Finite Group Databasebeta

← #30610833

Subgroups — #30610833

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#21461170C212yesmaximal, complemented
4#21461165C211yesmaximal, characteristic, complemented
5#21461158C212yesmaximal, complemented
6#21461155C211yesmaximal, characteristic, complemented
7#21461139C211yesmaximal, characteristic, complemented
8#21461134C212yesmaximal, complemented
9#21461111C211yesmaximal, characteristic, complemented
10C2×D4⋊#92420C212yesmaximal, complemented
11#21459420C211yesmaximal, 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
26#16840612C2211yescharacteristic, complemented
27#16840612C2211yescharacteristic, complemented
28#16840612C2212yescomplemented
29D4⋊#92420C2211yescharacteristic
30D4⋊#92420C2212yes—
31D4⋊#92420C2211yescharacteristic
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
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×#11758224—21no—
77C2×#11758224C2×C411yescharacteristic
78C2×#11758224D411yescharacteristic
79C23×Dic61—22no—
80#14519777C2×C411yescharacteristic
81#14519770—22no—
82#14519770—22no—
83#14519768—21no—
84#14519768C2×C412yes—
85#14519764—21no—
86#14519764—21no—
87#14519764C2×C412yes—
88#14519761—22no—
89#14519758—22no—
90#14519758—22no—
91#14519758—22no—
92#14519756—21no—
93#14519756C2×C412yes—
94#14519754—22no—
95#14519754—22no—
96#14519749—22no—
97#14519749—22no—
98#14519748—21no—
99#14519748C2×C412yes—
100#14519746—22no—
101C4×Dic122C2×C411yescharacteristic
102C4×Dic122C2×C411yescharacteristic
103#14519742D411yescharacteristic
104#14519742C2311yescharacteristic
105D4×Dic61—21no—
106D4×Dic61—22no—
107D4×Dic61—22no—
108D4×Dic61—21no—
109D4×Dic61—22no—
110D4×Dic61—21no—
111D4×Dic61—22no—
112D4×Dic61C2×C412yes—
113D4×Dic61C2×C412yes—
114D4×Dic61D411yescharacteristic
115D4×Dic61C2311yescharacteristic
116D4×Dic61C2312yes—
117C4×C22⋊D61—21no—
118C4×C22⋊D61C2×C412yes—
119#14519737—21no—
120#14519737D412yes—
121#14519735C2×C411yescharacteristic
122#14519735D411yescharacteristic
123#14519733—21no—
124#14519733—22no—
125#14519733D412yes—
126C2×C4⋊Dic61—21no—
127C2×C4⋊Dic61C2×C412yes—
128C2×C22⋊Dic61—22no—
129C2×C22⋊Dic61—22no—
130C2×C4×Dic61—21no—
131C2×C4×Dic61C2312yes—
132C42×D61C2311yescharacteristic
133C22×D4×C61—21no—
134C22×D4×C61C2×C412yes—
135#127×C61C2×C411yescharacteristic
136#121×C61—21no—
137#121×C61C2×C412yes—
138#120×C61—22no—
139C4×D4×C61C2×C411yescharacteristic
140C4×D4×C61C2×C411yescharacteristic
141C24×C61—22no—
142C2×D4×C61—24no—
143C2×D4×C61—22no—
144C2×D4×C61—22no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—42no—
148C2×D4×C61—44no—
149C2×D4×C61C22⋊C411yescharacteristic
150C2×D4×C61C22×C412yes—
151C2×D4×C61C22×C411yescharacteristic
152C22×C4×C61—21no—
153C22×C4×C61C22×C412yes—
154C2×C22⋊D61—21no—
155C2×C22⋊D61—22no—
156C2×C22⋊D61C22⋊C412yes—
157C22×Dic61—22no—
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61—22no—
161C22×Dic61—22no—
162C22×Dic61—22no—
163C22×Dic61—82no—
164C22×Dic61—82no—
165C22×Dic61C2×D412yes—
166C22×Dic61C2×D412yes—
167#11758224—24no—
168#11758224—22no—
169#11758224—41no—
170#11758224—81no—
171#11758224—81no—
172C2×C4×D61C22×C411yescharacteristic
173C2×C4×D61C2×D411yescharacteristic
174C2×C4×D61C2×D411yescharacteristic
175C2×Dic122—21no—
176C2×Dic122C22⋊C411yescharacteristic
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×C61C22⋊C411yescharacteristic
191C4⋊C4×C61C22×C411yescharacteristic
192C22⋊C4×C61—21no—
193C22⋊C4×C61—22no—
194C22⋊C4×C61C22⋊C412yes—
195C42×C61C22×C411yescharacteristic
196C22⋊Dic61—22no—
197C22⋊Dic61—22no—
198C22⋊Dic61—22no—
199C22⋊Dic61—22no—
200C22⋊Dic61—22no—
201C22⋊Dic61—22no—
202C22⋊Dic61—21no—
