Finite Group Databasebeta

← #29663112

Subgroups — #29663112

Order 15616.

662 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456946C211yesmaximal, characteristic
2#21456743C211yesmaximal, characteristic
3#498×D61C211yesmaximal, characteristic, complemented
4#21454528C211yesmaximal, characteristic
5#21445319C211yesmaximal, characteristic, complemented
6#21445318C211yesmaximal, characteristic, complemented
7#21445315C211yesmaximal, characteristic, complemented
8#21445197C211yesmaximal, characteristic, complemented
9#21445196C211yesmaximal, characteristic, complemented
10#21445193C211yesmaximal, characteristic, complemented
11#21445192C211yesmaximal, characteristic, complemented
12#21444566C211yesmaximal, characteristic, complemented
13#21444502C211yesmaximal, characteristic, complemented
14#21444498C211yesmaximal, characteristic, complemented
15C61×#1691C211yesmaximal, characteristic, complemented
16C2×#14519785—21no—
17#16840309C2211yescharacteristic
18C4⋊Q8×D61C2211yescharacteristic
19C4⋊Q8×D61C2211yescharacteristic
20#16840160C2211yescharacteristic
21#16840159—21no—
22#16840159—21no—
23#16840159—21no—
24#16840158C2211yescharacteristic
25#16840158C2211yescharacteristic
26#16840133—21no—
27#16840111—21no—
28#16840107—21no—
29#16840082—21no—
30#16840079—21no—
31#16840053C2211yescharacteristic
32#16840052C2211yescharacteristic
33#16840049C2211yescharacteristic
34#16839968C2211yescharacteristic
35#16839967C2211yescharacteristic
36#16839964C2211yescharacteristic
37#16839902—21no—
38#16839899—21no—
39#16839841C2211yescharacteristic
40#16839838—21no—
41D4×#92418C2211yescharacteristic
42#16839827C2211yescharacteristic
43#16839825—21no—
44#16839814C2211yescharacteristic
45#16839814C2211yescharacteristic
46#106×D61—21no—
47#106×D61—21no—
48#16839784C2211yescharacteristic
49#16839727—21no—
50C4×C8×D61C2211yescharacteristic
51#16839515C2211yescharacteristic
52#16839512C2211yescharacteristic
53#16839512C2211yescharacteristic
54#16839511C2211yescharacteristic
55#16839510C2211yescharacteristic
56#16839510C2211yescharacteristic
57#16839509C2211yescharacteristic
58#16839508C2211yescharacteristic
59#16839507C2211yescharacteristic
60C61×#498C2211yescharacteristic
61C61×#476C2211yescharacteristic
62C61×#461C2211yescharacteristic
63C61×#436C2211yescharacteristic
64C61×#335C2211yescharacteristic
65C61×#333C2211yescharacteristic
66C61×#332C2211yescharacteristic
67C2×#11758222—21no—
68C2×Q8×D61—21no—
69C2×Q8×D61—21no—
70C2×#11758190—21no—
71C2×#11758200—21no—
72C2×#11758201—21no—
73#14519785—44no—
74C2×#11758189—21no—
75C2×#11758189—21no—
76C22×#92418—21no—
77C2×C8×D61—21no—
78C2×C8×D61D411yescharacteristic
79C2×C8×D61D411yescharacteristic
80#14519777C2311yescharacteristic
81#14519777C2311yescharacteristic
82#14519776—21no—
83#14519776—21no—
84#14519776—21no—
85#14519776—21no—
86#14519776D411yescharacteristic
87#14519775—21no—
88#14519775—21no—
89#14519773D411yescharacteristic
90#14519763—21no—
91#14519752D411yescharacteristic
92#14519750—21no—
93#14519748D411yescharacteristic
94C4×D244C2311yescharacteristic
95C4×C22⋊D61—21no—
96C4⋊C4×D61—21no—
97C4⋊C4×D61—21no—
98C4⋊C4×D61—21no—
99C4⋊C4×D61—21no—
100C42×D61C2311yescharacteristic
101#14519709—21no—
102#14519709—21no—
103#14519709—21no—
104#14519708—21no—
105#14519708—21no—
106#14519708—21no—
107#14519708—21no—
108#14519708—21no—
109#14519708—21no—
110C4⋊#92418C2311yescharacteristic
