Finite Group Databasebeta

← D61×#1521 #29647330

Subgroups — D61×#1521 #29647330

Order 15616.

1074 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#529×D61C211yesmaximal, characteristic
2#431×D61C211yesmaximal, characteristic, complemented
3#383×D61C211yesmaximal, characteristic, complemented
4#21444397C211yesmaximal, characteristic, complemented
5#21444396C211yesmaximal, characteristic, complemented
6#21444395C212yesmaximal, complemented
7#21444394C211yesmaximal, characteristic, complemented
8#21444393C212yesmaximal, complemented
9#328×D61C212yesmaximal, complemented
10#327×D61C212yesmaximal
11C61×#1521C211yesmaximal, 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#16839815C2211yescharacteristic, complemented
35#16839814—21no—
36#16839813—21no—
37#16839812C2212yescomplemented
38C4⋊C8×D61—21no—
39C22⋊C8×D61C2212yes—
40C4×C8×D61—21no—
41#16839630C2211yescharacteristic, complemented
42#16839629—21no—
43#16839629—21no—
44#16839629C2212yescomplemented
45#95×D61—21no—
46#95×D61—21no—
47#95×D61C2212yes—
48#16839500C2212yescomplemented
49#16839499C2212yescomplemented
50#16839498C2212yescomplemented
51#16839497C2212yes—
52#16839496C2212yes—
53#16839495C2212yes—
54C61×#529C2211yescharacteristic
55C61×#431C2211yescharacteristic, complemented
56C61×#383C2211yescharacteristic, complemented
57C61×#328C2212yescomplemented
58C61×#327C2212yes—
59C2×Q8×D61C2×C411yescharacteristic
60C2×D4×D61—21no—
61C2×D4×D61C2×C411yescharacteristic
62C22×C4×D61—21no—
63C22×C4×D61—22no—
64C22×C4×D61D411yescharacteristic
65C22×C4×D61D411yescharacteristic
66C22×C4×D61C2311yescharacteristic
67C2×C8×D61—22no—
68#14519772—21no—
69#14519772—21no—
70#14519772—21no—
71#14519771—21no—
72#14519770—21no—
73#14519770—21no—
74#14519770—21no—
75#14519769C2×C411yescharacteristic, complemented
76#14519768C2×C411yescharacteristic, complemented
77#14519768C2×C411yescharacteristic, complemented
78#14519767—21no—
79#14519767—21no—
80#14519766C2×C411yescharacteristic, complemented
81#14519765C2×C411yescharacteristic, complemented
82#14519764C2×C411yescharacteristic, complemented
83#14519763—21no—
84#14519763—21no—
85#14519762—21no—
86#14519762—21no—
87#14519761—21no—
88#14519760—21no—
89#14519759—21no—
90#14519759—21no—
91#14519758—21no—
92#14519757C2×C411yescharacteristic
93#14519756C2311yescharacteristic
94#14519755—21no—
95#14519754—21no—
96#14519753C2×C411yescharacteristic
97#14519752C2×C411yescharacteristic
98#14519751C2311yescharacteristic
99#14519750—21no—
100#14519749—21no—
101#14519748C2×C411yescharacteristic
102Q8×Dic61C2×C411yescharacteristic, complemented
103C4×Dic122—21no—
104C4×Dic122C2×C411yescharacteristic, complemented
105#14519742—21no—
106#14519742C2×C411yescharacteristic, complemented
107C4×D244—21no—
108C4×D244C2×C411yescharacteristic, complemented
109D4×Dic61—21no—
110D4×Dic61C2×C411yescharacteristic, complemented
111#14519739—21no—
