Finite Group Databasebeta

← #30611359

Subgroups — #30611359

Order 15616.

1038 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462667C211yesmaximal, characteristic, complemented
2#21462336C211yesmaximal, characteristic, complemented
3#21461263C211yesmaximal, characteristic, complemented
4#21461262C211yesmaximal, characteristic, complemented
5#21461257C211yesmaximal, characteristic, complemented
6#21461256C211yesmaximal, characteristic, complemented
7#21461247C211yesmaximal, characteristic, complemented
8#21461246C211yesmaximal, characteristic, complemented
9#21461197C211yesmaximal, characteristic, complemented
10#21461196C211yesmaximal, characteristic, complemented
11#21461193C211yesmaximal, characteristic, complemented
12#21461192C211yesmaximal, characteristic, complemented
13D61⋊#328C211yesmaximal, characteristic, complemented
14C2×#16840614C211yesmaximal, characteristic, complemented
15#21459659C211yesmaximal, characteristic
16#16840790—21no—
17#16840789—21no—
18#16840789—21no—
19D4×#92420—21no—
20#16840781C2211yescharacteristic, complemented
21#16840780C2211yescharacteristic, complemented
22C2×#14519834C2211yescharacteristic
23C2×#14519834C2211yescharacteristic, complemented
24D61⋊(C22⋊C8)C2211yescharacteristic
25D61⋊(C22⋊C8)C2211yescharacteristic, complemented
26#16840712—21no—
27#16840711—21no—
28#16840710—21no—
29#16840707C2211yescharacteristic, complemented
30#16840705C2211yescharacteristic, complemented
31#16840704C2211yescharacteristic
32C22⋊C4×#6923—21no—
33C4×C22⋊#6923C2211yescharacteristic, complemented
34#16840698C2211yescharacteristic, complemented
35C2×(C2×#6923)⋊C4C2211yescharacteristic
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
75C23×#6923—21no—
76C2×D61⋊C8—21no—
77C2×D61⋊C8—21no—
78C22×#92420—21no—
79C22×#92420—21no—
80C2×C4⋊#6923—21no—
81C2×C22⋊#6923—21no—
82C2×C22⋊#6923—21no—
83C2×C22⋊#6923—21no—
84C2×C4×#6923—21no—
85C2×C4×#6923—21no—
86#14519844—21no—
87C4⋊#92420—21no—
88#14519834—21no—
89#14519834—21no—
90#14519834C2311yescharacteristic
91#14519834C2311yescharacteristic
92#14519834C2311yescharacteristic
93#14519834C2311yescharacteristic
94C22⋊#92420—21no—
95C22⋊#92420—21no—
96C4×#92420—21no—
97C4×#92420—21no—
98(C2×#6923)⋊C4—21no—
99(C2×#6923)⋊C4—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, complemented
108C2×#11758222C2×C411yescharacteristic, complemented
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, complemented
121#14519767—21no—
122#14519766C2×C411yescharacteristic, complemented
123#14519765—21no—
124#14519765C2×C411yescharacteristic, complemented
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, complemented
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, complemented
151#14519752C2311yescharacteristic
152#14519752C2311yescharacteristic
153#14519751C2×C411yescharacteristic, complemented
154#14519750—21no—
155#14519750—21no—
156#14519750—21no—
157#14519747—21no—
158#14519747—21no—
159#14519747—21no—
160#14519745—21no—
161#14519742C2×C411yescharacteristic, complemented
162C4×D244—21no—
163C4×D244—21no—
164C4×D244—21no—
165C4×D244—21no—
166C4×D244—21no—
167C4×D244C2×C411yescharacteristic
168C4×D244C2×C411yescharacteristic, complemented
169D4×Dic61D411yescharacteristic
170#14519739—21no—
171#14519739—21no—
172#14519739—21no—
173#14519739—21no—
174#14519739C2×C411yescharacteristic, complemented
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, complemented
