Finite Group Databasebeta

← D61×#1483 #29646538

Subgroups — D61×#1483 #29646538

Order 15616.

1162 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#529×D61C211yesmaximal, characteristic
2C2×C4⋊C8×D61C211yesmaximal, characteristic, complemented
3C4×M16×D61C211yesmaximal, characteristic, complemented
4#21444233C211yesmaximal, characteristic, complemented
5#21444232C211yesmaximal, characteristic, complemented
6#21444231C212yesmaximal, complemented
7#21444230C211yesmaximal, characteristic, complemented
8#21444229C212yesmaximal, complemented
9Q8⋊C8×D61C212yesmaximal, complemented
10D4⋊C8×D61C212yesmaximal, complemented
11C61×#1483C211yesmaximal, characteristic, complemented
12C2×M16×D61—21no—
13C22×C8×D61—21no—
14#16840299C2211yescharacteristic
15#16840298C411yescharacteristic
16#16840297C411yescharacteristic
17#16840296C2211yescharacteristic
18#16840295—21no—
19#16840294C2211yescharacteristic
20#16840293C411yescharacteristic
21#16840292—21no—
22#16840291C411yescharacteristic
23#16840290—21no—
24#16840289—21no—
25#126×D61—21no—
26#125×D61C411yescharacteristic
27#124×D61C411yescharacteristic
28#123×D61—21no—
29C22⋊Q8×D61C411yescharacteristic
30#121×D61C411yescharacteristic
31C4×Q8×D61C2211yescharacteristic
32C4×D4×D61—21no—
33C4×D4×D61C2211yescharacteristic
34#117×D61—21no—
35C2×C42×D61C2211yescharacteristic
36C2×C4⋊#92418C2211yescharacteristic, complemented
37C2×#14519706—21no—
38C4⋊C8×D61—21no—
39C4⋊C8×D61—21no—
40C4⋊C8×D61C2212yes—
41C4⋊C8×D61C2212yescomplemented
42C4×#11758194C2211yescharacteristic, complemented
43#16839714—21no—
44M16×Dic61—21no—
45C4×#11758189C2212yescomplemented
46#97×D61—21no—
47C4×C8×D61C2212yes—
48#16839494C2212yescomplemented
49Q8⋊#92418C2212yescomplemented
50#16839492C2212yescomplemented
51#16839491C2212yescomplemented
52D4⋊#92418C2212yescomplemented
53#16839489C2212yescomplemented
54C61×#529C2211yescharacteristic
55C2×C4⋊C8×C61C2211yescharacteristic, complemented
56C4×M16×C61C2211yescharacteristic, complemented
57C61×Q8⋊C8C2212yescomplemented
58C61×D4⋊C8C2212yescomplemented
59C2×Q8×D61C2×C411yescharacteristic
60C2×D4×D61—21no—
61C2×D4×D61C2×C411yescharacteristic
62C22×C4×D61—21no—
63C22×C4×D61C2×C411yescharacteristic
64C22×C4×D61D411yescharacteristic
65C22×C4×D61D411yescharacteristic
66C2×#11758194—21no—
67C2×#11758189—22no—
68M16×D61—28no—
69C22×#92418—21no—
70C2×C8×D61—22no—
71C2×C8×D61—22no—
72C2×C8×D61—22no—
73C2×C8×D61—44no—
74#14519772—21no—
75#14519772—21no—
76#14519772—21no—
77#14519771—21no—
78#14519770—21no—
79#14519770—21no—
80#14519770—21no—
81#14519769C2×C411yescharacteristic
82#14519768C2×C411yescharacteristic
83#14519768C2×C411yescharacteristic
84#14519767—21no—
85#14519767—21no—
86#14519766C2×C411yescharacteristic
87#14519765C2×C411yescharacteristic
88#14519764C2×C411yescharacteristic