112#14519739C2×C411yescharacteristic, complemented
113C4×C22⋊D61—21no—
114C4×C22⋊D61—21no—
115C4×C22⋊D61—21no—
116#14519737—21no—
117#14519737—21no—
118#14519737—21no—
119#14519736—21no—
120#14519735—21no—
121#14519735—21no—
122#14519734—21no—
123#14519734—21no—
124#14519733—21no—
125#14519733—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
132C22⋊C4×D61—21no—
133C22⋊C4×D61—21no—
134C22⋊C4×D61—21no—
135C22⋊C4×D61—21no—
136C22⋊C4×D61—21no—
137C2×C4×Dic61D411yescharacteristic
138C2×C4×Dic61D411yescharacteristic
139C2×C4×Dic61C2311yescharacteristic
140C42×D61—21no—
141C42×D61C2×C411yescharacteristic
142C42×D61C2×C411yescharacteristic
143C42×D61C2×C411yescharacteristic
144C42×D61C2×C411yescharacteristic
145C42×D61D411yescharacteristic
146C42×D61D411yescharacteristic
147C42×D61D411yescharacteristic
148C42×D61D411yescharacteristic
149C4⋊#92418—21no—
150#14519706—22no—
151C22⋊#92418C2312yes—
152#14519689—22no—
153C4×#92418—21no—
154C8×Dic61—22no—
155#14519684—21no—
156#14519684—21no—
157#14519684—22no—
158#14519684—22no—
159#14519684—22no—
160#14519684C2312yes—
161#126×C61—21no—
162#125×C61C2×C411yescharacteristic, complemented
163#124×C61C2×C411yescharacteristic, complemented
164#123×C61—21no—
165C22⋊Q8×C61C2311yescharacteristic
166#121×C61C2311yescharacteristic
167C4×Q8×C61C2×C411yescharacteristic, complemented
168C4×D4×C61—21no—
169C4×D4×C61C2×C411yescharacteristic, complemented
170#117×C61—21no—
171C2×C42×C61C2311yescharacteristic
172C4⋊C8×C61—21no—
173C22⋊C8×C61C2312yes—
174C4×C8×C61—21no—
175#95×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—44no—
199C2×D244—21no—
200C2×D244C22×C411yescharacteristic
201C2×C4×D61—24no—
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—44no—
211C2×C4×D61—44no—
212C2×C4×D61—44no—
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×D61C22×C411yescharacteristic
223C2×C4×D61C2×D411yescharacteristic
224C2×C4×D61C2×D411yescharacteristic
225C2×Dic122—21no—
226C2×Dic122C22×C411yescharacteristic
227C2×C8×C61—22no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
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—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61C22×C411yescharacteristic
264C4⋊Dic61C22×C411yescharacteristic
265#11758196—21no—
266#11758196—21no—
267#11758196—21no—
268#11758196—21no—
269#11758196—21no—
270#11758196—21no—
271#11758196—21no—
272#11758196—21no—
273#11758196—21no—
274#11758196—21no—
275C4×Dic61—21no—
276C4×Dic61—21no—
277C4×Dic61—21no—
278C4×Dic61C22⋊C411yescharacteristic
279C4×Dic61C22⋊C411yescharacteristic
280C4×Dic61C22⋊C411yescharacteristic
281C4×Dic61C22⋊C411yescharacteristic
282C4×Dic61C22⋊C411yescharacteristic
283C4×Dic61C22⋊C411yescharacteristic
284C4×Dic61C22⋊C411yescharacteristic
285C4×Dic61C22⋊C411yescharacteristic
286C4×Dic61C22×C411yescharacteristic
287C4×Dic61C22×C411yescharacteristic
288C4×Dic61C2×D411yescharacteristic
289C4×Dic61C2×D411yescharacteristic
