Finite Group Databasebeta

← #30610836

Subgroups — #30610836

Order 15616.

1096 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462747C211yesmaximal, characteristic, complemented
2C4×#14519864C211yesmaximal, characteristic, complemented
3#21461172C212yesmaximal, complemented
4#21461166C211yesmaximal, characteristic, complemented
5#21461160C212yesmaximal, complemented
6#21461157C211yesmaximal, characteristic, complemented
7#21461140C211yesmaximal, characteristic, complemented
8#21461136C212yesmaximal, complemented
9#21461113C211yesmaximal, characteristic, complemented
10C2×#16840610C212yesmaximal, complemented
11#21459430C211yesmaximal, characteristic
12C2×#14519864—21no—
13#16840812—21no—
14#16840791—22no—
15D4×#92420—21no—
16#16840783C2212yescomplemented
17#16840781C2211yescharacteristic, complemented
18#16840766C2211yescharacteristic, complemented
19C2×C4⋊#92420C2212yescomplemented
20#16840727—21no—
21#16840726—22no—
22C4×#11758213C2211yescharacteristic, complemented
23C4×#11758217C2212yescomplemented
24C4×D61⋊C8C2211yescharacteristic, complemented
25C2×C4×#92420C2212yescomplemented
26Q8⋊#92420C2211yescharacteristic, complemented
27Q8⋊#92420C2211yescharacteristic, complemented
28Q8⋊#92420C2212yescomplemented
29#16840610C2211yescharacteristic
30#16840610C2212yes—
31#16840610C2211yescharacteristic
32#16840610C2212yescomplemented
33#16840610C2212yescomplemented
34#16840610C2212yescomplemented
35#16840610C2212yescomplemented
36#16840497C411yescharacteristic
37#16840473C411yescharacteristic
38#16840465—21no—
39#16840460C412yes—
40#16840439—22no—
41#16840407—21no—
42#16840403C412yes—
43D4×D244C411yescharacteristic
44#16840313C2211yescharacteristic
45#16840298C2212yes—
46#16840297—21no—
47#16840275—22no—
48C4×#11758226C2211yescharacteristic
49C4×#11758224C2211yescharacteristic
50C2×#14519739C2212yes—
51C4×D4×D61—21no—
52C61×#554C411yescharacteristic
53#14519864—28no—
54C2×#11758213—21no—
55C2×#11758213—21no—
56C2×#11758217—22no—
57C2×D61⋊C8—21no—
58C22×#92420—22no—
59C22×#92420—22no—
60C4⋊#92420—22no—
61C4⋊#92420—21no—
62C4⋊#92420C2311yescharacteristic
63C4⋊#92420C2312yes—
64C4⋊#92420C2311yescharacteristic
65#14519834—21no—
66C22⋊#92420—22no—
67#14519832—22no—
68#14519832—21no—
69#14519832—22no—
70C4×#92420—22no—
71C4×#92420—21no—
72C4×#92420—21no—
73C4×#92420C2311yescharacteristic
74C4×#92420C2312yes—
75C4×#92420C2311yescharacteristic
76C2×#11758226—21no—
77C2×#11758226C2×C411yescharacteristic
78C2×#11758224D411yescharacteristic
79C22×D244C2×C412yes—
80C2×D4×D61—21no—
81C22×C4×D61—22no—
82#14519774C2×C411yescharacteristic
83#14519772—22no—
84#14519772—22no—
85#14519768C2×C412yes—
86#14519766—21no—
87#14519766C2×C412yes—
88#14519765—21no—
89#14519762—22no—
90#14519762—22no—
91#14519762—22no—
92#14519761—22no—
93#14519757—21no—
94#14519753—22no—
95#14519752—21no—
96#14519752—21no—
97#14519752—22no—
98#14519752C2×C412yes—
99#14519751—22no—
100#14519751C2×C412yes—
101#14519747—22no—
102#14519747—22no—
