Finite Group Databasebeta

← #29646989

Subgroups — #29646989

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#21459427C211yesmaximal, characteristic
2#21454945C211yesmaximal, characteristic, complemented
3C4×#14519783C211yesmaximal, characteristic, complemented
4#21444276C212yesmaximal, complemented
5#21444260C212yesmaximal, complemented
6#21444256C211yesmaximal, characteristic, complemented
7#21444236C211yesmaximal, characteristic, complemented
8#21444229C212yesmaximal, complemented
9#21444202C211yesmaximal, characteristic, complemented
10D4⋊C8×D61C212yesmaximal, complemented
11C61×#1492C211yesmaximal, characteristic, complemented
12C2×#14519783—21no—
13#16840498C411yescharacteristic
14#16840473C411yescharacteristic
15#16840473C411yescharacteristic
16#16840459—21no—
17#16840459C412yes—
18#16840442—22no—
19#16840409—21no—
20#16840409C412yes—
21#16840397C411yescharacteristic
22#16840294—21no—
23#16840294C2212yes—
24#16840269—22no—
25C4×#11758222C2211yescharacteristic
26C4×#11758222C2211yescharacteristic
27C4×D4×D61—21no—
28C4×D4×D61C2212yes—
29#16839889—21no—
30#16839831—22no—
31#16839827—21no—
32#16839818C2212yescomplemented
33#16839815C2211yescharacteristic, complemented
34C4⋊C8×D61C2212yescomplemented
35#16839717—21no—
36#16839716—22no—
37C4×#11758194C2211yescharacteristic, complemented
38C4×#11758189C2212yescomplemented
39C4×C8×D61C2212yescomplemented
40#16839494C2211yescharacteristic, complemented
41#16839494C2211yescharacteristic, complemented
42#16839492C2212yescomplemented
43#16839491C2211yescharacteristic
44#16839491C2211yescharacteristic
45D4⋊#92418C2212yescomplemented
46D4⋊#92418C2212yescomplemented
47#16839489C2212yes—
48C61×#532C2211yescharacteristic
49C61×#423C2211yescharacteristic, complemented
50C2×C4×C8×C61C2211yescharacteristic, complemented
51C61×D4⋊C8C2212yescomplemented
52C61×D4⋊C8C2212yescomplemented
53C2×#11758222C2×C411yescharacteristic
54C2×#11758222D411yescharacteristic
55C2×D4×D61—21no—
56C2×D4×D61C2×C412yes—
57C22×C4×D61—22no—
58#14519783—28no—
59C2×#11758194—21no—
60C2×#11758189—22no—
61C2×C8×D61—22no—
62C2×C8×D61—22no—
63#14519770—22no—
64#14519770—22no—
65#14519768—21no—
66#14519768C2×C412yes—
67#14519764—21no—
68#14519764C2×C412yes—
69#14519759—22no—
70#14519759—22no—
71#14519758—22no—
72#14519758—22no—
73#14519757—21no—
74#14519757C2×C412yes—
75#14519753—22no—
76#14519753—22no—
77#14519748—22no—
78#14519748—22no—
79#14519748—21no—
80#14519748C2×C412yes—
81#14519745—22no—
82#14519745—22no—
83C4×Dic122C2×C411yescharacteristic
84C4×Dic122C2×C411yescharacteristic
85C4×Dic122D411yescharacteristic
86C4×Dic122C2311yescharacteristic
87C4×D244C2×C411yescharacteristic
88C4×D244C2×C411yescharacteristic
89C4×D244D411yescharacteristic
90C4×D244C2311yescharacteristic
91D4×Dic61—21no—
92D4×Dic61C2×C412yes—
93#14519739—21no—
94#14519739C2×C412yes—
95C4×C22⋊D61—21no—
96C4×C22⋊D61—21no—
97C4×C22⋊D61—22no—
98C4×C22⋊D61—22no—
99C4×C22⋊D61C2×C412yes—
100C4×C22⋊D61D412yes—
101#14519737—22no—
102#14519737—22no—
103#14519736—22no—
104#14519736C2×C411yescharacteristic
105#14519736D411yescharacteristic
106#14519734—21no—
107#14519734D412yes—
108C4⋊C4×D61—21no—
109C4⋊C4×D61C2×C412yes—
110C22⋊C4×D61—22no—
111C22⋊C4×D61—22no—
112C42×D61—21no—
113C42×D61C2312yes—
114C4⋊#92418C2311yescharacteristic
115C4⋊#92418C2311yescharacteristic
116#14519706—22no—