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, complemented
198#123×C61—21no—
199C22⋊Q8×C61C2×C411yescharacteristic
200C22⋊Q8×C61C2×C411yescharacteristic, complemented
201C4×Q8×C61C2×C411yescharacteristic, complemented
202C4×D4×C61C2×C411yescharacteristic
203#117×C61—21no—
204#117×C61C2×C411yescharacteristic, complemented
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—
213C22×#6923—42no—
214C22×#6923—42no—
215C22×#6923—81no—
216C2×Q8×C61C22×C411yescharacteristic
217C2×D4×C61C22⋊C411yescharacteristic
218C22×C4×C61—21no—
219C22×C4×C61C22×C411yescharacteristic
220C22×C4×C61C22×C411yescharacteristic
221C2×C22⋊D61—21no—
222C2×C22⋊D61—21no—
223C2×C22⋊D61C22⋊C411yescharacteristic
224C2×C22⋊D61C22⋊C411yescharacteristic
225C22×Dic61C2×D411yescharacteristic
226C22×Dic61C2×D411yescharacteristic
227#11758226—81no—
228Q8×D61—81no—
229D4×D61—22no—
230D4×D61—22no—
231#11758222—81no—
232C2×D244—21no—
233C2×D244—21no—
234C2×D244—21no—
235C2×D244—21no—
236C2×D244—21no—
237C2×D244—21no—
238C2×D244—21no—
239C2×D244—42no—
240C2×D244—42no—
241C2×D244—81no—
242C2×D244C22⋊C411yescharacteristic
243C2×D244C22×C411yescharacteristic
244C2×D244C22×C411yescharacteristic
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×C4×D61—81no—
252C2×C4×D61—81no—
253C2×C4×D61C22×C411yescharacteristic
254C2×C4×D61C22×C411yescharacteristic
255C2×C4×D61C2×D411yescharacteristic
256C2×C4×D61C2×D411yescharacteristic
257C2×C4×D61C2×D411yescharacteristic
258C2×C4×D61C2×D411yescharacteristic
259C2×C4×D61C2×D411yescharacteristic
260C2×C4×D61C2×D411yescharacteristic
261C2×C4×D61C2411yescharacteristic
262C2×Dic122—21no—
263C2×Dic122C22×C411yescharacteristic
264C22⋊#6923—42no—
265C22⋊#6923—42no—
266C22⋊#6923—81no—
267C2×#92420—21no—
268C2×#92420—21no—
269C2×#92420—21no—
270C2×#92420—21no—
271C2×#92420—81no—
272C2×#92420—81no—
273C4⋊#6923—81no—
274C4×#6923—42no—
275C4×#6923—81no—
276D61⋊C8—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—41no—
343C22×D61—41no—
344C22×D61—41no—
345C22×D61—41no—
346C22×D61—42no—
347C22×D61—81no—
348C22×D61—81no—
349C22×D61C2×C22⋊C411yescharacteristic
350C22×D61C2×C22⋊C411yescharacteristic
351C22×D61#13512yes—
352C22×D61#13512yes—
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—
366C2×#6923—84no—
367Q8×C61—41no—
368D4×C61—22no—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
371C2×C4×C61—21no—
372C2×C4×C61—21no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61—42no—
376C2×C4×C61C2×C22⋊C411yescharacteristic
377C2×C4×C61C2×C22⋊C411yescharacteristic
378C2×C4×C61C2×C22⋊C411yescharacteristic
379C2×C4×C61C2×C22⋊C411yescharacteristic
380C2×C4×C61C23×C411yescharacteristic
381C22⋊D61—22no—
382C22⋊D61—22no—
383C22⋊D61—81no—
384C22⋊D61—81no—
385C2×Dic61—21no—
386C2×Dic61—21no—
387C2×Dic61—41no—
388C2×Dic61—41no—
389C2×Dic61C2×C22⋊C411yescharacteristic
390C2×Dic61C2×C22⋊C411yescharacteristic
391C2×Dic61C2×C22⋊C411yescharacteristic
392C2×Dic61C2×C22⋊C411yescharacteristic
393C2×Dic61C22×D411yescharacteristic
394D244—22no—
395D244—41no—
396D244—41no—
397D244—41no—
398D244—41no—
399D244—41no—
400D244—41no—
401D244—42no—
402D244—42no—
403D244—81no—
404D244—81no—
405D244—81no—
406C4×D61—21no—
407C4×D61—21no—
408C4×D61—41no—
409C4×D61—41no—
410C4×D61—41no—
411C4×D61—41no—
412C4×D61—41no—
413C4×D61—41no—
414C4×D61—41no—
415C4×D61—41no—
416C4×D61—81no—
417C4×D61—81no—
418C4×D61—81no—
