Finite Group Databasebeta

← SD32×C22⋊D79 #34444937

Subgroups — SD32×C22⋊D79 #34444937

Order 20224.

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×D79C211yesmaximal, characteristic, complemented
2Q16×C22⋊D79C211yesmaximal, characteristic, complemented
3D8×C22⋊D79C211yesmaximal, characteristic
4#23765654C211yesmaximal, characteristic, complemented
5#23765496C211yesmaximal, characteristic, complemented
6#23765493C211yesmaximal, characteristic, complemented
7#23765443C211yesmaximal, characteristic, complemented
8#23765438C211yesmaximal, characteristic, complemented
9#23765329C211yesmaximal, characteristic, complemented
10#23765327C211yesmaximal, characteristic, complemented
11#23765317C211yesmaximal, characteristic, complemented
12#23765315C211yesmaximal, characteristic, complemented
13SD32×Dic79C211yesmaximal, characteristic, complemented
14C16×C22⋊D79C211yesmaximal, characteristic, complemented
15C22×SD32×C79C211yesmaximal, characteristic, complemented
16C2×Q16×D79C2211yescharacteristic, complemented
17C2×D8×D79C2211yescharacteristic
18Q8×C22⋊D79—21no—
19D4×C22⋊D79—21no—
20C2×#14579106C2211yescharacteristic, complemented
21C2×#14579105C2211yescharacteristic
22C2×#14579105C2211yescharacteristic, complemented
23C2×#14579104C2211yescharacteristic, complemented
24C2×#14579104C2211yescharacteristic, complemented
25SD32×D79—24no—
26C2×C16×D79C2211yescharacteristic, complemented
27#19098941C2211yescharacteristic, complemented
28#19098938C2211yescharacteristic
29#19098804C2211yescharacteristic, complemented
30#19098801C2211yescharacteristic, complemented
31#19098799C2211yescharacteristic
32#19098796C2211yescharacteristic
33#19098771—21no—
34#19098756—21no—
35#19098719—21no—
36#19098717—21no—
37#19098697—21no—
38#19098695—21no—
39Q16×Dic79C2211yescharacteristic, complemented
40D8×Dic79C2211yescharacteristic
41C8×C22⋊D79C2211yescharacteristic
42#19098391C2211yescharacteristic, complemented
43Dic79⋊C16C2211yescharacteristic, complemented
44#19098368C2211yescharacteristic, complemented
45#19098367C2211yescharacteristic, complemented
46#19098367C2211yescharacteristic, complemented
47#19098365C2211yescharacteristic, complemented
48#19098364C2211yescharacteristic
49#19098364C2211yescharacteristic, complemented
50C22⋊(C79⋊C16)C2211yescharacteristic, complemented
51(C2×D79)⋊C16C2211yescharacteristic, complemented
52C16×Dic79C2211yescharacteristic, complemented
53C22×Q16×C79C2211yescharacteristic, complemented
54C22×D8×C79C2211yescharacteristic
55C2×SD32×C79—24no—
56C2×SD32×C79C2211yescharacteristic
57C2×SD32×C79C2211yescharacteristic
58C2×SD32×C79C2211yescharacteristic, complemented
59C2×SD32×C79C2211yescharacteristic, complemented
60C22×C16×C79C2211yescharacteristic, complemented
61C2×Q8×D79—21no—
62C22×C22⋊D79—41no—
63C2×D4×D79—21no—
64C2×Dic316C2311yescharacteristic
65C2×#11929614—21no—
66C2×#11929614—21no—
67Q16×D79—22no—
68Q16×D79—41no—
69C2×D632C2311yescharacteristic
70C2×#11929609—21no—
71C2×#11929609—21no—
72D8×D79—22no—
73D8×D79—41no—
74C2×C8×D79C2311yescharacteristic
75#14579159—21no—
76#14579159—41no—
77#14579157—21no—
