Finite Group Databasebeta

← #30610481

Subgroups — #30610481

Order 15616.

1222 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462741C211yesmaximal, characteristic, complemented
2#21462630C211yesmaximal, characteristic, complemented
3#21461160C211yesmaximal, characteristic, complemented
4#21461159C211yesmaximal, characteristic, complemented
5#21461157C211yesmaximal, characteristic, complemented
6#21461154C211yesmaximal, characteristic, complemented
7#21461153C211yesmaximal, characteristic, complemented
8#21461150C211yesmaximal, characteristic, complemented
9#21461146C211yesmaximal, characteristic, complemented
10#21461145C211yesmaximal, characteristic, complemented
11#21461119C211yesmaximal, characteristic, complemented
12#21461117C211yesmaximal, characteristic, complemented
13#21461113C211yesmaximal, characteristic, complemented
14D61⋊(D4⋊C8)C211yesmaximal, characteristic, complemented
15#21459025C211yesmaximal, characteristic
16#16840814—21no—
17#16840814—21no—
18#16840795—21no—
19#16840795—21no—
20#16840794—21no—
21#16840794—21no—
22#16840792—21no—
23#16840792—21no—
24#16840784C2211yescharacteristic, complemented
25#16840783C2211yescharacteristic, complemented
26#16840781C2211yescharacteristic, complemented
27#16840781C2211yescharacteristic, complemented
28#16840780C2211yescharacteristic, complemented
29#16840779C2211yescharacteristic, complemented
30#16840766C2211yescharacteristic, complemented
31#16840765C2211yescharacteristic, complemented
32D61⋊(C4⋊C8)C2211yescharacteristic, complemented
33C4×#11758213C2211yescharacteristic, complemented
34C4×#11758217C2211yescharacteristic, complemented
35C4×D61⋊C8C2211yescharacteristic, complemented
36Q8⋊#92420C2211yescharacteristic, complemented
37Q8⋊#92420C2211yescharacteristic, complemented
38Q8⋊#92420C2211yescharacteristic, complemented
39Q8⋊#92420C2211yescharacteristic, complemented
40#16840610C2211yescharacteristic, complemented
41#16840610C2211yescharacteristic, complemented
42#16840610C2211yescharacteristic, complemented
43#16840610C2211yescharacteristic, complemented
44#16840610C2211yescharacteristic, complemented
45#16840610C2211yescharacteristic, complemented
46#16840610C2211yescharacteristic, complemented
47#16840610C2211yescharacteristic, complemented
48D4⋊#92420C2211yescharacteristic, complemented
49D4⋊#92420C2211yescharacteristic, complemented
50D4⋊#92420C2211yescharacteristic, complemented
51D4⋊#92420C2211yescharacteristic, complemented
52C2×#14519823C411yescharacteristic
53#16840244C411yescharacteristic
54#16840244C411yescharacteristic
55#16840243—21no—
56#16840243C411yescharacteristic
57#16840236—21no—
58#16840236C411yescharacteristic
59#16840234—21no—
60#16840234—21no—
61#16840234C411yescharacteristic
62#16840234C411yescharacteristic
63#41×Dic61C2211yescharacteristic
