Finite Group Databasebeta

← D61⋊#1509 #30610932

Subgroups — D61⋊#1509 #30610932

Order 15616.

1206 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#432C211yesmaximal, characteristic, complemented
2C2×C4×C4⋊#6923C211yesmaximal, characteristic, complemented
3#21461223C212yesmaximal, complemented
4#21461222C212yesmaximal, complemented
5#21461221C212yesmaximal, complemented
6#21461220C212yesmaximal, complemented
7D61⋊#328C212yesmaximal, complemented
8D61⋊#327C212yesmaximal
9#529×D61C211yesmaximal, characteristic
10C22×C4⋊#6923—21no—
11C22×C4×#6923—21no—
12#16840785C2212yescomplemented
13#16840784C2212yescomplemented
14#16840783—21no—
15#16840782—21no—
16D61⋊(C4⋊C8)—21no—
17D61⋊(C22⋊C8)C2212yes—
18#16840721—21no—
19C4×C4⋊#6923—21no—
20C4×C4⋊#6923—21no—
21C4×C4⋊#6923C2212yescomplemented
22C4×C4⋊#6923C2212yescomplemented
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—
56C2×C4×#6923—22no—
57C2×C4×#6923—22no—
58C2×C4×#6923—44no—
59#14519844—22no—
60C4⋊#92420—22no—
61#14519834C2314yes—
62C22⋊#92420—22no—
63#14519832—22no—
64#14519832—22no—
65(C2×#6923)⋊C4—22no—
66(C2×#6923)⋊C4C2314yes—
67C2×Q8×D61C2×C411yescharacteristic
68C2×D4×D61—21no—
69C2×D4×D61C2×C411yescharacteristic
70C22×C4×D61—21no—
71C22×C4×D61D411yescharacteristic
72C22×C4×D61D411yescharacteristic
73C22×C4×D61C2311yescharacteristic
74#14519772—21no—
75#14519772—21no—
76#14519772—21no—
77#14519771—21no—
78#14519770—21no—
79#14519770—21no—
80#14519770—21no—
81#14519769C2×C411yescharacteristic, complemented
82#14519768C2×C411yescharacteristic, complemented
83#14519768C2×C411yescharacteristic, complemented
84#14519767—21no—
85#14519767—21no—
86#14519766C2×C411yescharacteristic, complemented
87#14519765C2×C411yescharacteristic, complemented
88#14519764C2×C411yescharacteristic, complemented
89#14519763—21no—
90#14519763—21no—
91#14519762—21no—
92#14519762—21no—
93#14519761—21no—
94#14519760—21no—
95#14519759—21no—
96#14519759—21no—
97#14519758—21no—
98#14519757C2311yescharacteristic
99#14519756C2×C411yescharacteristic
100#14519755—21no—
101#14519754—21no—
102#14519753C2311yescharacteristic
103#14519752C2311yescharacteristic
104#14519751C2×C411yescharacteristic
105#14519750—21no—
106#14519749—21no—
107#14519748C2311yescharacteristic
108Q8×Dic61C2×C411yescharacteristic, complemented
109C4×Dic122—21no—
110C4×Dic122C2×C411yescharacteristic, complemented
111#14519742—21no—
112#14519742C2×C411yescharacteristic, complemented
113C4×D244—21no—
114C4×D244C2×C411yescharacteristic, complemented
115D4×Dic61—21no—
116D4×Dic61C2×C411yescharacteristic, complemented
117#14519739—21no—
118#14519739C2×C411yescharacteristic, complemented
119C4×C22⋊D61—21no—
120C4×C22⋊D61—21no—
121C4×C22⋊D61—21no—
122#14519737—21no—
123#14519737—21no—
124#14519737—21no—
125#14519736—21no—
126#14519735—21no—
127#14519735—21no—
128#14519734—21no—
129#14519734—21no—
130#14519733—21no—
131#14519733—21no—
132C4⋊C4×D61—21no—
133C4⋊C4×D61—21no—
134C4⋊C4×D61—21no—