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#14519757C2×C411yescharacteristic
99#14519756C2×C411yescharacteristic
100#14519755—21no—
101#14519754—21no—
102#14519753C2×C411yescharacteristic
103#14519752C2×C411yescharacteristic
104#14519751C2×C411yescharacteristic
105#14519750—21no—
106#14519749—21no—
107#14519748C2×C411yescharacteristic
108Q8×Dic61C2×C411yescharacteristic
109C4×Dic122—21no—
110C4×Dic122C2311yescharacteristic
111#14519742—21no—
112#14519742C2×C411yescharacteristic
113C4×D244—21no—
114C4×D244C2311yescharacteristic
115D4×Dic61—21no—
116D4×Dic61C2×C411yescharacteristic
117#14519739—21no—
118#14519739C2×C411yescharacteristic
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
155C4⋊#92418—21no—
156C4⋊#92418C2312yes—
157#14519706—22no—
158#14519706—22no—
159#14519688—21no—
160#14519687—22no—
161C4×#92418C2312yes—
162C8×Dic61—22no—
163C2×M16×C61—21no—
164C22×C8×C61—21no—
165#126×C61—21no—
166#125×C61C2×C411yescharacteristic
167#124×C61C2×C411yescharacteristic
168#123×C61—21no—
169C22⋊Q8×C61C2×C411yescharacteristic
170#121×C61C2×C411yescharacteristic
171C4×Q8×C61C2311yescharacteristic
172C4×D4×C61—21no—
173C4×D4×C61C2311yescharacteristic
174#117×C61—21no—
175C2×C42×C61C2311yescharacteristic
176C4⋊C8×C61—21no—
177C4⋊C8×C61C2312yes—
178#97×C61—21no—
179C4×C8×C61C2312yes—
180C23×D61—21no—
181C23×D61C22⋊C411yescharacteristic
182C2×Q8×C61C22×C411yescharacteristic
183C2×D4×C61—21no—
184C2×D4×C61C22×C411yescharacteristic
185C22×C4×C61—21no—
186C22×C4×C61C22×C411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C2×C22⋊D61—21no—
190C2×C22⋊D61—21no—
191C2×C22⋊D61—21no—
192C22×Dic61—21no—
193C22×Dic61C22⋊C411yescharacteristic
194C22×Dic61C22⋊C411yescharacteristic
195C22×Dic61C22⋊C411yescharacteristic
196Q8×D61—24no—
197D4×D61—24no—
198D4×D61—44no—
199C2×D244—21no—
200C2×D244C22×C411yescharacteristic
201C2×C4×D61—24no—
202C2×C4×D61—24no—
203C2×C4×D61—22no—
204C2×C4×D61—22no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61—21no—
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61—42no—
211C2×C4×D61—42no—
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×D61C2×D411yescharacteristic
221C2×C4×D61C2×D411yescharacteristic
222C2×C4×D61C2×D411yescharacteristic
223C2×C4×D61C2×D411yescharacteristic
224C2×Dic122—21no—
225C2×Dic122C22×C411yescharacteristic
226M16×C61—24no—
227C2×C8×C61—22no—
228C2×C8×C61—22no—
229C2×C8×C61—42no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61C22×C411yescharacteristic
235C4⋊C4×C61C22×C411yescharacteristic
236C22⋊C4×C61—21no—
237C22⋊C4×C61—21no—
238C22⋊C4×C61—21no—
239C22⋊C4×C61—21no—
240C22⋊C4×C61—21no—
241C42×C61—21no—
242C42×C61C22×C411yescharacteristic
243C42×C61C2×D411yescharacteristic
244C42×C61C2×D411yescharacteristic
245C42×C61C2411yescharacteristic
246C22⋊Dic61—21no—
