Finite Group Databasebeta

← #30616720

Subgroups — #30616720

Order 15616.

1174 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D61⋊M16C211yesmaximal, characteristic, complemented
2#21462266C211yesmaximal, characteristic, complemented
3#21462001C212yesmaximal, complemented
4#21461948C212yesmaximal, complemented
5#21461835C212yesmaximal
6#21461834C212yesmaximal, complemented
7#21461591C212yesmaximal, complemented
8#21461589C212yesmaximal, complemented
9#529×D61C211yesmaximal, characteristic
10C2×D61⋊M16C2212yes—
11C2×#14519840C2214yes—
12C2×#14519839C2214yes—
13C4×#11758213—21no—
14C4×#11758213—21no—
15C4×#11758217—21no—
16C4×#11758217—21no—
17#16840721C2212yes—
18C4×D61⋊C8C2212yes—
19#16840707—21no—
20#16840706C2212yes—
21#16840705—21no—
22#16840704C2212yes—
23C4×C4⋊#6923C2212yes—
24C4×C22⋊#6923—21no—
25#16840698—21no—
26#16840635C2214yes—
27#16840635C2214yes—
28#16840299C411yescharacteristic, complemented
29#16840298C411yescharacteristic, complemented
30#16840297C411yescharacteristic, complemented
31#16840296C411yescharacteristic, complemented
32#16840295—21no—
33#16840294C411yescharacteristic, complemented
34#16840293C411yescharacteristic, complemented
35#16840292—21no—
36#16840291C411yescharacteristic, complemented
37#16840290—21no—
38#16840289—21no—
39#126×D61—21no—
40#125×D61C2211yescharacteristic
41#124×D61C2211yescharacteristic
42#123×D61—21no—
43C22⋊Q8×D61C2211yescharacteristic
44#121×D61C2211yescharacteristic
45C4×Q8×D61C2211yescharacteristic
46C4×D4×D61—21no—
47C4×D4×D61C2211yescharacteristic
48#117×D61—21no—
49C2×C42×D61C2211yescharacteristic
50C61×#529C411yescharacteristic, complemented
51C2×#11758213—22no—
52D61⋊M16—28no—
53C2×#11758217—22no—
54C2×D61⋊C8C2314yes—
55C2×C4⋊#6923C2314yes—
56C2×C22⋊#6923—22no—
57C2×C4×#6923—22no—
58#14519840—28no—
59#14519839—28no—
60#14519832—22no—
61#14519832—22no—
62C4×#92420—22no—
63C4×#92420—22no—
64(C2×#6923)⋊C4—22no—
65(C2×#6923)⋊C4—22no—
66(C2×#6923)⋊C4—22no—
67(C2×#6923)⋊C4—22no—
68C2×Q8×D61C2311yescharacteristic
69C2×D4×D61—21no—
70C2×D4×D61C2311yescharacteristic
71C22×C4×D61—21no—
72C22×C4×D61D411yescharacteristic
73C22×C4×D61D411yescharacteristic
74C22×C4×D61C2311yescharacteristic
75#14519772—21no—
76#14519772—21no—
77#14519772—21no—
78#14519771—21no—
79#14519770—21no—
80#14519770—21no—
81#14519770—21no—
82#14519769C2×C411yescharacteristic
83#14519768C2×C411yescharacteristic
84#14519768C2×C411yescharacteristic
85#14519767—21no—
86#14519767—21no—
87#14519766C2×C411yescharacteristic
88#14519765C2×C411yescharacteristic
89#14519764C2×C411yescharacteristic
90#14519763—21no—
91#14519763—21no—
92#14519762—21no—
93#14519762—21no—
94#14519761—21no—
95#14519760—21no—
96#14519759—21no—
97#14519759—21no—
98#14519758—21no—
99#14519757C2×C411yescharacteristic
100#14519756C2×C411yescharacteristic