111C4⋊#92418C2311yescharacteristic
112C4⋊#92418C2311yescharacteristic
113#14519706—21no—
114#14519702—21no—
115#14519701—21no—
116#14519700—21no—
117#14519699—21no—
118#14519698—21no—
119#14519697—21no—
120C22⋊#92418—21no—
121#14519689—21no—
122#14519689—21no—
123#14519689—21no—
124#14519689—21no—
125C4×#92418C2311yescharacteristic
126C8×Dic61—21no—
127C8×Dic61—21no—
128C8×Dic61D411yescharacteristic
129C8×Dic61D411yescharacteristic
130C2×SD16×C61—21no—
131C2×M16×C61—21no—
132C4⋊Q8×C61C2311yescharacteristic
133C4⋊Q8×C61C2311yescharacteristic
134C4×D4×C61C2311yescharacteristic
135#106×C61—21no—
136#106×C61—21no—
137#106×C61—21no—
138C4⋊C8×C61C2311yescharacteristic
139C4⋊C8×C61C2311yescharacteristic
140C4⋊C8×C61C2311yescharacteristic
141#103×C61—21no—
142#102×C61—21no—
143C22⋊C8×C61—21no—
144C4×C8×C61C2311yescharacteristic
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×D4×C61C2×D411yescharacteristic
148C22×C4×C61—21no—
149C2×C22⋊D61—21no—
150C2×C22⋊D61—21no—
151C2×C22⋊D61—21no—
152Q8×D61—81no—
153Q8×D61—81no—
154Q8×D61—82no—
155#11758222—42no—
156#11758222—42no—
157C2×D244—21no—
158C2×D244C2×D411yescharacteristic
159C2×C4×D61—21no—
160C2×C4×D61—41no—
161C2×C4×D61—41no—
162C2×C4×D61C2×D411yescharacteristic
163C2×C4×D61C2×D411yescharacteristic
164C2×C4×D61#4111yescharacteristic
165C2×Dic122—21no—
166C2×Dic122—21no—
167C2×Dic122—21no—
168C2×Dic122—41no—
169C2×Dic122—41no—
170SD16×C61—81no—
171M16×C61—42no—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61C2×D411yescharacteristic
176C2×C8×C61C2×D411yescharacteristic
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61C2×D411yescharacteristic
182C22⋊C4×C61—21no—
183C42×C61C2411yescharacteristic
184C22⋊Dic61—21no—
185#11758201—81no—
186#11758200—81no—
187#11758198—21no—
188#11758198—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61C2×D411yescharacteristic
194#11758196—21no—
195#11758196—41no—
196#11758196—41no—
197#11758196—41no—
198#11758196—41no—
199C4×Dic61C2×D411yescharacteristic
200C4×Dic61C2×D411yescharacteristic
201C4×Dic61#4111yescharacteristic
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—42no—
206C2×#92418C2×D411yescharacteristic
207C2×#92418C2×D411yescharacteristic
208#11758190—81no—
209#11758189—42no—
210#11758189—42no—
211C8×D61—22no—
212C8×D61—42no—
213C8×D61SD1614yescomplemented
214C23×C61—21no—
215C22×D61—21no—
216C22×D61#12111yescharacteristic
217Q8×C61—41no—
218Q8×C61—41no—
219Q8×C61—81no—
220D4×C61—21no—
221D4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61C22×D411yescharacteristic
228C2×C4×C61C22×D411yescharacteristic
229C2×C4×C61C2×#4111yescharacteristic
230C22⋊D61—42no—
231C22⋊D61—42no—
232C22⋊D61—42no—
233C2×Dic61—21no—
234C2×Dic61—41no—
235C2×Dic61—41no—
236C2×Dic61#12111yescharacteristic
237C2×Dic61#12111yescharacteristic
238C2×Dic61#12111yescharacteristic
239D244—21no—
240D244—21no—
241D244—42no—
242C4×D61—21no—
243C4×D61—21no—
244C4×D61—22no—
245C4×D61—41no—
246C4×D61—41no—
247C4×D61—82no—
248C4×D61—82no—
249C4×D61C2×SD1612yes—
250C4×D61#13712yes—
251Dic122—42no—
252Dic122—41no—
253Dic122—41no—
254Dic122—82no—
255Dic122—82no—
256Dic122—81no—
257C8×C61—21no—
258C8×C61—41no—
259C8×C61—41no—
260C8×C61—41no—
261C8×C61C2×SD1612yes—
262#92418—21no—
263#92418—41no—
264#92418—41no—
265#92418—41no—
266#92418C2×SD1612yes—
267#19191—611nomaximal, Sylow
268C22×C61—41no—
269C22×C61—41no—
270C22×C61—41no—
271C22×C61C2×#12111yescharacteristic
