Finite Group Databasebeta

← #29647373

Subgroups — #29647373

Order 15616.

1036 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459113C211yesmaximal, characteristic
2#431×D61C211yesmaximal, characteristic, complemented
3#21448216C211yesmaximal, characteristic, complemented
4#21444397C211yesmaximal, characteristic, complemented
5#21444396C211yesmaximal, characteristic, complemented
6#21444394C211yesmaximal, characteristic, complemented
7#21444381C212yesmaximal, complemented
8#21444377C212yesmaximal, complemented
9#21444309C212yesmaximal, complemented
10#21444307C212yesmaximal, complemented
11C61×#1521C211yesmaximal, characteristic, complemented
12#16840318C411yescharacteristic, complemented
13#16840316C411yescharacteristic, complemented
14#16840314C2211yescharacteristic
15#16840311C411yescharacteristic, complemented
16#16840309C411yescharacteristic, complemented
17#16840307C2211yescharacteristic
18#16840297C411yescharacteristic, complemented
19#16840296C2211yescharacteristic
20#16840295—21no—
21#16840295—21no—
22#16840291C411yescharacteristic, complemented
23#16840290—21no—
24#16840289—21no—
25#16840275C2211yescharacteristic
26#16840272C2211yescharacteristic
27#16840271—21no—
28#16840270—21no—
29C4×#11758226C411yescharacteristic, complemented
30#16840230—21no—
31C4×#11758224—21no—
32C4×#11758224C411yescharacteristic, complemented
33C2×C42×D61C2211yescharacteristic
34#16839815C2211yescharacteristic
35#16839814—21no—
36#16839813—21no—
37#16839812C2212yes—
38C4⋊C8×D61—21no—
39C22⋊C8×D61C2212yes—
40C4×C8×D61—21no—
41#16839630C2211yescharacteristic
42#16839626C2212yes—
43#16839624—21no—
44#16839621—21no—
45#16839613—21no—
46#16839609C2212yes—
47#16839607—21no—
48#16839500C2212yes—
49#16839499C2212yes—
50#16839498C2212yes—
51#16839497C2212yes—
52#16839496C2212yes—
53#16839495C2212yes—
54C61×#529C2211yescharacteristic
55C61×#431C2211yescharacteristic
56C61×#383C2211yescharacteristic
57C61×#328C2212yes—
58C61×#327C2212yes—
59C2×#11758226C2×C411yescharacteristic
60C2×#11758222—21no—
61C2×#11758224—21no—
62C2×#11758224C2×C411yescharacteristic
63C22×C4×D61D411yescharacteristic
64C22×C4×D61D411yescharacteristic
65C22×C4×D61C2311yescharacteristic
66C2×C8×D61—22no—
67#14519776C2×C411yescharacteristic
68#14519776C2×C411yescharacteristic
69#14519775C2×C411yescharacteristic
70#14519773C2×C411yescharacteristic
71#14519772—21no—
72#14519771—21no—
73#14519770—21no—
74#14519769C2×C411yescharacteristic
75#14519767—21no—
76#14519767—21no—
77#14519765C2×C411yescharacteristic
78#14519763—21no—
79#14519763—21no—
80#14519762—21no—
81#14519762—21no—
82#14519760—21no—
83#14519759—21no—
84#14519759—21no—
85#14519757C2×C411yescharacteristic
86#14519756C2311yescharacteristic
87#14519755—21no—
88#14519755—21no—
89#14519755—21no—
90#14519754—21no—
91#14519753C2×C411yescharacteristic
92#14519752C2×C411yescharacteristic
93#14519751C2311yescharacteristic
94#14519750—21no—
