Finite Group Databasebeta

← #29646926

Subgroups — #29646926

Order 15616.

1004 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459386C211yesmaximal, characteristic
2#21454785C211yesmaximal, characteristic, complemented
3#21454388C211yesmaximal, characteristic, complemented
4#21444283C212yesmaximal, complemented
5#21444257C212yesmaximal, complemented
6#21444243C211yesmaximal, characteristic, complemented
7#21444231C212yesmaximal, complemented
8#21444222C211yesmaximal, characteristic, complemented
9#21444205C212yesmaximal, complemented
10C2×#16839491C211yesmaximal, characteristic, complemented
11C61×#1493C211yesmaximal, characteristic, complemented
12C2×#14519785—21no—
13#16840486C411yescharacteristic
14#16840478C411yescharacteristic
15#16840473C411yescharacteristic
16#16840465—21no—
17#16840454C412yes—
18#16840450—21no—
19#16840439—22no—
20#16840415C411yescharacteristic
21#16840403C412yes—
22#16840299—22no—
23#16840299C2212yes—
24#16840274—21no—
25C4×#11758226C2212yes—
26C4×#11758222C2211yescharacteristic
27C2×C4×D244C2211yescharacteristic
28#117×D61—21no—
29#16839892—21no—
30#16839841—21no—
31#16839833—22no—
32#16839815C2211yescharacteristic
33#16839813C2212yescomplemented
34#16839790—21no—
35#16839787—22no—
36#16839784C2212yescomplemented
37C2×C4⋊#92418C2211yescharacteristic
38C4⋊C8×D61C2212yescomplemented
39C4×#11758189C2212yescomplemented
40Q8⋊#92418C2212yescomplemented
41Q8⋊#92418C2212yescomplemented
42#16839491C2211yescharacteristic
43#16839491C2211yescharacteristic
44#16839491C2211yescharacteristic
45#16839491C2211yescharacteristic
46#16839489C2212yes—
47#16839489C2212yes—
48C61×#533C2211yescharacteristic
49C61×#423C2211yescharacteristic
50C2×C4×C8×C61C2211yescharacteristic
51C61×Q8⋊C8C2212yescomplemented
52C61×Q8⋊C8C2212yescomplemented
53C2×#11758226C2×C412yes—
54C2×#11758222D411yescharacteristic
55C22×D244C2×C411yescharacteristic
56C22×C4×D61—21no—
57#14519785—44no—
58C2×#11758189—22no—
59C2×#11758189—22no—
60C22×#92418—21no—
61C2×C8×D61—22no—
62#14519772—22no—
63#14519772—22no—
64#14519772—22no—
65#14519768—22no—
66#14519768C2×C412yes—
67#14519766—22no—
68#14519766C2×C412yes—
69#14519762—22no—
70#14519762—22no—
71#14519762—22no—
72#14519761—22no—
73#14519757—21no—
74#14519757—21no—
75#14519753—22no—
76#14519753C2×C412yes—
77#14519752—21no—
78#14519752—21no—
79#14519752—22no—
80#14519752C2×C412yes—
81#14519747—22no—
82Q8×Dic61C2×C412yes—
83C4×Dic122C2×C411yescharacteristic
84C4×Dic122D411yescharacteristic
85C4×D244—22no—
86C4×D244—22no—
87C4×D244—21no—
88C4×D244—21no—
89C4×D244C2×C411yescharacteristic
90C4×D244C2×C411yescharacteristic
91C4×D244C2×C411yescharacteristic
92C4×D244D411yescharacteristic
93C4×D244C2311yescharacteristic
94C4×D244C2311yescharacteristic
95#14519739—22no—
96#14519739C2×C412yes—
97C4×C22⋊D61C2×C412yes—
98C4×C22⋊D61D412yes—
99#14519736D411yescharacteristic
100#14519735—21no—
101#14519735—21no—
102#14519735—22no—
103#14519735C2×C412yes—
