Finite Group Databasebeta

← #30612550

Subgroups — #30612550

Order 15616.

684 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462743C211yesmaximal, characteristic, complemented
2#21462682C211yesmaximal, characteristic, complemented
3#21461468C211yesmaximal, characteristic, complemented
4#21461467C211yesmaximal, characteristic, complemented
5#21461463C211yesmaximal, characteristic, complemented
6#21461462C211yesmaximal, characteristic, complemented
7#21461455C211yesmaximal, characteristic, complemented
8#21461453C211yesmaximal, characteristic, complemented
9#21461451C211yesmaximal, characteristic, complemented
10#21461450C211yesmaximal, characteristic, complemented
11#21461371C211yesmaximal, characteristic, complemented
12#21461113C211yesmaximal, characteristic, complemented
13D61⋊(D4⋊C8)C211yesmaximal, characteristic, complemented
14#21461017C211yesmaximal, characteristic, complemented
15#21454624C211yesmaximal, characteristic
16#16840813C2211yescharacteristic, complemented
17#16840813C2211yescharacteristic, complemented
18#16840797C2211yescharacteristic
19#16840797C2211yescharacteristic
20#16840796C2211yescharacteristic
21#16840796C2211yescharacteristic
22#16840796C2211yescharacteristic, complemented
23#16840796C2211yescharacteristic, complemented
24#16840795—21no—
25#16840795—21no—
26#16840792—21no—
27#16840792—21no—
28#16840785—21no—
29#16840781C2211yescharacteristic
30#16840780C2211yescharacteristic
31#16840767—21no—
32D61⋊(C4⋊C8)C2211yescharacteristic
33#16840734—21no—
34#16840733—21no—
35C4×D61⋊C8C2211yescharacteristic
36#16840626C2211yescharacteristic, complemented
37#16840625C2211yescharacteristic, complemented
38#16840624C2211yescharacteristic, complemented
39#16840623C2211yescharacteristic, complemented
40Q8⋊#92420C2211yescharacteristic, complemented
41Q8⋊#92420C2211yescharacteristic, complemented
42#16840610C2211yescharacteristic
43#16840610C2211yescharacteristic
44#16840610C2211yescharacteristic, complemented
45#16840610C2211yescharacteristic, complemented
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48#16840603C2211yescharacteristic, complemented
49#16840603C2211yescharacteristic, complemented
50C8×#92420C2211yescharacteristic, complemented
51C8×#92420C2211yescharacteristic, complemented
52C2×#14519804C411yescharacteristic
53C4×#11758226C2211yescharacteristic
54C4×D4×D61C2211yescharacteristic
55#16839875C411yescharacteristic
56#16839872C411yescharacteristic
57#16839860C411yescharacteristic
58SD16×Dic61C2211yescharacteristic
59#16839847C2211yescharacteristic
60#16839844C2211yescharacteristic
61#16839842C2211yescharacteristic
62#16839803C411yescharacteristic
63#16839765C411yescharacteristic
64#16839762C411yescharacteristic
65#16839714C2211yescharacteristic
66C61×#440C411yescharacteristic
67C2×#11758213—21no—
68C2×#11758213—21no—
69C2×#11758213—21no—
70C2×#11758213—21no—
71C2×#11758217—21no—
72C2×#11758217—21no—
73C2×D61⋊C8—21no—
74C2×D61⋊C8—21no—
75#14519844—21no—
76#14519844—21no—
77#14519844—21no—
78#14519844D411yescharacteristic
79#14519844D411yescharacteristic
80C4⋊#92420C2311yescharacteristic
