Finite Group Databasebeta

← #30616731

Subgroups — #30616731

Order 15616.

1214 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
1#21462496C211yesmaximal, characteristic, complemented
2C2×#16840698C211yesmaximal, characteristic, complemented
3#21462006C212yesmaximal, complemented
4#21461956C212yesmaximal, complemented
5#21461837C212yesmaximal, complemented
6#21461836C212yesmaximal, complemented
7#21461583C212yesmaximal, complemented
8#21461582C212yesmaximal, complemented
9#21459113C211yesmaximal, characteristic
10C22×C4×#6923C2212yes—
11#16840784—21no—
12#16840783—21no—
13#16840781—21no—
14#16840778—21no—
15#16840766C2212yes—
16C2×#14519842C2214yes—
17C2×#14519841C2214yes—
18#16840733C2212yes—
19C4×#11758213C2212yes—
20#16840698—21no—
21#16840698—21no—
22#16840698C2212yes—
23#16840698C2212yes—
24C2×(C2×#6923)⋊C4—21no—
25C2×(C2×#6923)⋊C4—21no—
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
51C23×#6923—22no—
52C2×#11758213C2314yes—
53C2×C4×#6923—22no—
54C2×C4×#6923—28no—
55C2×C4×#6923C2314yes—
56C4⋊#92420—22no—
57C4⋊#92420—22no—
58#14519842—28no—
59#14519841—28no—
60#14519834—22no—
61C22⋊#92420—22no—
62#14519832—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×#11758226C2311yescharacteristic
69C2×#11758222—21no—
70C2×#11758224—21no—
71C2×#11758224C2311yescharacteristic
72C22×C4×D61D411yescharacteristic
73C22×C4×D61D411yescharacteristic
74C22×C4×D61C2311yescharacteristic
75#14519776C2×C411yescharacteristic, complemented
76#14519776C2×C411yescharacteristic, complemented
77#14519775C2×C411yescharacteristic, complemented
78#14519773C2×C411yescharacteristic, complemented
79#14519772—21no—
80#14519771—21no—
81#14519770—21no—
82#14519769C2×C411yescharacteristic, complemented
83#14519767—21no—
84#14519767—21no—
85#14519765C2×C411yescharacteristic, complemented
86#14519763—21no—
87#14519763—21no—
88#14519762—21no—
89#14519762—21no—
90#14519760—21no—
91#14519759—21no—
92#14519759—21no—
93#14519757C2×C411yescharacteristic
94#14519756C2×C411yescharacteristic
95#14519755—21no—
96#14519755—21no—
97#14519755—21no—
98#14519754—21no—
99#14519753C2×C411yescharacteristic
100#14519752C2×C411yescharacteristic
101#14519751C2×C411yescharacteristic
102#14519750—21no—
103#14519750—21no—
104#14519750—21no—
105#14519749—21no—
106#14519748C2×C411yescharacteristic
107#14519747—21no—
108#14519745—21no—
109Q8×Dic61C2×C411yescharacteristic, complemented
110C4×Dic122—21no—
111C4×Dic122C2×C411yescharacteristic, complemented
112#14519742—21no—
113#14519742—21no—
114#14519742—21no—
115#14519742C2×C411yescharacteristic, complemented
116C4×D244—21no—
117C4×D244C2×C411yescharacteristic, complemented
118D4×Dic61—21no—
119D4×Dic61C2×C411yescharacteristic, complemented
120#14519739—21no—
121#14519739—21no—
122#14519739—21no—
123#14519739C2×C411yescharacteristic, complemented
124C4×C22⋊D61—21no—
125C4×C22⋊D61—21no—
126C4×C22⋊D61—21no—
127#14519737—21no—
128#14519737—21no—
129#14519737—21no—
130#14519737—21no—
131#14519737—21no—
132#14519737—21no—
133#14519737—21no—
134#14519735—21no—
135#14519735—21no—
136#14519735C2311yescharacteristic
137#14519735C2311yescharacteristic
138#14519734—21no—
139#14519734—21no—
140#14519733—21no—
141#14519733—21no—
142#14519733—21no—
143C2×C4×Dic61—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, complemented
158#124×C61C2×C411yescharacteristic, complemented
159#123×C61—21no—
160C22⋊Q8×C61C2×C411yescharacteristic
161#121×C61C2×C411yescharacteristic
162C4×Q8×C61C2×C411yescharacteristic, complemented
163C4×D4×C61—21no—
164C4×D4×C61C2×C411yescharacteristic, complemented
165#117×C61—21no—
166C2×C42×C61C2×C411yescharacteristic
