Finite Group Databasebeta

← #30610970

Subgroups — #30610970

Order 15616.

1108 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840785C211yesmaximal, characteristic, complemented
2C4×#14519856C211yesmaximal, characteristic, complemented
3#21461222C212yesmaximal, complemented
4#21461220C212yesmaximal, complemented
5#21461212C212yesmaximal, complemented
6#21461209C212yesmaximal, complemented
7#21461197C212yesmaximal, complemented
8#21461195C212yesmaximal, complemented
9#21459113C211yesmaximal, characteristic
10C2×#14519856—21no—
11#16840785—21no—
12#16840785—21no—
13#16840785C2212yes—
14#16840785C2212yes—
15C2×#14519844—21no—
16C2×#14519834C2212yes—
17C2×#14519832—21no—
18C4×C4⋊#6923—21no—
19C4×C4⋊#6923C2212yes—
20C4×C22⋊#6923—21no—
21C4×C22⋊#6923C2212yes—
22#16840698C2212yes—
23C42×#6923—21no—
24#16840616C2214yes—
25#16840615C2214yes—
26#16840614C2214yes—
27#16840613C2214yes—
28#16840318C411yescharacteristic, complemented
29#16840316C2211yescharacteristic
30#16840314C411yescharacteristic, complemented
31#16840311C411yescharacteristic, complemented
32#16840309C2211yescharacteristic
33#16840307C411yescharacteristic, complemented
34#16840297C2211yescharacteristic
35#16840296C411yescharacteristic, complemented
36#16840295—21no—
37#16840295—21no—
38#16840291C2211yescharacteristic
39#16840290—21no—
40#16840289—21no—
41#16840275C2211yescharacteristic
42#16840272C2211yescharacteristic
43#16840271—21no—
44#16840270—21no—
45C4×#11758226C411yescharacteristic, complemented
46#16840230—21no—
47C4×#11758224—21no—
48C4×#11758224C411yescharacteristic, complemented
49C2×C42×D61C2211yescharacteristic
50C61×#529C411yescharacteristic, complemented
51C22×#92420—22no—
52#14519856—28no—
53C2×C4⋊#6923—22no—
54C2×C22⋊#6923—22no—
55C2×C4×#6923—22no—
56C2×C4×#6923—22no—
57C2×C4×#6923—22no—
58#14519844—22no—
59#14519844—22no—
60#14519834—22no—
61#14519834C2314yes—
62#14519832—22no—
63#14519832—22no—
64(C2×#6923)⋊C4—22no—
65(C2×#6923)⋊C4C2314yes—
66C2×#11758226C2×C411yescharacteristic
67C2×#11758222—21no—
68C2×#11758224—21no—
69C2×#11758224C2×C411yescharacteristic
70C22×C4×D61D411yescharacteristic
71C22×C4×D61D411yescharacteristic
72C22×C4×D61C2311yescharacteristic
73#14519776C2×C411yescharacteristic
74#14519776C2×C411yescharacteristic
75#14519775C2×C411yescharacteristic
76#14519773C2×C411yescharacteristic
77#14519772—21no—
78#14519771—21no—
79#14519770—21no—
80#14519769C2×C411yescharacteristic
81#14519767—21no—
82#14519767—21no—
83#14519765C2×C411yescharacteristic
84#14519763—21no—
85#14519763—21no—
86#14519762—21no—
87#14519762—21no—
88#14519760—21no—
89#14519759—21no—
90#14519759—21no—
91#14519757C2311yescharacteristic
92#14519756C2×C411yescharacteristic
93#14519755—21no—
94#14519755—21no—
95#14519755—21no—
96#14519754—21no—
97#14519753C2311yescharacteristic
98#14519752C2311yescharacteristic
99#14519751C2×C411yescharacteristic
100#14519750—21no—
101#14519750—21no—
102#14519750—21no—
103#14519749—21no—
104#14519748C2311yescharacteristic
105#14519747—21no—
106#14519745—21no—
107Q8×Dic61C2×C411yescharacteristic
108C4×Dic122—21no—
109C4×Dic122C2×C411yescharacteristic