78#14579140—21no—
79#14579140—41no—
80#14579137—21no—
81#14579137—41no—
82#14579135—21no—
83#14579133—41no—
84#14579132—21no—
85#14579130—41no—
86#14579129—41no—
87Q8×Dic79—21no—
88D4×Dic79—21no—
89C4×C22⋊D79—41no—
90C4×C22⋊D79D411yescharacteristic
91#14579106—22no—
92#14579105—22no—
93#14579105—41no—
94#14579104—22no—
95#14579104—41no—
96C2×C79⋊C16C2311yescharacteristic
97C2×C79⋊C16C2311yescharacteristic
98C16×D79—22no—
99#14579095C2311yescharacteristic
100#14579095C2311yescharacteristic
101Dic79⋊C8D411yescharacteristic
102#14579086—21no—
103#14579085—21no—
104#14579085—21no—
105#14579083—21no—
106#14579082—21no—
107#14579082—21no—
108C22⋊(C79⋊C8)D411yescharacteristic
109(C2×D79)⋊C8D411yescharacteristic
110C8×Dic79C2311yescharacteristic
111C22×Q8×C79—21no—
112C22×D4×C79—21no—
113C2×Q16×C79—22no—
114C2×Q16×C79—21no—
115C2×Q16×C79—41no—
116C2×Q16×C79C2311yescharacteristic
117C2×Q16×C79C2311yescharacteristic
118C2×D8×C79—22no—
119C2×D8×C79—21no—
120C2×D8×C79—41no—
121C2×D8×C79C2311yescharacteristic
122C2×D8×C79C2311yescharacteristic
123C22×C8×C79C2311yescharacteristic
124SD32×C79—22no—
125SD32×C79—22no—
126SD32×C79—22no—
127SD32×C79D414yescomplemented
128C2×C16×C79—22no—
129C2×C16×C79C2311yescharacteristic
130C2×C16×C79C2311yescharacteristic
131C23×D79—41no—
132C2×Dic158—21no—
133C2×Dic158—41no—
134Q8×D79—42no—
135Q8×D79—81no—
136C2×D316—21no—
137C2×C22⋊D79—41no—
138C2×C22⋊D79—41no—
139C2×C22⋊D79—41no—
140C2×C22⋊D79—41no—
141C2×C22⋊D79—41no—
142C2×C22⋊D79—84no—
143C2×C22⋊D79D811yescharacteristic
144D4×D79—42no—
145D4×D79—81no—
146C22×Dic79—41no—
147C2×C4×D79—41no—
148C2×C4×D79C2×D411yescharacteristic
149Dic316—21no—
150Dic316—21no—
151#11929614—42no—
152#11929614—81no—
153D632—21no—
154D632—21no—
155#11929609—42no—
156#11929609—81no—
157C2×C79⋊C8C2×D411yescharacteristic
158C2×C79⋊C8C2×D411yescharacteristic
159C8×D79—21no—
160C8×D79—21no—
161C4⋊Dic79—21no—
162C4⋊Dic79—21no—
163C4⋊Dic79—41no—
164Dic79⋊C4—41no—
165Dic79⋊C4—41no—
166Dic79⋊C4—41no—
167Dic79⋊C4—41no—
168Dic79⋊C4D811yescharacteristic
169C22⋊Dic79—41no—
170C22⋊Dic79—41no—
171C22⋊Dic79—41no—
172C22⋊Dic79D811yescharacteristic
173(C2×D79)⋊C4—41no—
174(C2×D79)⋊C4—41no—
175(C2×D79)⋊C4D811yescharacteristic
176C4×Dic79—41no—
177C4×Dic79C2×D411yescharacteristic
178C79⋊C16—21no—
179C79⋊C16—21no—
180C24×C79—41no—
181C2×Q8×C79—21no—
182C2×Q8×C79—21no—
183C2×Q8×C79—42no—
184C2×Q8×C79—41no—
185C2×Q8×C79—81no—
186C2×D4×C79—21no—
187C2×D4×C79—21no—
188C2×D4×C79—42no—
189C2×D4×C79—41no—
190C2×D4×C79—81no—
191C22×C4×C79—41no—
192C22×C4×C79C2×D411yescharacteristic
193Q16×C79—21no—
194Q16×C79—21no—
195Q16×C79—21no—
196Q16×C79—42no—
197Q16×C79C2×D412yescomplemented
198D8×C79—21no—
199D8×C79—21no—
200D8×C79—21no—
201D8×C79—42no—
202D8×C79C2×D412yes—
203C2×C8×C79—21no—
204C2×C8×C79—21no—
205C2×C8×C79C2×D411yescharacteristic
206C2×C8×C79C2411yescharacteristic
207C16×C79—21no—
208C16×C79C2×D412yescomplemented
209C23×C79—41no—
210C23×C79—41no—
211C23×C79—82no—
212C23×C79—82no—
213C23×C79—161no—
214C23×C79C2×D811yescharacteristic
215C22×D79—41no—
216C22×D79—82no—
217C22×D79—82no—
218C22×D79—161no—
