Finite Group Databasebeta

← #30610876

Subgroups — #30610876

Order 15616.

936 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462749C211yesmaximal, characteristic, complemented
2#21462504C211yesmaximal, characteristic, complemented
3#21461183C211yesmaximal, characteristic, complemented
4#21461177C211yesmaximal, characteristic, complemented
5#21461173C211yesmaximal, characteristic, complemented
6#21461162C211yesmaximal, characteristic, complemented
7#21461153C211yesmaximal, characteristic, complemented
8#21461148C211yesmaximal, characteristic, complemented
9#21461137C211yesmaximal, characteristic, complemented
10#21461133C211yesmaximal, characteristic, complemented
11#21461129C211yesmaximal, characteristic, complemented
12#21461122C211yesmaximal, characteristic, complemented
13#21461117C211yesmaximal, characteristic, complemented
14D61⋊(Q8⋊C8)C211yesmaximal, characteristic, complemented
15#21459439C211yesmaximal, characteristic
16#16840813—21no—
17#16840792—21no—
18#16840792—21no—
19#16840790—21no—
20#16840787—21no—
21#16840787—21no—
22#16840784C2211yescharacteristic
23#16840784C2211yescharacteristic
24#16840781C2211yescharacteristic
25#16840781C2211yescharacteristic
26#16840781C2211yescharacteristic
27#16840780C2211yescharacteristic
28#16840780C2211yescharacteristic
29#16840769—21no—
30#16840766C2211yescharacteristic
31D61⋊(C4⋊C8)C2211yescharacteristic
32D61⋊(C4⋊C8)C2211yescharacteristic
33#16840737—21no—
34C4×#11758213C2211yescharacteristic
35C4×D61⋊C8C2211yescharacteristic
36#16840612C2211yescharacteristic
37#16840612C2211yescharacteristic
38#16840612C2211yescharacteristic
39#16840612C2211yescharacteristic
40#16840612C2211yescharacteristic
41#16840612C2211yescharacteristic
42#16840612C2211yescharacteristic
43#16840612C2211yescharacteristic
44Q8⋊#92420C2211yescharacteristic
45Q8⋊#92420C2211yescharacteristic
46Q8⋊#92420C2211yescharacteristic
47Q8⋊#92420C2211yescharacteristic
48#16840610C2211yescharacteristic
49#16840610C2211yescharacteristic
50#16840610C2211yescharacteristic
51#16840610C2211yescharacteristic
52#16840485—21no—
53#16840485C411yescharacteristic
54#16840450—21no—
55#16840450—21no—
56#16840450C411yescharacteristic
57#16840450C411yescharacteristic
58Q8×D244C411yescharacteristic
59#16840424C411yescharacteristic
60#16840424C411yescharacteristic
61#16840415—21no—
62#16840415C411yescharacteristic
63#16840317—21no—
64#16840317C2211yescharacteristic
65#16840297—21no—
66#16840297—21no—
67#16840297C2211yescharacteristic
68#16840297C2211yescharacteristic
69C4×#11758226—21no—
70C4×#11758226C2211yescharacteristic
71C4×#11758226C2211yescharacteristic
72C4×Q8×D61C2211yescharacteristic
73C4×Q8×D61C2211yescharacteristic
74C61×#557C411yescharacteristic
75C2×#11758213—21no—
76C2×#11758213—21no—
77C2×D61⋊C8—21no—
78C2×D61⋊C8—21no—
79C2×D61⋊C8—21no—
80#14519844—21no—
81#14519844—21no—
