Finite Group Databasebeta

← #30611392

Subgroups — #30611392

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#21461244C211yesmaximal, characteristic, complemented
5#21461233C211yesmaximal, characteristic, complemented
6#21461230C211yesmaximal, characteristic, complemented
7#21461227C211yesmaximal, characteristic, complemented
8#21461225C211yesmaximal, characteristic, complemented
9#21461222C211yesmaximal, characteristic, complemented
10#21461221C211yesmaximal, characteristic, complemented
11#21461218C211yesmaximal, characteristic, complemented
12#21461214C211yesmaximal, characteristic, complemented
13#21461196C211yesmaximal, characteristic, complemented
14#21461195C211yesmaximal, characteristic, complemented
15#21459648C211yesmaximal, 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#16840615C2211yescharacteristic, complemented
37#16840615C2211yescharacteristic, complemented
38#16840615C2211yescharacteristic, complemented
39#16840615C2211yescharacteristic, complemented
40#16840615C2211yescharacteristic, complemented
41#16840615C2211yescharacteristic, complemented
42#16840615C2211yescharacteristic, complemented
43#16840615C2211yescharacteristic, complemented
44#16840614C2211yescharacteristic
45#16840614C2211yescharacteristic
46#16840614C2211yescharacteristic
47#16840614C2211yescharacteristic
48#16840613C2211yescharacteristic
49#16840613C2211yescharacteristic
50#16840613C2211yescharacteristic
51#16840613C2211yescharacteristic
52#16840464—21no—
53#16840460C411yescharacteristic, complemented
54#16840458—21no—
55#16840451C411yescharacteristic, complemented
56#16840450C411yescharacteristic, complemented
57#16840437—21no—
58#16840435—21no—
59#16840421C411yescharacteristic, complemented
60#16840418C411yescharacteristic, complemented
61#16840409C411yescharacteristic, complemented
62#16840407C411yescharacteristic, complemented
63#16840353—21no—
64#16840348—21no—
65#16840320—21no—
66#16840297C2211yescharacteristic
67#16840294C2211yescharacteristic
68#16840274C2211yescharacteristic
69#16840272C2211yescharacteristic
70C2×#14519757C2211yescharacteristic
71#121×D61C2211yescharacteristic
72#16840234—21no—
73C4×D4×D61C2211yescharacteristic
74C61×#553C411yescharacteristic, 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×#11758222C2×C411yescharacteristic
108C2×#11758224C2×C411yescharacteristic
109C22×Dic122C2×C411yescharacteristic
110C2×D4×D61—21no—
111C2×D4×D61C2×C411yescharacteristic
112C2×D4×D61D411yescharacteristic
113C22×C4×D61C2311yescharacteristic
114C22×C4×D61C2311yescharacteristic
115#14519772—21no—
116#14519772—21no—
117#14519772—21no—
118#14519770—21no—
119#14519770—21no—
120#14519769—21no—
121#14519768—21no—
122#14519768C2×C411yescharacteristic
123#14519765C2×C411yescharacteristic
124#14519764C2×C411yescharacteristic
125#14519763—21no—
126#14519763—21no—
127#14519762—21no—
128#14519762—21no—
129#14519762—21no—
130#14519761—21no—
131#14519761—21no—
132#14519759—21no—
133#14519759—21no—
134#14519759—21no—
135#14519759—21no—
136#14519757—21no—
137#14519757—21no—
138#14519757C2×C411yescharacteristic
139#14519757C2×C411yescharacteristic
140#14519757C2×C411yescharacteristic
141#14519757C2311yescharacteristic
142#14519757C2311yescharacteristic
143#14519756C2×C411yescharacteristic
144#14519755—21no—
145#14519754—21no—
146#14519752C2×C411yescharacteristic
147#14519752C2311yescharacteristic
148#14519751—21no—
149#14519751—21no—
150#14519751C2×C411yescharacteristic
151#14519750—21no—
