Finite Group Databasebeta

← D61×#1509 #29647136

Subgroups — D61×#1509 #29647136

Order 15616.

1206 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#529×D61C211yesmaximal, characteristic
2#432×D61C211yesmaximal, characteristic, complemented
3C4×C4⋊C4×D61C211yesmaximal, characteristic, complemented
4#21444345C211yesmaximal, characteristic, complemented
5#21444344C211yesmaximal, characteristic, complemented
6#21444343C212yesmaximal, complemented
7#21444342C211yesmaximal, characteristic, complemented
8#21444341C212yesmaximal, complemented
9#328×D61C212yesmaximal, complemented
10#327×D61C212yesmaximal
11C61×#1509C211yesmaximal, 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×C4⋊C4×D61—21no—
34C2×C42×D61—21no—
35C2×C42×D61C2211yescharacteristic
36#16839819C2211yescharacteristic, complemented
37#16839818—21no—
38#16839817—21no—
39#16839816C2212yescomplemented
40C4⋊C8×D61—21no—
41C22⋊C8×D61C2212yes—
42#97×D61—21no—
43C4⋊C4×Dic61—21no—
44C4×#11758196—21no—
45C4×C4⋊Dic61C2211yescharacteristic, complemented
46#16839613C2212yescomplemented
47#95×D61C2212yes—
48#16839500C2212yescomplemented
49#16839499C2212yescomplemented
50#16839498C2212yescomplemented
51#16839497C2212yes—
52#16839496C2212yes—
53#16839495C2212yes—
54C61×#529C2211yescharacteristic
55C61×#432C2211yescharacteristic, complemented
56C4×C4⋊C4×C61C2211yescharacteristic, complemented
57C61×#328C2212yescomplemented
58C61×#327C2212yes—
59C2×Q8×D61C2×C411yescharacteristic
60C2×D4×D61—21no—
61C2×D4×D61C2×C411yescharacteristic
62C22×C4×D61—22no—
63C22×C4×D61—21no—
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—
126C2×C4⋊Dic61—21no—
127C2×#11758196—22no—
128C4⋊C4×D61—28no—
129C4⋊C4×D61—21no—
130C4⋊C4×D61—21no—
131C4⋊C4×D61—21no—
132C4⋊C4×D61—21no—
133C4⋊C4×D61C2×C411yescharacteristic
134C4⋊C4×D61C2×C411yescharacteristic
135C22⋊C4×D61—21no—
136C22⋊C4×D61—21no—
137C22⋊C4×D61—21no—
138C22⋊C4×D61—21no—
139C22⋊C4×D61—21no—
140C2×C4×Dic61—21no—
141C2×C4×Dic61—22no—
142C2×C4×Dic61D411yescharacteristic
143C2×C4×Dic61D411yescharacteristic
144C2×C4×Dic61C2311yescharacteristic
145C42×D61—21no—
146C42×D61—44no—
147C42×D61C2×C411yescharacteristic
148C42×D61C2×C411yescharacteristic
149C42×D61C2×C411yescharacteristic
150C42×D61C2×C411yescharacteristic
151C42×D61D411yescharacteristic
152C42×D61D411yescharacteristic
153C42×D61D411yescharacteristic
154C42×D61D411yescharacteristic
155C4⋊#92418—21no—
156#14519706—22no—
157C22⋊#92418C2312yes—
158#14519689—22no—
159#14519688—21no—
160#14519687—22no—
161#14519684—22no—
162#14519684C2312yes—
163#126×C61—21no—
164#125×C61C2×C411yescharacteristic, complemented
165#124×C61C2×C411yescharacteristic, complemented
166#123×C61—21no—
167C22⋊Q8×C61C2311yescharacteristic
168#121×C61C2311yescharacteristic
169C4×Q8×C61C2×C411yescharacteristic, complemented
170C4×D4×C61—21no—
171C4×D4×C61C2×C411yescharacteristic, complemented
172#117×C61—21no—
173C2×C4⋊C4×C61—21no—
174C2×C42×C61—21no—
175C2×C42×C61C2311yescharacteristic
176C4⋊C8×C61—21no—
