Finite Group Databasebeta

← #29645973

Subgroups — #29645973

Order 15616.

1020 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840297C211yesmaximal, characteristic
2#21454449C211yesmaximal, characteristic, complemented
3#431×D61C211yesmaximal, characteristic, complemented
4#21444175C211yesmaximal, characteristic, complemented
5#21444172C211yesmaximal, characteristic, complemented
6#21444170C211yesmaximal, characteristic, complemented
7#21444166C214yesmaximal, complemented
8#21444132C214yesmaximal, complemented
9C61×#1470C211yesmaximal, characteristic, complemented
10#16840297—21no—
11#16840297—21no—
12#16840297—21no—
13#16840297—21no—
14#16840297—21no—
15#16840297—21no—
16#16840297—21no—
17#16840297—21no—
18C2×#14519772C412yes—
19C2×#14519765C2211yescharacteristic
20C2×#14519762C2212yes—
21C2×#14519757C411yescharacteristic
22C2×#14519752C411yescharacteristic
23C2×#14519742C411yescharacteristic
24C2×#14519739C411yescharacteristic
25C2×#14519739C412yes—
26C2×#14519735C2212yes—
27C2×C42×D61C2211yescharacteristic
28#16839819C2211yescharacteristic
29#16839817—21no—
30#16839815C2211yescharacteristic
31#16839814—21no—
32#16839814—21no—
33#16839813—21no—
34#16839812C2212yes—
35#16839812C2212yes—
36#16839784—21no—
37C4⋊C8×D61—21no—
38#16839724C2212yes—
39C22⋊C8×D61C2212yes—
40#16839714—21no—
41C4×C8×D61—21no—
42#16839488C2214yes—
43#16839485C2214yes—
44#16839485C2214yes—
45C2×#125×C61C2211yescharacteristic
46C61×#432C2211yescharacteristic
47C61×#431C2211yescharacteristic
48C61×#324C2214yes—
49C22×Dic122C2×C411yescharacteristic
50C22×D244C2×C412yes—
51C22×D244C2×C411yescharacteristic
52C22×C4×D61C2×C412yes—
53C22×C4×D61C2×C411yescharacteristic
54C22×C4×D61C2×C411yescharacteristic
55C22×C4×D61C2311yescharacteristic
56C2×#11758189—22no—
57C2×C8×D61—22no—
58#14519772—22no—
59#14519772—22no—
60#14519772—22no—
61#14519772—22no—
62#14519765—21no—
63#14519765—21no—
64#14519765—21no—
65#14519765—21no—
66#14519762—22no—
67#14519762—22no—
68#14519762—22no—
69#14519762—22no—
70#14519757—21no—
71#14519757—21no—
72#14519757—21no—
73#14519757—21no—
74#14519752—21no—
75#14519752—21no—
76#14519752—21no—
77#14519752—21no—
78#14519742—21no—
79#14519742—21no—
80#14519742—21no—
81#14519742—21no—
82#14519739—22no—
83#14519739—22no—
84#14519739—22no—
85#14519739—22no—
86#14519739—21no—
87#14519739—21no—
88#14519739—21no—
89#14519739—21no—
90#14519735—22no—
91#14519735—22no—
92#14519735—22no—
93#14519735—22no—
94C2×C4⋊Dic61C2×C412yes—
95C2×#11758196C2×C412yes—
96C2×#11758198C2×C412yes—
97C2×#11758198C2×C412yes—
98C2×#11758198C2×C412yes—
99C2×#11758198C2×C412yes—
100C2×#11758198C2312yes—
101C2×C4×Dic61C2×C412yes—
102C2×C4×Dic61C2×C411yescharacteristic
103C2×C4×Dic61C2×C411yescharacteristic
104C2×C4×Dic61C2311yescharacteristic
105C42×D61D411yescharacteristic
106C42×D61D411yescharacteristic
107C42×D61D411yescharacteristic