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—
182C2×C22⋊D61—21no—
183C2×C22⋊D61—21no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186C22×Dic61C22⋊C411yescharacteristic
187C22×Dic61C22⋊C411yescharacteristic
188C22×Dic61C2×D411yescharacteristic
189#11758226—24no—
190#11758224—24no—
191#11758224—44no—
192#11758222—44no—
193C2×D244—21no—
194C2×D244—21no—
195C2×D244C22×C411yescharacteristic
196C2×C4×D61—24no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61—42no—
201C2×C4×D61—42no—
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×Dic122—21no—
216C2×Dic122C22×C411yescharacteristic
217C2×#92420—24no—
218C4×#6923—28no—
219C4×#6923—24no—
220C4×#6923#4118yescomplemented
221#11758213—24no—
222#11758213—24no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61—21no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61C22×C411yescharacteristic
228C4⋊C4×C61C22×C411yescharacteristic
229C22⋊C4×C61—21no—
230C22⋊C4×C61—21no—
231C22⋊C4×C61—21no—
232C22⋊C4×C61—21no—
233C22⋊C4×C61—21no—
234C42×C61—21no—
235C42×C61C22⋊C411yescharacteristic
236C42×C61C22⋊C411yescharacteristic
237C42×C61C22×C411yescharacteristic
238C42×C61C22×C411yescharacteristic
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⋊Dic61C22×C411yescharacteristic
255C4⋊Dic61C22×C411yescharacteristic
256#11758196—21no—
257#11758196—21no—
258#11758196—21no—
259#11758196—21no—
260#11758196—21no—
261#11758196—21no—
262#11758196—21no—
263#11758196—21no—
264#11758196—21no—
265#11758196—21no—
266C4×Dic61—21no—
267C4×Dic61—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×D61C2×C22⋊C411yescharacteristic
290C22×D61C22×D411yescharacteristic
291C2×#6923—28no—
292C2×#6923—416no—
293C2×#6923—44no—
294C2×#6923—44no—
295Q8×C61—22no—
296D4×C61—22no—
297D4×C61—42no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—41no—
304C2×C4×C61—42no—
305C2×C4×C61C2×C22⋊C411yescharacteristic
306C2×C4×C61C2×C22⋊C411yescharacteristic
307C2×C4×C61C2×C22⋊C411yescharacteristic
308C2×C4×C61C2×C22⋊C411yescharacteristic
309C2×C4×C61C2×C22⋊C411yescharacteristic
310C2×C4×C61C23×C411yescharacteristic
311C22⋊D61—42no—
312C22⋊D61—42no—
313C22⋊D61—42no—
314C22⋊D61—42no—
315C22⋊D61—42no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—41no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324C2×Dic61C2×C22⋊C411yescharacteristic
325C2×Dic61C2×C22⋊C411yescharacteristic
326C2×Dic61C2×C22⋊C411yescharacteristic
327C2×Dic61C2×C22⋊C411yescharacteristic
328C2×Dic61C2×C22⋊C411yescharacteristic
329C2×Dic61C22×D411yescharacteristic
330D244—22no—
331D244—42no—
332D244—42no—
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—41no—
343C4×D61—41no—
344C4×D61—42no—
345C4×D61—42no—
346C4×D61—42no—
347C4×D61C2×#4114yes—
348Dic122—22no—
349Dic122—42no—
350Dic122—42no—
351#92420—44no—
352#21417—611nomaximal, Sylow
353C22×C61—21no—
354C22×C61—21no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61#42112yes—
359C22×C61C22×C22⋊C411yescharacteristic
360C2×D61—28no—
361C2×D61—21no—
362C2×D61—21no—
363C2×D61—21no—
364C2×D61—21no—
365C2×D61—41no—
366C2×D61—41no—
367C2×D61—41no—
368C2×D61#42112yes—
369C2×D61#52512yes—
370#6923—48no—
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#53212yes—
389#3444—611no—
390#2920—611no—
391C2×#376—611no—
392#1995—612no—
393#1963—612no—
394#1896—612no—
395#1896—612no—
396#1759—612no—
397#1759—612no—
398C2×C61—22no—
399C2×C61—81no—
400C2×C61#229711yescharacteristic
401C2×C61C2×#42111yescharacteristic
402C2×C61C2×#42111yescharacteristic
403D61—22no—
404D61—22no—
405D61—81no—
406#533—611no—
407#533—611no—
408#533—611no—
409#532—611no—
410#532—611no—
411#532—611no—
412#529—611no—
