Finite Group Databasebeta

← #29647259

Subgroups — #29647259

Order 15616.

1024 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#529×D61C211yesmaximal, characteristic
2#21454449C211yesmaximal, characteristic, complemented
3#21448212C211yesmaximal, characteristic, complemented
4#21444358C211yesmaximal, characteristic, complemented
5#21444357C211yesmaximal, characteristic, complemented
6#21444355C211yesmaximal, characteristic, complemented
7#21444350C212yesmaximal, complemented
8#21444346C212yesmaximal
9#21444304C212yesmaximal, complemented
10#21444302C212yesmaximal, complemented
11C61×#1512C211yesmaximal, characteristic, complemented
12#16840299C411yescharacteristic, complemented
13#16840298C2211yescharacteristic
14#16840297C411yescharacteristic, complemented
15#16840296C2211yescharacteristic
16#16840295—21no—
17#16840294C411yescharacteristic, complemented
18#16840293C2211yescharacteristic
19#16840292—21no—
20#16840291C411yescharacteristic, complemented
21#16840290—21no—
22#16840289—21no—
23#126×D61—21no—
24#125×D61C411yescharacteristic, complemented
25#124×D61C411yescharacteristic, complemented
26#123×D61—21no—
27C22⋊Q8×D61C2211yescharacteristic
28#121×D61C2211yescharacteristic
29C4×Q8×D61C411yescharacteristic, complemented
30C4×D4×D61—21no—
31C4×D4×D61C411yescharacteristic, complemented
32#117×D61—21no—
33C2×C42×D61C2211yescharacteristic
34#16839819C2211yescharacteristic, complemented
35#16839817—21no—
36#16839814—21no—
37#16839812C2212yescomplemented
38#16839784—21no—
39#16839724C2212yes—
40#16839714—21no—
41#16839629—21no—
42#16839628C2211yescharacteristic, complemented
43#16839624C2212yes—
44#16839619—21no—
45C4⋊C4×Dic61—21no—
46#16839609—21no—
47#16839607C2212yescomplemented
48#16839500C2212yescomplemented
49#16839499C2212yescomplemented
50#16839498C2212yescomplemented
51#16839497C2212yes—
52#16839496C2212yes—
53#16839495C2212yes—
54C61×#529C2211yescharacteristic
55C61×#432C2211yescharacteristic, complemented
56C61×#382C2211yescharacteristic, complemented
57C61×#328C2212yescomplemented
58C61×#327C2212yes—
59C2×Q8×D61C2×C411yescharacteristic
60C2×D4×D61—21no—
61C2×D4×D61C2×C411yescharacteristic
62C22×C4×D61—21no—
63C22×C4×D61D411yescharacteristic
64C22×C4×D61D411yescharacteristic
65C22×C4×D61C2311yescharacteristic
66C2×#11758189—22no—
67#14519772—21no—
68#14519772—21no—
69#14519772—21no—
70#14519771—21no—
71#14519770—21no—
72#14519770—21no—
73#14519770—21no—
74#14519769C2×C411yescharacteristic
75#14519768C2×C411yescharacteristic
76#14519768C2×C411yescharacteristic
77#14519767—21no—
78#14519767—21no—
79#14519766C2×C411yescharacteristic
80#14519765C2×C411yescharacteristic
81#14519764C2×C411yescharacteristic
82#14519763—21no—
83#14519763—21no—
84#14519762—21no—