104#14519734—22no—
105#14519734D412yes—
106#14519733—22no—
107C2×C4⋊Dic61C2×C411yescharacteristic
108C4⋊C4×D61—21no—
109C4⋊C4×D61—21no—
110C2×#11758198—21no—
111C22⋊C4×D61—22no—
112C42×D61—22no—
113C42×D61C2312yes—
114C4⋊#92418—21no—
115C4⋊#92418—21no—
116C4⋊#92418C2311yescharacteristic
117C4⋊#92418C2311yescharacteristic
118#14519706—22no—
119#14519706—22no—
120#14519706—22no—
121C22⋊#92418—21no—
122#14519689—22no—
123#14519687—22no—
124C4×#92418C2312yes—
125C2×M16×C61—21no—
126C22×C8×C61—21no—
127C4⋊Q8×C61C2×C411yescharacteristic
128C4⋊Q8×C61C2×C411yescharacteristic
129#125×C61—21no—
130C22⋊Q8×C61—21no—
131C22⋊Q8×C61C2×C412yes—
132C4×Q8×C61—21no—
133C4×Q8×C61C2312yes—
134#117×C61—21no—
135C2×C42×C61C2311yescharacteristic
136C4⋊C8×C61—21no—
137C4⋊C8×C61C2312yes—
138C4×C8×C61—21no—
139C4×C8×C61C2311yescharacteristic
140C4×C8×C61C2311yescharacteristic
141C23×D61—21no—
142C2×Q8×C61—21no—
143C2×Q8×C61C22×C412yes—
144C22×C4×C61C22×C411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C2×C22⋊D61C22⋊C412yes—
148C22×Dic61—21no—
149#11758226—24no—
150#11758226—42no—
151#11758222—22no—
152#11758222—22no—
153C2×D244—22no—
154C2×D244—22no—
155C2×D244—21no—
156C2×D244—22no—
157C2×D244—41no—
158C2×D244C22⋊C411yescharacteristic
159C2×D244C22×C411yescharacteristic
160C2×D244C22×C411yescharacteristic
161C2×C4×D61—21no—
162C2×C4×D61—21no—
163C2×C4×D61—21no—
164C2×C4×D61—21no—
165C2×C4×D61—22no—
166C2×C4×D61—22no—
167C2×C4×D61—42no—
168C2×C4×D61—42no—
169C2×C4×D61C22×C412yes—
170C2×C4×D61C2×D412yes—
171C2×C4×D61C2×D412yes—
172C2×Dic122C22⋊C411yescharacteristic
173M16×C61—42no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61—22no—
177C2×C8×C61—42no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—22no—
182C4⋊C4×C61—22no—
183C4⋊C4×C61C22×C412yes—
184C22⋊C4×C61—22no—
185C42×C61—22no—
186C42×C61C22×C411yescharacteristic
187C42×C61C2×D411yescharacteristic
188C42×C61C2×D411yescharacteristic
189C42×C61C2411yescharacteristic
190C22⋊Dic61C22⋊C412yes—
191#11758198—22no—
192#11758198—22no—
193#11758198—21no—
194#11758198—21no—
195#11758198—21no—
196#11758198—21no—
197#11758198—22no—
198#11758198—22no—
199#11758198—22no—
200#11758198—22no—
201#11758198C22⋊C412yes—
202#11758198C22⋊C412yes—
203C4⋊Dic61—21no—
204C4⋊Dic61—22no—
205C4⋊Dic61—22no—
206C4⋊Dic61C22⋊C411yescharacteristic
207C4⋊Dic61C22⋊C411yescharacteristic
208C4⋊Dic61C22×C411yescharacteristic
209C4⋊Dic61C22×C411yescharacteristic
210#11758196—22no—
211#11758196—22no—
212#11758196C22⋊C412yes—
213#11758196C22⋊C412yes—
214C4×Dic61—22no—
215C4×Dic61—22no—
216C4×Dic61C22×C412yes—
217C4×Dic61C2×D412yes—
218C4×Dic61C2×D412yes—
219C2×#92418—22no—
220C2×#92418—21no—
221C2×#92418—21no—
222C2×#92418—42no—
223#11758189—44no—
224#11758189—44no—
225C8×D61—44no—
226C23×C61C2×C22⋊C411yescharacteristic
227C22×D61—21no—
228C22×D61—21no—
229C22×D61—42no—
230C22×D61—42no—
231C22×D61—81no—
232C22×D61C2×C22⋊C412yes—
233Q8×C61—22no—
234Q8×C61—22no—