110#14519742—21no—
111#14519742—21no—
112#14519742—21no—
113#14519742C2×C411yescharacteristic
114C4×D244—21no—
115C4×D244C2×C411yescharacteristic
116D4×Dic61—21no—
117D4×Dic61C2×C411yescharacteristic
118#14519739—21no—
119#14519739—21no—
120#14519739—21no—
121#14519739C2×C411yescharacteristic
122C4×C22⋊D61—21no—
123C4×C22⋊D61—21no—
124C4×C22⋊D61—21no—
125#14519737—21no—
126#14519737—21no—
127#14519737—21no—
128#14519737—21no—
129#14519737—21no—
130#14519737—21no—
131#14519737—21no—
132#14519735—21no—
133#14519735—21no—
134#14519735C2×C411yescharacteristic
135#14519735C2×C411yescharacteristic
136#14519734—21no—
137#14519734—21no—
138#14519733—21no—
139#14519733—21no—
140#14519733—21no—
141C2×C4×Dic61—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
156#124×C61C2×C411yescharacteristic
157#123×C61—21no—
158C22⋊Q8×C61C2×C411yescharacteristic
159#121×C61C2×C411yescharacteristic
160C4×Q8×C61C2×C411yescharacteristic
161C4×D4×C61—21no—
162C4×D4×C61C2×C411yescharacteristic
163#117×C61—21no—
164C2×C42×C61C2×C411yescharacteristic
165C23×D61C2×D411yescharacteristic
166C22×#6923—24no—
167C2×Q8×C61C22×C411yescharacteristic
168C2×D4×C61—21no—
169C2×D4×C61C22×C411yescharacteristic
170C22×C4×C61—21no—
171C22×C4×C61C22⋊C411yescharacteristic
172C22×C4×C61C22⋊C411yescharacteristic
173C22×C4×C61C22×C411yescharacteristic
174C2×C22⋊D61—21no—
175C2×C22⋊D61—21no—
176C2×C22⋊D61—21no—
177C2×C22⋊D61—21no—
178C2×C22⋊D61—21no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61C22⋊C411yescharacteristic
182C22×Dic61C22⋊C411yescharacteristic
183C22×Dic61C2×D411yescharacteristic
184#11758226—42no—
185#11758224—42no—
186#11758224—44no—
187#11758222—44no—
188C2×D244—21no—
189C2×D244—21no—
190C2×D244C22×C411yescharacteristic
191C2×C4×D61—24no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—42no—
196C2×C4×D61—42no—
197C2×C4×D61C22⋊C411yescharacteristic
198C2×C4×D61C22⋊C411yescharacteristic
199C2×C4×D61C22⋊C411yescharacteristic
200C2×C4×D61C22⋊C411yescharacteristic
201C2×C4×D61C22×C411yescharacteristic
202C2×C4×D61C2×D411yescharacteristic
203C2×C4×D61C2×D411yescharacteristic
204C2×C4×D61C2×D411yescharacteristic
205C2×C4×D61C2×D411yescharacteristic
206C2×C4×D61C2×D411yescharacteristic
207C2×C4×D61C2×D411yescharacteristic
208C2×C4×D61C2411yescharacteristic
209C2×Dic122—21no—
210C2×Dic122—21no—
211C2×Dic122C22×C411yescharacteristic
212C22⋊#6923—28no—
213C2×#92420—24no—
214C2×#92420—44no—
215C4⋊#6923—28no—
216C4×#6923—28no—
217C4×#6923—44no—
218C4×#6923—44no—
219C4⋊C4×C61—21no—
220C4⋊C4×C61—21no—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61C22×C411yescharacteristic
224C4⋊C4×C61C22×C411yescharacteristic
225C22⋊C4×C61—21no—
226C22⋊C4×C61—21no—
227C22⋊C4×C61—21no—
228C22⋊C4×C61—21no—
229C22⋊C4×C61—21no—
230C42×C61—21no—
231C42×C61C22⋊C411yescharacteristic
232C42×C61C22⋊C411yescharacteristic
233C42×C61C22×C411yescharacteristic
234C42×C61C22×C411yescharacteristic
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⋊Dic61C22×C411yescharacteristic
251C4⋊Dic61C22×C411yescharacteristic
252#11758196—21no—
253#11758196—21no—
254#11758196—21no—
255#11758196—21no—
