Finite Group Databasebeta

← #30610830

Subgroups — #30610830

Order 15616.

948 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462631C211yesmaximal, characteristic, complemented
2#21462514C211yesmaximal, characteristic, complemented
3#21461178C211yesmaximal, characteristic, complemented
4#21461174C211yesmaximal, characteristic, complemented
5#21461173C211yesmaximal, characteristic, complemented
6#21461163C211yesmaximal, characteristic, complemented
7#21461156C211yesmaximal, characteristic, complemented
8#21461151C211yesmaximal, characteristic, complemented
9#21461138C211yesmaximal, characteristic, complemented
10#21461134C211yesmaximal, characteristic, complemented
11#21461133C211yesmaximal, characteristic, complemented
12#21461123C211yesmaximal, characteristic, complemented
13#21461116C211yesmaximal, characteristic, complemented
14#21461111C211yesmaximal, characteristic, complemented
15#21459413C211yesmaximal, characteristic
16#16840812—21no—
17#16840797—21no—
18#16840794—21no—
19#16840794—21no—
20#16840787—21no—
21#16840786—21no—
22#16840784C2211yescharacteristic
23#16840783C2211yescharacteristic
24#16840781C2211yescharacteristic
25#16840781C2211yescharacteristic
26#16840778C2211yescharacteristic
27#16840778C2211yescharacteristic
28#16840778C2211yescharacteristic
29#16840765C2211yescharacteristic
30C2×C4⋊#92420C2211yescharacteristic
31#16840735—21no—
32#16840726—21no—
33C4×#11758217C2211yescharacteristic
34C4×#11758217C2211yescharacteristic
35C4×D61⋊C8C2211yescharacteristic
36#16840612C2211yescharacteristic
37#16840612C2211yescharacteristic
38#16840612C2211yescharacteristic
39#16840612C2211yescharacteristic
40#16840612C2211yescharacteristic
41#16840612C2211yescharacteristic
42#16840612C2211yescharacteristic
43#16840612C2211yescharacteristic
44#16840610C2211yescharacteristic
45#16840610C2211yescharacteristic
46#16840610C2211yescharacteristic
47#16840610C2211yescharacteristic
48D4⋊#92420C2211yescharacteristic
49D4⋊#92420C2211yescharacteristic
50D4⋊#92420C2211yescharacteristic
51D4⋊#92420C2211yescharacteristic
52#16840496—21no—
53#16840495C411yescharacteristic
54#16840489C411yescharacteristic
55#16840480C411yescharacteristic
56#16840479—21no—
57#16840461—21no—
58#16840460C411yescharacteristic
59#16840455—21no—
60#16840430C411yescharacteristic
61#16840421C411yescharacteristic
62#16840418C411yescharacteristic
63#16840307—21no—
64#16840307C2211yescharacteristic
65#16840297C2211yescharacteristic
66#16840295—21no—
67#16840293C2211yescharacteristic
68#16840289—21no—
69#16840230C2211yescharacteristic
70C4×#11758224—21no—
71C4×#11758224C2211yescharacteristic
72C4×#11758224C2211yescharacteristic
73C2×#14519742C2211yescharacteristic
74C61×#553C411yescharacteristic
75C2×#11758217—21no—
76C2×#11758217—21no—
77C2×#11758217—21no—
78C2×D61⋊C8—21no—
79C22×#92420—21no—
80#14519844—21no—
81C4⋊#92420—21no—
82C4⋊#92420—21no—
83C4⋊#92420—21no—