235Q8×C61—81no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—22no—
239C2×C4×C61—22no—
240C2×C4×C61—41no—
241C2×C4×C61C2×C22⋊C411yescharacteristic
242C2×C4×C61C2×C22⋊C411yescharacteristic
243C2×C4×C61C2×C22⋊C411yescharacteristic
244C2×C4×C61AGL(1,ℤ/8)12yes—
245C2×C4×C61#13712yes—
246C2×C4×C61C23×C411yescharacteristic
247C2×C4×C61C22×D411yescharacteristic
248C2×C4×C61C22×D411yescharacteristic
249C22⋊D61—24no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—42no—
253C2×Dic61C2×C22⋊C412yes—
254C2×Dic61C2×C22⋊C412yes—
255C2×Dic61C2×C22⋊C412yes—
256D244—21no—
257D244—21no—
258D244—21no—
259D244—22no—
260D244—42no—
261D244—44no—
262D244—82no—
263D244#13112yescomplemented
264C4×D61—22no—
265C4×D61—22no—
266C4×D61—22no—
267C4×D61—22no—
268C4×D61—42no—
269C4×D61—44no—
270C4×D61—41no—
271C4×D61—41no—
272C4×D61—41no—
273C4×D61—41no—
274C4×D61—42no—
275C4×D61—42no—
276C4×D61—82no—
277Dic122—22no—
278C8×C61—22no—
279C8×C61—41no—
280C8×C61—42no—
281#92418—42no—
282#92418—41no—
283#92418—41no—
284#17512—611nomaximal, Sylow
285C22×C61—21no—
286C22×C61—21no—
287C22×C61#41712yes—
288C22×C61C22×C22⋊C411yescharacteristic
289C2×D61—22no—
290C2×D61—22no—
291C2×D61—22no—
292C2×D61—22no—
293C2×D61—41no—
294C2×D61—41no—
295C2×D61—41no—
296C2×D61—41no—
297C2×D61—41no—
298C2×D61—84no—
299C4×C61—21no—
300C4×C61—21no—
301C4×C61—21no—
302C4×C61—42no—
303C4×C61—42no—
304C4×C61#41712yes—
305C4×C61C2×#13111yescharacteristic
306C4×C61#56811yescharacteristic
307C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
308C4×C61C2×#13711yescharacteristic
309Dic61—22no—
310Dic61—22no—
311Dic61—22no—
312Dic61—41no—
313Dic61—41no—
314#3475—611no—
315#2965—611no—
316#2906—611no—
317#1495—612no—
318#1493D6111yescharacteristic, complemented
319#1489—612no—
320#1486—611no—
321#1483—612no—
322#1481—611no—
323#1477—612no—
324C2×D4⋊C8—611no—
325C2×C61—22no—
326C2×C61#288011yescharacteristic
327C2×C61C2×#41711yescharacteristic
328C2×C61#290111yescharacteristic
329D61—42no—
330D61—42no—
331D61—81no—
332C2×#131—1221no—
333#556—611no—
334#555—611no—
335#554—611no—
336#553—1221no—
337#552—612no—
338#552—1221no—
339#551—1222no—
340#547—611no—
341#546—612no—
342#533C2×D6111yescharacteristic
343#529—612no—
344#529—1222no—
345#525—1221no—
346C4×#41—611no—
347C4×#41—612no—
348C2×C4×D4—611no—
349C2×#117—1221no—
350#446—1221no—
351#436—1221no—
352#435—1222no—
353#431—611no—
354#431—612no—
355#424—1222no—
356#424—1221no—
357#423—612no—
358#423C2×D6111yescharacteristic
359C2×C4⋊C8—611no—
360C2×C4⋊C8—612no—
361C4×M16—612no—
362C2×C4×C8C2×D6111yescharacteristic
363Q8⋊C8—612no—
364Q8⋊C8—612no—
365Q8⋊C8C2×D6112yescomplemented
366Q8⋊C8C2×D6112yescomplemented
367D4⋊C8—612no—
368D4⋊C8—612no—
369D4⋊C8—611no—
370D4⋊C8—611no—
371D4⋊C8—611no—
372D4⋊C8—611no—
373C61#1751211yescharacteristic, complemented, Sylow
374C2×#41—611no—
375C2×#41—612no—
376C22×D4—611no—
377C23×C4—1221no—
378#131—2444no—
379C2×M16—21no—
380C2×M16—1222no—
