Finite Group Databasebeta

← #30610862

Subgroups — #30610862

Order 15616.

1008 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462750C211yesmaximal, characteristic, complemented
2#21462503C211yesmaximal, characteristic, complemented
3#21461174C212yesmaximal, complemented
4#21461165C211yesmaximal, characteristic, complemented
5#21461155C211yesmaximal, characteristic, complemented
6#21461144C212yesmaximal, complemented
7#21461139C211yesmaximal, characteristic, complemented
8#21461130C212yesmaximal, complemented
9#21461118C212yesmaximal, complemented
10#21461111C211yesmaximal, characteristic, complemented
11#21459420C211yesmaximal, characteristic
12#16840811—21no—
13#16840797—21no—
14#16840795—22no—
15#16840786—22no—
16#16840781C2211yescharacteristic, complemented
17#16840779C2212yescomplemented
18#16840778C2212yescomplemented
19#16840778C2212yescomplemented
20#16840769—21no—
21#16840766C2211yescharacteristic, complemented
22#16840765C2212yescomplemented
23#16840736—21no—
24C4×#11758213C2211yescharacteristic, complemented
25C4×D61⋊C8C2211yescharacteristic, complemented
26#16840612C2211yescharacteristic, complemented
27#16840612C2211yescharacteristic, complemented
28#16840612C2212yescomplemented
29D4⋊#92420C2211yescharacteristic
30D4⋊#92420C2211yescharacteristic
31D4⋊#92420C2212yes—
32D4⋊#92420C2212yescomplemented
33D4⋊#92420C2212yescomplemented
34D4⋊#92420C2212yescomplemented
35D4⋊#92420C2212yescomplemented
36#16840498C411yescharacteristic
37#16840469C411yescharacteristic
38#16840469C411yescharacteristic
39#16840464—21no—
40#16840464C412yes—
41#16840443—22no—
42#16840406—21no—
43#16840406C412yes—
44#16840310C2211yescharacteristic
45#16840293—21no—
46#16840293C2212yes—
47#16840268—22no—
48C4×#11758224C2211yescharacteristic
49C4×#11758224C2211yescharacteristic
50C2×D4×Dic61—21no—
51C2×D4×Dic61C2212yes—
52D42×C61C411yescharacteristic
53C2×#11758213—21no—
54C2×#11758213—21no—
55C2×#11758217—22no—
56C2×D61⋊C8—21no—
57#14519844—22no—
58#14519844—22no—
59C4⋊#92420—21no—
60C4⋊#92420—22no—
61C4⋊#92420C2311yescharacteristic
62C4⋊#92420C2312yes—
63C4⋊#92420C2311yescharacteristic
64#14519834—21no—
65C22⋊#92420—22no—
66C22⋊#92420—22no—
67C22⋊#92420—22no—
68#14519832—21no—
69C4×#92420—21no—
70C4×#92420—22no—
71C4×#92420—21no—
72C4×#92420C2311yescharacteristic
73C4×#92420C2311yescharacteristic
74C4×#92420C2312yes—
75C2×#11758224—21no—
76C2×#11758224C2×C411yescharacteristic
77C2×#11758224D411yescharacteristic
78C23×Dic61—22no—
79#14519777C2×C411yescharacteristic
80#14519770—22no—
81#14519770—22no—
82#14519768—21no—
83#14519768C2×C412yes—
84#14519764—21no—
85#14519764—21no—
86#14519764C2×C412yes—
87#14519761—22no—
88#14519758—22no—
89#14519758—22no—
90#14519758—22no—
91#14519756—21no—
92#14519756C2×C412yes—
93#14519754—22no—
94#14519754—22no—
95#14519749—22no—
96#14519749—22no—
97#14519748—21no—
98#14519748C2×C412yes—
99#14519746—22no—
100C4×Dic122C2×C411yescharacteristic