152#14519749—21no—
153#14519749—21no—
154#14519749—21no—
155#14519748—21no—
156#14519748C2311yescharacteristic
157#14519747—21no—
158#14519747—21no—
159#14519745—21no—
160#14519745—21no—
161C4×Dic122C2×C411yescharacteristic
162#14519742C2×C411yescharacteristic
163C4×D244—21no—
164C4×D244—21no—
165C4×D244C2×C411yescharacteristic
166D4×Dic61—21no—
167D4×Dic61—21no—
168D4×Dic61D411yescharacteristic
169#14519739—21no—
170#14519739C2×C411yescharacteristic
171#14519739D411yescharacteristic
172C4×C22⋊D61—21no—
173C4×C22⋊D61—21no—
174C4×C22⋊D61C2×C411yescharacteristic
175C4×C22⋊D61C2×C411yescharacteristic
176#14519737—21no—
177#14519737—21no—
178#14519737D411yescharacteristic
179#14519737D411yescharacteristic
180#14519736—21no—
181#14519735—21no—
182#14519735—21no—
183#14519735C2×C411yescharacteristic
184#14519734—21no—
185C2×C4⋊Dic61—21no—
186C4⋊C4×D61C2×C411yescharacteristic
187C4⋊C4×D61D411yescharacteristic
188C2×#11758198—21no—
189C2×#11758198—21no—
190C22⋊C4×D61—21no—
191C22⋊C4×D61—21no—
192C22⋊C4×D61D411yescharacteristic
193C22⋊C4×D61D411yescharacteristic
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
206C23×D61—21no—
207C23×D61C2×D411yescharacteristic
208C23×D61C2×D411yescharacteristic
209C22×#6923—21no—
210C22×#6923—21no—
211C22×#6923—21no—
212C22×#6923—21no—
213C2×D4×C61—21no—
214C2×D4×C61—21no—
215C2×D4×C61C22⋊C411yescharacteristic
216C2×D4×C61C22×C411yescharacteristic
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61C22×C411yescharacteristic
220C22×C4×C61C22×C411yescharacteristic
221C2×C22⋊D61—21no—
222C2×C22⋊D61—21no—
223C2×C22⋊D61—21no—
224C2×C22⋊D61—21no—
225C2×C22⋊D61—21no—
226C2×C22⋊D61C22⋊C411yescharacteristic
227C2×C22⋊D61C22⋊C411yescharacteristic
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61C2×D411yescharacteristic
231C22×Dic61C2×D411yescharacteristic
232#11758224—81no—
233D4×D61—41no—
234D4×D61—41no—
235D4×D61—42no—
236D4×D61—42no—
237D4×D61—81no—
238#11758222—81no—
239C2×D244—21no—
240C2×D244—21no—
241C2×D244C22⋊C411yescharacteristic
242C2×D244C22×C411yescharacteristic
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—81no—
247C2×C4×D61—81no—
248C2×C4×D61C22×C411yescharacteristic
249C2×C4×D61C22×C411yescharacteristic
250C2×C4×D61C2×D411yescharacteristic
251C2×C4×D61C2×D411yescharacteristic
252C2×C4×D61C2×D411yescharacteristic
253C2×C4×D61C2×D411yescharacteristic
254C2×C4×D61C2×D411yescharacteristic
255C2×C4×D61C2×D411yescharacteristic
256C2×C4×D61C2411yescharacteristic
257C2×Dic122—21no—
258C2×Dic122—81no—
259C2×Dic122C22×C411yescharacteristic
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×C61C22⋊C411yescharacteristic
282C4⋊C4×C61C22×C411yescharacteristic
283C4⋊C4×C61C22×C411yescharacteristic
284C4⋊C4×C61C22×C411yescharacteristic
285C22⋊C4×C61—21no—
286C22⋊C4×C61—21no—
287C22⋊C4×C61—21no—
288C22⋊C4×C61—21no—
289C22⋊C4×C61C22⋊C411yescharacteristic
290C22⋊C4×C61C22⋊C411yescharacteristic
291C42×C61—21no—
292C42×C61C22×C411yescharacteristic
293C22⋊Dic61—21no—
294C22⋊Dic61—21no—
295C22⋊Dic61—21no—
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#11758198C22⋊C411yescharacteristic
312#11758198C22⋊C411yescharacteristic
313#11758198C22⋊C411yescharacteristic
314#11758198C22⋊C411yescharacteristic
315C4⋊Dic61—21no—
316C4⋊Dic61—21no—
317C4⋊Dic61—21no—
318C4⋊Dic61—21no—
319C4⋊Dic61—21no—
320C4⋊Dic61—21no—
321C4⋊Dic61C22⋊C411yescharacteristic
322C4⋊Dic61C22×C411yescharacteristic
323#11758196—21no—
324#11758196—21no—
325#11758196—21no—