381C2×M16—1222no—
382C22×C8—21no—
383C22×C8—1222no—
384C22×C8—1221no—
385C4⋊Q8C4×D6111yescharacteristic
386C4⋊Q8C4×D6111yescharacteristic
387#126—1222no—
388#126—1222no—
389#126—1222no—
390#125—21no—
391#125—612no—
392#125—1222no—
393#124—612no—
394#124—1222no—
395#123—1222no—
396#123—1222no—
397#123—1222no—
398#123—1222no—
399C22⋊Q8—21no—
400C22⋊Q8—612no—
401C22⋊Q8—1221no—
402C22⋊Q8—1221no—
403C22⋊Q8—1222no—
404C22⋊Q8C4×D6112yes—
405#121—612no—
406#121—1222no—
407#121—1221no—
408#121—1221no—
409#120—1222no—
410C4×Q8—21no—
411C4×Q8—611no—
412C4×Q8—611no—
413C4×Q8—612no—
414C4×Q8C22×D6112yes—
415C4×D4—612no—
416C4×D4—612no—
417C4×D4—612no—
418C4×D4—611no—
419C4×D4—611no—
420C4×D4—611no—
421C4×D4—611no—
422C4×D4—611no—
423C4×D4—611no—
424C4×D4—1222no—
425C4×D4—1222no—
426C4×D4—1222no—
427C4×D4—1221no—
428C4×D4—1221no—
429#117—21no—
430#117—611no—
431#117—612no—
432#117—612no—
433#117—1222no—
434#117—1222no—
435#117—1222no—
436#117—1221no—
437#117—1221no—
438C2×C4⋊C4—611no—
439C2×C4⋊C4—1221no—
440C2×C4⋊C4—1221no—
441C2×C22⋊C4—1222no—
442C2×C22⋊C4—1221no—
443C2×C42—612no—
444C2×C42—1222no—
445C2×C42C22×D6111yescharacteristic
446C4⋊C8—21no—
447C4⋊C8—611no—
448C4⋊C8—611no—
449C4⋊C8—1222no—
450C4⋊C8—1222no—
451C4⋊C8—1222no—
452C4⋊C8—1221no—
453C4⋊C8—1221no—
454C4⋊C8C22×D6112yes—
455C22⋊C8—1222no—
456C22⋊C8—1221no—
457#97—1222no—
458C4×C8—21no—
459C4×C8—612no—
460C4×C8C22×D6111yescharacteristic
461C4×C8C22×D6111yescharacteristic
462C24—1221no—
463#41—1222no—
464#41—1222no—
465#41—1224no—
466#41—2442no—
467C2×Q8—21no—
468C2×Q8—611no—
469C2×Q8C2×C4×D6112yes—
470C2×D4—612no—
471C2×D4—611no—
472C2×D4—611no—
473C2×D4—611no—
474C2×D4—1222no—
475C2×D4—1222no—
476C2×D4—1222no—
477C2×D4—1221no—
478C2×D4—2441no—
479C22×C4—612no—
480C22×C4—612no—
481C22×C4—612no—
482C22×C4—1222no—
483C22×C4—1222no—
484C22×C4—1221no—
485C22×C4—1221no—
486C22×C4—1221no—
487C22×C4—1221no—
488C22×C4—1221no—
489C22×C4—2442no—
490C22×C4—2442no—
491C22×C4C2×C4×D6111yescharacteristic
492C22×C4D4×D6111yescharacteristic
493C22×C4D4×D6111yescharacteristic
494M16—42no—
495M16—2444no—
496M16—2444no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—22no—
500C2×C8—42no—
501C2×C8—1222no—
502C2×C8—1221no—
503C2×C8—1221no—
504C2×C8—2444no—
505C2×C8—2442no—
506C4⋊C4—22no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—22no—
510C4⋊C4—21no—
511C4⋊C4—611no—
512C4⋊C4—611no—
513C4⋊C4—612no—
514C4⋊C4—612no—
515C4⋊C4—611no—
516C4⋊C4—611no—
517C4⋊C4—1222no—
518C4⋊C4—1222no—
519C4⋊C4—1222no—
520C4⋊C4—1222no—
521C4⋊C4—1221no—
522C4⋊C4C2×C4×D6112yes—
523C22⋊C4—22no—
524C22⋊C4—612no—
525C22⋊C4—612no—
526C22⋊C4—612no—
527C22⋊C4—1222no—
528C22⋊C4—1222no—
529C22⋊C4—1222no—
530C22⋊C4—1222no—
531C22⋊C4—1222no—
532C22⋊C4—1222no—
533C22⋊C4—1221no—
534C22⋊C4—1221no—
535C22⋊C4—1221no—
536C22⋊C4—1221no—
537C42—22no—
538C42—612no—
539C42—612no—
540C42—612no—
541C42—1222no—
542C42—1222no—
543C42C2×C4×D6111yescharacteristic