108C42×D61D411yescharacteristic
109C42×D61D411yescharacteristic
110C42×D61D411yescharacteristic
111C42×D61D411yescharacteristic
112C42×D61D411yescharacteristic
113C4⋊#92418—21no—
114C4⋊#92418—21no—
115#14519706—22no—
116#14519706—22no—
117C22⋊#92418C2312yes—
118C22⋊#92418C2312yes—
119#14519689—22no—
120#14519689—22no—
121#14519688—21no—
122C4×#92418—21no—
123C8×Dic61—22no—
124C8×Dic61—22no—
125#125×C61—21no—
126#125×C61—21no—
127#125×C61—21no—
128#125×C61—21no—
129C2×C4⋊C4×C61C2×C411yescharacteristic
130C2×C4⋊C4×C61C2×C412yes—
131C2×C4⋊C4×C61C2×C411yescharacteristic
132C2×C4⋊C4×C61C2312yes—
133C2×C42×C61C2311yescharacteristic
134C4⋊C8×C61—21no—
135C4⋊C8×C61—21no—
136C22⋊C8×C61C2312yes—
137C22⋊C8×C61C2312yes—
138#97×C61—21no—
139C4×C8×C61—21no—
140C23×D61C22×C411yescharacteristic
141C23×D61C22×C412yes—
142C22×C4×C61C22×C412yes—
143C22×C4×C61C22×C411yescharacteristic
144C22×C4×C61C22×C411yescharacteristic
145C22×C4×C61C22×C412yes—
146C22×C4×C61C2411yescharacteristic
147C22×Dic61C22×C412yes—
148C22×Dic61C22×C411yescharacteristic
149C22×Dic61C22×C411yescharacteristic
150C22×Dic61C22×C411yescharacteristic
151C2×D244—22no—
152C2×D244—22no—
153C2×D244—21no—
154C2×D244—21no—
155C2×D244—42no—
156C2×D244—44no—
157C2×C4×D61—24no—
158C2×C4×D61—22no—
159C2×C4×D61—22no—
160C2×C4×D61—28no—
161C2×C4×D61—42no—
162C2×C4×D61—42no—
163C2×C4×D61C22⋊C411yescharacteristic
164C2×C4×D61C22⋊C411yescharacteristic
165C2×C4×D61C22⋊C411yescharacteristic
166C2×C4×D61C22⋊C411yescharacteristic
167C2×C4×D61C22⋊C411yescharacteristic
168C2×C4×D61C22⋊C411yescharacteristic
169C2×C4×D61C22⋊C411yescharacteristic
170C2×C4×D61C22⋊C411yescharacteristic
171C2×C4×D61C2×D411yescharacteristic
172C2×C4×D61C2×D411yescharacteristic
173C2×C4×D61C2×D411yescharacteristic
174C2×C4×D61C2×D411yescharacteristic
175C2×Dic122—21no—
176C2×Dic122—21no—
177C2×Dic122—42no—
178C2×C8×C61—22no—
179C2×C8×C61—22no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—22no—
183C4⋊C4×C61—22no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61—21no—
186C4⋊C4×C61—22no—
187C4⋊C4×C61—22no—
188C42×C61C2×D411yescharacteristic
189C42×C61C2×D411yescharacteristic
190C42×C61C2×D411yescharacteristic
191C42×C61C2×D411yescharacteristic
192#11758198—22no—
193#11758198—22no—
194#11758198—22no—
195#11758198—22no—
196#11758198—22no—
197#11758198—22no—
198#11758198—22no—
199#11758198—22no—
200#11758198—22no—
201#11758198—22no—
202C4⋊Dic61—22no—
203C4⋊Dic61—22no—
204#11758196—22no—
205#11758196—22no—
206C4×Dic61—22no—
207C4×Dic61—22no—
208C4×Dic61C22⋊C411yescharacteristic
209C4×Dic61C22⋊C411yescharacteristic
210C4×Dic61C22⋊C411yescharacteristic
211C4×Dic61C22⋊C411yescharacteristic
212C4×Dic61C22⋊C411yescharacteristic
213C4×Dic61C22⋊C411yescharacteristic
214C4×Dic61C22⋊C411yescharacteristic
215C4×Dic61C22⋊C411yescharacteristic
216C4×Dic61C2×D411yescharacteristic