117C22⋊#92418—21no—
118#14519689—22no—
119#14519688—21no—
120#14519687—22no—
121#14519687—22no—
122C4×#92418—21no—
123C4×#92418C2312yes—
124C8×Dic61—22no—
125C2×#41×C61—21no—
126C2×M16×C61—21no—
127C22×C8×C61—21no—
128C4⋊Q8×C61C2×C411yescharacteristic
129#127×C61C2×C411yescharacteristic
130#124×C61—21no—
131#121×C61—21no—
132#121×C61C2×C412yes—
133C4×D4×C61—21no—
134C4×D4×C61C2312yes—
135C2×C42×C61C2311yescharacteristic
136C4⋊C8×C61—21no—
137C4⋊C8×C61C2312yes—
138C4×C8×C61—21no—
139C4×C8×C61C2311yescharacteristic
140C4×C8×C61C2311yescharacteristic
141C23×D61—22no—
142#41×C61—81no—
143#41×C61—81no—
144C2×Q8×C61—21no—
145C2×D4×C61—22no—
146C2×D4×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61C22×C412yes—
149C22×C4×C61—22no—
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C2×C22⋊D61—21no—
154C2×C22⋊D61—22no—
155C2×C22⋊D61—22no—
156C2×C22⋊D61C22⋊C412yes—
157C22×Dic61—22no—
158D4×D61—24no—
159D4×D61—42no—
160D4×D61—44no—
161#11758222—24no—
162#11758222—22no—
163#11758222—41no—
164C2×D244C22⋊C411yescharacteristic
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—82no—
172C2×C4×D61—82no—
173C2×C4×D61C22×C412yes—
174C2×C4×D61C2×D412yes—
175C2×C4×D61C2×D412yes—
176C2×Dic122C22⋊C411yescharacteristic
177C2×Dic122C22×C411yescharacteristic
178M16×C61—81no—
179C2×C8×C61—24no—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
182C2×C8×C61—22no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61C22×C412yes—
185C22⋊C4×C61—22no—
186C22⋊C4×C61—22no—
187C42×C61C22×C411yescharacteristic
188C42×C61C2×D411yescharacteristic
189C42×C61C2×D411yescharacteristic
190C42×C61C2411yescharacteristic
191C22⋊Dic61—21no—
192C22⋊Dic61—22no—
193C22⋊Dic61—22no—
194C22⋊Dic61—22no—
195C22⋊Dic61—22no—
196C22⋊Dic61C22⋊C412yes—
197#11758198—22no—
198#11758198—21no—
199#11758198—21no—
200#11758198—22no—
201#11758198C22⋊C412yes—
202#11758198C22⋊C412yes—
203C4⋊Dic61—22no—
204C4⋊Dic61—22no—
205C4⋊Dic61C22⋊C411yescharacteristic
206C4⋊Dic61C22⋊C411yescharacteristic
207C4⋊Dic61C22×C411yescharacteristic
208C4⋊Dic61C22×C411yescharacteristic
209#11758196—21no—
210#11758196—21no—
211#11758196—22no—
212#11758196—22no—
213#11758196C22⋊C412yes—
214#11758196C22⋊C412yes—
215C4×Dic61—21no—
216C4×Dic61—21no—
217C4×Dic61—21no—
218C4×Dic61C22×C412yes—
219C4×Dic61C2×D412yes—
220C4×Dic61C2×D412yes—
221#11758194—24no—
222C2×#92418—22no—
223C2×#92418—21no—
224C2×#92418—21no—
225#11758189—28no—
226C8×D61—28no—
227C8×D61—82no—
228C23×C61—22no—
229C23×C61C2×C22⋊C411yescharacteristic
230C22×D61—21no—
231C22×D61—44no—
232C22×D61—44no—
233C22×D61—82no—
234C22×D61C2×C22⋊C412yes—
235Q8×C61—81no—
236D4×C61—22no—
237D4×C61—22no—
238D4×C61—42no—
239D4×C61—81no—
240D4×C61—82no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—22no—
246C2×C4×C61—22no—
247C2×C4×C61—42no—
248C2×C4×C61—42no—
249C2×C4×C61C2×C22⋊C411yescharacteristic
250C2×C4×C61C2×C22⋊C411yescharacteristic
251C2×C4×C61C2×C22⋊C411yescharacteristic
252C2×C4×C61C23×C411yescharacteristic
253C2×C4×C61C22×D411yescharacteristic
254C2×C4×C61C22×D411yescharacteristic
255C22⋊D61—24no—
256C22⋊D61—44no—
257C22⋊D61—42no—
258C22⋊D61—44no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—82no—
263C2×Dic61C2×C22⋊C412yes—
264C2×Dic61C2×C22⋊C412yes—
265C2×Dic61C2×C22⋊C412yes—
266D244—21no—
267D244#10414yes—
268D244#13112yescomplemented
269C4×D61—24no—
270C4×D61—22no—