544C42D4×D6111yescharacteristic
545C42D4×D6111yescharacteristic
546C42C23×D6111yescharacteristic
547C23—612no—
548C23—1221no—
549C23—1221no—
550C23—4881no—
551C23—2442no—
552C23—2442no—
553C23C22⋊C4×D6111yescharacteristic
554Q8—22no—
555Q8—22no—
556Q8—81no—
557Q8—1222no—
558D4—612no—
559D4—1224no—
560D4—1221no—
561D4—1221no—
562D4—1221no—
563D4—1222no—
564D4—4882no—
565D4—2442no—
566D4—2444no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—41no—
572C2×C4—612no—
573C2×C4—612no—
574C2×C4—612no—
575C2×C4—1222no—
576C2×C4—1222no—
577C2×C4—1222no—
578C2×C4—1222no—
579C2×C4—1221no—
580C2×C4—1221no—
581C2×C4—4882no—
582C2×C4—2442no—
583C2×C4—2444no—
584C2×C4—2442no—
585C2×C4—2442no—
586C2×C4—2442no—
587C2×C4—2441no—
588C2×C4—2441no—
589C2×C4—2441no—
590C2×C4—2441no—
591C2×C4C22⋊C4×D6111yescharacteristic
592C2×C4C22⋊C4×D6111yescharacteristic
593C2×C4C22⋊C4×D6111yescharacteristic
594C2×C4#1451980412yes—
595C2×C4#1451980912yes—
596C2×C4C22×C4×D6111yescharacteristic
597C2×C4C2×D4×D6111yescharacteristic
598C2×C4C2×D4×D6111yescharacteristic
599C8—22no—
600C8—41no—
601C8—42no—
602C8—2442no—
603C8—2441no—
604C8—2441no—
605C22—21no—
606C22—21no—
607C22—1222no—
608C22—1222no—
609C22—1222no—
610C22—1222no—
611C22—4884no—
612C22—2441no—
613C22—2441no—
614C22—2441no—
615C22—2441no—
616C22—2441no—
617C22#1683976212yes—
618C22C2×C22⋊C4×D6111yescharacteristic
619C4—21no—
620C4—21no—
621C4—21no—
622C4—42no—
623C4—42no—
624C4—1222no—
625C4—1222no—
626C4—1222no—
627C4—2441no—
628C4—2441no—
629C4#1683976212yes—
630C4#131×D6111yescharacteristic
631C4#1684052711yescharacteristic
632C4C2×#1451980411yescharacteristic
633C4C2×#1451980911yescharacteristic
634C2—22no—
635C2—4881no—
636C2—2442no—
637C2—2442no—
638C2#2145426711yescharacteristic
639C2C2×#1683976211yescharacteristic
640C2#2145436311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1493C2
socleC22×C61C22×C22⋊C4
prime radical#21459386C2
cosocleC42×C61C24
hypercenter#1493D61
hypocenterC61#17512
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1493

Complements

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

NH ≅ G/Ntype
2. #21454785C2semidirect
3. #21454388C2semidirect
4. #21444283C2semidirect
5. #21444257C2semidirect
6. #21444243C2semidirect
7. #21444231C2semidirect
8. #21444222C2semidirect
9. #21444205C2semidirect
10. C2×#16839491C2semidirect
11. C61×#1493C2semidirect
33. #16839813C22semidirect
36. #16839784C22semidirect
38. C4⋊C8×D61C22semidirect
39. C4×#11758189C22semidirect
40. Q8⋊#92418C22semidirect
41. Q8⋊#92418C22semidirect
51. C61×Q8⋊C8C22semidirect
52. C61×Q8⋊C8C22semidirect
263. D244#131semidirect
318. #1493D61semidirect
365. Q8⋊C8C2×D61semidirect
366. Q8⋊C8C2×D61semidirect
373. C61#17512semidirect

Maximal subgroups

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

subgroupindex
#214593862
#214547852
#214543882
#214442832
#214442572
#214442432
#214442312
#214442222
#214442052
C2×#168394912
C61×#14932
#1751261