Finite Group Databasebeta

← #30611391

Subgroups — #30611391

Order 15616.

1002 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462671C211yesmaximal, characteristic, complemented
2#21462340C211yesmaximal, characteristic, complemented
3#21461247C211yesmaximal, characteristic, complemented
4#21461246C211yesmaximal, characteristic, complemented
5#21461233C211yesmaximal, characteristic, complemented
6#21461232C211yesmaximal, characteristic, complemented
7#21461228C211yesmaximal, characteristic, complemented
8#21461226C211yesmaximal, characteristic, complemented
9#21461223C211yesmaximal, characteristic, complemented
10#21461222C211yesmaximal, characteristic, complemented
11#21461217C211yesmaximal, characteristic, complemented
12#21461216C211yesmaximal, characteristic, complemented
13#21461197C211yesmaximal, characteristic, complemented
14#21461196C211yesmaximal, characteristic, complemented
15#21459659C211yesmaximal, characteristic
16#16840794—21no—
17#16840793—21no—
18#16840792—21no—
19#16840791—21no—
20#16840785C2211yescharacteristic, complemented
21#16840784C2211yescharacteristic, complemented
22#16840734C2211yescharacteristic
23#16840733C2211yescharacteristic
24C2×#14519834C2211yescharacteristic, complemented
25D61⋊(C22⋊C8)C2211yescharacteristic, complemented
26#16840714—21no—
27#16840712—21no—
28#16840712—21no—
29#16840706C2211yescharacteristic, complemented
30#16840705C2211yescharacteristic
31#16840705C2211yescharacteristic, complemented
32C4⋊C4×#6923—21no—
33C4×C4⋊#6923C2211yescharacteristic, complemented
34C4×C22⋊#6923C2211yescharacteristic
35C4×C22⋊#6923C2211yescharacteristic, complemented
36#16840616C2211yescharacteristic, complemented
37#16840616C2211yescharacteristic, complemented
38#16840616C2211yescharacteristic, complemented
39#16840616C2211yescharacteristic, complemented
40#16840615C2211yescharacteristic, complemented
41#16840615C2211yescharacteristic, complemented
42#16840615C2211yescharacteristic, complemented
43#16840615C2211yescharacteristic, complemented
44#16840614C2211yescharacteristic
45#16840614C2211yescharacteristic
46#16840614C2211yescharacteristic
47#16840614C2211yescharacteristic
48#16840614C2211yescharacteristic
49#16840614C2211yescharacteristic
50#16840614C2211yescharacteristic
51#16840614C2211yescharacteristic
52#16840465—21no—
53#16840465C411yescharacteristic, complemented
54#16840463—21no—
55#16840456C411yescharacteristic, complemented
56#16840447C411yescharacteristic, complemented
57#16840436—21no—
58#16840435—21no—
59#16840424C411yescharacteristic, complemented
60#16840422C411yescharacteristic, complemented
61#16840408C411yescharacteristic, complemented
62#16840403C411yescharacteristic, complemented
63#16840360—21no—
64#16840351—21no—
65#16840323—21no—
66#16840299C2211yescharacteristic
