Finite Group Databasebeta

← #29647377

Subgroups — #29647377

Order 15616.

1036 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459116C211yesmaximal, characteristic
2#431×D61C211yesmaximal, characteristic, complemented
3#21448212C211yesmaximal, characteristic, complemented
4#21444395C214yesmaximal, complemented
5#21444383C211yesmaximal, characteristic, complemented
6#21444380C211yesmaximal, characteristic, complemented
7#21444378C211yesmaximal, characteristic, complemented
8#21444309C214yesmaximal, complemented
9C61×#1518C211yesmaximal, characteristic, complemented
10#16840317C411yescharacteristic, complemented
11#16840317C411yescharacteristic, complemented
12#16840313C411yescharacteristic, complemented
13#16840313C411yescharacteristic, complemented
14#16840312C2211yescharacteristic
15#16840299—21no—
16#16840299C412yescomplemented
17#16840298—21no—
18#16840298C2212yes—
19#16840297—21no—
20#16840297—21no—
21#16840275—21no—
22#16840275C2212yes—
23#16840274—21no—
24C4×#11758226—21no—
25C4×#11758226C412yescomplemented
26#16840230—21no—
27C2×C42×D61C2211yescharacteristic
28#16839815C2211yescharacteristic
29#16839814—21no—
30#16839813—21no—
31#16839812C2212yes—
32C4⋊C8×D61—21no—
33C22⋊C8×D61C2212yes—
34C4×C8×D61—21no—
35#16839629C2212yes—
36#16839628C2211yescharacteristic
37#16839624—21no—
38#16839619—21no—
39C4⋊C4×Dic61—21no—
40#16839609C2212yes—
41#16839607—21no—
42#16839499C2214yes—
43#16839497C2214yes—
44#16839495C2214yes—
45C61×#533C2211yescharacteristic
46C61×#431C2211yescharacteristic
47C61×#382C2211yescharacteristic
48C61×#328C2214yes—
49C2×#11758226—21no—
50C2×#11758226C2×C412yes—
51C2×#11758222—21no—
52C22×C4×D61D411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C22×C4×D61C2311yescharacteristic
55C2×C8×D61—22no—
56#14519777C2×C411yescharacteristic
57#14519774C2×C411yescharacteristic
58#14519772—22no—
59#14519772—22no—
60#14519768—21no—
61#14519768C2×C412yes—
62#14519766—21no—
63#14519766C2×C412yes—
64#14519765—21no—
65#14519762—22no—
66#14519762—22no—
67#14519761—22no—
68#14519757—21no—
69#14519757—21no—
70#14519753—21no—
71#14519753C2×C412yes—
72#14519752—21no—
73#14519752—21no—
74#14519752—21no—
75#14519752C2×C412yes—
76#14519751—21no—
77#14519751C2312yes—
78#14519747—22no—
79Q8×Dic61—21no—
80Q8×Dic61C2×C412yes—
81#14519742—21no—
82#14519742—21no—
83C4×D244—22no—
84C4×D244—22no—
85C4×D244—21no—
86C4×D244C2×C412yes—
87#14519739—22no—
88#14519739—22no—
89#14519739—21no—
90#14519739—21no—
91#14519739—21no—
92#14519739C2×C412yes—
93#14519737—22no—
94#14519737—22no—
95#14519735—21no—
96#14519735—22no—
97#14519735—22no—
98#14519735C2×C412yes—
99#14519734—22no—
100C2×C4⋊Dic61—21no—
101C2×#11758198—22no—
102C2×C4×Dic61—22no—
103C2×C4×Dic61D411yescharacteristic
104C2×C4×Dic61D411yescharacteristic
105C2×C4×Dic61C2311yescharacteristic
106C42×D61—22no—
107C42×D61C2×C411yescharacteristic
108C42×D61C2×C411yescharacteristic
109C42×D61C2×C411yescharacteristic
110C42×D61C2×C411yescharacteristic
