Finite Group Databasebeta

← SD32×C22⋊D61 #29836681

Subgroups — SD32×C22⋊D61 #29836681

Order 15616.

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×D61C211yesmaximal, characteristic, complemented
2Q16×C22⋊D61C211yesmaximal, characteristic, complemented
3D8×C22⋊D61C211yesmaximal, characteristic
4#21448073C211yesmaximal, characteristic, complemented
5#21447915C211yesmaximal, characteristic, complemented
6#21447912C211yesmaximal, characteristic, complemented
7#21447862C211yesmaximal, characteristic, complemented
8#21447857C211yesmaximal, characteristic, complemented
9#21447748C211yesmaximal, characteristic, complemented
10#21447746C211yesmaximal, characteristic, complemented
11#21447736C211yesmaximal, characteristic, complemented
12#21447734C211yesmaximal, characteristic, complemented
13SD32×Dic61C211yesmaximal, characteristic, complemented
14C16×C22⋊D61C211yesmaximal, characteristic, complemented
15C22×SD32×C61C211yesmaximal, characteristic, complemented
16C2×Q16×D61C2211yescharacteristic, complemented
17C2×D8×D61C2211yescharacteristic
18Q8×C22⋊D61—21no—
19D4×C22⋊D61—21no—
20C2×#14519722C2211yescharacteristic, complemented
21C2×#14519721C2211yescharacteristic
22C2×#14519721C2211yescharacteristic, complemented
23C2×#14519720C2211yescharacteristic, complemented
24C2×#14519720C2211yescharacteristic, complemented
25SD32×D61—24no—
26C2×C16×D61C2211yescharacteristic, complemented
27#16840140C2211yescharacteristic, complemented
28#16840137C2211yescharacteristic
29#16840003C2211yescharacteristic, complemented
30#16840000C2211yescharacteristic, complemented
31#16839998C2211yescharacteristic
32#16839995C2211yescharacteristic
33#16839970—21no—
34#16839955—21no—
35#16839918—21no—
36#16839916—21no—
37#16839896—21no—
38#16839894—21no—
39Q16×Dic61C2211yescharacteristic, complemented
40D8×Dic61C2211yescharacteristic
41C8×C22⋊D61C2211yescharacteristic
42#16839590C2211yescharacteristic, complemented
43#16839580C2211yescharacteristic, complemented
44#16839567C2211yescharacteristic, complemented
45#16839566C2211yescharacteristic, complemented
46#16839566C2211yescharacteristic, complemented
47#16839564C2211yescharacteristic, complemented
48#16839563C2211yescharacteristic
49#16839563C2211yescharacteristic, complemented
50C22⋊#11758185C2211yescharacteristic, complemented
51#16839541C2211yescharacteristic, complemented
52C16×Dic61C2211yescharacteristic, complemented
53C22×Q16×C61C2211yescharacteristic, complemented
54C22×D8×C61C2211yescharacteristic
55C2×SD32×C61—24no—
56C2×SD32×C61C2211yescharacteristic
57C2×SD32×C61C2211yescharacteristic
58C2×SD32×C61C2211yescharacteristic, complemented
59C2×SD32×C61C2211yescharacteristic, complemented
60C22×C16×C61C2211yescharacteristic, complemented
61C2×Q8×D61—21no—
62C22×C22⋊D61—41no—
63C2×D4×D61—21no—
64C2×Dic244C2311yescharacteristic
65C2×#11758202—21no—
66C2×#11758202—21no—
67Q16×D61—22no—
68Q16×D61—41no—
69C2×D488C2311yescharacteristic
70C2×#11758199—21no—
71C2×#11758199—21no—
72D8×D61—22no—
73D8×D61—41no—
74C2×C8×D61C2311yescharacteristic
75#14519775—21no—
76#14519775—41no—
