Finite Group Databasebeta

← #29647507

Subgroups — #29647507

Order 15616.

1042 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459113C211yesmaximal, characteristic
2#21454447C211yesmaximal, characteristic, complemented
3#383×D61C211yesmaximal, characteristic, complemented
4#21444397C211yesmaximal, characteristic, complemented
5#21444396C211yesmaximal, characteristic, complemented
6#21444394C211yesmaximal, characteristic, complemented
7#21444368C212yesmaximal, complemented
8#21444364C212yesmaximal, complemented
9#21444322C212yesmaximal, complemented
10#21444320C212yesmaximal, 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#16839818—21no—
35#16839816C2212yes—
36#16839815C2211yescharacteristic
37#16839813—21no—
38#16839784—21no—
39#16839724C2212yes—
40C4×#11758189—21no—
41#16839630C2211yescharacteristic
42#16839629—21no—
43#16839629—21no—
44#16839629C2212yes—
45#95×D61—21no—
46#95×D61—21no—
47#95×D61C2212yes—
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×D61—22no—
64C22×C4×D61D411yescharacteristic
65C22×C4×D61D411yescharacteristic
66C22×C4×D61C2311yescharacteristic
67C2×#11758189—22no—
68#14519776C2×C411yescharacteristic, complemented
69#14519776C2×C411yescharacteristic, complemented
70#14519775C2×C411yescharacteristic, complemented
71#14519773C2×C411yescharacteristic, complemented
72#14519772—21no—
73#14519771—21no—
74#14519770—21no—
75#14519769C2×C411yescharacteristic, complemented
76#14519767—21no—
77#14519767—21no—
78#14519765C2×C411yescharacteristic, complemented
79#14519763—21no—
80#14519763—21no—
81#14519762—21no—
82#14519762—21no—
83#14519760—21no—
84#14519759—21no—
85#14519759—21no—
86#14519757C2×C411yescharacteristic
87#14519756C2311yescharacteristic
88#14519755—21no—
89#14519755—21no—
90#14519755—21no—
91#14519754—21no—
92#14519753C2×C411yescharacteristic
93#14519752C2×C411yescharacteristic
94#14519751C2311yescharacteristic
95#14519750—21no—
96#14519750—21no—
97#14519750—21no—
98#14519749—21no—
99#14519748C2×C411yescharacteristic
100#14519747—21no—
101#14519745—21no—
102Q8×Dic61C2×C411yescharacteristic, complemented
103C4×Dic122—21no—
104C4×Dic122C2×C411yescharacteristic, complemented
105#14519742—21no—
106#14519742—21no—
107#14519742—21no—
108#14519742C2×C411yescharacteristic, complemented
109C4×D244—21no—
110C4×D244C2×C411yescharacteristic, complemented
111D4×Dic61—21no—
112D4×Dic61C2×C411yescharacteristic, complemented
113#14519739—21no—
114#14519739—21no—
115#14519739—21no—
116#14519739C2×C411yescharacteristic, complemented
117C4×C22⋊D61—21no—
118C4×C22⋊D61—21no—
119C4×C22⋊D61—21no—
120#14519737—21no—
121#14519737—21no—
122#14519737—21no—
123#14519737—21no—
124#14519737—21no—
125#14519737—21no—
126#14519737—21no—
127#14519735—21no—
128#14519735—21no—
129#14519735C2×C411yescharacteristic
130#14519735C2×C411yescharacteristic
131#14519734—21no—
132#14519734—21no—
133#14519733—21no—
134#14519733—21no—
135#14519733—21no—
136C2×C4×Dic61—21no—