247C22⋊Dic61—21no—
248C22⋊Dic61—21no—
249C22⋊Dic61—21no—
250C22⋊Dic61—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—21no—
260#11758198—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
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×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
290C4×Dic61C2×D411yescharacteristic
291C4×Dic61C2×D411yescharacteristic
292#11758194—24no—
293C2×#92418—22no—
294C2×#92418—22no—
295C2×#92418—42no—
296#11758189—28no—
297C8×D61—28no—
298C8×D61—44no—
299C8×D61—44no—
300C23×C61—21no—
301C23×C61C2×C22⋊C411yescharacteristic
302C22×D61—22no—
303C22×D61—22no—
304C22×D61—21no—
305C22×D61—42no—
306C22×D61—42no—
307C22×D61—42no—
308C22×D61#10414yes—
309C22×D61C2×C22⋊C411yescharacteristic
310C22×D61C2×C22⋊C411yescharacteristic
311Q8×C61—22no—
312D4×C61—22no—
313D4×C61—42no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61C2×C22⋊C411yescharacteristic
324C2×C4×C61C2×C22⋊C411yescharacteristic
325C2×C4×C61C2×C22⋊C411yescharacteristic
326C2×C4×C61C23×C411yescharacteristic
327C2×C4×C61C22×D411yescharacteristic
328C2×C4×C61C22×D411yescharacteristic
329C22⋊D61—42no—
330C22⋊D61—42no—
331C22⋊D61—42no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—21no—
336C2×Dic61—21no—
337C2×Dic61—21no—
338C2×Dic61—42no—
339C2×Dic61C2×C22⋊C411yescharacteristic
340C2×Dic61C2×C22⋊C411yescharacteristic
341C2×Dic61C2×C22⋊C411yescharacteristic
342C2×Dic61C2×C22⋊C411yescharacteristic
343C2×Dic61C2×C22⋊C411yescharacteristic
344C2×Dic61C2×C22⋊C411yescharacteristic
345D244—22no—
346D244—42no—
347C4×D61—22no—
348C4×D61—22no—
349C4×D61—22no—
350C4×D61—22no—
351C4×D61—22no—
352C4×D61—22no—
353C4×D61—22no—
354C4×D61—21no—
355C4×D61—21no—
356C4×D61—22no—
357C4×D61—22no—
358C4×D61—42no—
359C4×D61—42no—
360C4×D61—42no—
361C4×D61—41no—
362C4×D61—41no—
363C4×D61—42no—
364C4×D61#13114yes—
365C4×D61AGL(1,ℤ/8)12yes—
366C4×D61#13712yes—
367Dic122—22no—
368Dic122—42no—
369C8×C61—24no—
370C8×C61—42no—
371#92418—24no—
372#92418—42no—
373C2×#1483—611nomaximal, Sylow
374C22×C61—21no—
375C22×C61—21no—
376C22×C61—41no—
377C22×C61—41no—
378C22×C61—41no—
379C22×C61C2×#10412yes—
380C22×C61C22×C22⋊C411yescharacteristic
381C2×D61—21no—
382C2×D61—21no—
383C2×D61—28no—
384C2×D61—41no—
385C2×D61—41no—
386C2×D61—41no—
387C2×D61—84no—
388C2×D61#40812yes—
389C2×D61#41712yes—
390C2×D61C2×#10412yes—
391C2×D61C2×#10412yes—
392C4×C61—21no—
393C4×C61—21no—
394C4×C61—21no—
395C4×C61—21no—
396C4×C61—41no—
397C4×C61—41no—
398C4×C61—41no—
399C4×C61C2×#13112yes—
400C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
401C4×C61C2×#13711yescharacteristic
402Dic61—21no—
403Dic61—21no—
404Dic61—21no—
405Dic61—21no—
406Dic61—41no—
407Dic61—41no—
408Dic61—41no—
409Dic61#40812yes—
410Dic61#41712yes—
411C2×#529—611no—
412C22×C4⋊C8—611no—
413C2×C4×M16—611no—