85#14519762—21no—
86#14519761—21no—
87#14519760—21no—
88#14519759—21no—
89#14519759—21no—
90#14519758—21no—
91#14519757C2×C411yescharacteristic
92#14519756C2311yescharacteristic
93#14519755—21no—
94#14519754—21no—
95#14519753C2×C411yescharacteristic
96#14519752C2×C411yescharacteristic
97#14519751C2311yescharacteristic
98#14519750—21no—
99#14519749—21no—
100#14519748C2×C411yescharacteristic
101Q8×Dic61C2×C411yescharacteristic
102C4×Dic122—21no—
103C4×Dic122C2×C411yescharacteristic
104#14519742—21no—
105#14519742C2×C411yescharacteristic
106C4×D244—21no—
107C4×D244C2×C411yescharacteristic
108D4×Dic61—21no—
109D4×Dic61C2×C411yescharacteristic
110#14519739—21no—
111#14519739C2×C411yescharacteristic
112C4×C22⋊D61—21no—
113C4×C22⋊D61—21no—
114C4×C22⋊D61—21no—
115#14519737—21no—
116#14519737—21no—
117#14519737—21no—
118#14519736—21no—
119#14519735—21no—
120#14519735—21no—
121#14519734—21no—
122#14519734—21no—
123#14519733—21no—
124#14519733—21no—
125C2×C4⋊Dic61—21no—
126C4⋊C4×D61—21no—
127C4⋊C4×D61—21no—
128C4⋊C4×D61—21no—
129C4⋊C4×D61—21no—
130C4⋊C4×D61C2×C411yescharacteristic
131C4⋊C4×D61C2×C411yescharacteristic
132C2×#11758198—22no—
133C22⋊C4×D61—21no—
134C22⋊C4×D61—21no—
135C22⋊C4×D61—21no—
136C22⋊C4×D61—21no—
137C22⋊C4×D61—21no—
138C2×C4×Dic61—22no—
139C2×C4×Dic61D411yescharacteristic
140C2×C4×Dic61D411yescharacteristic
141C2×C4×Dic61C2311yescharacteristic
142C42×D61—21no—
143C42×D61C2×C411yescharacteristic
144C42×D61C2×C411yescharacteristic
145C42×D61C2×C411yescharacteristic
146C42×D61C2×C411yescharacteristic
147C42×D61D411yescharacteristic
148C42×D61D411yescharacteristic
149C42×D61D411yescharacteristic
150C42×D61D411yescharacteristic
151C4⋊#92418—21no—
152#14519706—22no—
153C22⋊#92418C2312yes—
154#14519689—22no—
155#14519688—21no—
156C8×Dic61—22no—
157#14519684—21no—
158#14519684—22no—
159#14519684—22no—
160#14519684C2312yes—
161#126×C61—21no—
162#125×C61C2×C411yescharacteristic
163#124×C61C2×C411yescharacteristic
164#123×C61—21no—
165C22⋊Q8×C61C2311yescharacteristic
166#121×C61C2311yescharacteristic
167C4×Q8×C61C2×C411yescharacteristic
168C4×D4×C61—21no—
169C4×D4×C61C2×C411yescharacteristic
170#117×C61—21no—
171C2×C4⋊C4×C61—21no—
172C2×C42×C61C2311yescharacteristic
173C4⋊C8×C61—21no—
174C22⋊C8×C61C2312yes—
175#97×C61—21no—
176#95×C61—21no—
177#95×C61C2312yes—
178C23×D61—21no—
179C23×D61C2×D411yescharacteristic
180C2×Q8×C61C22×C411yescharacteristic
181C2×D4×C61—21no—
182C2×D4×C61C22×C411yescharacteristic
183C22×C4×C61—21no—
184C22×C4×C61—22no—
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2411yescharacteristic
188C2×C22⋊D61—21no—
189C2×C22⋊D61—21no—
190C2×C22⋊D61—21no—
191C22×Dic61—21no—
192C22×Dic61—22no—
193C22×Dic61C2×D411yescharacteristic
194C22×Dic61C2×D411yescharacteristic
