Finite Group Databasebeta

← #29836685

Subgroups — #29836685

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
1C22×#14519721C211yesmaximal, characteristic, complemented
2C2×SD32×D61C211yesmaximal, characteristic, complemented
3#21457568C211yesmaximal, characteristic, complemented
4D8×C22⋊D61C211yesmaximal, characteristic
5#21448073C211yesmaximal, characteristic, complemented
6#21447917C211yesmaximal, characteristic, complemented
7#21447914C211yesmaximal, characteristic, complemented
8#21447862C211yesmaximal, characteristic, complemented
9#21447858C211yesmaximal, characteristic, complemented
10#21447749C211yesmaximal, characteristic, complemented
11#21447738C211yesmaximal, characteristic, complemented
12#21447734C211yesmaximal, characteristic, complemented
13#21447674C211yesmaximal, characteristic, complemented
14#21447636C211yesmaximal, characteristic, complemented
15C61×#2187C211yesmaximal, characteristic, complemented
16C22×Dic244C2211yescharacteristic, complemented
17C2×Q16×D61C2211yescharacteristic, complemented
18C2×D8×D61C2211yescharacteristic
19#16840425—21no—
20D4×C22⋊D61—21no—
21C2×#14519722C2211yescharacteristic, complemented
22C2×#14519722C2211yescharacteristic, complemented
23C2×#14519721—24no—
24C2×#14519721C2211yescharacteristic
25C2×#14519721C2211yescharacteristic
26C2×#14519721C2211yescharacteristic, complemented
27C2×#14519721C2211yescharacteristic, complemented
28C2×#14519720C2211yescharacteristic, complemented
29SD32×D61—24no—
30C22×#11758185C2211yescharacteristic, complemented
31C2×C16×D61C2211yescharacteristic, complemented
32#16840140C2211yescharacteristic, complemented
33#16840137C2211yescharacteristic
34#16840004C2211yescharacteristic, complemented
35#16839998C2211yescharacteristic
36#16839995C2211yescharacteristic
37#16839971—21no—
38#16839955—21no—
39#16839919—21no—
40#16839917—21no—
41#16839896—21no—
42#16839894—21no—
43#16839856C2211yescharacteristic, complemented
44D8×Dic61C2211yescharacteristic
45C8×C22⋊D61C2211yescharacteristic
46#16839589C2211yescharacteristic, complemented
47#16839580C2211yescharacteristic, complemented
48#16839567C2211yescharacteristic, complemented
49#16839567C2211yescharacteristic, complemented
50#16839566C2211yescharacteristic, complemented
51#16839562C2211yescharacteristic, complemented
52#16839541C2211yescharacteristic, complemented
53C16×Dic61C2211yescharacteristic, complemented
54C22×D8×C61C2211yescharacteristic
55C2×SD32×C61C2211yescharacteristic
56C2×SD32×C61C2211yescharacteristic, complemented
57C61×#467C2211yescharacteristic, complemented
58C61×#357C2211yescharacteristic
59C61×#357C2211yescharacteristic, complemented
60C61×C22⋊C16C2211yescharacteristic, complemented
61C22×Dic122—21no—
62C2×Q8×D61—21no—
63C22×C22⋊D61—41no—
64C2×D4×D61—21no—
65C2×Dic244—22no—
66C2×Dic244—21no—
67C2×Dic244—41no—
68C2×Dic244C2311yescharacteristic
69C2×Dic244C2311yescharacteristic
70C2×#11758202—21no—
71C2×#11758202—21no—
72Q16×D61—22no—
73Q16×D61—41no—
74C2×D488C2311yescharacteristic
75C2×#11758199—21no—
76C2×#11758199—21no—
77D8×D61—22no—
78D8×D61—41no—
79C2×C8×D61C2311yescharacteristic
80#14519776—41no—
81#14519775—21no—
82#14519773—21no—
83#14519757—21no—
84#14519755—41no—
85#14519754—41no—
86#14519751—21no—
87#14519749—41no—
88#14519748—21no—
89#14519746—41no—
90#14519745—41no—
91#14519742—21no—
92D4×Dic61—21no—
93C4×C22⋊D61D411yescharacteristic
94#14519737—41no—
95#14519722—22no—
96#14519722—41no—
97#14519721—22no—
98#14519721—22no—
99#14519721—22no—
100#14519721D414yescomplemented
101#14519720—22no—