256#11758196—21no—
257#11758196—21no—
258#11758196—21no—
259#11758196—21no—
260#11758196—21no—
261#11758196—21no—
262C4×Dic61—21no—
263C4×Dic61—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—41no—
285C22×D61C2×C22⋊C411yescharacteristic
286C22×D61C22×D411yescharacteristic
287C2×#6923—28no—
288C2×#6923—44no—
289C2×#6923—44no—
290Q8×C61—41no—
291D4×C61—41no—
292D4×C61—42no—
293C2×C4×C61—22no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—42no—
300C2×C4×C61C2×C22⋊C411yescharacteristic
301C2×C4×C61C2×C22⋊C411yescharacteristic
302C2×C4×C61C2×C22⋊C411yescharacteristic
303C2×C4×C61C2×C22⋊C411yescharacteristic
304C2×C4×C61C2×C22⋊C411yescharacteristic
305C2×C4×C61C23×C411yescharacteristic
306C22⋊D61—42no—
307C22⋊D61—42no—
308C22⋊D61—42no—
309C22⋊D61—42no—
310C22⋊D61—42no—
311C2×Dic61—22no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—41no—
316C2×Dic61—42no—
317C2×Dic61—42no—
318C2×Dic61#10414yes—
319C2×Dic61C2×C22⋊C411yescharacteristic
320C2×Dic61C2×C22⋊C411yescharacteristic
321C2×Dic61C2×C22⋊C411yescharacteristic
322C2×Dic61C2×C22⋊C411yescharacteristic
323C2×Dic61C2×C22⋊C411yescharacteristic
324C2×Dic61C22×D411yescharacteristic
325D244—41no—
326D244—42no—
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—41no—
337C4×D61—41no—
338C4×D61—41no—
339C4×D61—41no—
340C4×D61—42no—
341C4×D61—42no—
342C4×D61—42no—
343Dic122—42no—
344Dic122—42no—
345Dic122—41no—
346#92420—44no—
347#17543—611nomaximal, Sylow
348C22×C61—21no—
349C22×C61—21no—
350C22×C61—41no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61C2×#10412yes—
354C22×C61C22×C22⋊C411yescharacteristic
355C2×D61—21no—
356C2×D61—21no—
357C2×D61—21no—
358C2×D61—21no—
359C2×D61—21no—
360C2×D61—44no—
361C2×D61—41no—
362C2×D61—41no—
363C2×D61—41no—
364C2×D61#57512yes—
365#6923—48no—
366C4×C61—21no—
367C4×C61—21no—
368C4×C61—21no—
369C4×C61—21no—
370C4×C61—21no—
371C4×C61—21no—
372C4×C61—41no—
373C4×C61—41no—
374C4×C61—41no—
375Dic61—21no—
376Dic61—21no—
377Dic61—21no—
378Dic61—41no—
379Dic61—41no—
380Dic61—41no—
381Dic61#41012yes—
382Dic61C2×#10412yes—
383Dic61C2×#10412yes—
384#3444—611no—
385C2×#432—611no—
386C4×#117—611no—
387#1509—612no—
388#1509—612no—
389#1506—612no—
390#1505—612no—
391#1501—612no—
392#1501—612no—
393C2×C61—22no—
394C2×C61—81no—
395C2×C61C2×#41011yescharacteristic
396C2×C61#289611yescharacteristic
397C2×C61C22×#10411yescharacteristic
398D61—22no—
399D61—41no—
400D61—81no—
401#533—611no—
402#533—611no—
403#533—611no—
404#532—611no—
405#532—611no—
406#532—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
415#525—611no—
416#525—611no—
417#525—1221no—
418#525—1221no—
419C4×#41—611no—
420C4×#41—611no—
421C4×#41—1221no—
422C4×#41—1221no—
423C2×#117—1221no—
424C22×C42—611no—
425#432—612no—
426#432—612no—
427#432—1221no—
428#432—1221no—
429C2×C4⋊C8—1221no—
430C2×C22⋊C8—612no—
431C2×#97—1221no—
432C4×C4⋊C4—612no—
433C4×C4⋊C4—1221no—
434C4×C22⋊C4—612no—
435C4×C22⋊C4—1221no—
436#376—612no—
437C43—1221no—
438#328—614no—
439#328—614no—
440#327—614no—
441#327—614no—
442C61#1754311yescharacteristic, complemented, Sylow
443C2×#41—611no—
444C2×#41—611no—
445C2×#41—1221no—