135C4⋊C4×D61—21no—
136C4⋊C4×D61C2×C411yescharacteristic
137C4⋊C4×D61C2×C411yescharacteristic
138C22⋊C4×D61—21no—
139C22⋊C4×D61—21no—
140C22⋊C4×D61—21no—
141C22⋊C4×D61—21no—
142C22⋊C4×D61—21no—
143C2×C4×Dic61C2×C411yescharacteristic
144C2×C4×Dic61D411yescharacteristic
145C2×C4×Dic61D411yescharacteristic
146C42×D61—21no—
147C42×D61C2×C411yescharacteristic
148C42×D61C2×C411yescharacteristic
149C42×D61D411yescharacteristic
150C42×D61D411yescharacteristic
151C42×D61D411yescharacteristic
152C42×D61D411yescharacteristic
153C42×D61C2311yescharacteristic
154C42×D61C2311yescharacteristic
155#126×C61—21no—
156#125×C61C2×C411yescharacteristic, complemented
157#124×C61C2×C411yescharacteristic, complemented
158#123×C61—21no—
159C22⋊Q8×C61C2×C411yescharacteristic
160#121×C61C2×C411yescharacteristic
161C4×Q8×C61C2×C411yescharacteristic, complemented
162C4×D4×C61—21no—
163C4×D4×C61C2×C411yescharacteristic, complemented
164#117×C61—21no—
165C2×C42×C61C2×C411yescharacteristic
166C23×D61—21no—
167C23×D61C2×D411yescharacteristic
168C22×#6923—28no—
169C22×#6923—24no—
170C22×#6923—44no—
171C22×#6923—44no—
172C2×Q8×C61C22×C411yescharacteristic
173C2×D4×C61—21no—
174C2×D4×C61C22×C411yescharacteristic
175C22×C4×C61—21no—
176C22×C4×C61C22⋊C411yescharacteristic
177C22×C4×C61C22⋊C411yescharacteristic
178C22×C4×C61C22×C411yescharacteristic
179C2×C22⋊D61—21no—
180C2×C22⋊D61—21no—
181C2×C22⋊D61—21no—
182C22×Dic61—21no—
183C22×Dic61C22⋊C411yescharacteristic
184C22×Dic61C22⋊C411yescharacteristic
185C22×Dic61C2×D411yescharacteristic
186Q8×D61—42no—
187D4×D61—42no—
188D4×D61—42no—
189D4×D61—42no—
190C2×D244—21no—
191C2×D244C22×C411yescharacteristic
192C2×C4×D61—22no—
193C2×C4×D61—22no—
194C2×C4×D61—24no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61—42no—
201C2×C4×D61—44no—
202C2×C4×D61C22⋊C411yescharacteristic
203C2×C4×D61C22⋊C411yescharacteristic
204C2×C4×D61C22⋊C411yescharacteristic
205C2×C4×D61C22⋊C411yescharacteristic
206C2×C4×D61C22×C411yescharacteristic
207C2×C4×D61C2×D411yescharacteristic
208C2×C4×D61C2×D411yescharacteristic
209C2×C4×D61C2×D411yescharacteristic
210C2×C4×D61C2×D411yescharacteristic
211C2×C4×D61C2×D411yescharacteristic
212C2×C4×D61C2×D411yescharacteristic
213C2×C4×D61C2411yescharacteristic
214C2×Dic122—21no—
215C2×Dic122C22×C411yescharacteristic
216C2×#92420—24no—
217C4⋊#6923—28no—
218C4⋊#6923—28no—
219C4×#6923—44no—
220C4×#6923—44no—
221D61⋊C8—44no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61—21no—
226C4⋊C4×C61C22×C411yescharacteristic
227C4⋊C4×C61C22×C411yescharacteristic
228C22⋊C4×C61—21no—
229C22⋊C4×C61—21no—
230C22⋊C4×C61—21no—
231C22⋊C4×C61—21no—
232C22⋊C4×C61—21no—
233C42×C61—21no—
234C42×C61C22⋊C411yescharacteristic
235C42×C61C22⋊C411yescharacteristic
236C42×C61C22×C411yescharacteristic
237C42×C61C22×C411yescharacteristic
238C22⋊Dic61—21no—
239C22⋊Dic61—21no—
240C22⋊Dic61—21no—
241C22⋊Dic61—21no—
242C22⋊Dic61—21no—
243#11758198—21no—
244#11758198—21no—
245#11758198—21no—
