Finite Group Databasebeta

← #29646878

Subgroups — #29646878

Order 15616.

980 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459383C211yesmaximal, characteristic
2#41×#92418C211yesmaximal, characteristic, complemented
3#21444277C212yesmaximal, complemented
4#21444273C211yesmaximal, characteristic, complemented
5#21444251C212yesmaximal, complemented
6#21444243C211yesmaximal, characteristic, complemented
7#21444225C212yesmaximal, complemented
8#21444221C211yesmaximal, characteristic, complemented
9#21444199C212yesmaximal, complemented
10C2×#16839489C211yesmaximal, characteristic, complemented
11C61×#2925C211yesmaximal, characteristic, complemented
12#16840485C411yescharacteristic
13#16840477C411yescharacteristic
14#16840472C411yescharacteristic
15#16840462—21no—
16#16840453—21no—
17#16840452C412yes—
18#16840441—22no—
19#16840417C411yescharacteristic
20#16840408C412yes—
21#16840319C2211yescharacteristic
22#16840296C2212yes—
23#16840290—22no—
24#16840269—21no—
25C4×#11758222C2212yes—
26C2×C4×D244C2211yescharacteristic
27#117×D61—21no—
28Q8×#92418—21no—
29D4×#92418—21no—
30D4×#92418—22no—
31#16839815C2211yescharacteristic
32#16839815C2212yescomplemented
33C2×C4×#92418C2211yescharacteristic
34C2×C4×#92418C2212yescomplemented
35#16839492C2212yescomplemented
36#16839492C2212yescomplemented
37#16839492C2212yescomplemented
38#16839492C2212yescomplemented
39#16839489C2211yescharacteristic
40#16839489C2211yescharacteristic
41#16839489C2211yescharacteristic
42#16839489C2211yescharacteristic
43#16839489C2212yes—
44#16839489C2212yes—
45C4×#41×C61C2211yescharacteristic
46C61×#433—22no—
47C61×#432C2212yescomplemented
48C61×#431C2212yescomplemented
49C61×#423C2211yescharacteristic
50C2×C4⋊C8×C61C2211yescharacteristic
51C61×#408—21no—
52C61×#405—21no—
53C2×#11758222C2×C412yes—
54C22×D244C2×C411yescharacteristic
55C22×C4×D61—21no—
56C22×#92418—21no—
57C22×#92418—22no—
58#14519777C2×C411yescharacteristic
59#14519777C2×C411yescharacteristic
60#14519772—22no—
61#14519771—22no—
62#14519770—22no—
63#14519769—21no—
64#14519769C2×C412yes—
65#14519767—22no—
66#14519765C2×C412yes—
67#14519763—22no—
68#14519762—22no—
69#14519760—22no—
70#14519759—22no—
71#14519758—22no—
72#14519756—21no—
73#14519756C2×C412yes—
74#14519756C2×C412yes—
75#14519755—22no—
76#14519753—21no—
77#14519753—21no—
78#14519751C2×C412yes—
79#14519750—22no—
80#14519748—21no—
81#14519748—21no—
82#14519745—22no—
83C4×Dic122—21no—
84C4×Dic122C2×C412yes—
85C4×Dic122C2312yes—
86C4×D244—21no—
87C4×D244—21no—
88C4×D244C2×C411yescharacteristic
89C4×D244C2×C412yes—
90C4×D244C2×C411yescharacteristic
91C4×D244C2311yescharacteristic
92C4×D244C2311yescharacteristic
93C4×C22⋊D61—22no—
94C4×C22⋊D61—22no—
95C4×C22⋊D61—22no—
96#14519736—21no—
97#14519736C2×C412yes—
98#14519735—21no—
99#14519735—21no—
100#14519734—22no—
101#14519734—22no—
102#14519733—22no—
103C2×C4⋊Dic61C2×C411yescharacteristic
104C4⋊C4×D61—21no—
105C4⋊C4×D61—21no—
106C2×#11758198—21no—
107C22⋊C4×D61—22no—