195C22×Dic61C2×D411yescharacteristic
196Q8×D61—42no—
197D4×D61—42no—
198D4×D61—42no—
199D4×D61—42no—
200C2×D244—21no—
201C2×D244C22×C411yescharacteristic
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61—42no—
208C2×C4×D61—42no—
209C2×C4×D61—44no—
210C2×C4×D61—41no—
211C2×C4×D61—41no—
212C2×C4×D61C22⋊C411yescharacteristic
213C2×C4×D61C22⋊C411yescharacteristic
214C2×C4×D61C22⋊C411yescharacteristic
215C2×C4×D61C22⋊C411yescharacteristic
216C2×C4×D61C22⋊C411yescharacteristic
217C2×C4×D61C22⋊C411yescharacteristic
218C2×C4×D61C22⋊C411yescharacteristic
219C2×C4×D61C22⋊C411yescharacteristic
220C2×C4×D61C22×C411yescharacteristic
221C2×C4×D61C22×C411yescharacteristic
222C2×C4×D61C2×D411yescharacteristic
223C2×C4×D61C2×D411yescharacteristic
224C2×Dic122—21no—
225C2×Dic122C22×C411yescharacteristic
226C2×C8×C61—22no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—42no—
232C4⋊C4×C61C22×C411yescharacteristic
233C4⋊C4×C61C22×C411yescharacteristic
234C22⋊C4×C61—21no—
235C22⋊C4×C61—21no—
236C22⋊C4×C61—21no—
237C22⋊C4×C61—21no—
238C22⋊C4×C61—21no—
239C42×C61—21no—
240C42×C61C22×C411yescharacteristic
241C42×C61C22×C411yescharacteristic
242C42×C61C2×D411yescharacteristic
243C42×C61C2×D411yescharacteristic
244C22⋊Dic61—21no—
245C22⋊Dic61—21no—
246C22⋊Dic61—21no—
247C22⋊Dic61—21no—
248C22⋊Dic61—21no—
249#11758198—21no—
250#11758198—21no—
251#11758198—21no—
252#11758198—21no—
253#11758198—21no—
254#11758198—21no—
255#11758198—21no—
256#11758198—21no—
257#11758198—21no—
258#11758198—21no—
259#11758198—44no—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61—42no—
265C4⋊Dic61C22×C411yescharacteristic
266C4⋊Dic61C22×C411yescharacteristic
267#11758196—21no—
268#11758196—21no—
269#11758196—21no—
270#11758196—21no—
271#11758196—21no—
272#11758196—21no—
273#11758196—21no—
274#11758196—21no—
275#11758196—21no—
276#11758196—21no—
277C4×Dic61—21no—
278C4×Dic61—21no—
279C4×Dic61—21no—
280C4×Dic61—44no—
281C4×Dic61C22⋊C411yescharacteristic
282C4×Dic61C22⋊C411yescharacteristic
283C4×Dic61C22⋊C411yescharacteristic
284C4×Dic61C22⋊C411yescharacteristic
285C4×Dic61C22⋊C411yescharacteristic
286C4×Dic61C22⋊C411yescharacteristic
287C4×Dic61C22⋊C411yescharacteristic
288C4×Dic61C22⋊C411yescharacteristic
289C4×Dic61C22×C411yescharacteristic
290C4×Dic61C22×C411yescharacteristic
291C4×Dic61C2×D411yescharacteristic
292C4×Dic61C2×D411yescharacteristic
293C2×#92418—22no—
294#11758189—44no—
295C23×C61—21no—
296C23×C61C22×D411yescharacteristic
297C22×D61—21no—
298C22×D61—21no—
299C22×D61—22no—
300C22×D61—21no—
301C22×D61—41no—
302C22×D61—42no—
303C22×D61—42no—
304C22×D61—42no—
305C22×D61C2×C22⋊C411yescharacteristic
306C22×D61C2×C22⋊C411yescharacteristic
307Q8×C61—41no—
308D4×C61—41no—
309D4×C61—41no—