177C22⋊C8×C61C2312yes—
178#97×C61—21no—
179#95×C61C2312yes—
180C23×D61—21no—
181C23×D61C2×D411yescharacteristic
182C2×Q8×C61C22×C411yescharacteristic
183C2×D4×C61—21no—
184C2×D4×C61C22×C411yescharacteristic
185C22×C4×C61—22no—
186C22×C4×C61—21no—
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2411yescharacteristic
190C2×C22⋊D61—21no—
191C2×C22⋊D61—21no—
192C2×C22⋊D61—21no—
193C22×Dic61—22no—
194C22×Dic61—21no—
195C22×Dic61C2×D411yescharacteristic
196C22×Dic61C2×D411yescharacteristic
197C22×Dic61C2×D411yescharacteristic
198Q8×D61—42no—
199D4×D61—42no—
200D4×D61—42no—
201D4×D61—42no—
202C2×D244—21no—
203C2×D244C22×C411yescharacteristic
204C2×C4×D61—22no—
205C2×C4×D61—22no—
206C2×C4×D61—24no—
207C2×C4×D61—28no—
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61—21no—
211C2×C4×D61—21no—
212C2×C4×D61—21no—
213C2×C4×D61—42no—
214C2×C4×D61—44no—
215C2×C4×D61—44no—
216C2×C4×D61—44no—
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×D61C22⋊C411yescharacteristic
224C2×C4×D61C22⋊C411yescharacteristic
225C2×C4×D61C22×C411yescharacteristic
226C2×C4×D61C22×C411yescharacteristic
227C2×C4×D61C2×D411yescharacteristic
228C2×C4×D61C2×D411yescharacteristic
229C2×Dic122—21no—
230C2×Dic122C22×C411yescharacteristic
231C2×C8×C61—22no—
232C4⋊C4×C61—24no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61C22×C411yescharacteristic
238C4⋊C4×C61C22×C411yescharacteristic
239C22⋊C4×C61—21no—
240C22⋊C4×C61—21no—
241C22⋊C4×C61—21no—
242C22⋊C4×C61—21no—
243C22⋊C4×C61—21no—
244C42×C61—21no—
245C42×C61—42no—
246C42×C61C22×C411yescharacteristic
247C42×C61C22×C411yescharacteristic
248C42×C61C2×D411yescharacteristic
249C42×C61C2×D411yescharacteristic
250C22⋊Dic61—21no—
251C22⋊Dic61—21no—
252C22⋊Dic61—21no—
253C22⋊Dic61—21no—
254C22⋊Dic61—21no—
255#11758198—21no—
256#11758198—21no—
257#11758198—21no—
258#11758198—21no—
259#11758198—21no—
260#11758198—21no—
261#11758198—21no—
262#11758198—21no—
263#11758198—21no—
264#11758198—21no—
265C4⋊Dic61—24no—
266C4⋊Dic61—21no—
267C4⋊Dic61—21no—
268C4⋊Dic61—21no—
269C4⋊Dic61—21no—
270C4⋊Dic61C22×C411yescharacteristic
271C4⋊Dic61C22×C411yescharacteristic
272#11758196—28no—
273#11758196—21no—
274#11758196—21no—
275#11758196—21no—
276#11758196—21no—
277#11758196—21no—
278#11758196—21no—
279#11758196—21no—
280#11758196—21no—
281#11758196—21no—
282#11758196—21no—
283C4×Dic61—21no—
284C4×Dic61—21no—
285C4×Dic61—21no—
286C4×Dic61—44no—
287C4×Dic61—42no—
288C4×Dic61C22⋊C411yescharacteristic
289C4×Dic61C22⋊C411yescharacteristic
290C4×Dic61C22⋊C411yescharacteristic
291C4×Dic61C22⋊C411yescharacteristic
292C4×Dic61C22⋊C411yescharacteristic
293C4×Dic61C22⋊C411yescharacteristic
294C4×Dic61C22⋊C411yescharacteristic
295C4×Dic61C22⋊C411yescharacteristic
296C4×Dic61C22×C411yescharacteristic
297C4×Dic61C22×C411yescharacteristic
298C4×Dic61C2×D411yescharacteristic
299C4×Dic61C2×D411yescharacteristic
300C2×#92418—22no—
301C8×D61—44no—
302C23×C61—21no—
303C23×C61C22×D411yescharacteristic
304C22×D61—22no—
305C22×D61—22no—