203C22⋊Dic61—22no—
204C22⋊Dic61C22⋊C412yes—
205#11758198—21no—
206#11758198C22⋊C412yes—
207C4⋊Dic61—21no—
208C4⋊Dic61—22no—
209C4⋊Dic61—22no—
210C4⋊Dic61C22⋊C411yescharacteristic
211C4⋊Dic61C22×C411yescharacteristic
212C4⋊Dic61C22×C412yes—
213#11758196—21no—
214#11758196—22no—
215#11758196—22no—
216#11758196—21no—
217#11758196C22⋊C412yes—
218#11758196C22⋊C412yes—
219C4×Dic61—21no—
220C4×Dic61—21no—
221C4×Dic61—21no—
222C4×Dic61C22×C412yes—
223C4×Dic61C2×D411yescharacteristic
224C4×Dic61C2×D412yes—
225C4×Dic61C2×D411yescharacteristic
226C4×Dic61C2×D412yes—
227C4×Dic61C2411yescharacteristic
228C23×C61—21no—
229C23×C61—22no—
230C23×C61—44no—
231C23×C61—44no—
232C23×C61—82no—
233C23×C61C2×C22⋊C412yes—
234C22×D61C2×C22⋊C411yescharacteristic
235D4×C61—22no—
236D4×C61—21no—
237D4×C61—22no—
238D4×C61—44no—
239D4×C61—44no—
240D4×C61—42no—
241D4×C61—81no—
242D4×C61#10414yes—
243D4×C61#13112yescomplemented
244C2×C4×C61—22no—
245C2×C4×C61—22no—
246C2×C4×C61—21no—
247C2×C4×C61—42no—
248C2×C4×C61C2×C22⋊C412yes—
249C2×C4×C61C2×C22⋊C411yescharacteristic
250C2×C4×C61C2×C22⋊C411yescharacteristic
251C2×C4×C61C23×C411yescharacteristic
252C22⋊D61—24no—
253C22⋊D61—42no—
254C22⋊D61—82no—
255C2×Dic61—24no—
256C2×Dic61—22no—
257C2×Dic61—22no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—22no—
261C2×Dic61—42no—
262C2×Dic61—42no—
263C2×Dic61—41no—
264C2×Dic61—42no—
265C2×Dic61—41no—
266C2×Dic61—82no—
267C2×Dic61—82no—
268C2×Dic61—82no—
269C2×Dic61C2×C22⋊C411yescharacteristic
270C2×Dic61C2×C22⋊C412yes—
271C2×Dic61C2×C22⋊C412yes—
272C2×Dic61C22×D411yescharacteristic
273C2×Dic61C22×D411yescharacteristic
274C4×D61—21no—
275C4×D61—21no—
276C4×D61—22no—
277C4×D61—21no—
278C4×D61—21no—
279Dic122—22no—
280Dic122—21no—
281Dic122—21no—
282Dic122—81no—
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×C61—22no—
293C22×C61—41no—
294C22×C61—41no—
295C22×C61—42no—
296C22×C61—42no—
297C22×C61—42no—
298C22×C61—88no—
299C22×C61C2×#10414yes—
300C22×C61C22×C22⋊C411yescharacteristic
301C2×D61—21no—
302C2×D61—21no—
303C2×D61—21no—
304C4×C61—22no—
305C4×C61—21no—
306C4×C61—41no—
307C4×C61C2×#10412yes—
308C4×C61C2×#13111yescharacteristic
309C4×C61#56811yescharacteristic
310Dic61—21no—
311Dic61—22no—
312Dic61—21no—
313Dic61—22no—
314Dic61—41no—
315Dic61—42no—
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—42no—
332C2×C61—82no—
333C2×C61#288011yescharacteristic
334C2×C61#289711yescharacteristic
335C2×C61C22×#10411yescharacteristic
336D61—41no—
337C2×#131—1221no—
338#559—611no—
339#554—611no—
340#554—611no—
341#553—612no—
342#553—1221no—
343#551—1222no—
344#546—612no—
345#546—1221no—
346D42#692311yescharacteristic
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—21no—
383C22×D4C2×#692312yes—
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⋊Q8—611no—
393#127C2×#692311yescharacteristic
394#126—1222no—
395#126—1222no—
396#125—612no—
397#125—1221no—
398#124—612no—
399#124—1221no—
400#124—1221no—
401#123—1222no—
402#123—1222no—
403#123—1222no—
404#123—1222no—
405C22⋊Q8—612no—
406C22⋊Q8—1222no—
407C22⋊Q8—1221no—
408C22⋊Q8—1222no—
409#121—21no—
410#121—612no—
411#121—1222no—
412#121—1221no—
413#121—1222no—
414#121C2×#692312yes—
415#120—22no—
416#120—1222no—
417C4×Q8—611no—
418C4×Q8—611no—
419C4×Q8—611no—
420C4×Q8—611no—
421C4×D4—611no—
422C4×D4—612no—
423C4×D4—612no—
424C4×D4—611no—
425C4×D4—612no—
426C4×D4—612no—
427C4×D4—612no—
428C4×D4—1222no—
429C4×D4—1222no—
430C4×D4—1221no—
431C4×D4—1221no—
432C4×D4—1222no—
433C4×D4—1221no—
434C4×D4—1221no—
435C4×D4—1222no—
436C4×D4—1221no—
437C4×D4C2×#692311yescharacteristic
438C4×D4C2×#692311yescharacteristic
439#117—611no—
440#117—612no—
441#117—611no—