310D4×C61—41no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—42no—
319C2×C4×C61—42no—
320C2×C4×C61—42no—
321C2×C4×C61—42no—
322C2×C4×C61C2×C22⋊C411yescharacteristic
323C2×C4×C61C2×C22⋊C411yescharacteristic
324C2×C4×C61C2×C22⋊C411yescharacteristic
325C2×C4×C61C2×C22⋊C411yescharacteristic
326C2×C4×C61C23×C411yescharacteristic
327C2×C4×C61C22×D411yescharacteristic
328C22⋊D61—42no—
329C22⋊D61—42no—
330C22⋊D61—41no—
331C22⋊D61—41no—
332C2×Dic61—21no—
333C2×Dic61—21no—
334C2×Dic61—22no—
335C2×Dic61—21no—
336C2×Dic61—21no—
337C2×Dic61—21no—
338C2×Dic61—41no—
339C2×Dic61—42no—
340C2×Dic61—42no—
341C2×Dic61—42no—
342C2×Dic61—42no—
343C2×Dic61C2×C22⋊C411yescharacteristic
344C2×Dic61C2×C22⋊C411yescharacteristic
345C2×Dic61C2×C22⋊C411yescharacteristic
346C2×Dic61C2×C22⋊C411yescharacteristic
347C2×Dic61C2×C22⋊C411yescharacteristic
348C2×Dic61C2×C22⋊C411yescharacteristic
349D244—41no—
350D244—42no—
351C4×D61—22no—
352C4×D61—22no—
353C4×D61—22no—
354C4×D61—22no—
355C4×D61—41no—
356C4×D61—41no—
357C4×D61—41no—
358C4×D61—41no—
359C4×D61—41no—
360C4×D61—41no—
361C4×D61—41no—
362C4×D61—41no—
363C4×D61—42no—
364C4×D61—42no—
365C4×D61—42no—
366C4×D61—42no—
367C4×D61—42no—
368Dic122—42no—
369Dic122—41no—
370C8×C61—42no—
371#92418—42no—
372#17554—611nomaximal, Sylow
373C22×C61—21no—
374C22×C61—21no—
375C22×C61—41no—
376C22×C61—41no—
377C22×C61—41no—
378C22×C61C22×C22⋊C411yescharacteristic
379C22×C61#57511yescharacteristic
380C22×C61#57511yescharacteristic
381C2×D61—21no—
382C2×D61—21no—
383C2×D61—21no—
384C2×D61—21no—
385C2×D61—21no—
386C2×D61—42no—
387C2×D61—42no—
388C2×D61—41no—
389C2×D61—41no—
390C2×D61—41no—
391C2×D61—84no—
392C2×D61#41012yes—
393C4×C61—21no—
394C4×C61—21no—
395C4×C61—21no—
396C4×C61—21no—
397C4×C61—21no—
398C4×C61—21no—
399C4×C61—41no—
400C4×C61—41no—
401C4×C61—41no—
402C4×C61—82no—
403Dic61—21no—
404Dic61—21no—
405Dic61—21no—
406Dic61—21no—
407Dic61—21no—
408Dic61—41no—
409Dic61—41no—
410Dic61—41no—
411Dic61—82no—
412Dic61#42112yes—
413C2×#529—611no—
414#2920—611no—
415#2283—611no—
416#1512—611no—
417#1512—611no—
418#1512—611no—
419#1512D6111yescharacteristic, complemented
420#1511—612no—
421#1510—612no—
422#1500—612no—
423#1500—612no—
424C2×C61—21no—
425C2×C61—21no—
426C2×C61—81no—
427C2×C61C2×#41011yescharacteristic
428C2×C61#289611yescharacteristic
429C2×C61C2×#42111yescharacteristic
430D61—22no—
431D61—41no—
432D61—81no—
433#529—611no—
434#529—611no—
435#529—611no—
436#529—611no—
437#529—611no—
438#529—611no—
439#529—611no—
440#529—1221no—
441#529—1221no—
442#529—1221no—
443#529—1221no—
444#529C2×D6111yescharacteristic
445C2×#126—1221no—
446C2×#125—611no—
447C2×#124—611no—
448C2×#123—1221no—
449C2×C22⋊Q8—611no—
450C2×#121—611no—
451C2×C4×Q8—611no—
452C2×C4×D4—611no—
453C2×C4×D4—1221no—