101C4×Dic122C2×C411yescharacteristic
102#14519742D411yescharacteristic
103#14519742C2311yescharacteristic
104D4×Dic61—21no—
105D4×Dic61—22no—
106D4×Dic61—22no—
107D4×Dic61—21no—
108D4×Dic61—22no—
109D4×Dic61—21no—
110D4×Dic61—22no—
111D4×Dic61C2×C412yes—
112D4×Dic61C2×C412yes—
113D4×Dic61D411yescharacteristic
114D4×Dic61C2311yescharacteristic
115D4×Dic61C2312yes—
116C4×C22⋊D61—21no—
117C4×C22⋊D61C2×C412yes—
118#14519737—21no—
119#14519737D412yes—
120#14519735C2×C411yescharacteristic
121#14519735D411yescharacteristic
122#14519733—21no—
123#14519733—22no—
124#14519733D412yes—
125C2×C4⋊Dic61—21no—
126C2×C4⋊Dic61C2×C412yes—
127C2×C22⋊Dic61—22no—
128C2×C22⋊Dic61—22no—
129C2×C4×Dic61—21no—
130C2×C4×Dic61C2312yes—
131C42×D61C2311yescharacteristic
132C22×D4×C61—21no—
133C22×D4×C61C2×C412yes—
134#127×C61C2×C411yescharacteristic
135#121×C61—21no—
136#121×C61C2×C412yes—
137#120×C61—22no—
138C4×D4×C61C2×C411yescharacteristic
139C4×D4×C61C2×C411yescharacteristic
140C24×C61—22no—
141C2×D4×C61—24no—
142C2×D4×C61—22no—
143C2×D4×C61—22no—
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61—42no—
147C2×D4×C61—44no—
148C2×D4×C61C22⋊C411yescharacteristic
149C2×D4×C61C22×C412yes—
150C2×D4×C61C22×C411yescharacteristic
151C22×C4×C61—21no—
152C22×C4×C61C22×C412yes—
153C2×C22⋊D61—21no—
154C2×C22⋊D61—22no—
155C2×C22⋊D61C22⋊C412yes—
156C22×Dic61—22no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61—22no—
160C22×Dic61—22no—
161C22×Dic61—22no—
162C22×Dic61—82no—
163C22×Dic61—82no—
164C22×Dic61C2×D412yes—
165C22×Dic61C2×D412yes—
166#11758224—22no—
167#11758224—41no—
168#11758224—42no—
169#11758224—81no—
170#11758224—81no—
171C2×C4×D61C22×C411yescharacteristic
172C2×C4×D61C2×D411yescharacteristic
173C2×C4×D61C2×D411yescharacteristic
174C2×Dic122—21no—
175C2×Dic122C22⋊C411yescharacteristic
176C2×Dic122C22×C411yescharacteristic
177#11758217—82no—
178C2×#92420—21no—
179C2×#92420—21no—
180C2×#92420—21no—
181C2×#92420—22no—
182C2×#92420—21no—
183C2×#92420—22no—
184#11758213—42no—
185#11758213—81no—
186D61⋊C8—42no—
187C4⋊C4×C61C22⋊C411yescharacteristic
188C4⋊C4×C61C22×C411yescharacteristic
189C22⋊C4×C61—21no—
190C22⋊C4×C61—22no—
191C22⋊C4×C61C22⋊C412yes—
192C42×C61C22×C411yescharacteristic
193C22⋊Dic61—22no—
194C22⋊Dic61—22no—
195C22⋊Dic61—22no—
196C22⋊Dic61—22no—
197C22⋊Dic61—22no—
198C22⋊Dic61—22no—
199C22⋊Dic61—21no—
200C22⋊Dic61—22no—
201C22⋊Dic61C22⋊C412yes—
202#11758198—21no—
203#11758198C22⋊C412yes—
204C4⋊Dic61—21no—
205C4⋊Dic61—22no—
206C4⋊Dic61—22no—
207C4⋊Dic61C22⋊C411yescharacteristic
208C4⋊Dic61C22×C411yescharacteristic
209C4⋊Dic61C22×C412yes—
210#11758196—21no—
211#11758196—22no—
212#11758196—22no—
213#11758196—21no—
214#11758196C22⋊C412yes—
215#11758196C22⋊C412yes—
216C4×Dic61—21no—
217C4×Dic61—21no—
218C4×Dic61—21no—
219C4×Dic61C22×C412yes—
220C4×Dic61C2×D411yescharacteristic
221C4×Dic61C2×D411yescharacteristic
222C4×Dic61C2×D412yes—
223C4×Dic61C2×D412yes—