64C4×#11758226C2211yescharacteristic
65C4×#11758226C2211yescharacteristic
66#16840230—21no—
67#16840230C2211yescharacteristic
68C2×#14519739—21no—
69C2×#14519739C2211yescharacteristic
70C4×D4×D61—21no—
71C4×D4×D61—21no—
72C4×D4×D61C2211yescharacteristic
73C4×D4×D61C2211yescharacteristic
74C61×#520C411yescharacteristic
75C2×#11758213—21no—
76C2×#11758213—21no—
77C2×#11758217—21no—
78C2×#11758217—21no—
79C2×D61⋊C8—21no—
80C2×D61⋊C8—21no—
81#14519844—21no—
82#14519844—21no—
83#14519844—21no—
84#14519844—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—
95C22⋊#92420—21no—
96C22⋊#92420—21no—
97#14519832—21no—
98#14519832—21no—
99#14519832—21no—
100#14519832—21no—
101C4×#92420—21no—
102C4×#92420—21no—
103C4×#92420C2311yescharacteristic
104C4×#92420C2311yescharacteristic
105C4×#92420C2311yescharacteristic
106C4×#92420C2311yescharacteristic
107#14519823—24no—
108#14519823—24no—
109C2×#11758226C2×C411yescharacteristic
110C2×#11758226C2×C411yescharacteristic
111C2×#11758222—21no—
112C2×#11758222C2×C411yescharacteristic
113C22×D244—21no—
114C22×D244C2×C411yescharacteristic
115C2×D4×D61—21no—
116C2×D4×D61—21no—
117C2×D4×D61C2×C411yescharacteristic
118C2×D4×D61C2×C411yescharacteristic
119C22×C4×D61—21no—
120C22×C4×D61—21no—
121C22×C4×D61—21no—
122Q8×Dic61C2×C411yescharacteristic
123Q8×Dic61C2311yescharacteristic
124#14519742—21no—
125#14519742D411yescharacteristic
126#14519742D411yescharacteristic
127C4×D244—21no—
128C4×D244—21no—
129C4×D244—21no—
130C4×D244—21no—
131C4×D244C2×C411yescharacteristic
132C4×D244C2×C411yescharacteristic
133C4×D244C2×C411yescharacteristic
134C4×D244C2×C411yescharacteristic
135D4×Dic61—21no—
136D4×Dic61—21no—
137D4×Dic61C2×C411yescharacteristic
138D4×Dic61C2311yescharacteristic
139#14519739—21no—
140#14519739—21no—
141#14519739—21no—
142#14519739—21no—
143#14519739—21no—
144#14519739—21no—
145#14519739—21no—
146#14519739—21no—
147#14519739—21no—
148#14519739C2×C411yescharacteristic
149#14519739C2×C411yescharacteristic
150#14519739D411yescharacteristic
151#14519739D411yescharacteristic
152#14519739C2311yescharacteristic
153#14519739C2311yescharacteristic
154C4×C22⋊D61—21no—
155C4×C22⋊D61—21no—
156C4×C22⋊D61—21no—
157C4×C22⋊D61—21no—
158C4×C22⋊D61—21no—
159C4×C22⋊D61—21no—
160#14519737—21no—
161#14519737—21no—
162#14519737—21no—
163#14519737—21no—
164#14519737D411yescharacteristic
165#14519737D411yescharacteristic
166#14519737D411yescharacteristic
167#14519737D411yescharacteristic
168#14519736—21no—
169#14519736C2×C411yescharacteristic
170#14519735—21no—
171#14519735—21no—
172#14519735C2×C411yescharacteristic
173#14519735C2×C411yescharacteristic
174#14519734—21no—
175#14519734—21no—
176#14519734C2×C411yescharacteristic
177#14519734C2×C411yescharacteristic
178C4⋊C4×D61—21no—
179C4⋊C4×D61—21no—
180C4⋊C4×D61C2×C411yescharacteristic
181C4⋊C4×D61C2×C411yescharacteristic