84C4⋊#92420—21no—
85C4⋊#92420C2311yescharacteristic
86C4⋊#92420C2311yescharacteristic
87C4⋊#92420C2311yescharacteristic
88C4⋊#92420C2311yescharacteristic
89#14519834—21no—
90#14519834—21no—
91#14519834—21no—
92C22⋊#92420—21no—
93C22⋊#92420—21no—
94C22⋊#92420—21no—
95C22⋊#92420—21no—
96#14519832—21no—
97#14519832—21no—
98#14519832—21no—
99#14519832—21no—
100C4×#92420—21no—
101C4×#92420—21no—
102C4×#92420—21no—
103C4×#92420C2311yescharacteristic
104C4×#92420C2311yescharacteristic
105C4×#92420C2311yescharacteristic
106C4×#92420C2311yescharacteristic
107C2×#11758222C2×C411yescharacteristic
108C2×#11758224—21no—
109C2×#11758224C2×C411yescharacteristic
110C2×#11758224D411yescharacteristic
111C22×Dic122C2×C411yescharacteristic
112#14519776—21no—
113#14519776C2×C411yescharacteristic
114#14519773—21no—
115#14519773C2×C411yescharacteristic
116#14519772—21no—
117#14519772—21no—
118#14519771—21no—
119#14519770—21no—
120#14519770—21no—
121#14519768C2×C411yescharacteristic
122#14519767—21no—
123#14519767—21no—
124#14519765C2×C411yescharacteristic
125#14519764C2×C411yescharacteristic
126#14519763—21no—
127#14519763—21no—
128#14519763—21no—
129#14519763—21no—
130#14519763—21no—
131#14519762—21no—
132#14519762—21no—
133#14519760—21no—
134#14519759—21no—
135#14519758—21no—
136#14519757C2×C411yescharacteristic
137#14519756C2×C411yescharacteristic
138#14519755—21no—
139#14519754—21no—
140#14519752C2×C411yescharacteristic
141#14519751—21no—
142#14519751C2×C411yescharacteristic
143#14519750—21no—
144#14519749—21no—
145#14519749—21no—
146#14519749—21no—
147#14519749—21no—
148C4×Dic122—21no—
149C4×Dic122C2×C411yescharacteristic
150C4×Dic122C2×C411yescharacteristic
151#14519742—21no—
152#14519742—21no—
153#14519742—21no—
154#14519742C2×C411yescharacteristic
155#14519742C2×C411yescharacteristic
156#14519742C2×C411yescharacteristic
157#14519742D411yescharacteristic
158#14519742C2311yescharacteristic
159#14519742C2311yescharacteristic
160D4×Dic61—21no—
161D4×Dic61—21no—
162D4×Dic61D411yescharacteristic
163D4×Dic61C2311yescharacteristic
164#14519739—21no—
165#14519739C2×C411yescharacteristic
166#14519739C2311yescharacteristic
167C4×C22⋊D61—21no—
168C4×C22⋊D61—21no—
169C4×C22⋊D61—21no—
170C4×C22⋊D61C2×C411yescharacteristic
171C4×C22⋊D61C2×C411yescharacteristic
172#14519737—21no—
173#14519737—21no—
174#14519737—21no—
175#14519737—21no—
176#14519737—21no—
177#14519737—21no—
178#14519737D411yescharacteristic
179#14519737D411yescharacteristic
180#14519735—21no—
181#14519735C2×C411yescharacteristic
182#14519735D411yescharacteristic
183#14519734—21no—
184#14519733—21no—
185#14519733—21no—
186#14519733D411yescharacteristic
187#14519733D411yescharacteristic
188C2×#11758196—21no—
189C2×C4×Dic61—21no—
190C2×C4×Dic61—21no—
191C2×C4×Dic61C2311yescharacteristic
192C2×C4×Dic61C2311yescharacteristic
193C42×D61—21no—
194C42×D61C2311yescharacteristic
195#126×C61—21no—