217C4×Dic61C2×D411yescharacteristic
218C4×Dic61C2×D411yescharacteristic
219C4×Dic61C2×D411yescharacteristic
220C2×#92418—22no—
221C2×#92418—22no—
222#11758189—44no—
223C8×D61—44no—
224C23×C61C23×C411yescharacteristic
225C22×D61—22no—
226C22×D61—22no—
227C22×D61—22no—
228C22×D61—24no—
229C22×D61—41no—
230C22×D61—42no—
231C22×D61—42no—
232C22×D61C2×C22⋊C411yescharacteristic
233C22×D61C2×C22⋊C411yescharacteristic
234C2×C4×C61—22no—
235C2×C4×C61—22no—
236C2×C4×C61—22no—
237C2×C4×C61—22no—
238C2×C4×C61—24no—
239C2×C4×C61—41no—
240C2×C4×C61—42no—
241C2×C4×C61C2×C22⋊C411yescharacteristic
242C2×C4×C61C2×C22⋊C411yescharacteristic
243C2×C4×C61C2×C22⋊C411yescharacteristic
244C2×C4×C61C2×C22⋊C411yescharacteristic
245C2×C4×C61C22×D411yescharacteristic
246C2×C4×C61C22×D411yescharacteristic
247C2×Dic61—22no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—42no—
251C2×Dic61C2×C22⋊C411yescharacteristic
252C2×Dic61C2×C22⋊C411yescharacteristic
253C2×Dic61C2×C22⋊C411yescharacteristic
254C2×Dic61C2×C22⋊C411yescharacteristic
255C2×Dic61C2×C22⋊C411yescharacteristic
256C2×Dic61C2×C22⋊C411yescharacteristic
257C2×Dic61#13114yes—
258D244—42no—
259D244—44no—
260D244—44no—
261D244—42no—
262C4×D61—22no—
263C4×D61—22no—
264C4×D61—22no—
265C4×D61—22no—
266C4×D61—22no—
267C4×D61—22no—
268C4×D61—22no—
269C4×D61—22no—
270C4×D61—41no—
271C4×D61—41no—
272C4×D61—41no—
273C4×D61—41no—
274C4×D61—44no—
275C4×D61—44no—
276Dic122—42no—
277Dic122—42no—
278C8×C61—42no—
279C8×C61—42no—
280#92418—42no—
281#92418—42no—
282#17376—611nomaximal, Sylow
283C22×C61—21no—
284C22×C61—21no—
285C22×C61C22×C22⋊C411yescharacteristic
286C22×C61C2×#13112yes—
287C2×D61—21no—
288C2×D61—21no—
289C2×D61—21no—
290C2×D61—21no—
291C2×D61—21no—
292C2×D61—44no—
293C2×D61—42no—
294C2×D61—42no—
295C2×D61—42no—
296C2×D61—84no—
297C2×D61#41012yes—
298C4×C61—21no—
299C4×C61—21no—
300C4×C61—21no—
301C4×C61—21no—
302C4×C61—21no—
303C4×C61—42no—
304C4×C61—42no—
305C4×C61#41312yes—
306Dic61—21no—
307Dic61—21no—
308Dic61—21no—
309Dic61—21no—
310Dic61—42no—
311Dic61#40812yes—
312Dic61#40812yes—
313C2×#529—611no—
314#2920—611no—
315C2×#431—611no—
316#1470—611no—
317#1470D6111yescharacteristic, complemented
318#1469—611no—
319#1469—611no—
320#1468—614no—
321#1458—614no—
322C2×C61—22no—
323C2×C61C2×#40811yescharacteristic
324C2×C61C2×#41011yescharacteristic
325C2×C61C2×#41311yescharacteristic
326D61—22no—
327D61—41no—
328D61—82no—
329#529—1221no—
330#529—1221no—
331#529—1221no—
332#529—1221no—
333#529—1221no—
334#529—1221no—
335#529—1221no—
336#529—1221no—
337C2×#126—612no—
338C2×#125C2×D6111yescharacteristic
339C2×#124—611no—
340C2×#123—612no—
341C2×C22⋊Q8—611no—
342C2×#121—611no—
343C2×C4×Q8—611no—
344C2×C4×D4—611no—
345C2×C4×D4—612no—
346C2×#117—612no—
347C22×C42—611no—
348#432—611no—
349#432—1221no—
350#432C2×D6111yescharacteristic
351#431—611no—
352#431—612no—
