Finite Group Databasebeta

← D61⋊#1500 #30610900

Subgroups — D61⋊#1500 #30610900

Order 15616.

1182 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#431C211yesmaximal, characteristic, complemented
2C2×#16840698C211yesmaximal, characteristic, complemented
3#21461193C212yesmaximal, complemented
4#21461192C212yesmaximal, complemented
5#21461191C212yesmaximal, complemented
6#21461190C212yesmaximal, complemented
7D61⋊#328C212yesmaximal, complemented
8D61⋊#327C212yesmaximal
9#529×D61C211yesmaximal, characteristic
10C22×C4×#6923—21no—
11#16840781C2212yescomplemented
12#16840780C2212yescomplemented
13#16840779—21no—
14#16840778—21no—
15D61⋊(C4⋊C8)—21no—
16D61⋊(C22⋊C8)C2212yes—
17C4×D61⋊C8—21no—
18#16840698—21no—
19#16840698—21no—
20#16840698C2212yescomplemented
21#16840698C2212yescomplemented
22C2×(C2×#6923)⋊C4—21no—
23C2×(C2×#6923)⋊C4C2212yes—
24#16840616C2214yescomplemented
25#16840615C2214yescomplemented
26#16840614C2214yes—
27#16840613C2214yes—
28#16840299C2211yescharacteristic
29#16840298C411yescharacteristic, complemented
30#16840297C2211yescharacteristic
31#16840296C411yescharacteristic, complemented
32#16840295—21no—
33#16840294C2211yescharacteristic
34#16840293C411yescharacteristic, complemented
35#16840292—21no—
36#16840291C2211yescharacteristic
37#16840290—21no—
38#16840289—21no—
39#126×D61—21no—
40#125×D61C411yescharacteristic, complemented
41#124×D61C411yescharacteristic, complemented
42#123×D61—21no—
43C22⋊Q8×D61C2211yescharacteristic
44#121×D61C2211yescharacteristic
45C4×Q8×D61C411yescharacteristic, complemented
46C4×D4×D61—21no—
47C4×D4×D61C411yescharacteristic, complemented
48#117×D61—21no—
49C2×C42×D61C2211yescharacteristic
50C61×#529C411yescharacteristic, complemented
51C23×#6923—22no—
52C2×D61⋊C8—22no—
53C2×C4×#6923—28no—
54C2×C4×#6923—22no—
55C2×C4×#6923—22no—
56#14519844—22no—
57C4⋊#92420—22no—
58#14519834C2314yes—
59C22⋊#92420—22no—
60C4×#92420—22no—
61C4×#92420—22no—
62(C2×#6923)⋊C4—22no—
63(C2×#6923)⋊C4—22no—
64(C2×#6923)⋊C4—22no—
65(C2×#6923)⋊C4C2314yes—
66C2×Q8×D61C2×C411yescharacteristic
67C2×D4×D61—21no—
68C2×D4×D61C2×C411yescharacteristic
69C22×C4×D61—21no—
70C22×C4×D61D411yescharacteristic
71C22×C4×D61D411yescharacteristic
72C22×C4×D61C2311yescharacteristic
73#14519772—21no—
74#14519772—21no—
75#14519772—21no—
76#14519771—21no—
77#14519770—21no—
78#14519770—21no—
79#14519770—21no—
80#14519769C2×C411yescharacteristic, complemented
81#14519768C2×C411yescharacteristic, complemented
82#14519768C2×C411yescharacteristic, complemented
83#14519767—21no—
84#14519767—21no—
85#14519766C2×C411yescharacteristic, complemented
86#14519765C2×C411yescharacteristic, complemented