326#11758196—21no—
327#11758196—21no—
328#11758196C22⋊C411yescharacteristic
329#11758196C22⋊C411yescharacteristic
330C4×Dic61—21no—
331C4×Dic61—21no—
332C4×Dic61—21no—
333C4×Dic61C22×C411yescharacteristic
334C4×Dic61C2×D411yescharacteristic
335C4×Dic61C2×D411yescharacteristic
336C23×C61—21no—
337C23×C61C2×C22⋊C411yescharacteristic
338C23×C61C2×C22⋊C411yescharacteristic
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—
366D4×C61—41no—
367D4×C61—41no—
368D4×C61—42no—
369D4×C61—81no—
370C2×C4×C61—21no—
371C2×C4×C61—21no—
372C2×C4×C61—21no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61—81no—
376C2×C4×C61—81no—
377C2×C4×C61C2×C22⋊C411yescharacteristic
378C2×C4×C61C2×C22⋊C411yescharacteristic
379C2×C4×C61C2×C22⋊C411yescharacteristic
380C2×C4×C61C2×C22⋊C411yescharacteristic
381C2×C4×C61C23×C411yescharacteristic
382C22⋊D61—41no—
383C22⋊D61—41no—
384C22⋊D61—42no—
385C22⋊D61—41no—
386C22⋊D61—41no—
387C22⋊D61—81no—
388C22⋊D61—81no—
389C22⋊D61—81no—
390C2×Dic61—21no—
391C2×Dic61—21no—
392C2×Dic61—21no—
393C2×Dic61—41no—
394C2×Dic61—41no—
395C2×Dic61—81no—
396C2×Dic61—81no—
397C2×Dic61C2×C22⋊C411yescharacteristic
398C2×Dic61C2×C22⋊C411yescharacteristic
399C2×Dic61C2×C22⋊C411yescharacteristic
400C2×Dic61C2×C22⋊C411yescharacteristic
401C2×Dic61C22×D411yescharacteristic
402D244—41no—
403D244—41no—
404D244—41no—
405D244—41no—
406D244—81no—
407C4×D61—21no—
408C4×D61—21no—
409C4×D61—41no—
410C4×D61—41no—
411C4×D61—41no—
412C4×D61—41no—
413C4×D61—41no—
414C4×D61—41no—
415C4×D61—41no—
416C4×D61—41no—
417C4×D61—42no—
418C4×D61—81no—
419C4×D61—81no—
420Dic122—41no—
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×C61—41no—
435C22×C61—41no—
436C22×C61—41no—
437C22×C61C22×C22⋊C411yescharacteristic
438C2×D61—21no—
439C2×D61—21no—
440C2×D61—21no—
441C2×D61—21no—
442C2×D61—21no—
443C2×D61—21no—
444C2×D61—21no—
445C2×D61—21no—
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—
468Dic61—21no—
469Dic61—21no—
470Dic61—21no—
471Dic61—21no—
472Dic61—21no—
473Dic61—41no—
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—81no—
494C2×C61#288311yescharacteristic
495C2×C61#289611yescharacteristic
496C2×C61#290111yescharacteristic
497D61—21no—
498D61—21no—
499D61—41no—
500D61—41no—
501D61—81no—
502#553—611no—
503#553—1221no—
504#553—1221no—
505#553#692311yescharacteristic, complemented
506#552—611no—
507#552—611no—
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—611no—
581#125—1221no—
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—611no—
603C22⋊Q8—611no—
604C22⋊Q8—1221no—
605C22⋊Q8—1221no—
606C22⋊Q8—1221no—
607C22⋊Q8—1221no—
608#121—21no—
609#121—611no—
610#121—611no—
611#121—611no—
612#121—611no—
613#121—1221no—
614#121—1221no—
615#121—1221no—
616#121—1221no—
617#121—1221no—
618#121—1221no—
619#121—1221no—
620#121C2×#692311yescharacteristic
621#121C2×#692311yescharacteristic
622#120—1221no—
623#120—1221no—
624#120—1221no—
625#120—1221no—
626C4×Q8—611no—
627C4×Q8—611no—
628C4×D4—21no—
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×D4C2×#692311yescharacteristic
647C4×D4C2×#692311yescharacteristic
648#117—611no—
649#117—1221no—
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—611no—
700C2×Q8—1221no—
701C2×Q8—4881no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—611no—
705C2×D4—611no—
706C2×D4—611no—
707C2×D4—611no—
708C2×D4—1221no—
709C2×D4—1221no—
710C2×D4—1221no—
711C2×D4—1221no—
712C2×D4—1221no—
713C2×D4—1221no—
714C2×D4—1221no—
715C2×D4—4881no—
716C2×D4—2441no—
