Finite Group Databasebeta

← #29646737

Subgroups — #29646737

Order 15616.

1002 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459116C211yesmaximal, characteristic
2#21454451C211yesmaximal, characteristic, complemented
3C2×#16839813C211yesmaximal, characteristic, complemented
4#21444274C211yesmaximal, characteristic, complemented
5#21444271C211yesmaximal, characteristic, complemented
6#21444269C211yesmaximal, characteristic, complemented
7#21444252C214yesmaximal, complemented
8#21444226C214yesmaximal, complemented
9C61×#1493C211yesmaximal, characteristic, complemented
10#16840317C411yescharacteristic
11#16840317C411yescharacteristic
12#16840313C411yescharacteristic
13#16840313C411yescharacteristic
14#16840312C2211yescharacteristic
15#16840299—21no—
16#16840299C2212yes—
17#16840298—21no—
18#16840298C412yes—
19#16840297—21no—
20#16840297—21no—
21#16840275—21no—
22#16840275C412yes—
23#16840274—21no—
24C4×#11758226—21no—
25C4×#11758226C2212yes—
26#16840230—21no—
27C2×C42×D61C2211yescharacteristic
28#16839818—21no—
29#16839818C2212yes—
30#16839814—21no—
31#16839814C2212yes—
32#16839813—21no—
33#16839813—21no—
34#16839813C2212yes—
35#16839813C2212yes—
36#16839786C2211yescharacteristic
37C2×#14519706—21no—
38#16839725—21no—
39C2×#14519689—21no—
40M16×Dic61—21no—
41C2×C4×#92418C2211yescharacteristic
42Q8⋊#92418C2214yescomplemented
43#16839491C2214yescomplemented
44#16839489C2214yescomplemented
45C61×#533C2211yescharacteristic
46C61×#423C2211yescharacteristic
47C2×C4×C8×C61C2211yescharacteristic
48C61×Q8⋊C8C2214yescomplemented
49C2×#11758226—21no—
50C2×#11758226C2×C412yes—
51C2×#11758222—21no—
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C22×C4×D61D411yescharacteristic
55C2×#11758194—21no—
56C22×#92418—21no—
57#14519777C2×C411yescharacteristic
58#14519774C2×C411yescharacteristic
59#14519772—22no—
60#14519772—22no—
61#14519768—21no—
62#14519768C2×C412yes—
63#14519766—21no—
64#14519766C2×C412yes—
65#14519765—21no—
66#14519762—22no—
67#14519762—22no—
68#14519761—22no—
69#14519757—21no—
70#14519757—21no—
71#14519753—21no—
72#14519753C2×C412yes—
73#14519752—21no—
74#14519752—21no—
75#14519752—21no—
76#14519752C2×C412yes—
77#14519751—21no—
78#14519751C2×C412yes—
79#14519747—22no—
80Q8×Dic61—21no—
81Q8×Dic61C2×C412yes—
82#14519742—21no—
83#14519742—21no—
84C4×D244—22no—
85C4×D244—22no—
86C4×D244—21no—
87C4×D244C2312yes—
88#14519739—22no—
89#14519739—22no—
90#14519739—21no—
91#14519739—21no—
92#14519739—21no—
93#14519739C2×C412yes—
94#14519737—22no—
95#14519737—22no—
96#14519735—21no—
97#14519735—22no—
98#14519735—22no—
99#14519735C2×C412yes—
100#14519734—22no—
101C2×C4×Dic61C2×C411yescharacteristic
102C2×C4×Dic61D411yescharacteristic
103C2×C4×Dic61D411yescharacteristic
104C42×D61—22no—
105C42×D61C2×C411yescharacteristic
106C42×D61C2×C411yescharacteristic
107C42×D61D411yescharacteristic