290C2×#92418—22no—
291C8×D61—44no—
292C23×C61—21no—
293C23×C61C22×D411yescharacteristic
294C22×D61—22no—
295C22×D61—22no—
296C22×D61—21no—
297C22×D61—42no—
298C22×D61—42no—
299C22×D61—42no—
300C22×D61C2×C22⋊C411yescharacteristic
301C22×D61C2×C22⋊C411yescharacteristic
302C22×D61#13514yes—
303Q8×C61—41no—
304D4×C61—41no—
305D4×C61—42no—
306C2×C4×C61—22no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—42no—
313C2×C4×C61—42no—
314C2×C4×C61—42no—
315C2×C4×C61—42no—
316C2×C4×C61C2×C22⋊C411yescharacteristic
317C2×C4×C61C2×C22⋊C411yescharacteristic
318C2×C4×C61C2×C22⋊C411yescharacteristic
319C2×C4×C61C2×C22⋊C411yescharacteristic
320C2×C4×C61C23×C411yescharacteristic
321C2×C4×C61C22×D411yescharacteristic
322C22⋊D61—42no—
323C22⋊D61—42no—
324C22⋊D61—42no—
325C2×Dic61—22no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—42no—
332C2×Dic61—42no—
333C2×Dic61—42no—
334C2×Dic61—42no—
335C2×Dic61C2×C22⋊C411yescharacteristic
336C2×Dic61C2×C22⋊C411yescharacteristic
337C2×Dic61C2×C22⋊C411yescharacteristic
338C2×Dic61C2×C22⋊C411yescharacteristic
339C2×Dic61C2×C22⋊C411yescharacteristic
340C2×Dic61C2×C22⋊C411yescharacteristic
341D244—41no—
342D244—42no—
343C4×D61—22no—
344C4×D61—22no—
345C4×D61—22no—
346C4×D61—22no—
347C4×D61—22no—
348C4×D61—22no—
349C4×D61—22no—
350C4×D61—22no—
351C4×D61—41no—
352C4×D61—41no—
353C4×D61—41no—
354C4×D61—41no—
355C4×D61—42no—
356C4×D61—42no—
357C4×D61—42no—
358C4×D61—42no—
359C4×D61—42no—
360C4×D61—88no—
361Dic122—42no—
362Dic122—41no—
363C8×C61—42no—
364#92418—42no—
365C2×#1521—611nomaximal, Sylow
366C22×C61—21no—
367C22×C61—21no—
368C22×C61—41no—
369C22×C61—41no—
370C22×C61—41no—
371C22×C61C22×C22⋊C411yescharacteristic
372C22×C61C2×#13512yes—
373C2×D61—21no—
374C2×D61—21no—
375C2×D61—28no—
376C2×D61—41no—
377C2×D61—41no—
378C2×D61—41no—
379C2×D61—84no—
380C2×D61#41012yes—
381C2×D61#41612yes—
382C2×D61#41612yes—
383C2×D61#42112yes—
384C4×C61—21no—
385C4×C61—21no—
386C4×C61—21no—
387C4×C61—21no—
388C4×C61—21no—
389C4×C61—21no—
390C4×C61—41no—
391C4×C61—41no—
392C4×C61—41no—
393C4×C61—82no—
394Dic61—21no—
395Dic61—21no—
396Dic61—21no—
397Dic61—21no—
398Dic61—21no—
399Dic61—21no—
400Dic61—41no—
401Dic61—41no—
402Dic61—41no—
403Dic61—82no—
404C2×#529—611no—
405C2×#431—611no—
406C2×#383—611no—
407#1521—611no—
408#1521—611no—
409#1521—612no—
410#1521—612no—
411#1521—611no—
412#1521D6111yescharacteristic, direct product factor
413C2×#328—612no—
414C2×#327—612no—
415C2×C61—22no—
416C2×C61—81no—
417C2×C61C2×#41011yescharacteristic
418C2×C61C2×#41611yescharacteristic
419C2×C61C2×#42111yescharacteristic
420D61—22no—
421D61—81no—
422D61#152114yesdirect product factor
423#529—611no—
424#529—611no—
425#529—611no—
426#529—611no—
427#529—611no—
428#529—611no—
429#529—611no—
430#529—1221no—
431#529—1221no—
432#529—1221no—
433#529—1221no—
434#529C2×D6111yescharacteristic
435C2×#126—1221no—
436C2×#125—611no—