77#14519773—21no—
78#14519756—21no—
79#14519756—41no—
80#14519753—21no—
81#14519753—41no—
82#14519751—21no—
83#14519749—41no—
84#14519748—21no—
85#14519746—41no—
86#14519745—41no—
87Q8×Dic61—21no—
88D4×Dic61—21no—
89C4×C22⋊D61—41no—
90C4×C22⋊D61D411yescharacteristic
91#14519722—22no—
92#14519721—22no—
93#14519721—41no—
94#14519720—22no—
95#14519720—41no—
96C2×#11758185C2311yescharacteristic
97C2×#11758185C2311yescharacteristic
98C16×D61—22no—
99#14519711C2311yescharacteristic
100#14519711C2311yescharacteristic
101#14519706D411yescharacteristic
102#14519702—21no—
103#14519701—21no—
104#14519701—21no—
105#14519699—21no—
106#14519698—21no—
107#14519698—21no—
108C22⋊#92418D411yescharacteristic
109#14519689D411yescharacteristic
110C8×Dic61C2311yescharacteristic
111C22×Q8×C61—21no—
112C22×D4×C61—21no—
113C2×Q16×C61—22no—
114C2×Q16×C61—21no—
115C2×Q16×C61—41no—
116C2×Q16×C61C2311yescharacteristic
117C2×Q16×C61C2311yescharacteristic
118C2×D8×C61—22no—
119C2×D8×C61—21no—
120C2×D8×C61—41no—
121C2×D8×C61C2311yescharacteristic
122C2×D8×C61C2311yescharacteristic
123C22×C8×C61C2311yescharacteristic
124SD32×C61—22no—
125SD32×C61—22no—
126SD32×C61—22no—
127SD32×C61D414yescomplemented
128C2×C16×C61—22no—
129C2×C16×C61C2311yescharacteristic
130C2×C16×C61C2311yescharacteristic
131C24×C61—41no—
132C23×D61—41no—
133C2×Q8×C61—21no—
134C2×Q8×C61—21no—
135C2×Q8×C61—42no—
136C2×Q8×C61—41no—
137C2×Q8×C61—81no—
138C2×D4×C61—21no—
139C2×D4×C61—21no—
140C2×D4×C61—42no—
141C2×D4×C61—41no—
142C2×D4×C61—81no—
143C22×C4×C61—41no—
144C22×C4×C61C2×D411yescharacteristic
145C2×C22⋊D61—41no—
146C2×C22⋊D61—41no—
147C2×C22⋊D61—41no—
148C2×C22⋊D61—41no—
149C2×C22⋊D61—41no—
150C2×C22⋊D61—84no—
151C2×C22⋊D61D811yescharacteristic
152C22×Dic61—41no—
153Q8×D61—42no—
154Q8×D61—81no—
155D4×D61—42no—
156D4×D61—81no—
157C2×D244—21no—
158C2×C4×D61—41no—
159C2×C4×D61C2×D411yescharacteristic
160C2×Dic122—21no—
161C2×Dic122—41no—
162Q16×C61—21no—
163Q16×C61—21no—
164Q16×C61—21no—
165Q16×C61—42no—
166Q16×C61C2×D412yescomplemented
167D8×C61—21no—
168D8×C61—21no—
169D8×C61—21no—
170D8×C61—42no—
171D8×C61C2×D412yes—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61C2×D411yescharacteristic
175C2×C8×C61C2411yescharacteristic
176C22⋊Dic61—41no—
177C22⋊Dic61—41no—
178C22⋊Dic61—41no—
179C22⋊Dic61D811yescharacteristic
180#11758202—42no—
181#11758202—81no—
182#11758199—42no—
183#11758199—81no—
184#11758198—41no—
185#11758198—41no—
186#11758198D811yescharacteristic
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—41no—
190#11758196—41no—
191#11758196—41no—
192#11758196—41no—
193#11758196—41no—
194#11758196D811yescharacteristic
195C4×Dic61—41no—
196C4×Dic61C2×D411yescharacteristic
197C2×#92418C2×D411yescharacteristic
198C2×#92418C2×D411yescharacteristic
199Dic244—21no—
200Dic244—21no—
201D488—21no—
202D488—21no—
203C8×D61—21no—
204C8×D61—21no—
205C16×C61—21no—
206C16×C61C2×D412yescomplemented
207#11758185—21no—
208#11758185—21no—
209C23×C61—41no—
210C23×C61—41no—
211C23×C61—82no—
212C23×C61—82no—
213C23×C61—161no—
214C23×C61C2×D811yescharacteristic
215C22×D61—41no—