101#14519755—21no—
102#14519754—21no—
103#14519753C2×C411yescharacteristic
104#14519752C2×C411yescharacteristic
105#14519751C2×C411yescharacteristic
106#14519750—21no—
107#14519749—21no—
108#14519748C2×C411yescharacteristic
109Q8×Dic61C2×C411yescharacteristic
110C4×Dic122—21no—
111C4×Dic122C2×C411yescharacteristic
112#14519742—21no—
113#14519742C2×C411yescharacteristic
114C4×D244—21no—
115C4×D244C2×C411yescharacteristic
116D4×Dic61—21no—
117D4×Dic61C2×C411yescharacteristic
118#14519739—21no—
119#14519739C2×C411yescharacteristic
120C4×C22⋊D61—21no—
121C4×C22⋊D61—21no—
122C4×C22⋊D61—21no—
123#14519737—21no—
124#14519737—21no—
125#14519737—21no—
126#14519736—21no—
127#14519735—21no—
128#14519735—21no—
129#14519734—21no—
130#14519734—21no—
131#14519733—21no—
132#14519733—21no—
133C4⋊C4×D61—21no—
134C4⋊C4×D61—21no—
135C4⋊C4×D61—21no—
136C4⋊C4×D61—21no—
137C4⋊C4×D61C2311yescharacteristic
138C4⋊C4×D61C2311yescharacteristic
139C22⋊C4×D61—21no—
140C22⋊C4×D61—21no—
141C22⋊C4×D61—21no—
142C22⋊C4×D61—21no—
143C22⋊C4×D61—21no—
144C2×C4×Dic61C2×C411yescharacteristic
145C2×C4×Dic61D411yescharacteristic
146C2×C4×Dic61D411yescharacteristic
147C42×D61—21no—
148C42×D61C2×C411yescharacteristic
149C42×D61C2×C411yescharacteristic
150C42×D61D411yescharacteristic
151C42×D61D411yescharacteristic
152C42×D61D411yescharacteristic
153C42×D61D411yescharacteristic
154C42×D61C2311yescharacteristic
155C42×D61C2311yescharacteristic
156#126×C61—21no—
157#125×C61C2×C411yescharacteristic
158#124×C61C2×C411yescharacteristic
159#123×C61—21no—
160C22⋊Q8×C61C2×C411yescharacteristic
161#121×C61C2×C411yescharacteristic
162C4×Q8×C61C2×C411yescharacteristic
163C4×D4×C61—21no—
164C4×D4×C61C2×C411yescharacteristic
165#117×C61—21no—
166C2×C42×C61C2×C411yescharacteristic
167C23×D61—21no—
168C23×D61C2×D411yescharacteristic
169C22×#6923—24no—
170C2×Q8×C61C22×C411yescharacteristic
171C2×D4×C61—21no—
172C2×D4×C61C22×C411yescharacteristic
173C22×C4×C61—21no—
174C22×C4×C61C22⋊C411yescharacteristic
175C22×C4×C61C22⋊C411yescharacteristic
176C22×C4×C61C22×C411yescharacteristic
177C2×C22⋊D61—21no—
178C2×C22⋊D61—21no—
179C2×C22⋊D61—21no—
180C22×Dic61—21no—
181C22×Dic61C22⋊C411yescharacteristic
182C22×Dic61C22⋊C411yescharacteristic
183C22×Dic61C2×D411yescharacteristic
184Q8×D61—24no—
185D4×D61—24no—
186D4×D61—44no—
187C2×D244—21no—
188C2×D244C22×C411yescharacteristic
189C2×C4×D61—24no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—42no—
196C2×C4×D61—42no—
197C2×C4×D61—44no—
198C2×C4×D61C22⋊C411yescharacteristic
199C2×C4×D61C22⋊C411yescharacteristic
200C2×C4×D61C22⋊C411yescharacteristic
201C2×C4×D61C22⋊C411yescharacteristic
202C2×C4×D61C22×C411yescharacteristic
203C2×C4×D61C2×D411yescharacteristic
204C2×C4×D61C2×D411yescharacteristic
205C2×C4×D61C2×D411yescharacteristic
206C2×C4×D61C2×D411yescharacteristic