414#1483—611no—
415#1483—611no—
416#1483—612no—
417#1483—612no—
418#1483—611no—
419#1483D6111yescharacteristic, direct product factor
420C2×Q8⋊C8—612no—
421C2×D4⋊C8—612no—
422C2×C61—22no—
423C2×C61—81no—
424C2×C61C2×#40811yescharacteristic
425C2×C61C2×#41711yescharacteristic
426C2×C61C22×#10411yescharacteristic
427D61—22no—
428D61—81no—
429D61#148314yesdirect product factor
430C22×M16—1221no—
431C23×C8—1221no—
432#529—611no—
433#529—611no—
434#529—611no—
435#529—611no—
436#529—611no—
437#529—611no—
438#529—611no—
439#529—1221no—
440#529—1221no—
441#529—1221no—
442#529—1221no—
443#529C2×D6111yescharacteristic
444C2×#126—1221no—
445C2×#125—611no—
446C2×#124—611no—
447C2×#123—1221no—
448C2×C22⋊Q8—611no—
449C2×#121—611no—
450C2×C4×Q8—611no—
451C2×C4×D4—611no—
452C2×C4×D4—1221no—
453C2×#117—1221no—
454C22×C42—611no—
455C2×C4⋊C8—611no—
456C2×C4⋊C8—612no—
457C2×C4⋊C8—612no—
458C2×C4⋊C8—1221no—
459C2×C4⋊C8—1221no—
460C2×C4⋊C8—1221no—
461C2×C4⋊C8C2×D6111yescharacteristic, complemented
462C4×M16—611no—
463C4×M16—612no—
464C4×M16—1221no—
465C4×M16—1221no—
466C4×M16C2×D6111yescharacteristic, complemented
467C2×#97—1221no—
468C2×C4×C8—612no—
469Q8⋊C8—612no—
470Q8⋊C8—612no—
471Q8⋊C8—612no—
472Q8⋊C8C2×D6112yescomplemented
473D4⋊C8—612no—
474D4⋊C8—612no—
475D4⋊C8—612no—
476D4⋊C8C2×D6112yescomplemented
477C61C2×#148311yescharacteristic, complemented, Sylow
478C22×Q8—611no—
479C22×D4—611no—
480C22×D4—1221no—
481C23×C4—611no—
482C23×C4—611no—
483C23×C4—611no—
484C23×C4—1221no—
485C2×M16—21no—
486C2×M16—1222no—
487C2×M16—1228no—
488C2×M16—1221no—
489C22×C8—21no—
490C22×C8—1222no—
491C22×C8—1222no—
492C22×C8—1222no—
493C22×C8—1221no—
494C22×C8—2444no—
495#126—21no—
496#126—1221no—
497#126—1221no—
498#126—1221no—
499#126—1221no—
500#126—1221no—
501#126—1221no—
502#126—1221no—
503#125—611no—
504#125—611no—
505#125—611no—
506#125—1221no—
507#125—1221no—
508#125C4×D6111yescharacteristic
509#124—611no—
510#124—611no—
511#124—611no—
512#124—1221no—
513#124—1221no—
514#124C4×D6111yescharacteristic
515#123—21no—
516#123—1221no—
517#123—1221no—
518#123—1221no—
519#123—1221no—
520#123—1221no—
521#123—1221no—
522#123—1221no—
523C22⋊Q8—611no—
524C22⋊Q8—611no—
525C22⋊Q8—611no—
526C22⋊Q8—1221no—
527C22⋊Q8—1221no—
528C22⋊Q8C4×D6111yescharacteristic
529#121—611no—
530#121—611no—
531#121—611no—
532#121—1221no—
533#121—1221no—
534#121C4×D6111yescharacteristic
535C4×Q8—611no—
536C4×Q8—611no—
537C4×Q8—611no—
538C4×Q8—1221no—
539C4×Q8—1221no—
540C4×Q8C22×D6111yescharacteristic
541C4×D4—21no—
542C4×D4—611no—
543C4×D4—611no—
544C4×D4—611no—
545C4×D4—1221no—
546C4×D4—1221no—
547C4×D4—1221no—
548C4×D4—1221no—
549C4×D4—1221no—
550C4×D4—1221no—
551C4×D4—1221no—
552C4×D4—1221no—
553C4×D4—1221no—
554C4×D4C22×D6111yescharacteristic
555#117—21no—
556#117—1221no—
557#117—1221no—