82#14519844—21no—
83#14519844—21no—
84C4⋊#92420—21no—
85C4⋊#92420—21no—
86C4⋊#92420—21no—
87C4⋊#92420C2311yescharacteristic
88C4⋊#92420C2311yescharacteristic
89C4⋊#92420C2311yescharacteristic
90C4⋊#92420C2311yescharacteristic
91#14519834—21no—
92#14519834—21no—
93#14519834—21no—
94#14519834—21no—
95#14519834—21no—
96#14519834—21no—
97#14519834—21no—
98#14519832—21no—
99#14519832—21no—
100#14519832—21no—
101C4×#92420—21no—
102C4×#92420—21no—
103C4×#92420C2311yescharacteristic
104C4×#92420C2311yescharacteristic
105C4×#92420C2311yescharacteristic
106C4×#92420C2311yescharacteristic
107C2×#11758226—21no—
108C2×#11758226C2×C411yescharacteristic
109C2×#11758226D411yescharacteristic
110C2×Q8×D61C2×C411yescharacteristic
111C2×Q8×D61C2×C411yescharacteristic
112#14519777—21no—
113#14519777C2×C411yescharacteristic
114#14519772—21no—
115#14519772—21no—
116#14519772—21no—
117#14519772—21no—
118#14519772—21no—
119#14519772—21no—
120#14519768—21no—
121#14519768—21no—
122#14519768—21no—
123#14519765—21no—
124#14519765—21no—
125#14519765C2×C411yescharacteristic
126#14519765C2×C411yescharacteristic
127#14519762—21no—
128#14519762—21no—
129#14519762—21no—
130#14519762—21no—
131#14519762—21no—
132#14519762—21no—
133#14519757—21no—
134#14519757—21no—
135#14519757—21no—
136#14519757—21no—
137#14519757C2×C411yescharacteristic
138#14519757C2×C411yescharacteristic
139#14519757C2×C411yescharacteristic
140#14519757C2×C411yescharacteristic
141#14519753—21no—
142#14519753—21no—
143#14519753—21no—
144#14519752—21no—
145#14519752—21no—
146#14519752C2×C411yescharacteristic
147#14519752C2×C411yescharacteristic
148Q8×Dic61—21no—
149Q8×Dic61D411yescharacteristic
150Q8×Dic61C2311yescharacteristic
151C4×Dic122—21no—
152C4×Dic122—21no—
153C4×Dic122C2×C411yescharacteristic
154C4×Dic122C2×C411yescharacteristic
155#14519742—21no—
156#14519742—21no—
157#14519742C2311yescharacteristic
158#14519742C2311yescharacteristic
159C4×D244—21no—
160C4×D244—21no—
161C4×D244—21no—
162C4×D244—21no—
163C4×D244C2×C411yescharacteristic
164C4×D244C2×C411yescharacteristic
165C4×D244C2×C411yescharacteristic
166C4×D244C2×C411yescharacteristic
167#14519739—21no—
168#14519739—21no—
169#14519739—21no—
170#14519739D411yescharacteristic
171#14519739D411yescharacteristic
172#14519739D411yescharacteristic
173#14519739C2311yescharacteristic
174#14519735—21no—
175#14519735—21no—
176#14519735—21no—
177#14519735—21no—
178#14519735—21no—
179#14519735—21no—
180#14519735—21no—
181#14519735C2×C411yescharacteristic
182#14519735D411yescharacteristic
183#14519735D411yescharacteristic
184#14519735D411yescharacteristic
185C4⋊C4×D61—21no—
186C4⋊C4×D61—21no—
187C4⋊C4×D61C2×C411yescharacteristic
188C4⋊C4×D61C2×C411yescharacteristic
189C42×D61—21no—
190C42×D61—21no—
191C42×D61—21no—
192C42×D61C2311yescharacteristic
193C42×D61C2311yescharacteristic
194C42×D61C2311yescharacteristic