207C2×C4×D61C2×D411yescharacteristic
208C2×C4×D61C2×D411yescharacteristic
209C2×C4×D61C2411yescharacteristic
210C2×Dic122—21no—
211C2×Dic122C22×C411yescharacteristic
212C22⋊#6923—44no—
213#11758217—28no—
214C2×#92420—24no—
215C4⋊#6923—24no—
216C4⋊#6923—24no—
217C4×#6923—44no—
218#11758213—28no—
219D61⋊C8—24no—
220D61⋊C8#4118yes—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61C22×C411yescharacteristic
226C4⋊C4×C61C22×C411yescharacteristic
227C22⋊C4×C61—21no—
228C22⋊C4×C61—21no—
229C22⋊C4×C61—21no—
230C22⋊C4×C61—21no—
231C22⋊C4×C61—21no—
232C42×C61—21no—
233C42×C61C22⋊C411yescharacteristic
234C42×C61C22⋊C411yescharacteristic
235C42×C61C22×C411yescharacteristic
236C42×C61C22×C411yescharacteristic
237C22⋊Dic61—21no—
238C22⋊Dic61—21no—
239C22⋊Dic61—21no—
240C22⋊Dic61—21no—
241C22⋊Dic61—21no—
242#11758198—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—
252C4⋊Dic61—21no—
253C4⋊Dic61—21no—
254C4⋊Dic61—21no—
255C4⋊Dic61—21no—
256C4⋊Dic61C22×C411yescharacteristic
257C4⋊Dic61C22×C411yescharacteristic
258#11758196—21no—
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—
268C4×Dic61—21no—
269C4×Dic61—21no—
270C4×Dic61—21no—
271C4×Dic61C22⋊C411yescharacteristic
272C4×Dic61C22⋊C411yescharacteristic
273C4×Dic61C22⋊C411yescharacteristic
274C4×Dic61C22⋊C411yescharacteristic
275C4×Dic61C22⋊C411yescharacteristic
276C4×Dic61C22⋊C411yescharacteristic
277C4×Dic61C22×C411yescharacteristic
278C4×Dic61C22×C411yescharacteristic
279C4×Dic61C2×D411yescharacteristic
280C4×Dic61C2×D411yescharacteristic
281C4×Dic61C2×D411yescharacteristic
282C4×Dic61C2×D411yescharacteristic
283C23×C61—21no—
284C23×C61C2×C22⋊C411yescharacteristic
285C22×D61—22no—
286C22×D61—22no—
287C22×D61—22no—
288C22×D61—21no—
289C22×D61—42no—
290C22×D61—42no—
291C22×D61—42no—
292C22×D61C2×C22⋊C411yescharacteristic
293C22×D61C22×D411yescharacteristic
294C2×#6923—44no—
295C2×#6923—44no—
296C2×#6923—44no—
297Q8×C61—22no—
298D4×C61—22no—
299D4×C61—42no—
300C2×C4×C61—22no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—42no—
307C2×C4×C61C2×C22⋊C411yescharacteristic
308C2×C4×C61C2×C22⋊C411yescharacteristic
309C2×C4×C61C2×C22⋊C411yescharacteristic
310C2×C4×C61C2×C22⋊C411yescharacteristic
311C2×C4×C61C2×C22⋊C411yescharacteristic
312C2×C4×C61C23×C411yescharacteristic
313C22⋊D61—42no—
314C22⋊D61—42no—
315C22⋊D61—42no—
316C2×Dic61—22no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—42no—
323C2×Dic61C2×C22⋊C411yescharacteristic
324C2×Dic61C2×C22⋊C411yescharacteristic
325C2×Dic61C2×C22⋊C411yescharacteristic
326C2×Dic61C2×C22⋊C411yescharacteristic
327C2×Dic61C2×C22⋊C411yescharacteristic
328C2×Dic61C22×D411yescharacteristic
329D244—22no—
330D244—42no—
331C4×D61—22no—
332C4×D61—22no—
333C4×D61—22no—
334C4×D61—22no—
335C4×D61—22no—
336C4×D61—22no—
337C4×D61—22no—
338C4×D61—41no—
339C4×D61—41no—
340C4×D61—41no—