95#14519750—21no—
96#14519750—21no—
97#14519749—21no—
98#14519748C2×C411yescharacteristic
99#14519747—21no—
100#14519745—21no—
101Q8×Dic61C2×C411yescharacteristic
102C4×Dic122—21no—
103C4×Dic122C2×C411yescharacteristic
104#14519742—21no—
105#14519742—21no—
106#14519742—21no—
107#14519742C2×C411yescharacteristic
108C4×D244—21no—
109C4×D244C2×C411yescharacteristic
110D4×Dic61—21no—
111D4×Dic61C2×C411yescharacteristic
112#14519739—21no—
113#14519739—21no—
114#14519739—21no—
115#14519739C2×C411yescharacteristic
116C4×C22⋊D61—21no—
117C4×C22⋊D61—21no—
118C4×C22⋊D61—21no—
119#14519737—21no—
120#14519737—21no—
121#14519737—21no—
122#14519737—21no—
123#14519737—21no—
124#14519737—21no—
125#14519737—21no—
126#14519735—21no—
127#14519735—21no—
128#14519735C2×C411yescharacteristic
129#14519735C2×C411yescharacteristic
130#14519734—21no—
131#14519734—21no—
132#14519733—21no—
133#14519733—21no—
134#14519733—21no—
135C2×#11758196—22no—
136C2×#11758198—22no—
137C2×C4×Dic61—21no—
138C2×C4×Dic61—22no—
139C2×C4×Dic61D411yescharacteristic
140C2×C4×Dic61D411yescharacteristic
141C2×C4×Dic61C2311yescharacteristic
142C42×D61—21no—
143C42×D61C2×C411yescharacteristic
144C42×D61C2×C411yescharacteristic
145C42×D61C2×C411yescharacteristic
146C42×D61C2×C411yescharacteristic
147C42×D61D411yescharacteristic
148C42×D61D411yescharacteristic
149C42×D61D411yescharacteristic
150C42×D61D411yescharacteristic
151C4⋊#92418—21no—
152#14519706—22no—
153C22⋊#92418C2312yes—
154#14519689—22no—
155C4×#92418—21no—
156C8×Dic61—22no—
157#14519684—21no—
158#14519684—21no—
159#14519684—22no—
160#14519684C2312yes—
161#126×C61—21no—
162#125×C61C2×C411yescharacteristic
163#124×C61C2×C411yescharacteristic
164#123×C61—21no—
165C22⋊Q8×C61C2311yescharacteristic
166#121×C61C2311yescharacteristic
167C4×Q8×C61C2×C411yescharacteristic
168C4×D4×C61—21no—
169C4×D4×C61C2×C411yescharacteristic
170#117×C61—21no—
171C2×C42×C61C2311yescharacteristic
172C4⋊C8×C61—21no—
173C22⋊C8×C61C2312yes—
174C4×C8×C61—21no—
175#95×C61—21no—
176#95×C61—21no—
177#95×C61C2312yes—
178C23×D61C2×D411yescharacteristic
179C2×Q8×C61C22×C411yescharacteristic
180C2×D4×C61—21no—
181C2×D4×C61C22×C411yescharacteristic
182C22×C4×C61—21no—
183C22×C4×C61—22no—
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2411yescharacteristic
187C2×C22⋊D61—21no—
188C2×C22⋊D61—21no—
189C2×C22⋊D61—21no—
190C2×C22⋊D61—21no—
191C2×C22⋊D61—21no—
192C22×Dic61—21no—
193C22×Dic61—21no—
194C22×Dic61—22no—
195C22×Dic61C2×D411yescharacteristic
196C22×Dic61C2×D411yescharacteristic
197C22×Dic61C2×D411yescharacteristic
198#11758226—42no—
199#11758224—42no—
200#11758224—44no—
201#11758222—44no—
202C2×D244—21no—
203C2×D244—21no—
204C2×D244C22×C411yescharacteristic
205C2×C4×D61—24no—
206C2×C4×D61—21no—
207C2×C4×D61—21no—
208C2×C4×D61—21no—
209C2×C4×D61—42no—
210C2×C4×D61—42no—
211C2×C4×D61C22⋊C411yescharacteristic
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×D61C22×C411yescharacteristic