102C2×#11758185—22no—
103C2×#11758185C2311yescharacteristic
104C2×#11758185C2311yescharacteristic
105C16×D61—22no—
106#14519711C2311yescharacteristic
107#14519706D411yescharacteristic
108#14519700—21no—
109#14519700—21no—
110#14519699—21no—
111#14519698—21no—
112#14519698—21no—
113C22⋊#92418D411yescharacteristic
114#14519689D411yescharacteristic
115C8×Dic61C2311yescharacteristic
116C22×D4×C61—21no—
117C2×Q16×C61C2311yescharacteristic
118C2×D8×C61—22no—
119C2×D8×C61—21no—
120C2×D8×C61—41no—
121C2×D8×C61C2311yescharacteristic
122C2×D8×C61C2311yescharacteristic
123C22×C8×C61C2311yescharacteristic
124C22⋊Q8×C61—21no—
125SD32×C61—22no—
126SD32×C61—41no—
127C2×C16×C61C2311yescharacteristic
128C2×C16×C61C2311yescharacteristic
129#107×C61C2311yescharacteristic
130#103×C61—21no—
131C24×C61—41no—
132C23×D61—41no—
133C2×Q8×C61—21no—
134C2×D4×C61—21no—
135C2×D4×C61—21no—
136C2×D4×C61—42no—
137C2×D4×C61—41no—
138C2×D4×C61—81no—
139C22×C4×C61C2×D411yescharacteristic
140C2×C22⋊D61—41no—
141C2×C22⋊D61—41no—
142C2×C22⋊D61—41no—
143C2×C22⋊D61—41no—
144C2×C22⋊D61—41no—
145C2×C22⋊D61—84no—
146C2×C22⋊D61D811yescharacteristic
147C22×Dic61—41no—
148C22×Dic61—41no—
149Q8×D61—42no—
150Q8×D61—81no—
151D4×D61—42no—
152D4×D61—81no—
153C2×D244—21no—
154C2×C4×D61—41no—
155C2×C4×D61C2×D411yescharacteristic
156C2×Dic122—21no—
157C2×Dic122—21no—
158C2×Dic122—42no—
159C2×Dic122—41no—
160C2×Dic122—41no—
161C2×Dic122—81no—
162Q16×C61—21no—
163Q16×C61—21no—
164D8×C61—21no—
165D8×C61—21no—
166D8×C61—21no—
167D8×C61—42no—
168D8×C61C2×D412yes—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C2×C8×C61C2×D411yescharacteristic
172C2×C8×C61C2411yescharacteristic
173C4⋊C4×C61—21no—
174C4⋊C4×C61—41no—
175C22⋊C4×C61—41no—
176C22⋊Dic61—41no—
177C22⋊Dic61—41no—
178C22⋊Dic61D811yescharacteristic
179#11758202—42no—
180#11758202—81no—
181#11758199—42no—
182#11758199—81no—
183#11758198—41no—
184#11758198—41no—
185#11758198D811yescharacteristic
186C4⋊Dic61—21no—
187C4⋊Dic61—41no—
188#11758196—41no—
189#11758196—41no—
190#11758196—41no—
191#11758196D811yescharacteristic
192C4×Dic61—41no—
193C4×Dic61C2×D411yescharacteristic
194C2×#92418C2×D411yescharacteristic
195C2×#92418C2×D411yescharacteristic
196Dic244—21no—
197Dic244—21no—
198Dic244—21no—
199Dic244—42no—
200Dic244C2×D412yescomplemented
201D488—21no—
202D488—21no—
203C8×D61—21no—
204C8×D61—21no—
205C16×C61—21no—
206C16×C61—21no—
207#11758185—21no—
208#11758185C2×D412yescomplemented
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—41no—
221Q8×C61—41no—
222D4×C61—22no—
223D4×C61—41no—
224D4×C61—41no—
225D4×C61—41no—
226D4×C61—82no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61C2×D811yescharacteristic
232C2×C4×C61C22×D411yescharacteristic
233C22⋊D61—82no—
234C22⋊D61—82no—
235C22⋊D61—82no—
236C22⋊D61—82no—
237C22⋊D61—161no—
238C22⋊D61SD3214yescomplemented
239C2×Dic61—41no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242C2×Dic61—82no—
243C2×Dic61—82no—
244C2×Dic61C2×D811yescharacteristic
245C2×Dic61C2×D811yescharacteristic
246C2×Dic61C2×D811yescharacteristic
247D244—41no—
248D244—41no—
249C4×D61—21no—
250C4×D61—21no—
251C4×D61—82no—
252Dic122—22no—
253Dic122—41no—
254Dic122—41no—
255Dic122—41no—
256Dic122—82no—
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—81no—
284C4×C61—81no—
285C4×C61D4211yescharacteristic
286C4×C61#57611yescharacteristic
287Dic61—21no—
288Dic61—21no—
289Dic61—42no—
290Dic61—81no—
291Dic61—81no—
292Dic61C2×SD3212yescomplemented
293C22×SD32—611no—
294C22×SD32—611no—
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#2187D6111yescharacteristic, complemented
