Finite Group Databasebeta

← #29647506

Subgroups — #29647506

Order 15616.

1042 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459111C211yesmaximal, characteristic
2#21454448C211yesmaximal, characteristic, complemented
3C2×#16839629C211yesmaximal, characteristic, complemented
4#21444395C212yesmaximal, complemented
5#21444393C212yesmaximal, complemented
6#21444368C212yesmaximal, complemented
7#21444364C212yesmaximal, complemented
8#21444324C211yesmaximal, characteristic, complemented
9#21444323C211yesmaximal, characteristic, complemented
10#21444321C211yesmaximal, characteristic, complemented
11C61×#1504C211yesmaximal, characteristic, complemented
12#16840315C411yescharacteristic, complemented
13#16840314C411yescharacteristic, complemented
14#16840314C2211yescharacteristic
15#16840308C411yescharacteristic, complemented
16#16840307C411yescharacteristic, complemented
17#16840307C2211yescharacteristic
18#16840298C411yescharacteristic, complemented
19#16840298C2211yescharacteristic
20#16840293C411yescharacteristic, complemented
21#16840293C2211yescharacteristic
22#16840292—21no—
23#16840292—21no—
24#16840289—21no—
25#16840289—21no—
26#16840273C2211yescharacteristic
27#16840268—21no—
28#16840268—21no—
29#41×Dic61C411yescharacteristic, complemented
30#16840230C411yescharacteristic, complemented
31C4×#11758224—21no—
32C4×#11758224—21no—
33C22×C4×Dic61C2211yescharacteristic
34#16839816—21no—
35#16839816C2212yes—
36#16839812—21no—
37#16839812C2212yes—
38#16839785—21no—
39#16839726C2211yescharacteristic
40M16×Dic61—21no—
41#16839629—21no—
42#16839629—21no—
43#16839629C2212yes—
44#16839629C2212yes—
45C2×#14519684—21no—
46C2×#14519684—21no—
47C2×#14519684C2211yescharacteristic
48#16839500C2212yes—
49#16839499C2212yes—
50#16839498C2212yes—
51#16839497C2212yes—
52#16839496C2212yes—
53#16839495C2212yes—
54C61×#525C2211yescharacteristic
55C61×#407C2211yescharacteristic
56C2×#95×C61C2211yescharacteristic
57C61×#328C2212yes—
58C61×#327C2212yes—
59C2×#11758222C2×C411yescharacteristic
60C2×#11758224—21no—
61C2×#11758224—21no—
62C23×Dic61—21no—
63C23×Dic61D411yescharacteristic
64C23×Dic61D411yescharacteristic
65C2×#11758194—21no—
66#14519776C2×C411yescharacteristic, complemented
67#14519776C2×C411yescharacteristic, complemented
68#14519775C2×C411yescharacteristic, complemented
69#14519773C2×C411yescharacteristic, complemented
70#14519772—21no—
71#14519772—21no—
72#14519770—21no—
73#14519770—21no—
74#14519768C2×C411yescharacteristic, complemented
75#14519768C2×C411yescharacteristic, complemented
76#14519767—21no—
77#14519767—21no—
78#14519766C2×C411yescharacteristic, complemented
79#14519764C2×C411yescharacteristic, complemented
80#14519763—21no—
81#14519763—21no—
82#14519761—21no—
83#14519761—21no—
84#14519760—21no—
85#14519758—21no—
86#14519758—21no—
87#14519756C2×C411yescharacteristic
88#14519756C2311yescharacteristic
89#14519754—21no—
90#14519754—21no—
91#14519754—21no—
92#14519754—21no—
93#14519751C2×C411yescharacteristic
94#14519751C2311yescharacteristic
95#14519749—21no—
96#14519749—21no—
97#14519749—21no—
98#14519749—21no—
99#14519746—21no—
100Q8×Dic61C2×C411yescharacteristic, complemented
101Q8×Dic61C2×C411yescharacteristic, complemented