341C4×D61—41no—
342C4×D61—42no—
343C4×D61—42no—
344C4×D61—42no—
345C4×D61—42no—
346C4×D61—42no—
347C4×D61C2×#4114yes—
348Dic122—22no—
349Dic122—42no—
350#92420—28no—
351#21411—611nomaximal, Sylow
352C22×C61—21no—
353C22×C61—21no—
354C22×C61—21no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61C22×C22⋊C411yescharacteristic
359C2×D61—21no—
360C2×D61—21no—
361C2×D61—21no—
362C2×D61—44no—
363C2×D61—41no—
364C2×D61—41no—
365C2×D61—41no—
366C2×D61—84no—
367C2×D61#53212yes—
368C2×D61#57512yes—
369C2×D61#57512yes—
370#6923—84no—
371C4×C61—21no—
372C4×C61—21no—
373C4×C61—21no—
374C4×C61—21no—
375C4×C61—21no—
376C4×C61—41no—
377C4×C61—41no—
378C4×C61—41no—
379C4×C61C4×#4112yes—
380Dic61—21no—
381Dic61—21no—
382Dic61—21no—
383Dic61—21no—
384Dic61—21no—
385Dic61—41no—
386Dic61—41no—
387Dic61—41no—
388Dic61#52512yes—
389C2×#529—611no—
390C2×C4×M16—611no—
391#2283—611no—
392#1991—612no—
393#1958—612no—
394#1895—612no—
395#1894—612no—
396#1763—612no—
397#1762—612no—
398C2×C61—41no—
399C2×C61—81no—
400C2×C61#229711yescharacteristic
401C2×C61#289611yescharacteristic
402C2×C61#289611yescharacteristic
403D61—41no—
404D61—81no—
405D61#318314yes—
406C22×M16—612no—
407#529—611no—
408#529—611no—
409#529—611no—
410#529—611no—
411#529—611no—
412#529—611no—
413#529—611no—
414#529—1221no—
415#529—1221no—
416#529—1221no—
417#529—1221no—
418#529#692311yescharacteristic, complemented
419C2×#126—1221no—
420C2×#125—611no—
421C2×#124—611no—
422C2×#123—1221no—
423C2×C22⋊Q8—611no—
424C2×#121—611no—
425C2×C4×Q8—611no—
426C2×C4×D4—611no—
427C2×C4×D4—1221no—
428C2×#117—1221no—
429C22×C42—611no—
430C2×#103—614no—
431C2×#102—614no—
432C4×M16—1221no—
433C4×M16—1221no—
434C4×M16—1221no—
435C4×M16—1221no—
436C2×#97—612no—
437C2×C4×C8—612no—
438#383—1221no—
439#382—612no—
440#381—1221no—
441#380—612no—
442C4×C4⋊C4—612no—
443C4×C22⋊C4—1221no—
444#376—1221no—
445#340—614no—
446#340—614no—
447C61#2141111yescharacteristic, complemented, Sylow
448C22×Q8—611no—
449C22×D4—611no—
450C22×D4—1221no—
451C23×C4—611no—
452C23×C4—611no—
453C23×C4—611no—
454C23×C4—1221no—
455C2×M16—1228no—
456C2×M16—1222no—
457C2×M16—1222no—
458C22×C8—614no—
459#126—21no—
460#126—1221no—
461#126—1221no—
462#126—1221no—
463#126—1221no—
464#126—1221no—
465#126—1221no—
466#126—1221no—
467#125—611no—
468#125—611no—
469#125—611no—
470#125—1221no—
471#125—1221no—
472#125C2×#692311yescharacteristic
473#124—611no—
474#124—611no—
475#124—611no—
476#124—1221no—
477#124—1221no—
478#124C2×#692311yescharacteristic
479#123—21no—
480#123—1221no—
481#123—1221no—
482#123—1221no—
483#123—1221no—
484#123—1221no—
485#123—1221no—
486#123—1221no—
487C22⋊Q8—611no—
488C22⋊Q8—611no—
489C22⋊Q8—611no—
490C22⋊Q8—1221no—
491C22⋊Q8—1221no—
492C22⋊Q8C2×#692311yescharacteristic
493#121—611no—
494#121—611no—
495#121—611no—
496#121—1221no—
497#121—1221no—