437C2×#124—611no—
438C2×#123—1221no—
439C2×C22⋊Q8—611no—
440C2×#121—611no—
441C2×C4×Q8—611no—
442C2×C4×D4—611no—
443C2×C4×D4—1221no—
444C2×#117—1221no—
445C22×C42—611no—
446#431—611no—
447#431—612no—
448#431—1221no—
449#431—1221no—
450#431C2×D6111yescharacteristic, complemented
451C2×C4⋊C8—1221no—
452C2×C22⋊C8—612no—
453C2×C4×C8—1221no—
454#383—611no—
455#383—612no—
456#383—1221no—
457#383—1221no—
458#383C2×D6111yescharacteristic, complemented
459C2×#95—612no—
460C2×#95—1221no—
461C2×#95—1221no—
462#328—612no—
463#328—612no—
464#328—612no—
465#328C2×D6112yescomplemented
466#327—612no—
467#327—612no—
468#327—612no—
469#327C2×D6112yes—
470C61C2×#152111yescharacteristic, complemented, Sylow
471C22×Q8—611no—
472C22×D4—611no—
473C22×D4—1221no—
474C23×C4—611no—
475C23×C4—611no—
476C23×C4—611no—
477C23×C4—1221no—
478C23×C4—1222no—
479C22×C8—1222no—
480#126—21no—
481#126—1221no—
482#126—1221no—
483#126—1221no—
484#126—1221no—
485#126—1221no—
486#126—1221no—
487#126—1221no—
488#125—611no—
489#125—611no—
490#125—611no—
491#125—1221no—
492#125—1221no—
493#125C4×D6111yescharacteristic, complemented
494#124—611no—
495#124—611no—
496#124—611no—
497#124—1221no—
498#124—1221no—
499#124C4×D6111yescharacteristic, complemented
500#123—21no—
501#123—1221no—
502#123—1221no—
503#123—1221no—
504#123—1221no—
505#123—1221no—
506#123—1221no—
507#123—1221no—
508C22⋊Q8—611no—
509C22⋊Q8—611no—
510C22⋊Q8—611no—
511C22⋊Q8—1221no—
512C22⋊Q8—1221no—
513C22⋊Q8C22×D6111yescharacteristic
514#121—611no—
515#121—611no—
516#121—611no—
517#121—1221no—
518#121—1221no—
519#121C22×D6111yescharacteristic
520C4×Q8—611no—
521C4×Q8—611no—
522C4×Q8—611no—
523C4×Q8—1221no—
524C4×Q8—1221no—
525C4×Q8C4×D6111yescharacteristic, complemented
526C4×D4—21no—
527C4×D4—611no—
528C4×D4—611no—
529C4×D4—611no—
530C4×D4—1221no—
531C4×D4—1221no—
532C4×D4—1221no—
533C4×D4—1221no—
534C4×D4—1221no—
535C4×D4—1221no—
536C4×D4—1221no—
537C4×D4—1221no—
538C4×D4—1221no—
539C4×D4C4×D6111yescharacteristic, complemented
540#117—21no—
541#117—1221no—
542#117—1221no—
543#117—1221no—
544#117—1221no—
545#117—1221no—
546#117—1221no—
547#117—1221no—
548C2×C4⋊C4—611no—
549C2×C4⋊C4—611no—
550C2×C4⋊C4—1221no—
551C2×C4⋊C4—1221no—
552C2×C4⋊C4—1221no—
553C2×C4⋊C4—1221no—
554C2×C22⋊C4—1221no—
555C2×C22⋊C4—1221no—
556C2×C22⋊C4—1221no—
557C2×C22⋊C4—1221no—
558C2×C22⋊C4—1221no—
559C2×C42—611no—
560C2×C42—611no—
561C2×C42—611no—
562C2×C42—611no—
563C2×C42—611no—
564C2×C42—611no—
565C2×C42—611no—
566C2×C42—611no—
567C2×C42—611no—
568C2×C42—611no—
569C2×C42—611no—
570C2×C42—1221no—
571C2×C42C22×D6111yescharacteristic
572C4⋊C8—21no—
573C4⋊C8—1222no—
574C4⋊C8—1221no—
575C22⋊C8—612no—
576C22⋊C8—1222no—
577C22⋊C8C22×D6112yes—
578C4×C8—21no—
579C4×C8—1222no—
580C4×C8—1221no—
581#95—21no—
582#95—21no—
583#95—612no—
584#95—1222no—
585#95—1222no—
586#95—1222no—
587#95—1221no—
588#95—1221no—
589#95C22×D6112yes—
590C24—611no—
591C24—1221no—
