Finite Group Databasebeta

← #29651780

Subgroups — #29651780

Order 15616.

654 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456375C211yesmaximal, characteristic
2#21454761C211yesmaximal, characteristic, complemented
3#21454564C211yesmaximal, characteristic
4#21444707C211yesmaximal, characteristic, complemented
5#21444706C211yesmaximal, characteristic, complemented
6#21444661C211yesmaximal, characteristic, complemented
7#21444657C211yesmaximal, characteristic, complemented
8#21444656C211yesmaximal, characteristic, complemented
9#21444622C211yesmaximal, characteristic, complemented
10C8×#11758201C211yesmaximal, characteristic, complemented
11#334×D61C211yesmaximal, characteristic, complemented
12#21444220C211yesmaximal, characteristic, complemented
13#21444216C211yesmaximal, characteristic
14#21444098C211yesmaximal, characteristic, complemented
15C61×#1583C211yesmaximal, characteristic, complemented
16C2×#14519785—21no—
17#16840316C2211yescharacteristic
18#16840309C2211yescharacteristic
19#16840159C411yescharacteristic
20#16840133C411yescharacteristic
21#16840111C411yescharacteristic
22#16840107C411yescharacteristic
23#16839994C411yescharacteristic
24#16839992C411yescharacteristic
25#16839990C411yescharacteristic
26#16839988C411yescharacteristic
27#16839893C2211yescharacteristic
28#16839892—21no—
29#16839892C2211yescharacteristic
30#16839891—21no—
31#16839886C2211yescharacteristic
32C4×#11758190C2211yescharacteristic
33C4×#11758201C2211yescharacteristic
34C4×#11758200C2211yescharacteristic
35#16839839C2211yescharacteristic
36#16839831—21no—
37#16839830—21no—
38C8×D244C2211yescharacteristic
39D4×#92418C2211yescharacteristic
40#16839813C2211yescharacteristic
41#16839787—21no—
42C4⋊C8×D61C2211yescharacteristic
43C4⋊C8×D61C2211yescharacteristic
44#16839727—21no—
45#16839716—21no—
46C4×#11758189C2211yescharacteristic
47C4×C8×D61C2211yescharacteristic
48#16839513C2211yescharacteristic
49#16839512C2211yescharacteristic
50#16839512C2211yescharacteristic
51#16839494C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53#16839492C2211yescharacteristic
54#16839491C2211yescharacteristic
55D4⋊#92418C2211yescharacteristic
56#16839489C2211yescharacteristic
57#16839484C2211yescharacteristic
58C8×#92418C2211yescharacteristic
59C8×#92418C2211yescharacteristic
60C8×Q8×C61C2211yescharacteristic
61C4×SD16×C61C2211yescharacteristic
62C61×#436C2211yescharacteristic
63C61×#334C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic
66C61×#322C2211yescharacteristic
67C2×#11758222—21no—
68C2×#11758190C2×C411yescharacteristic
69C2×#11758200C2×C411yescharacteristic
70C2×#11758201C2×C411yescharacteristic
71#14519785—44no—
72C2×#11758189—21no—
73C2×#11758189D411yescharacteristic
74C2×#11758189D411yescharacteristic
75C22×#92418—21no—
76C2×C8×D61—21no—
77C2×C8×D61—21no—
78C2×C8×D61—21no—
79C2×C8×D61C2×C411yescharacteristic
80C2×C8×D61C2×C411yescharacteristic