221C2×C4×D61C2×D411yescharacteristic
222C2×C4×D61C2×D411yescharacteristic
223C2×Dic122—21no—
224C2×Dic122—21no—
225C2×Dic122C22×C411yescharacteristic
226C2×C8×C61—22no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61C22×C411yescharacteristic
232C4⋊C4×C61C22×C411yescharacteristic
233C22⋊C4×C61—21no—
234C22⋊C4×C61—21no—
235C22⋊C4×C61—21no—
236C22⋊C4×C61—21no—
237C22⋊C4×C61—21no—
238C42×C61—21no—
239C42×C61C22×C411yescharacteristic
240C42×C61C22×C411yescharacteristic
241C42×C61C2×D411yescharacteristic
242C42×C61C2×D411yescharacteristic
243C22⋊Dic61—21no—
244C22⋊Dic61—21no—
245C22⋊Dic61—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—
255#11758198—21no—
256#11758198—44no—
257C4⋊Dic61—21no—
258C4⋊Dic61—21no—
259C4⋊Dic61C22×C411yescharacteristic
260C4⋊Dic61C22×C411yescharacteristic
261#11758196—21no—
262#11758196—21no—
263#11758196—21no—
264#11758196—21no—
265#11758196—21no—
266#11758196—21no—
267#11758196—21no—
268#11758196—21no—
269#11758196—21no—
270#11758196—21no—
271#11758196—44no—
272C4×Dic61—21no—
273C4×Dic61—21no—
274C4×Dic61—21no—
275C4×Dic61—21no—
276C4×Dic61—21no—
277C4×Dic61—44no—
278C4×Dic61C22⋊C411yescharacteristic
279C4×Dic61C22⋊C411yescharacteristic
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
290C2×#92418—22no—
291C8×D61—44no—
292C23×C61—21no—
293C23×C61C22×D411yescharacteristic
294C22×D61—22no—
295C22×D61—22no—
296C22×D61—21no—
297C22×D61—41no—
298C22×D61C2×C22⋊C411yescharacteristic
299C22×D61C2×C22⋊C411yescharacteristic
300Q8×C61—41no—
301D4×C61—41no—
302D4×C61—42no—
303C2×C4×C61—22no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—42no—
310C2×C4×C61—42no—
311C2×C4×C61—42no—
312C2×C4×C61—42no—
313C2×C4×C61C2×C22⋊C411yescharacteristic
314C2×C4×C61C2×C22⋊C411yescharacteristic
315C2×C4×C61C2×C22⋊C411yescharacteristic
316C2×C4×C61C2×C22⋊C411yescharacteristic
317C2×C4×C61C23×C411yescharacteristic
318C2×C4×C61C22×D411yescharacteristic
319C22⋊D61—42no—
320C22⋊D61—42no—
321C22⋊D61—42no—
322C22⋊D61—42no—
323C22⋊D61—42no—
324C2×Dic61—22no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—41no—
329C2×Dic61—42no—
330C2×Dic61—42no—
331C2×Dic61—42no—
332C2×Dic61—42no—
333C2×Dic61—42no—
334C2×Dic61C2×C22⋊C411yescharacteristic
335C2×Dic61C2×C22⋊C411yescharacteristic
336C2×Dic61C2×C22⋊C411yescharacteristic
337C2×Dic61C2×C22⋊C411yescharacteristic
338C2×Dic61C2×C22⋊C411yescharacteristic
339C2×Dic61C2×C22⋊C411yescharacteristic
340C2×Dic61#13514yes—
341D244—41no—
342D244—42no—
343D244—42no—
344C4×D61—22no—
345C4×D61—22no—
346C4×D61—22no—
347C4×D61—22no—
348C4×D61—22no—
349C4×D61—22no—
350C4×D61—22no—
351C4×D61—22no—
352C4×D61—41no—
353C4×D61—41no—
354C4×D61—41no—
355C4×D61—41no—
356C4×D61—42no—
357C4×D61—42no—
358C4×D61—42no—
359Dic122—42no—
360Dic122—42no—
361Dic122—41no—
362C8×C61—42no—
363#92418—42no—
364#17573—611nomaximal, Sylow
365C22×C61—21no—
366C22×C61—21no—
367C22×C61—41no—