498#121C2×#692311yescharacteristic
499C4×Q8—611no—
500C4×Q8—611no—
501C4×Q8—611no—
502C4×Q8—1221no—
503C4×Q8—1221no—
504C4×Q8C2×#692311yescharacteristic
505C4×D4—21no—
506C4×D4—611no—
507C4×D4—611no—
508C4×D4—611no—
509C4×D4—1221no—
510C4×D4—1221no—
511C4×D4—1221no—
512C4×D4—1221no—
513C4×D4—1221no—
514C4×D4—1221no—
515C4×D4—1221no—
516C4×D4—1221no—
517C4×D4—1221no—
518C4×D4C2×#692311yescharacteristic
519#117—21no—
520#117—1221no—
521#117—1221no—
522#117—1221no—
523#117—1221no—
524#117—1221no—
525#117—1221no—
526#117—1221no—
527C2×C4⋊C4—611no—
528C2×C4⋊C4—611no—
529C2×C4⋊C4—614no—
530C2×C4⋊C4—1221no—
531C2×C4⋊C4—1221no—
532C2×C4⋊C4—1221no—
533C2×C4⋊C4—1221no—
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—1221no—
536C2×C22⋊C4—1221no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4—1222no—
540C2×C42—611no—
541C2×C42—611no—
542C2×C42—611no—
543C2×C42—611no—
544C2×C42—611no—
545C2×C42—611no—
546C2×C42—611no—
547C2×C42—611no—
548C2×C42—611no—
549C2×C42—611no—
550C2×C42—611no—
551C2×C42—1221no—
552C2×C42—1222no—
553C2×C42C2×#692311yescharacteristic
554#103—1228no—
555#102—1228no—
556#97—1222no—
557#97—1222no—
558C4×C8—1222no—
559C4×C8—1222no—
560#95—1222no—
561#95—1222no—
562#95—1222no—
563#95—1222no—
564C24—611no—
565C24—1221no—
566C2×Q8—611no—
567C2×Q8—1221no—
568C2×Q8—1224no—
569C2×Q8C22×#692311yescharacteristic
570C2×D4—21no—
571C2×D4—611no—
572C2×D4—1221no—
573C2×D4—1224no—
574C2×D4—1221no—
575C2×D4—1221no—
576C2×D4—1221no—
577C2×D4—2444no—
578C2×D4C22×#692311yescharacteristic
579C22×C4—21no—
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—611no—
591C22×C4—611no—
592C22×C4—611no—
593C22×C4—611no—
594C22×C4—611no—
595C22×C4—1224no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1224no—
603C22×C4—2442no—
604C22×C4—2442no—
605C22×C4—2444no—
606C22×C4C22⋊#692311yescharacteristic
607C22×C4C22⋊#692311yescharacteristic
608C22×C4C22×#692311yescharacteristic
609M16—1228no—
610M16—1228no—
611C2×C8—618no—
612C2×C8—1224no—
613C2×C8—1224no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—611no—
619C4⋊C4—611no—
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⋊C4—1221no—
630C4⋊C4—1224no—
631C4⋊C4—1224no—
632C4⋊C4—1221no—
633C4⋊C4—1221no—
634C4⋊C4—1221no—
635C4⋊C4—1221no—
636C4⋊C4C22×#692311yescharacteristic
637C4⋊C4C22×#692311yescharacteristic
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—1221no—
644C22⋊C4—1221no—
645C22⋊C4—1221no—
646C22⋊C4—1221no—
647C22⋊C4—1221no—
648C22⋊C4—1221no—
649C22⋊C4—1221no—
650C22⋊C4—1221no—
651C22⋊C4—1221no—
652C22⋊C4—1221no—
653C22⋊C4—1221no—
654C22⋊C4—1221no—
655C22⋊C4—1221no—
656C22⋊C4—1221no—
657C22⋊C4—1221no—
658C22⋊C4—2444no—
659C42—21no—
660C42—611no—
661C42—611no—
662C42—611no—
663C42—611no—
664C42—611no—
665C42—611no—
666C42—611no—
667C42—611no—
668C42—611no—
669C42—611no—
670C42—611no—