271C4×D61—22no—
272C4×D61—22no—
273C4×D61—22no—
274C4×D61—42no—
275C4×D61—41no—
276C4×D61—41no—
277C4×D61—42no—
278C4×D61—82no—
279C4×D61—82no—
280Dic122—22no—
281Dic122—21no—
282Dic122—21no—
283C8×C61—22no—
284C8×C61—22no—
285C8×C61—42no—
286#92418—24no—
287#92418—41no—
288#92418—41no—
289#17517—611nomaximal, Sylow
290C22×C61—21no—
291C22×C61—21no—
292C22×C61—21no—
293C22×C61—42no—
294C22×C61—42no—
295C22×C61—42no—
296C22×C61C22×C22⋊C411yescharacteristic
297C2×D61—22no—
298C2×D61—22no—
299C2×D61—22no—
300C2×D61—41no—
301C2×D61—41no—
302C2×D61—88no—
303C2×D61C2×#10414yes—
304C4×C61—21no—
305C4×C61—21no—
306C4×C61—21no—
307C4×C61—42no—
308C4×C61C2×#10412yes—
309C4×C61C2×#13111yescharacteristic
310C4×C61#56811yescharacteristic
311C4×C61#57611yescharacteristic
312C4×C61#57711yescharacteristic
313Dic61—22no—
314Dic61—22no—
315Dic61—22no—
316Dic61—41no—
317Dic61—41no—
318Dic61—41no—
319#3481—611no—
320#2990—611no—
321C4×#131—611no—
322#1494—612no—
323#1492D6111yescharacteristic, complemented
324#1490—612no—
325#1489—611no—
326#1484—611no—
327#1483—612no—
328#1476—611no—
329C2×D4⋊C8—612no—
330C2×C61—41no—
331C2×C61—82no—
332C2×C61#288011yescharacteristic
333C2×C61#289711yescharacteristic
334C2×C61C22×#10411yescharacteristic
335D61—24no—
336D61—42no—
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—611no—
347#532C2×D6111yescharacteristic
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#423C2×D6111yescharacteristic, complemented
361C2×C4⋊C8—612no—
362#405—1222no—
363#405—1221no—
364C4×M16—611no—
365C4×M16—612no—
366C2×C4×C8—612no—
367C2×C4×C8C2×D6111yescharacteristic, complemented
368Q8⋊C8—612no—
369Q8⋊C8—611no—
370Q8⋊C8—611no—
371D4⋊C8—612no—
372D4⋊C8—612no—
373D4⋊C8—612no—
374D4⋊C8—611no—
375D4⋊C8—611no—
376D4⋊C8C2×D6112yescomplemented
377D4⋊C8C2×D6112yescomplemented
378C61#1751711yescharacteristic, complemented, Sylow
379C2×#41—21no—
380C2×#41—611no—
381C2×#41—611no—
382C22×D4—612no—
383C22×D4—1221no—
384C23×C4—1222no—
385#131—1228no—
386C2×M16—21no—
387C2×M16—1222no—
388C2×M16—1221no—
389C22×C8—21no—
390C22×C8—1222no—
391C22×C8—1222no—
392C4⋊Q8C4×D6111yescharacteristic
393#127C4×D6111yescharacteristic
394#126—1222no—
395#126—1222no—
396#125—612no—
397#125—1221no—
398#124—21no—
399#124—612no—
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#121C4×D6112yes—
415#120—1222no—
416#120—1222no—
417C4×Q8—611no—
418C4×Q8—611no—
419C4×Q8—611no—
420C4×Q8—611no—
421C4×D4—21no—
422C4×D4—612no—
423C4×D4—612no—
424C4×D4—612no—
425C4×D4—612no—
426C4×D4—611no—
427C4×D4—611no—
428C4×D4—611no—
429C4×D4—611no—
430C4×D4—1222no—
431C4×D4—1222no—
432C4×D4—1222no—
433C4×D4—1221no—
434C4×D4—1221no—
435C4×D4—1222no—
436C4×D4—1221no—
437C4×D4—1221no—
438C4×D4C22×D6112yes—
439#117—611no—
440#117—612no—
441#117—611no—
442#117—1222no—
443#117—1221no—
444C2×C4⋊C4—612no—
445C2×C4⋊C4—1221no—
446C2×C22⋊C4—1222no—
447C2×C22⋊C4—1222no—
448C2×C42—612no—
449C2×C42—1221no—
450C2×C42C22×D6111yescharacteristic
451C4⋊C8—21no—
452C4⋊C8—611no—
453C4⋊C8—611no—
454C4⋊C8—1222no—
455C4⋊C8C22×D6112yes—
456C22⋊C8—1222no—
457C22⋊C8—1221no—
458#97—1222no—
459#97—1222no—
460#97—1221no—
461C4×C8—21no—
462C4×C8—612no—
463C4×C8—1222no—
464C4×C8—1221no—
465C4×C8C22×D6111yescharacteristic
466C4×C8C22×D6111yescharacteristic
467C24—1222no—
468#41—81no—
469#41—81no—
470#41—1224no—
471#41—1222no—
472#41—2441no—