306C22×D61—21no—
307C22×D61—42no—
308C22×D61—42no—
309C22×D61—42no—
310C22×D61C2×C22⋊C411yescharacteristic
311C22×D61C2×C22⋊C411yescharacteristic
312C22×D61AGL(1,ℤ/8)12yes—
313C22×D61#13712yes—
314Q8×C61—41no—
315D4×C61—41no—
316D4×C61—41no—
317D4×C61—41no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
320C2×C4×C61—22no—
321C2×C4×C61—24no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—41no—
326C2×C4×C61—42no—
327C2×C4×C61—42no—
328C2×C4×C61—42no—
329C2×C4×C61C2×C22⋊C411yescharacteristic
330C2×C4×C61C2×C22⋊C411yescharacteristic
331C2×C4×C61C2×C22⋊C411yescharacteristic
332C2×C4×C61C2×C22⋊C411yescharacteristic
333C2×C4×C61C23×C411yescharacteristic
334C2×C4×C61C22×D411yescharacteristic
335C22⋊D61—42no—
336C22⋊D61—41no—
337C22⋊D61—41no—
338C22⋊D61—42no—
339C2×Dic61—21no—
340C2×Dic61—21no—
341C2×Dic61—22no—
342C2×Dic61—24no—
343C2×Dic61—21no—
344C2×Dic61—21no—
345C2×Dic61—21no—
346C2×Dic61—41no—
347C2×Dic61—42no—
348C2×Dic61—42no—
349C2×Dic61—42no—
350C2×Dic61C2×C22⋊C411yescharacteristic
351C2×Dic61C2×C22⋊C411yescharacteristic
352C2×Dic61C2×C22⋊C411yescharacteristic
353C2×Dic61C2×C22⋊C411yescharacteristic
354C2×Dic61C2×C22⋊C411yescharacteristic
355C2×Dic61C2×C22⋊C411yescharacteristic
356D244—41no—
357D244—42no—
358C4×D61—22no—
359C4×D61—22no—
360C4×D61—22no—
361C4×D61—22no—
362C4×D61—22no—
363C4×D61—22no—
364C4×D61—22no—
365C4×D61—22no—
366C4×D61—22no—
367C4×D61—41no—
368C4×D61—41no—
369C4×D61—416no—
370C4×D61—42no—
371C4×D61—42no—
372C4×D61—42no—
373C4×D61—42no—
374C4×D61—42no—
375C4×D61#10414yes—
376Dic122—42no—
377Dic122—41no—
378C8×C61—42no—
379#92418—42no—
380C2×#1509—611nomaximal, Sylow
381C22×C61—21no—
382C22×C61—21no—
383C22×C61—41no—
384C22×C61—41no—
385C22×C61—41no—
386C22×C61C22×C22⋊C411yescharacteristic
387C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
388C22×C61C2×#13711yescharacteristic
389C2×D61—21no—
390C2×D61—21no—
391C2×D61—24no—
392C2×D61—24no—
393C2×D61—41no—
394C2×D61—41no—
395C2×D61—41no—
396C2×D61—84no—
397C2×D61#41012yes—
398C2×D61#41712yes—
399C2×D61#41712yes—
400C2×D61C2×#10412yes—
401C4×C61—21no—
402C4×C61—21no—
403C4×C61—21no—
404C4×C61—21no—
405C4×C61—21no—
406C4×C61—44no—
407C4×C61—41no—
408C4×C61—41no—
409C4×C61—41no—
410C4×C61C2×#10412yes—
411Dic61—21no—
412Dic61—21no—
413Dic61—21no—
414Dic61—21no—
415Dic61—21no—
416Dic61—44no—
417Dic61—41no—
418Dic61—41no—
419Dic61—41no—
420Dic61C2×#10412yes—
421C2×#529—611no—
422C2×#432—611no—
423C2×C4×C4⋊C4—611no—
424#1509—611no—
425#1509—611no—
426#1509—612no—
427#1509—612no—
428#1509—611no—
429#1509D6111yescharacteristic, direct product factor
430C2×#328—612no—
431C2×#327—612no—
432C2×C61—21no—
433C2×C61—21no—
434C2×C61—81no—
435C2×C61C2×#41011yescharacteristic
436C2×C61C2×#41711yescharacteristic
437C2×C61C22×#10411yescharacteristic
438D61—22no—
439D61—81no—
440D61#150914yesdirect product factor
441#529—611no—
442#529—611no—
443#529—611no—
444#529—611no—
445#529—611no—
446#529—611no—
447#529—611no—
448#529—1221no—
449#529—1221no—