368C22×C61—41no—
369C22×C61—41no—
370C22×C61C22×C22⋊C411yescharacteristic
371C22×C61C2×#13512yes—
372C2×D61—21no—
373C2×D61—21no—
374C2×D61—21no—
375C2×D61—21no—
376C2×D61—21no—
377C2×D61—44no—
378C2×D61—41no—
379C2×D61—41no—
380C2×D61—41no—
381C2×D61#42112yes—
382C4×C61—21no—
383C4×C61—21no—
384C4×C61—21no—
385C4×C61—21no—
386C4×C61—21no—
387C4×C61—21no—
388C4×C61—41no—
389C4×C61—41no—
390C4×C61—41no—
391C4×C61—82no—
392Dic61—21no—
393Dic61—21no—
394Dic61—21no—
395Dic61—41no—
396Dic61—41no—
397Dic61—41no—
398Dic61—82no—
399Dic61#41012yes—
400Dic61#41612yes—
401Dic61#41612yes—
402#3444—611no—
403C2×#431—611no—
404#2283—611no—
405#1521—611no—
406#1521—611no—
407#1521—611no—
408#1521D6111yescharacteristic, complemented
409#1518—612no—
410#1517—612no—
411#1501—612no—
412#1501—612no—
413C2×C61—22no—
414C2×C61—81no—
415C2×C61C2×#41011yescharacteristic
416C2×C61C2×#41611yescharacteristic
417C2×C61C2×#42111yescharacteristic
418D61—22no—
419D61—41no—
420D61—81no—
421#533—611no—
422#533—611no—
423#533—611no—
424#532—611no—
425#532—611no—
426#532—611no—
427#529—611no—
428#529—611no—
429#529—611no—
430#529—1221no—
431#529—1221no—
432#529—1221no—
433#529—1221no—
434#529C2×D6111yescharacteristic
435#525—611no—
436#525—611no—
437#525—1221no—
438#525—1221no—
439C4×#41—611no—
440C4×#41—611no—
441C4×#41—1221no—
442C4×#41—1221no—
443C22×C42—611no—
444#431—611no—
445#431—612no—
446#431—1221no—
447#431—1221no—
448#431C2×D6111yescharacteristic
449C2×C4⋊C8—1221no—
450C2×C22⋊C8—612no—
451C2×C4×C8—1221no—
452#383—611no—
453#383C2×D6111yescharacteristic
454#382—612no—
455#381—1221no—
456#380—1221no—
457C4×C4⋊C4—1221no—
458C4×C22⋊C4—612no—
459#376—1221no—
460#328—612no—
461#328—612no—
462#328—612no—
463#328C2×D6112yes—
464#327—612no—
465#327—612no—
466#327—612no—
467#327C2×D6112yes—
468C61#1757311yescharacteristic, complemented, Sylow
469C2×#41—611no—
470C2×#41—611no—
471C2×#41—1221no—
472C2×#41—1221no—
473C23×C4—611no—
474C23×C4—611no—
475C23×C4—611no—
476C22×C8—1222no—
477C4⋊Q8—611no—
478C4⋊Q8—611no—
479C4⋊Q8—611no—
480#127—611no—
481#126—21no—
482#126—1221no—
483#126—1221no—
484#126—1221no—
485#125—611no—
486#125—1221no—
487#125—1221no—
488#125C4×D6111yescharacteristic
489#124—611no—
490#124—1221no—
491#124—1221no—
492#124C4×D6111yescharacteristic
493#123—21no—
494#123—1221no—
495#123—1221no—
496#123—1221no—
497#123—1221no—
498#123—1221no—
499C22⋊Q8—611no—
500C22⋊Q8—611no—
501C22⋊Q8—611no—
502C22⋊Q8—1221no—
503C22⋊Q8—1221no—
504C22⋊Q8—1221no—
505C22⋊Q8—1221no—
506C22⋊Q8C22×D6111yescharacteristic
507#121—611no—
508#121—611no—
509#121—611no—
510#121—1221no—
511#121—1221no—
512#121—1221no—
513#121—1221no—
514#121C22×D6111yescharacteristic
515#120—1221no—
516#120—1221no—
517C4×Q8—611no—
518C4×Q8—611no—
519C4×Q8—611no—
520C4×Q8—1221no—
521C4×Q8—1221no—
522C4×Q8—1221no—
523C4×Q8—1221no—
524C4×Q8C4×D6111yescharacteristic
525C4×D4—21no—
526C4×D4—611no—