81#14519776C2×C411yescharacteristic
82#14519776C2×C411yescharacteristic
83#14519775C2×C411yescharacteristic
84#14519773C2×C411yescharacteristic
85#14519767—21no—
86#14519763—21no—
87#14519757C2×C411yescharacteristic
88#14519755—21no—
89#14519753C2×C411yescharacteristic
90#14519752C2×C411yescharacteristic
91#14519750—21no—
92#14519748C2×C411yescharacteristic
93C4×Dic122—21no—
94C4×Dic122C2311yescharacteristic
95C4×D244C2311yescharacteristic
96C4×C22⋊D61—21no—
97#14519734—21no—
98C42×D61C2311yescharacteristic
99#14519709C2×C411yescharacteristic
100#14519708C2×C411yescharacteristic
101#14519708C2×C411yescharacteristic
102C4⋊#92418—21no—
103C4⋊#92418C2311yescharacteristic
104C4⋊#92418C2311yescharacteristic
105#14519706—21no—
106#14519706—21no—
107#14519706—21no—
108#14519706—21no—
109#14519706—21no—
110#14519702C2×C411yescharacteristic
111#14519701C2×C411yescharacteristic
112#14519700C2×C411yescharacteristic
113#14519699C2×C411yescharacteristic
114#14519698C2×C411yescharacteristic
115#14519697C2×C411yescharacteristic
116C22⋊#92418—21no—
117#14519689—21no—
118#14519689—21no—
119#14519689—21no—
120#14519688—21no—
121#14519687—21no—
122#14519687D411yescharacteristic
123#14519687D411yescharacteristic
124C4×#92418C2311yescharacteristic
125C4×#92418C2311yescharacteristic
126C4×#92418C2311yescharacteristic
127C8×Dic61—21no—
128C8×Dic61C2×C411yescharacteristic
129C8×Dic61C2×C411yescharacteristic
130C2×SD16×C61C2×C411yescharacteristic
131C2×M16×C61—21no—
132C4×Q8×C61C2311yescharacteristic
133C4×D4×C61C2311yescharacteristic
134#106×C61C2×C411yescharacteristic
135C4⋊C8×C61—21no—
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138#103×C61C2×C411yescharacteristic
139#102×C61C2×C411yescharacteristic
140C22⋊C8×C61—21no—
141C4×C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C4×C8×C61C2311yescharacteristic
145C2×Q8×C61C22×C411yescharacteristic
146C2×D4×C61C22×C411yescharacteristic
147C22×C4×C61—21no—
148C2×C22⋊D61—21no—
149C2×C22⋊D61—21no—
150C2×C22⋊D61—21no—
151#11758222—42no—
152#11758222—42no—
153C2×D244—21no—
154C2×D244C22×C411yescharacteristic
155C2×C4×D61—21no—
156C2×C4×D61C22×C411yescharacteristic
157C2×C4×D61C2×D411yescharacteristic
158C2×C4×D61#4111yescharacteristic
159C2×Dic122—21no—
160C2×Dic122—21no—
161C2×Dic122C22×C411yescharacteristic
162SD16×C61—41no—
163M16×C61—42no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61C22×C411yescharacteristic
168C2×C8×C61C22×C411yescharacteristic
169C2×C8×C61C2×D411yescharacteristic
170C2×C8×C61C2×D411yescharacteristic
171C4⋊C4×C61—21no—
172C4⋊C4×C61C22×C411yescharacteristic
173C4⋊C4×C61C22×C411yescharacteristic
174C22⋊C4×C61—21no—
175C42×C61—21no—
176C42×C61C2411yescharacteristic
177C22⋊Dic61—21no—
178#11758201—22no—
179#11758200—22no—
180#11758198—21no—
181#11758198—21no—
182#11758198—21no—
183#11758198—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61C22×C411yescharacteristic
