Finite Group Databasebeta

← #29646880

Subgroups — #29646880

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#21459386C211yesmaximal, characteristic
2#21454775C211yesmaximal, characteristic, complemented
3#21454484C211yesmaximal, characteristic, complemented
4#21444278C212yesmaximal, complemented
5#21444274C211yesmaximal, characteristic, complemented
6#21444252C212yesmaximal, complemented
7#21444245C211yesmaximal, characteristic, complemented
8#21444226C212yesmaximal, complemented
9#21444200C212yesmaximal, complemented
10C2×#16839489C211yesmaximal, characteristic, complemented
11C61×#1481C211yesmaximal, characteristic, complemented
12#16840486C411yescharacteristic
13#16840478C411yescharacteristic
14#16840473C411yescharacteristic
15#16840465—21no—
16#16840454C412yes—
17#16840450—21no—
18#16840439—22no—
19#16840415C411yescharacteristic
20#16840403C412yes—
21#16840299—22no—
22#16840299C2212yes—
23#16840274—21no—
24C4×#11758226C2212yes—
25C4×#11758222C2211yescharacteristic
26C2×C4×D244C2211yescharacteristic
27#117×D61—21no—
28#16839886—21no—
29#16839827—21no—
30#16839825—22no—
31#16839822—22no—
32#16839818C2212yescomplemented
33#16839814C2212yescomplemented
34#16839813C2212yescomplemented
35#16839786C2211yescharacteristic
36#16839728—21no—
37#16839717—21no—
38C2×C4×#92418C2211yescharacteristic
39C4×C8×D61C2212yescomplemented
40Q8⋊#92418C2212yescomplemented
41Q8⋊#92418C2212yescomplemented
42#16839491C2212yes—
43#16839491C2212yes—
44#16839489C2211yescharacteristic
45#16839489C2211yescharacteristic
46#16839489C2211yescharacteristic
47#16839489C2211yescharacteristic
48C61×#533C2211yescharacteristic
49C61×#431C2211yescharacteristic
50C2×C4⋊C8×C61C2211yescharacteristic
51C61×Q8⋊C8C2212yescomplemented
52C61×Q8⋊C8C2212yescomplemented
53C2×#11758226C2×C412yes—
54C2×#11758222D411yescharacteristic
55C22×D244C2×C411yescharacteristic
56C22×C4×D61—21no—
57C2×#11758194—21no—
58C22×#92418—21no—
59C2×C8×D61—22no—
60#14519772—22no—
61#14519772—22no—
62#14519772—22no—
63#14519768—22no—
64#14519768C2×C412yes—
65#14519766—22no—
66#14519766C2×C412yes—
67#14519762—22no—
68#14519762—22no—
69#14519762—22no—
70#14519761—22no—
71#14519757—21no—
72#14519757—21no—
73#14519753—22no—
74#14519753C2×C412yes—
75#14519752—21no—
76#14519752—21no—
77#14519752—22no—
78#14519752C2×C412yes—
79#14519747—22no—
80Q8×Dic61C2×C412yes—
81C4×Dic122C2×C411yescharacteristic
82C4×Dic122D411yescharacteristic
83C4×D244—22no—
84C4×D244—22no—
85C4×D244—21no—
86C4×D244—21no—
87C4×D244C2×C411yescharacteristic
88C4×D244C2×C411yescharacteristic
89C4×D244C2×C411yescharacteristic
90C4×D244D411yescharacteristic
91C4×D244C2311yescharacteristic
92C4×D244C2311yescharacteristic
93#14519739—22no—
94#14519739C2×C412yes—
95C4×C22⋊D61C2×C412yes—
96C4×C22⋊D61D412yes—
97#14519736D411yescharacteristic
98#14519735—21no—
99#14519735—21no—
100#14519735—22no—
101#14519735C2×C412yes—