87#14519764C2×C411yescharacteristic, complemented
88#14519763—21no—
89#14519763—21no—
90#14519762—21no—
91#14519762—21no—
92#14519761—21no—
93#14519760—21no—
94#14519759—21no—
95#14519759—21no—
96#14519758—21no—
97#14519757C2311yescharacteristic
98#14519756C2×C411yescharacteristic
99#14519755—21no—
100#14519754—21no—
101#14519753C2311yescharacteristic
102#14519752C2311yescharacteristic
103#14519751C2×C411yescharacteristic
104#14519750—21no—
105#14519749—21no—
106#14519748C2311yescharacteristic
107Q8×Dic61C2×C411yescharacteristic, complemented
108C4×Dic122—21no—
109C4×Dic122C2×C411yescharacteristic, complemented
110#14519742—21no—
111#14519742C2×C411yescharacteristic, complemented
112C4×D244—21no—
113C4×D244C2×C411yescharacteristic, complemented
114D4×Dic61—21no—
115D4×Dic61C2×C411yescharacteristic, complemented
116#14519739—21no—
117#14519739C2×C411yescharacteristic, complemented
118C4×C22⋊D61—21no—
119C4×C22⋊D61—21no—
120C4×C22⋊D61—21no—
121#14519737—21no—
122#14519737—21no—
123#14519737—21no—
124#14519736—21no—
125#14519735—21no—
126#14519735—21no—
127#14519734—21no—
128#14519734—21no—
129#14519733—21no—
130#14519733—21no—
131C4⋊C4×D61—21no—
132C4⋊C4×D61—21no—
133C4⋊C4×D61—21no—
134C4⋊C4×D61—21no—
135C4⋊C4×D61C2×C411yescharacteristic
136C4⋊C4×D61C2×C411yescharacteristic
137C22⋊C4×D61—21no—
138C22⋊C4×D61—21no—
139C22⋊C4×D61—21no—
140C22⋊C4×D61—21no—
141C22⋊C4×D61—21no—
142C2×C4×Dic61C2×C411yescharacteristic
143C2×C4×Dic61D411yescharacteristic
144C2×C4×Dic61D411yescharacteristic
145C42×D61—21no—
146C42×D61C2×C411yescharacteristic
147C42×D61C2×C411yescharacteristic
148C42×D61D411yescharacteristic
149C42×D61D411yescharacteristic
150C42×D61D411yescharacteristic
151C42×D61D411yescharacteristic
152C42×D61C2311yescharacteristic
153C42×D61C2311yescharacteristic
154#126×C61—21no—
155#125×C61C2×C411yescharacteristic, complemented
156#124×C61C2×C411yescharacteristic, complemented
157#123×C61—21no—
158C22⋊Q8×C61C2×C411yescharacteristic
159#121×C61C2×C411yescharacteristic
160C4×Q8×C61C2×C411yescharacteristic, complemented
161C4×D4×C61—21no—
162C4×D4×C61C2×C411yescharacteristic, complemented
163#117×C61—21no—
164C2×C42×C61C2×C411yescharacteristic
165C23×D61—21no—
166C23×D61C2×D411yescharacteristic
167C22×#6923—28no—
168C22×#6923—24no—
169C22×#6923—44no—
170C22×#6923—44no—
171C2×Q8×C61C22×C411yescharacteristic
172C2×D4×C61—21no—
173C2×D4×C61C22×C411yescharacteristic
174C22×C4×C61—21no—
175C22×C4×C61C22⋊C411yescharacteristic
176C22×C4×C61C22⋊C411yescharacteristic
177C22×C4×C61C22×C411yescharacteristic
178C2×C22⋊D61—21no—
179C2×C22⋊D61—21no—
180C2×C22⋊D61—21no—
181C22×Dic61—21no—
182C22×Dic61C22⋊C411yescharacteristic