419C4×D61—81no—
420C4×D61—81no—
421C4×D61—81no—
422Dic122—41no—
423Dic122—81no—
424#92420—41no—
425#92420—41no—
426#92420—41no—
427#92420—41no—
428#17615—611nomaximal, Sylow
429C22×C61—21no—
430C22×C61—21no—
431C22×C61—21no—
432C22×C61—21no—
433C22×C61—21no—
434C22×C61#41612yes—
435C22×C61C22×C22⋊C411yescharacteristic
436C2×D61—21no—
437C2×D61—21no—
438C2×D61—21no—
439C2×D61—21no—
440C2×D61—21no—
441C2×D61—21no—
442C2×D61—21no—
443C2×D61—42no—
444C2×D61—42no—
445C2×D61—41no—
446C2×D61—41no—
447C2×D61—41no—
448C2×D61—41no—
449C2×D61—41no—
450C2×D61—41no—
451C2×D61—81no—
452C2×D61—81no—
453C2×D61—162no—
454C2×D61#41612yes—
455C2×D61C2×#13511yescharacteristic
456C2×D61C2×#13511yescharacteristic
457#6923—42no—
458#6923—81no—
459#6923—81no—
460#6923—81no—
461C4×C61—21no—
462C4×C61—21no—
463C4×C61—21no—
464C4×C61—21no—
465C4×C61—21no—
466C4×C61—41no—
467C4×C61—41no—
468C4×C61—41no—
469C4×C61—41no—
470Dic61—21no—
471Dic61—21no—
472Dic61—21no—
473Dic61—21no—
474Dic61—21no—
475Dic61—41no—
476Dic61—41no—
477#3505—611no—
478#2972—611no—
479#2353—611no—
480#1521—611no—
481#1521—611no—
482#1520—611no—
483#1519—611no—
484#1516—611no—
485#1516—611no—
486#1501—611no—
487#1501—611no—
488#1500—611no—
489#1500—611no—
490C2×#328—611no—
491C2×#327—611no—
492C2×C61—22no—
493C2×C61—41no—
494C2×C61#288311yescharacteristic
495C2×C61C2×#41611yescharacteristic
496C2×C61#290111yescharacteristic
497D61—21no—
498D61—21no—
499D61—22no—
500D61—41no—
501D61—81no—
502D61—81no—
503#553—611no—
504#553—611no—
505#553—1221no—
506#553—1221no—
507#552—611no—
508#552#692311yescharacteristic, complemented
509#551—1221no—
510#551—1221no—
511#548—611no—
512#548—611no—
513#546—611no—
514#546—611no—
515#539—1221no—
516#538—1221no—
517#534—1221no—
518#529—611no—
519#529—611no—
520#525—611no—
521#525—611no—
522C2×C22⋊Q8—611no—
523C2×#121—611no—
524#518—1221no—
525C2×C4×D4—611no—
526C8×D4—1221no—
527C8×D4—1221no—
528C8×D4—1221no—
529C8×D4—1221no—
530#431—611no—
531#431—611no—
532C2×C22⋊C8—611no—
533C2×C22⋊C8—611no—
534C2×C22⋊C8—611no—
535C2×C22⋊C8—611no—
536#388—1221no—
537#387—1221no—
538#386—1221no—
539#383—611no—
540#381—611no—
541#380—611no—
542C4×C22⋊C4—611no—
543C4×C22⋊C4—1221no—
544#376—611no—
545C2×#95—611no—
546#328—611no—
547#328—611no—
548#328—611no—
549#328—611no—
550#328—611no—
551#328—611no—
552#328—611no—
553#328—611no—
554#327—611no—
555#327—611no—
556#327—611no—
557#327—611no—
558#327—611no—
559#327—611no—
560#327—611no—
561#327—611no—
562C61#1761511yescharacteristic, complemented, Sylow
563C2×#41—611no—
564C2×#41—611no—
565C22×Q8—611no—
566C22×D4—611no—
567C22×D4—611no—
568C22×D4—1221no—
569C23×C4—611no—
570C23×C4—611no—
571C23×C4—1221no—
572C22×C8—1221no—
573C22×C8—1221no—
574C22×C8—1221no—
575C22×C8—1221no—
576#126—21no—
577#126—1221no—
578#126—1221no—
579#126—1221no—
580#126—1221no—
581#126—1221no—
582#125—21no—
583#125—611no—
584#125—1221no—
585#125C2×#692311yescharacteristic, complemented
586#124—611no—
587#124—611no—
588#124—1221no—
589#124—1221no—
590#123—21no—
591#123—1221no—
592#123—1221no—
593#123—1221no—
594#123—1221no—
595#123—1221no—
596#123—1221no—
597#123—1221no—
598#123—1221no—
599#123—1221no—
600C22⋊Q8—611no—
601C22⋊Q8—611no—
602C22⋊Q8—611no—
603C22⋊Q8—611no—
604C22⋊Q8—1221no—
605C22⋊Q8—1221no—
606C22⋊Q8—1221no—
607C22⋊Q8—1221no—
608C22⋊Q8C2×#692311yescharacteristic
609C22⋊Q8C2×#692311yescharacteristic, complemented