527C4×D4—611no—
528C4×D4—611no—
529C4×D4—1221no—
530C4×D4—1221no—
531C4×D4—1221no—
532C4×D4—1221no—
533C4×D4—1221no—
534C4×D4—1221no—
535C4×D4—1221no—
536C4×D4—1221no—
537C4×D4—1221no—
538C4×D4—1221no—
539C4×D4—1221no—
540C4×D4—1221no—
541C4×D4—1221no—
542C4×D4—1221no—
543C4×D4—1221no—
544C4×D4C4×D6111yescharacteristic
545#117—21no—
546#117—611no—
547#117—611no—
548#117—1221no—
549#117—1221no—
550#117—1221no—
551#117—1221no—
552#117—1221no—
553#117—1221no—
554#117—1221no—
555C2×C4⋊C4—1222no—
556C2×C22⋊C4—1222no—
557C2×C42—611no—
558C2×C42—611no—
559C2×C42—611no—
560C2×C42—611no—
561C2×C42—611no—
562C2×C42—611no—
563C2×C42—611no—
564C2×C42—611no—
565C2×C42—611no—
566C2×C42—611no—
567C2×C42—611no—
568C2×C42—1221no—
569C2×C42—1221no—
570C2×C42—1222no—
571C2×C42C22×D6111yescharacteristic
572C4⋊C8—21no—
573C4⋊C8—1222no—
574C4⋊C8—1221no—
575C22⋊C8—612no—
576C22⋊C8—1222no—
577C22⋊C8C22×D6112yes—
578C4×C8—21no—
579C4×C8—1222no—
580C4×C8—1221no—
581#95—21no—
582#95—21no—
583#95—612no—
584#95—1222no—
585#95—1221no—
586#95—1221no—
587#95C22×D6112yes—
588C24—611no—
589#41—2444no—
590#41—2444no—
591#41—2442no—
592#41—2442no—
593C2×Q8—611no—
594C2×Q8—1221no—
595C2×Q8—1221no—
596C2×Q8C2×C4×D6111yescharacteristic
597C2×D4—21no—
598C2×D4—611no—
599C2×D4—1221no—
600C2×D4—1221no—
601C2×D4—1221no—
602C2×D4—1221no—
603C2×D4—1221no—
604C2×D4—1221no—
605C2×D4—1221no—
606C2×D4C2×C4×D6111yescharacteristic
607C22×C4—21no—
608C22×C4—22no—
609C22×C4—611no—
610C22×C4—611no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—611no—
614C22×C4—611no—
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—1224no—
625C22×C4—1221no—
626C22×C4—1221no—
627C22×C4—1221no—
628C22×C4—1221no—
629C22×C4—1221no—
630C22×C4—1222no—
631C22×C4—2442no—
632C22×C4—2442no—
633C22×C4D4×D6111yescharacteristic
634C22×C4D4×D6111yescharacteristic
635C22×C4C23×D6111yescharacteristic
636C2×C8—22no—
637C2×C8—1222no—
638C2×C8—2444no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—611no—
644C4⋊C4—611no—
645C4⋊C4—1221no—
646C4⋊C4—1221no—
647C4⋊C4—1221no—
648C4⋊C4—1221no—
649C4⋊C4—1221no—
650C4⋊C4—1221no—
651C4⋊C4—1221no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C4⋊C4—1221no—
655C4⋊C4—1221no—
656C4⋊C4—1221no—
657C4⋊C4—2444no—
658C4⋊C4C2×C4×D6111yescharacteristic
659C4⋊C4C2×C4×D6111yescharacteristic
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—1221no—
666C22⋊C4—1221no—
667C22⋊C4—1221no—
668C22⋊C4—1221no—
669C22⋊C4—1221no—
670C22⋊C4—1221no—
671C22⋊C4—1221no—
672C22⋊C4—1221no—
673C22⋊C4—1221no—
674C22⋊C4—1221no—
675C22⋊C4—1221no—
676C22⋊C4—1221no—
677C22⋊C4—1221no—
678C22⋊C4—2444no—
679C42—21no—
680C42—611no—
681C42—611no—
682C42—611no—
683C42—611no—
684C42—611no—
685C42—611no—
686C42—611no—
687C42—611no—
688C42—611no—
689C42—611no—
690C42—611no—
691C42—611no—
692C42—1221no—
693C42—1221no—
694C42—1221no—
695C42—1221no—
696C42—1221no—
697C42—2444no—
698C42C2×C4×D6111yescharacteristic