353#431—612no—
354#431—1221no—
355#431—1221no—
356#431—1221no—
357#431C2×D6111yescharacteristic
358#423—1221no—
359C2×C4⋊C8—1221no—
360#407—612no—
361C2×C22⋊C8—612no—
362C4×M16—1221no—
363C2×C4×C8—1221no—
364#324—614no—
365#324C2×D6114yes—
366#323—614no—
367#323—614no—
368C61#1737611yescharacteristic, complemented, Sylow
369C22×Q8—611no—
370C22×D4—612no—
371C22×D4—611no—
372C23×C4—611no—
373C23×C4—611no—
374C23×C4—611no—
375C23×C4—612no—
376C2×M16—1222no—
377C22×C8—1222no—
378#126—1222no—
379#126—1222no—
380#126—1222no—
381#126—1222no—
382#125—21no—
383#125—21no—
384#125—21no—
385#125—21no—
386#124—1221no—
387#124—1221no—
388#124—1221no—
389#124—1221no—
390#123—1222no—
391#123—1222no—
392#123—1222no—
393#123—1222no—
394C22⋊Q8—1221no—
395C22⋊Q8—1221no—
396C22⋊Q8—1221no—
397C22⋊Q8—1221no—
398#121—1221no—
399#121—1221no—
400#121—1221no—
401#121—1221no—
402C4×Q8—1221no—
403C4×Q8—1221no—
404C4×Q8—1221no—
405C4×Q8—1221no—
406C4×D4—1221no—
407C4×D4—1221no—
408C4×D4—1221no—
409C4×D4—1221no—
410C4×D4—1222no—
411C4×D4—1222no—
412C4×D4—1222no—
413C4×D4—1222no—
414#117—1222no—
415#117—1222no—
416#117—1222no—
417#117—1222no—
418C2×C4⋊C4—612no—
419C2×C4⋊C4—612no—
420C2×C4⋊C4C4×D6111yescharacteristic
421C2×C4⋊C4C4×D6112yes—
422C2×C4⋊C4C4×D6111yescharacteristic
423C2×C4⋊C4C22×D6112yes—
424C2×C22⋊C4—612no—
425C2×C22⋊C4—612no—
426C2×C22⋊C4—612no—
427C2×C22⋊C4—612no—
428C2×C22⋊C4—612no—
429C2×C42—611no—
430C2×C42—611no—
431C2×C42—611no—
432C2×C42—611no—
433C2×C42—611no—
434C2×C42—611no—
435C2×C42—611no—
436C2×C42—611no—
437C2×C42—611no—
438C2×C42—611no—
439C2×C42—611no—
440C2×C42—612no—
441C2×C42C22×D6111yescharacteristic
442C4⋊C8—21no—
443C4⋊C8—21no—
444C4⋊C8—1222no—
445C4⋊C8—1222no—
446C4⋊C8—1221no—
447C4⋊C8—1221no—
448C22⋊C8—612no—
449C22⋊C8—612no—
450C22⋊C8—1222no—
451C22⋊C8—1222no—
452C22⋊C8C22×D6112yes—
453C22⋊C8C22×D6112yes—
454#97—21no—
455#97—1221no—
456C4×C8—21no—
457C4×C8—1222no—
458C4×C8—1222no—
459C4×C8—1221no—
460C24—611no—
461C24—612no—
462C2×Q8—1221no—
463C2×Q8—1221no—
464C2×Q8—2442no—
465C2×D4—1222no—
466C2×D4—1222no—
467C2×D4—1221no—
468C2×D4—1221no—
469C2×D4—2442no—
470C2×D4—2444no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—611no—
478C22×C4—611no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—611no—
483C22×C4—611no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—612no—
487C22×C4—1224no—
488C22×C4—1222no—
489C22×C4—1222no—
490C22×C4—1228no—
491C22×C4—2442no—
492C22×C4—2442no—
493C22×C4C2×C4×D6112yes—
494C22×C4C2×C4×D6111yescharacteristic
495C22×C4C2×C4×D6111yescharacteristic
496C22×C4C2×C4×D6112yes—
497C22×C4C23×D6111yescharacteristic
498M16—2444no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—1222no—
502C2×C8—1222no—
503C2×C8—2444no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—1222no—
513C4⋊C4—1222no—
514C4⋊C4—1222no—
515C4⋊C4—1222no—
516C22⋊C4—1222no—