182C2×#11758198—21no—
183C2×#11758198—21no—
184C2×#11758198—21no—
185C22⋊C4×D61—21no—
186C22⋊C4×D61—21no—
187C22⋊C4×D61—21no—
188C22⋊C4×D61—21no—
189C22⋊C4×D61—21no—
190C22⋊C4×D61—21no—
191C2×C4×Dic61—21no—
192C2×C4×Dic61C2311yescharacteristic
193C42×D61—21no—
194C42×D61—21no—
195C42×D61C2311yescharacteristic
196C42×D61C2311yescharacteristic
197C2×#41×C61C2×C411yescharacteristic
198C4×Q8×C61C2×C411yescharacteristic
199C4×Q8×C61C2×C411yescharacteristic
200C4×D4×C61—21no—
201C4×D4×C61—21no—
202C4×D4×C61C2×C411yescharacteristic
203C4×D4×C61C2×C411yescharacteristic
204#117×C61—21no—
205#117×C61C2×C411yescharacteristic
206C2×C4⋊C4×C61—21no—
207C2×C4⋊C4×C61C2×C411yescharacteristic
208C23×D61—21no—
209C23×D61—21no—
210C23×D61—21no—
211#41×C61—22no—
212#41×C61—22no—
213C2×Q8×C61C22×C411yescharacteristic
214C2×D4×C61—21no—
215C2×D4×C61C22×C411yescharacteristic
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61C22×C411yescharacteristic
221C2×C22⋊D61—21no—
222C2×C22⋊D61—21no—
223C2×C22⋊D61C22⋊C411yescharacteristic
224C2×C22⋊D61C22⋊C411yescharacteristic
225C22×Dic61—21no—
226C22×Dic61—21no—
227C22×Dic61C2×D411yescharacteristic
228C22×Dic61C2×D411yescharacteristic
229#11758226—22no—
230#11758226—22no—
231#11758226—22no—
232#11758226M1614yescomplemented
233D4×D61—28no—
234D4×D61—28no—
235D4×D61—22no—
236D4×D61—22no—
237D4×D61—22no—
238D4×D61M1614yescomplemented
239#11758222—28no—
240#11758222—22no—
241#11758222—22no—
242C2×D244—28no—
243C2×D244—21no—
244C2×D244—21no—
245C2×D244—21no—
246C2×D244—22no—
247C2×D244—22no—
248C2×D244C22⋊C411yescharacteristic
249C2×D244C22×C411yescharacteristic
250C2×D244C22×C411yescharacteristic
251C2×C4×D61—21no—
252C2×C4×D61—21no—
253C2×C4×D61—21no—
254C2×C4×D61—21no—
255C2×C4×D61—21no—
256C2×C4×D61—21no—
257C2×C4×D61—21no—
258C2×C4×D61—21no—
259C2×C4×D61—21no—
260C2×C4×D61—21no—
261C2×C4×D61—21no—
262C2×C4×D61—21no—
263C2×C4×D61—81no—
264C2×C4×D61—81no—
265C2×C4×D61—81no—
266C2×C4×D61—81no—
267C2×C4×D61—81no—
268C2×C4×D61—81no—
269C2×C4×D61C22×C411yescharacteristic
270C2×C4×D61C22×C411yescharacteristic
271C2×C4×D61C2×D411yescharacteristic
272C2×C4×D61C2×D411yescharacteristic
273C2×C4×D61C2×D411yescharacteristic
274C2×C4×D61C2×D411yescharacteristic
275C2×Dic122C22⋊C411yescharacteristic
276#11758217—42no—
277#11758217—81no—
278C2×#92420—21no—
279C2×#92420—21no—
280C2×#92420—21no—
281C2×#92420—21no—
282C2×#92420—21no—
283C2×#92420—21no—
284C2×#92420—21no—
285C2×#92420—21no—
286#11758213—42no—
287#11758213—81no—
288D61⋊C8—42no—
289D61⋊C8—81no—
290C4⋊C4×C61—21no—
291C4⋊C4×C61—21no—
292C4⋊C4×C61—21no—
293C4⋊C4×C61C22⋊C411yescharacteristic
294C4⋊C4×C61C22⋊C411yescharacteristic
295C4⋊C4×C61C22×C411yescharacteristic
296C4⋊C4×C61C22×C411yescharacteristic
297C22⋊C4×C61—21no—
298C22⋊C4×C61—21no—
299C22⋊C4×C61C22⋊C411yescharacteristic