224C4×Dic61C2411yescharacteristic
225C23×C61—21no—
226C23×C61—22no—
227C23×C61—44no—
228C23×C61—44no—
229C23×C61—82no—
230C23×C61C2×C22⋊C412yes—
231C22×D61C2×C22⋊C411yescharacteristic
232D4×C61—22no—
233D4×C61—21no—
234D4×C61—22no—
235D4×C61—22no—
236D4×C61—44no—
237D4×C61—44no—
238D4×C61—42no—
239D4×C61—81no—
240D4×C61#13112yes—
241C2×C4×C61—22no—
242C2×C4×C61—22no—
243C2×C4×C61—21no—
244C2×C4×C61—42no—
245C2×C4×C61C2×C22⋊C412yes—
246C2×C4×C61C2×C22⋊C411yescharacteristic
247C2×C4×C61C2×C22⋊C411yescharacteristic
248C2×C4×C61C23×C411yescharacteristic
249C22⋊D61—42no—
250C22⋊D61—42no—
251C22⋊D61—82no—
252C2×Dic61—22no—
253C2×Dic61—22no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—22no—
257C2×Dic61—42no—
258C2×Dic61—42no—
259C2×Dic61—42no—
260C2×Dic61—41no—
261C2×Dic61—42no—
262C2×Dic61—41no—
263C2×Dic61—82no—
264C2×Dic61—82no—
265C2×Dic61—82no—
266C2×Dic61C2×C22⋊C411yescharacteristic
267C2×Dic61C2×C22⋊C412yes—
268C2×Dic61C2×C22⋊C412yes—
269C2×Dic61C22×D411yescharacteristic
270C2×Dic61C22×D411yescharacteristic
271C4×D61—21no—
272C4×D61—21no—
273C4×D61—22no—
274C4×D61—21no—
275C4×D61—21no—
276Dic122—22no—
277Dic122—21no—
278Dic122—21no—
279Dic122—81no—
280#92420—41no—
281#92420—41no—
282#92420—42no—
283#92420—42no—
284#92420—41no—
285#92420—41no—
286#17522—611nomaximal, Sylow
287C22×C61—22no—
288C22×C61—22no—
289C22×C61—22no—
290C22×C61—22no—
291C22×C61—41no—
292C22×C61—41no—
293C22×C61—42no—
294C22×C61—42no—
295C22×C61—42no—
296C22×C61—88no—
297C22×C61C22×C22⋊C411yescharacteristic
298C2×D61—21no—
299C2×D61—21no—
300C2×D61—21no—
301C4×C61—22no—
302C4×C61—21no—
303C4×C61—41no—
304C4×C61#42112yes—
305C4×C61C2×#13111yescharacteristic
306C4×C61#56811yescharacteristic
307Dic61—21no—
308Dic61—22no—
309Dic61—21no—
310Dic61—22no—
311Dic61—41no—
312Dic61—42no—
313Dic61—41no—
314Dic61#57611yescharacteristic
315Dic61#57711yescharacteristic
316#3481—611no—
317#2991—611no—
318#2922—611no—
319#1495—612no—
320#1492—611no—
321#1489—611no—
322#1486—612no—
323#1484—611no—
324#1482—612no—
325#1478—612no—
326#1476—611no—
327C2×C61—42no—
328C2×C61—42no—
329C2×C61—82no—
330C2×C61#288011yescharacteristic
331C2×C61#289711yescharacteristic
332C2×C61C2×#42111yescharacteristic
333D61—41no—
334#559—611no—
335#554—611no—
336#554—611no—
337#553—612no—
338#553—1221no—
339#551—1222no—
340#546—612no—
341#546—1221no—
342D42#692311yescharacteristic
343#532—611no—
344#529—612no—
345#529—1221no—
346#525—1222no—
347C4×#41—611no—
348C4×#41—611no—
349C2×C4×D4—612no—
350C2×C4×D4—1221no—
351C8×Q8—1221no—
352#436—1222no—
353#436—1221no—
354#433—1222no—
355#431—612no—
356#431—612no—
357#431—612no—
358#431—611no—
359#424—1221no—
360#423—612no—
361#423—611no—
362#408—1221no—
363C4×M16—611no—
364C2×C4×C8—611no—
365Q8⋊C8—611no—
366Q8⋊C8—611no—
367Q8⋊C8—612no—
368D4⋊C8—611no—
369D4⋊C8—611no—
370D4⋊C8—612no—
371D4⋊C8—612no—
372D4⋊C8—612no—
373D4⋊C8—612no—
374D4⋊C8—612no—
