
305#2185—431no—
306C4×SD32—431no—
307D4×C16—431no—
308C2×C43—22no—
309C2×C43—82no—
310C2×C43—161no—
311C2×C43D4×D811yescharacteristic
312C2×C43C22×SD3211yescharacteristic
313C2×C43#341611yescharacteristic
314D43—22no—
315D43—161no—
316C22×Q16—431no—
317C22×Q16C2×D4311yescharacteristic, complemented
318C22×D8—431no—
319C22×D8C2×D4311yescharacteristic
320D4×Q8—861no—
321D42—861no—
322C2×SD32—24no—
323C2×SD32—431no—
324C2×SD32—431no—
325C2×SD32—431no—
326C2×SD32—431no—
327C2×SD32—431no—
328C2×SD32—864no—
329C2×SD32C2×D4311yescharacteristic
330C2×SD32C2×D4311yescharacteristic
331C2×SD32C2×D4311yescharacteristic, complemented
332C2×SD32C2×D4311yescharacteristic, complemented
333C22×C16—431no—
334C22×C16C2×D4311yescharacteristic, complemented
335#494—431no—
336#493—431no—
337#467—431no—
338#467—431no—
339#466—431no—
340#466—431no—
341#462—861no—
342#459—861no—
343#451—861no—
344#451—861no—
345#447—861no—
346#447—861no—
347C4×Q16—431no—
348C4×D8—431no—
349C8×D4—431no—
350#367—431no—
351C4⋊C16—431no—
352#358—431no—
353#358—431no—
354#358—431no—
355#357—431no—
356#357—431no—
357#357—431no—
358C22⋊C16—431no—
359C22⋊C16—431no—
360C4×C16—431no—
361C43D4×SD3211yescharacteristic, complemented, Sylow
362C22×Q8—21no—
363C22×Q8—861no—
364C22×D4—21no—
365C22×D4—861no—
366C22×D4—1721no—
367C2×Q16—22no—
368C2×Q16—21no—
369C2×Q16—41no—
370C2×Q16—431no—
371C2×Q16—861no—
372C2×Q16—861no—
373C2×Q16—862no—
374C2×Q16—1721no—
375C2×Q16C22×D4311yescharacteristic
376C2×Q16C22×D4311yescharacteristic
377C2×D8—22no—
378C2×D8—21no—
379C2×D8—41no—
380C2×D8—431no—
381C2×D8—861no—
382C2×D8—861no—
383C2×D8—862no—
384C2×D8—1721no—
385C2×D8C22×D4311yescharacteristic
386C2×D8C22×D4311yescharacteristic
387C22×C8—431no—
388C22×C8C22×D4311yescharacteristic
389C4⋊Q8—861no—
390C4⋊Q8—1721no—
391#127—861no—
392C22⋊Q8—861no—
393C22⋊Q8—861no—
394C22⋊Q8—1721no—
395C22⋊Q8—1721no—
396#121—861no—
397#121—861no—
398#121—1721no—
399#120—1721no—
400#120—1721no—
401C4×Q8—861no—
402C4×D4—431no—
403C4×D4—861no—
404C4×D4—1721no—
405SD32—22no—
406SD32—22no—
407SD32—22no—
408SD32—862no—
409SD32—862no—
410SD32—862no—
411SD32—1721no—
412SD32—1721no—
413SD32C22⋊D4314yesdirect product factor
414C2×C16—22no—
415C2×C16—431no—
416C2×C16—431no—
417C2×C16—862no—
418C2×C16C22×D4311yescharacteristic
419C2×C16C22×D4311yescharacteristic
420#107—431no—
421#107—431no—
422C4⋊C8—431no—
423#103—861no—
424#103—861no—
425#103—861no—
426#102—861no—
427#102—861no—
428#102—861no—
429C22⋊C8—431no—
430C22⋊C8—431no—
431C4×C8—431no—
432C24—41no—
433C24—1721no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—42no—
437C2×Q8—41no—
438C2×Q8—81no—
439C2×Q8—861no—
440C2×Q8—3441no—
441C2×Q8—1721no—
442C2×Q8—1722no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—42no—
446C2×D4—41no—
447C2×D4—81no—
448C2×D4—431no—
449C2×D4—861no—
450C2×D4—3441no—
451C2×D4—3444no—
452C2×D4—1721no—
453C2×D4—1721no—
454C2×D4—1721no—
455C2×D4—1722no—
456C2×D4—1721no—
457C2×D4—1721no—
458C22×C4—41no—
459C22×C4—431no—
460C22×C4—1721no—
461C22×C4—1721no—
462C22×C4D4×D4311yescharacteristic
463Q16—21no—
464Q16—21no—
465Q16—21no—
466Q16—42no—
467Q16—861no—
468Q16—861no—
469Q16—3441no—
470Q16—1722no—
471Q16C2×C22⋊D4312yescomplemented
472D8—21no—
473D8—21no—
474D8—21no—
475D8—42no—
476D8—861no—
477D8—861no—
478D8—3441no—
479D8—1722no—
480D8C2×C22⋊D4312yes—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—431no—
484C2×C8—431no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8D4×D4311yescharacteristic
488C2×C8C23×D4311yescharacteristic
489C4⋊C4—431no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—1721no—
493C4⋊C4—1721no—
494C4⋊C4—1721no—
495C4⋊C4—1721no—
496C4⋊C4—1721no—
497C22⋊C4—431no—
498C22⋊C4—431no—
499C22⋊C4—1721no—
500C22⋊C4—1721no—
501C22⋊C4—1721no—
502C22⋊C4—1721no—
503C22⋊C4—1721no—
504C42—431no—
505C42—1721no—
506C16—21no—
507C16—861no—
508C16—861no—
509C16C2×C22⋊D4312yescomplemented
510C23—41no—
511C23—41no—
512C23—82no—
513C23—82no—
514C23—161no—
515C23—431no—
516C23—3442no—
517C23—3442no—
518C23—1721no—
519C23—6881no—
520C23D8×D4311yescharacteristic
521Q8—22no—
522Q8—41no—
523Q8—41no—
524Q8—41no—
525Q8—82no—
526Q8—3442no—
527Q8—1721no—
528Q8—1721no—
529D4—22no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—82no—
534D4—434no—
535D4—3442no—
536D4—3442no—
537D4—3442no—
538D4—3442no—
539D4—1721no—
540D4—1721no—
541D4—6881no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—82no—
547C2×C4—431no—
548C2×C4—431no—
549C2×C4—431no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—3442no—
553C2×C4—3442no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4D8×D4311yescharacteristic
558C2×C4C2×D4×D4311yescharacteristic
559C8—21no—
560C8—861no—
561C8—861no—
562C8C22×C22⋊D4311yescharacteristic
563C8#1306337011yescharacteristic
564C22—21no—
565C22—21no—
566C22—42no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22—164no—
573C22—432no—
574C22—861no—
575C22—861no—
576C22—3441no—
577C22—3441no—
578C22—3441no—
579C22—6884no—
580C22SD32×D4312yescomplemented
581C22C2×D8×D4311yescharacteristic
582C4—21no—
583C4—42no—
584C4—81no—
585C4—432no—
586C4—861no—
587C4—861no—
588C4—3441no—
589C4—3441no—
590C4—3441no—
591C4D4×C22⋊D4311yescharacteristic
592C4#1458370011yescharacteristic
593C2—22no—
594C2—82no—
595C2—161no—
596C2—862no—
597C2—6881no—
598C2D8×C22⋊D4311yescharacteristic
599C2C2×SD32×D4311yescharacteristic
600C2#1914773711yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC22×SD32×C43C2
socleC22×C43C22×D8
prime radicalD8×C22⋊D43C2
hypercenterC22×SD32D43
hypocenterC43D4×SD32
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×SD32