186C4⋊Dic61C22×C411yescharacteristic
187#11758196—21no—
188#11758196—21no—
189#11758196—21no—
190#11758196—21no—
191#11758196—21no—
192#11758196—21no—
193C4×Dic61—21no—
194C4×Dic61C22×C411yescharacteristic
195C4×Dic61C2×D411yescharacteristic
196C4×Dic61#4111yescharacteristic
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—42no—
201C2×#92418C22×C411yescharacteristic
202C2×#92418C22×C411yescharacteristic
203C2×#92418C2×D411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205#11758190—41no—
206#11758189—22no—
207#11758189—42no—
208#11758189SD1614yescomplemented
209C8×D61—22no—
210C8×D61—41no—
211C8×D61—42no—
212C8×D61—42no—
213C8×D61—42no—
214C23×C61—21no—
215C22×D61—21no—
216C22×D61C4×D411yescharacteristic
217Q8×C61—21no—
218Q8×C61—21no—
219D4×C61—21no—
220D4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61C23×C411yescharacteristic
227C2×C4×C61C22×D411yescharacteristic
228C2×C4×C61C2×#4111yescharacteristic
229C22⋊D61—42no—
230C22⋊D61—42no—
231C22⋊D61—81no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61C4×D411yescharacteristic
236C2×Dic61C4×D411yescharacteristic
237C2×Dic61C4×D411yescharacteristic
238D244—21no—
239D244—21no—
240D244—42no—
241C4×D61—21no—
242C4×D61—21no—
243C4×D61—41no—
244C4×D61—41no—
245C4×D61—41no—
246C4×D61C2×SD1612yes—
247C4×D61#13512yes—
248Dic122—21no—
249Dic122—21no—
250Dic122—42no—
251Dic122—81no—
252C8×C61—21no—
253C8×C61—21no—
254C8×C61—21no—
255C8×C61—41no—
256C8×C61—41no—
257C8×C61—41no—
258C8×C61C2×SD1612yes—
259#92418—21no—
260#92418—21no—
261#92418—41no—
262#92418—41no—
263#92418—41no—
264#92418#13112yescomplemented
265#92418C2×SD1612yes—
266#18067—611nomaximal, Sylow
267C22×C61—41no—
268C22×C61—41no—
269C22×C61—41no—
270C22×C61C2×C4×D411yescharacteristic
271C2×D61—21no—
272C2×D61—21no—
273C2×D61—41no—
274C2×D61—41no—
275C2×D61—41no—
276C2×D61C4×SD1612yes—
277C4×C61—21no—
278C4×C61—41no—
279C4×C61—41no—
280C4×C61—41no—
281C4×C61C2×#13111yescharacteristic
282C4×C61#56811yescharacteristic
283C4×C61C22×SD1611yescharacteristic
284C4×C61C2×#13511yescharacteristic
285Dic61—21no—
286Dic61—21no—
287Dic61—41no—
288Dic61—41no—
289Dic61—41no—
290Dic61C4×SD1612yes—
291#3167—611no—
292#2962—611no—
293#2935—611no—
294#1590—611no—
295#1590—611no—
296#1583—611no—
297#1583D6111yescharacteristic, complemented
298#1582—611no—
299#1582—611no—
300C8×SD16—611no—
301C8×SD16—611no—
302C2×#334—611no—
303#1481—611no—
304#1480—611no—
305C8×M16—611no—
306C2×C61—81no—
307C2×C61#293511yescharacteristic
308C2×C61C2×C4×SD1611yescharacteristic
309C2×C61#295711yescharacteristic
310D61—22no—
311D61—81no—
312C2×#131—1221no—
313#533—611no—
314#532—611no—
315#498—611no—
316#492—611no—
317#487—611no—
318#486—611no—
319#465—611no—
320#465—611no—
321#465—611no—
322#465—611no—
323#446—611no—
324#446—611no—
325#446—1221no—
326#446—1221no—
327C8×Q8—611no—
328C8×Q8C2×D6111yescharacteristic
329C4×SD16—611no—