216C22×D61—82no—
217C22×D61—82no—
218C22×D61—161no—
219C22×D61C2×D811yescharacteristic
220Q8×C61—22no—
221Q8×C61—41no—
222Q8×C61—41no—
223Q8×C61—41no—
224Q8×C61—82no—
225D4×C61—22no—
226D4×C61—41no—
227D4×C61—41no—
228D4×C61—41no—
229D4×C61—82no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—82no—
235C2×C4×C61C2×D811yescharacteristic
236C2×C4×C61C22×D411yescharacteristic
237C22⋊D61—82no—
238C22⋊D61—82no—
239C22⋊D61—82no—
240C22⋊D61—82no—
241C22⋊D61—161no—
242C22⋊D61SD3214yesdirect product factor
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—82no—
247C2×Dic61C2×D811yescharacteristic
248C2×Dic61C2×D811yescharacteristic
249C2×Dic61C2×D811yescharacteristic
250D244—41no—
251D244—41no—
252C4×D61—21no—
253C4×D61—21no—
254C4×D61—82no—
255Dic122—41no—
256Dic122—41no—
257Dic122—82no—
258C8×C61—21no—
259C8×C61C22×D411yescharacteristic
260C8×C61H(5,𝔽2)11yescharacteristic
261#92418—21no—
262#92418—21no—
263D4×SD32—611nomaximal, Sylow
264C22×C61—21no—
265C22×C61—21no—
266C22×C61—42no—
267C22×C61—81no—
268C22×C61—81no—
269C22×C61—81no—
270C22×C61—81no—
271C22×C61—81no—
272C22×C61—164no—
273C22×C61C2×SD3212yescomplemented
274C22×C61C22×D811yescharacteristic
275C2×D61—21no—
276C2×D61—21no—
277C2×D61—81no—
278C2×D61—81no—
279C2×D61—81no—
280C2×D61—164no—
281C2×D61C2×SD3212yescomplemented
282C4×C61—21no—
283C4×C61—42no—
284C4×C61—81no—
285C4×C61D4211yescharacteristic
286C4×C61#57611yescharacteristic
287Dic61—21no—
288Dic61—21no—
289Dic61—81no—
290Dic61—81no—
291Dic61—81no—
292Dic61C2×SD3212yescomplemented
293C22×SD32—611no—
294C22×SD32D6111yescharacteristic, complemented
295D4×Q16—611no—
296D4×D8—611no—
297#2248—611no—
298#2217—611no—
299#2217—611no—
300#2208—611no—
301#2207—611no—
302#2187—611no—
303#2187—611no—
304#2185—611no—
305#2185—611no—
306C4×SD32—611no—
307D4×C16—611no—
308C2×C61—22no—
309C2×C61—82no—
310C2×C61—161no—
311C2×C61D4×D811yescharacteristic
312C2×C61C22×SD3211yescharacteristic
313C2×C61#341611yescharacteristic
314D61—22no—
315D61—161no—
316C22×Q16—611no—
317C22×Q16C2×D6111yescharacteristic, complemented
318C22×D8—611no—
319C22×D8C2×D6111yescharacteristic
320D4×Q8—1221no—
321D42—1221no—
322C2×SD32—24no—
323C2×SD32—611no—
324C2×SD32—611no—
325C2×SD32—611no—
326C2×SD32—611no—
327C2×SD32—611no—
328C2×SD32—1224no—
329C2×SD32C2×D6111yescharacteristic
330C2×SD32C2×D6111yescharacteristic
331C2×SD32C2×D6111yescharacteristic, complemented
332C2×SD32C2×D6111yescharacteristic, complemented
333C22×C16—611no—
334C22×C16C2×D6111yescharacteristic, complemented
335#494—611no—
336#493—611no—
337#467—611no—
338#467—611no—
339#466—611no—
340#466—611no—
341#462—1221no—
342#459—1221no—
343#451—1221no—
344#451—1221no—
345#447—1221no—
346#447—1221no—
347C4×Q16—611no—
348C4×D8—611no—
349C8×D4—611no—
350#367—611no—
351C4⋊C16—611no—
352#358—611no—
353#358—611no—
354#358—611no—
355#357—611no—
356#357—611no—
357#357—611no—
358C22⋊C16—611no—
359C22⋊C16—611no—
360C4×C16—611no—
361C61D4×SD3211yescharacteristic, complemented, Sylow
362C22×Q8—21no—
363C22×Q8—1221no—
364C22×D4—21no—
365C22×D4—1221no—
366C22×D4—2441no—