108C42×D61—22no—
109C4⋊#92418—21no—
110C4⋊#92418—22no—
111C22⋊#92418—21no—
112C22⋊#92418—22no—
113C4×#92418—21no—
114C4×#92418—22no—
115C4×#92418C2311yescharacteristic
116C4×#92418C2311yescharacteristic
117C4×#92418C2312yes—
118C2×#41×C61D411yescharacteristic
119C2×M16×C61—21no—
120C22×C8×C61—21no—
121C4×Q8×C61C2×C411yescharacteristic
122C4×Q8×C61D411yescharacteristic
123C4×D4×C61C2×C412yes—
124C4×D4×C61C2×C411yescharacteristic
125C4×D4×C61D411yescharacteristic
126C4×D4×C61D412yes—
127#117×C61D411yescharacteristic
128#117×C61D412yes—
129C2×C42×C61C2311yescharacteristic
130C2×C42×C61C2312yes—
131C4⋊C8×C61—21no—
132C4⋊C8×C61—21no—
133C4⋊C8×C61C2311yescharacteristic
134C4⋊C8×C61C2311yescharacteristic
135C4⋊C8×C61C2312yes—
136C22⋊C8×C61—22no—
137C22⋊C8×C61—22no—
138#97×C61—22no—
139C4×C8×C61—22no—
140C23×D61—21no—
141#41×C61—22no—
142#41×C61—22no—
143C2×Q8×C61C22⋊C411yescharacteristic
144C2×D4×C61C22⋊C412yes—
145C2×D4×C61C22⋊C411yescharacteristic
146C22×C4×C61C22×C411yescharacteristic
147C22×C4×C61C22×C412yes—
148C22×C4×C61C2×D412yes—
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D412yes—
151C22×C4×C61C2×D411yescharacteristic
152C2×C22⋊D61—22no—
153C2×C22⋊D61—22no—
154C22×Dic61—21no—
155#11758222—24no—
156#11758222—42no—
157C2×D244—22no—
158C2×D244—21no—
159C2×D244—41no—
160C2×D244C22×C411yescharacteristic
161C2×D244C22×C411yescharacteristic
162C2×C4×D61—21no—
163C2×C4×D61—21no—
164C2×C4×D61—22no—
165C2×C4×D61—21no—
166C2×C4×D61—21no—
167C2×C4×D61—22no—
168C2×C4×D61—42no—
169C2×C4×D61—42no—
170C2×Dic122—21no—
171C2×Dic122C22×C412yes—
172M16×C61—42no—
173C2×C8×C61—21no—
174C2×C8×C61—22no—
175C2×C8×C61—21no—
176C2×C8×C61—42no—
177C4⋊C4×C61C22⋊C411yescharacteristic
178C4⋊C4×C61C22⋊C412yes—
179C4⋊C4×C61C22⋊C411yescharacteristic
180C4⋊C4×C61C22⋊C412yes—
181C22⋊C4×C61C22⋊C412yes—
182C22⋊C4×C61C22⋊C412yes—
183C22⋊C4×C61C22⋊C412yes—
184C42×C61C22×C411yescharacteristic
185C42×C61C22×C412yes—
186C42×C61C2×D412yes—
187C42×C61C2×D411yescharacteristic
188C42×C61C2×D412yes—
189C42×C61C2×D411yescharacteristic
190C42×C61C2411yescharacteristic
191C22⋊Dic61—22no—
192C22⋊Dic61—22no—
193C22⋊Dic61—22no—
194#11758198—22no—
195#11758198—22no—
196#11758198—21no—
197#11758198—21no—
198#11758198—22no—
199#11758198—22no—
200#11758198—21no—
201#11758198—21no—
202C4⋊Dic61—21no—
203C4⋊Dic61—21no—
204C4⋊Dic61—21no—
205C4⋊Dic61—21no—
206C4⋊Dic61C22×C411yescharacteristic
207C4⋊Dic61C22×C411yescharacteristic
208C4⋊Dic61C22×C412yes—
209#11758196—22no—
210#11758196—22no—
211#11758196—22no—
212#11758196—22no—
213#11758196—22no—
214#11758196—22no—
215C4×Dic61—22no—
216C4×Dic61—22no—
217C4×Dic61—22no—
218C2×#92418—21no—
219C2×#92418—21no—
220C2×#92418—22no—
221C2×#92418—42no—
222C2×#92418—44no—
223C23×C61C2×C22⋊C412yes—
224C23×C61C2×C22⋊C411yescharacteristic
225C22×D61—21no—
226C22×D61—21no—
227C22×D61—42no—
228C22×D61—42no—
229C22×D61—81no—
230Q8×C61—22no—
231D4×C61—24no—
232D4×C61—22no—
233C2×C4×C61—21no—
234C2×C4×C61—22no—