330C4×SD16—611no—
331C4×SD16—611no—
332C4×SD16C2×D6111yescharacteristic
333#436—611no—
334#436C2×D6111yescharacteristic
335#435—1221no—
336#435—1221no—
337C8×D4—611no—
338C8×D4—611no—
339#431—611no—
340#424—1221no—
341C2×C4⋊C8—611no—
342C2×C4⋊C8—611no—
343#408—1221no—
344#405—1221no—
345C4×M16—611no—
346C2×C4×C8—611no—
347#334—611no—
348#334—611no—
349#334—611no—
350#334C2×D6111yescharacteristic
351Q8⋊C8—611no—
352Q8⋊C8—611no—
353Q8⋊C8—611no—
354Q8⋊C8C2×D6111yescharacteristic
355D4⋊C8—611no—
356D4⋊C8—611no—
357D4⋊C8—611no—
358D4⋊C8C2×D6111yescharacteristic
359#322—611no—
360#322C2×D6111yescharacteristic
361C82—611no—
362C82—611no—
363C61#1806711yescharacteristic, complemented, Sylow
364C2×#41—1221no—
365C2×SD16—611no—
366C2×SD16—611no—
367C2×SD16—611no—
368C2×SD16C4×D6111yescharacteristic
369#131—2444no—
370C2×M16—21no—
371C2×M16—611no—
372C2×M16—611no—
373C2×M16—1221no—
374C22×C8—611no—
375C22×C8—611no—
376C22×C8—1221no—
377C22×C8—1221no—
378C22×C8—1221no—
379C22×C8—1221no—
380C4⋊Q8—611no—
381C4⋊Q8—611no—
382C4⋊Q8—611no—
383#127—611no—
384#125—1221no—
385#124—1221no—
386C22⋊Q8—611no—
387C22⋊Q8—611no—
388C22⋊Q8—1221no—
389#121—611no—
390#121—611no—
391#121—1221no—
392C4×Q8—611no—
393C4×Q8—1221no—
394C4×Q8C22×D6111yescharacteristic
395C4×D4—611no—
396C4×D4—1221no—
397C4×D4C22×D6111yescharacteristic
398#117—1221no—
399C2×C42—611no—
400#106—611no—
401#106—611no—
402#106—611no—
403#106C4×D6111yescharacteristic
404C4⋊C8—21no—
405C4⋊C8—611no—
406C4⋊C8—611no—
407C4⋊C8—1221no—
408C4⋊C8—1221no—
409C4⋊C8—1221no—
410C4⋊C8—1221no—
411C4⋊C8—1221no—
412C4⋊C8—1221no—
413C4⋊C8C22×D6111yescharacteristic
414C4⋊C8C22×D6111yescharacteristic
415#103—611no—
416#103—611no—
417#103—611no—
418#103C4×D6111yescharacteristic
419#102—611no—
420#102—611no—
421#102—611no—
422#102C4×D6111yescharacteristic
423C22⋊C8—21no—
424C22⋊C8—1221no—
425C22⋊C8—1221no—
426C22⋊C8—1221no—
427C22⋊C8—1221no—
428#97—611no—
429#97—611no—
430#97—1221no—
431#97—1221no—
432C4×C8—21no—
433C4×C8—611no—
434C4×C8—611no—
435C4×C8—611no—
436C4×C8—611no—
437C4×C8—611no—
438C4×C8—1221no—
439C4×C8C22×D6111yescharacteristic
440C4×C8C22×D6111yescharacteristic
441C4×C8C22×D6111yescharacteristic
442#41—2442no—
443#41—2442no—
444C2×Q8—611no—
445C2×Q8—1221no—
446C2×Q8—1221no—
447C2×Q8C2×C4×D6111yescharacteristic
448C2×D4—611no—
449C2×D4—1221no—
450C2×D4—1221no—
451C2×D4—1221no—
452C2×D4—1221no—
453C2×D4C2×C4×D6111yescharacteristic
454C22×C4—21no—
455C22×C4—611no—
456C22×C4—611no—
457C22×C4—611no—
458C22×C4—1221no—
459SD16—41no—
460SD16—1222no—
461SD16—1222no—
462SD16—2441no—
463M16—42no—
464M16—614no—
465M16—1222no—
466M16—2442no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—611no—
471C2×C8—611no—
472C2×C8—611no—
473C2×C8—611no—
474C2×C8—1222no—
475C2×C8—1221no—
476C2×C8—1221no—
477C2×C8—1221no—
478C2×C8—2441no—
479C2×C8—2442no—
480C2×C8—2442no—
481C2×C8—2442no—
482C2×C8—2442no—
