Finite Group Databasebeta

← #30616682

Subgroups — #30616682

Order 15616.

1256 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758213C211yesmaximal, characteristic, complemented
2C4×#14519856C211yesmaximal, characteristic, complemented
3#21461996C212yesmaximal, complemented
4#21461984C212yesmaximal, complemented
5#21461802C212yesmaximal, complemented
6#21461800C212yesmaximal, complemented
7C4×#14519842C212yesmaximal, complemented
8C4×#14519841C212yesmaximal, complemented
9#21459113C211yesmaximal, characteristic
10C22×#11758213C2212yes—
11C2×#14519856—21no—
12C2×#14519842C2214yes—
13C2×#14519841C2214yes—
14C4×#11758213—21no—
15C4×#11758213—21no—
16C4×#11758213C2212yes—
17C4×#11758213C2212yes—
18C2×#14519832—21no—
19C2×C4×#92420—21no—
20C4×C4⋊#6923—21no—
21C4×C4⋊#6923C2212yes—
22C4×C22⋊#6923—21no—
23C4×C22⋊#6923C2212yes—
24#16840698—21no—
25C42×#6923C2212yes—
26#16840632C2214yes—
27#16840632C2214yes—
28#16840318C2211yescharacteristic
29#16840316C411yescharacteristic, complemented
30#16840314C411yescharacteristic, complemented
31#16840311C2211yescharacteristic
32#16840309C411yescharacteristic, complemented
33#16840307C411yescharacteristic, complemented
34#16840297C411yescharacteristic, complemented
35#16840296C411yescharacteristic, complemented
36#16840295—21no—
37#16840295—21no—
38#16840291C411yescharacteristic, complemented
39#16840290—21no—
40#16840289—21no—
41#16840275C2211yescharacteristic
42#16840272C2211yescharacteristic
43#16840271—21no—
44#16840270—21no—
45C4×#11758226C2211yescharacteristic
46#16840230—21no—
47C4×#11758224—21no—
48C4×#11758224C2211yescharacteristic
49C2×C42×D61C2211yescharacteristic
50C61×#529C411yescharacteristic, complemented
51C2×#11758213—22no—
52C2×#11758213—28no—
53C2×#11758213C2314yes—
54C22×#92420—22no—
55#14519856—28no—
56C2×C4⋊#6923—22no—
57C2×C22⋊#6923—22no—
58C2×C4×#6923—22no—
59C2×C4×#6923—22no—
60C2×C4×#6923C2314yes—
61#14519842—28no—
62#14519841—28no—
63#14519832—22no—
64#14519832—22no—
65C4×#92420—22no—
66C4×#92420—22no—
67(C2×#6923)⋊C4—22no—
68(C2×#6923)⋊C4—22no—
69C2×#11758226C2311yescharacteristic
70C2×#11758222—21no—
71C2×#11758224—21no—
72C2×#11758224C2311yescharacteristic
73C22×C4×D61D411yescharacteristic
74C22×C4×D61D411yescharacteristic
75C22×C4×D61C2311yescharacteristic
76#14519776C2×C411yescharacteristic
77#14519776C2×C411yescharacteristic
78#14519775C2×C411yescharacteristic
79#14519773C2×C411yescharacteristic
80#14519772—21no—
81#14519771—21no—
82#14519770—21no—
83#14519769C2×C411yescharacteristic
84#14519767—21no—
85#14519767—21no—
86#14519765C2×C411yescharacteristic
87#14519763—21no—
88#14519763—21no—
89#14519762—21no—
90#14519762—21no—
91#14519760—21no—
92#14519759—21no—
93#14519759—21no—
94#14519757C2×C411yescharacteristic
95#14519756C2×C411yescharacteristic
96#14519755—21no—
97#14519755—21no—
98#14519755—21no—
99#14519754—21no—
100#14519753C2×C411yescharacteristic
101#14519752C2×C411yescharacteristic
102#14519751C2×C411yescharacteristic
103#14519750—21no—
104#14519750—21no—
105#14519750—21no—
106#14519749—21no—
107#14519748C2×C411yescharacteristic
108#14519747—21no—
109#14519745—21no—
110Q8×Dic61C2×C411yescharacteristic
111C4×Dic122—21no—
112C4×Dic122C2×C411yescharacteristic