450#529—1221no—
451#529—1221no—
452#529C2×D6111yescharacteristic
453C2×#126—1221no—
454C2×#125—611no—
455C2×#124—611no—
456C2×#123—1221no—
457C2×C22⋊Q8—611no—
458C2×#121—611no—
459C2×C4×Q8—611no—
460C2×C4×D4—611no—
461C2×C4×D4—1221no—
462C2×#117—1221no—
463C22×C4⋊C4—1221no—
464C22×C42—611no—
465C22×C42—1221no—
466#432—611no—
467#432—612no—
468#432—1221no—
469#432—1221no—
470#432C2×D6111yescharacteristic, complemented
471C2×C4⋊C8—1221no—
472C2×C22⋊C8—612no—
473C2×#97—1221no—
474C4×C4⋊C4—611no—
475C4×C4⋊C4—612no—
476C4×C4⋊C4—1221no—
477C4×C4⋊C4—1221no—
478C4×C4⋊C4C2×D6111yescharacteristic, complemented
479C2×#95—612no—
480#328—612no—
481#328—612no—
482#328—612no—
483#328C2×D6112yescomplemented
484#327—612no—
485#327—612no—
486#327—612no—
487#327C2×D6112yes—
488C61C2×#150911yescharacteristic, complemented, Sylow
489C22×Q8—611no—
490C22×D4—611no—
491C22×D4—1221no—
492C23×C4—611no—
493C23×C4—611no—
494C23×C4—611no—
495C23×C4—1221no—
496C23×C4—1222no—
497C22×C8—1222no—
498#126—21no—
499#126—1221no—
500#126—1221no—
501#126—1221no—
502#126—1221no—
503#126—1221no—
504#126—1221no—
505#126—1221no—
506#125—611no—
507#125—611no—
508#125—611no—
509#125—1221no—
510#125—1221no—
511#125C4×D6111yescharacteristic, complemented
512#124—611no—
513#124—611no—
514#124—611no—
515#124—1221no—
516#124—1221no—
517#124C4×D6111yescharacteristic, complemented
518#123—21no—
519#123—1221no—
520#123—1221no—
521#123—1221no—
522#123—1221no—
523#123—1221no—
524#123—1221no—
525#123—1221no—
526C22⋊Q8—611no—
527C22⋊Q8—611no—
528C22⋊Q8—611no—
529C22⋊Q8—1221no—
530C22⋊Q8—1221no—
531C22⋊Q8C22×D6111yescharacteristic
532#121—611no—
533#121—611no—
534#121—611no—
535#121—1221no—
536#121—1221no—
537#121C22×D6111yescharacteristic
538C4×Q8—611no—
539C4×Q8—611no—
540C4×Q8—611no—
541C4×Q8—1221no—
542C4×Q8—1221no—
543C4×Q8C4×D6111yescharacteristic, complemented
544C4×D4—21no—
545C4×D4—611no—
546C4×D4—611no—
547C4×D4—611no—
548C4×D4—1221no—
549C4×D4—1221no—
550C4×D4—1221no—
551C4×D4—1221no—
552C4×D4—1221no—
553C4×D4—1221no—
554C4×D4—1221no—
555C4×D4—1221no—
556C4×D4—1221no—
557C4×D4C4×D6111yescharacteristic, complemented
558#117—21no—
559#117—1221no—
560#117—1221no—
561#117—1221no—
562#117—1221no—
563#117—1221no—
564#117—1221no—
565#117—1221no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—611no—
568C2×C4⋊C4—611no—
569C2×C4⋊C4—1221no—
570C2×C4⋊C4—1221no—
571C2×C4⋊C4—1221no—
572C2×C4⋊C4—1221no—
573C2×C4⋊C4—1228no—
574C2×C4⋊C4—1222no—
575C2×C4⋊C4—1221no—
576C2×C22⋊C4—1221no—
577C2×C22⋊C4—1221no—
578C2×C22⋊C4—1221no—
579C2×C22⋊C4—1221no—
580C2×C22⋊C4—1221no—
581C2×C42—21no—
582C2×C42—611no—
583C2×C42—611no—
584C2×C42—611no—
585C2×C42—611no—
586C2×C42—611no—
587C2×C42—611no—
588C2×C42—611no—
589C2×C42—611no—
590C2×C42—611no—
591C2×C42—611no—
592C2×C42—611no—
593C2×C42—1221no—
594C2×C42—1222no—
595C2×C42—1221no—
596C2×C42—2444no—
597C2×C42C22×D6111yescharacteristic
598C4⋊C8—21no—
599C4⋊C8—1222no—
600C4⋊C8—1221no—
601C22⋊C8—612no—
602C22⋊C8—1222no—
603C22⋊C8C22×D6112yes—