454C2×#117—1221no—
455C22×C42—611no—
456#432—611no—
457#432—1221no—
458#432C2×D6111yescharacteristic, complemented
459#431—612no—
460#431—1221no—
461#423—1221no—
462#407—612no—
463C4×M16—1221no—
464#383—1221no—
465#382—611no—
466#382C2×D6111yescharacteristic, complemented
467#381—612no—
468#380—1221no—
469C4×C4⋊C4—1221no—
470C4×C22⋊C4—1221no—
471#376—612no—
472#328—612no—
473#328—612no—
474#328—612no—
475#328C2×D6112yescomplemented
476#327—612no—
477#327—612no—
478#327—612no—
479#327C2×D6112yes—
480C61#1755411yescharacteristic, complemented, Sylow
481C22×Q8—611no—
482C22×D4—611no—
483C22×D4—1221no—
484C23×C4—611no—
485C23×C4—611no—
486C23×C4—611no—
487C23×C4—1221no—
488C2×M16—1222no—
489#126—21no—
490#126—1221no—
491#126—1221no—
492#126—1221no—
493#126—1221no—
494#126—1221no—
495#126—1221no—
496#126—1221no—
497#125—611no—
498#125—611no—
499#125—611no—
500#125—1221no—
501#125—1221no—
502#125C4×D6111yescharacteristic
503#124—611no—
504#124—611no—
505#124—611no—
506#124—1221no—
507#124—1221no—
508#124C4×D6111yescharacteristic
509#123—21no—
510#123—1221no—
511#123—1221no—
512#123—1221no—
513#123—1221no—
514#123—1221no—
515#123—1221no—
516#123—1221no—
517C22⋊Q8—611no—
518C22⋊Q8—611no—
519C22⋊Q8—611no—
520C22⋊Q8—1221no—
521C22⋊Q8—1221no—
522C22⋊Q8C22×D6111yescharacteristic
523#121—611no—
524#121—611no—
525#121—611no—
526#121—1221no—
527#121—1221no—
528#121C22×D6111yescharacteristic
529C4×Q8—611no—
530C4×Q8—611no—
531C4×Q8—611no—
532C4×Q8—1221no—
533C4×Q8—1221no—
534C4×Q8C4×D6111yescharacteristic
535C4×D4—21no—
536C4×D4—611no—
537C4×D4—611no—
538C4×D4—611no—
539C4×D4—1221no—
540C4×D4—1221no—
541C4×D4—1221no—
542C4×D4—1221no—
543C4×D4—1221no—
544C4×D4—1221no—
545C4×D4—1221no—
546C4×D4—1221no—
547C4×D4—1221no—
548C4×D4C4×D6111yescharacteristic
549#117—21no—
550#117—1221no—
551#117—1221no—
552#117—1221no—
553#117—1221no—
554#117—1221no—
555#117—1221no—
556#117—1221no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—611no—
559C2×C4⋊C4—611no—
560C2×C4⋊C4—1221no—
561C2×C4⋊C4—1221no—
562C2×C4⋊C4—1221no—
563C2×C4⋊C4—1221no—
564C2×C4⋊C4—1221no—
565C2×C22⋊C4—1221no—
566C2×C22⋊C4—1221no—
567C2×C22⋊C4—1221no—
568C2×C22⋊C4—1221no—
569C2×C22⋊C4—1221no—
570C2×C22⋊C4—1222no—
571C2×C42—611no—
572C2×C42—611no—
573C2×C42—611no—
574C2×C42—611no—
575C2×C42—611no—
576C2×C42—611no—
577C2×C42—611no—
578C2×C42—611no—
579C2×C42—611no—
580C2×C42—611no—
581C2×C42—611no—
582C2×C42—1221no—
583C2×C42—1222no—
584C2×C42C22×D6111yescharacteristic
585C4⋊C8—21no—
586C4⋊C8—1222no—
587C4⋊C8—1221no—
588C22⋊C8—612no—
589C22⋊C8—1222no—
590C22⋊C8C22×D6112yes—
591#97—21no—
592#97—1221no—
593C4×C8—1222no—
594#95—21no—
595#95—612no—
596#95—1222no—
597#95—1222no—
598#95—1221no—
599#95C22×D6112yes—
600C24—611no—