81C4⋊#92420C2311yescharacteristic
82C4⋊#92420C2311yescharacteristic
83C4⋊#92420C2311yescharacteristic
84#14519834—21no—
85#14519834—21no—
86#14519834—21no—
87#14519834—21no—
88#14519834—21no—
89#14519834D411yescharacteristic
90#14519834D411yescharacteristic
91C22⋊#92420—21no—
92C22⋊#92420—21no—
93#14519832—21no—
94#14519832—21no—
95C4×#92420—21no—
96C4×#92420—21no—
97C4×#92420C2311yescharacteristic
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C2×#11758226C2×C411yescharacteristic
102C2×D4×D61C2×C411yescharacteristic
103C22×C4×D61—21no—
104#14519804—24no—
105C2×#11758201C2×C411yescharacteristic
106C2×D488C2×C411yescharacteristic
107C2×#11758199C2×C411yescharacteristic
108C2×#11758189C2×C411yescharacteristic
109C2×#11758189C2×C411yescharacteristic
110Q8×Dic61C2311yescharacteristic
111C4×D244—21no—
112C4×D244C2×C411yescharacteristic
113C4×D244C2×C411yescharacteristic
114D4×Dic61C2311yescharacteristic
115#14519739—21no—
116#14519739C2311yescharacteristic
117#14519739C2311yescharacteristic
118C4×C22⋊D61—21no—
119#14519737—21no—
120#14519735—21no—
121#14519735C2×C411yescharacteristic
122C4⋊C4×D61C2×C411yescharacteristic
123C22⋊C4×D61—21no—
124C42×D61—21no—
125C42×D61C2311yescharacteristic
126#14519710C2×C411yescharacteristic
127#14519709C2×C411yescharacteristic
128#14519708C2×C411yescharacteristic
129#14519701C2×C411yescharacteristic
130#14519699C2×C411yescharacteristic
131#14519699C2×C411yescharacteristic
132#14519698C2×C411yescharacteristic
133#14519697C2×C411yescharacteristic
134#14519697C2×C411yescharacteristic
135#14519688C2×C411yescharacteristic
136C8×Dic61C2311yescharacteristic
137C8×Dic61C2311yescharacteristic
138C2×SD16×C61C2×C411yescharacteristic
139C4×Q8×C61C2×C411yescharacteristic
140C4×D4×C61C2×C411yescharacteristic
141#107×C61C2×C411yescharacteristic
142#103×C61C2×C411yescharacteristic
143#102×C61C2×C411yescharacteristic
144#97×C61C2×C411yescharacteristic
145C23×D61—21no—
146C2×Q8×C61C22×C411yescharacteristic
147C2×D4×C61C22×C411yescharacteristic
148C22×C4×C61—21no—
149C2×C22⋊D61—21no—
150C22×Dic61—21no—
151#11758226—22no—
152#11758226—22no—
153D4×D61—22no—
154D4×D61—22no—
155C2×D244—21no—
156C2×D244C22×C411yescharacteristic
157C2×D244C22×C411yescharacteristic
158C2×C4×D61—21no—
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×C4×D61—21no—
163C2×C4×D61—21no—
164C2×C4×D61—81no—
165C2×C4×D61—81no—
166C2×C4×D61C22×C411yescharacteristic
167C2×C4×D61C2×D411yescharacteristic
168C2×C4×D61#4111yescharacteristic
169#11758217—81no—
170#11758217—81no—
171C2×#92420—21no—
172C2×#92420—21no—
173C2×#92420—21no—
174C2×#92420—21no—
175C2×#92420—21no—
176C2×#92420—21no—
177C2×#92420C2×D411yescharacteristic
178C2×#92420C2×D411yescharacteristic
179C2×#92420C2×D411yescharacteristic
180C2×#92420C2×D411yescharacteristic
181#11758213—81no—
182#11758213—81no—
183#11758213—81no—
184#11758213—81no—
185D61⋊C8—42no—
186D61⋊C8—81no—
187SD16×C61—22no—
188C2×C8×C61C22×C411yescharacteristic
189C2×C8×C61C22×C411yescharacteristic
190C4⋊C4×C61—21no—
191C4⋊C4×C61C22×C411yescharacteristic
192C4⋊C4×C61C22×C411yescharacteristic