473C2×Q8—21no—
474C2×Q8—611no—
475C2×Q8—611no—
476C2×D4—22no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—612no—
480C2×D4—611no—
481C2×D4—611no—
482C2×D4—1222no—
483C2×D4—1224no—
484C2×D4—1222no—
485C2×D4—1221no—
486C2×D4—2442no—
487C2×D4—2444no—
488C2×D4C2×C4×D6112yes—
489C22×C4—22no—
490C22×C4—612no—
491C22×C4—612no—
492C22×C4—612no—
493C22×C4—1222no—
494C22×C4—1222no—
495C22×C4—1222no—
496C22×C4—1221no—
497C22×C4—1221no—
498C22×C4—1221no—
499C22×C4—4882no—
500C22×C4—4882no—
501C22×C4C2×C4×D6111yescharacteristic
502C22×C4D4×D6111yescharacteristic
503C22×C4D4×D6111yescharacteristic
504M16—81no—
505M16—1228no—
506M16—1224no—
507C2×C8—24no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—22no—
511C2×C8—1228no—
512C2×C8—1222no—
513C2×C8—1221no—
514C2×C8—1221no—
515C2×C8—4882no—
516C4⋊C4—21no—
517C4⋊C4—611no—
518C4⋊C4—612no—
519C4⋊C4—612no—
520C4⋊C4—611no—
521C4⋊C4—611no—
522C4⋊C4—611no—
523C4⋊C4—1222no—
524C4⋊C4—1222no—
525C4⋊C4—1222no—
526C4⋊C4—1222no—
527C4⋊C4—1221no—
528C4⋊C4—1221no—
529C4⋊C4C2×C4×D6112yes—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—612no—
533C22⋊C4—612no—
534C22⋊C4—612no—
535C22⋊C4—1222no—
536C22⋊C4—1222no—
537C22⋊C4—1222no—
538C22⋊C4—1222no—
539C22⋊C4—1222no—
540C22⋊C4—1222no—
541C22⋊C4—1221no—
542C22⋊C4—1221no—
543C22⋊C4—1221no—
544C42—612no—
545C42—612no—
546C42—612no—
547C42—1221no—
548C42—1221no—
549C42—1221no—
550C42C2×C4×D6111yescharacteristic
551C42D4×D6111yescharacteristic
552C42D4×D6111yescharacteristic
553C42C23×D6111yescharacteristic
554C23—22no—
555C23—612no—
556C23—1221no—
557C23—4882no—
558C23—2444no—
559C23—2444no—
560C23C22⋊C4×D6111yescharacteristic
561Q8—81no—
562Q8—1222no—
563Q8—1221no—
564Q8—1221no—
565D4—22no—
566D4—22no—
567D4—42no—
568D4—81no—
569D4—82no—
570D4—612no—
571D4—614no—
572D4—1224no—
573D4—1221no—
574D4—2444no—
575D4—2442no—
576D4—2444no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—612no—
586C2×C4—612no—
587C2×C4—612no—
588C2×C4—1224no—
589C2×C4—1222no—
590C2×C4—1222no—
591C2×C4—1222no—
592C2×C4—1222no—
593C2×C4—1221no—
594C2×C4—1221no—
595C2×C4—1221no—
596C2×C4—4882no—
597C2×C4—4882no—
598C2×C4—4882no—
599C2×C4—2442no—
600C2×C4—2442no—
601C2×C4—2441no—
602C2×C4—2441no—
603C2×C4C22⋊C4×D6111yescharacteristic
604C2×C4C22⋊C4×D6111yescharacteristic
605C2×C4C22⋊C4×D6111yescharacteristic
606C2×C4C22×C4×D6111yescharacteristic
607C2×C4C2×D4×D6111yescharacteristic
608C2×C4C2×D4×D6111yescharacteristic
609C8—22no—
610C8—22no—
611C8—42no—
612C8—1224no—
613C8—2441no—
614C8—2441no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—614no—
622C22—1222no—
623C22—1222no—
624C22—1222no—
625C22—4888no—
626C22—2441no—
627C22—2441no—
628C22C2×C22⋊C4×D6111yescharacteristic
629C4—21no—
630C4—21no—
631C4—21no—
632C4—42no—
633C4—1222no—
634C4—1222no—
635C4—1222no—
636C4—2441no—
637C4—2441no—
638C4—2441no—
639C4#104×D6112yes—
640C4#131×D6111yescharacteristic
641C4#1684052711yescharacteristic
642C4#1684056311yescharacteristic
643C4#1684056811yescharacteristic
644C2—41no—
645C2—82no—
646C2—1224no—
647C2—2442no—
648C2#2145426711yescharacteristic
649C2#2145434011yescharacteristic
650C2C2×#104×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1492C2
socleC22×C61C22×C22⋊C4
prime radical#21459427C2
cosocleC42×C61C24
hypercenter#1492D61
hypocenterC61#17517
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1492