196#125×C61C2×C411yescharacteristic
197#123×C61—21no—
198#121×C61—21no—
199#121×C61C2×C411yescharacteristic
200#121×C61C2×C411yescharacteristic
201C4×D4×C61—21no—
202C4×D4×C61C2×C411yescharacteristic
203C4×D4×C61C2×C411yescharacteristic
204#117×C61C2×C411yescharacteristic
205C2×C4⋊C4×C61C2×C411yescharacteristic
206C2×D4×C61—21no—
207C2×D4×C61—21no—
208C2×D4×C61C22⋊C411yescharacteristic
209C2×D4×C61C22×C411yescharacteristic
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61C22×C411yescharacteristic
213C22×C4×C61C22×C411yescharacteristic
214C2×C22⋊D61—21no—
215C2×C22⋊D61—21no—
216C2×C22⋊D61—21no—
217C2×C22⋊D61—21no—
218C2×C22⋊D61—21no—
219C2×C22⋊D61C22⋊C411yescharacteristic
220C2×C22⋊D61C22⋊C411yescharacteristic
221C22×Dic61—21no—
222C22×Dic61—21no—
223C22×Dic61—21no—
224C22×Dic61C2×D411yescharacteristic
225C22×Dic61C2×D411yescharacteristic
226C22×Dic61C2×D411yescharacteristic
227C22×Dic61C2×D411yescharacteristic
228#11758224—22no—
229#11758224—41no—
230#11758224—41no—
231#11758224—41no—
232#11758224—42no—
233#11758224—42no—
234#11758222—22no—
235#11758222—41no—
236C2×D244—21no—
237C2×D244C22×C411yescharacteristic
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61C22×C411yescharacteristic
242C2×C4×D61C2×D411yescharacteristic
243C2×C4×D61C2×D411yescharacteristic
244C2×Dic122—22no—
245C2×Dic122—21no—
246C2×Dic122—21no—
247C2×Dic122—41no—
248C2×Dic122C22⋊C411yescharacteristic
249C2×Dic122C22×C411yescharacteristic
250C2×Dic122C22×C411yescharacteristic
251#11758217—42no—
252#11758217—42no—
253#11758217—42no—
254C2×#92420—21no—
255C2×#92420—21no—
256C2×#92420—21no—
257C2×#92420—21no—
258C2×#92420—21no—
259C2×#92420—21no—
260C2×#92420—21no—
261C2×#92420—21no—
262C2×#92420—42no—
263D61⋊C8—42no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61—21no—
266C4⋊C4×C61—21no—
267C4⋊C4×C61C22⋊C411yescharacteristic
268C4⋊C4×C61C22×C411yescharacteristic
269C4⋊C4×C61C22×C411yescharacteristic
270C4⋊C4×C61C22×C411yescharacteristic
271C22⋊C4×C61—21no—
272C22⋊C4×C61—21no—
273C22⋊C4×C61—21no—
274C22⋊C4×C61—21no—
275C22⋊C4×C61C22⋊C411yescharacteristic
276C22⋊C4×C61C22⋊C411yescharacteristic
277C42×C61—21no—
278C42×C61C22×C411yescharacteristic
279C22⋊Dic61—21no—
280C22⋊Dic61—21no—
281C22⋊Dic61—21no—
282C22⋊Dic61—21no—
283C22⋊Dic61C22⋊C411yescharacteristic
284C22⋊Dic61C22⋊C411yescharacteristic
285#11758198—21no—
286#11758198—21no—
287#11758198—21no—
288#11758198—21no—
289#11758198—21no—
290#11758198—21no—
291#11758198—21no—
292#11758198—21no—
293#11758198C22⋊C411yescharacteristic
294#11758198C22⋊C411yescharacteristic
295C4⋊Dic61—21no—
296C4⋊Dic61—21no—
297C4⋊Dic61C22⋊C411yescharacteristic
298C4⋊Dic61C22×C411yescharacteristic
299#11758196—21no—
300#11758196—21no—
301#11758196—21no—
302#11758196—21no—
303#11758196—21no—
304#11758196—21no—
305#11758196—21no—
306#11758196—21no—
307#11758196—21no—
308#11758196C22⋊C411yescharacteristic