Complements

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

NH ≅ G/Ntype
1. C2×SD32×D43C2semidirect
2. Q16×C22⋊D43C2semidirect
4. #19136849C2semidirect
5. #19136691C2semidirect
6. #19136688C2semidirect
7. #19136638C2semidirect
8. #19136633C2semidirect
9. #19136524C2semidirect
10. #19136522C2semidirect
11. #19136512C2semidirect
12. #19136510C2semidirect
13. SD32×Dic43C2semidirect
14. C16×C22⋊D43C2semidirect
15. C22×SD32×C43C2semidirect
16. C2×Q16×D43C22semidirect
20. C2×#13063270C22semidirect
22. C2×#13063269C22semidirect
23. C2×#13063268C22semidirect
24. C2×#13063268C22semidirect
26. C2×C16×D43C22semidirect
27. #14583277C22semidirect
29. #14583140C22semidirect
30. #14583137C22semidirect
39. Q16×Dic43C22semidirect
42. #14582727C22semidirect
43. Dic43⋊C16C22semidirect
44. #14582704C22semidirect
45. #14582703C22semidirect
46. #14582703C22semidirect
47. #14582701C22semidirect
49. #14582700C22semidirect
50. C22⋊(C43⋊C16)C22semidirect
51. (C2×D43)⋊C16C22semidirect
52. C16×Dic43C22semidirect
53. C22×Q16×C43C22semidirect
58. C2×SD32×C43C22semidirect
59. C2×SD32×C43C22semidirect
60. C22×C16×C43C22semidirect
127. SD32×C43D4semidirect
166. Q16×C43C2×D4semidirect
206. C16×C43C2×D4semidirect
242. C22⋊D43SD32direct (N × H)
273. C22×C43C2×SD32semidirect
281. C2×D43C2×SD32semidirect
292. Dic43C2×SD32semidirect
294. C22×SD32D43semidirect
317. C22×Q16C2×D43semidirect
331. C2×SD32C2×D43semidirect
332. C2×SD32C2×D43semidirect
334. C22×C16C2×D43semidirect
361. C43D4×SD32semidirect
413. SD32C22⋊D43direct (N × H)
471. Q16C2×C22⋊D43semidirect
509. C16C2×C22⋊D43semidirect
580. C22SD32×D43semidirect

Maximal subgroups

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

subgroupindex
C2×SD32×D432
Q16×C22⋊D432
D8×C22⋊D432
#191368492
#191366912
#191366882
#191366382
#191366332
#191365242
#191365222
#191365122
#191365102
SD32×Dic432
C16×C22⋊D432
C22×SD32×C432
D4×SD3243