610#121—611no—
611#121—611no—
612#121—611no—
613#121—611no—
614#121—611no—
615#121—611no—
616#121—1221no—
617#121—1221no—
618#121—1221no—
619#121—1221no—
620#121—1221no—
621#121—1221no—
622#121—1221no—
623#121—1221no—
624#120—1221no—
625#120—1221no—
626#120—1221no—
627#120—1221no—
628C4×Q8—611no—
629C4×Q8C2×#692311yescharacteristic, complemented
630C4×D4—611no—
631C4×D4—611no—
632C4×D4—611no—
633C4×D4—611no—
634C4×D4—611no—
635C4×D4—611no—
636C4×D4—611no—
637C4×D4—611no—
638C4×D4—611no—
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×D4—1221no—
648C4×D4—1221no—
649C4×D4C2×#692311yescharacteristic
650#117—21no—
651#117—611no—
652#117—1221no—
653#117—1221no—
654#117—1221no—
655#117C2×#692311yescharacteristic, complemented
656C2×C4⋊C4—611no—
657C2×C4⋊C4—611no—
658C2×C4⋊C4—1221no—
659C2×C4⋊C4—1221no—
660C2×C4⋊C4C2×#692311yescharacteristic
661C2×C22⋊C4—611no—
662C2×C22⋊C4—611no—
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—
673C4⋊C8—1221no—
674C4⋊C8—1221no—
675C22⋊C8—611no—
676C22⋊C8—611no—
677C22⋊C8—611no—
678C22⋊C8—611no—
679C22⋊C8—1221no—
680C22⋊C8—1221no—
681C22⋊C8—1221no—
682C22⋊C8—1221no—
683C4×C8—1221no—
684C4×C8—1221no—
685#95—611no—
686#95—611no—
687#95—611no—
688#95—611no—
689#95—1221no—
690#95—1221no—
691#95—1221no—
692#95—1221no—
693#95—1221no—
694C24—611no—
695C24—611no—
696C24—1221no—
697#41—4881no—
698#41—4881no—
699C2×Q8—611no—
700C2×Q8—1221no—
701C2×Q8—4881no—
702C2×Q8C22×#692311yescharacteristic
703C2×D4—611no—
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—1222no—
715C2×D4—1222no—
716C2×D4—1221no—
717C2×D4—1221no—
718C2×D4—1221no—
719C2×D4—4881no—
720C2×D4—2442no—
721C2×D4—2442no—
722C2×D4C22⋊#692311yescharacteristic
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—1221no—
745C22×C4—4881no—
746C22×C4—4881no—
747C22×C4—4881no—
748C22×C4—2442no—
749C22×C4—2442no—
750C22×C4C22×#692311yescharacteristic
751C22×C4C22×#692311yescharacteristic
752C2×C8—1221no—
753C2×C8—1221no—
754C2×C8—1221no—
755C2×C8—1221no—
756C2×C8—4881no—
757C2×C8—4881no—
758C2×C8—4881no—
759C2×C8—4881no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—611no—
767C4⋊C4—611no—
768C4⋊C4—611no—
769C4⋊C4—611no—
770C4⋊C4—1221no—
771C4⋊C4—1221no—
772C4⋊C4—1221no—
773C4⋊C4—1221no—
774C4⋊C4—1221no—
775C4⋊C4—1221no—
776C4⋊C4—1221no—
777C4⋊C4—1221no—
778C4⋊C4—4881no—
779C4⋊C4C22⋊#692311yescharacteristic
780C4⋊C4C22×#692311yescharacteristic
781C4⋊C4C22×#692311yescharacteristic
782C4⋊C4C22×#692311yescharacteristic
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—611no—
787C22⋊C4—611no—
788C22⋊C4—611no—
789C22⋊C4—611no—
790C22⋊C4—611no—
791C22⋊C4—611no—
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—1221no—
807C22⋊C4—1221no—
808C22⋊C4—1221no—
809C22⋊C4—4881no—
810C22⋊C4—2442no—
811C22⋊C4—2442no—
812C22⋊C4C22⋊#692311yescharacteristic
813C22⋊C4C22⋊#692311yescharacteristic
814C42—21no—
815C42—21no—
816C42—611no—
817C42—611no—
818C42—611no—
819C42—1221no—
820C42—1221no—
821C42—4881no—
822C42—2442no—
823C42C22×#692311yescharacteristic
824C23—611no—
825C23—611no—
826C23—612no—
827C23—612no—
828C23—611no—
829C23—1221no—
830C23—1221no—
831C23—1221no—
832C23—1221no—
833C23—4881no—
834C23—4881no—
835C23—2441no—
836C23—2441no—
837C23—2441no—
838C23—2441no—
839C23—2442no—
840C23C2×C22⋊#692311yescharacteristic
841C23C2×C22⋊#692311yescharacteristic
842Q8—41no—
843Q8—4881no—
844Q8—2441no—
845D4—22no—
846D4—1222no—