413#529—611no—
414#529—611no—
415#529—1221no—
416#529—1221no—
417#529—1221no—
418#529—1221no—
419#529#692311yescharacteristic, complemented
420#525—611no—
421#525—611no—
422#525—1221no—
423#525—1221no—
424C4×#41—611no—
425C4×#41—611no—
426C4×#41—1221no—
427C4×#41—1221no—
428C22×C42—611no—
429C22×C42—612no—
430#432—1221no—
431#432—1221no—
432#431—1221no—
433#431—1221no—
434#423—612no—
435C2×#104—614no—
436C2×#104—614no—
437#407—612no—
438C4×M16—612no—
439#376—612no—
440#376—612no—
441#376—1221no—
442#376—1221no—
443C2×#95—1221no—
444C2×#95—1221no—
445#339—614no—
446#339—614no—
447C61#2141711yescharacteristic, complemented, Sylow
448C2×#41—611no—
449C2×#41—611no—
450C2×#41—1221no—
451C2×#41—1221no—
452C23×C4—611no—
453C23×C4—611no—
454C23×C4—611no—
455C23×C4—1222no—
456C2×M16—614no—
457C4⋊Q8—611no—
458C4⋊Q8—611no—
459C4⋊Q8—611no—
460#127—611no—
461#126—21no—
462#126—1221no—
463#126—1221no—
464#126—1221no—
465#125—611no—
466#125—1221no—
467#125—1221no—
468#125C2×#692311yescharacteristic, complemented
469#124—611no—
470#124—1221no—
471#124—1221no—
472#124C2×#692311yescharacteristic, complemented
473#123—21no—
474#123—1221no—
475#123—1221no—
476#123—1221no—
477#123—1221no—
478#123—1221no—
479C22⋊Q8—611no—
480C22⋊Q8—611no—
481C22⋊Q8—611no—
482C22⋊Q8—1221no—
483C22⋊Q8—1221no—
484C22⋊Q8—1221no—
485C22⋊Q8—1221no—
486C22⋊Q8C2×#692311yescharacteristic
487#121—611no—
488#121—611no—
489#121—611no—
490#121—1221no—
491#121—1221no—
492#121—1221no—
493#121—1221no—
494#121C2×#692311yescharacteristic
495#120—1221no—
496#120—1221no—
497C4×Q8—611no—
498C4×Q8—611no—
499C4×Q8—611no—
500C4×Q8—1221no—
501C4×Q8—1221no—
502C4×Q8—1221no—
503C4×Q8—1221no—
504C4×Q8C2×#692311yescharacteristic, complemented
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×D4—1221no—
519C4×D4—1221no—
520C4×D4—1221no—
521C4×D4—1221no—
522C4×D4—1221no—
523C4×D4—1221no—
524C4×D4C2×#692311yescharacteristic, complemented
525#117—21no—
526#117—611no—
527#117—611no—
528#117—1221no—
529#117—1221no—
530#117—1221no—
531#117—1221no—
532#117—1221no—
533#117—1221no—
534#117—1221no—
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—611no—
544C2×C42—611no—
545C2×C42—611no—
546C2×C42—614no—
547C2×C42—1221no—
548C2×C42—1221no—
549C2×C42—1228no—
550C2×C42—1222no—
551C2×C42C2×#692311yescharacteristic
552C4⋊C8—1222no—
553C4⋊C8—1222no—
554#104—1228no—
555#104—1228no—
556C22⋊C8—1222no—
557C22⋊C8—1222no—
558#97—1222no—
559C4×C8—1222no—
560#95—1222no—
561#95—1222no—
562#95—1222no—
563#95—1222no—
564C24—611no—
565#41—1224no—
566#41—1224no—
567#41—2444no—
568#41—2444no—
569C2×Q8—611no—
570C2×Q8—1221no—
571C2×Q8—1221no—
572C2×Q8C22×#692311yescharacteristic
573C2×D4—21no—
574C2×D4—611no—
575C2×D4—1221no—
576C2×D4—1221no—
577C2×D4—1221no—
578C2×D4—1221no—
579C2×D4—1221no—
580C2×D4—1221no—
581C2×D4—1221no—
582C2×D4C22×#692311yescharacteristic
583C22×C4—21no—
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—611no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—611no—
599C22×C4—1224no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1221no—
603C22×C4—1221no—
604C22×C4—1224no—
605C22×C4—1228no—
606C22×C4—1221no—
607C22×C4—2442no—
608C22×C4—2442no—
609C22×C4—2444no—
610C22×C4—2444no—
611C22×C4C22⋊#692311yescharacteristic
612C22×C4C22⋊#692311yescharacteristic
613C22×C4C22×#692311yescharacteristic
614M16—1224no—
615M16—1224no—
616C2×C8—1224no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—611no—
622C4⋊C4—611no—
623C4⋊C4—1221no—
624C4⋊C4—1221no—
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—1221no—
634C4⋊C4—1221no—
635C4⋊C4C22×#692311yescharacteristic
636C4⋊C4C22×#692311yescharacteristic