446C2×#41—1221no—
447C23×C4—611no—
448C23×C4—611no—
449C23×C4—611no—
450C22×C8—1222no—
451C4⋊Q8—611no—
452C4⋊Q8—611no—
453C4⋊Q8—611no—
454#127—611no—
455#126—21no—
456#126—1221no—
457#126—1221no—
458#126—1221no—
459#125—611no—
460#125—1221no—
461#125—1221no—
462#125C2×#692311yescharacteristic
463#124—611no—
464#124—1221no—
465#124—1221no—
466#124C2×#692311yescharacteristic
467#123—21no—
468#123—1221no—
469#123—1221no—
470#123—1221no—
471#123—1221no—
472#123—1221no—
473C22⋊Q8—611no—
474C22⋊Q8—611no—
475C22⋊Q8—611no—
476C22⋊Q8—1221no—
477C22⋊Q8—1221no—
478C22⋊Q8—1221no—
479C22⋊Q8—1221no—
480C22⋊Q8C2×#692311yescharacteristic
481#121—611no—
482#121—611no—
483#121—611no—
484#121—1221no—
485#121—1221no—
486#121—1221no—
487#121—1221no—
488#121C2×#692311yescharacteristic
489#120—1221no—
490#120—1221no—
491C4×Q8—611no—
492C4×Q8—611no—
493C4×Q8—611no—
494C4×Q8—1221no—
495C4×Q8—1221no—
496C4×Q8—1221no—
497C4×Q8—1221no—
498C4×Q8C2×#692311yescharacteristic
499C4×D4—21no—
500C4×D4—611no—
501C4×D4—611no—
502C4×D4—611no—
503C4×D4—1221no—
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×D4—1221no—
514C4×D4—1221no—
515C4×D4—1221no—
516C4×D4—1221no—
517C4×D4—1221no—
518C4×D4C2×#692311yescharacteristic
519#117—21no—
520#117—611no—
521#117—611no—
522#117—1221no—
523#117—1221no—
524#117—1221no—
525#117—1221no—
526#117—1221no—
527#117—1221no—
528#117—1228no—
529#117—1221no—
530C2×C4⋊C4—1222no—
531C2×C22⋊C4—1222no—
532C2×C42—611no—
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—1221no—
544C2×C42—1221no—
545C2×C42—1222no—
546C2×C42—1222no—
547C2×C42—1222no—
548C2×C42C2×#692311yescharacteristic
549C4⋊C8—1222no—
550C4⋊C8—1222no—
551C22⋊C8—614no—
552C22⋊C8—1222no—
553#97—1222no—
554#97—1222no—
555#95—614no—
556#95—1222no—
557C24—611no—
558#41—2444no—
559#41—2444no—
560#41—2442no—
561#41—2442no—
562C2×Q8—611no—
563C2×Q8—1221no—
564C2×Q8—1221no—
565C2×Q8C22×#692311yescharacteristic
566C2×D4—21no—
567C2×D4—611no—
568C2×D4—1221no—
569C2×D4—1221no—
570C2×D4—1221no—
571C2×D4—1221no—
572C2×D4—1221no—
573C2×D4—1221no—
574C2×D4—1221no—
575C2×D4C22×#692311yescharacteristic
576C22×C4—21no—
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—611no—
591C22×C4—611no—
592C22×C4—1224no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4—1224no—
598C22×C4—1221no—
599C22×C4—2442no—
600C22×C4—2442no—
601C22×C4C22⋊#692311yescharacteristic
602C22×C4C22⋊#692311yescharacteristic
603C22×C4C22×#692311yescharacteristic
604C2×C8—1224no—
605C2×C8—2444no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—611no—
611C4⋊C4—611no—
612C4⋊C4—1221no—
613C4⋊C4—1221no—
614C4⋊C4—1221no—
615C4⋊C4—1221no—
616C4⋊C4—1221no—
617C4⋊C4—1221no—
618C4⋊C4—1221no—
619C4⋊C4—1221no—
620C4⋊C4—1228no—
621C4⋊C4—1221no—
622C4⋊C4—1221no—
623C4⋊C4—1221no—
624C4⋊C4—1221no—
625C4⋊C4C22×#692311yescharacteristic
626C4⋊C4C22×#692311yescharacteristic
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—1221no—
633C22⋊C4—1221no—
634C22⋊C4—1221no—
635C22⋊C4—1221no—
636C22⋊C4—1221no—
637C22⋊C4—1221no—
638C22⋊C4—1221no—
639C22⋊C4—1221no—
640C22⋊C4—1228no—
641C22⋊C4—1221no—
642C22⋊C4—1221no—
643C22⋊C4—1221no—