592C2×Q8—611no—
593C2×Q8—1221no—
594C2×Q8—2442no—
595C2×Q8C2×C4×D6111yescharacteristic
596C2×D4—21no—
597C2×D4—611no—
598C2×D4—1221no—
599C2×D4—1221no—
600C2×D4—1221no—
601C2×D4—1221no—
602C2×D4—2442no—
603C2×D4—2444no—
604C2×D4C2×C4×D6111yescharacteristic
605C22×C4—21no—
606C22×C4—22no—
607C22×C4—611no—
608C22×C4—611no—
609C22×C4—611no—
610C22×C4—611no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—611no—
614C22×C4—611no—
615C22×C4—611no—
616C22×C4—611no—
617C22×C4—611no—
618C22×C4—611no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—611no—
622C22×C4—1221no—
623C22×C4—1224no—
624C22×C4—1221no—
625C22×C4—1221no—
626C22×C4—1221no—
627C22×C4—1221no—
628C22×C4—1221no—
629C22×C4—1222no—
630C22×C4—2442no—
631C22×C4—2442no—
632C22×C4—2444no—
633C22×C4—2444no—
634C22×C4—2444no—
635C22×C4—2444no—
636C22×C4D4×D6111yescharacteristic
637C22×C4D4×D6111yescharacteristic
638C22×C4C23×D6111yescharacteristic
639C2×C8—22no—
640C2×C8—1222no—
641C2×C8—2444no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—611no—
647C4⋊C4—611no—
648C4⋊C4—1221no—
649C4⋊C4—1221no—
650C4⋊C4—1221no—
651C4⋊C4—1221no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C4⋊C4—1221no—
655C4⋊C4—1221no—
656C4⋊C4—1221no—
657C4⋊C4—1221no—
658C4⋊C4—1221no—
659C4⋊C4—1221no—
660C4⋊C4—1221no—
661C4⋊C4—1221no—
662C4⋊C4C2×C4×D6111yescharacteristic
663C4⋊C4C2×C4×D6111yescharacteristic
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—1221no—
670C22⋊C4—1221no—
671C22⋊C4—1221no—
672C22⋊C4—1221no—
673C22⋊C4—1221no—
674C22⋊C4—1221no—
675C22⋊C4—1221no—
676C22⋊C4—1221no—
677C22⋊C4—1221no—
678C22⋊C4—1221no—
679C22⋊C4—1221no—
680C22⋊C4—1221no—
681C22⋊C4—1221no—
682C22⋊C4—1221no—
683C22⋊C4—1221no—
684C42—21no—
685C42—611no—
686C42—611no—
687C42—611no—
688C42—611no—
689C42—611no—
690C42—611no—
691C42—611no—
692C42—611no—
693C42—611no—
694C42—611no—
695C42—611no—
696C42—611no—
697C42—1221no—
698C42—1221no—
699C42—1221no—
700C42C2×C4×D6111yescharacteristic
701C42C2×C4×D6111yescharacteristic
702C42D4×D6111yescharacteristic
703C42D4×D6111yescharacteristic
704C23—21no—
705C23—611no—
706C23—611no—
707C23—614no—
708C23—1222no—
709C23—1222no—
710C23—1221no—
711C23—2442no—
712C23—2442no—
713C23—2442no—
714C23C2×D4×D6111yescharacteristic
715Q8—41no—
716Q8—2441no—
717Q8—2442no—
718D4—41no—
719D4—42no—
720D4—2441no—
721D4—2442no—
722D4—2442no—
723D4—2442no—
724D4—2442no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—611no—
736C2×C4—611no—
737C2×C4—611no—
738C2×C4—611no—
739C2×C4—611no—
740C2×C4—611no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1221no—
751C2×C4—1221no—
752C2×C4—1221no—
753C2×C4—4888no—
754C2×C4—2441no—
755C2×C4—2441no—
756C2×C4—2441no—
757C2×C4—2441no—
758C2×C4—2442no—
759C2×C4—2442no—
760C2×C4—2442no—
761C2×C4—2442no—
762C2×C4—2442no—
763C2×C4—2441no—
764C2×C4—2441no—
765C2×C4—2442no—
766C2×C4—2442no—
767C2×C4—2442no—
768C2×C4—2442no—