558#117—1221no—
559#117—1221no—
560#117—1221no—
561#117—1221no—
562#117—1221no—
563C2×C4⋊C4—611no—
564C2×C4⋊C4—611no—
565C2×C4⋊C4—1221no—
566C2×C4⋊C4—1221no—
567C2×C4⋊C4—1221no—
568C2×C4⋊C4—1221no—
569C2×C22⋊C4—1221no—
570C2×C22⋊C4—1221no—
571C2×C22⋊C4—1221no—
572C2×C22⋊C4—1221no—
573C2×C22⋊C4—1221no—
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—611no—
583C2×C42—611no—
584C2×C42—611no—
585C2×C42—1221no—
586C2×C42C22×D6111yescharacteristic
587C4⋊C8—21no—
588C4⋊C8—612no—
589C4⋊C8—1222no—
590C4⋊C8—1222no—
591C4⋊C8—1221no—
592C4⋊C8C22×D6112yes—
593#97—21no—
594#97—1222no—
595#97—1221no—
596C4×C8—612no—
597C4×C8—1222no—
598C4×C8C22×D6112yes—
599C24—611no—
600C24—1221no—
601C2×Q8—611no—
602C2×Q8—1221no—
603C2×Q8—1224no—
604C2×Q8C2×C4×D6111yescharacteristic
605C2×D4—21no—
606C2×D4—611no—
607C2×D4—1221no—
608C2×D4—1224no—
609C2×D4—1221no—
610C2×D4—1221no—
611C2×D4—1221no—
612C2×D4—2444no—
613C2×D4C2×C4×D6111yescharacteristic
614C22×C4—21no—
615C22×C4—611no—
616C22×C4—611no—
617C22×C4—611no—
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—1222no—
631C22×C4—1224no—
632C22×C4—1222no—
633C22×C4—1221no—
634C22×C4—1224no—
635C22×C4—1221no—
636C22×C4—1221no—
637C22×C4—1221no—
638C22×C4—1221no—
639C22×C4—1221no—
640C22×C4—2442no—
641C22×C4—2442no—
642C22×C4C2×C4×D6111yescharacteristic
643C22×C4D4×D6111yescharacteristic
644C22×C4D4×D6111yescharacteristic
645M16—24no—
646M16—1228no—
647M16—1224no—
648C2×C8—22no—
649C2×C8—22no—
650C2×C8—42no—
651C2×C8—1228no—
652C2×C8—1222no—
653C2×C8—1222no—
654C2×C8—2444no—
655C2×C8—2444no—
656C2×C8—2442no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—611no—
662C4⋊C4—611no—
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—1221no—
673C4⋊C4—1221no—
674C4⋊C4—1221no—
675C4⋊C4—1221no—
676C4⋊C4—1221no—
677C4⋊C4C2×C4×D6111yescharacteristic
678C4⋊C4C2×C4×D6111yescharacteristic
679C22⋊C4—21no—
680C22⋊C4—21no—
681C22⋊C4—21no—
682C22⋊C4—21no—
683C22⋊C4—21no—
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—1221no—
696C22⋊C4—1221no—
697C22⋊C4—1221no—
698C22⋊C4—1221no—
699C42—21no—
700C42—611no—
701C42—611no—
702C42—611no—
703C42—611no—
704C42—611no—
705C42—611no—
706C42—611no—
707C42—611no—
708C42—611no—
709C42—611no—
710C42—611no—
711C42—611no—
712C42—1221no—
713C42—1221no—
714C42—1221no—
715C42C2×C4×D6111yescharacteristic
716C42D4×D6111yescharacteristic
717C42D4×D6111yescharacteristic
718C42C23×D6111yescharacteristic
719C23—21no—
720C23—611no—
721C23—611no—
722C23—614no—
723C23—1222no—
724C23—1222no—
725C23—1221no—
726C23—2442no—
727C23—2442no—
728C23—2442no—
729C23C22⋊C4×D6111yescharacteristic
730Q8—22no—
731Q8—1222no—
732Q8—2442no—
733D4—22no—
734D4—42no—
735D4—1222no—
736D4—2442no—
737D4—2442no—
738D4—2442no—
739D4—2442no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—611no—
750C2×C4—611no—