309#11758196C22⋊C411yescharacteristic
310#11758196C22⋊C411yescharacteristic
311#11758196C22⋊C411yescharacteristic
312C4×Dic61—21no—
313C4×Dic61—21no—
314C4×Dic61—21no—
315C4×Dic61—21no—
316C4×Dic61—21no—
317C4×Dic61—21no—
318C4×Dic61—21no—
319C4×Dic61C22×C411yescharacteristic
320C4×Dic61C22×C411yescharacteristic
321C4×Dic61C2×D411yescharacteristic
322C4×Dic61C2×D411yescharacteristic
323C4×Dic61C2×D411yescharacteristic
324C4×Dic61C2×D411yescharacteristic
325C4×Dic61C2×D411yescharacteristic
326C4×Dic61C2×D411yescharacteristic
327C4×Dic61C2411yescharacteristic
328C23×C61—21no—
329C23×C61C2×C22⋊C411yescharacteristic
330C23×C61C2×C22⋊C411yescharacteristic
331C22×D61—21no—
332C22×D61C2×C22⋊C411yescharacteristic
333D4×C61—21no—
334D4×C61—21no—
335D4×C61—41no—
336D4×C61—42no—
337D4×C61—81no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—81no—
346C2×C4×C61—81no—
347C2×C4×C61C2×C22⋊C411yescharacteristic
348C2×C4×C61C2×C22⋊C411yescharacteristic
349C2×C4×C61C2×C22⋊C411yescharacteristic
350C2×C4×C61C2×C22⋊C411yescharacteristic
351C2×C4×C61C23×C411yescharacteristic
352C22⋊D61—41no—
353C22⋊D61—41no—
354C22⋊D61—42no—
355C22⋊D61—42no—
356C22⋊D61—42no—
357C22⋊D61—42no—
358C22⋊D61—81no—
359C2×Dic61—21no—
360C2×Dic61—21no—
361C2×Dic61—21no—
362C2×Dic61—21no—
363C2×Dic61—21no—
364C2×Dic61—21no—
365C2×Dic61—21no—
366C2×Dic61—41no—
367C2×Dic61—41no—
368C2×Dic61—42no—
369C2×Dic61—42no—
370C2×Dic61—41no—
371C2×Dic61—41no—
372C2×Dic61C2×C22⋊C411yescharacteristic
373C2×Dic61C2×C22⋊C411yescharacteristic
374C2×Dic61C2×C22⋊C411yescharacteristic
375C2×Dic61C2×C22⋊C411yescharacteristic
376C2×Dic61C2×C22⋊C411yescharacteristic
377C2×Dic61C22×D411yescharacteristic
378C2×Dic61C22×D411yescharacteristic
379D244—21no—
380D244—21no—
381D244—81no—
382C4×D61—21no—
383C4×D61—21no—
384C4×D61—21no—
385C4×D61—21no—
386C4×D61—41no—
387C4×D61—42no—
388C4×D61—41no—
389C4×D61—41no—
390C4×D61—81no—
391Dic122—21no—
392Dic122—21no—
393Dic122—21no—
394Dic122—41no—
395Dic122—42no—
396Dic122—42no—
397Dic122#13112yes—
398#92420—22no—
399#92420—41no—
400#92420—41no—
401#92420—41no—
402#92420—41no—
403#92420—41no—
404#92420—41no—
405#92420—41no—
406#17516—611nomaximal, Sylow
407C22×C61—21no—
408C22×C61—21no—
409C22×C61—21no—
410C22×C61—21no—
411C22×C61—21no—
412C22×C61—21no—
413C22×C61—41no—
414C22×C61—41no—
415C22×C61—41no—
416C22×C61C22×C22⋊C411yescharacteristic
417C2×D61—21no—
418C2×D61—21no—
419C2×D61—21no—
420C2×D61—41no—
421C2×D61—41no—
422C2×D61—41no—
423C4×C61—21no—
424C4×C61—21no—
425C4×C61—21no—
426C4×C61—21no—
427C4×C61—41no—
428C4×C61—41no—
429C4×C61—41no—
430C4×C61C2×#13111yescharacteristic
431C4×C61#56811yescharacteristic
432Dic61—22no—
433Dic61—21no—
434Dic61—21no—
435Dic61—21no—
436Dic61—21no—
437Dic61—21no—
438Dic61—21no—
439Dic61—41no—
440Dic61—41no—
441Dic61#57511yescharacteristic
442Dic61#57511yescharacteristic
443#3480—611no—
444#2965—611no—
445#2925—611no—