300C22⋊C4×C61C22⋊C411yescharacteristic
301C42×C61—21no—
302C42×C61—21no—
303C42×C61C22×C411yescharacteristic
304C42×C61C22×C411yescharacteristic
305C22⋊Dic61—21no—
306C22⋊Dic61—21no—
307C22⋊Dic61—21no—
308#11758198—21no—
309#11758198—21no—
310#11758198—21no—
311#11758198—21no—
312#11758198—21no—
313#11758198—21no—
314#11758198—21no—
315#11758198—21no—
316#11758198—21no—
317#11758198—21no—
318#11758198C22⋊C411yescharacteristic
319#11758198C22⋊C411yescharacteristic
320#11758198C22⋊C411yescharacteristic
321#11758198C22⋊C411yescharacteristic
322C4⋊Dic61—21no—
323C4⋊Dic61—21no—
324C4⋊Dic61C22×C411yescharacteristic
325C4⋊Dic61C22×C411yescharacteristic
326#11758196—21no—
327#11758196—21no—
328#11758196C22⋊C411yescharacteristic
329#11758196C22⋊C411yescharacteristic
330#11758196C22⋊C411yescharacteristic
331#11758196C22⋊C411yescharacteristic
332C4×Dic61—21no—
333C4×Dic61—21no—
334C4×Dic61—21no—
335C4×Dic61—21no—
336C4×Dic61—21no—
337C4×Dic61C22×C411yescharacteristic
338C4×Dic61C2×D411yescharacteristic
339C4×Dic61C2×D411yescharacteristic
340C4×Dic61C2×D411yescharacteristic
341C4×Dic61C2×D411yescharacteristic
342C4×Dic61C2×D411yescharacteristic
343C4×Dic61C2×D411yescharacteristic
344C4×Dic61C2411yescharacteristic
345C23×C61—21no—
346C23×C61C2×C22⋊C411yescharacteristic
347C22×D61—21no—
348C22×D61—21no—
349C22×D61—24no—
350C22×D61—24no—
351C22×D61—24no—
352C22×D61—81no—
353C22×D61—81no—
354C22×D61—81no—
355C22×D61—81no—
356C22×D61—81no—
357C22×D61—81no—
358C22×D61C2×C22⋊C411yescharacteristic
359C22×D61C2×C22⋊C411yescharacteristic
360Q8×C61—21no—
361Q8×C61C2×M1612yes—
362D4×C61—24no—
363D4×C61—21no—
364D4×C61C2×M1612yes—
365C2×C4×C61—24no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
371C2×C4×C61—81no—
372C2×C4×C61—81no—
373C2×C4×C61—81no—
374C2×C4×C61C2×C22⋊C411yescharacteristic
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—24no—
381C22⋊D61—22no—
382C22⋊D61—22no—
383C22⋊D61—24no—
384C2×Dic61—21no—
385C2×Dic61—21no—
386C2×Dic61—21no—
387C2×Dic61—21no—
388C2×Dic61—41no—
389C2×Dic61—41no—
390C2×Dic61—41no—
391C2×Dic61—81no—
392C2×Dic61C2×C22⋊C411yescharacteristic
393C2×Dic61C2×C22⋊C411yescharacteristic
394C2×Dic61C2×C22⋊C411yescharacteristic
395C2×Dic61C2×C22⋊C411yescharacteristic
396C2×Dic61C22×D411yescharacteristic
397C2×Dic61C22×D411yescharacteristic
398D244—24no—
399D244—24no—
400D244—22no—
401D244—24no—
402D244—21no—
403D244—21no—
404D244C2×M1612yes—
405D244C2×M1612yes—
406C4×D61—24no—
407C4×D61—21no—
408C4×D61—21no—
409C4×D61—21no—
410C4×D61—21no—
411C4×D61—21no—
412C4×D61—21no—
413C4×D61—24no—
414C4×D61—41no—
415C4×D61—41no—
416C4×D61—41no—
417C4×D61—41no—
418C4×D61—41no—
419C4×D61—41no—
420C4×D61—81no—
421C4×D61—81no—
422C4×D61—81no—
423C4×D61—81no—
424C4×D61—81no—
425C4×D61—81no—
426C4×D61—81no—
427C4×D61—81no—
428C4×D61C2×M1612yes—