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×Q16—611no—
318C22×D8—611no—
319C22×D8C2×D6111yescharacteristic
320D4×Q8—1221no—
321D42—1221no—
322C2×SD32—611no—
323C2×SD32—611no—
324C2×SD32—611no—
325C2×SD32—611no—
326C2×SD32—611no—
327C2×SD32—611no—
328C2×SD32—611no—
329C2×SD32—1224no—
330C2×SD32—1224no—
331C2×SD32C2×D6111yescharacteristic
332C2×SD32C2×D6111yescharacteristic, complemented
333C22×C16—611no—
334C22×C16—611no—
335#494—611no—
336#493—611no—
337#467—611no—
338#467C2×D6111yescharacteristic, complemented
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#357C2×D6111yescharacteristic
357#357C2×D6111yescharacteristic, complemented
358C22⋊C16—611no—
359C22⋊C16C2×D6111yescharacteristic, complemented
360C4×C16—611no—
361C61D4×SD3211yescharacteristic, complemented, Sylow
362C22×Q8—1221no—
363C22×Q8—1221no—
364C22×D4—21no—
365C22×D4—1221no—
366C22×D4—2441no—
367C2×Q16—611no—
368C2×Q16—611no—
369C2×Q16—1222no—
370C2×Q16—1221no—
371C2×Q16—1221no—
372C2×Q16—1222no—
373C2×Q16—1221no—
374C2×Q16—2441no—
375C2×Q16—2441no—
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—21no—
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—41no—
407SD32—614no—
408SD32—1222no—
409SD32—1222no—
410SD32—1222no—
411SD32—1222no—
412SD32—1222no—
413SD32—2441no—
414C2×C16—611no—
415C2×C16—611no—
416C2×C16—1222no—
417C2×C16—1222no—
418C2×C16C22×D6111yescharacteristic
419C2×C16C22×D6111yescharacteristic
420#107—611no—
421#107C22×D6111yescharacteristic
422C4⋊C8—611no—
423#103—21no—
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—1221no—
436C2×Q8—1221no—
437C2×Q8—4881no—
438C2×Q8—4881no—
439C2×Q8—2442no—
440C2×Q8—2441no—
441C2×Q8—2442no—
442C2×Q8—2441no—
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—611no—
459C22×C4—2441no—
460C22×C4—2441no—
461C22×C4—2441no—
462C22×C4D4×D6111yescharacteristic
463Q16—21no—
464Q16—21no—
465Q16—612no—
466Q16—1221no—
467Q16—1221no—
468Q16—1221no—
469Q16—4881no—
470Q16—2442no—
471Q16—2442no—
472D8—21no—
473D8—21no—
474D8—21no—
475D8—42no—
476D8—1221no—
477D8—1221no—
478D8—4881no—
479D8—2442no—
480D8D4×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—21no—
490C4⋊C4—41no—
491C4⋊C4—611no—
492C4⋊C4—1221no—
493C4⋊C4—2441no—
494C4⋊C4—2441no—
495C4⋊C4—2441no—
496C4⋊C4—2441no—
497C22⋊C4—41no—
498C22⋊C4—611no—
499C22⋊C4—611no—
500C22⋊C4—2441no—
501C22⋊C4—2441no—
502C22⋊C4—2441no—
503C22⋊C4—2441no—
504C42—611no—
505C42—2441no—
506C16—21no—
507C16—21no—
508C16—612no—
509C16—1221no—
510C23—41no—
511C23—41no—
512C23—82no—
513C23—82no—
514C23—161no—
515C23—611no—
516C23—9761no—
517C23—4882no—
518C23—4882no—
519C23—2441no—
520C23D8×D6111yescharacteristic
521Q8—41no—
522Q8—41no—
523Q8—1222no—
524Q8—4882no—
525Q8—4882no—
526Q8—2441no—
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—611no—
547C2×C4—611no—
548C2×C4—611no—
549C2×C4—1221no—
550C2×C4—1221no—
551C2×C4—4882no—
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—
562C8C2×D4×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—81no—
584C4—81no—
585C4—612no—
586C4—1221no—
587C4—1221no—
588C4—4881no—
589C4—4881no—
590C4—2442no—
591C4#1684039411yescharacteristic
592C4#1684056611yescharacteristic
593C2—22no—
594C2—82no—
595C2—161no—
596C2—1222no—
597C2—9761no—
598C2#2145748911yescharacteristic
599C2C2×SD32×D6111yescharacteristic
600C2#2145896511yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2187C2
socleC22×C61C22×D8
prime radicalD8×C22⋊D61C2
hypercenter#2187D61
hypocenterC61D4×SD32
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2187