193C22⋊C4×C61—21no—
194C42×C61—21no—
195C42×C61C22×C411yescharacteristic
196C22⋊Dic61—21no—
197#11758201—22no—
198#11758199—22no—
199#11758198—21no—
200#11758198—21no—
201#11758198—21no—
202#11758198—21no—
203#11758198—21no—
204C4⋊Dic61—21no—
205C4⋊Dic61C22×C411yescharacteristic
206C4⋊Dic61C22×C411yescharacteristic
207#11758196—21no—
208C4×Dic61—21no—
209C4×Dic61—21no—
210C4×Dic61C2×D411yescharacteristic
211C4×Dic61#4111yescharacteristic
212C4×Dic61C2411yescharacteristic
213C2×#92418C22×C411yescharacteristic
214C2×#92418C22×C411yescharacteristic
215D488—22no—
216#11758189—22no—
217#11758189M1614yescomplemented
218C23×C61—21no—
219C22×D61—21no—
220C22×D61—21no—
221C22×D61—42no—
222C22×D61—81no—
223C22×D61—81no—
224C22×D61C4×D411yescharacteristic
225Q8×C61—21no—
226Q8×C61—21no—
227D4×C61—21no—
228D4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—81no—
233C2×C4×C61C4×D411yescharacteristic
234C2×C4×C61C4×D411yescharacteristic
235C2×C4×C61C23×C411yescharacteristic
236C22⋊D61—42no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—41no—
240C2×Dic61—41no—
241C2×Dic61C4×D411yescharacteristic
242C2×Dic61C22×D411yescharacteristic
243C2×Dic61C2×#4111yescharacteristic
244D244—21no—
245D244—21no—
246D244—21no—
247D244—21no—
248D244—42no—
249C4×D61—21no—
250C4×D61—21no—
251C4×D61—41no—
252C4×D61—41no—
253C4×D61—41no—
254C4×D61—41no—
255C4×D61—41no—
256C4×D61—42no—
257C4×D61—81no—
258C4×D61—81no—
259C4×D61—81no—
260C4×D61C2×M1612yes—
261C4×D61#13112yes—
262#92420—22no—
263#92420—21no—
264#92420—21no—
265#92420—21no—
266#92420—21no—
267#92420—41no—
268#92420—41no—
269#92420—41no—
270#92420—41no—
271#92420—41no—
272C8×C61—21no—
273C8×C61C2×M1612yes—
274#92418—21no—
275#92418C2×M1612yes—
276#17893—611nomaximal, Sylow
277C22×C61—41no—
278C22×C61—41no—
279C22×C61—41no—
280C22×C61C2×C4×D411yescharacteristic
281C2×D61—21no—
282C2×D61—21no—
283C2×D61—41no—
284C2×D61—41no—
285C2×D61—41no—
286C2×D61—41no—
287C2×D61—41no—
288C2×D61—41no—
289C2×D61—84no—
290C2×D61#43612yes—
291C4×C61—21no—
292C4×C61—21no—
293C4×C61—41no—
294C4×C61—41no—
295C4×C61—41no—
296C4×C61C22×M1611yescharacteristic
297C4×C61C2×#13111yescharacteristic
298Dic61—21no—
299Dic61—41no—
300Dic61—41no—
301Dic61#43612yes—
302Dic61#57611yescharacteristic
303Dic61#57711yescharacteristic
304#2989—611no—
305#2975—611no—
306C4×AGL(1,ℤ/8)—611no—
307#1594—611no—
308#1594—611no—
309#1592—611no—
310#1592—611no—
311#1590—611no—
312#1590—611no—
313#1589—611no—
314#1589—611no—
315#1565—611no—
316#1476—611no—
317C2×D4⋊C8—611no—
318C8×M16—611no—
319C2×C61—81no—
320C2×C61C2×#43611yescharacteristic
321C2×C61#294611yescharacteristic
322C2×C61#295611yescharacteristic
323D61—22no—
324D61—81no—
325D61—81no—
326C2×AGL(1,ℤ/8)—611no—
327C4×#41—611no—
328C2×C4×D4—611no—
329#446—611no—
330#446—611no—
331#442—611no—
332#442—611no—
333#440—611no—
334#440#692311yescharacteristic
335C4×SD16—611no—
336C4×SD16—611no—
337C4×D8—611no—
338C4×D8—611no—
339#436—611no—
340#436—611no—
341#436—611no—
342#436—611no—
343#436—611no—
344#436—611no—
345#436—1221no—
346#436—1221no—
347#435—1221no—
348#435—1221no—