67#16840297C2211yescharacteristic
68#16840275C2211yescharacteristic
69#16840274C2211yescharacteristic
70C22⋊Q8×D61C2211yescharacteristic
71C2×#14519752C2211yescharacteristic
72#16840236—21no—
73C4×D4×D61C2211yescharacteristic
74C61×#552C411yescharacteristic, complemented
75C2×#11758213—21no—
76C2×#11758217—21no—
77C2×D61⋊C8—21no—
78C22×#92420—21no—
79C2×C4⋊#6923—21no—
80C2×C4⋊#6923—21no—
81C2×C22⋊#6923—21no—
82C2×C22⋊#6923—21no—
83C2×C22⋊#6923—21no—
84C2×C22⋊#6923—21no—
85C2×C4×#6923—21no—
86C2×C4×#6923—21no—
87C2×C4×#6923—21no—
88#14519844—21no—
89C4⋊#92420—21no—
90#14519834—21no—
91#14519834—21no—
92#14519834C2311yescharacteristic
93#14519834C2311yescharacteristic
94#14519834C2311yescharacteristic
95#14519834C2311yescharacteristic
96C22⋊#92420—21no—
97C22⋊#92420—21no—
98#14519832—21no—
99#14519832—21no—
100(C2×#6923)⋊C4—21no—
101(C2×#6923)⋊C4—21no—
102(C2×#6923)⋊C4—21no—
103(C2×#6923)⋊C4C2311yescharacteristic
104(C2×#6923)⋊C4C2311yescharacteristic
105(C2×#6923)⋊C4C2311yescharacteristic
106(C2×#6923)⋊C4C2311yescharacteristic
107C2×#11758226C2×C411yescharacteristic
108C2×#11758222C2×C411yescharacteristic
109C2×Q8×D61C2×C411yescharacteristic
110C22×D244—21no—
111C22×D244C2×C411yescharacteristic
112C2×D4×D61D411yescharacteristic
113C22×C4×D61C2311yescharacteristic
114C22×C4×D61C2311yescharacteristic
115#14519772—21no—
116#14519772—21no—
117#14519772—21no—
118#14519772—21no—
119#14519771—21no—
120#14519768C2×C411yescharacteristic
121#14519767—21no—
122#14519766C2×C411yescharacteristic
123#14519765—21no—
124#14519765C2×C411yescharacteristic
125#14519763—21no—
126#14519762—21no—
127#14519762—21no—
128#14519762—21no—
129#14519762—21no—
130#14519762—21no—
131#14519762—21no—
132#14519761—21no—
133#14519760—21no—
134#14519759—21no—
135#14519757—21no—
136#14519757C2×C411yescharacteristic
137#14519757C2311yescharacteristic
138#14519756C2×C411yescharacteristic
139#14519755—21no—
140#14519755—21no—
141#14519754—21no—
142#14519753C2311yescharacteristic
143#14519752—21no—
144#14519752—21no—
145#14519752—21no—
146#14519752—21no—
147#14519752—21no—
148#14519752C2×C411yescharacteristic
149#14519752C2×C411yescharacteristic
150#14519752C2×C411yescharacteristic
151#14519752C2311yescharacteristic
152#14519752C2311yescharacteristic
153#14519751C2×C411yescharacteristic
154#14519750—21no—
155#14519750—21no—
156#14519750—21no—
157#14519747—21no—
158#14519747—21no—
159#14519747—21no—
160#14519745—21no—
161#14519742C2×C411yescharacteristic
162C4×D244—21no—
163C4×D244—21no—
164C4×D244—21no—
165C4×D244—21no—
166C4×D244—21no—
167C4×D244C2×C411yescharacteristic
168C4×D244C2×C411yescharacteristic
169D4×Dic61D411yescharacteristic
170#14519739—21no—
171#14519739—21no—
172#14519739—21no—
173#14519739—21no—
174#14519739C2×C411yescharacteristic