195C4⋊Q8×C61—21no—
196C4⋊Q8×C61C2×C411yescharacteristic
197#125×C61—21no—
198#125×C61—21no—
199#125×C61C2×C411yescharacteristic
200#125×C61C2×C411yescharacteristic
201C4×Q8×C61—21no—
202C4×Q8×C61C2×C411yescharacteristic
203C4×Q8×C61C2×C411yescharacteristic
204C4×Q8×C61C2×C411yescharacteristic
205C4×Q8×C61C2×C411yescharacteristic
206C2×Q8×C61—21no—
207C2×Q8×C61C22⋊C411yescharacteristic
208C2×Q8×C61C22×C411yescharacteristic
209#11758226—22no—
210#11758226—42no—
211#11758226—41no—
212#11758226—44no—
213Q8×D61—22no—
214Q8×D61—22no—
215Q8×D61—41no—
216Q8×D61—41no—
217C2×D244—21no—
218C2×D244—21no—
219C2×D244—21no—
220C2×D244C22⋊C411yescharacteristic
221C2×D244C22⋊C411yescharacteristic
222C2×D244C22⋊C411yescharacteristic
223C2×D244C22×C411yescharacteristic
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61C22×C411yescharacteristic
232C2×C4×D61C22×C411yescharacteristic
233C2×C4×D61C22×C411yescharacteristic
234C2×C4×D61C2×D411yescharacteristic
235C2×C4×D61C2×D411yescharacteristic
236C2×C4×D61C2×D411yescharacteristic
237C2×C4×D61C2×D411yescharacteristic
238C2×C4×D61C2×D411yescharacteristic
239C2×C4×D61C2×D411yescharacteristic
240C2×Dic122—21no—
241C2×Dic122—21no—
242C2×Dic122C22×C411yescharacteristic
243C2×Dic122C22×C411yescharacteristic
244C2×#92420—21no—
245C2×#92420—21no—
246C2×#92420—21no—
247C2×#92420—21no—
248C2×#92420—21no—
249C2×#92420—21no—
250C2×#92420—21no—
251C2×#92420—21no—
252#11758213—42no—
253#11758213—81no—
254D61⋊C8—42no—
255D61⋊C8—81no—
256D61⋊C8—81no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61—21no—
260C4⋊C4×C61—21no—
261C4⋊C4×C61—21no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61—21no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61C22⋊C411yescharacteristic
266C4⋊C4×C61C22⋊C411yescharacteristic
267C4⋊C4×C61C22⋊C411yescharacteristic
268C4⋊C4×C61C22×C411yescharacteristic
269C4⋊C4×C61C22×C411yescharacteristic
270C4⋊C4×C61C22×C411yescharacteristic
271C42×C61—21no—
272C42×C61—21no—
273C42×C61—21no—
274C42×C61C22×C411yescharacteristic
275C42×C61C22×C411yescharacteristic
276C42×C61C22×C411yescharacteristic
277#11758198—21no—
278#11758198—21no—
279#11758198—21no—
280#11758198—21no—
281#11758198—21no—
282#11758198—21no—
283#11758198—21no—
284#11758198—21no—
285#11758198—21no—
286#11758198—21no—
287#11758198—21no—
288#11758198—21no—
289#11758198—21no—
290#11758198C22⋊C411yescharacteristic
291#11758198C22⋊C411yescharacteristic
292#11758198C22⋊C411yescharacteristic
293#11758198C22⋊C411yescharacteristic
294#11758198C22⋊C411yescharacteristic
295#11758198C22⋊C411yescharacteristic
296C4⋊Dic61—21no—
297C4⋊Dic61—21no—
298C4⋊Dic61—21no—
299C4⋊Dic61—21no—
300C4⋊Dic61—21no—
301C4⋊Dic61—21no—
302C4⋊Dic61—21no—
303C4⋊Dic61C22⋊C411yescharacteristic
304C4⋊Dic61C22⋊C411yescharacteristic
305C4⋊Dic61C22⋊C411yescharacteristic
306C4⋊Dic61C22×C411yescharacteristic