219C22×D79C2×D811yescharacteristic
220Q8×C79—22no—
221Q8×C79—41no—
222Q8×C79—41no—
223Q8×C79—41no—
224Q8×C79—82no—
225D4×C79—22no—
226D4×C79—41no—
227D4×C79—41no—
228D4×C79—41no—
229D4×C79—82no—
230C2×C4×C79—21no—
231C2×C4×C79—21no—
232C2×C4×C79—41no—
233C2×C4×C79—41no—
234C2×C4×C79—82no—
235C2×C4×C79C2×D811yescharacteristic
236C2×C4×C79C22×D411yescharacteristic
237C22⋊D79—82no—
238C22⋊D79—82no—
239C22⋊D79—82no—
240C22⋊D79—82no—
241C22⋊D79—161no—
242C22⋊D79SD3214yesdirect product factor
243C2×Dic79—41no—
244C2×Dic79—41no—
245C2×Dic79—41no—
246C2×Dic79—82no—
247C2×Dic79C2×D811yescharacteristic
248C2×Dic79C2×D811yescharacteristic
249C2×Dic79C2×D811yescharacteristic
250D316—41no—
251D316—41no—
252C4×D79—21no—
253C4×D79—21no—
254C4×D79—82no—
255Dic158—41no—
256Dic158—41no—
257Dic158—82no—
258C8×C79—21no—
259C8×C79C22×D411yescharacteristic
260C8×C79H(5,𝔽2)11yescharacteristic
261C79⋊C8—21no—
262C79⋊C8—21no—
263C22×C79—21no—
264C22×C79—21no—
265C22×C79—42no—
266C22×C79—81no—
267C22×C79—81no—
268C22×C79—81no—
269C22×C79—81no—
270C22×C79—81no—
271C22×C79—164no—
272C22×C79C2×SD3212yescomplemented
273C22×C79C22×D811yescharacteristic
274C2×D79—21no—
275C2×D79—21no—
276C2×D79—81no—
277C2×D79—81no—
278C2×D79—81no—
279C2×D79—164no—
280C2×D79C2×SD3212yescomplemented
281C4×C79—21no—
282C4×C79—42no—
283C4×C79—81no—
284C4×C79D4211yescharacteristic
285C4×C79#57611yescharacteristic
286Dic79—21no—
287Dic79—21no—
288Dic79—81no—
289Dic79—81no—
290Dic79—81no—
291Dic79C2×SD3212yescomplemented
292D4×SD32—791nomaximal, Sylow
293C2×C79—22no—
294C2×C79—82no—
295C2×C79—161no—
296C2×C79D4×D811yescharacteristic
297C2×C79C22×SD3211yescharacteristic
298C2×C79#341611yescharacteristic
299D79—22no—
300D79—161no—
301C22×SD32—791no—
302C22×SD32D7911yescharacteristic, complemented
303D4×Q16—791no—
304D4×D8—791no—
305#2248—791no—
306#2217—791no—
307#2217—791no—
308#2208—791no—
309#2207—791no—
310#2187—791no—
311#2187—791no—
312#2185—791no—
313#2185—791no—
314C4×SD32—791no—
315D4×C16—791no—
316C79D4×SD3211yescharacteristic, complemented, Sylow
317C22×Q16—791no—
318C22×Q16C2×D7911yescharacteristic, complemented
319C22×D8—791no—
320C22×D8C2×D7911yescharacteristic
321D4×Q8—1581no—
322D42—1581no—
323C2×SD32—24no—
324C2×SD32—791no—
325C2×SD32—791no—
326C2×SD32—791no—
327C2×SD32—791no—
328C2×SD32—791no—
329C2×SD32—1584no—
330C2×SD32C2×D7911yescharacteristic
331C2×SD32C2×D7911yescharacteristic
332C2×SD32C2×D7911yescharacteristic, complemented
333C2×SD32C2×D7911yescharacteristic, complemented
334C22×C16—791no—
335C22×C16C2×D7911yescharacteristic, complemented
336#494—791no—
337#493—791no—
338#467—791no—
339#467—791no—
340#466—791no—
341#466—791no—
342#462—1581no—
343#459—1581no—
344#451—1581no—
345#451—1581no—
346#447—1581no—
347#447—1581no—
348C4×Q16—791no—
349C4×D8—791no—
350C8×D4—791no—
351#367—791no—
352C4⋊C16—791no—
353#358—791no—
354#358—791no—
355#358—791no—
356#357—791no—
357#357—791no—
358#357—791no—
359C22⋊C16—791no—
360C22⋊C16—791no—
361C4×C16—791no—
362C22×Q8—21no—
363C22×Q8—1581no—
364C22×D4—21no—
365C22×D4—3161no—
366C22×D4—1581no—
367C2×Q16—22no—
368C2×Q16—21no—