102C4×Dic122—21no—
103C4×Dic122—21no—
104#14519742—21no—
105#14519742—21no—
106#14519742C2×C411yescharacteristic, complemented
107#14519742C2×C411yescharacteristic, complemented
108D4×Dic61—21no—
109D4×Dic61—21no—
110D4×Dic61—21no—
111D4×Dic61—21no—
112D4×Dic61C2×C411yescharacteristic, complemented
113D4×Dic61C2×C411yescharacteristic, complemented
114#14519739C2×C411yescharacteristic, complemented
115#14519739C2×C411yescharacteristic, complemented
116C4×C22⋊D61—21no—
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#14519736—21no—
127#14519736C2×C411yescharacteristic
128#14519735—21no—
129#14519735—21no—
130#14519734—21no—
131#14519733—21no—
132#14519733—21no—
133#14519733—21no—
134#14519733—21no—
135C2×C4×Dic61—21no—
136C2×C4×Dic61C2×C411yescharacteristic
137C2×C4×Dic61C2×C411yescharacteristic
138C2×C4×Dic61C2×C411yescharacteristic
139C2×C4×Dic61C2×C411yescharacteristic
140C2×C4×Dic61D411yescharacteristic
141C2×C4×Dic61D411yescharacteristic
142C2×C4×Dic61D411yescharacteristic
143C2×C4×Dic61D411yescharacteristic
144C2×C4×Dic61D411yescharacteristic
145C2×C4×Dic61D411yescharacteristic
146C2×C4×Dic61C2311yescharacteristic
147C2×C4×Dic61C2311yescharacteristic
148C42×D61—21no—
149#14519706—22no—
150#14519706—22no—
151C22⋊#92418—21no—
152C22⋊#92418C2312yes—
153#14519687—22no—
154C8×Dic61—22no—
155#14519684—21no—
156#14519684—22no—
157#14519684—22no—
158#14519684—22no—
159#14519684—22no—
160#14519684C2312yes—
161C2×#41×C61C2×C411yescharacteristic
162C23×C4×C61—21no—
163C23×C4×C61C2311yescharacteristic
164C2×M16×C61—21no—
165#123×C61—21no—
166C22⋊Q8×C61C2×C411yescharacteristic
167C22⋊Q8×C61C2311yescharacteristic
168#121×C61C2×C411yescharacteristic
169#121×C61C2311yescharacteristic
170#120×C61—21no—
171C4×D4×C61—21no—
172C4×D4×C61—21no—
173#117×C61C2×C411yescharacteristic
174C22⋊C8×C61—21no—
175C22⋊C8×C61C2312yes—
176#95×C61—21no—
177#95×C61C2312yes—
178C24×C61C2×D411yescharacteristic
179#41×C61—42no—
180C2×Q8×C61C22×C411yescharacteristic
181C2×D4×C61—21no—
182C2×D4×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61C22×C411yescharacteristic
185C22×C4×C61—21no—
186C22×C4×C61—22no—
187C22×C4×C61—42no—
188C22×C4×C61—42no—
189C22×C4×C61—42no—
190C22×C4×C61—42no—
191C22×C4×C61C22×C411yescharacteristic
192C22×C4×C61C22×C411yescharacteristic
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61C2×D411yescharacteristic
196C22×C4×C61C2411yescharacteristic
197C2×C22⋊D61—21no—
198C2×C22⋊D61—21no—
199C2×C22⋊D61—21no—
200C2×C22⋊D61—21no—
201C2×C22⋊D61—21no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—22no—
205C22×Dic61—41no—
206C22×Dic61—41no—
207C22×Dic61—42no—
208C22×Dic61—42no—
209C22×Dic61—42no—
210C22×Dic61—42no—
211C22×Dic61C22⋊C411yescharacteristic
212C22×Dic61C22⋊C411yescharacteristic
213C22×Dic61C22⋊C411yescharacteristic
214C22×Dic61C22⋊C411yescharacteristic
215C22×Dic61C22⋊C411yescharacteristic
216C22×Dic61C22⋊C411yescharacteristic
217C22×Dic61C22⋊C411yescharacteristic
218C22×Dic61C22⋊C411yescharacteristic
219C22×Dic61C2×D411yescharacteristic
220C22×Dic61C2×D411yescharacteristic
221C22×Dic61C2×D411yescharacteristic
222C22×Dic61C2×D411yescharacteristic
223#11758224—42no—
224#11758224—42no—