113#14519742—21no—
114#14519742—21no—
115#14519742—21no—
116#14519742C2×C411yescharacteristic
117C4×D244—21no—
118C4×D244C2×C411yescharacteristic
119D4×Dic61—21no—
120D4×Dic61C2×C411yescharacteristic
121#14519739—21no—
122#14519739—21no—
123#14519739—21no—
124#14519739C2×C411yescharacteristic
125C4×C22⋊D61—21no—
126C4×C22⋊D61—21no—
127C4×C22⋊D61—21no—
128#14519737—21no—
129#14519737—21no—
130#14519737—21no—
131#14519737—21no—
132#14519737—21no—
133#14519737—21no—
134#14519737—21no—
135#14519735—21no—
136#14519735—21no—
137#14519735C2311yescharacteristic
138#14519735C2311yescharacteristic
139#14519734—21no—
140#14519734—21no—
141#14519733—21no—
142#14519733—21no—
143#14519733—21no—
144C2×C4×Dic61—21no—
145C2×C4×Dic61C2×C411yescharacteristic
146C2×C4×Dic61D411yescharacteristic
147C2×C4×Dic61D411yescharacteristic
148C42×D61—21no—
149C42×D61C2×C411yescharacteristic
150C42×D61C2×C411yescharacteristic
151C42×D61D411yescharacteristic
152C42×D61D411yescharacteristic
153C42×D61D411yescharacteristic
154C42×D61D411yescharacteristic
155C42×D61C2311yescharacteristic
156C42×D61C2311yescharacteristic
157#126×C61—21no—
158#125×C61C2×C411yescharacteristic
159#124×C61C2×C411yescharacteristic
160#123×C61—21no—
161C22⋊Q8×C61C2×C411yescharacteristic
162#121×C61C2×C411yescharacteristic
163C4×Q8×C61C2×C411yescharacteristic
164C4×D4×C61—21no—
165C4×D4×C61C2×C411yescharacteristic
166#117×C61—21no—
167C2×C42×C61C2×C411yescharacteristic
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—
180C2×C22⋊D61—21no—
181C2×C22⋊D61—21no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61C22⋊C411yescharacteristic
185C22×Dic61C22⋊C411yescharacteristic
186C22×Dic61C2×D411yescharacteristic
187#11758226—24no—
188#11758224—24no—
189#11758224—44no—
190#11758222—44no—
191C2×D244—21no—
192C2×D244—21no—
193C2×D244C22×C411yescharacteristic
194C2×C4×D61—24no—
195C2×C4×D61—24no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—42no—
200C2×C4×D61C22⋊C411yescharacteristic
201C2×C4×D61C22⋊C411yescharacteristic
202C2×C4×D61C22⋊C411yescharacteristic
203C2×C4×D61C22⋊C411yescharacteristic
204C2×C4×D61C22×C411yescharacteristic
205C2×C4×D61C2×D411yescharacteristic
206C2×C4×D61C2×D411yescharacteristic
207C2×C4×D61C2×D411yescharacteristic
208C2×C4×D61C2×D411yescharacteristic
209C2×C4×D61C2×D411yescharacteristic
210C2×C4×D61C2×D411yescharacteristic
211C2×C4×D61C2411yescharacteristic
212C2×Dic122—21no—
213C2×Dic122—21no—
214C2×Dic122C22×C411yescharacteristic
215C22⋊#6923—28no—
216C2×#92420—28no—
217C2×#92420—24no—
218C4⋊#6923—28no—
219C4×#6923—28no—
220C4×#6923—24no—
221C4×#6923—24no—
222C4×#6923—44no—
223#11758213—28no—
224#11758213—24no—
225#11758213#4118yescomplemented
226C4⋊C4×C61—21no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61C22×C411yescharacteristic
231C4⋊C4×C61C22×C411yescharacteristic
232C22⋊C4×C61—21no—
233C22⋊C4×C61—21no—
234C22⋊C4×C61—21no—
235C22⋊C4×C61—21no—
236C22⋊C4×C61—21no—
237C42×C61—21no—
238C42×C61C22⋊C411yescharacteristic
239C42×C61C22⋊C411yescharacteristic
240C42×C61C22×C411yescharacteristic
241C42×C61C22×C411yescharacteristic
242C22⋊Dic61—21no—
243C22⋊Dic61—21no—
244C22⋊Dic61—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—
253#11758198—21no—