601C24—1221no—
602C2×Q8—611no—
603C2×Q8—1221no—
604C2×Q8—2442no—
605C2×Q8C2×C4×D6111yescharacteristic
606C2×D4—21no—
607C2×D4—611no—
608C2×D4—1221no—
609C2×D4—1221no—
610C2×D4—1221no—
611C2×D4—1221no—
612C2×D4—2442no—
613C2×D4—2442no—
614C2×D4—2442no—
615C2×D4C2×C4×D6111yescharacteristic
616C22×C4—21no—
617C22×C4—22no—
618C22×C4—611no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—611no—
622C22×C4—611no—
623C22×C4—611no—
624C22×C4—611no—
625C22×C4—611no—
626C22×C4—611no—
627C22×C4—611no—
628C22×C4—611no—
629C22×C4—611no—
630C22×C4—611no—
631C22×C4—611no—
632C22×C4—611no—
633C22×C4—1221no—
634C22×C4—1221no—
635C22×C4—1221no—
636C22×C4—1221no—
637C22×C4—1221no—
638C22×C4—1221no—
639C22×C4—1222no—
640C22×C4—2441no—
641C22×C4—2441no—
642C22×C4—2442no—
643C22×C4—2442no—
644C22×C4—2444no—
645C22×C4D4×D6111yescharacteristic
646C22×C4D4×D6111yescharacteristic
647C22×C4C23×D6111yescharacteristic
648M16—2444no—
649C2×C8—22no—
650C2×C8—1222no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—42no—
656C4⋊C4—611no—
657C4⋊C4—611no—
658C4⋊C4—1221no—
659C4⋊C4—1221no—
660C4⋊C4—1221no—
661C4⋊C4—1221no—
662C4⋊C4—1221no—
663C4⋊C4—1221no—
664C4⋊C4—1221no—
665C4⋊C4—1221no—
666C4⋊C4—1221no—
667C4⋊C4—1221no—
668C4⋊C4—1221no—
669C4⋊C4—1221no—
670C4⋊C4—1221no—
671C4⋊C4—1221no—
672C4⋊C4—2442no—
673C4⋊C4C2×C4×D6111yescharacteristic
674C4⋊C4C2×C4×D6111yescharacteristic
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—21no—
678C22⋊C4—21no—
679C22⋊C4—21no—
680C22⋊C4—1221no—
681C22⋊C4—1221no—
682C22⋊C4—1221no—
683C22⋊C4—1221no—
684C22⋊C4—1221no—
685C22⋊C4—1221no—
686C22⋊C4—1221no—
687C22⋊C4—1221no—
688C22⋊C4—1221no—
689C22⋊C4—1221no—
690C22⋊C4—1221no—
691C22⋊C4—1221no—
692C22⋊C4—1221no—
693C22⋊C4—1221no—
694C22⋊C4—1221no—
695C22⋊C4—2444no—
696C42—21no—
697C42—611no—
698C42—611no—
699C42—611no—
700C42—611no—
701C42—611no—
702C42—611no—
703C42—611no—
704C42—611no—
705C42—611no—
706C42—611no—
707C42—611no—
708C42—611no—
709C42—1221no—
710C42—1221no—
711C42—1221no—
712C42—2444no—
713C42C2×C4×D6111yescharacteristic
714C42C2×C4×D6111yescharacteristic
715C42D4×D6111yescharacteristic
716C42D4×D6111yescharacteristic
717C23—21no—
718C23—611no—
719C23—611no—
720C23—1222no—
721C23—1221no—
722C23—1221no—
723C23—1221no—
724C23—2441no—
725C23—2442no—
726C23—2442no—
727C23—2442no—
728C23C2×D4×D6111yescharacteristic
729Q8—41no—
730Q8—2441no—
731Q8—2442no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—2441no—
736D4—2442no—
737D4—2442no—
738D4—2442no—
739D4—2441no—
740D4—2441no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—611no—
753C2×C4—611no—
754C2×C4—611no—
755C2×C4—611no—
756C2×C4—611no—
757C2×C4—611no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—1221no—
764C2×C4—1221no—
765C2×C4—1221no—