429C4×D61C2×M1612yes—
430Dic122—22no—
431#92420—22no—
432#92420—41no—
433#92420—41no—
434#92420—41no—
435#92420—41no—
436#92420—41no—
437#92420—41no—
438#92420—41no—
439#17453—611nomaximal, Sylow
440C22×C61—21no—
441C22×C61—22no—
442C22×C61—21no—
443C22×C61—21no—
444C22×C61—41no—
445C22×C61—41no—
446C22×C61C22×C22⋊C411yescharacteristic
447C2×D61—21no—
448C2×D61—21no—
449C2×D61—21no—
450C2×D61—22no—
451C2×D61—22no—
452C2×D61—21no—
453C2×D61—21no—
454C2×D61—41no—
455C2×D61—41no—
456C2×D61—41no—
457C2×D61—41no—
458C2×D61—84no—
459C2×D61—84no—
460C2×D61—84no—
461C2×D61#40712yes—
462C4×C61—21no—
463C4×C61—22no—
464C4×C61—21no—
465C4×C61—21no—
466C4×C61—21no—
467C4×C61—21no—
468C4×C61—41no—
469C4×C61—41no—
470C4×C61C22×M1611yescharacteristic
471C4×C61C22×M1611yescharacteristic
472Dic61—21no—
473Dic61—21no—
474Dic61—21no—
475Dic61—21no—
476Dic61—41no—
477Dic61—41no—
478Dic61#40712yes—
479Dic61#57611yescharacteristic
480Dic61#57711yescharacteristic
481C4×H(5,𝔽2)—611no—
482#2989—611no—
483#2965—611no—
484#1490—611no—
485#1490—611no—
486#1489—611no—
487#1489—611no—
488#1488—611no—
489#1488—611no—
490#1486—611no—
491#1486—611no—
492#1478—611no—
493#1477—611no—
494#1476—611no—
495C2×D4⋊C8—611no—
496C2×C61—41no—
497C2×C61—42no—
498C2×C61C2×#40711yescharacteristic
499C2×C61#289711yescharacteristic
500C2×C61#290111yescharacteristic
501D61—22no—
502D61—41no—
503D61—42no—
504D61—42no—
505C2×H(5,𝔽2)—611no—
506#520—611no—
507#520—611no—
508#520—611no—
509#520—1221no—
510#520#692311yescharacteristic
511#518—611no—
512#518—611no—
513#518—611no—
514#518—1221no—
515#518—1221no—
516#518—1221no—
517C4×#41—611no—
518C4×#41—611no—
519C4×#41—611no—
520C4×#41—611no—
521C4×#41—1221no—
522C2×C4×D4—611no—
523C2×C4×D4—611no—
524C2×C4×D4—611no—
525C2×C4×D4—1221no—
526C2×C4×D4—1221no—
527C2×C4×D4—1221no—
528#446—1221no—
529#446—1221no—
530#436—1221no—
531#436—1221no—
532#435—1221no—
533#435—1221no—
534#435—1221no—
535#435—1221no—
536#432—611no—
537#432—611no—
538#431—611no—
539#431—611no—
540#431—611no—
541#431—611no—
542#423—611no—
543#423—611no—
544C2×C4⋊C8—611no—
545C4×M16—611no—
546C4×M16—611no—
547C2×C4×C8—611no—
548Q8⋊C8—611no—
549Q8⋊C8—611no—
550Q8⋊C8—611no—
551Q8⋊C8—611no—
552D4⋊C8—611no—
553D4⋊C8—611no—
554D4⋊C8—611no—
555D4⋊C8—611no—
556D4⋊C8—611no—
557D4⋊C8—611no—
558D4⋊C8—611no—
559D4⋊C8—611no—
560D4⋊C8—611no—
561D4⋊C8—611no—
562D4⋊C8—611no—
563D4⋊C8—611no—
564C61#1745311yescharacteristic, complemented, Sylow
565H(5,𝔽2)—1224no—
566H(5,𝔽2)—1224no—
567C2×#41—611no—
568C2×#41—611no—
569C2×#41—611no—
570C2×#41—1221no—
571C2×#41C2×#692311yescharacteristic
572C22×D4—611no—
573C22×D4—611no—
574C22×D4—611no—
575C22×D4—1221no—
576C22×D4—1221no—
577C22×D4—1221no—
578C23×C4—1221no—
579C23×C4—1221no—
580C23×C4—1221no—
581C2×M16—1221no—
582C2×M16—1221no—
583C2×M16—1221no—
584C2×M16—1221no—