103Q8×Dic61C2311yescharacteristic
104C4×Dic122C2×C411yescharacteristic
105#14519742D411yescharacteristic
106C4×D244—21no—
107C4×D244—21no—
108C4×D244C2×C411yescharacteristic
109D4×Dic61D411yescharacteristic
110#14519739—21no—
111#14519739—22no—
112#14519739—21no—
113#14519739—22no—
114#14519739C2×C412yes—
115#14519739C2×C412yes—
116#14519739C2311yescharacteristic
117#14519739C2312yes—
118C4×C22⋊D61—22no—
119C4×C22⋊D61C2×C412yes—
120#14519737—22no—
121#14519737D412yes—
122#14519735—21no—
123#14519735—22no—
124#14519735C2×C411yescharacteristic
125#14519735D411yescharacteristic
126#14519733D412yes—
127C4⋊C4×D61—21no—
128C2×#11758198—22no—
129C22⋊C4×D61—22no—
130C2×C4×Dic61C2312yes—
131C42×D61—21no—
132C42×D61C2311yescharacteristic
133C4⋊Q8×C61C2×C411yescharacteristic
134#125×C61—21no—
135C22⋊Q8×C61—22no—
136C22⋊Q8×C61C2×C412yes—
137C4×Q8×C61C2×C411yescharacteristic
138C4×D4×C61—21no—
139C4×D4×C61C2×C411yescharacteristic
140C2×C4⋊C4×C61C2×C412yes—
141C23×D61—22no—
142C2×Q8×C61—21no—
143C2×Q8×C61C22×C411yescharacteristic
144C2×D4×C61C22⋊C411yescharacteristic
145C22×C4×C61—22no—
146C22×C4×C61C22×C412yes—
147C2×C22⋊D61—22no—
148C2×C22⋊D61C22⋊C412yes—
149C22×Dic61C2×D412yes—
150C22×Dic61C2×D412yes—
151#11758226—22no—
152#11758226—41no—
153#11758226—81no—
154#11758226—81no—
155#11758224—24no—
156D4×D61—44no—
157C2×D244—24no—
158C2×D244—21no—
159C2×D244—21no—
160C2×D244—22no—
161C2×D244—22no—
162C2×D244—21no—
163C2×D244—42no—
164C2×D244C22×C412yes—
165C2×D244C22×C411yescharacteristic
166C2×C4×D61—21no—
167C2×C4×D61—21no—
168C2×C4×D61—21no—
169C2×C4×D61—22no—
170C2×C4×D61—22no—
171C2×C4×D61—22no—
172C2×C4×D61—82no—
173C2×C4×D61—82no—
174C2×C4×D61C22×C411yescharacteristic
175C2×C4×D61C2×D411yescharacteristic
176C2×C4×D61C2×D411yescharacteristic
177C2×Dic122C22⋊C411yescharacteristic
178#11758217—28no—
179C2×#92420—28no—
180C2×#92420—21no—
181C2×#92420—22no—
182C2×#92420—21no—
183C2×#92420—21no—
184C2×#92420—21no—
185C2×#92420—22no—
186C2×#92420—82no—
187#11758213—24no—
188#11758213—81no—
189D61⋊C8—24no—
190C4⋊C4×C61—22no—
191C4⋊C4×C61—21no—
192C4⋊C4×C61—21no—
193C4⋊C4×C61—22no—
194C4⋊C4×C61C22⋊C411yescharacteristic
195C4⋊C4×C61C22×C411yescharacteristic
196C4⋊C4×C61C22×C412yes—
197C22⋊C4×C61—22no—
198C22⋊C4×C61C22⋊C412yes—
199C42×C61—21no—
200C42×C61C22×C411yescharacteristic
201C22⋊Dic61C22⋊C412yes—
202#11758198—21no—
203#11758198—21no—
204#11758198—22no—
205#11758198—22no—
206#11758198—22no—
207#11758198—22no—
208#11758198—22no—
209#11758198—22no—
210#11758198—21no—
211#11758198—22no—
212#11758198C22⋊C412yes—
213C4⋊Dic61—22no—
214C4⋊Dic61—21no—
215C4⋊Dic61C22⋊C411yescharacteristic
216C4⋊Dic61C22×C411yescharacteristic
217#11758196—22no—
218#11758196C22⋊C412yes—
219#11758196C22⋊C412yes—
220C4×Dic61—21no—
221C4×Dic61—21no—
222C4×Dic61C22×C412yes—
223C4×Dic61C2×D411yescharacteristic
224C4×Dic61C2×D412yes—
225C4×Dic61C2×D411yescharacteristic
226C4×Dic61C2×D412yes—
227C4×Dic61C2411yescharacteristic