137C2×C4×Dic61D411yescharacteristic
138C2×C4×Dic61D411yescharacteristic
139C2×C4×Dic61C2311yescharacteristic
140C42×D61—21no—
141C42×D61C2×C411yescharacteristic
142C42×D61C2×C411yescharacteristic
143C42×D61C2×C411yescharacteristic
144C42×D61C2×C411yescharacteristic
145C42×D61D411yescharacteristic
146C42×D61D411yescharacteristic
147C42×D61D411yescharacteristic
148C42×D61D411yescharacteristic
149C4⋊#92418—21no—
150#14519706—22no—
151C22⋊#92418C2312yes—
152#14519689—22no—
153#14519687—22no—
154C4×#92418—21no—
155#14519684—21no—
156#14519684—21no—
157#14519684—22no—
158#14519684—22no—
159#14519684—22no—
160#14519684C2312yes—
161#126×C61—21no—
162#125×C61C2×C411yescharacteristic, complemented
163#124×C61C2×C411yescharacteristic, complemented
164#123×C61—21no—
165C22⋊Q8×C61C2311yescharacteristic
166#121×C61C2311yescharacteristic
167C4×Q8×C61C2×C411yescharacteristic, complemented
168C4×D4×C61—21no—
169C4×D4×C61C2×C411yescharacteristic, complemented
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—21no—
206C2×C4×D61—21no—
207C2×C4×D61—21no—
208C2×C4×D61—42no—
209C2×C4×D61—42no—
210C2×C4×D61—42no—
211C2×C4×D61—44no—
212C2×C4×D61—44no—
213C2×C4×D61—44no—
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×D61C22⋊C411yescharacteristic
222C2×C4×D61C22×C411yescharacteristic
223C2×C4×D61C22×C411yescharacteristic
224C2×C4×D61C2×D411yescharacteristic
225C2×C4×D61C2×D411yescharacteristic
226C2×Dic122—21no—
227C2×Dic122—21no—
228C2×Dic122C22×C411yescharacteristic
229C2×C8×C61—22no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61C22×C411yescharacteristic
235C4⋊C4×C61C22×C411yescharacteristic
236C22⋊C4×C61—21no—
237C22⋊C4×C61—21no—
238C22⋊C4×C61—21no—
239C22⋊C4×C61—21no—
240C22⋊C4×C61—21no—
241C42×C61—21no—
242C42×C61C22×C411yescharacteristic
243C42×C61C22×C411yescharacteristic
244C42×C61C2×D411yescharacteristic
245C42×C61C2×D411yescharacteristic
246C22⋊Dic61—21no—
247C22⋊Dic61—21no—
248C22⋊Dic61—21no—
249#11758198—21no—
250#11758198—21no—
251#11758198—21no—
252#11758198—21no—
253#11758198—21no—
254#11758198—21no—
255#11758198—21no—
256#11758198—21no—
257#11758198—21no—
258#11758198—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61C22×C411yescharacteristic
262C4⋊Dic61C22×C411yescharacteristic
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—21no—
272#11758196—21no—
273C4×Dic61—21no—
274C4×Dic61—21no—
275C4×Dic61—21no—
276C4×Dic61—21no—
277C4×Dic61—21no—
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—
291#11758189—44no—
292C23×C61—21no—
293C23×C61C22×D411yescharacteristic
294C22×D61—22no—
295C22×D61—22no—
296C22×D61—22no—
297C22×D61—21no—
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—41no—
330C2×Dic61—42no—
331C2×Dic61—42no—
332C2×Dic61—42no—
333C2×Dic61—42no—
334C2×Dic61—42no—
335C2×Dic61C2×C22⋊C411yescharacteristic
336C2×Dic61C2×C22⋊C411yescharacteristic
337C2×Dic61C2×C22⋊C411yescharacteristic
338C2×Dic61C2×C22⋊C411yescharacteristic