517C22⋊C4—1222no—
518C22⋊C4—1222no—
519C22⋊C4—1222no—
520C22⋊C4—1222no—
521C22⋊C4—1222no—
522C22⋊C4—1222no—
523C22⋊C4—1222no—
524C22⋊C4—1222no—
525C22⋊C4—1222no—
526C42—611no—
527C42—611no—
528C42—611no—
529C42—611no—
530C42—611no—
531C42—611no—
532C42—611no—
533C42—611no—
534C42—611no—
535C42—611no—
536C42—611no—
537C42—611no—
538C42—1222no—
539C42—1222no—
540C42D4×D6111yescharacteristic
541C42D4×D6111yescharacteristic
542C42D4×D6111yescharacteristic
543C42D4×D6111yescharacteristic
544C23—611no—
545C23—611no—
546C23—1222no—
547C23—1222no—
548C23—1224no—
549C23—1222no—
550C23—2441no—
551C23—2442no—
552C23—2442no—
553C23C22×C4×D6111yescharacteristic
554Q8—2442no—
555Q8—2442no—
556D4—2442no—
557D4—2444no—
558D4—2444no—
559D4—2442no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—611no—
568C2×C4—611no—
569C2×C4—614no—
570C2×C4—611no—
571C2×C4—611no—
572C2×C4—611no—
573C2×C4—611no—
574C2×C4—1222no—
575C2×C4—1222no—
576C2×C4—1222no—
577C2×C4—1222no—
578C2×C4—1222no—
579C2×C4—1222no—
580C2×C4—1222no—
581C2×C4—1222no—
582C2×C4—1222no—
583C2×C4—2441no—
584C2×C4—2441no—
585C2×C4—2441no—
586C2×C4—2441no—
587C2×C4—2444no—
588C2×C4—2444no—
589C2×C4—2441no—
590C2×C4—2441no—
591C2×C4—2442no—
592C2×C4C22⋊C4×D6111yescharacteristic
593C2×C4C22⋊C4×D6111yescharacteristic
594C2×C4C22⋊C4×D6111yescharacteristic
595C2×C4C22⋊C4×D6111yescharacteristic
596C2×C4C2×D4×D6111yescharacteristic
597C2×C4C2×D4×D6111yescharacteristic
598C8—42no—
599C8—42no—
600C8—2442no—
601C8—2442no—
602C22—21no—
603C22—21no—
604C22—612no—
605C22—1221no—
606C22—1221no—
607C22—1221no—
608C22—1221no—
609C22—1221no—
610C22—4884no—
611C22—2444no—
612C22—2442no—
613C22—2442no—
614C22—2442no—
615C22C2×C22⋊C4×D6111yescharacteristic
616C22#131×D6112yes—
617C4—21no—
618C4—21no—
619C4—21no—
620C4—21no—
621C4—21no—
622C4—42no—
623C4—42no—
624C4—612no—
625C4—612no—
626C4—1221no—
627C4—1221no—
628C4—1221no—
629C4—1221no—
630C4—2442no—
631C4#1683974512yes—
632C2—22no—
633C2—1222no—
634C2—4882no—
635C2—2441no—
636C2#408×D6111yescharacteristic
637C2#410×D6111yescharacteristic
638C2C2×#1683974511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1470C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519752C4
cosocleC22×C4×C61C24
hypercenter#1470D61
hypocenterC61#17376
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1470

Complements

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

NH ≅ G/Ntype
2. #21454449C2semidirect
3. #431×D61C2semidirect
4. #21444175C2semidirect
5. #21444172C2semidirect
6. #21444170C2semidirect
7. #21444166C2semidirect
8. #21444132C2semidirect
9. C61×#1470C2semidirect
317. #1470D61semidirect
368. C61#17376semidirect

Maximal subgroups

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

subgroupindex
C2×#168402972
#214544492
#431×D612
#214441752
#214441722
#214441702
#214441662
#214441322
C61×#14702
#1737661