367C2×Q16—22no—
368C2×Q16—21no—
369C2×Q16—41no—
370C2×Q16—611no—
371C2×Q16—1221no—
372C2×Q16—1221no—
373C2×Q16—1222no—
374C2×Q16—2441no—
375C2×Q16C22×D6111yescharacteristic
376C2×Q16C22×D6111yescharacteristic
377C2×D8—22no—
378C2×D8—21no—
379C2×D8—41no—
380C2×D8—611no—
381C2×D8—1221no—
382C2×D8—1221no—
383C2×D8—1222no—
384C2×D8—2441no—
385C2×D8C22×D6111yescharacteristic
386C2×D8C22×D6111yescharacteristic
387C22×C8—611no—
388C22×C8C22×D6111yescharacteristic
389C4⋊Q8—1221no—
390C4⋊Q8—2441no—
391#127—1221no—
392C22⋊Q8—1221no—
393C22⋊Q8—1221no—
394C22⋊Q8—2441no—
395C22⋊Q8—2441no—
396#121—1221no—
397#121—1221no—
398#121—2441no—
399#120—2441no—
400#120—2441no—
401C4×Q8—1221no—
402C4×D4—611no—
403C4×D4—1221no—
404C4×D4—2441no—
405SD32—22no—
406SD32—22no—
407SD32—22no—
408SD32—1222no—
409SD32—1222no—
410SD32—1222no—
411SD32—2441no—
412SD32—2441no—
413SD32C22⋊D6114yesdirect product factor
414C2×C16—22no—
415C2×C16—611no—
416C2×C16—611no—
417C2×C16—1222no—
418C2×C16C22×D6111yescharacteristic
419C2×C16C22×D6111yescharacteristic
420#107—611no—
421#107—611no—
422C4⋊C8—611no—
423#103—1221no—
424#103—1221no—
425#103—1221no—
426#102—1221no—
427#102—1221no—
428#102—1221no—
429C22⋊C8—611no—
430C22⋊C8—611no—
431C4×C8—611no—
432C24—41no—
433C24—2441no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—42no—
437C2×Q8—41no—
438C2×Q8—81no—
439C2×Q8—1221no—
440C2×Q8—4881no—
441C2×Q8—2441no—
442C2×Q8—2442no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—42no—
446C2×D4—41no—
447C2×D4—81no—
448C2×D4—611no—
449C2×D4—1221no—
450C2×D4—4881no—
451C2×D4—4884no—
452C2×D4—2441no—
453C2×D4—2441no—
454C2×D4—2441no—
455C2×D4—2442no—
456C2×D4—2441no—
457C2×D4—2441no—
458C22×C4—41no—
459C22×C4—611no—
460C22×C4—2441no—
461C22×C4—2441no—
462C22×C4D4×D6111yescharacteristic
463Q16—21no—
464Q16—21no—
465Q16—21no—
466Q16—42no—
467Q16—1221no—
468Q16—1221no—
469Q16—4881no—
470Q16—2442no—
471Q16C2×C22⋊D6112yescomplemented
472D8—21no—
473D8—21no—
474D8—21no—
475D8—42no—
476D8—1221no—
477D8—1221no—
478D8—4881no—
479D8—2442no—
480D8C2×C22⋊D6112yes—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—611no—
484C2×C8—611no—
485C2×C8—1221no—
486C2×C8—1221no—
487C2×C8D4×D6111yescharacteristic
488C2×C8C23×D6111yescharacteristic
489C4⋊C4—611no—
490C4⋊C4—1221no—
491C4⋊C4—1221no—
492C4⋊C4—2441no—
493C4⋊C4—2441no—
494C4⋊C4—2441no—
495C4⋊C4—2441no—
496C4⋊C4—2441no—
497C22⋊C4—611no—
498C22⋊C4—611no—
499C22⋊C4—2441no—
500C22⋊C4—2441no—
501C22⋊C4—2441no—
502C22⋊C4—2441no—
503C22⋊C4—2441no—
504C42—611no—
505C42—2441no—
506C16—21no—
507C16—1221no—
508C16—1221no—
509C16C2×C22⋊D6112yescomplemented
510C23—41no—
511C23—41no—
512C23—82no—
513C23—82no—
514C23—161no—
515C23—611no—
516C23—9761no—
517C23—4882no—
518C23—4882no—
519C23—2441no—
520C23D8×D6111yescharacteristic
521Q8—22no—
522Q8—41no—
523Q8—41no—
524Q8—41no—
525Q8—82no—
526Q8—4882no—
527Q8—2441no—
528Q8—2441no—
529D4—22no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—82no—
534D4—614no—
535D4—9761no—
536D4—4882no—
537D4—4882no—
538D4—4882no—
539D4—4882no—
540D4—2441no—