235C2×C4×C61—21no—
236C2×C4×C61—22no—
237C2×C4×C61—22no—
238C2×C4×C61—22no—
239C2×C4×C61—41no—
240C2×C4×C61—42no—
241C2×C4×C61C2×C22⋊C412yes—
242C2×C4×C61C2×C22⋊C412yes—
243C2×C4×C61C2×C22⋊C411yescharacteristic
244C2×C4×C61C2×C22⋊C412yes—
245C2×C4×C61C2×C22⋊C411yescharacteristic
246C2×C4×C61C2×C22⋊C411yescharacteristic
247C2×C4×C61#13512yes—
248C2×C4×C61#13512yes—
249C2×C4×C61C23×C411yescharacteristic
250C2×C4×C61C22×D411yescharacteristic
251C2×C4×C61C22×D411yescharacteristic
252C22⋊D61—44no—
253C22⋊D61—82no—
254C2×Dic61—21no—
255C2×Dic61—22no—
256C2×Dic61—22no—
257C2×Dic61—21no—
258C2×Dic61—42no—
259D244—21no—
260D244—21no—
261D244—21no—
262D244—42no—
263D244#13112yes—
264C4×D61—44no—
265C4×D61—41no—
266C4×D61—41no—
267C4×D61—41no—
268C4×D61—41no—
269C4×D61—42no—
270C4×D61—42no—
271C4×D61—82no—
272Dic122—22no—
273Dic122—22no—
274Dic122—81no—
275C8×C61—41no—
276C8×C61—41no—
277C8×C61—42no—
278#92418—22no—
279#92418—41no—
280#92418—42no—
281#17508—611nomaximal, Sylow
282C22×C61—21no—
283C22×C61—21no—
284C22×C61—22no—
285C22×C61—22no—
286C22×C61—22no—
287C22×C61#41612yes—
288C22×C61C22×C22⋊C411yescharacteristic
289C2×D61—22no—
290C2×D61—41no—
291C2×D61—41no—
292C2×D61—41no—
293C2×D61—41no—
294C2×D61—41no—
295C2×D61—84no—
296C4×C61—22no—
297C4×C61—21no—
298C4×C61—22no—
299C4×C61—21no—
300C4×C61—21no—
301C4×C61—22no—
302C4×C61#41612yes—
303C4×C61C2×#13111yescharacteristic
304C4×C61#56811yescharacteristic
305C4×C61C2×#13511yescharacteristic
306C4×C61C2×#13511yescharacteristic
307Dic61—42no—
308Dic61—41no—
309Dic61—41no—
310Dic61—42no—
311#3475—611no—
312C8×#41—611no—
313#2925D6111yescharacteristic, complemented
314#1494—612no—
315#1493—611no—
316#1488—612no—
317#1486—611no—
318#1482—612no—
319#1481—611no—
320#1476—612no—
321C2×D4⋊C8—611no—
322C2×C61—22no—
323C2×C61—42no—
324C2×C61#288011yescharacteristic
325C2×C61C2×#41611yescharacteristic
326C2×C61#290111yescharacteristic
327D61—42no—
328D61—81no—
329#556—611no—
330#555—611no—
331#554—611no—
332#553—1221no—
333#552—612no—
334#552—1221no—
335#551—1222no—
336#547—611no—
337#546—612no—
338#533—611no—
339#529—612no—
340#529—1222no—
341#525—1221no—
342C4×#41—612no—
343C4×#41C2×D6111yescharacteristic
344C2×C4×D4—611no—
345C2×#117—1221no—
346C8×Q8—1221no—
347C8×D4—1222no—
348C8×D4—1221no—
349#433—22no—
350#432C2×D6112yescomplemented
351#431—611no—
352#431—612no—
353#431C2×D6112yescomplemented
354#423C2×D6111yescharacteristic
355C2×C4⋊C8C2×D6111yescharacteristic
356#408—21no—
357#405—21no—
358C2×C4×C8—611no—
359C2×C4×C8—612no—
360Q8⋊C8—612no—
361Q8⋊C8—612no—
362Q8⋊C8—612no—
363Q8⋊C8—612no—
364D4⋊C8—611no—
365D4⋊C8—611no—
366D4⋊C8—611no—
367D4⋊C8—611no—
368D4⋊C8—612no—
369D4⋊C8—612no—
370C61#1750811yescharacteristic, complemented, Sylow
371C2×#41—612no—
372C2×#41C22⋊D6111yescharacteristic
373C22×D4—611no—
374C23×C4—1221no—
375C2×M16—21no—
376C22×C8—21no—
377C22×C8—1221no—
378C22×C8—1222no—
379C4⋊Q8—611no—
380C4⋊Q8—611no—
381#126—1222no—
382#126—1222no—