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—1221no—
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—
655C42—21no—
656C42—611no—
657C42—611no—
658C42—611no—
659C42—611no—
660C42—611no—
661C42—611no—
662C42—611no—
663C42—611no—
664C42—611no—
665C42—611no—
666C42—611no—
667C42—611no—
668C42—618no—
669C42—1221no—
670C42—1221no—
671C42—1221no—
672C42—1221no—
673C42—1224no—
674C42—1228no—
675C42—1221no—
676C42C22⋊#692311yescharacteristic
677C42C22⋊#692311yescharacteristic
678C42C22×#692311yescharacteristic
679C42C22×#692311yescharacteristic
680C23—21no—
681C23—611no—
682C23—611no—
683C23—1222no—
684C23—1222no—
685C23—1222no—
686C23—1221no—
687C23C2×C22⋊#692311yescharacteristic
688Q8—22no—
689Q8—1222no—
690Q8—2442no—
691Q8—2442no—
692D4—22no—
693D4—42no—
694D4—1222no—
695D4—2442no—
696D4—2442no—
697D4—2442no—
698D4—2442no—
699D4—2442no—
700D4—2442no—
701D4—2442no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—611no—
710C2×C4—614no—
711C2×C4—611no—
712C2×C4—611no—
713C2×C4—611no—
714C2×C4—611no—
715C2×C4—611no—
716C2×C4—1222no—
717C2×C4—1222no—
718C2×C4—1222no—
719C2×C4—1222no—
720C2×C4—1222no—
721C2×C4—1222no—
722C2×C4—1222no—
723C2×C4—1228no—
724C2×C4—1221no—
725C2×C4—1221no—
726C2×C4—1221no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2441no—
731C2×C4—2441no—
732C2×C4—2441no—
733C2×C4—2442no—
734C2×C4—2442no—
735C2×C4—2442no—
736C2×C4—2442no—
737C2×C4—2441no—
738C2×C4—2442no—
739C2×C4—24416no—
740C2×C4—2444no—
741C2×C4—2444no—
742C2×C4C2×C22⋊#692311yescharacteristic
743C2×C4C2×C22⋊#692311yescharacteristic
744C2×C4C2×C22⋊#692311yescharacteristic
745C2×C4C2×C22⋊#692311yescharacteristic
746C2×C4C2×C22⋊#692311yescharacteristic
747C2×C4C23×#692311yescharacteristic
748C8—2444no—
749C22—21no—
750C22—21no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—612no—
755C22—612no—
756C22—1228no—
757C22—1221no—
758C22—1221no—
759C22—1221no—
760C22—1221no—
761C22—2441no—
762C22—2441no—
763C22—2441no—
764C22#1684075912yes—
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—2448no—
781C4—2441no—
782C4—2441no—
783C4—2441no—
784C4#41×#692312yes—
785C2—22no—
786C2—81no—
787C2—1222no—
788C2—1222no—
789C2—4881no—
790C2#2146228011yescharacteristic
791C2D61⋊#42111yescharacteristic
792C2C2×#1684075911yescharacteristic
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#21417
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. #21462496C2semidirect
2. C2×#16840698C2semidirect
3. #21462006C2semidirect
4. #21461956C2semidirect
5. #21461837C2semidirect
6. #21461836C2semidirect
7. #21461583C2semidirect
8. #21461582C2semidirect
29. #16840316C4semidirect
30. #16840314C4semidirect
32. #16840309C4semidirect
33. #16840307C4semidirect
34. #16840297C4semidirect
35. #16840296C4semidirect
38. #16840291C4semidirect
50. C61×#529C4semidirect
75. #14519776C2×C4semidirect
76. #14519776C2×C4semidirect
77. #14519775C2×C4semidirect
78. #14519773C2×C4semidirect
82. #14519769C2×C4semidirect
85. #14519765C2×C4semidirect
109. Q8×Dic61C2×C4semidirect
111. C4×Dic122C2×C4semidirect
115. #14519742C2×C4semidirect
117. C4×D244C2×C4semidirect
119. D4×Dic61C2×C4semidirect
123. #14519739C2×C4semidirect
157. #125×C61C2×C4semidirect
158. #124×C61C2×C4semidirect
162. C4×Q8×C61C2×C4semidirect
164. C4×D4×C61C2×C4semidirect
220. C4×#6923#41semidirect
419. #529#6923semidirect
447. C61#21417semidirect
468. #125C2×#6923semidirect
472. #124C2×#6923semidirect
504. C4×Q8C2×#6923semidirect
524. C4×D4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214624962
C2×#168406982
#214620062
#214619562
#214618372
#214618362
#214615832
#214615822
#214591132
#2141761