183C22×Dic61C22⋊C411yescharacteristic
184C22×Dic61C2×D411yescharacteristic
185Q8×D61—42no—
186D4×D61—42no—
187D4×D61—44no—
188C2×D244—21no—
189C2×D244C22×C411yescharacteristic
190C2×C4×D61—24no—
191C2×C4×D61—24no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—42no—
198C2×C4×D61—44no—
199C2×C4×D61C22⋊C411yescharacteristic
200C2×C4×D61C22⋊C411yescharacteristic
201C2×C4×D61C22⋊C411yescharacteristic
202C2×C4×D61C22⋊C411yescharacteristic
203C2×C4×D61C22×C411yescharacteristic
204C2×C4×D61C2×D411yescharacteristic
205C2×C4×D61C2×D411yescharacteristic
206C2×C4×D61C2×D411yescharacteristic
207C2×C4×D61C2×D411yescharacteristic
208C2×C4×D61C2×D411yescharacteristic
209C2×C4×D61C2×D411yescharacteristic
210C2×C4×D61C2411yescharacteristic
211C2×Dic122—21no—
212C2×Dic122C22×C411yescharacteristic
213C2×#92420—24no—
214C4×#6923—28no—
215C4×#6923—28no—
216D61⋊C8—44no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61—21no—
220C4⋊C4×C61—21no—
221C4⋊C4×C61C22×C411yescharacteristic
222C4⋊C4×C61C22×C411yescharacteristic
223C22⋊C4×C61—21no—
224C22⋊C4×C61—21no—
225C22⋊C4×C61—21no—
226C22⋊C4×C61—21no—
227C22⋊C4×C61—21no—
228C42×C61—21no—
229C42×C61C22⋊C411yescharacteristic
230C42×C61C22⋊C411yescharacteristic
231C42×C61C22×C411yescharacteristic
232C42×C61C22×C411yescharacteristic
233C22⋊Dic61—21no—
234C22⋊Dic61—21no—
235C22⋊Dic61—21no—
236C22⋊Dic61—21no—
237C22⋊Dic61—21no—
238#11758198—21no—
239#11758198—21no—
240#11758198—21no—
241#11758198—21no—
242#11758198—21no—
243#11758198—21no—
244#11758198—21no—
245#11758198—21no—
246#11758198—21no—
247#11758198—21no—
248C4⋊Dic61—21no—
249C4⋊Dic61—21no—
250C4⋊Dic61—21no—
251C4⋊Dic61—21no—
252C4⋊Dic61C22×C411yescharacteristic
253C4⋊Dic61C22×C411yescharacteristic
254#11758196—21no—
255#11758196—21no—
256#11758196—21no—
257#11758196—21no—
258#11758196—21no—
259#11758196—21no—
260#11758196—21no—
261#11758196—21no—
262#11758196—21no—
263#11758196—21no—
264C4×Dic61—21no—
265C4×Dic61—21no—
266C4×Dic61—21no—
267C4×Dic61C22⋊C411yescharacteristic
268C4×Dic61C22⋊C411yescharacteristic
269C4×Dic61C22⋊C411yescharacteristic
270C4×Dic61C22⋊C411yescharacteristic
271C4×Dic61C22⋊C411yescharacteristic
272C4×Dic61C22⋊C411yescharacteristic
273C4×Dic61C22×C411yescharacteristic
274C4×Dic61C22×C411yescharacteristic
275C4×Dic61C2×D411yescharacteristic
276C4×Dic61C2×D411yescharacteristic
277C4×Dic61C2×D411yescharacteristic
278C4×Dic61C2×D411yescharacteristic
279C23×C61—21no—
280C23×C61C2×C22⋊C411yescharacteristic
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—21no—
284C22×D61—42no—
285C22×D61—42no—
286C22×D61—42no—
287C22×D61C2×C22⋊C411yescharacteristic
288C22×D61#13514yes—
289C22×D61C22×D411yescharacteristic