339C2×Dic61C2×C22⋊C411yescharacteristic
340C2×Dic61C2×C22⋊C411yescharacteristic
341D244—41no—
342D244—42no—
343D244—42no—
344C4×D61—22no—
345C4×D61—22no—
346C4×D61—22no—
347C4×D61—22no—
348C4×D61—41no—
349C4×D61—41no—
350C4×D61—41no—
351C4×D61—41no—
352C4×D61—41no—
353C4×D61—41no—
354C4×D61—41no—
355C4×D61—41no—
356C4×D61—42no—
357C4×D61—42no—
358C4×D61—42no—
359C4×D61—88no—
360Dic122—42no—
361Dic122—42no—
362Dic122—41no—
363C8×C61—42no—
364#92418—42no—
365#17593—611nomaximal, Sylow
366C22×C61—21no—
367C22×C61—21no—
368C22×C61—41no—
369C22×C61—41no—
370C22×C61—41no—
371C22×C61C22×C22⋊C411yescharacteristic
372C22×C61#57512yes—
373C2×D61—28no—
374C2×D61—21no—
375C2×D61—21no—
376C2×D61—21no—
377C2×D61—21no—
378C2×D61—41no—
379C2×D61—41no—
380C2×D61—41no—
381C2×D61#41012yes—
382C2×D61#42112yes—
383C4×C61—21no—
384C4×C61—21no—
385C4×C61—21no—
386C4×C61—21no—
387C4×C61—21no—
388C4×C61—21no—
389C4×C61—41no—
390C4×C61—41no—
391C4×C61—41no—
392C4×C61—82no—
393Dic61—21no—
394Dic61—21no—
395Dic61—21no—
396Dic61—21no—
397Dic61—21no—
398Dic61—21no—
399Dic61—41no—
400Dic61—41no—
401Dic61—41no—
402Dic61—82no—
403#3444—611no—
404#2920—611no—
405C2×#383—611no—
406#1521—611no—
407#1521—611no—
408#1521—611no—
409#1521D6111yescharacteristic, complemented
410#1515—612no—
411#1514—612no—
412#1504—612no—
413#1504—612no—
414C2×C61—22no—
415C2×C61—81no—
416C2×C61C2×#41011yescharacteristic
417C2×C61#289611yescharacteristic
418C2×C61C2×#42111yescharacteristic
419D61—22no—
420D61—22no—
421D61—81no—
422#533—611no—
423#533—611no—
424#533—611no—
425#532—611no—
426#532—611no—
427#532—611no—
428#529—611no—
429#529—611no—
430#529—611no—
431#529—1221no—
432#529—1221no—
433#529—1221no—
434#529—1221no—
435#529C2×D6111yescharacteristic
436#525—611no—
437#525—611no—
438#525—1221no—
439#525—1221no—
440C4×#41—611no—
441C4×#41—611no—
442C4×#41—1221no—
443C4×#41—1221no—
444C22×C42—611no—
445#432—612no—
446#432—1221no—
447#431—611no—
448#431—1221no—
449#431C2×D6111yescharacteristic
450#423—1221no—
451#407—612no—
452C4×M16—1221no—
453#383—611no—
454#383—612no—
455#383—1221no—
456#383—1221no—
457#383C2×D6111yescharacteristic
458C2×#95—612no—
459C2×#95—1221no—
460C2×#95—1221no—
461#328—612no—
462#328—612no—
463#328—612no—
464#328C2×D6112yes—
465#327—612no—
466#327—612no—
467#327—612no—
468#327C2×D6112yes—
469C61#1759311yescharacteristic, complemented, Sylow
470C2×#41—611no—
471C2×#41—611no—
472C2×#41—1221no—
473C2×#41—1221no—
474C23×C4—611no—
475C23×C4—611no—
476C23×C4—611no—
477C23×C4—1222no—
478C2×M16—1222no—
479C4⋊Q8—611no—
480C4⋊Q8—611no—
481C4⋊Q8—611no—
482#127—611no—
483#126—21no—
484#126—1221no—
485#126—1221no—
486#126—1221no—
487#125—611no—
488#125—1221no—
489#125—1221no—
490#125C4×D6111yescharacteristic, complemented
491#124—611no—
492#124—1221no—
493#124—1221no—
494#124C4×D6111yescharacteristic, complemented
495#123—21no—
496#123—1221no—
497#123—1221no—
498#123—1221no—
499#123—1221no—
500#123—1221no—