111C42×D61D411yescharacteristic
112C42×D61D411yescharacteristic
113C42×D61D411yescharacteristic
114C42×D61D411yescharacteristic
115C4⋊#92418—21no—
116#14519706—22no—
117C22⋊#92418C2312yes—
118#14519689—22no—
119C4×#92418—21no—
120C8×Dic61—22no—
121#14519684—21no—
122#14519684—22no—
123#14519684—22no—
124#14519684C2312yes—
125C4⋊Q8×C61C2×C411yescharacteristic
126C4⋊Q8×C61C2×C411yescharacteristic
127#125×C61—21no—
128C22⋊Q8×C61—21no—
129C22⋊Q8×C61C2312yes—
130C4×Q8×C61—21no—
131C4×Q8×C61C2×C412yes—
132#117×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C42×C61C2311yescharacteristic
135C4⋊C8×C61—21no—
136C22⋊C8×C61C2312yes—
137C4×C8×C61—21no—
138#95×C61—21no—
139#95×C61C2312yes—
140C23×D61C2×D411yescharacteristic
141C2×Q8×C61—21no—
142C2×Q8×C61C22×C412yes—
143C22×C4×C61—22no—
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2411yescharacteristic
147C2×C22⋊D61—22no—
148C22×Dic61—22no—
149C22×Dic61C2×D411yescharacteristic
150C22×Dic61C2×D411yescharacteristic
151C22×Dic61C2×D411yescharacteristic
152#11758226—44no—
153#11758226—44no—
154#11758222—42no—
155#11758222—42no—
156C2×D244—22no—
157C2×D244—22no—
158C2×D244—21no—
159C2×D244—21no—
160C2×D244C22×C412yes—
161C2×C4×D61—22no—
162C2×C4×D61—22no—
163C2×C4×D61—22no—
164C2×C4×D61—22no—
165C2×C4×D61—22no—
166C2×C4×D61—42no—
167C2×C4×D61—42no—
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×D61C22⋊C411yescharacteristic
175C2×C4×D61C22⋊C411yescharacteristic
176C2×C4×D61C22×C411yescharacteristic
177C2×C4×D61C22×C411yescharacteristic
178C2×C4×D61C2×D411yescharacteristic
179C2×C4×D61C2×D411yescharacteristic
180C2×Dic122—21no—
181C2×C8×C61—22no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61—22no—
186C4⋊C4×C61—22no—
187C4⋊C4×C61—42no—
188C4⋊C4×C61C22×C412yes—
189C22⋊C4×C61—22no—
190C42×C61—22no—
191C42×C61C22×C411yescharacteristic
192C42×C61C22×C411yescharacteristic
193C42×C61C2×D411yescharacteristic
194C42×C61C2×D411yescharacteristic
195#11758198—22no—
196#11758198—22no—
197#11758198—22no—
198#11758198—22no—
199#11758198—22no—
200#11758198—22no—
201#11758198—22no—
202#11758198—22no—
203#11758198—44no—
204C4⋊Dic61—21no—
205C4⋊Dic61—22no—
206C4⋊Dic61—22no—
207C4⋊Dic61—42no—
208C4⋊Dic61C22×C412yes—
209#11758196—22no—
210#11758196—22no—
211C4×Dic61—22no—
212C4×Dic61—22no—
213C4×Dic61—44no—
214C4×Dic61C22⋊C411yescharacteristic
215C4×Dic61C22⋊C411yescharacteristic
216C4×Dic61C22⋊C411yescharacteristic
217C4×Dic61C22⋊C411yescharacteristic
218C4×Dic61C22⋊C411yescharacteristic
219C4×Dic61C22⋊C411yescharacteristic
220C4×Dic61C22⋊C411yescharacteristic
221C4×Dic61C22⋊C411yescharacteristic
222C4×Dic61C22×C411yescharacteristic
223C4×Dic61C22×C411yescharacteristic
224C4×Dic61C2×D411yescharacteristic
225C4×Dic61C2×D411yescharacteristic
226C2×#92418—22no—
227C8×D61—44no—
228C23×C61C22×D411yescharacteristic
229C22×D61—21no—
230C22×D61—21no—
231C22×D61—22no—
232C22×D61—22no—
233C22×D61—41no—
234C22×D61C2×C22⋊C411yescharacteristic
235C22×D61C2×C22⋊C411yescharacteristic