446#1496—611no—
447#1495—611no—
448#1494—611no—
449#1491—611no—
450#1489—611no—
451#1488—611no—
452#1484—611no—
453#1483—611no—
454#1482—611no—
455#1479—611no—
456#1477—611no—
457#1476—611no—
458C2×C61—41no—
459C2×C61—41no—
460C2×C61—81no—
461C2×C61#288011yescharacteristic
462C2×C61#289611yescharacteristic
463C2×C61#290111yescharacteristic
464D61—41no—
465D61—81no—
466#559—611no—
467#559—1221no—
468#557—611no—
469#556—611no—
470#556—1221no—
471#553—611no—
472#553—1221no—
473#553—1221no—
474#553#692311yescharacteristic
475#550—611no—
476#548—611no—
477#548—611no—
478#532—611no—
479#532—1221no—
480#529—611no—
481#529—611no—
482#529—1221no—
483#529—1221no—
484C4×#41—611no—
485C4×#41—611no—
486C4×#41—611no—
487C4×#41—1221no—
488C2×C4×Q8—611no—
489#446—1221no—
490#436—1221no—
491#435—1221no—
492#435—1221no—
493#433—1221no—
494#433—1221no—
495#432—611no—
496#432—611no—
497#431—611no—
498#431—611no—
499#431—611no—
500#431—611no—
501#431—611no—
502#423—611no—
503C2×C4⋊C8—611no—
504#408—1221no—
505#405—1221no—
506C4×M16—611no—
507C4×M16—611no—
508C2×C4×C8—611no—
509Q8⋊C8—611no—
510Q8⋊C8—611no—
511Q8⋊C8—611no—
512Q8⋊C8—611no—
513Q8⋊C8—611no—
514Q8⋊C8—611no—
515Q8⋊C8—611no—
516Q8⋊C8—611no—
517D4⋊C8—611no—
518D4⋊C8—611no—
519D4⋊C8—611no—
520D4⋊C8—611no—
521D4⋊C8—611no—
522D4⋊C8—611no—
523D4⋊C8—611no—
524D4⋊C8—611no—
525C61#1751611yescharacteristic, complemented, Sylow
526C2×#41—611no—
527C2×#41—611no—
528C2×#41—611no—
529C2×#41—1221no—
530C22×Q8—611no—
531C2×M16—1221no—
532C2×M16—1221no—
533C2×M16—1221no—
534C22×C8—1221no—
535C22×C8—1221no—
536C4⋊Q8—611no—
537C4⋊Q8—1221no—
538#127—611no—
539#127—1221no—
540#126—21no—
541#126—1221no—
542#126—1221no—
543#126—1221no—
544#126—1221no—
545#126—1221no—
546#125—611no—
547#125—1221no—
548#125—1221no—
549#125C2×#692311yescharacteristic
550#124—611no—
551#124—611no—
552#124—1221no—
553#124—1221no—
554#124—1221no—
555#124—1221no—
556#124—1221no—
557#123—21no—
558#123—1221no—
559#123—1221no—
560#123—1221no—
561#123—1221no—
562#123—1221no—
563C22⋊Q8—611no—
564C22⋊Q8—611no—
565C22⋊Q8—1221no—
566C22⋊Q8—1221no—
567#121—21no—
568#121—611no—
569#121—611no—
570#121—1221no—
571#121—1221no—
572#121—1221no—
573#121—1221no—
574#121—1221no—
575#121—1221no—
576#121C2×#692311yescharacteristic
577#121C2×#692311yescharacteristic
578C4×Q8—611no—
579C4×Q8—611no—
580C4×Q8—611no—
581C4×Q8—611no—
582C4×Q8—611no—
583C4×Q8—611no—
584C4×Q8—611no—
585C4×Q8—611no—
586C4×Q8—1221no—
587C4×Q8—1221no—
588C4×Q8—1221no—
589C4×Q8—1221no—
590C4×D4—21no—
591C4×D4—611no—
592C4×D4—611no—
593C4×D4—611no—
594C4×D4—611no—
595C4×D4—611no—
596C4×D4—611no—
597C4×D4—611no—
598C4×D4—611no—
599C4×D4—1221no—
600C4×D4—1221no—
601C4×D4—1221no—
602C4×D4—1221no—
603C4×D4—1221no—
604C4×D4—1221no—
605C4×D4—1221no—
606C4×D4—1221no—
607C4×D4—1221no—
608C4×D4—1221no—
609C4×D4—1221no—
610C4×D4—1221no—
611C4×D4C2×#692311yescharacteristic