442#117—1221no—
443#117—1222no—
444C2×C4⋊C4—612no—
445C2×C4⋊C4—1221no—
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—22no—
468#41—1224no—
469#41—1222no—
470#41—4881no—
471#41—4881no—
472#41—2441no—
473C2×Q8—611no—
474C2×Q8—611no—
475C2×Q8—1221no—
476C2×D4—24no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—42no—
482C2×D4—44no—
483C2×D4—612no—
484C2×D4—1222no—
485C2×D4—1221no—
486C2×D4C22⋊#692311yescharacteristic
487C2×D4C22×#692312yes—
488C2×D4C22×#692311yescharacteristic
489C22×C4—21no—
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—1222no—
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—611no—
517C4⋊C4—612no—
518C4⋊C4—612no—
519C4⋊C4—611no—
520C4⋊C4—612no—
521C4⋊C4—1222no—
522C4⋊C4—1221no—
523C4⋊C4—1222no—
524C4⋊C4—1222no—
525C4⋊C4—1221no—
526C4⋊C4—1221no—
527C4⋊C4—1222no—
528C4⋊C4C22⋊#692311yescharacteristic
529C4⋊C4C22×#692311yescharacteristic
530C22⋊C4—21no—
531C22⋊C4—22no—
532C22⋊C4—612no—
533C22⋊C4—612no—
534C22⋊C4—1221no—
535C22⋊C4—1221no—
536C22⋊C4—1222no—
537C22⋊C4—1222no—
538C22⋊C4—1222no—
539C22⋊C4—1222no—
540C22⋊C4—1222no—
541C22⋊C4—1222no—
542C22⋊C4—1222no—
543C22⋊C4C22⋊#692312yes—
544C42—611no—
545C42—612no—
546C42—611no—
547C42—612no—
548C42—611no—
549C42—612no—
550C42—1221no—
551C42—1221no—
552C42—1221no—
553C42C22×#692311yescharacteristic
554C23—21no—
555C23—22no—
556C23—44no—
557C23—44no—
558C23—82no—
559C23—611no—
560C23C2×C22⋊#692312yes—
561Q8—1222no—
562Q8—1221no—
563Q8—1221no—
564Q8—4881no—
565D4—22no—
566D4—21no—
567D4—22no—
568D4—44no—
569D4—44no—
570D4—42no—
571D4—81no—
572D4—1224no—
573D4—4882no—
574D4—2442no—
575D4#1451984114yes—
576D4#1451986412yescomplemented
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—42no—
581C2×C4—611no—
582C2×C4—611no—
583C2×C4—612no—
584C2×C4—612no—
585C2×C4—611no—
586C2×C4—1221no—
587C2×C4—1221no—
588C2×C4—1222no—
589C2×C4—1222no—
590C2×C4—1224no—
591C2×C4—1222no—
592C2×C4—1221no—
593C2×C4—1221no—
594C2×C4—1221no—
595C2×C4—1221no—
596C2×C4—1222no—
597C2×C4—4882no—
598C2×C4—4882no—
599C2×C4—4882no—
600C2×C4—2441no—
601C2×C4—2441no—
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—22no—
618C22—41no—
619C22—41no—
620C22—42no—
621C22—42no—
622C22—42no—
623C22—88no—
624C22—1221no—
625C22—1221no—
626C22—1221no—
627C22C2×#1451984114yes—
628C22C22×C22⋊#692311yescharacteristic
629C4—22no—
630C4—21no—
631C4—41no—
632C4—611no—
633C4—611no—
634C4—1221no—
635C4—1222no—
636C4—1221no—
637C4—1222no—
638C4—2441no—
639C4—2441no—
640C4—2442no—
641C4C2×#1451984112yes—
642C4C2×#1451986411yescharacteristic
643C4#1684084011yescharacteristic
644C2—24no—
645C2—42no—
646C2—82no—
647C2—2441no—
648C2#2146240711yescharacteristic
649C2#2146244011yescharacteristic
650C2C22×#1451984111yescharacteristic
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#17517
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. #21462747C2semidirect
2. C4×#14519864C2semidirect
3. #21461170C2semidirect
4. #21461165C2semidirect
5. #21461158C2semidirect
6. #21461155C2semidirect
7. #21461139C2semidirect
8. #21461134C2semidirect
9. #21461111C2semidirect
10. C2×D4⋊#92420C2semidirect
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. #16840612C22semidirect
27. #16840612C22semidirect
28. #16840612C22semidirect
32. D4⋊#92420C22semidirect
33. D4⋊#92420C22semidirect
34. D4⋊#92420C22semidirect
35. D4⋊#92420C22semidirect
243. D4×C61#131semidirect
378. C61#17517semidirect
576. D4#14519864semidirect

Maximal subgroups

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

subgroupindex
#214627472
C4×#145198642
#214611702
#214611652
#214611582
#214611552
#214611392
#214611342
#214611112
C2×D4⋊#924202
#214594202
#1751761