102#14519734—22no—
103#14519734D412yes—
104#14519733—22no—
105C2×C4⋊Dic61C2×C411yescharacteristic
106C4⋊C4×D61—21no—
107C4⋊C4×D61—21no—
108C2×#11758198—21no—
109C22⋊C4×D61—22no—
110C42×D61—22no—
111C42×D61C2312yes—
112C4⋊#92418—21no—
113C4⋊#92418C2312yes—
114#14519706—22no—
115#14519689—22no—
116#14519689—22no—
117#14519689—22no—
118#14519687—22no—
119C4×#92418—21no—
120C4×#92418C2311yescharacteristic
121C4×#92418C2311yescharacteristic
122C8×Dic61—22no—
123C8×Dic61—22no—
124C22×C8×C61—21no—
125C4⋊Q8×C61C2×C411yescharacteristic
126C4⋊Q8×C61C2×C411yescharacteristic
127#125×C61—21no—
128C22⋊Q8×C61—21no—
129C22⋊Q8×C61C2×C412yes—
130C4×Q8×C61—21no—
131C4×Q8×C61C2312yes—
132#117×C61—21no—
133C2×C42×C61C2311yescharacteristic
134C4⋊C8×C61—21no—
135C4⋊C8×C61—21no—
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138C22⋊C8×C61—21no—
139C4×C8×C61C2312yes—
140C23×D61—21no—
141C2×Q8×C61—21no—
142C2×Q8×C61C22×C412yes—
143C22×C4×C61C22×C411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C2×C22⋊D61C22⋊C412yes—
147C22×Dic61—21no—
148#11758226—24no—
149#11758226—42no—
150#11758222—22no—
151#11758222—22no—
152C2×D244—22no—
153C2×D244—22no—
154C2×D244—21no—
155C2×D244—22no—
156C2×D244—41no—
157C2×D244C22⋊C411yescharacteristic
158C2×D244C22×C411yescharacteristic
159C2×D244C22×C411yescharacteristic
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×C4×D61—21no—
163C2×C4×D61—21no—
164C2×C4×D61—22no—
165C2×C4×D61—22no—
166C2×C4×D61—42no—
167C2×C4×D61—42no—
168C2×C4×D61C22×C412yes—
169C2×C4×D61C2×D412yes—
170C2×C4×D61C2×D412yes—
171C2×Dic122C22⋊C411yescharacteristic
172C2×C8×C61—22no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61—42no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—22no—
180C4⋊C4×C61—22no—
181C4⋊C4×C61C22×C412yes—
182C22⋊C4×C61—22no—
183C42×C61—22no—
184C42×C61C22×C411yescharacteristic
185C42×C61C2×D411yescharacteristic
186C42×C61C2×D411yescharacteristic
187C42×C61C2411yescharacteristic
188C22⋊Dic61C22⋊C412yes—
189#11758198—22no—
190#11758198—22no—
191#11758198—21no—
192#11758198—21no—
193#11758198—21no—
194#11758198—21no—
195#11758198—22no—
196#11758198—22no—
197#11758198—22no—
198#11758198—22no—
199#11758198C22⋊C412yes—
200#11758198C22⋊C412yes—
201C4⋊Dic61—21no—
202C4⋊Dic61—22no—
203C4⋊Dic61—22no—
204C4⋊Dic61C22⋊C411yescharacteristic
205C4⋊Dic61C22⋊C411yescharacteristic
206C4⋊Dic61C22×C411yescharacteristic
207C4⋊Dic61C22×C411yescharacteristic
208#11758196—22no—
209#11758196—22no—
210#11758196C22⋊C412yes—
211#11758196C22⋊C412yes—
212C4×Dic61—22no—
213C4×Dic61—22no—
214C4×Dic61C22×C412yes—
215C4×Dic61C2×D412yes—
216C4×Dic61C2×D412yes—
217#11758194—42no—
218C2×#92418—21no—
219C2×#92418—22no—
220C2×#92418—21no—
221C2×#92418—42no—
222C8×D61—44no—
223C23×C61C2×C22⋊C411yescharacteristic
224C22×D61—21no—
225C22×D61—21no—
226C22×D61—42no—
227C22×D61—42no—
228C22×D61—81no—
229C22×D61C2×C22⋊C412yes—