Complements

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

NH ≅ G/Ntype
1. C22×#14519721C2semidirect
2. C2×SD32×D61C2semidirect
3. #21457568C2semidirect
5. #21448073C2semidirect
6. #21447917C2semidirect
7. #21447914C2semidirect
8. #21447862C2semidirect
9. #21447858C2semidirect
10. #21447749C2semidirect
11. #21447738C2semidirect
12. #21447734C2semidirect
13. #21447674C2semidirect
14. #21447636C2semidirect
15. C61×#2187C2semidirect
16. C22×Dic244C22semidirect
17. C2×Q16×D61C22semidirect
21. C2×#14519722C22semidirect
22. C2×#14519722C22semidirect
26. C2×#14519721C22semidirect
27. C2×#14519721C22semidirect
28. C2×#14519720C22semidirect
30. C22×#11758185C22semidirect
31. C2×C16×D61C22semidirect
32. #16840140C22semidirect
34. #16840004C22semidirect
43. #16839856C22semidirect
46. #16839589C22semidirect
47. #16839580C22semidirect
48. #16839567C22semidirect
49. #16839567C22semidirect
50. #16839566C22semidirect
51. #16839562C22semidirect
52. #16839541C22semidirect
53. C16×Dic61C22semidirect
56. C2×SD32×C61C22semidirect
57. C61×#467C22semidirect
59. C61×#357C22semidirect
60. C61×C22⋊C16C22semidirect
100. #14519721D4semidirect
200. Dic244C2×D4semidirect
208. #11758185C2×D4semidirect
238. C22⋊D61SD32semidirect
273. C22×C61C2×SD32semidirect
281. C2×D61C2×SD32semidirect
292. Dic61C2×SD32semidirect
303. #2187D61semidirect
332. C2×SD32C2×D61semidirect
338. #467C2×D61semidirect
357. #357C2×D61semidirect
359. C22⋊C16C2×D61semidirect
361. C61D4×SD32semidirect
580. C22SD32×D61semidirect

Maximal subgroups

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

subgroupindex
C22×#145197212
C2×SD32×D612
#214575682
D8×C22⋊D612
#214480732
#214479172
#214479142
#214478622
#214478582
#214477492
#214477382
#214477342
#214476742
#214476362
C61×#21872
D4×SD3261