175#14519739D411yescharacteristic
176C4×C22⋊D61C2×C411yescharacteristic
177C4×C22⋊D61C2×C411yescharacteristic
178#14519737—21no—
179#14519737D411yescharacteristic
180#14519737D411yescharacteristic
181#14519736—21no—
182#14519735—21no—
183#14519735C2×C411yescharacteristic
184#14519734—21no—
185C4⋊C4×D61—21no—
186C4⋊C4×D61C2×C411yescharacteristic
187C4⋊C4×D61D411yescharacteristic
188C2×#11758198—21no—
189C22⋊C4×D61—21no—
190C22⋊C4×D61—21no—
191C22⋊C4×D61—21no—
192C22⋊C4×D61D411yescharacteristic
193C22⋊C4×D61D411yescharacteristic
194C42×D61C2311yescharacteristic
195#126×C61—21no—
196#125×C61—21no—
197#125×C61C2×C411yescharacteristic
198#123×C61—21no—
199C22⋊Q8×C61C2×C411yescharacteristic
200C22⋊Q8×C61C2×C411yescharacteristic
201C4×Q8×C61C2×C411yescharacteristic
202C4×D4×C61C2×C411yescharacteristic
203#117×C61—21no—
204#117×C61C2×C411yescharacteristic
205C2×C4⋊C4×C61C2×C411yescharacteristic
206C23×D61—21no—
207C23×D61C2×D411yescharacteristic
208C23×D61C2×D411yescharacteristic
209C22×#6923—21no—
210C22×#6923—21no—
211C22×#6923—21no—
212C22×#6923—21no—
213C2×Q8×C61C22×C411yescharacteristic
214C2×D4×C61C22⋊C411yescharacteristic
215C22×C4×C61—21no—
216C22×C4×C61C22×C411yescharacteristic
217C22×C4×C61C22×C411yescharacteristic
218C2×C22⋊D61—21no—
219C2×C22⋊D61—21no—
220C2×C22⋊D61C22⋊C411yescharacteristic
221C2×C22⋊D61C22⋊C411yescharacteristic
222C22×Dic61C2×D411yescharacteristic
223C22×Dic61C2×D411yescharacteristic
224#11758226—81no—
225Q8×D61—81no—
226D4×D61—41no—
227D4×D61—41no—
228#11758222—81no—
229C2×D244—21no—
230C2×D244—21no—
231C2×D244—21no—
232C2×D244—21no—
233C2×D244—21no—
234C2×D244—21no—
235C2×D244—21no—
236C2×D244—42no—
237C2×D244—42no—
238C2×D244—81no—
239C2×D244C22⋊C411yescharacteristic
240C2×D244C22×C411yescharacteristic
241C2×D244C22×C411yescharacteristic
242C2×C4×D61—21no—
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61—81no—
249C2×C4×D61—81no—
250C2×C4×D61C22×C411yescharacteristic
251C2×C4×D61C22×C411yescharacteristic
252C2×C4×D61C2×D411yescharacteristic
253C2×C4×D61C2×D411yescharacteristic
254C2×C4×D61C2×D411yescharacteristic
255C2×C4×D61C2×D411yescharacteristic
256C2×C4×D61C2×D411yescharacteristic
257C2×C4×D61C2×D411yescharacteristic
258C2×C4×D61C2411yescharacteristic
259C2×Dic122—21no—
260C2×Dic122C22×C411yescharacteristic
261C22⋊#6923—42no—
262C22⋊#6923—42no—
263C22⋊#6923—81no—
264C22⋊#6923—81no—
265#11758217—81no—
266C2×#92420—21no—
267C2×#92420—21no—
268C2×#92420—21no—
269C2×#92420—21no—
270C2×#92420—81no—
271C4⋊#6923—42no—
272C4⋊#6923—42no—
273C4×#6923—42no—
274C4×#6923—81no—
275C4×#6923—81no—
276#11758213—81no—
277D61⋊C8—81no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61—21no—
280C4⋊C4×C61—21no—
281C4⋊C4×C61—21no—
282C4⋊C4×C61—21no—
283C4⋊C4×C61—21no—
284C4⋊C4×C61C22⋊C411yescharacteristic