290C2×#6923—28no—
291C2×#6923—44no—
292C2×#6923—416no—
293C2×#6923—44no—
294Q8×C61—41no—
295D4×C61—41no—
296D4×C61—42no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—41no—
303C2×C4×C61—42no—
304C2×C4×C61C2×C22⋊C411yescharacteristic
305C2×C4×C61C2×C22⋊C411yescharacteristic
306C2×C4×C61C2×C22⋊C411yescharacteristic
307C2×C4×C61C2×C22⋊C411yescharacteristic
308C2×C4×C61C2×C22⋊C411yescharacteristic
309C2×C4×C61C23×C411yescharacteristic
310C22⋊D61—42no—
311C22⋊D61—42no—
312C22⋊D61—42no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—41no—
319C2×Dic61—42no—
320C2×Dic61C2×C22⋊C411yescharacteristic
321C2×Dic61C2×C22⋊C411yescharacteristic
322C2×Dic61C2×C22⋊C411yescharacteristic
323C2×Dic61C2×C22⋊C411yescharacteristic
324C2×Dic61C2×C22⋊C411yescharacteristic
325C2×Dic61C22×D411yescharacteristic
326D244—41no—
327D244—42no—
328C4×D61—22no—
329C4×D61—22no—
330C4×D61—22no—
331C4×D61—22no—
332C4×D61—22no—
333C4×D61—22no—
334C4×D61—22no—
335C4×D61—22no—
336C4×D61—22no—
337C4×D61—41no—
338C4×D61—41no—
339C4×D61—42no—
340C4×D61—42no—
341C4×D61—42no—
342C4×D61—42no—
343C4×D61—42no—
344C4×D61#10414yes—
345Dic122—42no—
346Dic122—41no—
347#92420—44no—
348C2×#1500—611nomaximal, Sylow
349C22×C61—21no—
350C22×C61—21no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61#41612yes—
355C22×C61C22×C22⋊C411yescharacteristic
356C2×D61—21no—
357C2×D61—21no—
358C2×D61—28no—
359C2×D61—41no—
360C2×D61—41no—
361C2×D61—41no—
362C2×D61—84no—
363C2×D61#41012yes—
364C2×D61#41612yes—
365C2×D61C2×#10412yes—
366C2×D61C2×#13512yes—
367#6923—48no—
368C4×C61—21no—
369C4×C61—21no—
370C4×C61—21no—
371C4×C61—21no—
372C4×C61—21no—
373C4×C61—41no—
374C4×C61—41no—
375C4×C61—41no—
376C4×C61C2×#10412yes—
377Dic61—21no—
378Dic61—21no—
379Dic61—21no—
380Dic61—21no—
381Dic61—21no—
382Dic61—41no—
383Dic61—41no—
384Dic61—41no—
385Dic61C2×#10412yes—
386C2×#529—611no—
387C2×#431—611no—
388C2×#376—611no—
389#1500—612no—
390#1500—612no—
391#1500—612no—
392#1500—612no—
393C2×#328—612no—
394C2×#327—612no—
395C2×C61—22no—
396C2×C61—81no—
397C2×C61C2×#41011yescharacteristic
398C2×C61C2×#41611yescharacteristic
399C2×C61C22×#10411yescharacteristic
400D61—22no—
401D61—81no—
402D61#150014yescomplemented
403#529—611no—
404#529—611no—
405#529—611no—
406#529—611no—
407#529—611no—
408#529—611no—
409#529—611no—
410#529—1221no—
411#529—1221no—
412#529—1221no—
413#529—1221no—
414#529#692311yescharacteristic, complemented
415C2×#126—1221no—
416C2×#125—611no—
417C2×#124—611no—
418C2×#123—1221no—
419C2×C22⋊Q8—611no—
420C2×#121—611no—
421C2×C4×Q8—611no—
422C2×C4×D4—611no—
423C2×C4×D4—1221no—
424C2×#117—1221no—
425C22×C42—611no—
426C22×C42—1221no—
427#431—612no—