585C22×C8—1221no—
586C22×C8—1221no—
587C4×Q8—611no—
588C4×Q8—611no—
589C4×Q8—611no—
590C4×Q8—611no—
591C4×Q8—1221no—
592C4×Q8C2×#692311yescharacteristic
593C4×Q8C2×#692311yescharacteristic
594C4×D4—21no—
595C4×D4—21no—
596C4×D4—611no—
597C4×D4—611no—
598C4×D4—611no—
599C4×D4—611no—
600C4×D4—611no—
601C4×D4—611no—
602C4×D4—611no—
603C4×D4—611no—
604C4×D4—611no—
605C4×D4—611no—
606C4×D4—611no—
607C4×D4—611no—
608C4×D4—611no—
609C4×D4—611no—
610C4×D4—611no—
611C4×D4—611no—
612C4×D4—1221no—
613C4×D4—1221no—
614C4×D4—1221no—
615C4×D4—1221no—
616C4×D4—1221no—
617C4×D4—1221no—
618C4×D4—1221no—
619C4×D4—1221no—
620C4×D4—1221no—
621C4×D4—1221no—
622C4×D4—1221no—
623C4×D4—1221no—
624C4×D4—1221no—
625C4×D4—1221no—
626C4×D4—1221no—
627C4×D4—1221no—
628C4×D4—1221no—
629C4×D4—1221no—
630C4×D4—1221no—
631C4×D4—1221no—
632C4×D4—1221no—
633C4×D4—1221no—
634C4×D4—1221no—
635C4×D4—1221no—
636C4×D4—1221no—
637C4×D4C2×#692311yescharacteristic
638C4×D4C2×#692311yescharacteristic
639#117—21no—
640#117—611no—
641#117—611no—
642#117—611no—
643#117—611no—
644#117—611no—
645#117—1221no—
646#117—1221no—
647#117—1221no—
648#117—1221no—
649#117—1221no—
650#117C2×#692311yescharacteristic
651C2×C4⋊C4—21no—
652C2×C4⋊C4—611no—
653C2×C4⋊C4—611no—
654C2×C4⋊C4—1221no—
655C2×C4⋊C4—1221no—
656C2×C4⋊C4C2×#692311yescharacteristic
657C2×C22⋊C4—1221no—
658C2×C22⋊C4—1221no—
659C2×C22⋊C4—1221no—
660C2×C22⋊C4—1221no—
661C2×C22⋊C4—1221no—
662C2×C22⋊C4—1221no—
663C2×C22⋊C4—1221no—
664C2×C22⋊C4—1221no—
665C2×C22⋊C4—1221no—
666C2×C42—611no—
667C2×C42—611no—
668C2×C42—611no—
669C2×C42—1221no—
670C2×C42—1221no—
671C2×C42—1221no—
672C4⋊C8—611no—
673C4⋊C8—611no—
674C4⋊C8—611no—
675C4⋊C8—611no—
676C4⋊C8—1221no—
677C4⋊C8—1221no—
678C4⋊C8—1221no—
679C4⋊C8—1221no—
680C4⋊C8—1221no—
681C4⋊C8—1221no—
682C22⋊C8—1221no—
683C22⋊C8—1221no—
684C22⋊C8—1221no—
685C22⋊C8—1221no—
686C22⋊C8—1221no—
687C22⋊C8—1221no—
688#97—1221no—
689#97—1221no—
690#97—1221no—
691#97—1221no—
692C4×C8—611no—
693C4×C8—611no—
694C4×C8—611no—
695C4×C8—611no—
696C4×C8—1221no—
697C4×C8—1221no—
698C24—1221no—
699C24—1221no—
700C24—1221no—
701#41—22no—
702#41—22no—
703#41—614no—
704#41—1222no—
705#41—1222no—
706#41—1228no—
707#41—1222no—
708#41—1222no—
709#41—1222no—
710C2×Q8—611no—
711C2×Q8C22×#692311yescharacteristic
712C2×D4—21no—
713C2×D4—614no—
714C2×D4—611no—
715C2×D4—611no—
716C2×D4—611no—
717C2×D4—611no—
718C2×D4—611no—
719C2×D4—1222no—
720C2×D4—1222no—
721C2×D4—1221no—
722C2×D4—1221no—
723C2×D4—1228no—
724C2×D4—1222no—
725C2×D4—1221no—
726C2×D4—1221no—
727C2×D4—1222no—
728C2×D4—1228no—
729C2×D4—1228no—
730C2×D4—1222no—
731C2×D4—1221no—
732C2×D4C22×#692311yescharacteristic
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—611no—
738C22×C4—611no—
739C22×C4—611no—
740C22×C4—611no—
741C22×C4—611no—
742C22×C4—611no—
743C22×C4—611no—