699C42C2×C4×D6111yescharacteristic
700C42D4×D6111yescharacteristic
701C42D4×D6111yescharacteristic
702C23—21no—
703C23—611no—
704C23—611no—
705C23—1222no—
706C23—1222no—
707C23—1221no—
708C23—2441no—
709C23C2×D4×D6111yescharacteristic
710Q8—41no—
711Q8—2441no—
712Q8—2442no—
713Q8—2442no—
714D4—41no—
715D4—42no—
716D4—2441no—
717D4—2442no—
718D4—2442no—
719D4—2442no—
720D4—2442no—
721D4—2442no—
722D4—2442no—
723D4—2442no—
724C2×C4—22no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—611no—
735C2×C4—611no—
736C2×C4—611no—
737C2×C4—614no—
738C2×C4—611no—
739C2×C4—611no—
740C2×C4—611no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1221no—
751C2×C4—1221no—
752C2×C4—1221no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4—2441no—
756C2×C4—2441no—
757C2×C4—2442no—
758C2×C4—2442no—
759C2×C4—2442no—
760C2×C4—2442no—
761C2×C4—2442no—
762C2×C4—2441no—
763C2×C4—2442no—
764C2×C4—2442no—
765C2×C4—2442no—
766C2×C4C22⋊C4×D6111yescharacteristic
767C2×C4C22⋊C4×D6111yescharacteristic
768C2×C4C22⋊C4×D6111yescharacteristic
769C2×C4C22⋊C4×D6111yescharacteristic
770C2×C4C22×C4×D6111yescharacteristic
771C2×C4C2×D4×D6111yescharacteristic
772C8—42no—
773C8—2442no—
774C22—21no—
775C22—21no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—612no—
780C22—1221no—
781C22—1221no—
782C22—1221no—
783C22—1221no—
784C22—1221no—
785C22—2444no—
786C22—2441no—
787C22—2441no—
788C22—2441no—
789C22C2×C22⋊C4×D6111yescharacteristic
790C22#135×D6112yes—
791C4—21no—
792C4—21no—
793C4—21no—
794C4—21no—
795C4—21no—
796C4—21no—
797C4—41no—
798C4—41no—
799C4—41no—
800C4—82no—
801C4—612no—
802C4—612no—
803C4—612no—
804C4—1221no—
805C4—1221no—
806C4—1221no—
807C4—4882no—
808C4—2441no—
809C4—2441no—
810C4—2441no—
811C2—22no—
812C2—81no—
813C2—1222no—
814C2—4881no—
815C2—2441no—
816C2#410×D6111yescharacteristic
817C2#416×D6111yescharacteristic
818C2#421×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1521C2
socleC22×C61C22×C22⋊C4
prime radical#21459113C2
cosocleC22×C4×C61C24
hypercenter#1521D61
hypocenterC61#17573
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1521

Complements

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

NH ≅ G/Ntype
2. #431×D61C2semidirect
3. #21448216C2semidirect
4. #21444397C2semidirect
5. #21444396C2semidirect
6. #21444394C2semidirect
7. #21444381C2semidirect
8. #21444377C2semidirect
9. #21444309C2semidirect
10. #21444307C2semidirect
11. C61×#1521C2semidirect
12. #16840318C4semidirect
13. #16840316C4semidirect
15. #16840311C4semidirect
16. #16840309C4semidirect
18. #16840297C4semidirect
22. #16840291C4semidirect
29. C4×#11758226C4semidirect
32. C4×#11758224C4semidirect
408. #1521D61semidirect
468. C61#17573semidirect

Maximal subgroups

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

subgroupindex
#214591132
#431×D612
#214482162
#214443972
#214443962
#214443942
#214443812
#214443772
#214443092
#214443072
C61×#15212
#1757361