375C61#1752211yescharacteristic, complemented, Sylow
376C2×#41—611no—
377C2×#41—611no—
378C2×#41—1221no—
379C22×D4—21no—
380C22×D4C2×#692312yes—
381C23×C4—1222no—
382C2×M16—1222no—
383C2×M16—1221no—
384C2×M16—1221no—
385C22×C8—1221no—
386C4⋊Q8—611no—
387#127C2×#692311yescharacteristic
388#126—1222no—
389#126—1222no—
390#125—612no—
391#125—1221no—
392#124—612no—
393#124—1221no—
394#124—1221no—
395#123—1222no—
396#123—1222no—
397#123—1222no—
398#123—1222no—
399C22⋊Q8—612no—
400C22⋊Q8—1222no—
401C22⋊Q8—1221no—
402C22⋊Q8—1222no—
403#121—21no—
404#121—612no—
405#121—1222no—
406#121—1221no—
407#121—1222no—
408#121C2×#692312yes—
409#120—22no—
410#120—1222no—
411C4×Q8—611no—
412C4×Q8—611no—
413C4×Q8—611no—
414C4×Q8—611no—
415C4×D4—611no—
416C4×D4—612no—
417C4×D4—612no—
418C4×D4—611no—
419C4×D4—612no—
420C4×D4—612no—
421C4×D4—612no—
422C4×D4—1222no—
423C4×D4—1222no—
424C4×D4—1221no—
425C4×D4—1221no—
426C4×D4—1222no—
427C4×D4—1221no—
428C4×D4—1221no—
429C4×D4—1222no—
430C4×D4—1221no—
431C4×D4C2×#692311yescharacteristic
432C4×D4C2×#692311yescharacteristic
433#117—611no—
434#117—612no—
435#117—611no—
436#117—1221no—
437#117—1222no—
438C2×C4⋊C4—612no—
439C2×C4⋊C4—1221no—
440C2×C22⋊C4—1222no—
441C2×C22⋊C4—1222no—
442C2×C42—612no—
443C2×C42—611no—
444C2×C42—1221no—
445C4⋊C8—611no—
446C4⋊C8—612no—
447C4⋊C8—611no—
448C4⋊C8—1221no—
449C4⋊C8—1222no—
450C4⋊C8—1222no—
451C4⋊C8—1222no—
452C22⋊C8—1222no—
453C22⋊C8—1222no—
454C22⋊C8—1222no—
455C22⋊C8—1221no—
456#97—1221no—
457C4×C8—611no—
458C4×C8—611no—
459C4×C8—612no—
460C4×C8—1221no—
461C4×C8—1221no—
462C4×C8—1222no—
463C24—22no—
464#41—1222no—
465#41—4881no—
466#41—4881no—
467#41—2442no—
468#41—2441no—
469C2×Q8—611no—
470C2×Q8—611no—
471C2×Q8—1221no—
472C2×D4—24no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—42no—
478C2×D4—44no—
479C2×D4—612no—
480C2×D4—1222no—
481C2×D4—1221no—
482C2×D4C22⋊#692311yescharacteristic
483C2×D4C22×#692312yes—
484C2×D4C22×#692311yescharacteristic
485C22×C4—21no—
486C22×C4—612no—
487C22×C4—612no—
488C22×C4—611no—
489C22×C4—611no—
490C22×C4—611no—
491C22×C4—1222no—
492C22×C4—1222no—
493C22×C4—1221no—
494C22×C4—1221no—
495C22×C4—1222no—
496C22×C4—1222no—
497C22×C4—4882no—
498C22×C4—4882no—
499C22×C4C22×#692312yes—
500M16—4881no—
501M16—4882no—
502M16—2442no—
503C2×C8—1221no—
504C2×C8—1221no—
505C2×C8—1222no—
506C2×C8—1221no—
507C2×C8—1222no—
508C2×C8—1221no—
509C2×C8—2442no—
510C4⋊C4—611no—
511C4⋊C4—612no—
512C4⋊C4—612no—
513C4⋊C4—611no—
514C4⋊C4—612no—
515C4⋊C4—1222no—
516C4⋊C4—1221no—
517C4⋊C4—1222no—
518C4⋊C4—1222no—
519C4⋊C4—1221no—
520C4⋊C4—1221no—
521C4⋊C4—1222no—
522C4⋊C4C22⋊#692311yescharacteristic
523C4⋊C4C22×#692311yescharacteristic
524C22⋊C4—21no—
525C22⋊C4—22no—
526C22⋊C4—612no—
527C22⋊C4—612no—
528C22⋊C4—1221no—
529C22⋊C4—1221no—
530C22⋊C4—1222no—
531C22⋊C4—1222no—
532C22⋊C4—1222no—
533C22⋊C4—1222no—
534C22⋊C4—1222no—
535C22⋊C4—1222no—
536C22⋊C4—1222no—
537C22⋊C4C22⋊#692312yes—
538C42—611no—