285C4⋊C4×C61C22×C411yescharacteristic
286C4⋊C4×C61C22×C411yescharacteristic
287C4⋊C4×C61C22×C411yescharacteristic
288C22⋊C4×C61—21no—
289C22⋊C4×C61—21no—
290C22⋊C4×C61—21no—
291C22⋊C4×C61C22⋊C411yescharacteristic
292C22⋊C4×C61C22⋊C411yescharacteristic
293C42×C61—21no—
294C42×C61—21no—
295C42×C61C22×C411yescharacteristic
296C22⋊Dic61—21no—
297C22⋊Dic61C22⋊C411yescharacteristic
298C22⋊Dic61C22⋊C411yescharacteristic
299#11758198—21no—
300#11758198—21no—
301#11758198—21no—
302#11758198—21no—
303#11758198—21no—
304#11758198—21no—
305#11758198—21no—
306#11758198—21no—
307#11758198—21no—
308#11758198—21no—
309#11758198—21no—
310#11758198—21no—
311#11758198—21no—
312#11758198—21no—
313#11758198—21no—
314#11758198—21no—
315#11758198C22⋊C411yescharacteristic
316#11758198C22⋊C411yescharacteristic
317#11758198C22⋊C411yescharacteristic
318#11758198C22⋊C411yescharacteristic
319C4⋊Dic61—21no—
320C4⋊Dic61—21no—
321C4⋊Dic61—21no—
322C4⋊Dic61C22⋊C411yescharacteristic
323C4⋊Dic61C22×C411yescharacteristic
324#11758196—21no—
325#11758196—21no—
326#11758196—21no—
327#11758196—21no—
328#11758196—21no—
329#11758196C22⋊C411yescharacteristic
330#11758196C22⋊C411yescharacteristic
331C4×Dic61—21no—
332C4×Dic61—21no—
333C4×Dic61C22×C411yescharacteristic
334C4×Dic61C2×D411yescharacteristic
335C4×Dic61C2×D411yescharacteristic
336C23×C61C2×C22⋊C411yescharacteristic
337C23×C61C2×C22⋊C411yescharacteristic
338C22×D61—21no—
339C22×D61—21no—
340C22×D61—21no—
341C22×D61—21no—
342C22×D61—21no—
343C22×D61—21no—
344C22×D61—41no—
345C22×D61—41no—
346C22×D61—41no—
347C22×D61—41no—
348C22×D61—42no—
349C22×D61—81no—
350C22×D61—81no—
351C22×D61C2×C22⋊C411yescharacteristic
352C22×D61C2×C22⋊C411yescharacteristic
353C22×D61C22×D411yescharacteristic
354C2×#6923—22no—
355C2×#6923—41no—
356C2×#6923—41no—
357C2×#6923—41no—
358C2×#6923—41no—
359C2×#6923—41no—
360C2×#6923—41no—
361C2×#6923—41no—
362C2×#6923—41no—
363C2×#6923—41no—
364C2×#6923—41no—
365C2×#6923—41no—
366Q8×C61—41no—
367D4×C61—41no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
371C2×C4×C61—21no—
372C2×C4×C61—41no—
373C2×C4×C61—41no—
374C2×C4×C61—42no—
375C2×C4×C61C2×C22⋊C411yescharacteristic
376C2×C4×C61C2×C22⋊C411yescharacteristic
377C2×C4×C61C2×C22⋊C411yescharacteristic
378C2×C4×C61C2×C22⋊C411yescharacteristic
379C2×C4×C61C23×C411yescharacteristic
380C22⋊D61—41no—
381C22⋊D61—41no—
382C22⋊D61—81no—
383C22⋊D61—81no—
384C2×Dic61—21no—
385C2×Dic61—21no—
386C2×Dic61—41no—
387C2×Dic61—41no—
388C2×Dic61C2×C22⋊C411yescharacteristic
389C2×Dic61C2×C22⋊C411yescharacteristic
390C2×Dic61C2×C22⋊C411yescharacteristic
391C2×Dic61C2×C22⋊C411yescharacteristic
392C2×Dic61C22×D411yescharacteristic
393D244—41no—
394D244—41no—
395D244—41no—
396D244—42no—
397D244—42no—
398D244—41no—
399D244—41no—
400D244—41no—
401D244—41no—