228C23×C61C2×C22⋊C412yes—
229C22×D61—21no—
230C22×D61—22no—
231C22×D61—44no—
232C22×D61—44no—
233C22×D61—82no—
234C22×D61C2×C22⋊C411yescharacteristic
235Q8×C61—21no—
236Q8×C61—21no—
237Q8×C61—81no—
238D4×C61#10414yes—
239C2×C4×C61—22no—
240C2×C4×C61—22no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—22no—
244C2×C4×C61—82no—
245C2×C4×C61C2×C22⋊C412yes—
246C2×C4×C61C2×C22⋊C411yescharacteristic
247C2×C4×C61C2×C22⋊C411yescharacteristic
248C2×C4×C61C23×C411yescharacteristic
249C22⋊D61—24no—
250C22⋊D61—44no—
251C2×Dic61—24no—
252C2×Dic61—22no—
253C2×Dic61—22no—
254C2×Dic61—21no—
255C2×Dic61C2×C22⋊C411yescharacteristic
256C2×Dic61C2×C22⋊C412yes—
257C2×Dic61C2×C22⋊C412yes—
258C2×Dic61C22×D411yescharacteristic
259C2×Dic61C22×D411yescharacteristic
260D244—22no—
261D244—21no—
262D244—22no—
263D244—44no—
264D244—42no—
265D244—42no—
266D244—81no—
267D244—82no—
268D244#13112yescomplemented
269C4×D61—21no—
270C4×D61—21no—
271C4×D61—22no—
272C4×D61—21no—
273C4×D61—21no—
274C4×D61—42no—
275C4×D61—42no—
276C4×D61—41no—
277C4×D61—42no—
278C4×D61—41no—
279C4×D61—42no—
280C4×D61—82no—
281C4×D61—82no—
282Dic122—22no—
283#92420—22no—
284#92420—22no—
285#92420—24no—
286#92420—42no—
287#92420—41no—
288#92420—41no—
289#17517—611nomaximal, Sylow
290C22×C61—22no—
291C22×C61—22no—
292C22×C61C2×#10414yes—
293C22×C61C22×C22⋊C411yescharacteristic
294C2×D61—21no—
295C2×D61—22no—
296C2×D61—21no—
297C2×D61—21no—
298C2×D61—41no—
299C2×D61—41no—
300C2×D61—42no—
301C2×D61—42no—
302C2×D61—42no—
303C2×D61—88no—
304C4×C61—22no—
305C4×C61—21no—
306C4×C61—41no—
307C4×C61—41no—
308C4×C61—42no—
309C4×C61C2×#10412yes—
310C4×C61C2×#13111yescharacteristic
311C4×C61#56811yescharacteristic
312Dic61—21no—
313Dic61—22no—
314Dic61—21no—
315Dic61—22no—
316Dic61—41no—
317Dic61#57611yescharacteristic
318Dic61#57711yescharacteristic
319#3481—611no—
320#2990—611no—
321C4×#131—611no—
322#1494—612no—
323#1492—611no—
324#1490—612no—
325#1489—611no—
326#1484—611no—
327#1483—612no—
328#1476—611no—
329C2×D4⋊C8—612no—
330C2×C61—24no—
331C2×C61#288011yescharacteristic
332C2×C61#289711yescharacteristic
333C2×C61C22×#10411yescharacteristic
334D61—41no—
335D61—42no—
336D61—82no—
337C2×#131—1221no—
338#559—611no—
339#554—611no—
340#554#692311yescharacteristic
341#553—612no—
342#553—1221no—
343#551—1222no—
344#546—612no—
345#546—1221no—
346D42—611no—
347#532—611no—
348#529—612no—
349#529—1221no—
350#525—1222no—
351C4×#41—611no—
352C4×#41—611no—
353C2×C4×D4—612no—
354C2×C4×D4—1221no—
355#446—1221no—
356#435—1222no—
357C8×D4—1221no—
358#432—612no—
359#431—611no—
360#423—611no—
361C2×C4⋊C8—612no—
362#405—1222no—
363#405—1221no—
364C4×M16—612no—
365C4×M16—611no—
366C2×C4×C8—612no—
367C2×C4×C8—611no—
368Q8⋊C8—611no—
369Q8⋊C8—611no—
370Q8⋊C8—612no—
371D4⋊C8—611no—
372D4⋊C8—612no—
373D4⋊C8—611no—
374D4⋊C8—612no—
375D4⋊C8—612no—
376D4⋊C8—612no—
377D4⋊C8—612no—
378C61#1751711yescharacteristic, complemented, Sylow
379C2×#41—611no—
380C2×#41—611no—
381C2×#41—1221no—
382C22×D4—612no—