230Q8×C61—22no—
231Q8×C61—22no—
232Q8×C61—81no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—22no—
236C2×C4×C61—22no—
237C2×C4×C61—41no—
238C2×C4×C61C2×C22⋊C411yescharacteristic
239C2×C4×C61C2×C22⋊C411yescharacteristic
240C2×C4×C61C2×C22⋊C411yescharacteristic
241C2×C4×C61#13512yes—
242C2×C4×C61#13512yes—
243C2×C4×C61C23×C411yescharacteristic
244C2×C4×C61C22×D411yescharacteristic
245C2×C4×C61C22×D411yescharacteristic
246C22⋊D61—24no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—42no—
250C2×Dic61C2×C22⋊C412yes—
251C2×Dic61C2×C22⋊C412yes—
252C2×Dic61C2×C22⋊C412yes—
253D244—21no—
254D244—21no—
255D244—21no—
256D244—22no—
257D244—42no—
258D244—44no—
259D244—82no—
260D244#13112yes—
261C4×D61—22no—
262C4×D61—22no—
263C4×D61—22no—
264C4×D61—22no—
265C4×D61—42no—
266C4×D61—44no—
267C4×D61—41no—
268C4×D61—41no—
269C4×D61—41no—
270C4×D61—41no—
271C4×D61—42no—
272C4×D61—42no—
273C4×D61—82no—
274Dic122—22no—
275C8×C61—42no—
276C8×C61—41no—
277C8×C61—41no—
278#92418—22no—
279#92418—41no—
280#92418—42no—
281#17508—611nomaximal, Sylow
282C22×C61—21no—
283C22×C61—21no—
284C22×C61#41612yes—
285C22×C61C22×C22⋊C411yescharacteristic
286C2×D61—22no—
287C2×D61—22no—
288C2×D61—22no—
289C2×D61—22no—
290C2×D61—41no—
291C2×D61—41no—
292C2×D61—41no—
293C2×D61—41no—
294C2×D61—41no—
295C2×D61—84no—
296C4×C61—21no—
297C4×C61—21no—
298C4×C61—21no—
299C4×C61—42no—
300C4×C61—42no—
301C4×C61#41612yes—
302C4×C61C2×#13111yescharacteristic
303C4×C61#56811yescharacteristic
304C4×C61C2×#13511yescharacteristic
305C4×C61C2×#13511yescharacteristic
306Dic61—22no—
307Dic61—22no—
308Dic61—22no—
309Dic61—41no—
310Dic61—41no—
311#3475—611no—
312C8×#41—611no—
313#2925—611no—
314#1494—612no—
315#1493—611no—
316#1488—612no—
317#1486—611no—
318#1482—612no—
319#1481D6111yescharacteristic, complemented
320#1476—612no—
321C2×D4⋊C8—611no—
322C2×C61—22no—
323C2×C61#288011yescharacteristic
324C2×C61C2×#41611yescharacteristic
325C2×C61#290111yescharacteristic
326D61—42no—
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#533C2×D6111yescharacteristic
339#529—612no—
340#529—1222no—
341#525—1221no—
342C4×#41—611no—
343C4×#41—612no—
344C2×C4×D4—611no—
345C2×#117—1221no—
346C8×Q8—1221no—
347C8×D4—1222no—
348C8×D4—1221no—
349#433—1222no—
350#432—612no—
351#431—612no—
352#431—612no—
353#431C2×D6111yescharacteristic
354#423—611no—
355C2×C4⋊C8C2×D6111yescharacteristic
356#408—1221no—
357#405—1221no—
358C2×C4×C8—611no—
359C2×C4×C8—612no—
360Q8⋊C8—612no—
361Q8⋊C8—612no—
362Q8⋊C8C2×D6112yescomplemented
363Q8⋊C8C2×D6112yescomplemented
364D4⋊C8—611no—
365D4⋊C8—611no—
366D4⋊C8—611no—
367D4⋊C8—611no—
368D4⋊C8—612no—
369D4⋊C8—612no—
370C61#1750811yescharacteristic, complemented, Sylow
371C2×#41—611no—
372C2×#41—612no—
373C22×D4—611no—
374C23×C4—1221no—
375C2×M16—1221no—
376C22×C8—21no—
377C22×C8—1222no—
378C22×C8—1221no—
379C4⋊Q8C4×D6111yescharacteristic