254#11758198—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×Dic61—21no—
273C4×Dic61—21no—
274C4×Dic61C22⋊C411yescharacteristic
275C4×Dic61C22⋊C411yescharacteristic
276C4×Dic61C22⋊C411yescharacteristic
277C4×Dic61C22⋊C411yescharacteristic
278C4×Dic61C22⋊C411yescharacteristic
279C4×Dic61C22⋊C411yescharacteristic
280C4×Dic61C22×C411yescharacteristic
281C4×Dic61C22×C411yescharacteristic
282C4×Dic61C2×D411yescharacteristic
283C4×Dic61C2×D411yescharacteristic
284C4×Dic61C2×D411yescharacteristic
285C4×Dic61C2×D411yescharacteristic
286C23×C61—21no—
287C23×C61C2×C22⋊C411yescharacteristic
288C22×D61—22no—
289C22×D61—22no—
290C22×D61—21no—
291C22×D61—41no—
292C22×D61C2×C22⋊C411yescharacteristic
293C22×D61C22×D411yescharacteristic
294C2×#6923—28no—
295C2×#6923—44no—
296C2×#6923—44no—
297Q8×C61—22no—
298D4×C61—22no—
299D4×C61—42no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
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—
316C22⋊D61—42no—
317C22⋊D61—42no—
318C2×Dic61—22no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—41no—
323C2×Dic61—42no—
324C2×Dic61—42no—
325C2×Dic61#10414yescomplemented
326C2×Dic61C2×C22⋊C411yescharacteristic
327C2×Dic61C2×C22⋊C411yescharacteristic
328C2×Dic61C2×C22⋊C411yescharacteristic
329C2×Dic61C2×C22⋊C411yescharacteristic
330C2×Dic61C2×C22⋊C411yescharacteristic
331C2×Dic61C22×D411yescharacteristic
332D244—22no—
333D244—42no—
334D244—42no—
335C4×D61—22no—
336C4×D61—22no—
337C4×D61—22no—
338C4×D61—22no—
339C4×D61—22no—
340C4×D61—22no—
341C4×D61—22no—
342C4×D61—22no—
343C4×D61—22no—
344C4×D61—41no—
345C4×D61—41no—
346C4×D61—42no—
347C4×D61—42no—
348C4×D61—42no—
349C4×D61C2×#4114yes—
350Dic122—22no—
351Dic122—42no—
352Dic122—42no—
353#92420—28no—
354#21382—611nomaximal, Sylow
355C22×C61—21no—
356C22×C61—21no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61C2×#10412yes—
361C22×C61C22×C22⋊C411yescharacteristic
362C2×D61—21no—
363C2×D61—21no—
364C2×D61—21no—
365C2×D61—21no—
366C2×D61—21no—
367C2×D61—44no—
368C2×D61—41no—
369C2×D61—41no—
370C2×D61—41no—
371C2×D61#53212yes—
372#6923—48no—
373C4×C61—21no—
374C4×C61—21no—
375C4×C61—21no—
376C4×C61—21no—
377C4×C61—41no—
378C4×C61—41no—
379C4×C61—41no—
380C4×C61#42112yes—
381C4×C61C4×#4112yes—
382Dic61—21no—
383Dic61—21no—
384Dic61—21no—
385Dic61—41no—
386Dic61—41no—
387Dic61—41no—
388Dic61C2×#10412yes—
389Dic61C2×#10412yes—
390Dic61#52512yes—
391#3444—611no—
392C2×C4×M16—611no—
393C4×#117—611no—
394#1986—612no—
395#1980—612no—
396#1871—612no—
397#1871—612no—
398C4×#104—612no—
399C4×#104—612no—
400C2×C61—22no—
401C2×C61—81no—
402C2×C61#229711yescharacteristic
403C2×C61C22×#10411yescharacteristic
404C2×C61C2×#42111yescharacteristic
405D61—22no—
406D61—41no—
407D61—81no—
408C22×M16—612no—
409#533—611no—
410#533—611no—
411#533—611no—
412#532—611no—
413#532—611no—
414#532—611no—
415#529—611no—
416#529—611no—
417#529—611no—
418#529—1221no—
419#529—1221no—
420#529—1221no—
421#529—1221no—
422#529#692311yescharacteristic, complemented
423#525—611no—
424#525—611no—
425#525—1221no—
426#525—1221no—
427C4×#41—611no—
428C4×#41—611no—
429C4×#41—1221no—
430C4×#41—1221no—
431C2×#117—1221no—
432C22×C42—611no—
433C2×#104—614no—
434C2×#104—614no—
435C4×M16—612no—
436C4×M16—612no—
437C4×M16—1221no—