501C22⋊Q8—611no—
502C22⋊Q8—611no—
503C22⋊Q8—611no—
504C22⋊Q8—1221no—
505C22⋊Q8—1221no—
506C22⋊Q8—1221no—
507C22⋊Q8—1221no—
508C22⋊Q8C22×D6111yescharacteristic
509#121—611no—
510#121—611no—
511#121—611no—
512#121—1221no—
513#121—1221no—
514#121—1221no—
515#121—1221no—
516#121C22×D6111yescharacteristic
517#120—1221no—
518#120—1221no—
519C4×Q8—611no—
520C4×Q8—611no—
521C4×Q8—611no—
522C4×Q8—1221no—
523C4×Q8—1221no—
524C4×Q8—1221no—
525C4×Q8—1221no—
526C4×Q8C4×D6111yescharacteristic, complemented
527C4×D4—21no—
528C4×D4—611no—
529C4×D4—611no—
530C4×D4—611no—
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×D4—1221no—
545C4×D4—1221no—
546C4×D4C4×D6111yescharacteristic, complemented
547#117—21no—
548#117—611no—
549#117—611no—
550#117—1221no—
551#117—1221no—
552#117—1221no—
553#117—1221no—
554#117—1221no—
555#117—1221no—
556#117—1221no—
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×C42C22×D6111yescharacteristic
571C4⋊C8—21no—
572C4⋊C8—1222no—
573C4⋊C8—1221no—
574C22⋊C8—612no—
575C22⋊C8—1222no—
576C22⋊C8C22×D6112yes—
577#97—1222no—
578C4×C8—21no—
579C4×C8—1221no—
580#95—21no—
581#95—21no—
582#95—612no—
583#95—1222no—
584#95—1222no—
585#95—1222no—
586#95—1221no—
587#95—1221no—
588#95C22×D6112yes—
589C24—611no—
590#41—2444no—
591#41—2444no—
592#41—2442no—
593#41—2442no—
594C2×Q8—611no—
595C2×Q8—1221no—
596C2×Q8—1221no—
597C2×Q8C2×C4×D6111yescharacteristic
598C2×D4—21no—
599C2×D4—611no—
600C2×D4—1221no—
601C2×D4—1221no—
602C2×D4—1221no—
603C2×D4—1221no—
604C2×D4—1221no—
605C2×D4—1221no—
606C2×D4—1221no—
607C2×D4C2×C4×D6111yescharacteristic
608C22×C4—21no—
609C22×C4—22no—
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—611no—
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×C4—2442no—
634C22×C4—2444no—
635C22×C4—2444no—
636C22×C4—2444no—
637C22×C4D4×D6111yescharacteristic
638C22×C4D4×D6111yescharacteristic
639C22×C4C23×D6111yescharacteristic
640M16—2444no—
641C2×C8—22no—
642C2×C8—1222no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—611no—
648C4⋊C4—611no—
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—1221no—
658C4⋊C4—1221no—
659C4⋊C4—1221no—
660C4⋊C4—1221no—
661C4⋊C4C2×C4×D6111yescharacteristic
662C4⋊C4C2×C4×D6111yescharacteristic
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
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—1221no—
679C22⋊C4—1221no—
680C22⋊C4—1221no—
681C42—21no—
682C42—611no—
683C42—611no—
684C42—611no—
685C42—611no—
686C42—611no—
687C42—611no—
688C42—611no—
689C42—611no—
690C42—611no—
691C42—611no—
692C42—611no—
693C42—611no—
694C42—1221no—
695C42—1221no—
696C42—1221no—
697C42—1221no—
698C42—1221no—
699C42C2×C4×D6111yescharacteristic
700C42C2×C4×D6111yescharacteristic
701C42D4×D6111yescharacteristic
702C42D4×D6111yescharacteristic
703C23—21no—
704C23—611no—
705C23—611no—
706C23—1222no—
707C23—1222no—
708C23—1222no—
709C23—1221no—
710C23C2×D4×D6111yescharacteristic
711Q8—41no—
712Q8—2441no—
713Q8—2442no—
714Q8—2442no—