744C22×C4—611no—
745C22×C4—1221no—
746C22×C4—1221no—
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×C4—4881no—
760C22×C4—4881no—
761C22×C4—4881no—
762C22×C4—4881no—
763C22×C4—4881no—
764C22×C4—4881no—
765C22×C4C22×#692311yescharacteristic
766M16—4881no—
767M16—4881no—
768M16—2442no—
769M16—2442no—
770C2×C8—1221no—
771C2×C8—1221no—
772C2×C8—1221no—
773C2×C8—1221no—
774C2×C8—1221no—
775C2×C8—1221no—
776C2×C8—1221no—
777C2×C8—1221no—
778C2×C8—4881no—
779C2×C8—2442no—
780C4⋊C4—21no—
781C4⋊C4—21no—
782C4⋊C4—21no—
783C4⋊C4—611no—
784C4⋊C4—611no—
785C4⋊C4—611no—
786C4⋊C4—611no—
787C4⋊C4—611no—
788C4⋊C4—611no—
789C4⋊C4—1221no—
790C4⋊C4—1221no—
791C4⋊C4—1221no—
792C4⋊C4—1221no—
793C4⋊C4C22⋊#692311yescharacteristic
794C4⋊C4C22⋊#692311yescharacteristic
795C4⋊C4C22×#692311yescharacteristic
796C4⋊C4C22×#692311yescharacteristic
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—611no—
800C22⋊C4—611no—
801C22⋊C4—611no—
802C22⋊C4—611no—
803C22⋊C4—1221no—
804C22⋊C4—1221no—
805C22⋊C4—1221no—
806C22⋊C4—1221no—
807C22⋊C4—1221no—
808C22⋊C4—1221no—
809C22⋊C4—1221no—
810C22⋊C4—1221no—
811C22⋊C4—1221no—
812C22⋊C4—1221no—
813C22⋊C4—1221no—
814C22⋊C4—1221no—
815C22⋊C4—1221no—
816C22⋊C4C22⋊#692311yescharacteristic
817C22⋊C4C22⋊#692311yescharacteristic
818C42—21no—
819C42—21no—
820C42—611no—
821C42—611no—
822C42—611no—
823C42—611no—
824C42—611no—
825C42—611no—
826C42—611no—
827C42—611no—
828C42—1221no—
829C42—1221no—
830C42—1221no—
831C42—1221no—
832C42—1221no—
833C42C22×#692311yescharacteristic
834C42C22×#692311yescharacteristic
835C23—21no—
836C23—611no—
837C23—611no—
838C23—1224no—
839C23—1224no—
840C23—1224no—
841C23—1221no—
842C23—1221no—
843C23—4881no—
844C23—4881no—
845C23—4881no—
846C23—4881no—
847C23—4881no—
848C23—4881no—
849C23C2×C22⋊#692311yescharacteristic
850Q8—21no—
851Q8—1222no—
852Q8D61⋊M1612yes—
853D4—24no—
854D4—21no—
855D4—612no—
856D4—612no—
857D4—1222no—
858D4—1224no—
859D4—1224no—
860D4—1224no—
861D4—1222no—
862D4—1224no—
863D4—1222no—
864D4—1224no—
865D4—1221no—
866D4—1221no—
867D4D61⋊M1612yes—
868C2×C4—24no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—81no—
875C2×C4—81no—
876C2×C4—81no—
877C2×C4—611no—
878C2×C4—611no—
879C2×C4—612no—
880C2×C4—612no—
881C2×C4—611no—
882C2×C4—611no—
883C2×C4—611no—
884C2×C4—611no—
885C2×C4—1221no—
886C2×C4—1221no—
887C2×C4—1221no—
888C2×C4—1221no—
889C2×C4—1224no—
890C2×C4—1224no—
891C2×C4—1221no—
892C2×C4—1221no—
893C2×C4—1221no—
894C2×C4—1221no—
895C2×C4—1221no—
896C2×C4—1221no—
897C2×C4—4881no—
898C2×C4—4881no—
899C2×C4—4881no—
900C2×C4—4881no—
901C2×C4—4881no—
902C2×C4—4881no—
903C2×C4—4881no—
904C2×C4—4881no—
905C2×C4—4881no—
906C2×C4—2441no—
907C2×C4—2441no—
908C2×C4—2441no—
909C2×C4—2441no—
910C2×C4—2441no—
911C2×C4—2441no—
912C2×C4—2441no—
913C2×C4—2441no—
914C2×C4—2441no—
915C2×C4C2×C22⋊#692311yescharacteristic