438C4×M16—1221no—
439C2×#97—1221no—
440C2×C4×C8—1221no—
441C4×C4⋊C4—612no—
442C4×C4⋊C4—1221no—
443C4×C22⋊C4—612no—
444C4×C22⋊C4—1221no—
445#376—1221no—
446C43—612no—
447#339—614no—
448#339—614no—
449C61#2138211yescharacteristic, complemented, Sylow
450C2×#41—611no—
451C2×#41—611no—
452C2×#41—1221no—
453C2×#41—1221no—
454C23×C4—611no—
455C23×C4—611no—
456C23×C4—611no—
457C2×M16—614no—
458C2×M16—1228no—
459C2×M16—1222no—
460C22×C8—1222no—
461C4⋊Q8—611no—
462C4⋊Q8—611no—
463C4⋊Q8—611no—
464#127—611no—
465#126—21no—
466#126—1221no—
467#126—1221no—
468#126—1221no—
469#125—611no—
470#125—1221no—
471#125—1221no—
472#125C2×#692311yescharacteristic
473#124—611no—
474#124—1221no—
475#124—1221no—
476#124C2×#692311yescharacteristic
477#123—21no—
478#123—1221no—
479#123—1221no—
480#123—1221no—
481#123—1221no—
482#123—1221no—
483C22⋊Q8—611no—
484C22⋊Q8—611no—
485C22⋊Q8—611no—
486C22⋊Q8—1221no—
487C22⋊Q8—1221no—
488C22⋊Q8—1221no—
489C22⋊Q8—1221no—
490C22⋊Q8C2×#692311yescharacteristic
491#121—611no—
492#121—611no—
493#121—611no—
494#121—1221no—
495#121—1221no—
496#121—1221no—
497#121—1221no—
498#121C2×#692311yescharacteristic
499#120—1221no—
500#120—1221no—
501C4×Q8—611no—
502C4×Q8—611no—
503C4×Q8—611no—
504C4×Q8—1221no—
505C4×Q8—1221no—
506C4×Q8—1221no—
507C4×Q8—1221no—
508C4×Q8C2×#692311yescharacteristic
509C4×D4—21no—
510C4×D4—611no—
511C4×D4—611no—
512C4×D4—611no—
513C4×D4—1221no—
514C4×D4—1221no—
515C4×D4—1221no—
516C4×D4—1221no—
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×D4—1221no—
527C4×D4—1221no—
528C4×D4C2×#692311yescharacteristic
529#117—21no—
530#117—611no—
531#117—611no—
532#117—1221no—
533#117—1221no—
534#117—1221no—
535#117—1221no—
536#117—1221no—
537#117—1221no—
538#117—1228no—
539#117—1221no—
540C2×C4⋊C4—1222no—
541C2×C22⋊C4—1222no—
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—611no—
552C2×C42—611no—
553C2×C42—614no—
554C2×C42—1221no—
555C2×C42—1221no—
556C2×C42—1222no—
557C2×C42—1222no—
558C2×C42C2×#692311yescharacteristic
559#104—1228no—
560#104—1228no—
561#97—1222no—
562#97—1222no—
563C4×C8—1222no—
564C4×C8—1222no—
565#95—1222no—
566#95—1222no—
567C24—611no—
568#41—1224no—
569#41—1224no—
570#41—2444no—
571#41—2444no—
572C2×Q8—611no—
573C2×Q8—1221no—
574C2×Q8—1221no—
575C2×Q8C22×#692311yescharacteristic
576C2×D4—21no—
577C2×D4—611no—
578C2×D4—1221no—
579C2×D4—1221no—
580C2×D4—1221no—
581C2×D4—1221no—
582C2×D4—1221no—
583C2×D4—1221no—
584C2×D4—1221no—
585C2×D4C22×#692311yescharacteristic
586C22×C4—21no—
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—611no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—1224no—
603C22×C4—1224no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1224no—
609C22×C4—1221no—
610C22×C4—2442no—
611C22×C4C22⋊#692311yescharacteristic
612C22×C4C22⋊#692311yescharacteristic
613C22×C4C22×#692311yescharacteristic
614M16—618no—
615M16—1224no—
616M16—1228no—
617C2×C8—1224no—
618C2×C8—1228no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—611no—
624C4⋊C4—611no—
625C4⋊C4—1221no—
626C4⋊C4—1221no—
627C4⋊C4—1221no—
628C4⋊C4—1221no—
629C4⋊C4—1221no—
630C4⋊C4—1221no—
631C4⋊C4—1221no—
632C4⋊C4—1221no—
633C4⋊C4—1228no—
634C4⋊C4—1221no—
635C4⋊C4—1221no—
636C4⋊C4—1221no—
637C4⋊C4—1221no—