349#432—1221no—
350#431—611no—
351#431—611no—
352#428—611no—
353#423—1221no—
354C2×C4⋊C8—611no—
355#418—611no—
356#417—611no—
357#407—1221no—
358#407—1221no—
359C4×M16—611no—
360C2×C4×C8—611no—
361#335—611no—
362#335—611no—
363#334—611no—
364#334—611no—
365Q8⋊C8—611no—
366Q8⋊C8—611no—
367D4⋊C8—611no—
368D4⋊C8—611no—
369D4⋊C8—611no—
370D4⋊C8—611no—
371D4⋊C8—611no—
372D4⋊C8—611no—
373#322—611no—
374#322—611no—
375C82—611no—
376C82—611no—
377C61#1789311yescharacteristic, complemented, Sylow
378C2×#41—611no—
379C22×D4—611no—
380C23×C4—1221no—
381AGL(1,ℤ/8)—1224no—
382C2×SD16—611no—
383C2×SD16C2×#692311yescharacteristic
384C2×D8—611no—
385C2×D8—611no—
386C2×M16—611no—
387C2×M16—611no—
388C2×M16—1221no—
389C2×M16—1221no—
390C2×M16—1221no—
391C2×M16—1221no—
392C2×M16—1221no—
393C2×M16—1221no—
394C22×C8—1221no—
395C22×C8—1221no—
396C4×Q8—611no—
397C4×Q8C2×#692311yescharacteristic
398C4×D4—611no—
399C4×D4—611no—
400C4×D4—611no—
401C4×D4—611no—
402C4×D4—611no—
403C4×D4—1221no—
404C4×D4—1221no—
405C4×D4—1221no—
406C4×D4—1221no—
407C4×D4C2×#692311yescharacteristic
408#117—611no—
409#117—1221no—
410C2×C4⋊C4—611no—
411C2×C22⋊C4—1221no—
412C2×C42—611no—
413C2×C42—1221no—
414#107—611no—
415#107C2×#692311yescharacteristic
416#106—611no—
417#106—611no—
418C4⋊C8—611no—
419C4⋊C8—611no—
420C4⋊C8—611no—
421C4⋊C8—611no—
422C4⋊C8—611no—
423C4⋊C8—611no—
424C4⋊C8—1221no—
425C4⋊C8—1221no—
426C4⋊C8—1221no—
427#103—611no—
428#103C2×#692311yescharacteristic
429#102—611no—
430#102—611no—
431#102—611no—
432#102—611no—
433#102—611no—
434#102C2×#692311yescharacteristic
435C22⋊C8—611no—
436C22⋊C8—611no—
437C22⋊C8—1221no—
438C22⋊C8—1221no—
439C22⋊C8—1221no—
440C22⋊C8—1221no—
441C22⋊C8—1221no—
442C22⋊C8—1221no—
443C22⋊C8—1221no—
444#97—611no—
445#97—1221no—
446#97—1221no—
447#97C2×#692311yescharacteristic
448C4×C8—611no—
449C4×C8—611no—
450C4×C8—611no—
451C4×C8—611no—
452C4×C8—611no—
453C4×C8—611no—
454C4×C8—1221no—
455C4×C8—1221no—
456C24—1221no—
457#41—1222no—
458#41—1222no—
459C2×Q8C22×#692311yescharacteristic
460C2×D4—611no—
461C2×D4—611no—
462C2×D4—1221no—
463C2×D4—1222no—
464C2×D4—1222no—
465C2×D4—1221no—
466C2×D4C22×#692311yescharacteristic
467C22×C4—21no—
468C22×C4—611no—
469C22×C4—611no—
470C22×C4—611no—
471C22×C4—1221no—
472C22×C4—1221no—
473C22×C4—1221no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4—1221no—
477C22×C4—1221no—
478C22×C4—4881no—
479C22×C4—4881no—
480SD16—22no—
481SD16—1222no—
482D8—1222no—
483D8—1222no—
484M16—614no—
485M16—1222no—
486M16—4881no—
487M16—4881no—
488M16—4881no—
489M16—4881no—
490M16—4881no—
491M16—4881no—
492C2×C8—611no—
493C2×C8—611no—
494C2×C8—611no—
495C2×C8—611no—
496C2×C8—611no—
497C2×C8—611no—
498C2×C8—1221no—
499C2×C8—1221no—
500C2×C8—1221no—
501C2×C8—1221no—
502C2×C8—1221no—
503C2×C8—1221no—
504C2×C8—4881no—
505C2×C8—2442no—
506C2×C8C22×#692311yescharacteristic
507C2×C8C22×#692311yescharacteristic
508C4⋊C4—21no—
509C4⋊C4—611no—
510C4⋊C4—611no—
511C4⋊C4—1221no—
512C4⋊C4—1221no—
513C4⋊C4C22×#692311yescharacteristic
514C4⋊C4C22×#692311yescharacteristic
515C22⋊C4—21no—
516C22⋊C4—1221no—