307#11758196—21no—
308#11758196—21no—
309#11758196—21no—
310#11758196—21no—
311#11758196—21no—
312#11758196—21no—
313C4×Dic61—21no—
314C4×Dic61—21no—
315C4×Dic61—21no—
316C4×Dic61—21no—
317C4×Dic61—21no—
318C4×Dic61—21no—
319C4×Dic61C2×D411yescharacteristic
320C4×Dic61C2×D411yescharacteristic
321C4×Dic61C2×D411yescharacteristic
322C4×Dic61C2×D411yescharacteristic
323C4×Dic61C2×D411yescharacteristic
324C4×Dic61C2×D411yescharacteristic
325C4×Dic61C2411yescharacteristic
326C22×D61—21no—
327C22×D61C2×C22⋊C411yescharacteristic
328C22×D61C2×C22⋊C411yescharacteristic
329C22×D61C2×C22⋊C411yescharacteristic
330Q8×C61—21no—
331Q8×C61—41no—
332Q8×C61—42no—
333Q8×C61#13112yes—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61C2×C22⋊C411yescharacteristic
339C2×C4×C61C2×C22⋊C411yescharacteristic
340C2×C4×C61C2×C22⋊C411yescharacteristic
341C2×C4×C61C2×C22⋊C411yescharacteristic
342C2×C4×C61C2×C22⋊C411yescharacteristic
343C2×C4×C61C2×C22⋊C411yescharacteristic
344C2×C4×C61C23×C411yescharacteristic
345C2×Dic61—21no—
346C2×Dic61—21no—
347C2×Dic61—21no—
348C2×Dic61C2×C22⋊C411yescharacteristic
349C2×Dic61C2×C22⋊C411yescharacteristic
350C2×Dic61C2×C22⋊C411yescharacteristic
351C2×Dic61C22×D411yescharacteristic
352C2×Dic61C22×D411yescharacteristic
353D244—22no—
354D244—22no—
355D244—21no—
356D244—21no—
357D244—41no—
358D244—42no—
359D244—42no—
360D244—42no—
361C4×D61—22no—
362C4×D61—21no—
363C4×D61—21no—
364C4×D61—21no—
365C4×D61—21no—
366C4×D61—21no—
367C4×D61—21no—
368C4×D61—21no—
369C4×D61—21no—
370C4×D61—21no—
371C4×D61—21no—
372C4×D61—21no—
373C4×D61—21no—
374C4×D61—41no—
375C4×D61—41no—
376C4×D61—42no—
377C4×D61—42no—
378C4×D61—42no—
379C4×D61—42no—
380C4×D61—42no—
381C4×D61—42no—
382C4×D61—41no—
383C4×D61—41no—
384Dic122—21no—
385Dic122—21no—
386Dic122—21no—
387Dic122—21no—
388Dic122—42no—
389Dic122—42no—
390#92420—41no—
391#92420—41no—
392#92420—41no—
393#92420—41no—
394#92420—41no—
395#92420—41no—
396#92420—41no—
397#92420—41no—
398#17524—611nomaximal, Sylow
399C22×C61C22×C22⋊C411yescharacteristic
400C2×D61—21no—
401C2×D61—21no—
402C2×D61—21no—
403C2×D61—21no—
404C2×D61—21no—
405C2×D61—21no—
406C2×D61—21no—
407C2×D61—21no—
408C2×D61—41no—
409C2×D61—41no—
410C2×D61—41no—
411C2×D61#42112yes—
412C4×C61—22no—
413C4×C61—21no—
414C4×C61—21no—
415C4×C61—21no—
416C4×C61—21no—
417C4×C61—21no—
418C4×C61—21no—
419C4×C61—41no—
420C4×C61—41no—
421C4×C61—41no—
422C4×C61C2×#13111yescharacteristic
423C4×C61#56811yescharacteristic
424Dic61—21no—
425Dic61—21no—
426Dic61—21no—
427Dic61—21no—
428Dic61—41no—
429Dic61—41no—
430Dic61—41no—
431Dic61#57711yescharacteristic
432Dic61#57811yescharacteristic
433#3482—611no—
434#2990—611no—
435#2922—611no—
436#1497—611no—
437#1495—611no—
438#1494—611no—
439#1491—611no—
440#1488—611no—
441#1487—611no—
442#1483—611no—
443#1482—611no—
444#1481—611no—
445#1479—611no—
446#1477—611no—