383C22×D4—1221no—
384C23×C4—1222no—
385#131—1228no—
386C2×M16—1222no—
387C2×M16—1221no—
388C2×M16—1221no—
389C22×C8—1222no—
390C22×C8—1221no—
391C22×C8—1222no—
392C4⋊Q8C2×#692311yescharacteristic
393#127—611no—
394#126—1222no—
395#126—1222no—
396#125—21no—
397#125—612no—
398#124—612no—
399#124—1221no—
400#124—1221no—
401#123—1222no—
402#123—1222no—
403#123—1222no—
404#123—1222no—
405C22⋊Q8—22no—
406C22⋊Q8—1221no—
407C22⋊Q8—1222no—
408C22⋊Q8C2×#692312yes—
409#121—612no—
410#121—612no—
411#121—1222no—
412#121—1221no—
413#121—1222no—
414#121—1221no—
415#120—1222no—
416#120—1222no—
417C4×Q8—611no—
418C4×Q8—611no—
419C4×Q8—611no—
420C4×Q8C2×#692311yescharacteristic
421C4×D4—21no—
422C4×D4—611no—
423C4×D4—612no—
424C4×D4—612no—
425C4×D4—611no—
426C4×D4—612no—
427C4×D4—612no—
428C4×D4—612no—
429C4×D4—611no—
430C4×D4—1221no—
431C4×D4—1221no—
432C4×D4—1222no—
433C4×D4—1222no—
434C4×D4—1221no—
435C4×D4—1222no—
436C4×D4—1222no—
437C4×D4—1221no—
438C4×D4C2×#692311yescharacteristic
439#117—611no—
440#117—612no—
441#117—611no—
442#117—1221no—
443#117—1222no—
444C2×C4⋊C4—1221no—
445C2×C4⋊C4C2×#692312yes—
446C2×C22⋊C4—1222no—
447C2×C22⋊C4—1222no—
448C2×C42—612no—
449C2×C42—611no—
450C2×C42—1221no—
451C4⋊C8—611no—
452C4⋊C8—612no—
453C4⋊C8—611no—
454C4⋊C8—1222no—
455C4⋊C8—1221no—
456C22⋊C8—1222no—
457C22⋊C8—1221no—
458#97—1221no—
459#97—1222no—
460#97—1222no—
461C4×C8—611no—
462C4×C8—612no—
463C4×C8—611no—
464C4×C8—1221no—
465C4×C8—1222no—
466C4×C8—1221no—
467C24—1222no—
468#41—1224no—
469#41—1222no—
470#41—4881no—
471#41—4881no—
472#41—2441no—
473C2×Q8—21no—
474C2×Q8—611no—
475C2×Q8C22×#692311yescharacteristic
476C2×D4—612no—
477C2×D4—611no—
478C2×D4—612no—
479C2×D4—1224no—
480C2×D4—1222no—
481C2×D4—1221no—
482C2×D4—1222no—
483C2×D4—1221no—
484C2×D4—1222no—
485C2×D4—1221no—
486C2×D4—2442no—
487C2×D4—2444no—
488C2×D4C22⋊#692311yescharacteristic
489C22×C4—22no—
490C22×C4—612no—
491C22×C4—612no—
492C22×C4—611no—
493C22×C4—611no—
494C22×C4—611no—
495C22×C4—1222no—
496C22×C4—1222no—
497C22×C4—1221no—
498C22×C4—1221no—
499C22×C4—1222no—
500C22×C4—1221no—
501C22×C4—4882no—
502C22×C4—4882no—
503C22×C4C22×#692312yes—
504M16—1224no—
505M16—1228no—
506M16—4881no—
507C2×C8—1221no—
508C2×C8—1222no—
509C2×C8—1221no—
510C2×C8—1224no—
511C2×C8—1228no—
512C2×C8—1221no—
513C2×C8—1221no—
514C2×C8—1222no—
515C2×C8—4882no—
516C4⋊C4—21no—
517C4⋊C4—22no—
518C4⋊C4—21no—
519C4⋊C4—22no—
520C4⋊C4—611no—
521C4⋊C4—612no—
522C4⋊C4—612no—
523C4⋊C4—611no—
524C4⋊C4—1222no—
525C4⋊C4—1221no—
526C4⋊C4—1222no—
527C4⋊C4C22⋊#692311yescharacteristic
528C4⋊C4C22×#692311yescharacteristic
529C4⋊C4C22×#692312yes—
530C22⋊C4—22no—
531C22⋊C4—612no—
532C22⋊C4—612no—
533C22⋊C4—1221no—
534C22⋊C4—1222no—
535C22⋊C4—1222no—
536C22⋊C4—1222no—
537C22⋊C4—1222no—
538C22⋊C4—1222no—
539C22⋊C4—1222no—
540C22⋊C4—1221no—
541C22⋊C4—1221no—
542C22⋊C4—1222no—
543C22⋊C4C22⋊#692312yes—
544C42—21no—
545C42—611no—
546C42—612no—
547C42—611no—
548C42—612no—
549C42—611no—
550C42—612no—