108C42×D61D411yescharacteristic
109C42×D61D411yescharacteristic
110C42×D61D411yescharacteristic
111C42×D61C2311yescharacteristic
112C42×D61C2311yescharacteristic
113C4⋊#92418—21no—
114C4⋊#92418C2312yes—
115#14519706—22no—
116#14519706—22no—
117#14519689—22no—
118#14519689—22no—
119#14519689—22no—
120#14519689—22no—
121#14519687—22no—
122C4×#92418—21no—
123C4×#92418C2312yes—
124C8×Dic61—22no—
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×C61C2312yes—
140C23×D61C22⋊C411yescharacteristic
141C2×Q8×C61—21no—
142C2×Q8×C61C22×C412yes—
143C22×C4×C61C22×C411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C2×C22⋊D61—22no—
147C22×Dic61C22⋊C411yescharacteristic
148C22×Dic61C22⋊C411yescharacteristic
149C22×Dic61C22⋊C411yescharacteristic
150#11758226—44no—
151#11758226—44no—
152#11758222—42no—
153#11758222—42no—
154C2×D244—22no—
155C2×D244—22no—
156C2×D244—21no—
157C2×D244—21no—
158C2×D244C22×C412yes—
159C2×C4×D61—22no—
160C2×C4×D61—22no—
161C2×C4×D61—22no—
162C2×C4×D61—22no—
163C2×C4×D61—22no—
164C2×C4×D61—42no—
165C2×C4×D61—42no—
166C2×C4×D61C22⋊C411yescharacteristic
167C2×C4×D61C22⋊C411yescharacteristic
168C2×C4×D61C22⋊C411yescharacteristic
169C2×C4×D61C22⋊C411yescharacteristic
170C2×C4×D61C22⋊C411yescharacteristic
171C2×C4×D61C22⋊C411yescharacteristic
172C2×C4×D61C22×C411yescharacteristic
173C2×C4×D61C22×C411yescharacteristic
174C2×C4×D61C2×D411yescharacteristic
175C2×C4×D61C2×D411yescharacteristic
176C2×C4×D61C2×D411yescharacteristic
177C2×C4×D61C2×D411yescharacteristic
178C2×Dic122—21no—
179M16×C61—42no—
180C2×C8×C61—22no—
181C2×C8×C61—22no—
182C2×C8×C61—42no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61—21no—
186C4⋊C4×C61—22no—
187C4⋊C4×C61—22no—
188C4⋊C4×C61C22×C412yes—
189C22⋊C4×C61—22no—
190C42×C61—22no—
191C42×C61C22×C411yescharacteristic
192C42×C61C2×D411yescharacteristic
193C42×C61C2×D411yescharacteristic
194C42×C61C2411yescharacteristic
195#11758198—22no—
196#11758198—22no—
197#11758198—22no—
198#11758198—22no—
199#11758198—22no—
200#11758198—22no—
201#11758198—22no—
202#11758198—22no—
203C4⋊Dic61—21no—
204C4⋊Dic61—22no—
205C4⋊Dic61—22no—
206C4⋊Dic61C22×C412yes—
207#11758196—22no—
208#11758196—22no—
209C4×Dic61—22no—
210C4×Dic61—22no—
211C4×Dic61C22⋊C411yescharacteristic
212C4×Dic61C22⋊C411yescharacteristic
213C4×Dic61C22⋊C411yescharacteristic
214C4×Dic61C22⋊C411yescharacteristic
215C4×Dic61C22⋊C411yescharacteristic
216C4×Dic61C22⋊C411yescharacteristic
217C4×Dic61C22×C411yescharacteristic
218C4×Dic61C22×C411yescharacteristic
219C4×Dic61C2×D411yescharacteristic
220C4×Dic61C2×D411yescharacteristic
221C4×Dic61C2×D411yescharacteristic
222C4×Dic61C2×D411yescharacteristic
223#11758194—42no—
224C2×#92418—22no—
225C2×#92418—22no—
226C2×#92418—42no—
227C23×C61C2×C22⋊C411yescharacteristic
228C22×D61—22no—
229C22×D61—22no—
230C22×D61—41no—
231C22×D61—41no—
232C22×D61C2×C22⋊C411yescharacteristic