447C2×Q8⋊C8—611no—
448C2×C61#288011yescharacteristic
449C2×C61#289811yescharacteristic
450C2×C61C2×#42111yescharacteristic
451D61—22no—
452D61—41no—
453D61—41no—
454D61—81no—
455#557#692311yescharacteristic
456#556—611no—
457#556—1221no—
458#552—611no—
459#552—611no—
460#552—1221no—
461#552—1221no—
462D4×Q8—611no—
463#548—611no—
464#548—611no—
465#547—611no—
466#547—1221no—
467#533—611no—
468#533—1221no—
469#529—611no—
470#529—611no—
471#529—1221no—
472#529—1221no—
473C4×#41—611no—
474C4×#41—611no—
475C4×#41—1221no—
476C2×C4×Q8—611no—
477C2×C4×Q8—611no—
478#446—1221no—
479#435—1221no—
480#435—1221no—
481C8×D4—1221no—
482#433—1221no—
483#433—1221no—
484#432—611no—
485#432—611no—
486#431—611no—
487#431—611no—
488#431—611no—
489#431—611no—
490#431—611no—
491#424—1221no—
492#423—611no—
493C2×C4⋊C8—611no—
494C2×C4⋊C8—611no—
495#408—1221no—
496C4×M16—611no—
497C2×C4×C8—611no—
498Q8⋊C8—611no—
499Q8⋊C8—611no—
500Q8⋊C8—611no—
501Q8⋊C8—611no—
502Q8⋊C8—611no—
503Q8⋊C8—611no—
504Q8⋊C8—611no—
505Q8⋊C8—611no—
506Q8⋊C8—611no—
507Q8⋊C8—611no—
508Q8⋊C8—611no—
509Q8⋊C8—611no—
510D4⋊C8—611no—
511D4⋊C8—611no—
512D4⋊C8—611no—
513D4⋊C8—611no—
514C61#1752411yescharacteristic, complemented, Sylow
515C2×#41—611no—
516C2×#41—611no—
517C2×#41—1221no—
518C22×Q8—611no—
519C22×Q8—611no—
520C2×M16—1221no—
521C2×M16—1221no—
522C22×C8—1221no—
523C22×C8—1221no—
524C22×C8—1221no—
525C4⋊Q8—21no—
526C4⋊Q8—611no—
527C4⋊Q8—1221no—
528C4⋊Q8C2×#692311yescharacteristic
529#126—1221no—
530#126—1221no—
531#126—1221no—
532#126—1221no—
533#126—1221no—
534#126—1221no—
535#125—21no—
536#125—21no—
537#125—1221no—
538#125—1221no—
539#125—1221no—
540#125C2×#692311yescharacteristic
541#125C2×#692311yescharacteristic
542#124—611no—
543#124—611no—
544#124—1221no—
545#124—1221no—
546#123—1221no—
547#123—1221no—
548#123—1221no—
549#123—1221no—
550#123—1221no—
551#123—1221no—
552C22⋊Q8—611no—
553C22⋊Q8—611no—
554C22⋊Q8—611no—
555C22⋊Q8—611no—
556C22⋊Q8—1221no—
557C22⋊Q8—1221no—
558C22⋊Q8—1221no—
559C22⋊Q8—1221no—
560C22⋊Q8—1221no—
561C22⋊Q8—1221no—
562C22⋊Q8—1221no—
563#121—611no—
564#121—611no—
565#121—1221no—
566#121—1221no—
567C4×Q8—21no—
568C4×Q8—611no—
569C4×Q8—611no—
570C4×Q8—611no—
571C4×Q8—611no—
572C4×Q8—611no—
573C4×Q8—611no—
574C4×Q8—1221no—
575C4×Q8—1221no—
576C4×Q8—1221no—
577C4×Q8—1221no—
578C4×Q8—1221no—
579C4×Q8C2×#692311yescharacteristic
580C4×Q8C2×#692311yescharacteristic
581C4×Q8C2×#692311yescharacteristic
582C4×Q8C2×#692311yescharacteristic
583C4×D4—611no—
584C4×D4—611no—
585C4×D4—611no—
586C4×D4—611no—
587C4×D4—611no—
588C4×D4—611no—
589C4×D4—611no—
590C4×D4—611no—
591C4×D4—1221no—
592C4×D4—1221no—
593C4×D4—1221no—
594C4×D4—1221no—
595C4×D4—1221no—
596C4×D4—1221no—
597C4×D4—1221no—
598#117—611no—
599#117—611no—
600#117—611no—
601#117—611no—
602#117—1221no—
603#117—1221no—
604#117—1221no—
605#117—1221no—
606#117—1221no—