847D4—1222no—
848D4—1222no—
849D4—4881no—
850D4—4881no—
851D4—4881no—
852D4—4881no—
853D4—4881no—
854D4—2441no—
855D4—2441no—
856D4—2441no—
857D4—2441no—
858D4—2441no—
859D4—2441no—
860D4—2442no—
861D4—2442no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—42no—
869C2×C4—611no—
870C2×C4—611no—
871C2×C4—611no—
872C2×C4—611no—
873C2×C4—611no—
874C2×C4—1221no—
875C2×C4—1221no—
876C2×C4—1222no—
877C2×C4—1221no—
878C2×C4—1221no—
879C2×C4—4881no—
880C2×C4—4881no—
881C2×C4—4881no—
882C2×C4—4881no—
883C2×C4—4881no—
884C2×C4—4881no—
885C2×C4—4884no—
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×C4—2441no—
906C2×C4—2441no—
907C2×C4C2×C22⋊#692311yescharacteristic
908C2×C4C2×C22⋊#692311yescharacteristic
909C2×C4C2×C22⋊#692311yescharacteristic
910C2×C4C2×C22⋊#692311yescharacteristic
911C2×C4C23×#692311yescharacteristic
912C8—2441no—
913C8—2441no—
914C8—2441no—
915C8—2441no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—611no—
922C22—611no—
923C22—612no—
924C22—1221no—
925C22—1221no—
926C22—1221no—
927C22—1221no—
928C22—1221no—
929C22—1221no—
930C22—1221no—
931C22—9762no—
932C22—4881no—
933C22—4881no—
934C22—2442no—
935C22—2442no—
936C22—2441no—
937C22—2441no—
938C22—2441no—
939C22—2441no—
940C22—2441no—
941C22—2441no—
942C22#1684075212yes—
943C22C22×C22⋊#692311yescharacteristic
944C4—21no—
945C4—21no—
946C4—21no—
947C4—21no—
948C4—21no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—41no—
953C4—1221no—
954C4—1221no—
955C4—1221no—
956C4—1221no—
957C4—1221no—
958C4—4881no—
959C4—4881no—
960C4—4881no—
961C4—2442no—
962C4—2441no—
963C4—2441no—
964C2—22no—
965C2—41no—
966C2—1221no—
967C2—1221no—
968C2—1222no—
969C2—4881no—
970C2—4881no—
971C2—2441no—
972C2#2146241911yescharacteristic
973C2C2×#1684075211yescharacteristic
974C2#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#17615
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. #21462667C2semidirect
2. #21462336C2semidirect
3. #21461263C2semidirect
4. #21461262C2semidirect
5. #21461257C2semidirect
6. #21461256C2semidirect
7. #21461247C2semidirect
8. #21461246C2semidirect
9. #21461197C2semidirect
10. #21461196C2semidirect
11. #21461193C2semidirect
12. #21461192C2semidirect
13. D61⋊#328C2semidirect
14. C2×#16840614C2semidirect
20. #16840781C22semidirect
21. #16840780C22semidirect
23. C2×#14519834C22semidirect
25. D61⋊(C22⋊C8)C22semidirect
29. #16840707C22semidirect
30. #16840705C22semidirect
33. C4×C22⋊#6923C22semidirect
34. #16840698C22semidirect
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
107. C2×#11758226C2×C4semidirect
108. C2×#11758222C2×C4semidirect
120. #14519768C2×C4semidirect
122. #14519766C2×C4semidirect
124. #14519765C2×C4semidirect
136. #14519757C2×C4semidirect
150. #14519752C2×C4semidirect
153. #14519751C2×C4semidirect
161. #14519742C2×C4semidirect
168. C4×D244C2×C4semidirect
174. #14519739C2×C4semidirect
183. #14519735C2×C4semidirect
197. #125×C61C2×C4semidirect
200. C22⋊Q8×C61C2×C4semidirect
201. C4×Q8×C61C2×C4semidirect
204. #117×C61C2×C4semidirect
508. #552#6923semidirect
562. C61#17615semidirect
585. #125C2×#6923semidirect
609. C22⋊Q8C2×#6923semidirect
629. C4×Q8C2×#6923semidirect
655. #117C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214626672
#214623362
#214612632
#214612622
#214612572
#214612562
#214612472
#214612462
#214611972
#214611962
#214611932
#214611922
D61⋊#3282
C2×#168406142
#214596592
#1761561