402D244—81no—
403D244—81no—
404D244—81no—
405C4×D61—21no—
406C4×D61—21no—
407C4×D61—41no—
408C4×D61—41no—
409C4×D61—41no—
410C4×D61—41no—
411C4×D61—41no—
412C4×D61—41no—
413C4×D61—41no—
414C4×D61—41no—
415C4×D61—81no—
416C4×D61—81no—
417C4×D61—81no—
418C4×D61—81no—
419C4×D61—81no—
420C4×D61—81no—
421Dic122—41no—
422Dic122—81no—
423#92420—41no—
424#92420—41no—
425#92420—41no—
426#92420—41no—
427#17625—611nomaximal, Sylow
428C22×C61—21no—
429C22×C61—21no—
430C22×C61—21no—
431C22×C61—21no—
432C22×C61—21no—
433C22×C61—21no—
434C22×C61C22×C22⋊C411yescharacteristic
435C2×D61—21no—
436C2×D61—21no—
437C2×D61—21no—
438C2×D61—21no—
439C2×D61—21no—
440C2×D61—21no—
441C2×D61—21no—
442C2×D61—21no—
443C2×D61—41no—
444C2×D61—41no—
445C2×D61—41no—
446C2×D61—41no—
447C2×D61—41no—
448C2×D61—41no—
449C2×D61—81no—
450C2×D61—81no—
451C2×D61—81no—
452C2×D61—81no—
453C2×D61—162no—
454C2×D61#57511yescharacteristic
455C2×D61#57511yescharacteristic
456#6923—42no—
457#6923—81no—
458#6923—81no—
459#6923—81no—
460C4×C61—21no—
461C4×C61—21no—
462C4×C61—21no—
463C4×C61—21no—
464C4×C61—21no—
465C4×C61—41no—
466C4×C61—41no—
467C4×C61—41no—
468C4×C61—41no—
469Dic61—21no—
470Dic61—21no—
471Dic61—21no—
472Dic61—21no—
473Dic61—21no—
474Dic61—41no—
475Dic61—41no—
476#3505—611no—
477#2973—611no—
478#2357—611no—
479#1516—611no—
480#1516—611no—
481#1512—611no—
482#1512—611no—
483#1511—611no—
484#1510—611no—
485#1509—611no—
486#1509—611no—
487#1508—611no—
488#1507—611no—
489#1501—611no—
490#1501—611no—
491C2×C61—41no—
492C2×C61—41no—
493C2×C61#288311yescharacteristic
494C2×C61#289611yescharacteristic
495C2×C61#290111yescharacteristic
496D61—21no—
497D61—21no—
498D61—41no—
499D61—41no—
500D61—81no—
501D61—81no—
502#553—611no—
503#553—611no—
504#553—1221no—
505#553—1221no—
506#552—611no—
507#552#692311yescharacteristic, complemented
508#551—1221no—
509#551—1221no—
510#548—611no—
511#548—611no—
512#546—611no—
513#546—611no—
514#539—1221no—
515#538—1221no—
516#534—1221no—
517#529—611no—
518#529—611no—
519#525—611no—
520#525—611no—
521C2×C22⋊Q8—611no—
522C2×#121—611no—
523#518—1221no—
524C2×C4×D4—611no—
525#435—1221no—
526#435—1221no—
527#435—1221no—
528#435—1221no—
529#432—611no—
530#432—611no—
531#407—611no—
532#407—611no—
533C2×C22⋊C8—611no—
534C2×C22⋊C8—611no—
535#390—1221no—
536#388—1221no—
537#388—1221no—
538#382—611no—
539#381—611no—
540#381—611no—
541C4×C4⋊C4—611no—
542C4×C4⋊C4—1221no—
543C4×C22⋊C4—611no—
544C4×C22⋊C4—611no—
545#328—611no—
546#328—611no—
547#328—611no—
548#328—611no—
549#328—611no—
550#328—611no—
551#328—611no—
552#328—611no—
553#327—611no—
554#327—611no—
555#327—611no—
556#327—611no—
557#327—611no—
558#327—611no—
559#327—611no—
560#327—611no—
561C61#1762511yescharacteristic, complemented, Sylow
562C2×#41—611no—
563C2×#41—611no—