607#117—1221no—
608#117—1221no—
609C2×C4⋊C4—611no—
610C2×C4⋊C4—611no—
611C2×C4⋊C4—1221no—
612C2×C4⋊C4—1221no—
613C2×C42—611no—
614C2×C42—611no—
615C2×C42—611no—
616C2×C42—1221no—
617C2×C42—1221no—
618C2×C42—1221no—
619C4⋊C8—611no—
620C4⋊C8—611no—
621C4⋊C8—611no—
622C4⋊C8—611no—
623C4⋊C8—1221no—
624C4⋊C8—1221no—
625C4⋊C8—1221no—
626C4⋊C8—1221no—
627C4⋊C8—1221no—
628C4⋊C8—1221no—
629C4⋊C8—1221no—
630C22⋊C8—1221no—
631C22⋊C8—1221no—
632C22⋊C8—1221no—
633C22⋊C8—1221no—
634C22⋊C8—1221no—
635C22⋊C8—1221no—
636C22⋊C8—1221no—
637#97—1221no—
638#97—1221no—
639#97—1221no—
640C4×C8—611no—
641C4×C8—611no—
642C4×C8—611no—
643C4×C8—611no—
644C4×C8—1221no—
645C4×C8—1221no—
646#41—1222no—
647#41—2442no—
648#41—2441no—
649#41—2444no—
650C2×Q8—21no—
651C2×Q8—611no—
652C2×Q8—611no—
653C2×Q8—1221no—
654C2×Q8—1221no—
655C2×Q8—1222no—
656C2×Q8—1222no—
657C2×Q8—2441no—
658C2×Q8—2441no—
659C2×Q8C22⋊#692311yescharacteristic
660C2×Q8C22×#692311yescharacteristic
661C2×D4—611no—
662C2×D4—611no—
663C2×D4—611no—
664C2×D4—611no—
665C2×D4—1221no—
666C2×D4—1221no—
667C2×D4—1221no—
668C22×C4—611no—
669C22×C4—611no—
670C22×C4—611no—
671C22×C4—611no—
672C22×C4—611no—
673C22×C4—611no—
674C22×C4—611no—
675C22×C4—611no—
676C22×C4—611no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—1221no—
680C22×C4—1221no—
681C22×C4—1221no—
682C22×C4—1221no—
683C22×C4—1221no—
684M16—4881no—
685M16—2442no—
686C2×C8—1221no—
687C2×C8—1221no—
688C2×C8—1221no—
689C2×C8—1221no—
690C2×C8—1221no—
691C2×C8—1221no—
692C2×C8—1221no—
693C2×C8—1221no—
694C2×C8—4881no—
695C2×C8—4881no—
696C2×C8—2442no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—611no—
706C4⋊C4—611no—
707C4⋊C4—611no—
708C4⋊C4—611no—
709C4⋊C4—1221no—
710C4⋊C4—1221no—
711C4⋊C4—1221no—
712C4⋊C4—1221no—
713C4⋊C4—1221no—
714C4⋊C4—1221no—
715C4⋊C4—1221no—
716C4⋊C4—1221no—
717C4⋊C4—1221no—
718C4⋊C4—1221no—
719C4⋊C4—1221no—
720C4⋊C4—1221no—
721C4⋊C4—1221no—
722C4⋊C4C22⋊#692311yescharacteristic
723C4⋊C4C22⋊#692311yescharacteristic
724C4⋊C4C22⋊#692311yescharacteristic
725C4⋊C4C22×#692311yescharacteristic
726C4⋊C4C22×#692311yescharacteristic
727C4⋊C4C22×#692311yescharacteristic
728C22⋊C4—611no—
729C22⋊C4—611no—
730C22⋊C4—611no—
731C22⋊C4—611no—
732C22⋊C4—611no—
733C22⋊C4—611no—
734C22⋊C4—1221no—
735C22⋊C4—1221no—
736C22⋊C4—1221no—
737C22⋊C4—1221no—
738C22⋊C4—1221no—
739C22⋊C4—1221no—
740C22⋊C4—1221no—
741C22⋊C4—1221no—
742C22⋊C4—1221no—
743C22⋊C4—1221no—
744C22⋊C4—1221no—
745C22⋊C4—1221no—
746C22⋊C4—1221no—
747C42—21no—
748C42—21no—
749C42—21no—
750C42—611no—
751C42—611no—
752C42—611no—
753C42—611no—
754C42—611no—
755C42—611no—
756C42—611no—
757C42—1221no—
758C42—1221no—
759C42—1221no—
760C42—1221no—
761C42—1221no—
762C42—1221no—
763C42C22×#692311yescharacteristic
764C42C22×#692311yescharacteristic
765C42C22×#692311yescharacteristic
766C23—611no—
767C23—611no—
768C23—611no—
769C23—1221no—