380C4⋊Q8C4×D6111yescharacteristic
381#126—1222no—
382#126—1222no—
383#126—1222no—
384#125—21no—
385#125—612no—
386#125—1222no—
387#124—612no—
388#124—1222no—
389#123—1222no—
390#123—1222no—
391#123—1222no—
392#123—1222no—
393C22⋊Q8—21no—
394C22⋊Q8—612no—
395C22⋊Q8—1221no—
396C22⋊Q8—1221no—
397C22⋊Q8—1222no—
398C22⋊Q8C4×D6112yes—
399#121—612no—
400#121—1222no—
401#121—1221no—
402#121—1221no—
403#120—1222no—
404C4×Q8—21no—
405C4×Q8—611no—
406C4×Q8—611no—
407C4×Q8—612no—
408C4×Q8C22×D6112yes—
409C4×D4—612no—
410C4×D4—612no—
411C4×D4—612no—
412C4×D4—611no—
413C4×D4—611no—
414C4×D4—611no—
415C4×D4—611no—
416C4×D4—611no—
417C4×D4—611no—
418C4×D4—1222no—
419C4×D4—1222no—
420C4×D4—1222no—
421C4×D4—1221no—
422C4×D4—1221no—
423#117—21no—
424#117—611no—
425#117—612no—
426#117—612no—
427#117—1222no—
428#117—1222no—
429#117—1222no—
430#117—1221no—
431#117—1221no—
432C2×C4⋊C4—611no—
433C2×C4⋊C4—1221no—
434C2×C4⋊C4—1221no—
435C2×C22⋊C4—1222no—
436C2×C22⋊C4—1221no—
437C2×C42—612no—
438C2×C42—1222no—
439C2×C42C22×D6111yescharacteristic
440C4⋊C8—21no—
441C4⋊C8—21no—
442C4⋊C8—612no—
443C4⋊C8—1222no—
444C4⋊C8—1221no—
445C4⋊C8C22×D6111yescharacteristic
446C4⋊C8C22×D6111yescharacteristic
447C22⋊C8—21no—
448C22⋊C8—1222no—
449C22⋊C8—1222no—
450C22⋊C8—1222no—
451#97—1222no—
452C4×C8—611no—
453C4×C8—611no—
454C4×C8—1222no—
455C4×C8—1222no—
456C4×C8—1221no—
457C4×C8C22×D6112yes—
458C24—1221no—
459#41—1222no—
460#41—1222no—
461#41—1224no—
462#41—2442no—
463C2×Q8—21no—
464C2×Q8—611no—
465C2×Q8C2×C4×D6112yes—
466C2×D4—612no—
467C2×D4—611no—
468C2×D4—611no—
469C2×D4—611no—
470C2×D4—1222no—
471C2×D4—1222no—
472C2×D4—1222no—
473C2×D4—1221no—
474C2×D4—2441no—
475C22×C4—612no—
476C22×C4—612no—
477C22×C4—612no—
478C22×C4—1222no—
479C22×C4—1222no—
480C22×C4—1221no—
481C22×C4—1221no—
482C22×C4—1221no—
483C22×C4—1221no—
484C22×C4—1221no—
485C22×C4—2442no—
486C22×C4—2442no—
487C22×C4C2×C4×D6111yescharacteristic
488C22×C4D4×D6111yescharacteristic
489C22×C4D4×D6111yescharacteristic
490M16—2442no—
491C2×C8—22no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—42no—
495C2×C8—1221no—
496C2×C8—1221no—
497C2×C8—1222no—
498C2×C8—2444no—
499C2×C8—2442no—
500C4⋊C4—22no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—22no—
504C4⋊C4—21no—
505C4⋊C4—611no—
506C4⋊C4—611no—
507C4⋊C4—612no—
508C4⋊C4—612no—
509C4⋊C4—611no—
510C4⋊C4—611no—
511C4⋊C4—1222no—
512C4⋊C4—1222no—
513C4⋊C4—1222no—
514C4⋊C4—1222no—
515C4⋊C4—1221no—
516C4⋊C4C2×C4×D6112yes—
517C22⋊C4—22no—
518C22⋊C4—612no—
519C22⋊C4—612no—
520C22⋊C4—612no—
521C22⋊C4—1222no—
522C22⋊C4—1222no—
523C22⋊C4—1222no—
524C22⋊C4—1222no—
525C22⋊C4—1222no—
526C22⋊C4—1222no—
527C22⋊C4—1221no—
528C22⋊C4—1221no—
529C22⋊C4—1221no—
530C22⋊C4—1221no—
531C42—22no—
532C42—612no—
533C42—612no—
534C42—612no—
535C42—1222no—
536C42—1222no—
537C42C2×C4×D6111yescharacteristic
538C42D4×D6111yescharacteristic
539C42D4×D6111yescharacteristic