769C2×C4C22⋊C4×D6111yescharacteristic
770C2×C4C22⋊C4×D6111yescharacteristic
771C2×C4C22⋊C4×D6111yescharacteristic
772C2×C4C22⋊C4×D6111yescharacteristic
773C2×C4C22×C4×D6111yescharacteristic
774C2×C4C2×D4×D6111yescharacteristic
775C8—42no—
776C8—2442no—
777C22—21no—
778C22—21no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—612no—
783C22—612no—
784C22—612no—
785C22—612no—
786C22—1228no—
787C22—1221no—
788C22—1221no—
789C22—4884no—
790C22—2441no—
791C22—2441no—
792C22—2441no—
793C22C2×C22⋊C4×D6111yescharacteristic
794C22#135×D6112yes—
795C4—21no—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—41no—
802C4—41no—
803C4—41no—
804C4—82no—
805C4—1221no—
806C4—1221no—
807C4—1221no—
808C4—1221no—
809C4—1221no—
810C4—1221no—
811C4—4882no—
812C4—2441no—
813C4—2441no—
814C4—2441no—
815C2—22no—
816C2—81no—
817C2—614no—
818C2—1222no—
819C2—4881no—
820C2#410×D6111yescharacteristic
821C2#416×D6111yescharacteristic
822C2#421×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1521C2
socleC22×C61C22×C22⋊C4
prime radical#121×D61C22
cosocleC22×C4×C61C24
hypercenter#1521D61
hypocenterC61C2×#1521
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1521

Complements

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

NH ≅ G/Ntype
2. #431×D61C2semidirect
3. #383×D61C2semidirect
4. #21444397C2semidirect
5. #21444396C2semidirect
6. #21444395C2semidirect
7. #21444394C2semidirect
8. #21444393C2semidirect
9. #328×D61C2semidirect
11. C61×#1521C2semidirect
12. #16840299C4semidirect
14. #16840297C4semidirect
17. #16840294C4semidirect
20. #16840291C4semidirect
24. #125×D61C4semidirect
25. #124×D61C4semidirect
29. C4×Q8×D61C4semidirect
31. C4×D4×D61C4semidirect
34. #16839815C22semidirect
37. #16839812C22semidirect
41. #16839630C22semidirect
44. #16839629C22semidirect
48. #16839500C22semidirect
49. #16839499C22semidirect
50. #16839498C22semidirect
55. C61×#431C22semidirect
56. C61×#383C22semidirect
57. C61×#328C22semidirect
75. #14519769C2×C4semidirect
76. #14519768C2×C4semidirect
77. #14519768C2×C4semidirect
80. #14519766C2×C4semidirect
81. #14519765C2×C4semidirect
82. #14519764C2×C4semidirect
102. Q8×Dic61C2×C4semidirect
104. C4×Dic122C2×C4semidirect
106. #14519742C2×C4semidirect
108. C4×D244C2×C4semidirect
110. D4×Dic61C2×C4semidirect
112. #14519739C2×C4semidirect
162. #125×C61C2×C4semidirect
163. #124×C61C2×C4semidirect
167. C4×Q8×C61C2×C4semidirect
169. C4×D4×C61C2×C4semidirect
412. #1521D61direct (N × H)
422. D61#1521direct (N × H)
450. #431C2×D61semidirect
458. #383C2×D61semidirect
465. #328C2×D61semidirect
470. C61C2×#1521semidirect
493. #125C4×D61semidirect
499. #124C4×D61semidirect
525. C4×Q8C4×D61semidirect
539. C4×D4C4×D61semidirect

Maximal subgroups

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

subgroupindex
#529×D612
#431×D612
#383×D612
#214443972
#214443962
#214443952
#214443942
#214443932
#328×D612
#327×D612
C61×#15212
C2×#152161