564C22×Q8—611no—
565C22×D4—611no—
566C22×D4—611no—
567C22×D4—1221no—
568C23×C4—611no—
569C23×C4—611no—
570C2×M16—1221no—
571C2×M16—1221no—
572C22×C8—1221no—
573C22×C8—1221no—
574#126—21no—
575#126—1221no—
576#126—1221no—
577#126—1221no—
578#126—1221no—
579#126—1221no—
580#125—21no—
581#125—611no—
582#125—1221no—
583#125C2×#692311yescharacteristic
584#124—611no—
585#124—611no—
586#124—1221no—
587#124—1221no—
588#123—21no—
589#123—1221no—
590#123—1221no—
591#123—1221no—
592#123—1221no—
593#123—1221no—
594#123—1221no—
595#123—1221no—
596#123—1221no—
597#123—1221no—
598C22⋊Q8—611no—
599C22⋊Q8—611no—
600C22⋊Q8—611no—
601C22⋊Q8—611no—
602C22⋊Q8—1221no—
603C22⋊Q8—1221no—
604C22⋊Q8—1221no—
605C22⋊Q8—1221no—
606C22⋊Q8C2×#692311yescharacteristic
607C22⋊Q8C2×#692311yescharacteristic
608#121—611no—
609#121—611no—
610#121—611no—
611#121—611no—
612#121—611no—
613#121—611no—
614#121—1221no—
615#121—1221no—
616#121—1221no—
617#121—1221no—
618#121—1221no—
619#121—1221no—
620#121—1221no—
621#121—1221no—
622#120—1221no—
623#120—1221no—
624#120—1221no—
625#120—1221no—
626C4×Q8—611no—
627C4×Q8C2×#692311yescharacteristic
628C4×D4—611no—
629C4×D4—611no—
630C4×D4—611no—
631C4×D4—611no—
632C4×D4—611no—
633C4×D4—611no—
634C4×D4—611no—
635C4×D4—611no—
636C4×D4—611no—
637C4×D4—1221no—
638C4×D4—1221no—
639C4×D4—1221no—
640C4×D4—1221no—
641C4×D4—1221no—
642C4×D4—1221no—
643C4×D4—1221no—
644C4×D4—1221no—
645C4×D4—1221no—
646C4×D4—1221no—
647C4×D4C2×#692311yescharacteristic
648#117—21no—
649#117—611no—
650#117—1221no—
651#117—1221no—
652#117—1221no—
653#117C2×#692311yescharacteristic
654C2×C4⋊C4—611no—
655C2×C4⋊C4—611no—
656C2×C4⋊C4—1221no—
657C2×C4⋊C4—1221no—
658C2×C4⋊C4—1221no—
659C2×C4⋊C4C2×#692311yescharacteristic
660C2×C22⋊C4—611no—
661C2×C22⋊C4—611no—
662C2×C22⋊C4—1221no—
663C2×C22⋊C4—1221no—
664C2×C22⋊C4—1221no—
665C2×C22⋊C4—1221no—
666C2×C22⋊C4—1221no—
667C2×C22⋊C4—1221no—
668C2×C22⋊C4—1221no—
669C2×C22⋊C4—1221no—
670C2×C42—611no—
671C2×C42—1221no—
672C2×C42—1221no—
673C2×C42—1221no—
674C4⋊C8—1221no—
675C4⋊C8—1221no—
676C22⋊C8—611no—
677C22⋊C8—611no—
678C22⋊C8—611no—
679C22⋊C8—611no—
680C22⋊C8—1221no—
681C22⋊C8—1221no—
682C22⋊C8—1221no—
683C22⋊C8—1221no—
684#97—1221no—
685#97—1221no—
686#95—611no—
687#95—611no—
688#95—611no—
689#95—611no—
690#95—1221no—
691#95—1221no—
692#95—1221no—
693C24—611no—
694C24—611no—
695C24—1221no—
696#41—4881no—
697#41—4881no—
698C2×Q8—611no—
699C2×Q8—1221no—
700C2×Q8—4881no—
701C2×Q8C22×#692311yescharacteristic
702C2×D4—611no—
703C2×D4—611no—
704C2×D4—611no—
705C2×D4—611no—
706C2×D4—611no—
707C2×D4—1221no—
708C2×D4—1221no—
709C2×D4—1221no—
710C2×D4—1221no—
711C2×D4—1221no—
712C2×D4—1221no—
713C2×D4—1221no—
714C2×D4—1221no—
715C2×D4—1221no—
716C2×D4—4881no—
717C2×D4—2442no—
718C2×D4—2442no—
719C2×D4—2441no—
720C2×D4—2441no—