766C2×C4—1221no—
767C2×C4—1221no—
768C2×C4—2441no—
769C2×C4—2441no—
770C2×C4—2441no—
771C2×C4—2441no—
772C2×C4—2441no—
773C2×C4—2441no—
774C2×C4—2441no—
775C2×C4—2441no—
776C2×C4—2442no—
777C2×C4—2442no—
778C2×C4—2442no—
779C2×C4—2442no—
780C2×C4—2442no—
781C2×C4—2442no—
782C2×C4—2441no—
783C2×C4—2442no—
784C2×C4—2442no—
785C2×C4—2442no—
786C2×C4C22⋊C4×D6111yescharacteristic
787C2×C4C22⋊C4×D6111yescharacteristic
788C2×C4C22⋊C4×D6111yescharacteristic
789C2×C4C22⋊C4×D6111yescharacteristic
790C2×C4C22×C4×D6111yescharacteristic
791C2×C4C2×D4×D6111yescharacteristic
792C8—42no—
793C8—2442no—
794C22—21no—
795C22—21no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—612no—
800C22—1221no—
801C22—1221no—
802C22—1221no—
803C22—1221no—
804C22—1221no—
805C22—4884no—
806C22—2442no—
807C22—2442no—
808C22—2441no—
809C22—2441no—
810C22—2441no—
811C22C2×C22⋊C4×D6111yescharacteristic
812C22#1684055811yescharacteristic
813C22#1684056111yescharacteristic
814C4—21no—
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—21no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—82no—
824C4—612no—
825C4—1221no—
826C4—1221no—
827C4—1221no—
828C4—1221no—
829C4—1221no—
830C4—4882no—
831C4—2441no—
832C4—2441no—
833C4—2441no—
834C2—21no—
835C2—21no—
836C2—81no—
837C2—1222no—
838C2—4881no—
839C2—2441no—
840C2#410×D6111yescharacteristic
841C2#2145433511yescharacteristic
842C2#421×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1512C2
socleC22×C61C22×C22⋊C4
prime radical#121×D61C22
cosocleC22×C4×C61C24
hypercenter#1512D61
hypocenterC61#17554
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1512

Complements

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

NH ≅ G/Ntype
2. #21454449C2semidirect
3. #21448212C2semidirect
4. #21444358C2semidirect
5. #21444357C2semidirect
6. #21444355C2semidirect
7. #21444350C2semidirect
9. #21444304C2semidirect
10. #21444302C2semidirect
11. C61×#1512C2semidirect
12. #16840299C4semidirect
14. #16840297C4semidirect
17. #16840294C4semidirect
20. #16840291C4semidirect
24. #125×D61C4semidirect
25. #124×D61C4semidirect
29. C4×Q8×D61C4semidirect
31. C4×D4×D61C4semidirect
34. #16839819C22semidirect
37. #16839812C22semidirect
42. #16839628C22semidirect
47. #16839607C22semidirect
48. #16839500C22semidirect
49. #16839499C22semidirect
50. #16839498C22semidirect
55. C61×#432C22semidirect
56. C61×#382C22semidirect
57. C61×#328C22semidirect
419. #1512D61semidirect
458. #432C2×D61semidirect
466. #382C2×D61semidirect
475. #328C2×D61semidirect
480. C61#17554semidirect

Maximal subgroups

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

subgroupindex
#529×D612
#214544492
#214482122
#214443582
#214443572
#214443552
#214443502
#214443462
#214443042
#214443022
C61×#15122
#1755461