233C22×D61C2×C22⋊C411yescharacteristic
234Q8×C61—24no—
235Q8×C61—42no—
236C2×C4×C61—22no—
237C2×C4×C61—22no—
238C2×C4×C61—22no—
239C2×C4×C61—22no—
240C2×C4×C61C2×C22⋊C411yescharacteristic
241C2×C4×C61C2×C22⋊C411yescharacteristic
242C2×C4×C61C2×C22⋊C411yescharacteristic
243C2×C4×C61#13512yes—
244C2×C4×C61#13512yes—
245C2×C4×C61C23×C411yescharacteristic
246C2×C4×C61C22×D411yescharacteristic
247C2×C4×C61C22×D411yescharacteristic
248C22⋊D61—44no—
249C2×Dic61—22no—
250C2×Dic61—22no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61C2×C22⋊C411yescharacteristic
254C2×Dic61C2×C22⋊C411yescharacteristic
255C2×Dic61C2×C22⋊C411yescharacteristic
256C2×Dic61C2×C22⋊C411yescharacteristic
257C2×Dic61C2×C22⋊C411yescharacteristic
258C2×Dic61C2×C22⋊C411yescharacteristic
259D244—24no—
260D244—44no—
261D244—44no—
262D244—42no—
263D244—42no—
264C4×D61—22no—
265C4×D61—22no—
266C4×D61—21no—
267C4×D61—21no—
268C4×D61—21no—
269C4×D61—21no—
270C4×D61—22no—
271C4×D61—22no—
272C4×D61—22no—
273C4×D61—22no—
274C4×D61—41no—
275C4×D61—41no—
276C4×D61—41no—
277C4×D61—41no—
278C4×D61—44no—
279C4×D61—44no—
280C4×D61—42no—
281C4×D61—42no—
282Dic122—42no—
283C8×C61—42no—
284C8×C61—42no—
285#92418—42no—
286#92418—42no—
287#17489—611nomaximal, Sylow
288C22×C61—21no—
289C22×C61—21no—
290C22×C61#41612yes—
291C22×C61C22×C22⋊C411yescharacteristic
292C2×D61—21no—
293C2×D61—21no—
294C2×D61—21no—
295C2×D61—21no—
296C2×D61—21no—
297C2×D61—21no—
298C2×D61—44no—
299C2×D61—42no—
300C2×D61—42no—
301C2×D61—42no—
302C4×C61—21no—
303C4×C61—21no—
304C4×C61—42no—
305C4×C61—42no—
306C4×C61#41612yes—
307C4×C61#42112yes—
308C4×C61#56812yes—
309C4×C61C2×#13511yescharacteristic
310C4×C61C2×#13511yescharacteristic
311Dic61—21no—
312Dic61—21no—
313Dic61—21no—
314Dic61—21no—
315Dic61—21no—
316Dic61—21no—
317Dic61—42no—
318#3444—611no—
319#2920—611no—
320C2×#431—611no—
321#1493—611no—
322#1493D6111yescharacteristic, complemented
323#1492—611no—
324#1492—611no—
325#1488—614no—
326#1482—614no—
327C2×C61—22no—
328C2×C61#287911yescharacteristic
329C2×C61C2×#41611yescharacteristic
330C2×C61C2×#42111yescharacteristic
331D61—41no—
332D61—41no—
333D61—82no—
334#533—611no—
335#533—611no—
336#533C2×D6111yescharacteristic
337#532—611no—
338#532—611no—
339#532—611no—
340#529—612no—
341#529—612no—
342#529—1221no—
343#529—1221no—
344#529—1221no—
345#529—1221no—
346#525—612no—
347#525—1221no—
348#525—1221no—
349C4×#41—612no—
350C4×#41—1221no—
351C4×#41—1221no—
352C22×C42—611no—
353#432—612no—
354#432—1221no—
355#431—612no—
356#431—612no—
357#431—612no—
358#431—1221no—
359#431—1221no—
360#431—1221no—
361#423—611no—
362#423C2×D6111yescharacteristic
363C2×C4⋊C8—1221no—
364#407—1221no—
365C2×C22⋊C8—1221no—
366C4×M16—1221no—
367C2×C4×C8—611no—
368C2×C4×C8C2×D6111yescharacteristic
369Q8⋊C8—614no—
370Q8⋊C8C2×D6114yescomplemented
371D4⋊C8—614no—
372D4⋊C8—614no—
373C61#1748911yescharacteristic, complemented, Sylow