236Q8×C61—42no—
237Q8×C61—42no—
238C2×C4×C61—22no—
239C2×C4×C61—22no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—42no—
243C2×C4×C61—42no—
244C2×C4×C61—42no—
245C2×C4×C61C2×C22⋊C411yescharacteristic
246C2×C4×C61C2×C22⋊C411yescharacteristic
247C2×C4×C61C2×C22⋊C411yescharacteristic
248C2×C4×C61C2×C22⋊C411yescharacteristic
249C2×C4×C61#13512yes—
250C2×C4×C61#13512yes—
251C2×C4×C61C23×C411yescharacteristic
252C2×C4×C61C22×D411yescharacteristic
253C22⋊D61—42no—
254C22⋊D61—42no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—22no—
258C2×Dic61—22no—
259C2×Dic61—41no—
260C2×Dic61—42no—
261C2×Dic61—42no—
262C2×Dic61—42no—
263C2×Dic61C2×C22⋊C411yescharacteristic
264C2×Dic61C2×C22⋊C411yescharacteristic
265C2×Dic61C2×C22⋊C411yescharacteristic
266C2×Dic61C2×C22⋊C411yescharacteristic
267C2×Dic61C2×C22⋊C411yescharacteristic
268C2×Dic61C2×C22⋊C411yescharacteristic
269D244—42no—
270D244—42no—
271D244—44no—
272D244—44no—
273D244—42no—
274C4×D61—22no—
275C4×D61—22no—
276C4×D61—22no—
277C4×D61—22no—
278C4×D61—22no—
279C4×D61—22no—
280C4×D61—22no—
281C4×D61—22no—
282C4×D61—41no—
283C4×D61—41no—
284C4×D61—41no—
285C4×D61—41no—
286C4×D61—44no—
287C4×D61—44no—
288C4×D61—44no—
289Dic122—42no—
290C8×C61—42no—
291#92418—42no—
292#17573—611nomaximal, Sylow
293C22×C61—21no—
294C22×C61—21no—
295C22×C61C22×C22⋊C411yescharacteristic
296C22×C61C2×#13511yescharacteristic
297C22×C61C2×#13511yescharacteristic
298C2×D61—21no—
299C2×D61—21no—
300C2×D61—21no—
301C2×D61—21no—
302C2×D61—21no—
303C2×D61—42no—
304C2×D61—42no—
305C2×D61—42no—
306C2×D61—42no—
307C2×D61—42no—
308C2×D61#42112yes—
309C4×C61—21no—
310C4×C61—21no—
311C4×C61—21no—
312C4×C61—21no—
313C4×C61—42no—
314C4×C61—42no—
315C4×C61—82no—
316C4×C61#41612yes—
317C4×C61#41612yes—
318Dic61—21no—
319Dic61—21no—
320Dic61—21no—
321Dic61—21no—
322Dic61—21no—
323Dic61—42no—
324Dic61—82no—
325Dic61#41012yes—
326#3444—611no—
327C2×#431—611no—
328#2283—611no—
329#1521—614no—
330#1518—611no—
331#1518D6111yescharacteristic, complemented
332#1517—611no—
333#1517—611no—
334#1501—614no—
335C2×C61—21no—
336C2×C61—21no—
337C2×C61C2×#41011yescharacteristic
338C2×C61C2×#41611yescharacteristic
339C2×C61C2×#42111yescharacteristic
340D61—22no—
341D61—41no—
342D61—82no—
343#533—611no—
344#533—611no—
345#533C2×D6111yescharacteristic
346#532—611no—
347#532—611no—
348#532—611no—
349#529—612no—
350#529—612no—
351#529—1221no—
352#529—1221no—
353#529—1221no—
354#529—1221no—
355#525—612no—
356#525—1221no—
357#525—1221no—
358C4×#41—612no—
359C4×#41—1221no—
360C4×#41—1221no—
361C22×C42—611no—
362#431—611no—
363#431—612no—
364#431—1221no—
365#431—1221no—
366#431C2×D6111yescharacteristic
367C2×C4⋊C8—1221no—
368C2×C22⋊C8—612no—
369C2×C4×C8—1221no—
370#383—612no—
371#382—611no—
372#382C2×D6111yescharacteristic
373#381—1221no—
374#380—1221no—
375C4×C4⋊C4—1221no—
376C4×C22⋊C4—612no—
377#376—1221no—
378#328—614no—
379#328C2×D6114yes—
380#327—614no—
381#327—614no—