483C2×C8C2×C4×D6111yescharacteristic
484C2×C8C2×C4×D6111yescharacteristic
485C2×C8D4×D6111yescharacteristic
486C2×C8D4×D6111yescharacteristic
487C4⋊C4—21no—
488C4⋊C4—611no—
489C4⋊C4—611no—
490C4⋊C4—1221no—
491C4⋊C4—1221no—
492C4⋊C4—1221no—
493C4⋊C4—1221no—
494C4⋊C4—1221no—
495C4⋊C4—1221no—
496C4⋊C4—1221no—
497C4⋊C4C2×C4×D6111yescharacteristic
498C4⋊C4C2×C4×D6111yescharacteristic
499C22⋊C4—21no—
500C22⋊C4—1221no—
501C22⋊C4—1221no—
502C22⋊C4—1221no—
503C22⋊C4—1221no—
504C22⋊C4—1221no—
505C42—21no—
506C42—611no—
507C42—611no—
508C42—611no—
509C42—1221no—
510C42C23×D6111yescharacteristic
511C23—21no—
512C23—611no—
513C23—1221no—
514Q8—21no—
515Q8—21no—
516Q8—1221no—
517Q8—1221no—
518Q8—4881no—
519Q8—2442no—
520D4—21no—
521D4—21no—
522D4—1221no—
523D4—1221no—
524D4—4881no—
525D4—2442no—
526D4—2442no—
527D4—2442no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—611no—
534C2×C4—612no—
535C2×C4—612no—
536C2×C4—611no—
537C2×C4—611no—
538C2×C4—1221no—
539C2×C4—1221no—
540C2×C4—1221no—
541C2×C4—1221no—
542C2×C4—1221no—
543C2×C4—2441no—
544C2×C4—2441no—
545C2×C4—2441no—
546C2×C4C22×C4×D6111yescharacteristic
547C2×C4C2×D4×D6111yescharacteristic
548C2×C4#41×D6111yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8—612no—
556C8—612no—
557C8—1221no—
558C8—1221no—
559C8—2441no—
560C8—2441no—
561C8—2441no—
562C8SD16×D6112yes—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—612no—
567C22—1221no—
568C22—1221no—
569C22—2441no—
570C22—2441no—
571C22—2441no—
572C22C4×D4×D6111yescharacteristic
573C4—21no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—612no—
578C4—1221no—
579C4—1221no—
580C4—2441no—
581C4—2441no—
582C4—2441no—
583C4#131×D6111yescharacteristic
584C4#1684052811yescharacteristic
585C4C2×SD16×D6111yescharacteristic
586C4#135×D6111yescharacteristic
587C2—81no—
588C2—1222no—
589C2—4881no—
590C2#2145456011yescharacteristic
591C2C4×SD16×D6111yescharacteristic
592C2#2145473311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1583C2
socleC22×C61C2×C4×D4
prime radical#16840309C22
cosocleC42×C61C24
hypercenter#1583D61
hypocenterC61#18067
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1583

Complements

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

NH ≅ G/Ntype
2. #21454761C2semidirect
4. #21444707C2semidirect
5. #21444706C2semidirect
6. #21444661C2semidirect
7. #21444657C2semidirect
8. #21444656C2semidirect
9. #21444622C2semidirect
10. C8×#11758201C2semidirect
11. #334×D61C2semidirect
12. #21444220C2semidirect
14. #21444098C2semidirect
15. C61×#1583C2semidirect
208. #11758189SD16semidirect
264. #92418#131semidirect
297. #1583D61semidirect
363. C61#18067semidirect

Maximal subgroups

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

subgroupindex
#214563752
#214547612
#214545642
#214447072
#214447062
#214446612
#214446572
#214446562
#214446222
C8×#117582012
#334×D612
#214442202
#214442162
#214440982
C61×#15832
#1806761