374C2×#41—612no—
375C2×#41—1221no—
376C2×#41—1221no—
377C23×C4—611no—
378C23×C4—611no—
379C23×C4—611no—
380C2×M16—21no—
381C2×M16—1221no—
382C22×C8—21no—
383C22×C8—1221no—
384C4⋊Q8—611no—
385C4⋊Q8C4×D6111yescharacteristic
386C4⋊Q8C4×D6111yescharacteristic
387#127—611no—
388#126—1222no—
389#126—1222no—
390#125—21no—
391#125—612no—
392#125—1221no—
393#124—612no—
394#124—1221no—
395#124—1221no—
396#123—1222no—
397#123—1222no—
398#123—1222no—
399C22⋊Q8—21no—
400C22⋊Q8—612no—
401C22⋊Q8—1221no—
402C22⋊Q8—1221no—
403C22⋊Q8—1221no—
404C22⋊Q8C4×D6112yes—
405#121—612no—
406#121—612no—
407#121—1221no—
408#121—1221no—
409#121—1221no—
410#121—1221no—
411#120—1222no—
412C4×Q8—21no—
413C4×Q8—612no—
414C4×Q8—1221no—
415C4×Q8—1221no—
416C4×Q8—1221no—
417C4×Q8C22×D6112yes—
418C4×D4—612no—
419C4×D4—612no—
420C4×D4—1222no—
421C4×D4—1222no—
422C4×D4—1221no—
423C4×D4—1221no—
424C4×D4—1221no—
425C4×D4—1222no—
426C4×D4—1222no—
427C4×D4—1222no—
428C4×D4—1222no—
429C4×D4—1221no—
430#117—21no—
431#117—612no—
432#117—1222no—
433#117—1222no—
434#117—1222no—
435#117—1221no—
436C2×C42—611no—
437C2×C42—611no—
438C2×C42—611no—
439C2×C42—611no—
440C2×C42—611no—
441C2×C42—611no—
442C2×C42—611no—
443C2×C42—611no—
444C2×C42—611no—
445C2×C42—611no—
446C2×C42—611no—
447C2×C42—1222no—
448C2×C42C22×D6111yescharacteristic
449C4⋊C8—21no—
450C4⋊C8—612no—
451C4⋊C8—1222no—
452C4⋊C8—1222no—
453C4⋊C8—1221no—
454C4⋊C8C22×D6112yes—
455C22⋊C8—1222no—
456C22⋊C8—1222no—
457C22⋊C8—1222no—
458C22⋊C8—1222no—
459#97—1222no—
460C4×C8—21no—
461C4×C8—612no—
462C4×C8—1222no—
463C4×C8—1221no—
464C4×C8C22×D6112yes—
465C24—611no—
466#41—2444no—
467#41—2444no—
468#41—2442no—
469#41—2442no—
470C2×Q8—21no—
471C2×Q8—1221no—
472C2×Q8C2×C4×D6112yes—
473C2×D4—612no—
474C2×D4—1222no—
475C2×D4—1222no—
476C2×D4—1222no—
477C2×D4—1221no—
478C2×D4—1221no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—611no—
483C22×C4—611no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—611no—
488C22×C4—611no—
489C22×C4—611no—
490C22×C4—611no—
491C22×C4—611no—
492C22×C4—611no—
493C22×C4—611no—
494C22×C4—1222no—
495C22×C4—1222no—
496C22×C4—1222no—
497C22×C4—1222no—
498C22×C4—1222no—
499C22×C4—2442no—
500C22×C4—2442no—
501C22×C4C2×C4×D6111yescharacteristic
502C22×C4D4×D6111yescharacteristic
503C22×C4D4×D6111yescharacteristic
504M16—42no—
505M16—2442no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—42no—
509C2×C8—1222no—
510C2×C8—1222no—
511C2×C8—2442no—
512C4⋊C4—22no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—22no—
517C4⋊C4—612no—
518C4⋊C4—1222no—
519C4⋊C4—1222no—
520C4⋊C4—1222no—
521C4⋊C4—1222no—
522C4⋊C4—1221no—
523C4⋊C4C2×C4×D6112yes—
524C22⋊C4—22no—
525C22⋊C4—1222no—
526C22⋊C4—1222no—
527C22⋊C4—1222no—
528C22⋊C4—1222no—
529C22⋊C4—1222no—
530C22⋊C4—1222no—
531C22⋊C4—1222no—
532C22⋊C4—1222no—
533C42—22no—
534C42—611no—
535C42—611no—