428#431—612no—
429#431—1221no—
430#431—1221no—
431C2×C4⋊C8—1221no—
432C2×C22⋊C8—612no—
433C2×C4×C8—1221no—
434#376—612no—
435#376—612no—
436#376—1221no—
437#376—1221no—
438C2×#95—612no—
439C2×#95—1221no—
440#328—614no—
441#328—614no—
442#327—614no—
443#327—614no—
444C61C2×#150011yescharacteristic, complemented, Sylow
445C22×Q8—611no—
446C22×D4—611no—
447C22×D4—1221no—
448C23×C4—611no—
449C23×C4—611no—
450C23×C4—611no—
451C23×C4—1221no—
452C23×C4—1222no—
453C22×C8—1222no—
454#126—21no—
455#126—1221no—
456#126—1221no—
457#126—1221no—
458#126—1221no—
459#126—1221no—
460#126—1221no—
461#126—1221no—
462#125—611no—
463#125—611no—
464#125—611no—
465#125—1221no—
466#125—1221no—
467#125C2×#692311yescharacteristic, complemented
468#124—611no—
469#124—611no—
470#124—611no—
471#124—1221no—
472#124—1221no—
473#124C2×#692311yescharacteristic, complemented
474#123—21no—
475#123—1221no—
476#123—1221no—
477#123—1221no—
478#123—1221no—
479#123—1221no—
480#123—1221no—
481#123—1221no—
482C22⋊Q8—611no—
483C22⋊Q8—611no—
484C22⋊Q8—611no—
485C22⋊Q8—1221no—
486C22⋊Q8—1221no—
487C22⋊Q8C2×#692311yescharacteristic
488#121—611no—
489#121—611no—
490#121—611no—
491#121—1221no—
492#121—1221no—
493#121C2×#692311yescharacteristic
494C4×Q8—611no—
495C4×Q8—611no—
496C4×Q8—611no—
497C4×Q8—1221no—
498C4×Q8—1221no—
499C4×Q8C2×#692311yescharacteristic, complemented
500C4×D4—21no—
501C4×D4—611no—
502C4×D4—611no—
503C4×D4—611no—
504C4×D4—1221no—
505C4×D4—1221no—
506C4×D4—1221no—
507C4×D4—1221no—
508C4×D4—1221no—
509C4×D4—1221no—
510C4×D4—1221no—
511C4×D4—1221no—
512C4×D4—1221no—
513C4×D4C2×#692311yescharacteristic, complemented
514#117—21no—
515#117—1221no—
516#117—1221no—
517#117—1221no—
518#117—1221no—
519#117—1221no—
520#117—1221no—
521#117—1221no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—611no—
524C2×C4⋊C4—1221no—
525C2×C4⋊C4—1221no—
526C2×C4⋊C4—1221no—
527C2×C4⋊C4—1221no—
528C2×C22⋊C4—1221no—
529C2×C22⋊C4—1221no—
530C2×C22⋊C4—1221no—
531C2×C22⋊C4—1221no—
532C2×C22⋊C4—1221no—
533C2×C42—611no—
534C2×C42—611no—
535C2×C42—611no—
536C2×C42—611no—
537C2×C42—611no—
538C2×C42—611no—
539C2×C42—611no—
540C2×C42—611no—
541C2×C42—611no—
542C2×C42—611no—
543C2×C42—611no—
544C2×C42—1221no—
545C2×C42—1222no—
546C2×C42—1222no—
547C2×C42—1228no—
548C2×C42C2×#692311yescharacteristic
549C4⋊C8—1222no—
550C4⋊C8—1222no—
551C22⋊C8—614no—
552C22⋊C8—1222no—
553C4×C8—1222no—
554C4×C8—1222no—
555#95—614no—
556#95—1222no—
557#95—1222no—
558#95—1222no—
559C24—611no—
560C24—1221no—
561C2×Q8—611no—
562C2×Q8—1221no—
563C2×Q8—2442no—
564C2×Q8C22×#692311yescharacteristic
565C2×D4—21no—
566C2×D4—611no—
567C2×D4—1221no—
568C2×D4—1221no—
569C2×D4—1221no—