717C2×D4—2441no—
718C2×D4—2442no—
719C2×D4—2442no—
720C2×D4C22⋊#692311yescharacteristic
721C2×D4C22×#692311yescharacteristic
722C22×C4—21no—
723C22×C4—21no—
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—611no—
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—611no—
760C4⋊C4—611no—
761C4⋊C4—611no—
762C4⋊C4—611no—
763C4⋊C4—1221no—
764C4⋊C4—1221no—
765C4⋊C4—1221no—
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—21no—
784C22⋊C4—611no—
785C22⋊C4—611no—
786C22⋊C4—611no—
787C22⋊C4—611no—
788C22⋊C4—611no—
789C22⋊C4—611no—
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—611no—
814C42—611no—
815C42—611no—
816C42—1221no—
817C42—1221no—
818C42—1221no—
819C42—4881no—
820C42—4881no—
821C42—2442no—
822C42C22×#692311yescharacteristic
823C23—21no—
824C23—611no—
825C23—611no—
826C23—611no—
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—4881no—
842Q8—2441no—
843Q8—2441no—
844D4—41no—
845D4—41no—
846D4—42no—
847D4—81no—
848D4—4881no—
849D4—4881no—
850D4—4881no—
851D4—4881no—
852D4—2441no—
853D4—2441no—
854D4—2441no—
855D4—2441no—
856D4—2441no—
857D4—2441no—
858D4—2442no—
859D4—2441no—
860D4—2441no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—81no—
867C2×C4—81no—
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—1221no—
879C2×C4—4881no—
880C2×C4—4881no—
881C2×C4—4881no—
882C2×C4—4881no—
883C2×C4—2441no—
884C2×C4—2441no—
885C2×C4—2441no—
886C2×C4—2441no—
887C2×C4—2441no—
888C2×C4—2441no—
889C2×C4—2441no—
890C2×C4—2441no—
891C2×C4—2442no—
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—41no—
921C22—41no—
922C22—41no—
923C22—611no—
924C22—611no—
925C22—1221no—
926C22—1221no—
927C22—1221no—
928C22—1221no—
929C22—1221no—
930C22—1221no—
931C22—1221no—
932C22—1221no—
933C22—9762no—
934C22—4881no—
935C22—4881no—
936C22—4881no—
937C22—4881no—
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—1221no—
951C4—1221no—
952C4—1221no—
953C4—1221no—
954C4—1221no—
955C4—4881no—
956C4—4881no—
957C4—4881no—
958C4—2442no—
959C4—2441no—
960C4—2441no—
961C4—2441no—
962C2—41no—
963C2—41no—
964C2—81no—
965C2—1221no—
966C2—1221no—
967C2—4881no—
968C2—2441no—
969C2—2441no—
970C2#2146241911yescharacteristic
971C2#2146243911yescharacteristic
972C2#2146244911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#553C4
socleC22×C61C22×C22⋊C4
prime radical#21459648C2
cosocleC2×C4×D61C24
hypercenter#553#6923
hypocenterC61#17625
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #21462671C2semidirect
2. #21462340C2semidirect
3. #21461247C2semidirect
4. #21461244C2semidirect
5. #21461233C2semidirect
6. #21461230C2semidirect
7. #21461227C2semidirect
8. #21461225C2semidirect
9. #21461222C2semidirect
10. #21461221C2semidirect
11. #21461218C2semidirect
12. #21461214C2semidirect
13. #21461196C2semidirect
14. #21461195C2semidirect
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. #16840615C22semidirect
37. #16840615C22semidirect
38. #16840615C22semidirect
39. #16840615C22semidirect
40. #16840615C22semidirect
41. #16840615C22semidirect
42. #16840615C22semidirect
43. #16840615C22semidirect
53. #16840460C4semidirect
55. #16840451C4semidirect
56. #16840450C4semidirect
59. #16840421C4semidirect
60. #16840418C4semidirect
61. #16840409C4semidirect
62. #16840407C4semidirect
74. C61×#553C4semidirect
505. #553#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
#214612442
#214612332
#214612302
#214612272
#214612252
#214612222
#214612212
#214612182
#214612142
#214611962
#214611952
#214596482
#1762561