382C61#1757311yescharacteristic, complemented, Sylow
383C2×#41—612no—
384C2×#41—1221no—
385C2×#41—1221no—
386C23×C4—611no—
387C23×C4—611no—
388C23×C4—611no—
389C22×C8—1222no—
390C4⋊Q8—611no—
391C4⋊Q8C4×D6111yescharacteristic
392C4⋊Q8C4×D6111yescharacteristic
393#127—611no—
394#126—1222no—
395#126—1222no—
396#125—21no—
397#125—612no—
398#125—1221no—
399#124—612no—
400#124—1221no—
401#124—1221no—
402#123—1222no—
403#123—1222no—
404#123—1222no—
405C22⋊Q8—21no—
406C22⋊Q8—612no—
407C22⋊Q8—1221no—
408C22⋊Q8—1221no—
409C22⋊Q8—1221no—
410C22⋊Q8C22×D6112yes—
411#121—612no—
412#121—612no—
413#121—1221no—
414#121—1221no—
415#121—1221no—
416#121—1221no—
417#120—1222no—
418C4×Q8—21no—
419C4×Q8—612no—
420C4×Q8—1221no—
421C4×Q8—1221no—
422C4×Q8—1221no—
423C4×Q8C4×D6112yes—
424C4×D4—612no—
425C4×D4—612no—
426C4×D4—1222no—
427C4×D4—1222no—
428C4×D4—1221no—
429C4×D4—1221no—
430C4×D4—1221no—
431C4×D4—1222no—
432C4×D4—1222no—
433C4×D4—1222no—
434C4×D4—1222no—
435C4×D4—1221no—
436#117—21no—
437#117—612no—
438#117—1222no—
439#117—1222no—
440#117—1222no—
441#117—1221no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—1221no—
444C2×C22⋊C4—1222no—
445C2×C42—611no—
446C2×C42—611no—
447C2×C42—611no—
448C2×C42—611no—
449C2×C42—611no—
450C2×C42—611no—
451C2×C42—611no—
452C2×C42—611no—
453C2×C42—611no—
454C2×C42—611no—
455C2×C42—611no—
456C2×C42—1222no—
457C2×C42—1222no—
458C2×C42C22×D6111yescharacteristic
459C4⋊C8—21no—
460C4⋊C8—1222no—
461C4⋊C8—1221no—
462C22⋊C8—612no—
463C22⋊C8—1222no—
464C22⋊C8C22×D6112yes—
465C4×C8—21no—
466C4×C8—1222no—
467C4×C8—1221no—
468#95—21no—
469#95—612no—
470#95—1222no—
471#95—1222no—
472#95—1221no—
473#95C22×D6112yes—
474C24—611no—
475#41—2444no—
476#41—2444no—
477#41—2442no—
478#41—2442no—
479C2×Q8—21no—
480C2×Q8—1221no—
481C2×Q8C2×C4×D6112yes—
482C2×D4—612no—
483C2×D4—1222no—
484C2×D4—1222no—
485C2×D4—1222no—
486C2×D4—1221no—
487C2×D4—1221no—
488C22×C4—22no—
489C22×C4—611no—
490C22×C4—611no—
491C22×C4—611no—
492C22×C4—611no—
493C22×C4—611no—
494C22×C4—611no—
495C22×C4—611no—
496C22×C4—611no—
497C22×C4—611no—
498C22×C4—611no—
499C22×C4—611no—
500C22×C4—611no—
501C22×C4—611no—
502C22×C4—611no—
503C22×C4—611no—
504C22×C4—1222no—
505C22×C4—1222no—
506C22×C4—1222no—
507C22×C4—1222no—
508C22×C4—1222no—
509C22×C4—1222no—
510C22×C4—2442no—
511C22×C4—2442no—
512C22×C4D4×D6111yescharacteristic
513C22×C4D4×D6111yescharacteristic
514C22×C4C23×D6111yescharacteristic
515C2×C8—22no—
516C2×C8—1222no—
517C2×C8—2444no—
518C4⋊C4—22no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—22no—
523C4⋊C4—42no—
524C4⋊C4—612no—
525C4⋊C4—1222no—
526C4⋊C4—1222no—
527C4⋊C4—1222no—
528C4⋊C4—1222no—
529C4⋊C4—1221no—
530C4⋊C4—2442no—
531C4⋊C4C2×C4×D6112yes—
532C22⋊C4—22no—
533C22⋊C4—1222no—
534C22⋊C4—1222no—
535C22⋊C4—1222no—
536C22⋊C4—1222no—
537C22⋊C4—1222no—
538C22⋊C4—1222no—
539C22⋊C4—1222no—
540C22⋊C4—1222no—
541C22⋊C4—2444no—
542C42—22no—
543C42—611no—
544C42—611no—
545C42—611no—
546C42—611no—
547C42—611no—
548C42—611no—
549C42—611no—