644C22⋊C4—1221no—
645C22⋊C4—1221no—
646C42—21no—
647C42—611no—
648C42—611no—
649C42—611no—
650C42—611no—
651C42—611no—
652C42—611no—
653C42—611no—
654C42—611no—
655C42—611no—
656C42—611no—
657C42—611no—
658C42—611no—
659C42—1221no—
660C42—1221no—
661C42—1221no—
662C42—1221no—
663C42—1228no—
664C42—1221no—
665C42—2444no—
666C42—2444no—
667C42C22⋊#692311yescharacteristic
668C42C22⋊#692311yescharacteristic
669C42C22×#692311yescharacteristic
670C42C22×#692311yescharacteristic
671C23—21no—
672C23—611no—
673C23—611no—
674C23—1222no—
675C23—1222no—
676C23—1221no—
677C23—2441no—
678C23C2×C22⋊#692311yescharacteristic
679Q8—41no—
680Q8—2441no—
681Q8—2442no—
682Q8—2442no—
683D4—41no—
684D4—42no—
685D4—2441no—
686D4—2442no—
687D4—2442no—
688D4—2442no—
689D4—2442no—
690D4—2442no—
691D4—2442no—
692D4—2442no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—614no—
701C2×C4—611no—
702C2×C4—611no—
703C2×C4—611no—
704C2×C4—611no—
705C2×C4—611no—
706C2×C4—611no—
707C2×C4—1222no—
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—1228no—
717C2×C4—1221no—
718C2×C4—1221no—
719C2×C4—1221no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4—2442no—
725C2×C4—2442no—
726C2×C4—2442no—
727C2×C4—2442no—
728C2×C4—2442no—
729C2×C4—2441no—
730C2×C4—2444no—
731C2×C4—2444no—
732C2×C4C2×C22⋊#692311yescharacteristic
733C2×C4C2×C22⋊#692311yescharacteristic
734C2×C4C2×C22⋊#692311yescharacteristic
735C2×C4C2×C22⋊#692311yescharacteristic
736C2×C4C2×C22⋊#692311yescharacteristic
737C2×C4C23×#692311yescharacteristic
738C8—2444no—
739C22—21no—
740C22—21no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—612no—
745C22—1221no—
746C22—1221no—
747C22—1221no—
748C22—1221no—
749C22—1221no—
750C22—2444no—
751C22—2441no—
752C22—2441no—
753C22—2441no—
754C22D61⋊#10412yes—
755C22C22×C22⋊#692311yescharacteristic
756C4—21no—
757C4—21no—
758C4—21no—
759C4—21no—
760C4—21no—
761C4—21no—
762C4—41no—
763C4—41no—
764C4—41no—
765C4—612no—
766C4—612no—
767C4—612no—
768C4—1221no—
769C4—1221no—
770C4—1221no—
771C4—2448no—
772C4—2441no—
773C4—2441no—
774C4—2441no—
775C2—22no—
776C2—81no—
777C2—1222no—
778C2—4881no—
779C2—2441no—
780C2D61⋊#41011yescharacteristic
781C2#2146243911yescharacteristic
782C2C2×D61⋊#10411yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#529C4
socleC22×C61C22×C22⋊C4
prime radical#21459113C2
cosocleC2×C4×D61C24
hypercenter#529#6923
hypocenterC61#17543
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. C2×#16840785C2semidirect
2. C4×#14519856C2semidirect
3. #21461222C2semidirect
4. #21461220C2semidirect
5. #21461212C2semidirect
6. #21461209C2semidirect
7. #21461197C2semidirect
8. #21461195C2semidirect
28. #16840318C4semidirect
30. #16840314C4semidirect
31. #16840311C4semidirect
33. #16840307C4semidirect
35. #16840296C4semidirect
45. C4×#11758226C4semidirect
48. C4×#11758224C4semidirect
50. C61×#529C4semidirect
414. #529#6923semidirect
442. C61#17543semidirect

Maximal subgroups

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

subgroupindex
C2×#168407852
C4×#145198562
#214612222
#214612202
#214612122
#214612092
#214611972
#214611952
#214591132
#1754361