916C2×C4C2×C22⋊#692311yescharacteristic
917C2×C4C2×C22⋊#692311yescharacteristic
918C2×C4C2×C22⋊#692311yescharacteristic
919C2×C4C2×C22⋊#692311yescharacteristic
920C2×C4C23×#692311yescharacteristic
921C8—1222no—
922C8—2441no—
923C8—2441no—
924C8—2441no—
925C8—2441no—
926C8—2441no—
927C8—2441no—
928C8—2441no—
929C22—21no—
930C22—22no—
931C22—21no—
932C22—21no—
933C22—41no—
934C22—41no—
935C22—612no—
936C22—1221no—
937C22—1221no—
938C22—1222no—
939C22—1222no—
940C22—1221no—
941C22—1221no—
942C22—1221no—
943C22—4884no—
944C22—4884no—
945C22—4884no—
946C22—2441no—
947C22—2441no—
948C22—2441no—
949C22—2441no—
950C22C22×C22⋊#692311yescharacteristic
951C4—21no—
952C4—22no—
953C4—21no—
954C4—21no—
955C4—21no—
956C4—21no—
957C4—41no—
958C4—41no—
959C4—612no—
960C4—611no—
961C4—611no—
962C4—1221no—
963C4—1221no—
964C4—1221no—
965C4—1221no—
966C4—2441no—
967C4—2441no—
968C4C2×D61⋊M1611yescharacteristic
969C4C2×D61⋊M1611yescharacteristic
970C2—41no—
971C2—42no—
972C2—1222no—
973C2—2441no—
974C2—2442no—
975C2—2442no—
976C2D61⋊#40711yescharacteristic
977C2#2146244011yescharacteristic
978C2#2146245011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#520C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519823C4
cosocleC4×Dic61C24
hypercenter#520#6923
hypocenterC61#17453
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #21462741C2semidirect
2. #21462630C2semidirect
3. #21461160C2semidirect
4. #21461159C2semidirect
5. #21461157C2semidirect
6. #21461154C2semidirect
7. #21461153C2semidirect
8. #21461150C2semidirect
9. #21461146C2semidirect
10. #21461145C2semidirect
11. #21461119C2semidirect
12. #21461117C2semidirect
13. #21461113C2semidirect
14. D61⋊(D4⋊C8)C2semidirect
24. #16840784C22semidirect
25. #16840783C22semidirect
26. #16840781C22semidirect
27. #16840781C22semidirect
28. #16840780C22semidirect
29. #16840779C22semidirect
30. #16840766C22semidirect
31. #16840765C22semidirect
32. D61⋊(C4⋊C8)C22semidirect
33. C4×#11758213C22semidirect
34. C4×#11758217C22semidirect
35. C4×D61⋊C8C22semidirect
36. Q8⋊#92420C22semidirect
37. Q8⋊#92420C22semidirect
38. Q8⋊#92420C22semidirect
39. Q8⋊#92420C22semidirect
40. #16840610C22semidirect
41. #16840610C22semidirect
42. #16840610C22semidirect
43. #16840610C22semidirect
44. #16840610C22semidirect
45. #16840610C22semidirect
46. #16840610C22semidirect
47. #16840610C22semidirect
48. D4⋊#92420C22semidirect
49. D4⋊#92420C22semidirect
50. D4⋊#92420C22semidirect
51. D4⋊#92420C22semidirect
232. #11758226M16semidirect
238. D4×D61M16semidirect
564. C61#17453semidirect

Maximal subgroups

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

subgroupindex
#214627412
#214626302
#214611602
#214611592
#214611572
#214611542
#214611532
#214611502
#214611462
#214611452
#214611192
#214611172
#214611132
D61⋊(D4⋊C8)2
#214590252
#1745361