225#11758224—44no—
226#11758222—42no—
227C2×D244C22×C411yescharacteristic
228C2×C4×D61—21no—
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122C22×C411yescharacteristic
234M16×C61—42no—
235C2×C8×C61—22no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—21no—
238C4⋊C4×C61C22×C411yescharacteristic
239C4⋊C4×C61C22×C411yescharacteristic
240C22⋊C4×C61—21no—
241C22⋊C4×C61—21no—
242C22⋊C4×C61—21no—
243C22⋊C4×C61—21no—
244C22⋊C4×C61—21no—
245C42×C61—21no—
246C22⋊Dic61—21no—
247C22⋊Dic61—21no—
248C22⋊Dic61—21no—
249C22⋊Dic61—21no—
250C22⋊Dic61—21no—
251C22⋊Dic61—21no—
252C22⋊Dic61—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⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61C22×C411yescharacteristic
264C4⋊Dic61C22×C411yescharacteristic
265#11758196—21no—
266#11758196—21no—
267#11758196—21no—
268#11758196—21no—
269#11758196—21no—
270#11758196—21no—
271#11758196—21no—
272#11758196—21no—
273#11758196—21no—
274#11758196—21no—
275C4×Dic61—21no—
276C4×Dic61—21no—
277C4×Dic61—21no—
278C4×Dic61—21no—
279C4×Dic61—21no—
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×Dic61C22×C411yescharacteristic
289C4×Dic61C22×C411yescharacteristic
290C4×Dic61C22×C411yescharacteristic
291C4×Dic61C22×C411yescharacteristic
292C4×Dic61C2×D411yescharacteristic
293C4×Dic61C2×D411yescharacteristic
294C4×Dic61C2×D411yescharacteristic
295C4×Dic61C2×D411yescharacteristic
296#11758194—42no—
297C2×#92418—22no—
298C23×C61—21no—
299C23×C61—21no—
300C23×C61—22no—
301C23×C61—22no—
302C23×C61—21no—
303C23×C61C2×C22⋊C411yescharacteristic
304C23×C61C2×C22⋊C411yescharacteristic
305C23×C61C22×D411yescharacteristic
306C22×D61—21no—
307Q8×C61—41no—
308D4×C61—41no—
309D4×C61—41no—
310D4×C61—41no—
311D4×C61—42no—
312D4×C61—42no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—42no—
323C2×C4×C61—42no—
324C2×C4×C61—42no—
325C2×C4×C61—42no—
326C2×C4×C61—84no—
327C2×C4×C61C2×C22⋊C411yescharacteristic
328C2×C4×C61C2×C22⋊C411yescharacteristic
329C2×C4×C61C23×C411yescharacteristic
330C2×C4×C61C22×D411yescharacteristic
331C22⋊D61—42no—
332C22⋊D61—42no—
333C22⋊D61—41no—
334C22⋊D61—41no—
335C22⋊D61—42no—
336C22⋊D61—42no—
337C2×Dic61—21no—
338C2×Dic61—21no—
339C2×Dic61—21no—
340C2×Dic61—21no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—21no—
344C2×Dic61—21no—
345C2×Dic61—21no—
346C2×Dic61—41no—
347C2×Dic61—41no—
348C2×Dic61—41no—
349C2×Dic61—41no—
350C2×Dic61—41no—
351C2×Dic61—41no—
352C2×Dic61—41no—
353C2×Dic61—41no—
354C2×Dic61—42no—
355C2×Dic61—42no—
356C2×Dic61—42no—
357C2×Dic61—42no—
358C2×Dic61—42no—
359C2×Dic61—84no—
360C2×Dic61C2×C22⋊C411yescharacteristic
361C2×Dic61C2×C22⋊C411yescharacteristic
362C2×Dic61C2×C22⋊C411yescharacteristic
363C2×Dic61C2×C22⋊C411yescharacteristic
364C2×Dic61C2×C22⋊C411yescharacteristic
365C2×Dic61C2×C22⋊C411yescharacteristic
366C2×Dic61C2×C22⋊C411yescharacteristic
367C2×Dic61C2×C22⋊C411yescharacteristic
368D244—41no—
369C4×D61—42no—
370C4×D61—42no—
371C4×D61—42no—
372Dic122—42no—
373Dic122—42no—
374Dic122—41no—
375C8×C61—42no—
376#92418—42no—
377#17593—611nomaximal, Sylow
378C22×C61—24no—
379C22×C61—24no—
380C22×C61—21no—
381C22×C61—21no—
382C22×C61—21no—
383C22×C61—21no—
384C22×C61—21no—
385C22×C61—21no—