272C2×D61—21no—
273C2×D61—21no—
274C2×D61—41no—
275C2×D61—41no—
276C2×D61—41no—
277C2×D61#46112yes—
278C4×C61—21no—
279C4×C61—41no—
280C4×C61—81no—
281C4×C61—81no—
282C4×C61C22×SD1611yescharacteristic
283C4×C61C2×#13711yescharacteristic
284C4×C61#57711yescharacteristic
285C4×C61#57711yescharacteristic
286Dic61—21no—
287Dic61—41no—
288Dic61—81no—
289Dic61—81no—
290Dic61#46112yes—
291Dic61#47112yes—
292#3227—611no—
293#3206—611no—
294C2×#498—611no—
295#2931—611no—
296#1691—611no—
297#1691—611no—
298#1691—611no—
299#1691D6111yescharacteristic, complemented
300#1671—611no—
301#1671—611no—
302#1671—611no—
303#1671—611no—
304#1564—611no—
305#1549—611no—
306#1548—611no—
307C2×C61—81no—
308C2×C61C2×#46111yescharacteristic
309C2×C61#305711yescharacteristic
310C2×C61C2×#47111yescharacteristic
311D61—22no—
312D61—81no—
313C2×#131—1221no—
314#532—611no—
315C2×C4⋊Q8—611no—
316C2×C4⋊Q8—611no—
317#498—611no—
318#498—611no—
319#498—611no—
320#498—1221no—
321#498—1221no—
322#498—1221no—
323#498C2×D6111yescharacteristic
324#492—1221no—
325#487—1221no—
326#486—1221no—
327#481—1221no—
328#481—1221no—
329#476—611no—
330#476—611no—
331#476—611no—
332#476C2×D6111yescharacteristic
333#461—611no—
334#461—611no—
335#461—611no—
336#461C2×D6111yescharacteristic
337#448—1221no—
338#448—1221no—
339#436—611no—
340#436—1221no—
341#436C2×D6111yescharacteristic
342C8×D4—611no—
343C8×D4—611no—
344C8×D4—1221no—
345#431—611no—
346#431—611no—
347C2×#106—1221no—
348C2×#106—1221no—
349#423—611no—
350#408—1221no—
351C2×C4×C8—611no—
352#335—611no—
353#335C2×D6111yescharacteristic
354#334—611no—
355#334—611no—
356#333—611no—
357#333—611no—
358#333—611no—
359#333C2×D6111yescharacteristic
360#332—611no—
361#332—611no—
362#332—611no—
363#332C2×D6111yescharacteristic
364C61#1919111yescharacteristic, complemented, Sylow
365C2×#41—1221no—
366C22×Q8—1221no—
367C22×Q8—1221no—
368C2×SD16—21no—
369C2×SD16—1221no—
370C2×SD16—1221no—
371C2×SD16—1221no—
372#131—2444no—
373C2×M16—21no—
374C2×M16—1221no—
375C2×M16—1221no—
376C22×C8—611no—
377C22×C8—611no—
378C22×C8—1221no—
379C22×C8—1221no—
380C4⋊Q8—611no—
381C4⋊Q8—611no—
382C4⋊Q8—611no—
383C4⋊Q8—1221no—
384C4⋊Q8—1221no—
385C4⋊Q8—1221no—
386C4⋊Q8—1221no—
387C4⋊Q8—1221no—
388C4⋊Q8—1221no—
389C4⋊Q8C22×D6111yescharacteristic
390C4⋊Q8C22×D6111yescharacteristic
391#127—611no—
392#124—1221no—
393#121—611no—
394#121—611no—
395#121—1221no—
396C4×D4—611no—
397C4×D4—1221no—
398C4×D4C22×D6111yescharacteristic
399C2×C4⋊C4—1221no—
400C2×C4⋊C4—1221no—
401C2×C4⋊C4—1221no—
402C2×C4⋊C4—1221no—
403C2×C42—611no—
404#106—21no—
405#106—21no—
406#106—21no—
407#106—1221no—
408#106—1221no—
409#106—1221no—
410#106—1221no—
411#106—1221no—
412#106—1221no—
413#106—1221no—
414#106—1221no—
415#106—1221no—
416C4⋊C8—611no—
417C4⋊C8—611no—
418C4⋊C8—611no—
419C4⋊C8—1221no—
420C4⋊C8C22×D6111yescharacteristic
421C4⋊C8C22×D6111yescharacteristic
422C4⋊C8C22×D6111yescharacteristic
423#103—21no—
424#103—1221no—
425#103—1221no—
426#103—1221no—
427#102—21no—
428#102—1221no—
429#102—1221no—
430#102—1221no—
431C22⋊C8—21no—
432C22⋊C8—1221no—
433C22⋊C8—1221no—
434C22⋊C8—1221no—
435C22⋊C8—1221no—
436C22⋊C8—1221no—
437C4×C8—611no—
438C4×C8—611no—
439C4×C8—611no—
440C4×C8—1221no—
441C4×C8—1221no—
442C4×C8C22×D6111yescharacteristic
443#41—2442no—
444#41—2442no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—1221no—
448C2×Q8—1221no—
449C2×Q8—1221no—