383#126—1222no—
384#125—612no—
385#125—1222no—
386#125—1221no—
387#124—612no—
388#124—1222no—
389#123—1222no—
390#123—1222no—
391#123—1222no—
392#123—1222no—
393C22⋊Q8—612no—
394C22⋊Q8—612no—
395C22⋊Q8—1221no—
396C22⋊Q8—1221no—
397C22⋊Q8—1221no—
398C22⋊Q8—1222no—
399#121—612no—
400#121—1221no—
401#121—1221no—
402#121—1222no—
403#120—1222no—
404C4×Q8—612no—
405C4×Q8—612no—
406C4×Q8—1221no—
407C4×Q8C4×D6111yescharacteristic
408C4×Q8D24411yescharacteristic
409C4×D4—611no—
410C4×D4—611no—
411C4×D4—612no—
412C4×D4—611no—
413C4×D4—611no—
414C4×D4—1222no—
415C4×D4—1222no—
416C4×D4—1222no—
417C4×D4—1221no—
418C4×D4—1221no—
419C4×D4C4×D6112yes—
420C4×D4C4×D6111yescharacteristic
421C4×D4D24412yes—
422C4×D4D24411yescharacteristic
423#117—612no—
424#117—1221no—
425#117—1221no—
426#117—1221no—
427#117—1222no—
428#117—1222no—
429#117—1222no—
430#117C22⋊D6111yescharacteristic
431#117C22⋊D6112yes—
432C2×C4⋊C4—611no—
433C2×C4⋊C4—1221no—
434C2×C4⋊C4—1221no—
435C2×C22⋊C4—1221no—
436C2×C22⋊C4—1222no—
437C2×C42—1222no—
438C2×C42C22×D6111yescharacteristic
439C2×C42C22×D6112yes—
440C4⋊C8—21no—
441C4⋊C8—21no—
442C4⋊C8—1222no—
443C4⋊C8—1221no—
444C4⋊C8C22×D6111yescharacteristic
445C4⋊C8C22×D6111yescharacteristic
446C4⋊C8C22×D6112yes—
447C22⋊C8—22no—
448C22⋊C8—22no—
449C22⋊C8—1221no—
450C22⋊C8—1222no—
451#97—22no—
452C4×C8—22no—
453C4×C8—611no—
454C4×C8—611no—
455C4×C8—612no—
456C4×C8—1222no—
457C4×C8—1221no—
458C24—1221no—
459#41—22no—
460#41—22no—
461#41—1224no—
462#41—2442no—
463C2×Q8—612no—
464C2×Q8—1221no—
465C2×Q8#1175819811yescharacteristic
466C2×D4—611no—
467C2×D4—611no—
468C2×D4—1222no—
469C2×D4—1222no—
470C2×D4—1222no—
471C2×D4—1221no—
472C2×D4—2441no—
473C2×D4#1175819812yes—
474C2×D4#1175819811yescharacteristic
475C22×C4—1221no—
476C22×C4—1222no—
477C22×C4—1221no—
478C22×C4—1221no—
479C22×C4—1222no—
480C22×C4—1221no—
481C22×C4—1221no—
482C22×C4—2442no—
483C22×C4—2442no—
484C22×C4C2×C4×D6111yescharacteristic
485C22×C4C2×C4×D6112yes—
486C22×C4C2×D24411yescharacteristic
487C22×C4C2×D24412yes—
488C22×C4C2×C22⋊D6112yes—
489C22×C4C2×C22⋊D6111yescharacteristic
490M16—42no—
491C2×C8—21no—
492C2×C8—22no—
493C2×C8—21no—
494C2×C8—42no—
495C2×C8—1221no—
496C2×C8—1221no—
497C2×C8—1222no—
498C2×C8—2444no—
499C2×C8—2442no—
500C4⋊C4—611no—
501C4⋊C4—611no—
502C4⋊C4—612no—
503C4⋊C4—1222no—
504C4⋊C4—1221no—
505C4⋊C4—1222no—
506C4⋊C4—1222no—
507C4⋊C4—1221no—
508C4⋊C4—1221no—
509C4⋊C4—1222no—
510C4⋊C4—1222no—
511C4⋊C4—1222no—
512C4⋊C4—1221no—
513C4⋊C4#1175819811yescharacteristic
514C4⋊C4#1175819811yescharacteristic
515C4⋊C4#1175819812yes—
516C4⋊C4#1175819812yes—
517C22⋊C4—1222no—
518C22⋊C4—1222no—
519C22⋊C4—1222no—
520C22⋊C4—1221no—
521C22⋊C4—1221no—
522C22⋊C4—1222no—
523C22⋊C4—1222no—
524C22⋊C4—1221no—
525C22⋊C4—1221no—
526C22⋊C4—1222no—
527C22⋊C4—1222no—
528C22⋊C4#1175819812yes—
529C22⋊C4#1175819812yes—
530C22⋊C4#1175819812yes—
531C42—1222no—
532C42—1222no—
533C42—1222no—
534C42C2×C4×D6111yescharacteristic
535C42C2×C4×D6112yes—