Complements

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

NH ≅ G/Ntype
2. #21454945C2semidirect
3. C4×#14519783C2semidirect
4. #21444276C2semidirect
5. #21444260C2semidirect
6. #21444256C2semidirect
7. #21444236C2semidirect
8. #21444229C2semidirect
9. #21444202C2semidirect
10. D4⋊C8×D61C2semidirect
11. C61×#1492C2semidirect
32. #16839818C22semidirect
33. #16839815C22semidirect
34. C4⋊C8×D61C22semidirect
37. C4×#11758194C22semidirect
38. C4×#11758189C22semidirect
39. C4×C8×D61C22semidirect
40. #16839494C22semidirect
41. #16839494C22semidirect
42. #16839492C22semidirect
45. D4⋊#92418C22semidirect
46. D4⋊#92418C22semidirect
49. C61×#423C22semidirect
50. C2×C4×C8×C61C22semidirect
51. C61×D4⋊C8C22semidirect
52. C61×D4⋊C8C22semidirect
268. D244#131semidirect
323. #1492D61semidirect
360. #423C2×D61semidirect
367. C2×C4×C8C2×D61semidirect
376. D4⋊C8C2×D61semidirect
377. D4⋊C8C2×D61semidirect
378. C61#17517semidirect

Maximal subgroups

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

subgroupindex
#214594272
#214549452
C4×#145197832
#214442762
#214442602
#214442562
#214442362
#214442292
#214442022
D4⋊C8×D612
C61×#14922
#1751761