386C22×C61—41no—
387C22×C61—41no—
388C22×C61—41no—
389C22×C61#41012yes—
390C22×C61#42112yes—
391C22×C61C22×C22⋊C411yescharacteristic
392C22×C61#57511yescharacteristic
393C22×C61#57511yescharacteristic
394C2×D61—41no—
395C2×D61—41no—
396C2×D61—41no—
397C4×C61—21no—
398C4×C61—21no—
399C4×C61—21no—
400C4×C61—21no—
401C4×C61—41no—
402C4×C61—41no—
403C4×C61—41no—
404C4×C61—82no—
405Dic61—21no—
406Dic61—21no—
407Dic61—21no—
408Dic61—21no—
409Dic61—21no—
410Dic61—21no—
411Dic61—21no—
412Dic61—21no—
413Dic61—41no—
414Dic61—41no—
415Dic61—41no—
416Dic61—82no—
417#3444—611no—
418#2920—611no—
419C2×#383—611no—
420#1521—612no—
421#1521—612no—
422#1515—612no—
423#1514—612no—
424#1504—611no—
425#1504—611no—
426#1504—611no—
427#1504D6111yescharacteristic, complemented
428C2×C61—21no—
429C2×C61—21no—
430C2×C61—22no—
431C2×C61—22no—
432C2×C61—81no—
433C2×C61C2×#41011yescharacteristic
434C2×C61#289611yescharacteristic
435C2×C61C2×#42111yescharacteristic
436D61—81no—
437#533—611no—
438#533—611no—
439#533—611no—
440#532—611no—
441#532—611no—
442#532—611no—
443#529—611no—
444#529—611no—
445#529—611no—
446#529—611no—
447#529—1221no—
448#529—1221no—
449#529—1221no—
450#529—1221no—
451#525—611no—
452#525—1221no—
453#525—1221no—
454#525C2×D6111yescharacteristic
455C4×#41—611no—
456C4×#41—611no—
457C4×#41—1221no—
458C4×#41—1221no—
459C22×C42—611no—
460#432—612no—
461#432—1221no—
462#431—612no—
463#431—1221no—
464#423—1221no—
465#407—611no—
466#407C2×D6111yescharacteristic
467C4×M16—1221no—
468#383—612no—
469#383—612no—
470#383—1221no—
471#383—1221no—
472C2×#95—611no—
473C2×#95—1221no—
474C2×#95—1221no—
475C2×#95C2×D6111yescharacteristic
476#328—612no—
477#328—612no—
478#328—612no—
479#328C2×D6112yes—
480#327—612no—
481#327—612no—
482#327—612no—
483#327C2×D6112yes—
484C61#1759311yescharacteristic, complemented, Sylow
485C2×#41—611no—
486C2×#41—1221no—
487C2×#41—1221no—
488C2×#41C4×D6111yescharacteristic
489C23×C4—21no—
490C23×C4—611no—
491C23×C4—611no—
492C23×C4—1221no—
493C23×C4C22×D6111yescharacteristic
494C2×M16—21no—
495C2×M16—1221no—
496C4⋊Q8—611no—
497C4⋊Q8—611no—
498C4⋊Q8—611no—
499#127—611no—
500#126—1221no—
501#126—1221no—
502#126—1221no—
503#126—1221no—
504#125—611no—
505#125—611no—
506#125—1221no—
507#125—1221no—
508#124—611no—
509#124—611no—
510#124—1221no—
511#124—1221no—
512#123—21no—
513#123—1221no—
514#123—1221no—
515#123—1221no—
516#123—1221no—
517#123—1221no—
518C22⋊Q8—611no—
519C22⋊Q8—611no—
520C22⋊Q8—1221no—
521C22⋊Q8—1221no—
522C22⋊Q8—1221no—
523C22⋊Q8—1221no—
524C22⋊Q8C4×D6111yescharacteristic
525C22⋊Q8C22×D6111yescharacteristic
526#121—611no—
527#121—611no—
528#121—1221no—
529#121—1221no—
530#121—1221no—
531#121—1221no—
532#121C4×D6111yescharacteristic
533#121C22×D6111yescharacteristic
534#120—21no—
535#120—1221no—
536C4×Q8—611no—
537C4×Q8—611no—
538C4×Q8—611no—
539C4×Q8—611no—
540C4×Q8—1221no—
541C4×Q8—1221no—
542C4×Q8—1221no—
543C4×Q8—1221no—
544C4×D4—21no—
545C4×D4—21no—
546C4×D4—611no—
547C4×D4—611no—
548C4×D4—611no—
549C4×D4—611no—
550C4×D4—1221no—
551C4×D4—1221no—
552C4×D4—1221no—
553C4×D4—1221no—
554C4×D4—1221no—
555C4×D4—1221no—
556C4×D4—1221no—
557C4×D4—1221no—
558C4×D4—1221no—
559C4×D4—1221no—