536C42C2×D24412yes—
537C42C2×D24411yescharacteristic
538C42C2×C22⋊D6112yes—
539C42C2×C22⋊D6111yescharacteristic
540C42C23×D6111yescharacteristic
541C23—1221no—
542C23—1221no—
543C23—4881no—
544C23—2442no—
545C23—2442no—
546C23C2×#1175819812yes—
547C23C2×#1175819811yescharacteristic
548Q8—22no—
549Q8—1222no—
550Q8—1222no—
551Q8—4881no—
552D4—24no—
553D4—22no—
554D4—612no—
555D4—1221no—
556D4—1221no—
557D4—1221no—
558D4—4882no—
559D4—2442no—
560D4—2444no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—42no—
568C2×C4—41no—
569C2×C4—1221no—
570C2×C4—1222no—
571C2×C4—1222no—
572C2×C4—1221no—
573C2×C4—4882no—
574C2×C4—2444no—
575C2×C4—2442no—
576C2×C4—2442no—
577C2×C4—2442no—
578C2×C4—2441no—
579C2×C4—2441no—
580C2×C4—2441no—
581C2×C4—2441no—
582C2×C4C2×#1175819812yes—
583C2×C4C2×#1175819812yes—
584C2×C4C2×#1175819812yes—
585C2×C4C2×#1175819811yescharacteristic
586C2×C4C2×#1175819811yescharacteristic
587C2×C4C2×#1175819811yescharacteristic
588C2×C4#1451979712yes—
589C2×C4#1451979712yes—
590C2×C4C22×C4×D6111yescharacteristic
591C2×C4C22×C22⋊D6111yescharacteristic
592C2×C4C22×D24411yescharacteristic
593C8—41no—
594C8—41no—
595C8—42no—
596C8—1222no—
597C8—2441no—
598C8—2442no—
599C22—21no—
600C22—21no—
601C22—22no—
602C22—22no—
603C22—22no—
604C22—1222no—
605C22—4884no—
606C22—2441no—
607C22—2441no—
608C22—2441no—
609C22—2441no—
610C22—2441no—
611C22#1683975612yes—
612C22C22×#1175819811yescharacteristic
613C4—21no—
614C4—22no—
615C4—21no—
616C4—22no—
617C4—21no—
618C4—22no—
619C4—2442no—
620C4—2442no—
621C4—2441no—
622C4—2441no—
623C4#1683975612yes—
624C4#131×D6111yescharacteristic
625C4#1684052711yescharacteristic
626C4C2×#1451979711yescharacteristic
627C4C2×#1451979711yescharacteristic
628C2—22no—
629C2—42no—
630C2—4881no—
631C2—2442no—
632C2#2145426611yescharacteristic
633C2C2×#1683975611yescharacteristic
634C2#2145436411yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#2925C2
socleC22×C61C22×C22⋊C4
prime radical#21459383C2
cosocleC42×C61C24
hypercenter#2925D61
hypocenterC61#17508
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2925

Complements

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

NH ≅ G/Ntype
2. #41×#92418C2semidirect
3. #21444277C2semidirect
4. #21444273C2semidirect
5. #21444251C2semidirect
6. #21444243C2semidirect
7. #21444225C2semidirect
8. #21444221C2semidirect
9. #21444199C2semidirect
10. C2×#16839489C2semidirect
11. C61×#2925C2semidirect
32. #16839815C22semidirect
34. C2×C4×#92418C22semidirect
35. #16839492C22semidirect
36. #16839492C22semidirect
37. #16839492C22semidirect
38. #16839492C22semidirect
47. C61×#432C22semidirect
48. C61×#431C22semidirect
313. #2925D61semidirect
350. #432C2×D61semidirect
353. #431C2×D61semidirect
370. C61#17508semidirect

Maximal subgroups

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

subgroupindex
#214593832
#41×#924182
#214442772
#214442732
#214442512
#214442432
#214442252
#214442212
#214441992
C2×#168394892
C61×#29252
#1750861