671C42—611no—
672C42—1221no—
673C42—1221no—
674C42—1221no—
675C42—2444no—
676C42C22⋊#692311yescharacteristic
677C42C22⋊#692311yescharacteristic
678C42C22×#692311yescharacteristic
679C42C22×#692311yescharacteristic
680C23—21no—
681C23—611no—
682C23—611no—
683C23—1222no—
684C23—1222no—
685C23—1222no—
686C23—1221no—
687C23—2442no—
688C23—2442no—
689C23—2442no—
690C23C2×C22⋊#692311yescharacteristic
691Q8—22no—
692Q8—1222no—
693Q8—2442no—
694D4—22no—
695D4—42no—
696D4—1222no—
697D4—2442no—
698D4—2442no—
699D4—2442no—
700D4—2442no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—42no—
708C2×C4—611no—
709C2×C4—614no—
710C2×C4—611no—
711C2×C4—611no—
712C2×C4—611no—
713C2×C4—611no—
714C2×C4—611no—
715C2×C4—1222no—
716C2×C4—1222no—
717C2×C4—1222no—
718C2×C4—1222no—
719C2×C4—1222no—
720C2×C4—1222no—
721C2×C4—1222no—
722C2×C4—1222no—
723C2×C4—1221no—
724C2×C4—1221no—
725C2×C4—1221no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2442no—
731C2×C4—2442no—
732C2×C4—2442no—
733C2×C4—2442no—
734C2×C4—2442no—
735C2×C4—2441no—
736C2×C4—2441no—
737C2×C4—2442no—
738C2×C4—2444no—
739C2×C4—2444no—
740C2×C4—2444no—
741C2×C4C2×C22⋊#692311yescharacteristic
742C2×C4C2×C22⋊#692311yescharacteristic
743C2×C4C2×C22⋊#692311yescharacteristic
744C2×C4C2×C22⋊#692311yescharacteristic
745C2×C4C2×C22⋊#692311yescharacteristic
746C2×C4C23×#692311yescharacteristic
747C8—1228no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—612no—
755C22—612no—
756C22—612no—
757C22—1221no—
758C22—1221no—
759C22—1221no—
760C22—4884no—
761C22—2444no—
762C22—2441no—
763C22—2441no—
764C22—2441no—
765C22C22×C22⋊#692311yescharacteristic
766C4—21no—
767C4—21no—
768C4—21no—
769C4—21no—
770C4—21no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—612no—
775C4—1221no—
776C4—1221no—
777C4—1221no—
778C4—1221no—
779C4—1221no—
780C4—4884no—
781C4—2441no—
782C4—2441no—
783C4—2441no—
784C4#41×#692312yes—
785C2—41no—
786C2—81no—
787C2—614no—
788C2—4881no—
789C2—2441no—
790C2#2146228011yescharacteristic
791C2#2146243911yescharacteristic
792C2#2146243911yescharacteristic
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
hypocenterC61#21411
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C4×D61⋊M16C2semidirect
2. #21462266C2semidirect
3. #21462001C2semidirect
4. #21461948C2semidirect
6. #21461834C2semidirect
7. #21461591C2semidirect
8. #21461589C2semidirect
28. #16840299C4semidirect
29. #16840298C4semidirect
30. #16840297C4semidirect
31. #16840296C4semidirect
33. #16840294C4semidirect
34. #16840293C4semidirect
36. #16840291C4semidirect
50. C61×#529C4semidirect
418. #529#6923semidirect
447. C61#21411semidirect

Maximal subgroups

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

subgroupindex
C4×D61⋊M162
#214622662
#214620012
#214619482
#214618352
#214618342
#214615912
#214615892
#529×D612
#2141161