450C2×Q8—4881no—
451C2×Q8—4881no—
452C2×Q8—4882no—
453C2×Q8—2441no—
454C2×Q8—2441no—
455C2×D4—611no—
456C2×D4—1221no—
457C2×D4—1221no—
458C2×D4—1221no—
459C2×D4—1221no—
460C2×D4D4×D6111yescharacteristic
461C22×C4—21no—
462C22×C4—611no—
463C22×C4—611no—
464C22×C4—611no—
465C22×C4—1221no—
466C22×C4—2441no—
467C22×C4—2441no—
468SD16—81no—
469SD16—4881no—
470SD16—4881no—
471SD16—4881no—
472M16—42no—
473M16—2442no—
474M16—2442no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—611no—
479C2×C8—614no—
480C2×C8—611no—
481C2×C8—1222no—
482C2×C8—1221no—
483C2×C8—1221no—
484C2×C8—1221no—
485C2×C8—2442no—
486C2×C8—2442no—
487C2×C8D4×D6111yescharacteristic
488C2×C8D4×D6111yescharacteristic
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—611no—
494C4⋊C4—1221no—
495C4⋊C4—1221no—
496C4⋊C4—1221no—
497C4⋊C4—1221no—
498C4⋊C4—1221no—
499C4⋊C4—2441no—
500C4⋊C4—2441no—
501C4⋊C4—2441no—
502C4⋊C4—2441no—
503C4⋊C4D4×D6111yescharacteristic
504C22⋊C4—21no—
505C22⋊C4—1221no—
506C22⋊C4—1221no—
507C22⋊C4—1221no—
508C42—611no—
509C42—611no—
510C42—611no—
511C42C23×D6111yescharacteristic
512C23—21no—
513C23—611no—
514C23—1221no—
515Q8—41no—
516Q8—41no—
517Q8—81no—
518Q8—4881no—
519Q8—4882no—
520Q8—4882no—
521Q8—2442no—
522Q8—2441no—
523Q8—2441no—
524D4—21no—
525D4—21no—
526D4—1221no—
527D4—1221no—
528D4—2442no—
529D4—2442no—
530D4—2442no—
531D4—2442no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—611no—
538C2×C4—611no—
539C2×C4—612no—
540C2×C4—612no—
541C2×C4—611no—
542C2×C4—1222no—
543C2×C4—1221no—
544C2×C4—1221no—
545C2×C4—1221no—
546C2×C4—4882no—
547C2×C4—4882no—
548C2×C4—2441no—
549C2×C4—2441no—
550C2×C4—2441no—
551C2×C4—2441no—
552C2×C4C2×D4×D6111yescharacteristic
553C2×C4C2×D4×D6111yescharacteristic
554C2×C4#41×D6111yescharacteristic
555C8—21no—
556C8—41no—
557C8—41no—
558C8—41no—
559C8—612no—
560C8—1221no—
561C8—2441no—
562C8—2441no—
563C8—2441no—
564C8SD16×D6112yes—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—612no—
569C22—1221no—
570C22—1221no—
571C22—2441no—
572C22—2441no—
573C22—2441no—
574C22#121×D6111yescharacteristic
575C4—21no—
576C4—41no—
577C4—81no—
578C4—81no—
579C4—612no—
580C4—612no—
581C4—1221no—
582C4—4881no—
583C4—4881no—
584C4—2441no—
585C4C2×SD16×D6111yescharacteristic
586C4#137×D6111yescharacteristic
587C4#1684057111yescharacteristic
588C4#1684057211yescharacteristic
589C2—81no—
590C2—1222no—
591C2—4881no—
592C2#461×D6111yescharacteristic
593C2#2145545611yescharacteristic
594C2#471×D6111yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1691C2
socleC22×C61C2×#121
prime radical#16840309C22
hypercenter#1691D61
hypocenterC61#19191
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1691

Complements

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

NH ≅ G/Ntype
3. #498×D61C2semidirect
5. #21445319C2semidirect
6. #21445318C2semidirect
7. #21445315C2semidirect
8. #21445197C2semidirect
9. #21445196C2semidirect
10. #21445193C2semidirect
11. #21445192C2semidirect
12. #21444566C2semidirect
13. #21444502C2semidirect
14. #21444498C2semidirect
15. C61×#1691C2semidirect
213. C8×D61SD16semidirect
299. #1691D61semidirect
364. C61#19191semidirect

Maximal subgroups

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

subgroupindex
#214569462
#214567432
#498×D612
#214545282
#214453192
#214453182
#214453152
#214451972
#214451962
#214451932
#214451922
#214445662
#214445022
#214444982
C61×#16912
#1919161