604#97—21no—
605#97—1222no—
606#97—1221no—
607#95—612no—
608#95—1222no—
609#95C22×D6112yes—
610C24—611no—
611C24—1221no—
612C2×Q8—611no—
613C2×Q8—1221no—
614C2×Q8—2442no—
615C2×Q8C2×C4×D6111yescharacteristic
616C2×D4—21no—
617C2×D4—611no—
618C2×D4—1221no—
619C2×D4—1221no—
620C2×D4—1221no—
621C2×D4—1221no—
622C2×D4—2442no—
623C2×D4—2442no—
624C2×D4—2442no—
625C2×D4C2×C4×D6111yescharacteristic
626C22×C4—22no—
627C22×C4—21no—
628C22×C4—611no—
629C22×C4—611no—
630C22×C4—611no—
631C22×C4—611no—
632C22×C4—611no—
633C22×C4—611no—
634C22×C4—611no—
635C22×C4—611no—
636C22×C4—611no—
637C22×C4—611no—
638C22×C4—611no—
639C22×C4—611no—
640C22×C4—611no—
641C22×C4—611no—
642C22×C4—611no—
643C22×C4—1224no—
644C22×C4—1221no—
645C22×C4—1222no—
646C22×C4—1222no—
647C22×C4—1221no—
648C22×C4—1221no—
649C22×C4—1221no—
650C22×C4—1228no—
651C22×C4—1221no—
652C22×C4—1222no—
653C22×C4—1221no—
654C22×C4—2444no—
655C22×C4—2442no—
656C22×C4—2444no—
657C22×C4—2444no—
658C22×C4D4×D6111yescharacteristic
659C22×C4D4×D6111yescharacteristic
660C22×C4C23×D6111yescharacteristic
661C2×C8—22no—
662C2×C8—1222no—
663C2×C8—2444no—
664C4⋊C4—24no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—611no—
670C4⋊C4—611no—
671C4⋊C4—1221no—
672C4⋊C4—1221no—
673C4⋊C4—1221no—
674C4⋊C4—1221no—
675C4⋊C4—1221no—
676C4⋊C4—1221no—
677C4⋊C4—1221no—
678C4⋊C4—1221no—
679C4⋊C4—1221no—
680C4⋊C4—1221no—
681C4⋊C4—1228no—
682C4⋊C4—1224no—
683C4⋊C4—1221no—
684C4⋊C4—1221no—
685C4⋊C4—1221no—
686C4⋊C4—1221no—
687C4⋊C4C2×C4×D6111yescharacteristic
688C4⋊C4C2×C4×D6111yescharacteristic
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—21no—
692C22⋊C4—21no—
693C22⋊C4—21no—
694C22⋊C4—1221no—
695C22⋊C4—1221no—
696C22⋊C4—1221no—
697C22⋊C4—1221no—
698C22⋊C4—1221no—
699C22⋊C4—1221no—
700C22⋊C4—1221no—
701C22⋊C4—1221no—
702C22⋊C4—1221no—
703C22⋊C4—1221no—
704C22⋊C4—1221no—
705C22⋊C4—1221no—
706C22⋊C4—1221no—
707C22⋊C4—1221no—
708C22⋊C4—1221no—
709C42—21no—
710C42—42no—
711C42—611no—
712C42—611no—
713C42—611no—
714C42—611no—
715C42—611no—
716C42—611no—
717C42—611no—
718C42—611no—
719C42—611no—
720C42—611no—
721C42—611no—
722C42—611no—
723C42—1221no—
724C42—1221no—
725C42—1221no—
726C42—2442no—
727C42—2444no—
728C42C2×C4×D6111yescharacteristic
729C42C2×C4×D6111yescharacteristic
730C42D4×D6111yescharacteristic
731C42D4×D6111yescharacteristic
732C23—21no—
733C23—611no—
734C23—611no—
735C23—612no—
736C23—612no—
737C23—1222no—
738C23—1222no—
739C23—1221no—
740C23—2442no—
741C23—2442no—
742C23—2442no—
743C23C2×D4×D6111yescharacteristic
744Q8—41no—
745Q8—2441no—
746Q8—2442no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—2441no—
751D4—2442no—
752D4—2442no—
753D4—2442no—
754D4—2441no—
755D4—2441no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—611no—
768C2×C4—614no—
769C2×C4—611no—
770C2×C4—611no—
771C2×C4—611no—
772C2×C4—611no—
773C2×C4—611no—
774C2×C4—1222no—
775C2×C4—1222no—
776C2×C4—1222no—
777C2×C4—1222no—
778C2×C4—1222no—
779C2×C4—1222no—
780C2×C4—1222no—
781C2×C4—1222no—