638C4⋊C4C22×#692311yescharacteristic
639C4⋊C4C22×#692311yescharacteristic
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
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—1228no—
654C22⋊C4—1221no—
655C22⋊C4—1221no—
656C22⋊C4—1221no—
657C22⋊C4—1221no—
658C22⋊C4—1221no—
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—1221no—
676C42—1224no—
677C42—1224no—
678C42—1228no—
679C42—1221no—
680C42—2444no—
681C42C22⋊#692311yescharacteristic
682C42C22⋊#692311yescharacteristic
683C42C22×#692311yescharacteristic
684C42C22×#692311yescharacteristic
685C23—21no—
686C23—611no—
687C23—611no—
688C23—1222no—
689C23—1222no—
690C23—1221no—
691C23—2441no—
692C23C2×C22⋊#692311yescharacteristic
693Q8—22no—
694Q8—1222no—
695Q8—2442no—
696Q8—2442no—
697D4—22no—
698D4—42no—
699D4—1222no—
700D4—2442no—
701D4—2442no—
702D4—2442no—
703D4—2442no—
704D4—2442no—
705D4—2442no—
706D4—2442no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—42no—
714C2×C4—614no—
715C2×C4—611no—
716C2×C4—611no—
717C2×C4—611no—
718C2×C4—614no—
719C2×C4—611no—
720C2×C4—611no—
721C2×C4—611no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—1222no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1228no—
733C2×C4—1221no—
734C2×C4—1221no—
735C2×C4—1221no—
736C2×C4—2441no—
737C2×C4—2441no—
738C2×C4—2442no—
739C2×C4—2442no—
740C2×C4—2442no—
741C2×C4—2442no—
742C2×C4—2441no—
743C2×C4—2444no—
744C2×C4—2444no—
745C2×C4—2442no—
746C2×C4C2×C22⋊#692311yescharacteristic
747C2×C4C2×C22⋊#692311yescharacteristic
748C2×C4C2×C22⋊#692311yescharacteristic
749C2×C4C2×C22⋊#692311yescharacteristic
750C2×C4C2×C22⋊#692311yescharacteristic
751C2×C4C23×#692311yescharacteristic
752C8—1228no—
753C22—21no—
754C22—21no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—612no—
759C22—1221no—
760C22—1221no—
761C22—1221no—
762C22—1221no—
763C22—1221no—
764C22—2444no—
765C22—2441no—
766C22—2441no—
767C22—2441no—
768C22D61⋊#10412yes—
769C22C22×C22⋊#692311yescharacteristic
770C4—21no—
771C4—21no—
772C4—21no—
773C4—21no—
774C4—41no—
775C4—41no—
776C4—41no—
777C4—612no—
778C4—612no—
779C4—612no—
780C4—1221no—
781C4—1221no—
782C4—1221no—
783C4—2448no—
784C4—2441no—
785C4—2441no—
786C4—2441no—
787C4#1684075912yes—
788C4#41×#692312yes—
789C2—22no—
790C2—81no—
791C2—1222no—
792C2—4881no—
793C2—2441no—
794C2#2146228011yescharacteristic
795C2C2×D61⋊#10411yescharacteristic
796C2C2×#1684075911yescharacteristic
subgroupG/H
centerC2×C4C2×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#21382
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C2×C4×#11758213C2semidirect
2. C4×#14519856C2semidirect
3. #21461996C2semidirect
4. #21461984C2semidirect
5. #21461802C2semidirect
6. #21461800C2semidirect
7. C4×#14519842C2semidirect
8. C4×#14519841C2semidirect
29. #16840316C4semidirect
30. #16840314C4semidirect
32. #16840309C4semidirect
33. #16840307C4semidirect
34. #16840297C4semidirect
35. #16840296C4semidirect
38. #16840291C4semidirect
50. C61×#529C4semidirect
225. #11758213#41semidirect
325. C2×Dic61#104semidirect
422. #529#6923semidirect
449. C61#21382semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117582132
C4×#145198562
#214619962
#214619842
#214618022
#214618002
C4×#145198422
C4×#145198412
#214591132
#2138261