770Q8—21no—
771Q8—41no—
772Q8—42no—
773Q8—1221no—
774Q8—1221no—
775Q8—1221no—
776Q8—1221no—
777Q8—2442no—
778Q8—2442no—
779Q8#1451986512yes—
780D4—1222no—
781D4—1222no—
782D4—1221no—
783D4—1221no—
784D4—2441no—
785D4—2442no—
786D4—2442no—
787D4—2442no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—611no—
793C2×C4—611no—
794C2×C4—611no—
795C2×C4—611no—
796C2×C4—611no—
797C2×C4—1221no—
798C2×C4—1221no—
799C2×C4—1221no—
800C2×C4—1221no—
801C2×C4—1221no—
802C2×C4—1221no—
803C2×C4—1222no—
804C2×C4—1221no—
805C2×C4—1221no—
806C2×C4—1221no—
807C2×C4—1221no—
808C2×C4—1221no—
809C2×C4—1221no—
810C2×C4—1221no—
811C2×C4—1221no—
812C2×C4—1221no—
813C2×C4—2441no—
814C2×C4—2441no—
815C2×C4—2442no—
816C2×C4—2442no—
817C2×C4—2442no—
818C2×C4—2442no—
819C2×C4—2441no—
820C2×C4—2441no—
821C2×C4—2442no—
822C2×C4—2442no—
823C2×C4C2×C22⋊#692311yescharacteristic
824C2×C4C2×C22⋊#692311yescharacteristic
825C2×C4C2×C22⋊#692311yescharacteristic
826C2×C4C2×C22⋊#692311yescharacteristic
827C2×C4C2×C22⋊#692311yescharacteristic
828C2×C4C2×C22⋊#692311yescharacteristic
829C2×C4C23×#692311yescharacteristic
830C8—2441no—
831C8—2441no—
832C8—2441no—
833C8—2441no—
834C8—2441no—
835C8—2441no—
836C8—2441no—
837C8—2441no—
838C22—612no—
839C22—1221no—
840C22—1221no—
841C22—1221no—
842C22—1221no—
843C22—1221no—
844C22—1221no—
845C22—1221no—
846C22—1221no—
847C22—2441no—
848C22—2441no—
849C22—2441no—
850C22C22×C22⋊#692311yescharacteristic
851C4—22no—
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—21no—
857C4—21no—
858C4—41no—
859C4—41no—
860C4—41no—
861C4—611no—
862C4—611no—
863C4—1221no—
864C4—1221no—
865C4—1221no—
866C4—1221no—
867C4—2441no—
868C4—2441no—
869C4—2441no—
870C4C2×#1451986511yescharacteristic
871C4#1684084211yescharacteristic
872C2—1222no—
873C2—4881no—
874C2—2441no—
875C2—2441no—
876C2#2146240811yescharacteristic
877C2#2146244111yescharacteristic
878C2D61⋊#42111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#557C4
socleC22×C61C22×C22⋊C4
prime radical#21459439C2
cosocleC4×Dic61C24
hypercenter#557#6923
hypocenterC61#17524
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #557

Complements

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

NH ≅ G/Ntype
1. #21462749C2semidirect
2. #21462504C2semidirect
3. #21461183C2semidirect
4. #21461177C2semidirect
5. #21461173C2semidirect
6. #21461162C2semidirect
7. #21461153C2semidirect
8. #21461148C2semidirect
9. #21461137C2semidirect
10. #21461133C2semidirect
11. #21461129C2semidirect
12. #21461122C2semidirect
13. #21461117C2semidirect
14. D61⋊(Q8⋊C8)C2semidirect
514. C61#17524semidirect

Maximal subgroups

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

subgroupindex
#214627492
#214625042
#214611832
#214611772
#214611732
#214611622
#214611532
#214611482
#214611372
#214611332
#214611292
#214611222
#214611172
D61⋊(Q8⋊C8)2
#214594392
#1752461