550C42—611no—
551C42—611no—
552C42—611no—
553C42—611no—
554C42—611no—
555C42—1222no—
556C42—1222no—
557C42—2444no—
558C42C2×C4×D6111yescharacteristic
559C42C2×C4×D6111yescharacteristic
560C42D4×D6111yescharacteristic
561C42D4×D6111yescharacteristic
562C23—611no—
563C23—611no—
564C23—1222no—
565C23—1221no—
566C23—1221no—
567C23—1222no—
568C23—2441no—
569C23C2×D4×D6111yescharacteristic
570Q8—42no—
571Q8—42no—
572Q8—2442no—
573D4—2442no—
574D4—2442no—
575D4—2444no—
576D4—2444no—
577D4—2442no—
578D4—2442no—
579D4—2442no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—611no—
588C2×C4—611no—
589C2×C4—611no—
590C2×C4—611no—
591C2×C4—611no—
592C2×C4—611no—
593C2×C4—1222no—
594C2×C4—1222no—
595C2×C4—1222no—
596C2×C4—1222no—
597C2×C4—1222no—
598C2×C4—1221no—
599C2×C4—1221no—
600C2×C4—1222no—
601C2×C4—1222no—
602C2×C4—1222no—
603C2×C4—1222no—
604C2×C4—1222no—
605C2×C4—2441no—
606C2×C4—2441no—
607C2×C4—2441no—
608C2×C4—2441no—
609C2×C4—2444no—
610C2×C4—2444no—
611C2×C4—2441no—
612C2×C4—2442no—
613C2×C4—2442no—
614C2×C4—2442no—
615C2×C4—2444no—
616C2×C4C22⋊C4×D6111yescharacteristic
617C2×C4C22⋊C4×D6111yescharacteristic
618C2×C4C22⋊C4×D6111yescharacteristic
619C2×C4C22⋊C4×D6111yescharacteristic
620C2×C4#1451979812yes—
621C2×C4#1451980012yes—
622C2×C4C22×C4×D6111yescharacteristic
623C2×C4C2×D4×D6111yescharacteristic
624C8—42no—
625C8—2442no—
626C22—21no—
627C22—21no—
628C22—612no—
629C22—1221no—
630C22—1221no—
631C22—1221no—
632C22—1221no—
633C22—1221no—
634C22—2442no—
635C22—2442no—
636C22—2442no—
637C22—2442no—
638C22—2442no—
639C22C2×C22⋊C4×D6111yescharacteristic
640C22C2×#1451979811yescharacteristic
641C22C2×#1451980011yescharacteristic
642C4—21no—
643C4—21no—
644C4—21no—
645C4—21no—
646C4—42no—
647C4—42no—
648C4—82no—
649C4—612no—
650C4—1221no—
651C4—1221no—
652C4—1221no—
653C4—1221no—
654C4—1221no—
655C4—4882no—
656C4—2442no—
657C4#1683975712yes—
658C4#1683975712yes—
659C2—21no—
660C2—21no—
661C2—1222no—
662C2—4882no—
663C2—2441no—
664C2#410×D6111yescharacteristic
665C2C2×#1683975711yescharacteristic
666C2#421×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1518C2
socleC22×C61C22×C22⋊C4
prime radical#21459116C2
cosocleC22×C4×C61C24
hypercenter#1518D61
hypocenterC61#17573
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1518

Complements

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

NH ≅ G/Ntype
2. #431×D61C2semidirect
3. #21448212C2semidirect
4. #21444395C2semidirect
5. #21444383C2semidirect
6. #21444380C2semidirect
7. #21444378C2semidirect
8. #21444309C2semidirect
9. C61×#1518C2semidirect
10. #16840317C4semidirect
11. #16840317C4semidirect
12. #16840313C4semidirect
13. #16840313C4semidirect
16. #16840299C4semidirect
25. C4×#11758226C4semidirect
331. #1518D61semidirect
382. C61#17573semidirect

Maximal subgroups

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

subgroupindex
#214591162
#431×D612
#214482122
#214443952
#214443832
#214443802
#214443782
#214443092
C61×#15182
#1757361