369C2×Q16—41no—
370C2×Q16—3161no—
371C2×Q16—791no—
372C2×Q16—1581no—
373C2×Q16—1581no—
374C2×Q16—1582no—
375C2×Q16C22×D7911yescharacteristic
376C2×Q16C22×D7911yescharacteristic
377C2×D8—22no—
378C2×D8—21no—
379C2×D8—41no—
380C2×D8—3161no—
381C2×D8—791no—
382C2×D8—1581no—
383C2×D8—1581no—
384C2×D8—1582no—
385C2×D8C22×D7911yescharacteristic
386C2×D8C22×D7911yescharacteristic
387C22×C8—791no—
388C22×C8C22×D7911yescharacteristic
389C4⋊Q8—3161no—
390C4⋊Q8—1581no—
391#127—1581no—
392C22⋊Q8—3161no—
393C22⋊Q8—3161no—
394C22⋊Q8—1581no—
395C22⋊Q8—1581no—
396#121—3161no—
397#121—1581no—
398#121—1581no—
399#120—3161no—
400#120—3161no—
401C4×Q8—1581no—
402C4×D4—3161no—
403C4×D4—791no—
404C4×D4—1581no—
405SD32—22no—
406SD32—22no—
407SD32—22no—
408SD32—3161no—
409SD32—3161no—
410SD32—1582no—
411SD32—1582no—
412SD32—1582no—
413SD32C22⋊D7914yesdirect product factor
414C2×C16—22no—
415C2×C16—791no—
416C2×C16—791no—
417C2×C16—1582no—
418C2×C16C22×D7911yescharacteristic
419C2×C16C22×D7911yescharacteristic
420#107—791no—
421#107—791no—
422C4⋊C8—791no—
423#103—1581no—
424#103—1581no—
425#103—1581no—
426#102—1581no—
427#102—1581no—
428#102—1581no—
429C22⋊C8—791no—
430C22⋊C8—791no—
431C4×C8—791no—
432C24—41no—
433C24—3161no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—42no—
437C2×Q8—41no—
438C2×Q8—81no—
439C2×Q8—3161no—
440C2×Q8—3162no—
441C2×Q8—6321no—
442C2×Q8—1581no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—42no—
446C2×D4—41no—
447C2×D4—81no—
448C2×D4—3161no—
449C2×D4—3161no—
450C2×D4—3161no—
451C2×D4—3161no—
452C2×D4—3161no—
453C2×D4—3162no—
454C2×D4—791no—
455C2×D4—6324no—
456C2×D4—6321no—
457C2×D4—1581no—
458C22×C4—41no—
459C22×C4—3161no—
460C22×C4—3161no—
461C22×C4—791no—
462C22×C4D4×D7911yescharacteristic
463Q16—21no—
464Q16—21no—
465Q16—21no—
466Q16—42no—
467Q16—3162no—
468Q16—6321no—
469Q16—1581no—
470Q16—1581no—
471Q16C2×C22⋊D7912yescomplemented
472D8—21no—
473D8—21no—
474D8—21no—
475D8—42no—
476D8—3162no—
477D8—6321no—
478D8—1581no—
479D8—1581no—
480D8C2×C22⋊D7912yes—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—791no—
484C2×C8—791no—
485C2×C8—1581no—
486C2×C8—1581no—
487C2×C8D4×D7911yescharacteristic
488C2×C8C23×D7911yescharacteristic
489C4⋊C4—3161no—
490C4⋊C4—3161no—
491C4⋊C4—3161no—
492C4⋊C4—3161no—
493C4⋊C4—3161no—
494C4⋊C4—791no—
495C4⋊C4—1581no—
496C4⋊C4—1581no—
497C22⋊C4—3161no—
498C22⋊C4—3161no—
499C22⋊C4—3161no—
500C22⋊C4—3161no—
501C22⋊C4—3161no—
502C22⋊C4—791no—
503C22⋊C4—791no—
504C42—3161no—
505C42—791no—
506C16—21no—
507C16—1581no—
508C16—1581no—
509C16C2×C22⋊D7912yescomplemented
510C23—41no—
511C23—41no—
512C23—82no—
513C23—82no—
514C23—161no—
515C23—3161no—
516C23—791no—
517C23—6322no—
518C23—6322no—
519C23—12641no—
520C23D8×D7911yescharacteristic
521Q8—22no—
522Q8—41no—
523Q8—41no—
524Q8—41no—
525Q8—82no—
526Q8—3161no—
527Q8—3161no—
528Q8—6322no—
529D4—22no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—82no—
534D4—3161no—
535D4—3161no—
536D4—794no—
537D4—6322no—
538D4—6322no—
539D4—6322no—
540D4—6322no—
541D4—12641no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—82no—