560C4×D4—1221no—
561C4×D4—1221no—
562C4×D4—1221no—
563C4×D4—1221no—
564#117—611no—
565#117—1221no—
566#117—1221no—
567#117—1221no—
568#117—1221no—
569#117—1221no—
570#117—1221no—
571#117—1221no—
572#117—1221no—
573#117C4×D6111yescharacteristic
574C2×C42—611no—
575C2×C42—611no—
576C2×C42—611no—
577C2×C42—611no—
578C2×C42—611no—
579C2×C42—611no—
580C2×C42—611no—
581C2×C42—611no—
582C2×C42—611no—
583C2×C42—611no—
584C2×C42—611no—
585C2×C42—611no—
586C2×C42—1221no—
587C2×C42—1221no—
588C4⋊C8—1222no—
589C4⋊C8—1222no—
590C22⋊C8—21no—
591C22⋊C8—612no—
592C22⋊C8—1221no—
593C22⋊C8C22×D6112yes—
594#97—1222no—
595C4×C8—1222no—
596#95—21no—
597#95—612no—
598#95—1222no—
599#95—1222no—
600#95—1222no—
601#95—1222no—
602#95—1221no—
603#95C22×D6112yes—
604C24D4×D6111yescharacteristic
605#41—42no—
606#41—2442no—
607#41—2444no—
608#41—2442no—
609#41—2442no—
610C2×Q8—611no—
611C2×Q8—1221no—
612C2×Q8—1221no—
613C2×Q8C2×C4×D6111yescharacteristic
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—611no—
618C2×D4—1221no—
619C2×D4—1221no—
620C2×D4—1221no—
621C2×D4—1221no—
622C2×D4—1221no—
623C2×D4C2×C4×D6111yescharacteristic
624C22×C4—21no—
625C22×C4—22no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—611no—
631C22×C4—611no—
632C22×C4—611no—
633C22×C4—611no—
634C22×C4—611no—
635C22×C4—611no—
636C22×C4—611no—
637C22×C4—611no—
638C22×C4—611no—
639C22×C4—611no—
640C22×C4—611no—
641C22×C4—611no—
642C22×C4—1221no—
643C22×C4—1221no—
644C22×C4—1221no—
645C22×C4—1221no—
646C22×C4—1221no—
647C22×C4—1222no—
648C22×C4—2442no—
649C22×C4—2441no—
650C22×C4—2441no—
651C22×C4—2442no—
652C22×C4—2442no—
653C22×C4—2442no—
654C22×C4C2×C4×D6111yescharacteristic
655C22×C4C2×C4×D6111yescharacteristic
656C22×C4D4×D6111yescharacteristic
657C22×C4D4×D6111yescharacteristic
658C22×C4D4×D6111yescharacteristic
659C22×C4C23×D6111yescharacteristic
660M16—42no—
661M16—2442no—
662C2×C8—22no—
663C2×C8—1222no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—611no—
667C4⋊C4—611no—
668C4⋊C4—1221no—
669C4⋊C4—1221no—
670C4⋊C4—1221no—
671C4⋊C4—1221no—
672C4⋊C4—1221no—
673C4⋊C4—1221no—
674C4⋊C4—1221no—
675C4⋊C4—1221no—
676C4⋊C4—1221no—
677C4⋊C4—1221no—
678C4⋊C4—1221no—
679C4⋊C4—1221no—
680C4⋊C4—1221no—
681C4⋊C4—1221no—
682C4⋊C4C2×C4×D6111yescharacteristic
683C4⋊C4C2×C4×D6111yescharacteristic
684C22⋊C4—21no—
685C22⋊C4—21no—
686C22⋊C4—21no—
687C22⋊C4—21no—
688C22⋊C4—21no—
689C22⋊C4—1221no—
690C22⋊C4—1221no—
691C22⋊C4—1221no—
692C22⋊C4—1221no—
693C22⋊C4—1221no—
694C22⋊C4—1221no—
695C22⋊C4—1221no—
696C22⋊C4—1221no—
697C22⋊C4—1221no—
698C22⋊C4—1221no—
699C22⋊C4—1221no—
700C22⋊C4—1221no—
701C22⋊C4—1221no—
702C42—21no—
703C42—611no—
704C42—611no—
705C42—611no—
706C42—611no—
707C42—611no—
708C42—611no—
709C42—611no—
710C42—611no—
711C42—611no—
712C42—611no—
713C42—611no—
714C42—611no—
715C42—611no—
716C42—611no—
717C42—611no—
718C42—611no—
719C42—1221no—
720C42—1221no—
721C42—1221no—
722C42—1221no—
723C42—1221no—
724C23—22no—
725C23—22no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—1221no—
730C23C22⋊C4×D6111yescharacteristic
731C23C22⋊C4×D6111yescharacteristic
732C23C2×D4×D6111yescharacteristic
733Q8—41no—
734Q8—2441no—
735Q8—2442no—
736Q8—2442no—
737D4—41no—
738D4—42no—