715D4—41no—
716D4—42no—
717D4—2441no—
718D4—2442no—
719D4—2442no—
720D4—2442no—
721D4—2442no—
722D4—2442no—
723D4—2442no—
724D4—2442no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—611no—
736C2×C4—611no—
737C2×C4—611no—
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—1221no—
747C2×C4—1221no—
748C2×C4—1221no—
749C2×C4—4888no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4—2441no—
756C2×C4—2441no—
757C2×C4—2441no—
758C2×C4—2442no—
759C2×C4—2442no—
760C2×C4—2442no—
761C2×C4—2441no—
762C2×C4—2441no—
763C2×C4—2442no—
764C2×C4—2442no—
765C2×C4—2442no—
766C2×C4—2442no—
767C2×C4—2442no—
768C2×C4C22⋊C4×D6111yescharacteristic
769C2×C4C22⋊C4×D6111yescharacteristic
770C2×C4C22⋊C4×D6111yescharacteristic
771C2×C4C22⋊C4×D6111yescharacteristic
772C2×C4C22×C4×D6111yescharacteristic
773C2×C4C2×D4×D6111yescharacteristic
774C8—42no—
775C8—2442no—
776C22—21no—
777C22—21no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—612no—
782C22—612no—
783C22—1228no—
784C22—1221no—
785C22—1221no—
786C22—1221no—
787C22—1221no—
788C22—2441no—
789C22—2441no—
790C22—2441no—
791C22C2×C22⋊C4×D6111yescharacteristic
792C22#1684055912yes—
793C4—21no—
794C4—21no—
795C4—21no—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—41no—
800C4—41no—
801C4—41no—
802C4—82no—
803C4—1221no—
804C4—1221no—
805C4—1221no—
806C4—1221no—
807C4—1221no—
808C4—1221no—
809C4—4882no—
810C4—2441no—
811C4—2441no—
812C4—2441no—
813C2—22no—
814C2—81no—
815C2—1222no—
816C2—1222no—
817C2—4881no—
818C2#410×D6111yescharacteristic
819C2#2145433411yescharacteristic
820C2#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#17593
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. #21454447C2semidirect
3. #383×D61C2semidirect
4. #21444397C2semidirect
5. #21444396C2semidirect
6. #21444394C2semidirect
7. #21444368C2semidirect
8. #21444364C2semidirect
9. #21444322C2semidirect
10. #21444320C2semidirect
11. C61×#1521C2semidirect
12. #16840318C4semidirect
13. #16840316C4semidirect
15. #16840311C4semidirect
16. #16840309C4semidirect
18. #16840297C4semidirect
22. #16840291C4semidirect
29. C4×#11758226C4semidirect
32. C4×#11758224C4semidirect
68. #14519776C2×C4semidirect
69. #14519776C2×C4semidirect
70. #14519775C2×C4semidirect
71. #14519773C2×C4semidirect
75. #14519769C2×C4semidirect
78. #14519765C2×C4semidirect
102. Q8×Dic61C2×C4semidirect
104. C4×Dic122C2×C4semidirect
108. #14519742C2×C4semidirect
110. C4×D244C2×C4semidirect
112. D4×Dic61C2×C4semidirect
116. #14519739C2×C4semidirect
162. #125×C61C2×C4semidirect
163. #124×C61C2×C4semidirect
167. C4×Q8×C61C2×C4semidirect
169. C4×D4×C61C2×C4semidirect
409. #1521D61semidirect
469. C61#17593semidirect
490. #125C4×D61semidirect
494. #124C4×D61semidirect
526. C4×Q8C4×D61semidirect
546. C4×D4C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214591132
#214544472
#383×D612
#214443972
#214443962
#214443942
#214443682
#214443642
#214443222
#214443202
C61×#15212
#1759361