539C42—611no—
540C42—612no—
541C42—612no—
542C42—611no—
543C42—612no—
544C42—1221no—
545C42—1221no—
546C42—1221no—
547C42C22×#692311yescharacteristic
548C23—21no—
549C23—22no—
550C23—44no—
551C23—44no—
552C23—82no—
553C23—611no—
554C23C2×C22⋊#692312yes—
555Q8—1222no—
556Q8—1221no—
557Q8—1221no—
558Q8—4881no—
559D4—22no—
560D4—22no—
561D4—21no—
562D4—22no—
563D4—44no—
564D4—44no—
565D4—42no—
566D4—81no—
567D4—4882no—
568D4—2442no—
569D4—2442no—
570D4#1451986412yes—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—21no—
574C2×C4—42no—
575C2×C4—611no—
576C2×C4—611no—
577C2×C4—612no—
578C2×C4—612no—
579C2×C4—611no—
580C2×C4—1221no—
581C2×C4—1221no—
582C2×C4—1222no—
583C2×C4—1222no—
584C2×C4—1222no—
585C2×C4—1221no—
586C2×C4—1221no—
587C2×C4—1221no—
588C2×C4—1221no—
589C2×C4—1222no—
590C2×C4—4882no—
591C2×C4—4882no—
592C2×C4—4882no—
593C2×C4—2441no—
594C2×C4—2441no—
595C2×C4—2442no—
596C2×C4—2442no—
597C2×C4—2442no—
598C2×C4—2442no—
599C2×C4C2×C22⋊#692312yes—
600C2×C4C2×C22⋊#692311yescharacteristic
601C2×C4C2×C22⋊#692311yescharacteristic
602C2×C4C23×#692311yescharacteristic
603C8—2441no—
604C8—2442no—
605C8—2441no—
606C8—2441no—
607C8—2441no—
608C8—2442no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—41no—
614C22—41no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—88no—
619C22—1221no—
620C22—1221no—
621C22—1221no—
622C22C22×C22⋊#692311yescharacteristic
623C4—22no—
624C4—21no—
625C4—41no—
626C4—611no—
627C4—611no—
628C4—1221no—
629C4—1222no—
630C4—1221no—
631C4—1222no—
632C4—2441no—
633C4—2441no—
634C4—2442no—
635C4#1684076012yes—
636C4C2×#1451986411yescharacteristic
637C4#1684084011yescharacteristic
638C2—42no—
639C2—42no—
640C2—82no—
641C2—2441no—
642C2#2146240711yescharacteristic
643C2#2146244011yescharacteristic
644C2C2×#1684076011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingD42×C61C4
socleC22×C61C22×C22⋊C4
prime radical#21459420C2
cosocleC4×Dic61C24
hypercenterD42#6923
hypocenterC61#17522
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #21462750C2semidirect
2. #21462503C2semidirect
3. #21461174C2semidirect
4. #21461165C2semidirect
5. #21461155C2semidirect
6. #21461144C2semidirect
7. #21461139C2semidirect
8. #21461130C2semidirect
9. #21461118C2semidirect
10. #21461111C2semidirect
16. #16840781C22semidirect
17. #16840779C22semidirect
18. #16840778C22semidirect
19. #16840778C22semidirect
21. #16840766C22semidirect
22. #16840765C22semidirect
24. C4×#11758213C22semidirect
25. C4×D61⋊C8C22semidirect
26. #16840612C22semidirect
27. #16840612C22semidirect
28. #16840612C22semidirect
32. D4⋊#92420C22semidirect
33. D4⋊#92420C22semidirect
34. D4⋊#92420C22semidirect
35. D4⋊#92420C22semidirect
375. C61#17522semidirect

Maximal subgroups

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

subgroupindex
#214627502
#214625032
#214611742
#214611652
#214611552
#214611442
#214611392
#214611302
#214611182
#214611112
#214594202
#1752261