721C2×D4C22⋊#692311yescharacteristic
722C22×C4—21no—
723C22×C4—611no—
724C22×C4—611no—
725C22×C4—611no—
726C22×C4—611no—
727C22×C4—611no—
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—4881no—
745C22×C4—4881no—
746C22×C4C22×#692311yescharacteristic
747C22×C4C22×#692311yescharacteristic
748M16—4881no—
749M16—4881no—
750C2×C8—1221no—
751C2×C8—1221no—
752C2×C8—1221no—
753C2×C8—1221no—
754C2×C8—4881no—
755C2×C8—4881no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—611no—
763C4⋊C4—611no—
764C4⋊C4—611no—
765C4⋊C4—611no—
766C4⋊C4—1221no—
767C4⋊C4—1221no—
768C4⋊C4—1221no—
769C4⋊C4—1221no—
770C4⋊C4—1221no—
771C4⋊C4—1221no—
772C4⋊C4—1221no—
773C4⋊C4—1221no—
774C4⋊C4—2442no—
775C4⋊C4—2442no—
776C4⋊C4C22⋊#692311yescharacteristic
777C4⋊C4C22×#692311yescharacteristic
778C4⋊C4C22×#692311yescharacteristic
779C4⋊C4C22×#692311yescharacteristic
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—611no—
784C22⋊C4—611no—
785C22⋊C4—611no—
786C22⋊C4—611no—
787C22⋊C4—611no—
788C22⋊C4—611no—
789C22⋊C4—1221no—
790C22⋊C4—1221no—
791C22⋊C4—1221no—
792C22⋊C4—1221no—
793C22⋊C4—1221no—
794C22⋊C4—1221no—
795C22⋊C4—1221no—
796C22⋊C4—1221no—
797C22⋊C4—1221no—
798C22⋊C4—1221no—
799C22⋊C4—1221no—
800C22⋊C4—1221no—
801C22⋊C4—1221no—
802C22⋊C4—1221no—
803C22⋊C4—1221no—
804C22⋊C4—1221no—
805C22⋊C4—1221no—
806C22⋊C4—4881no—
807C22⋊C4—4881no—
808C22⋊C4—2442no—
809C22⋊C4—2442no—
810C22⋊C4C22⋊#692311yescharacteristic
811C22⋊C4C22⋊#692311yescharacteristic
812C42—21no—
813C42—21no—
814C42—611no—
815C42—611no—
816C42—611no—
817C42—1221no—
818C42—1221no—
819C42—4881no—
820C42—4881no—
821C42—2442no—
822C42C22×#692311yescharacteristic
823C23—611no—
824C23—611no—
825C23—611no—
826C23—1221no—
827C23—1221no—
828C23—1221no—
829C23—1221no—
830C23—1221no—
831C23—1221no—
832C23—4881no—
833C23—4881no—
834C23—2441no—
835C23—2441no—
836C23—2441no—
837C23—2441no—
838C23—2442no—
839C23C2×C22⋊#692311yescharacteristic
840C23C2×C22⋊#692311yescharacteristic
841Q8—41no—
842Q8—4881no—
843Q8—2441no—
844D4—41no—
845D4—4881no—
846D4—4881no—
847D4—4881no—
848D4—4881no—
849D4—4881no—
850D4—2441no—
851D4—2441no—
852D4—2441no—
853D4—2441no—
854D4—2441no—
855D4—2441no—
856D4—2441no—
857D4—2442no—
858D4—2442no—
859D4—2441no—
860D4—2441no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—42no—
868C2×C4—611no—
869C2×C4—611no—
870C2×C4—611no—
871C2×C4—611no—
872C2×C4—611no—
873C2×C4—1221no—
874C2×C4—1221no—
875C2×C4—1222no—
876C2×C4—1221no—
877C2×C4—1221no—
878C2×C4—4881no—
879C2×C4—4881no—
880C2×C4—4881no—
881C2×C4—4881no—
882C2×C4—4881no—
883C2×C4—4881no—
884C2×C4—2441no—
885C2×C4—2441no—
886C2×C4—2441no—
887C2×C4—2441no—
888C2×C4—2441no—
889C2×C4—2441no—
890C2×C4—2441no—
891C2×C4—2441no—
892C2×C4—2441no—
893C2×C4—2441no—
894C2×C4—2441no—
895C2×C4—2441no—
896C2×C4—2441no—