612C4×D4C2×#692311yescharacteristic
613#117—611no—
614#117—611no—
615#117—611no—
616#117—611no—
617#117—1221no—
618#117—1221no—
619#117—1221no—
620#117—1221no—
621#117C2×#692311yescharacteristic
622C2×C4⋊C4—1221no—
623C2×C4⋊C4C2×#692311yescharacteristic
624C2×C42—611no—
625C2×C42—611no—
626C2×C42—611no—
627C2×C42—1221no—
628C2×C42—1221no—
629C2×C42—1221no—
630C4⋊C8—611no—
631C4⋊C8—611no—
632C4⋊C8—611no—
633C4⋊C8—611no—
634C4⋊C8—1221no—
635C4⋊C8—1221no—
636C4⋊C8—1221no—
637C4⋊C8—1221no—
638C4⋊C8—1221no—
639C22⋊C8—1221no—
640C22⋊C8—1221no—
641C22⋊C8—1221no—
642C22⋊C8—1221no—
643C22⋊C8—1221no—
644C22⋊C8—1221no—
645C22⋊C8—1221no—
646#97—1221no—
647#97—1221no—
648#97—1221no—
649#97—1221no—
650C4×C8—611no—
651C4×C8—611no—
652C4×C8—611no—
653C4×C8—611no—
654C4×C8—1221no—
655C4×C8—1221no—
656C4×C8—1221no—
657#41—1222no—
658#41—1222no—
659#41—2441no—
660#41—2441no—
661#41—2441no—
662#41—2441no—
663#41—2442no—
664#41—2442no—
665C2×Q8—611no—
666C2×Q8—611no—
667C2×Q8—611no—
668C2×Q8—1221no—
669C2×Q8—1222no—
670C2×Q8—1221no—
671C2×Q8—2441no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—611no—
675C2×D4—611no—
676C2×D4—611no—
677C2×D4—1221no—
678C2×D4—1221no—
679C2×D4—1221no—
680C2×D4—1221no—
681C2×D4—1221no—
682C2×D4—1221no—
683C2×D4C22⋊#692311yescharacteristic
684C2×D4C22×#692311yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—611no—
688C22×C4—611no—
689C22×C4—611no—
690C22×C4—611no—
691C22×C4—611no—
692C22×C4—611no—
693C22×C4—611no—
694C22×C4—1221no—
695C22×C4—1221no—
696C22×C4—1221no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4—1221no—
700C22×C4C22×#692311yescharacteristic
701C22×C4C22×#692311yescharacteristic
702M16—2442no—
703M16—2442no—
704M16—2442no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8—1221no—
708C2×C8—1221no—
709C2×C8—1221no—
710C2×C8—1221no—
711C2×C8—1221no—
712C2×C8—1221no—
713C2×C8—2442no—
714C2×C8—2442no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—611no—
719C4⋊C4—611no—
720C4⋊C4—611no—
721C4⋊C4—611no—
722C4⋊C4—611no—
723C4⋊C4—611no—
724C4⋊C4—1221no—
725C4⋊C4—1221no—
726C4⋊C4—1221no—
727C4⋊C4—1221no—
728C4⋊C4—1221no—
729C4⋊C4—1221no—
730C4⋊C4—1221no—
731C4⋊C4—1221no—
732C4⋊C4—1221no—
733C4⋊C4—1221no—
734C4⋊C4—1221no—
735C4⋊C4C22⋊#692311yescharacteristic
736C4⋊C4C22×#692311yescharacteristic
737C4⋊C4C22×#692311yescharacteristic
738C4⋊C4C22×#692311yescharacteristic
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—611no—
744C22⋊C4—611no—
745C22⋊C4—611no—
746C22⋊C4—611no—
747C22⋊C4—1221no—
748C22⋊C4—1221no—
749C22⋊C4—1221no—
750C22⋊C4—1221no—
751C22⋊C4—1221no—
752C22⋊C4—1221no—
753C22⋊C4—1221no—
754C22⋊C4—1221no—
755C22⋊C4—1221no—
756C22⋊C4—1221no—
757C22⋊C4—1221no—
758C22⋊C4—1221no—
759C22⋊C4C22⋊#692311yescharacteristic
760C22⋊C4C22⋊#692311yescharacteristic
761C42—21no—
762C42—611no—
763C42—611no—
764C42—611no—
765C42—611no—
766C42—611no—
767C42—611no—
768C42—611no—
769C42—611no—
770C42—611no—