570C2×D4—1221no—
571C2×D4—2442no—
572C2×D4—2444no—
573C2×D4C22×#692311yescharacteristic
574C22×C4—21no—
575C22×C4—611no—
576C22×C4—611no—
577C22×C4—611no—
578C22×C4—611no—
579C22×C4—611no—
580C22×C4—611no—
581C22×C4—611no—
582C22×C4—611no—
583C22×C4—611no—
584C22×C4—611no—
585C22×C4—611no—
586C22×C4—611no—
587C22×C4—611no—
588C22×C4—611no—
589C22×C4—611no—
590C22×C4—1224no—
591C22×C4—1221no—
592C22×C4—1224no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4—1224no—
598C22×C4—1228no—
599C22×C4—1221no—
600C22×C4—2444no—
601C22×C4—2442no—
602C22×C4—2444no—
603C22×C4—2444no—
604C22×C4C22⋊#692311yescharacteristic
605C22×C4C22⋊#692311yescharacteristic
606C22×C4C22×#692311yescharacteristic
607C2×C8—1224no—
608C2×C8—2444no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—611no—
614C4⋊C4—611no—
615C4⋊C4—1221no—
616C4⋊C4—1221no—
617C4⋊C4—1221no—
618C4⋊C4—1221no—
619C4⋊C4—1221no—
620C4⋊C4—1221no—
621C4⋊C4—1221no—
622C4⋊C4—1221no—
623C4⋊C4—1221no—
624C4⋊C4—1221no—
625C4⋊C4—1221no—
626C4⋊C4—1221no—
627C4⋊C4—1221no—
628C4⋊C4—1221no—
629C4⋊C4C22×#692311yescharacteristic
630C4⋊C4C22×#692311yescharacteristic
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—1221no—
637C22⋊C4—1221no—
638C22⋊C4—1221no—
639C22⋊C4—1221no—
640C22⋊C4—1221no—
641C22⋊C4—1221no—
642C22⋊C4—1221no—
643C22⋊C4—1221no—
644C22⋊C4—1221no—
645C22⋊C4—1221no—
646C22⋊C4—1221no—
647C22⋊C4—1221no—
648C22⋊C4—1221no—
649C22⋊C4—1221no—
650C22⋊C4—1221no—
651C42—21no—
652C42—611no—
653C42—611no—
654C42—611no—
655C42—611no—
656C42—611no—
657C42—611no—
658C42—611no—
659C42—611no—
660C42—611no—
661C42—611no—
662C42—611no—
663C42—611no—
664C42—1221no—
665C42—1221no—
666C42—1228no—
667C42—1228no—
668C42—1221no—
669C42C22⋊#692311yescharacteristic
670C42C22⋊#692311yescharacteristic
671C42C22×#692311yescharacteristic
672C42C22×#692311yescharacteristic
673C23—21no—
674C23—611no—
675C23—614no—
676C23—611no—
677C23—1222no—
678C23—1222no—
679C23—1221no—
680C23—2442no—
681C23—2442no—
682C23—2442no—
683C23C2×C22⋊#692311yescharacteristic
684Q8—41no—
685Q8—2441no—
686Q8—2442no—
687D4—41no—
688D4—42no—
689D4—2441no—
690D4—2442no—
691D4—2442no—
692D4—2442no—
693D4—2442no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—611no—
702C2×C4—614no—
703C2×C4—611no—
704C2×C4—611no—
705C2×C4—611no—
706C2×C4—611no—
707C2×C4—611no—
708C2×C4—1222no—
709C2×C4—1222no—
710C2×C4—1222no—
711C2×C4—1222no—
712C2×C4—1222no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—1222no—
716C2×C4—1222no—
717C2×C4—1222no—
718C2×C4—1222no—
719C2×C4—1228no—
720C2×C4—1221no—
721C2×C4—1221no—
722C2×C4—1221no—
723C2×C4—2441no—
724C2×C4—2441no—
725C2×C4—2442no—
726C2×C4—2442no—
727C2×C4—2442no—