246#11758198—21no—
247#11758198—21no—
248#11758198—21no—
249#11758198—21no—
250#11758198—21no—
251#11758198—21no—
252#11758198—21no—
253C4⋊Dic61—21no—
254C4⋊Dic61—21no—
255C4⋊Dic61—21no—
256C4⋊Dic61—21no—
257C4⋊Dic61C22×C411yescharacteristic
258C4⋊Dic61C22×C411yescharacteristic
259#11758196—21no—
260#11758196—21no—
261#11758196—21no—
262#11758196—21no—
263#11758196—21no—
264#11758196—21no—
265#11758196—21no—
266#11758196—21no—
267#11758196—21no—
268#11758196—21no—
269C4×Dic61—21no—
270C4×Dic61—21no—
271C4×Dic61—21no—
272C4×Dic61C22⋊C411yescharacteristic
273C4×Dic61C22⋊C411yescharacteristic
274C4×Dic61C22⋊C411yescharacteristic
275C4×Dic61C22⋊C411yescharacteristic
276C4×Dic61C22⋊C411yescharacteristic
277C4×Dic61C22⋊C411yescharacteristic
278C4×Dic61C22×C411yescharacteristic
279C4×Dic61C22×C411yescharacteristic
280C4×Dic61C2×D411yescharacteristic
281C4×Dic61C2×D411yescharacteristic
282C4×Dic61C2×D411yescharacteristic
283C4×Dic61C2×D411yescharacteristic
284C23×C61—21no—
285C23×C61C2×C22⋊C411yescharacteristic
286C22×D61—22no—
287C22×D61—22no—
288C22×D61—21no—
289C22×D61—42no—
290C22×D61—42no—
291C22×D61—42no—
292C22×D61C2×C22⋊C411yescharacteristic
293C22×D61AGL(1,ℤ/8)12yes—
294C22×D61#13712yes—
295C22×D61C22×D411yescharacteristic
296C2×#6923—28no—
297C2×#6923—44no—
298C2×#6923—416no—
299C2×#6923—44no—
300Q8×C61—41no—
301D4×C61—41no—
302D4×C61—42no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—41no—
309C2×C4×C61—42no—
310C2×C4×C61C2×C22⋊C411yescharacteristic
311C2×C4×C61C2×C22⋊C411yescharacteristic
312C2×C4×C61C2×C22⋊C411yescharacteristic
313C2×C4×C61C2×C22⋊C411yescharacteristic
314C2×C4×C61C2×C22⋊C411yescharacteristic
315C2×C4×C61C23×C411yescharacteristic
316C22⋊D61—42no—
317C22⋊D61—42no—
318C22⋊D61—41no—
319C22⋊D61—41no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—41no—
326C2×Dic61—42no—
327C2×Dic61C2×C22⋊C411yescharacteristic
328C2×Dic61C2×C22⋊C411yescharacteristic
329C2×Dic61C2×C22⋊C411yescharacteristic
330C2×Dic61C2×C22⋊C411yescharacteristic
331C2×Dic61C2×C22⋊C411yescharacteristic
332C2×Dic61C22×D411yescharacteristic
333D244—41no—
334D244—41no—
335D244—41no—
336C4×D61—21no—
337C4×D61—21no—
338C4×D61—21no—
339C4×D61—21no—
340C4×D61—22no—
341C4×D61—22no—
342C4×D61—22no—
343C4×D61—22no—
344C4×D61—22no—
345C4×D61—22no—
346C4×D61—22no—
347C4×D61—41no—
348C4×D61—41no—
349C4×D61—42no—
350C4×D61—42no—
351C4×D61—42no—
352C4×D61—42no—
353C4×D61—42no—
354C4×D61#10414yes—
355Dic122—42no—
356Dic122—41no—
357#92420—44no—
358C2×#1509—611nomaximal, Sylow
359C22×C61—21no—
360C22×C61—21no—
361C22×C61—41no—
362C22×C61—41no—
363C22×C61—41no—
364C22×C61#41712yes—
365C22×C61C22×C22⋊C411yescharacteristic
366C2×D61—21no—
367C2×D61—21no—
368C2×D61—24no—
369C2×D61—24no—
370C2×D61—41no—
371C2×D61—41no—
372C2×D61—41no—
373C2×D61—84no—
374C2×D61#41012yes—
375C2×D61#41712yes—
376C2×D61C2×#10412yes—
377C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
378C2×D61C2×#13711yescharacteristic
379#6923—48no—