897C2×C4—2441no—
898C2×C4—2441no—
899C2×C4—2441no—
900C2×C4—2441no—
901C2×C4—2441no—
902C2×C4—2441no—
903C2×C4—2441no—
904C2×C4—2441no—
905C2×C4C2×C22⋊#692311yescharacteristic
906C2×C4C2×C22⋊#692311yescharacteristic
907C2×C4C2×C22⋊#692311yescharacteristic
908C2×C4C2×C22⋊#692311yescharacteristic
909C2×C4C23×#692311yescharacteristic
910C8—2441no—
911C8—2441no—
912C8—2441no—
913C8—2441no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—611no—
921C22—611no—
922C22—1221no—
923C22—1221no—
924C22—1221no—
925C22—1221no—
926C22—1221no—
927C22—1221no—
928C22—1221no—
929C22—1221no—
930C22—9762no—
931C22—4881no—
932C22—4881no—
933C22—4881no—
934C22—4881no—
935C22—2441no—
936C22—2441no—
937C22—2441no—
938C22—2441no—
939C22—2441no—
940C22—2441no—
941C22C22×C22⋊#692311yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—21no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—1221no—
952C4—1221no—
953C4—1221no—
954C4—1221no—
955C4—1221no—
956C4—4881no—
957C4—4881no—
958C4—4881no—
959C4—2442no—
960C4—2441no—
961C4—2441no—
962C2—41no—
963C2—41no—
964C2—1221no—
965C2—1221no—
966C2—4881no—
967C2—4881no—
968C2—2441no—
969C2—2441no—
970C2#2146241911yescharacteristic
971C2#2146243911yescharacteristic
972C2#2146245011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#552C4
socleC22×C61C22×C22⋊C4
prime radical#21459659C2
cosocleC2×C4×D61C24
hypercenter#552#6923
hypocenterC61#17625
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
1. #21462671C2semidirect
2. #21462340C2semidirect
3. #21461247C2semidirect
4. #21461246C2semidirect
5. #21461233C2semidirect
6. #21461232C2semidirect
7. #21461228C2semidirect
8. #21461226C2semidirect
9. #21461223C2semidirect
10. #21461222C2semidirect
11. #21461217C2semidirect
12. #21461216C2semidirect
13. #21461197C2semidirect
14. #21461196C2semidirect
20. #16840785C22semidirect
21. #16840784C22semidirect
24. C2×#14519834C22semidirect
25. D61⋊(C22⋊C8)C22semidirect
29. #16840706C22semidirect
31. #16840705C22semidirect
33. C4×C4⋊#6923C22semidirect
35. C4×C22⋊#6923C22semidirect
36. #16840616C22semidirect
37. #16840616C22semidirect
38. #16840616C22semidirect
39. #16840616C22semidirect
40. #16840615C22semidirect
41. #16840615C22semidirect
42. #16840615C22semidirect
43. #16840615C22semidirect
53. #16840465C4semidirect
55. #16840456C4semidirect
56. #16840447C4semidirect
59. #16840424C4semidirect
60. #16840422C4semidirect
61. #16840408C4semidirect
62. #16840403C4semidirect
74. C61×#552C4semidirect
507. #552#6923semidirect
561. C61#17625semidirect

Maximal subgroups

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

subgroupindex
#214626712
#214623402
#214612472
#214612462
#214612332
#214612322
#214612282
#214612262
#214612232
#214612222
#214612172
#214612162
#214611972
#214611962
#214596592
#1762561