771C42—1221no—
772C42—1221no—
773C42—1221no—
774C42—1221no—
775C42—1221no—
776C42—1221no—
777C42—1221no—
778C42C22×#692311yescharacteristic
779C23—21no—
780C23—611no—
781C23—1221no—
782C23C2×C22⋊#692311yescharacteristic
783C23C2×C22⋊#692311yescharacteristic
784Q8—612no—
785Q8—1221no—
786Q8—1221no—
787Q8—1221no—
788Q8—2441no—
789Q8—2442no—
790Q8—2442no—
791D4—21no—
792D4—21no—
793D4—41no—
794D4—42no—
795D4—81no—
796D4—1221no—
797D4—1221no—
798D4—4881no—
799D4—4881no—
800D4—2441no—
801D4—2441no—
802D4—2442no—
803D4—2442no—
804D4—2442no—
805D4—2442no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—81no—
814C2×C4—81no—
815C2×C4—611no—
816C2×C4—611no—
817C2×C4—611no—
818C2×C4—611no—
819C2×C4—611no—
820C2×C4—611no—
821C2×C4—611no—
822C2×C4—1221no—
823C2×C4—1221no—
824C2×C4—1221no—
825C2×C4—1221no—
826C2×C4—1221no—
827C2×C4—1221no—
828C2×C4—1221no—
829C2×C4—1221no—
830C2×C4—1221no—
831C2×C4—1221no—
832C2×C4—1221no—
833C2×C4—4881no—
834C2×C4—2441no—
835C2×C4—2442no—
836C2×C4—2441no—
837C2×C4—2441no—
838C2×C4—2441no—
839C2×C4—2441no—
840C2×C4—2441no—
841C2×C4—2441no—
842C2×C4—2442no—
843C2×C4—2442no—
844C2×C4C2×C22⋊#692311yescharacteristic
845C2×C4C2×C22⋊#692311yescharacteristic
846C2×C4C2×C22⋊#692311yescharacteristic
847C2×C4C2×C22⋊#692311yescharacteristic
848C2×C4C23×#692311yescharacteristic
849C8—1222no—
850C8—2441no—
851C8—2441no—
852C8—2441no—
853C8—2441no—
854C8—2441no—
855C8—2441no—
856C8—2441no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—1221no—
867C22—1221no—
868C22—1221no—
869C22—2441no—
870C22—2441no—
871C22—2441no—
872C22C22×C22⋊#692311yescharacteristic
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—611no—
881C4—611no—
882C4—1221no—
883C4—1222no—
884C4—1221no—
885C4—1221no—
886C4—1221no—
887C4—1221no—
888C4—1221no—
889C4—2441no—
890C4—2441no—
891C4D61⋊#13111yescharacteristic
892C4#1684084111yescharacteristic
893C2—41no—
894C2—41no—
895C2—81no—
896C2—4881no—
897C2—2441no—
898C2#2146240911yescharacteristic
899C2#2146243911yescharacteristic
900C2#2146244911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#553C4
socleC22×C61C22×C22⋊C4
prime radical#21459413C2
cosocleC4×Dic61C24
hypercenter#553#6923
hypocenterC61#17516
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #21462631C2semidirect
2. #21462514C2semidirect
3. #21461178C2semidirect
4. #21461174C2semidirect
5. #21461173C2semidirect
6. #21461163C2semidirect
7. #21461156C2semidirect
8. #21461151C2semidirect
9. #21461138C2semidirect
10. #21461134C2semidirect
11. #21461133C2semidirect
12. #21461123C2semidirect
13. #21461116C2semidirect
14. #21461111C2semidirect
525. C61#17516semidirect

Maximal subgroups

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

subgroupindex
#214626312
#214625142
#214611782
#214611742
#214611732
#214611632
#214611562
#214611512
#214611382
#214611342
#214611332
#214611232
#214611162
#214611112
#214594132
#1751661