540C42C23×D6111yescharacteristic
541C23—612no—
542C23—1221no—
543C23—1221no—
544C23—4881no—
545C23—2442no—
546C23—2442no—
547C23C22⋊C4×D6111yescharacteristic
548Q8—22no—
549Q8—22no—
550Q8—81no—
551Q8—1222no—
552D4—612no—
553D4—1224no—
554D4—1221no—
555D4—1222no—
556D4—1221no—
557D4—1221no—
558D4—4882no—
559D4—2442no—
560D4—2444no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—41no—
566C2×C4—612no—
567C2×C4—612no—
568C2×C4—612no—
569C2×C4—1222no—
570C2×C4—1222no—
571C2×C4—1222no—
572C2×C4—1222no—
573C2×C4—1221no—
574C2×C4—1221no—
575C2×C4—4882no—
576C2×C4—2442no—
577C2×C4—2444no—
578C2×C4—2442no—
579C2×C4—2442no—
580C2×C4—2442no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4—2441no—
584C2×C4—2441no—
585C2×C4C22⋊C4×D6111yescharacteristic
586C2×C4C22⋊C4×D6111yescharacteristic
587C2×C4C22⋊C4×D6111yescharacteristic
588C2×C4#1451979812yes—
589C2×C4#1451980012yes—
590C2×C4C22×C4×D6111yescharacteristic
591C2×C4C2×D4×D6111yescharacteristic
592C2×C4C2×D4×D6111yescharacteristic
593C8—42no—
594C8—41no—
595C8—41no—
596C8—1222no—
597C8—2441no—
598C8—2442no—
599C22—21no—
600C22—21no—
601C22—1222no—
602C22—1222no—
603C22—1222no—
604C22—1222no—
605C22—4884no—
606C22—2441no—
607C22—2441no—
608C22—2441no—
609C22—2441no—
610C22—2441no—
611C22#1683975712yes—
612C22C2×C22⋊C4×D6111yescharacteristic
613C4—21no—
614C4—21no—
615C4—21no—
616C4—42no—
617C4—42no—
618C4—1222no—
619C4—1222no—
620C4—1222no—
621C4—2441no—
622C4—2441no—
623C4#1683975712yes—
624C4#131×D6111yescharacteristic
625C4#1684052711yescharacteristic
626C4C2×#1451979811yescharacteristic
627C4C2×#1451980011yescharacteristic
628C2—22no—
629C2—4881no—
630C2—2442no—
631C2—2442no—
632C2#2145426711yescharacteristic
633C2C2×#1683975711yescharacteristic
634C2#2145436511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1481C2
socleC22×C61C22×C22⋊C4
prime radical#21459386C2
cosocleC42×C61C24
hypercenter#1481D61
hypocenterC61#17508
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1481

Complements

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

NH ≅ G/Ntype
2. #21454775C2semidirect
3. #21454484C2semidirect
4. #21444278C2semidirect
5. #21444274C2semidirect
6. #21444252C2semidirect
7. #21444245C2semidirect
8. #21444226C2semidirect
9. #21444200C2semidirect
10. C2×#16839489C2semidirect
11. C61×#1481C2semidirect
32. #16839818C22semidirect
33. #16839814C22semidirect
34. #16839813C22semidirect
39. C4×C8×D61C22semidirect
40. Q8⋊#92418C22semidirect
41. Q8⋊#92418C22semidirect
51. C61×Q8⋊C8C22semidirect
52. C61×Q8⋊C8C22semidirect
319. #1481D61semidirect
362. Q8⋊C8C2×D61semidirect
363. Q8⋊C8C2×D61semidirect
370. C61#17508semidirect

Maximal subgroups

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

subgroupindex
#214593862
#214547752
#214544842
#214442782
#214442742
#214442522
#214442452
#214442262
#214442002
C2×#168394892
C61×#14812
#1750861