739D4—42no—
740D4—41no—
741D4—41no—
742D4—2441no—
743D4—2442no—
744D4—2442no—
745D4—2442no—
746D4—2442no—
747D4—2441no—
748D4—2441no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—84no—
763C2×C4—611no—
764C2×C4—611no—
765C2×C4—611no—
766C2×C4—611no—
767C2×C4—611no—
768C2×C4—611no—
769C2×C4—611no—
770C2×C4—611no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—1221no—
774C2×C4—1221no—
775C2×C4—1221no—
776C2×C4—1221no—
777C2×C4—1221no—
778C2×C4—1221no—
779C2×C4—1221no—
780C2×C4—4884no—
781C2×C4—2442no—
782C2×C4—2442no—
783C2×C4—2442no—
784C2×C4—2441no—
785C2×C4—2441no—
786C2×C4—2441no—
787C2×C4—2441no—
788C2×C4—2441no—
789C2×C4—2441no—
790C2×C4—2441no—
791C2×C4—2441no—
792C2×C4—2442no—
793C2×C4—2442no—
794C2×C4—2442no—
795C2×C4—2442no—
796C2×C4—2442no—
797C2×C4C22⋊C4×D6111yescharacteristic
798C2×C4C22⋊C4×D6111yescharacteristic
799C2×C4C22×C4×D6111yescharacteristic
800C2×C4C2×D4×D6111yescharacteristic
801C8—42no—
802C8—2442no—
803C22—24no—
804C22—24no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—2441no—
815C22—2441no—
816C22—2441no—
817C22#1683973412yes—
818C22#1683977712yes—
819C22C2×C22⋊C4×D6111yescharacteristic
820C22#1684055811yescharacteristic
821C22#1684056111yescharacteristic
822C4—21no—
823C4—21no—
824C4—21no—
825C4—21no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—82no—
830C4—1221no—
831C4—1221no—
832C4—1221no—
833C4—1221no—
834C4—1221no—
835C4—1221no—
836C4—1221no—
837C4—1221no—
838C4—4882no—
839C4—2441no—
840C4—2441no—
841C4—2441no—
842C2—21no—
843C2—21no—
844C2—22no—
845C2—22no—
846C2—81no—
847C2—4881no—
848C2C2×#1683973411yescharacteristic
849C2#2145433511yescharacteristic
850C2C2×#1683977711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1504C2
socleC22×C61C22×C22⋊C4
prime radical#21459111C2
cosocleC22×C4×C61C24
hypercenter#1504D61
hypocenterC61#17593
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1504

Complements

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

NH ≅ G/Ntype
2. #21454448C2semidirect
3. C2×#16839629C2semidirect
4. #21444395C2semidirect
5. #21444393C2semidirect
6. #21444368C2semidirect
7. #21444364C2semidirect
8. #21444324C2semidirect
9. #21444323C2semidirect
10. #21444321C2semidirect
11. C61×#1504C2semidirect
12. #16840315C4semidirect
13. #16840314C4semidirect
15. #16840308C4semidirect
16. #16840307C4semidirect
18. #16840298C4semidirect
20. #16840293C4semidirect
29. #41×Dic61C4semidirect
30. #16840230C4semidirect
66. #14519776C2×C4semidirect
67. #14519776C2×C4semidirect
68. #14519775C2×C4semidirect
69. #14519773C2×C4semidirect
74. #14519768C2×C4semidirect
75. #14519768C2×C4semidirect
78. #14519766C2×C4semidirect
79. #14519764C2×C4semidirect
100. Q8×Dic61C2×C4semidirect
101. Q8×Dic61C2×C4semidirect
106. #14519742C2×C4semidirect
107. #14519742C2×C4semidirect
112. D4×Dic61C2×C4semidirect
113. D4×Dic61C2×C4semidirect
114. #14519739C2×C4semidirect
115. #14519739C2×C4semidirect
427. #1504D61semidirect
484. C61#17593semidirect

Maximal subgroups

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

subgroupindex
#214591112
#214544482
C2×#168396292
#214443952
#214443932
#214443682
#214443642
#214443242
#214443232
#214443212
C61×#15042
#1759361