547C2×C4—3161no—
548C2×C4—3161no—
549C2×C4—3161no—
550C2×C4—791no—
551C2×C4—791no—
552C2×C4—791no—
553C2×C4—6322no—
554C2×C4—6322no—
555C2×C4—1581no—
556C2×C4—1581no—
557C2×C4D8×D7911yescharacteristic
558C2×C4C2×D4×D7911yescharacteristic
559C8—21no—
560C8—1581no—
561C8—1581no—
562C8C22×C22⋊D7911yescharacteristic
563C8#1457920611yescharacteristic
564C22—21no—
565C22—21no—
566C22—42no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22—164no—
573C22—792no—
574C22—6321no—
575C22—6321no—
576C22—6321no—
577C22—1581no—
578C22—1581no—
579C22—12644no—
580C22SD32×D7912yescomplemented
581C22C2×D8×D7911yescharacteristic
582C4—21no—
583C4—42no—
584C4—81no—
585C4—792no—
586C4—6321no—
587C4—6321no—
588C4—6321no—
589C4—1581no—
590C4—1581no—
591C4D4×C22⋊D7911yescharacteristic
592C4#1909936411yescharacteristic
593C2—22no—
594C2—82no—
595C2—161no—
596C2—1582no—
597C2—12641no—
598C2D8×C22⋊D7911yescharacteristic
599C2C2×SD32×D7911yescharacteristic
600C2#2377654211yescharacteristic
subgroupG/H
centerC22C2×D8×D79
commutator, cosocleC2×C8×C79C24
FrattiniC2×C8C23×D79
FittingC22×SD32×C79C2
socleC22×C79C22×D8
prime radicalD8×C22⋊D79C2
hypercenterC22×SD32D79
hypocenterC79D4×SD32
LCSG ▷ C2×C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79
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×D79C2semidirect
2. Q16×C22⋊D79C2semidirect
4. #23765654C2semidirect
5. #23765496C2semidirect
6. #23765493C2semidirect
7. #23765443C2semidirect
8. #23765438C2semidirect
9. #23765329C2semidirect
10. #23765327C2semidirect
11. #23765317C2semidirect
12. #23765315C2semidirect
13. SD32×Dic79C2semidirect
14. C16×C22⋊D79C2semidirect
15. C22×SD32×C79C2semidirect
16. C2×Q16×D79C22semidirect
20. C2×#14579106C22semidirect
22. C2×#14579105C22semidirect
23. C2×#14579104C22semidirect
24. C2×#14579104C22semidirect
26. C2×C16×D79C22semidirect
27. #19098941C22semidirect
29. #19098804C22semidirect
30. #19098801C22semidirect
39. Q16×Dic79C22semidirect
42. #19098391C22semidirect
43. Dic79⋊C16C22semidirect
44. #19098368C22semidirect
45. #19098367C22semidirect
46. #19098367C22semidirect
47. #19098365C22semidirect
49. #19098364C22semidirect
50. C22⋊(C79⋊C16)C22semidirect
51. (C2×D79)⋊C16C22semidirect
52. C16×Dic79C22semidirect
53. C22×Q16×C79C22semidirect
58. C2×SD32×C79C22semidirect
59. C2×SD32×C79C22semidirect
60. C22×C16×C79C22semidirect
127. SD32×C79D4semidirect
197. Q16×C79C2×D4semidirect
208. C16×C79C2×D4semidirect
242. C22⋊D79SD32direct (N × H)
272. C22×C79C2×SD32semidirect
280. C2×D79C2×SD32semidirect
291. Dic79C2×SD32semidirect
302. C22×SD32D79semidirect
316. C79D4×SD32semidirect
318. C22×Q16C2×D79semidirect
332. C2×SD32C2×D79semidirect
333. C2×SD32C2×D79semidirect
335. C22×C16C2×D79semidirect
413. SD32C22⋊D79direct (N × H)
471. Q16C2×C22⋊D79semidirect
509. C16C2×C22⋊D79semidirect
580. C22SD32×D79semidirect

Maximal subgroups

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

subgroupindex
C2×SD32×D792
Q16×C22⋊D792
D8×C22⋊D792
#237656542
#237654962
#237654932
#237654432
#237654382
#237653292
#237653272
#237653172
#237653152
SD32×Dic792
C16×C22⋊D792
C22×SD32×C792
D4×SD3279