380C4×C61—21no—
381C4×C61—21no—
382C4×C61—21no—
383C4×C61—21no—
384C4×C61—21no—
385C4×C61—41no—
386C4×C61—41no—
387C4×C61—41no—
388C4×C61C2×#10412yes—
389Dic61—21no—
390Dic61—21no—
391Dic61—21no—
392Dic61—21no—
393Dic61—21no—
394Dic61—41no—
395Dic61—41no—
396Dic61—41no—
397Dic61C2×#10412yes—
398C2×#529—611no—
399C2×#432—611no—
400C2×C4×C4⋊C4—611no—
401#1509—612no—
402#1509—612no—
403#1509—612no—
404#1509—612no—
405C2×#328—612no—
406C2×#327—612no—
407C2×C61—22no—
408C2×C61—81no—
409C2×C61C2×#41011yescharacteristic
410C2×C61C2×#41711yescharacteristic
411C2×C61C22×#10411yescharacteristic
412D61—21no—
413D61—21no—
414D61—81no—
415D61#150914yescomplemented
416#529—611no—
417#529—611no—
418#529—611no—
419#529—611no—
420#529—611no—
421#529—611no—
422#529—611no—
423#529—1221no—
424#529—1221no—
425#529—1221no—
426#529—1221no—
427#529#692311yescharacteristic, complemented
428C2×#126—1221no—
429C2×#125—611no—
430C2×#124—611no—
431C2×#123—1221no—
432C2×C22⋊Q8—611no—
433C2×#121—611no—
434C2×C4×Q8—611no—
435C2×C4×D4—611no—
436C2×C4×D4—1221no—
437C2×#117—1221no—
438C22×C4⋊C4—1221no—
439C22×C42—611no—
440C22×C42—1221no—
441#432—612no—
442#432—612no—
443#432—1221no—
444#432—1221no—
445C2×C4⋊C8—1221no—
446C2×C22⋊C8—612no—
447C2×#97—1221no—
448C4×C4⋊C4—612no—
449C4×C4⋊C4—612no—
450C4×C4⋊C4—1221no—
451C4×C4⋊C4—1221no—
452C2×#95—612no—
453#328—614no—
454#328—614no—
455#327—614no—
456#327—614no—
457C61C2×#150911yescharacteristic, complemented, Sylow
458C22×Q8—611no—
459C22×D4—611no—
460C22×D4—1221no—
461C23×C4—611no—
462C23×C4—611no—
463C23×C4—611no—
464C23×C4—1221no—
465C23×C4—1222no—
466C22×C8—1222no—
467#126—21no—
468#126—1221no—
469#126—1221no—
470#126—1221no—
471#126—1221no—
472#126—1221no—
473#126—1221no—
474#126—1221no—
475#125—611no—
476#125—611no—
477#125—611no—
478#125—1221no—
479#125—1221no—
480#125C2×#692311yescharacteristic, complemented
481#124—611no—
482#124—611no—
483#124—611no—
484#124—1221no—
485#124—1221no—
486#124C2×#692311yescharacteristic, complemented
487#123—21no—
488#123—1221no—
489#123—1221no—
490#123—1221no—
491#123—1221no—
492#123—1221no—
493#123—1221no—
494#123—1221no—
495C22⋊Q8—611no—
496C22⋊Q8—611no—
497C22⋊Q8—611no—
498C22⋊Q8—1221no—
499C22⋊Q8—1221no—
500C22⋊Q8C2×#692311yescharacteristic
501#121—611no—
502#121—611no—
503#121—611no—
504#121—1221no—
505#121—1221no—
506#121C2×#692311yescharacteristic
507C4×Q8—611no—
508C4×Q8—611no—
509C4×Q8—611no—
510C4×Q8—1221no—
511C4×Q8—1221no—
512C4×Q8C2×#692311yescharacteristic, complemented
513C4×D4—21no—
514C4×D4—611no—
515C4×D4—611no—
516C4×D4—611no—
517C4×D4—1221no—
518C4×D4—1221no—
519C4×D4—1221no—
520C4×D4—1221no—
521C4×D4—1221no—
522C4×D4—1221no—
523C4×D4—1221no—
524C4×D4—1221no—
525C4×D4—1221no—
526C4×D4C2×#692311yescharacteristic, complemented
527#117—21no—
528#117—1221no—
529#117—1221no—
530#117—1221no—
531#117—1221no—
532#117—1221no—
533#117—1221no—
534#117—1221no—
535C2×C4⋊C4—611no—
536C2×C4⋊C4—611no—
537C2×C4⋊C4—1221no—