751C2×C4—614no—
752C2×C4—612no—
753C2×C4—612no—
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—1222no—
764C2×C4—1222no—
765C2×C4—1222no—
766C2×C4—1222no—
767C2×C4—1222no—
768C2×C4—1222no—
769C2×C4—1222no—
770C2×C4—1221no—
771C2×C4—1221no—
772C2×C4—1221no—
773C2×C4—1221no—
774C2×C4—1221no—
775C2×C4—2442no—
776C2×C4—2442no—
777C2×C4—2442no—
778C2×C4—2442no—
779C2×C4—2442no—
780C2×C4—2441no—
781C2×C4—2441no—
782C2×C4C22⋊C4×D6111yescharacteristic
783C2×C4C22⋊C4×D6111yescharacteristic
784C2×C4C22⋊C4×D6111yescharacteristic
785C2×C4C22×C4×D6111yescharacteristic
786C2×C4C2×D4×D6111yescharacteristic
787C2×C4C2×D4×D6111yescharacteristic
788C8—24no—
789C8—42no—
790C8—1224no—
791C8—2442no—
792C22—21no—
793C22—21no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—612no—
798C22—612no—
799C22—612no—
800C22—612no—
801C22—1228no—
802C22—1221no—
803C22—1221no—
804C22—4884no—
805C22—2441no—
806C22—2441no—
807C22—2441no—
808C22#104×D6112yes—
809C22C2×C22⋊C4×D6111yescharacteristic
810C4—21no—
811C4—21no—
812C4—21no—
813C4—21no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—612no—
818C4—612no—
819C4—1221no—
820C4—1221no—
821C4—1221no—
822C4—1221no—
823C4—2441no—
824C4—2441no—
825C4—2441no—
826C4#131×D6112yes—
827C4AGL(1,ℤ/8)×D6111yescharacteristic
828C4#137×D6111yescharacteristic
829C2—22no—
830C2—81no—
831C2—614no—
832C2—1222no—
833C2—4881no—
834C2#408×D6111yescharacteristic
835C2#417×D6111yescharacteristic
836C2C2×#104×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1483C2
socleC22×C61C22×C22⋊C4
prime radical#121×D61C4
cosocleC42×C61C24
hypercenter#1483D61
hypocenterC61C2×#1483
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1483

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C8×D61C2semidirect
3. C4×M16×D61C2semidirect
4. #21444233C2semidirect
5. #21444232C2semidirect
6. #21444231C2semidirect
7. #21444230C2semidirect
8. #21444229C2semidirect
9. Q8⋊C8×D61C2semidirect
10. D4⋊C8×D61C2semidirect
11. C61×#1483C2semidirect
36. C2×C4⋊#92418C22semidirect
41. C4⋊C8×D61C22semidirect
42. C4×#11758194C22semidirect
45. C4×#11758189C22semidirect
48. #16839494C22semidirect
49. Q8⋊#92418C22semidirect
50. #16839492C22semidirect
51. #16839491C22semidirect
52. D4⋊#92418C22semidirect
53. #16839489C22semidirect
55. C2×C4⋊C8×C61C22semidirect
56. C4×M16×C61C22semidirect
57. C61×Q8⋊C8C22semidirect
58. C61×D4⋊C8C22semidirect
419. #1483D61direct (N × H)
429. D61#1483direct (N × H)
461. C2×C4⋊C8C2×D61semidirect
466. C4×M16C2×D61semidirect
472. Q8⋊C8C2×D61semidirect
476. D4⋊C8C2×D61semidirect
477. C61C2×#1483semidirect

Maximal subgroups

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

subgroupindex
#529×D612
C2×C4⋊C8×D612
C4×M16×D612
#214442332
#214442322
#214442312
#214442302
#214442292
Q8⋊C8×D612
D4⋊C8×D612
C61×#14832
C2×#148361