536C42—611no—
537C42—611no—
538C42—611no—
539C42—611no—
540C42—611no—
541C42—611no—
542C42—611no—
543C42—611no—
544C42—611no—
545C42—611no—
546C42—1222no—
547C42—1222no—
548C42C2×C4×D6111yescharacteristic
549C42D4×D6111yescharacteristic
550C42D4×D6111yescharacteristic
551C42C23×D6111yescharacteristic
552C23—611no—
553C23—611no—
554C23—1222no—
555C23—1222no—
556C23—2441no—
557C23—2441no—
558C23C22⋊C4×D6111yescharacteristic
559Q8—24no—
560Q8—42no—
561Q8—2442no—
562D4—1224no—
563D4—2444no—
564D4—2444no—
565D4—2444no—
566D4—2442no—
567D4—2442no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—611no—
573C2×C4—611no—
574C2×C4—611no—
575C2×C4—611no—
576C2×C4—611no—
577C2×C4—611no—
578C2×C4—1222no—
579C2×C4—1222no—
580C2×C4—1222no—
581C2×C4—1222no—
582C2×C4—1222no—
583C2×C4—1221no—
584C2×C4—1221no—
585C2×C4—1222no—
586C2×C4—1222no—
587C2×C4—1221no—
588C2×C4—1221no—
589C2×C4—1222no—
590C2×C4—2441no—
591C2×C4—2441no—
592C2×C4—2441no—
593C2×C4—2441no—
594C2×C4—2444no—
595C2×C4—2444no—
596C2×C4—2441no—
597C2×C4—2441no—
598C2×C4—2442no—
599C2×C4—2442no—
600C2×C4C22⋊C4×D6111yescharacteristic
601C2×C4C22⋊C4×D6111yescharacteristic
602C2×C4C22⋊C4×D6111yescharacteristic
603C2×C4#1451979812yes—
604C2×C4#1451980012yes—
605C2×C4C22×C4×D6111yescharacteristic
606C2×C4C2×D4×D6111yescharacteristic
607C2×C4C2×D4×D6111yescharacteristic
608C8—42no—
609C8—42no—
610C8—2442no—
611C8—2442no—
612C22—21no—
613C22—21no—
614C22—1221no—
615C22—1221no—
616C22—1221no—
617C22—1221no—
618C22—1221no—
619C22—1221no—
620C22—2444no—
621C22—2442no—
622C22—2442no—
623C22—2442no—
624C22#1683975712yes—
625C22C2×C22⋊C4×D6111yescharacteristic
626C4—21no—
627C4—21no—
628C4—42no—
629C4—42no—
630C4—1221no—
631C4—1221no—
632C4—1221no—
633C4—1221no—
634C4—1221no—
635C4—1221no—
636C4—2442no—
637C4#1683975712yes—
638C4#1683977712yes—
639C4#1684052712yes—
640C4C2×#1451979811yescharacteristic
641C4C2×#1451980011yescharacteristic
642C2—22no—
643C2—4882no—
644C2—2441no—
645C2—2441no—
646C2#2145426111yescharacteristic
647C2C2×#1683975711yescharacteristic
648C2C2×#1683977711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1493C2
socleC22×C61C22×C22⋊C4
prime radical#21459116C2
cosocleC42×C61C24
hypercenter#1493D61
hypocenterC61#17489
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. #21454451C2semidirect
3. C2×#16839813C2semidirect
4. #21444274C2semidirect
5. #21444271C2semidirect
6. #21444269C2semidirect
7. #21444252C2semidirect
8. #21444226C2semidirect
9. C61×#1493C2semidirect
42. Q8⋊#92418C22semidirect
43. #16839491C22semidirect
44. #16839489C22semidirect
48. C61×Q8⋊C8C22semidirect
322. #1493D61semidirect
370. Q8⋊C8C2×D61semidirect
373. C61#17489semidirect

Maximal subgroups

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

subgroupindex
#214591162
#214544512
C2×#168398132
#214442742
#214442712
#214442692
#214442522
#214442262
C61×#14932
#1748961