538C2×C4⋊C4—1221no—
539C2×C4⋊C4—1221no—
540C2×C4⋊C4—1221no—
541C2×C4⋊C4—1222no—
542C2×C4⋊C4—1222no—
543C2×C4⋊C4—1228no—
544C2×C22⋊C4—1221no—
545C2×C22⋊C4—1221no—
546C2×C22⋊C4—1221no—
547C2×C22⋊C4—1221no—
548C2×C22⋊C4—1221no—
549C2×C42—611no—
550C2×C42—611no—
551C2×C42—611no—
552C2×C42—611no—
553C2×C42—611no—
554C2×C42—611no—
555C2×C42—611no—
556C2×C42—611no—
557C2×C42—611no—
558C2×C42—611no—
559C2×C42—611no—
560C2×C42—1221no—
561C2×C42—1222no—
562C2×C42—1222no—
563C2×C42—2444no—
564C2×C42C2×#692311yescharacteristic
565C4⋊C8—1222no—
566C4⋊C8—1222no—
567C22⋊C8—614no—
568C22⋊C8—1222no—
569#97—1222no—
570#97—1222no—
571#95—614no—
572#95—1222no—
573C24—611no—
574C24—1221no—
575C2×Q8—611no—
576C2×Q8—1221no—
577C2×Q8—2442no—
578C2×Q8C22×#692311yescharacteristic
579C2×D4—21no—
580C2×D4—611no—
581C2×D4—1221no—
582C2×D4—1221no—
583C2×D4—1221no—
584C2×D4—1221no—
585C2×D4—2442no—
586C2×D4—2442no—
587C2×D4—2442no—
588C2×D4C22×#692311yescharacteristic
589C22×C4—21no—
590C22×C4—611no—
591C22×C4—611no—
592C22×C4—611no—
593C22×C4—611no—
594C22×C4—611no—
595C22×C4—611no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—1224no—
606C22×C4—1221no—
607C22×C4—1222no—
608C22×C4—1222no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1224no—
614C22×C4—1228no—
615C22×C4—1221no—
616C22×C4—2444no—
617C22×C4—2442no—
618C22×C4—2444no—
619C22×C4—2444no—
620C22×C4C22⋊#692311yescharacteristic
621C22×C4C22⋊#692311yescharacteristic
622C22×C4C22×#692311yescharacteristic
623C2×C8—1224no—
624C2×C8—2444no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—611no—
630C4⋊C4—611no—
631C4⋊C4—1221no—
632C4⋊C4—1221no—
633C4⋊C4—1221no—
634C4⋊C4—1221no—
635C4⋊C4—1221no—
636C4⋊C4—1221no—
637C4⋊C4—1221no—
638C4⋊C4—1221no—
639C4⋊C4—1221no—
640C4⋊C4—1221no—
641C4⋊C4—1228no—
642C4⋊C4—1228no—
643C4⋊C4—1221no—
644C4⋊C4—1221no—
645C4⋊C4—1221no—
646C4⋊C4—1221no—
647C4⋊C4C22×#692311yescharacteristic
648C4⋊C4C22×#692311yescharacteristic
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—1221no—
655C22⋊C4—1221no—
656C22⋊C4—1221no—
657C22⋊C4—1221no—
658C22⋊C4—1221no—
659C22⋊C4—1221no—
660C22⋊C4—1221no—
661C22⋊C4—1221no—
662C22⋊C4—1221no—
663C22⋊C4—1221no—
664C22⋊C4—1221no—
665C22⋊C4—1221no—
666C22⋊C4—1221no—
667C22⋊C4—1221no—
668C22⋊C4—1221no—
669C42—21no—
670C42—611no—
671C42—611no—
672C42—611no—
673C42—611no—
674C42—611no—
675C42—611no—
676C42—611no—
677C42—611no—
678C42—611no—
679C42—611no—
680C42—611no—
681C42—611no—
682C42—1221no—
683C42—1221no—
684C42—1221no—
685C42—2444no—
686C42—2444no—
687C42C22⋊#692311yescharacteristic
688C42C22⋊#692311yescharacteristic
689C42C22×#692311yescharacteristic
690C42C22×#692311yescharacteristic
691C23—21no—
692C23—611no—
693C23—612no—
694C23—612no—
695C23—611no—
696C23—1222no—
697C23—1222no—
698C23—1221no—
699C23—2442no—
700C23—2442no—
701C23—2442no—
702C23C2×C22⋊#692311yescharacteristic
703Q8—41no—
704Q8—2441no—
705Q8—2442no—
706D4—41no—
707D4—42no—
708D4—2441no—
709D4—2441no—
710D4—2441no—
711D4—2442no—