782C2×C4—1222no—
783C2×C4—1221no—
784C2×C4—1221no—
785C2×C4—1222no—
786C2×C4—1224no—
787C2×C4—1221no—
788C2×C4—1221no—
789C2×C4—1221no—
790C2×C4—2441no—
791C2×C4—2441no—
792C2×C4—2442no—
793C2×C4—2442no—
794C2×C4—2442no—
795C2×C4—2442no—
796C2×C4—24416no—
797C2×C4—2442no—
798C2×C4—2441no—
799C2×C4—2442no—
800C2×C4—2442no—
801C2×C4—2442no—
802C2×C4C22⋊C4×D6111yescharacteristic
803C2×C4C22⋊C4×D6111yescharacteristic
804C2×C4C22⋊C4×D6111yescharacteristic
805C2×C4C22⋊C4×D6111yescharacteristic
806C2×C4C22×C4×D6111yescharacteristic
807C2×C4C2×D4×D6111yescharacteristic
808C8—42no—
809C8—2442no—
810C22—21no—
811C22—21no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—612no—
816C22—612no—
817C22—612no—
818C22—612no—
819C22—1224no—
820C22—1224no—
821C22—1221no—
822C22—1221no—
823C22—4884no—
824C22—2441no—
825C22—2441no—
826C22—2441no—
827C22C2×C22⋊C4×D6111yescharacteristic
828C22AGL(1,ℤ/8)×D6111yescharacteristic
829C22#137×D6111yescharacteristic
830C4—21no—
831C4—21no—
832C4—21no—
833C4—21no—
834C4—21no—
835C4—44no—
836C4—41no—
837C4—41no—
838C4—41no—
839C4—612no—
840C4—1221no—
841C4—1221no—
842C4—1221no—
843C4—1221no—
844C4—1221no—
845C4—2444no—
846C4—2441no—
847C4—2441no—
848C4—2441no—
849C4#104×D6112yes—
850C2—21no—
851C2—21no—
852C2—81no—
853C2—614no—
854C2—1222no—
855C2—4881no—
856C2#410×D6111yescharacteristic
857C2#417×D6111yescharacteristic
858C2C2×#104×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1509C2
socleC22×C61C22×C22⋊C4
prime radical#121×D61C22
cosocleC22×C4×C61C24
hypercenter#1509D61
hypocenterC61C2×#1509
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1509

Complements

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

NH ≅ G/Ntype
2. #432×D61C2semidirect
3. C4×C4⋊C4×D61C2semidirect
4. #21444345C2semidirect
5. #21444344C2semidirect
6. #21444343C2semidirect
7. #21444342C2semidirect
8. #21444341C2semidirect
9. #328×D61C2semidirect
11. C61×#1509C2semidirect
12. #16840299C4semidirect
14. #16840297C4semidirect
17. #16840294C4semidirect
20. #16840291C4semidirect
24. #125×D61C4semidirect
25. #124×D61C4semidirect
29. C4×Q8×D61C4semidirect
31. C4×D4×D61C4semidirect
36. #16839819C22semidirect
39. #16839816C22semidirect
45. C4×C4⋊Dic61C22semidirect
46. #16839613C22semidirect
48. #16839500C22semidirect
49. #16839499C22semidirect
50. #16839498C22semidirect
55. C61×#432C22semidirect
56. C4×C4⋊C4×C61C22semidirect
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
164. #125×C61C2×C4semidirect
165. #124×C61C2×C4semidirect
169. C4×Q8×C61C2×C4semidirect
171. C4×D4×C61C2×C4semidirect
429. #1509D61direct (N × H)
440. D61#1509direct (N × H)
470. #432C2×D61semidirect
478. C4×C4⋊C4C2×D61semidirect
483. #328C2×D61semidirect
488. C61C2×#1509semidirect
511. #125C4×D61semidirect
517. #124C4×D61semidirect
543. C4×Q8C4×D61semidirect
557. 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
#432×D612
C4×C4⋊C4×D612
#214443452
#214443442
#214443432
#214443422
#214443412
#328×D612
#327×D612
C61×#15092
C2×#150961