541D4—2441no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—82no—
547C2×C4—611no—
548C2×C4—611no—
549C2×C4—611no—
550C2×C4—1221no—
551C2×C4—1221no—
552C2×C4—4882no—
553C2×C4—4882no—
554C2×C4—2441no—
555C2×C4—2441no—
556C2×C4—2441no—
557C2×C4D8×D6111yescharacteristic
558C2×C4C2×D4×D6111yescharacteristic
559C8—21no—
560C8—1221no—
561C8—1221no—
562C8C22×C22⋊D6111yescharacteristic
563C8#1451982211yescharacteristic
564C22—21no—
565C22—21no—
566C22—42no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22—164no—
573C22—612no—
574C22—1221no—
575C22—1221no—
576C22—9764no—
577C22—4881no—
578C22—4881no—
579C22—4881no—
580C22SD32×D6112yescomplemented
581C22C2×D8×D6111yescharacteristic
582C4—21no—
583C4—42no—
584C4—81no—
585C4—612no—
586C4—1221no—
587C4—1221no—
588C4—4881no—
589C4—4881no—
590C4—4881no—
591C4D4×C22⋊D6111yescharacteristic
592C4#1684056311yescharacteristic
593C2—22no—
594C2—82no—
595C2—161no—
596C2—1222no—
597C2—9761no—
598C2D8×C22⋊D6111yescharacteristic
599C2C2×SD32×D6111yescharacteristic
600C2#2145896111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC22×SD32×C61C2
socleC22×C61C22×D8
prime radicalD8×C22⋊D61C2
hypercenterC22×SD32D61
hypocenterC61D4×SD32
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
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×D61C2semidirect
2. Q16×C22⋊D61C2semidirect
4. #21448073C2semidirect
5. #21447915C2semidirect
6. #21447912C2semidirect
7. #21447862C2semidirect
8. #21447857C2semidirect
9. #21447748C2semidirect
10. #21447746C2semidirect
11. #21447736C2semidirect
12. #21447734C2semidirect
13. SD32×Dic61C2semidirect
14. C16×C22⋊D61C2semidirect
15. C22×SD32×C61C2semidirect
16. C2×Q16×D61C22semidirect
20. C2×#14519722C22semidirect
22. C2×#14519721C22semidirect
23. C2×#14519720C22semidirect
24. C2×#14519720C22semidirect
26. C2×C16×D61C22semidirect
27. #16840140C22semidirect
29. #16840003C22semidirect
30. #16840000C22semidirect
39. Q16×Dic61C22semidirect
42. #16839590C22semidirect
43. #16839580C22semidirect
44. #16839567C22semidirect
45. #16839566C22semidirect
46. #16839566C22semidirect
47. #16839564C22semidirect
49. #16839563C22semidirect
50. C22⋊#11758185C22semidirect
51. #16839541C22semidirect
52. C16×Dic61C22semidirect
53. C22×Q16×C61C22semidirect
58. C2×SD32×C61C22semidirect
59. C2×SD32×C61C22semidirect
60. C22×C16×C61C22semidirect
127. SD32×C61D4semidirect
166. Q16×C61C2×D4semidirect
206. C16×C61C2×D4semidirect
242. C22⋊D61SD32direct (N × H)
273. C22×C61C2×SD32semidirect
281. C2×D61C2×SD32semidirect
292. Dic61C2×SD32semidirect
294. C22×SD32D61semidirect
317. C22×Q16C2×D61semidirect
331. C2×SD32C2×D61semidirect
332. C2×SD32C2×D61semidirect
334. C22×C16C2×D61semidirect
361. C61D4×SD32semidirect
413. SD32C22⋊D61direct (N × H)
471. Q16C2×C22⋊D61semidirect
509. C16C2×C22⋊D61semidirect
580. C22SD32×D61semidirect

Maximal subgroups

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

subgroupindex
C2×SD32×D612
Q16×C22⋊D612
D8×C22⋊D612
#214480732
#214479152
#214479122
#214478622
#214478572
#214477482
#214477462
#214477362
#214477342
SD32×Dic612
C16×C22⋊D612
C22×SD32×C612
D4×SD3261