712D4—2441no—
713D4—2441no—
714D4—2442no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—611no—
723C2×C4—614no—
724C2×C4—611no—
725C2×C4—611no—
726C2×C4—611no—
727C2×C4—611no—
728C2×C4—611no—
729C2×C4—1222no—
730C2×C4—1221no—
731C2×C4—1221no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1221no—
736C2×C4—1221no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1228no—
743C2×C4—1221no—
744C2×C4—1221no—
745C2×C4—1221no—
746C2×C4—2441no—
747C2×C4—2441no—
748C2×C4—2442no—
749C2×C4—2442no—
750C2×C4—2442no—
751C2×C4—2442no—
752C2×C4—2442no—
753C2×C4—2441no—
754C2×C4—2444no—
755C2×C4—24416no—
756C2×C4—2444no—
757C2×C4—2442no—
758C2×C4C2×C22⋊#692311yescharacteristic
759C2×C4C2×C22⋊#692311yescharacteristic
760C2×C4C2×C22⋊#692311yescharacteristic
761C2×C4C2×C22⋊#692311yescharacteristic
762C2×C4C2×C22⋊#692311yescharacteristic
763C2×C4C23×#692311yescharacteristic
764C8—2444no—
765C22—21no—
766C22—21no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—612no—
771C22—612no—
772C22—612no—
773C22—611no—
774C22—611no—
775C22—1224no—
776C22—1224no—
777C22—1221no—
778C22—1221no—
779C22—4884no—
780C22—2441no—
781C22—2441no—
782C22—2441no—
783C22#1684075312yes—
784C22C22×C22⋊#692311yescharacteristic
785C4—21no—
786C4—21no—
787C4—21no—
788C4—21no—
789C4—21no—
790C4—41no—
791C4—41no—
792C4—41no—
793C4—612no—
794C4—1221no—
795C4—1221no—
796C4—1221no—
797C4—1221no—
798C4—1221no—
799C4—2448no—
800C4—2441no—
801C4—2441no—
802C4—2441no—
803C4D61⋊#10412yes—
804C2—22no—
805C2—81no—
806C2—614no—
807C2—1221no—
808C2—1221no—
809C2—4881no—
810C2D61⋊#41011yescharacteristic
811C2C2×#1684075311yescharacteristic
812C2C2×D61⋊#10411yescharacteristic
subgroupG/H
centerC22C22×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×#1509
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. D61⋊#432C2semidirect
2. C2×C4×C4⋊#6923C2semidirect
3. #21461223C2semidirect
4. #21461222C2semidirect
5. #21461221C2semidirect
6. #21461220C2semidirect
7. D61⋊#328C2semidirect
12. #16840785C22semidirect
13. #16840784C22semidirect
21. C4×C4⋊#6923C22semidirect
22. C4×C4⋊#6923C22semidirect
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
81. #14519769C2×C4semidirect
82. #14519768C2×C4semidirect
83. #14519768C2×C4semidirect
86. #14519766C2×C4semidirect
87. #14519765C2×C4semidirect
88. #14519764C2×C4semidirect
108. Q8×Dic61C2×C4semidirect
110. C4×Dic122C2×C4semidirect
112. #14519742C2×C4semidirect
114. C4×D244C2×C4semidirect
116. D4×Dic61C2×C4semidirect
118. #14519739C2×C4semidirect
156. #125×C61C2×C4semidirect
157. #124×C61C2×C4semidirect
161. C4×Q8×C61C2×C4semidirect
163. C4×D4×C61C2×C4semidirect
415. D61#1509semidirect
427. #529#6923semidirect
457. C61C2×#1509semidirect
480. #125C2×#6923semidirect
486. #124C2×#6923semidirect
512. C4×Q8C2×#6923semidirect
526. C4×D4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4322
C2×C4×C4⋊#69232
#214612232
#214612222
#214612212
#214612202
D61⋊#3282
D61⋊#3272
#529×D612
C2×#150961