551C42—1221no—
552C42—1221no—
553C42C22×#692311yescharacteristic
554C23—611no—
555C23—1221no—
556C23—1222no—
557C23—4882no—
558C23—2444no—
559C23—2444no—
560C23C2×C22⋊#692312yes—
561Q8—21no—
562Q8—21no—
563Q8—81no—
564Q8—1222no—
565D4—612no—
566D4—1224no—
567D4—1222no—
568D4—1221no—
569D4—1222no—
570D4—4881no—
571D4—4882no—
572D4—2444no—
573D4—2442no—
574D4—2444no—
575D4—2442no—
576D4#1451984214yes—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—82no—
583C2×C4—611no—
584C2×C4—611no—
585C2×C4—612no—
586C2×C4—612no—
587C2×C4—611no—
588C2×C4—1221no—
589C2×C4—1221no—
590C2×C4—1222no—
591C2×C4—1222no—
592C2×C4—1224no—
593C2×C4—1222no—
594C2×C4—1221no—
595C2×C4—1221no—
596C2×C4—1221no—
597C2×C4—4882no—
598C2×C4—4882no—
599C2×C4—2441no—
600C2×C4—2441no—
601C2×C4—2442no—
602C2×C4—2442no—
603C2×C4—2442no—
604C2×C4—2442no—
605C2×C4C2×C22⋊#692312yes—
606C2×C4C2×C22⋊#692311yescharacteristic
607C2×C4C2×C22⋊#692311yescharacteristic
608C2×C4C23×#692311yescharacteristic
609C8—1222no—
610C8—1222no—
611C8—1224no—
612C8—2441no—
613C8—2441no—
614C8—2442no—
615C22—22no—
616C22—22no—
617C22—1221no—
618C22—1222no—
619C22—1221no—
620C22—1221no—
621C22—4888no—
622C22—2442no—
623C22—2442no—
624C22—2442no—
625C22—2441no—
626C22—2441no—
627C22C2×#1451984214yes—
628C22C22×C22⋊#692311yescharacteristic
629C4—22no—
630C4—21no—
631C4—41no—
632C4—41no—
633C4—42no—
634C4—611no—
635C4—611no—
636C4—1221no—
637C4—1222no—
638C4—1221no—
639C4—1222no—
640C4—2441no—
641C4C2×#1451984212yes—
642C4D61⋊#13111yescharacteristic
643C4#1684084111yescharacteristic
644C2—24no—
645C2—4882no—
646C2—2441no—
647C2—2442no—
648C2#2146240911yescharacteristic
649C2#2146244011yescharacteristic
650C2C22×#1451984211yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#554C4
socleC22×C61C22×C22⋊C4
prime radical#21459430C2
cosocleC4×Dic61C24
hypercenter#554#6923
hypocenterC61#17517
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #554

Complements

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

NH ≅ G/Ntype
1. #21462747C2semidirect
2. C4×#14519864C2semidirect
3. #21461172C2semidirect
4. #21461166C2semidirect
5. #21461160C2semidirect
6. #21461157C2semidirect
7. #21461140C2semidirect
8. #21461136C2semidirect
9. #21461113C2semidirect
10. C2×#16840610C2semidirect
16. #16840783C22semidirect
17. #16840781C22semidirect
18. #16840766C22semidirect
19. C2×C4⋊#92420C22semidirect
22. C4×#11758213C22semidirect
23. C4×#11758217C22semidirect
24. C4×D61⋊C8C22semidirect
25. C2×C4×#92420C22semidirect
26. Q8⋊#92420C22semidirect
27. Q8⋊#92420C22semidirect
28. Q8⋊#92420C22semidirect
32. #16840610C22semidirect
33. #16840610C22semidirect
34. #16840610C22semidirect
35. #16840610C22semidirect
268. D244#131semidirect
378. C61#17517semidirect

Maximal subgroups

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

subgroupindex
#214627472
C4×#145198642
#214611722
#214611662
#214611602
#214611572
#214611402
#214611362
#214611132
C2×#168406102
#214594302
#1751761