517C22⋊C4—1221no—
518C22⋊C4—1221no—
519C22⋊C4—1221no—
520C22⋊C4—1221no—
521C22⋊C4—1221no—
522C42—21no—
523C42—611no—
524C42—611no—
525C42—611no—
526C42—1221no—
527C42—1221no—
528C42C22×#692311yescharacteristic
529C23—21no—
530C23—611no—
531C23—1221no—
532C23—1221no—
533C23—4881no—
534C23—4881no—
535C23—2442no—
536Q8—21no—
537Q8—21no—
538D4—21no—
539D4—21no—
540D4—1221no—
541D4—1221no—
542D4—1221no—
543D4—1221no—
544D4—2442no—
545D4—2442no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—81no—
550C2×C4—611no—
551C2×C4—611no—
552C2×C4—612no—
553C2×C4—612no—
554C2×C4—611no—
555C2×C4—1221no—
556C2×C4—1221no—
557C2×C4—1221no—
558C2×C4—1221no—
559C2×C4—4881no—
560C2×C4—4881no—
561C2×C4—4881no—
562C2×C4—2441no—
563C2×C4—2441no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4—2441no—
567C2×C4—2442no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4D4×#692311yescharacteristic
571C2×C4D4×#692311yescharacteristic
572C2×C4C23×#692311yescharacteristic
573C8—21no—
574C8—612no—
575C8—1221no—
576C8—1221no—
577C8—1221no—
578C8—1221no—
579C8—1222no—
580C8—1221no—
581C8—2441no—
582C8—2441no—
583C8—2441no—
584C8—2441no—
585C8—2441no—
586C8D61⋊M1612yes—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—612no—
591C22—1221no—
592C22—1221no—
593C22—4884no—
594C22—2441no—
595C22—2441no—
596C22—2441no—
597C22—2441no—
598C22—2441no—
599C22—2441no—
600C22C2×D4×#692311yescharacteristic
601C4—21no—
602C4—21no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—612no—
607C4—611no—
608C4—611no—
609C4—1221no—
610C4—2441no—
611C4—2441no—
612C4C2×D61⋊M1611yescharacteristic
613C4D61⋊#13111yescharacteristic
614C2—81no—
615C2—1222no—
616C2—4881no—
617C2—4881no—
618C2D61⋊#43611yescharacteristic
619C2#2146257611yescharacteristic
620C2#2146259411yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#440C4
socleC22×C61C2×C4×D4
prime radicalC2×#14519804C4
cosocleC4×Dic61C24
hypercenter#440#6923
hypocenterC61#17893
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #21462743C2semidirect
2. #21462682C2semidirect
3. #21461468C2semidirect
4. #21461467C2semidirect
5. #21461463C2semidirect
6. #21461462C2semidirect
7. #21461455C2semidirect
8. #21461453C2semidirect
9. #21461451C2semidirect
10. #21461450C2semidirect
11. #21461371C2semidirect
12. #21461113C2semidirect
13. D61⋊(D4⋊C8)C2semidirect
14. #21461017C2semidirect
16. #16840813C22semidirect
17. #16840813C22semidirect
22. #16840796C22semidirect
23. #16840796C22semidirect
36. #16840626C22semidirect
37. #16840625C22semidirect
38. #16840624C22semidirect
39. #16840623C22semidirect
40. Q8⋊#92420C22semidirect
41. Q8⋊#92420C22semidirect
44. #16840610C22semidirect
45. #16840610C22semidirect
48. #16840603C22semidirect
49. #16840603C22semidirect
50. C8×#92420C22semidirect
51. C8×#92420C22semidirect
217. #11758189M16semidirect
377. C61#17893semidirect

Maximal subgroups

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

subgroupindex
#214627432
#214626822
#214614682
#214614672
#214614632
#214614622
#214614552
#214614532
#214614512
#214614502
#214613712
#214611132
D61⋊(D4⋊C8)2
#214610172
#214546242
#1789361