728C2×C4—2442no—
729C2×C4—2442no—
730C2×C4—2441no—
731C2×C4—2444no—
732C2×C4—24416no—
733C2×C4—2444no—
734C2×C4—2442no—
735C2×C4C2×C22⋊#692311yescharacteristic
736C2×C4C2×C22⋊#692311yescharacteristic
737C2×C4C2×C22⋊#692311yescharacteristic
738C2×C4C2×C22⋊#692311yescharacteristic
739C2×C4C2×C22⋊#692311yescharacteristic
740C2×C4C23×#692311yescharacteristic
741C8—2444no—
742C22—21no—
743C22—21no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—612no—
748C22—612no—
749C22—612no—
750C22—612no—
751C22—1228no—
752C22—1221no—
753C22—1221no—
754C22—4884no—
755C22—2441no—
756C22—2441no—
757C22—2441no—
758C22#1684075212yes—
759C22C22×C22⋊#692311yescharacteristic
760C4—21no—
761C4—21no—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—41no—
766C4—41no—
767C4—41no—
768C4—612no—
769C4—1221no—
770C4—1221no—
771C4—1221no—
772C4—1221no—
773C4—1221no—
774C4—2448no—
775C4—2441no—
776C4—2441no—
777C4—2441no—
778C4D61⋊#10412yes—
779C2—22no—
780C2—81no—
781C2—614no—
782C2—1222no—
783C2—4881no—
784C2D61⋊#41011yescharacteristic
785C2C2×#1684075211yescharacteristic
786C2C2×D61⋊#10411yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#529C4
socleC22×C61C22×C22⋊C4
prime radical#121×D61C22
cosocleC2×C4×D61C24
hypercenter#529#6923
hypocenterC61C2×#1500
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. D61⋊#431C2semidirect
2. C2×#16840698C2semidirect
3. #21461193C2semidirect
4. #21461192C2semidirect
5. #21461191C2semidirect
6. #21461190C2semidirect
7. D61⋊#328C2semidirect
11. #16840781C22semidirect
12. #16840780C22semidirect
20. #16840698C22semidirect
21. #16840698C22semidirect
24. #16840616C22semidirect
25. #16840615C22semidirect
29. #16840298C4semidirect
31. #16840296C4semidirect
34. #16840293C4semidirect
40. #125×D61C4semidirect
41. #124×D61C4semidirect
45. C4×Q8×D61C4semidirect
47. C4×D4×D61C4semidirect
50. C61×#529C4semidirect
80. #14519769C2×C4semidirect
81. #14519768C2×C4semidirect
82. #14519768C2×C4semidirect
85. #14519766C2×C4semidirect
86. #14519765C2×C4semidirect
87. #14519764C2×C4semidirect
107. Q8×Dic61C2×C4semidirect
109. C4×Dic122C2×C4semidirect
111. #14519742C2×C4semidirect
113. C4×D244C2×C4semidirect
115. D4×Dic61C2×C4semidirect
117. #14519739C2×C4semidirect
155. #125×C61C2×C4semidirect
156. #124×C61C2×C4semidirect
160. C4×Q8×C61C2×C4semidirect
162. C4×D4×C61C2×C4semidirect
402. D61#1500semidirect
414. #529#6923semidirect
444. C61C2×#1500semidirect
467. #125C2×#6923semidirect
473. #124C2×#6923semidirect
499. C4×Q8C2×#6923semidirect
513. C4×D4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4312
C2×#168406982
#214611932
#214611922
#214611912
#214611902
D61⋊#3282
D61⋊#3272
#529×D612
C2×#150061