Finite Group Databasebeta

← #30610478

Subgroups — #30610478

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#21461159C211yesmaximal, characteristic, complemented
4#21461158C211yesmaximal, characteristic, complemented
5#21461156C211yesmaximal, characteristic, complemented
6#21461155C211yesmaximal, characteristic, complemented
7#21461152C211yesmaximal, characteristic, complemented
8#21461151C211yesmaximal, characteristic, complemented
9#21461145C211yesmaximal, characteristic, complemented
10#21461144C211yesmaximal, characteristic, complemented
11#21461119C211yesmaximal, characteristic, complemented
12#21461115C211yesmaximal, characteristic, complemented
13#21461111C211yesmaximal, characteristic, complemented
14D61⋊(D4⋊C8)C211yesmaximal, characteristic, complemented
15#21459023C211yesmaximal, 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
36#16840612C2211yescharacteristic, complemented
37#16840612C2211yescharacteristic, complemented
38#16840612C2211yescharacteristic, complemented
39#16840612C2211yescharacteristic, complemented
40#16840610C2211yescharacteristic, complemented
41#16840610C2211yescharacteristic, complemented
42#16840610C2211yescharacteristic, complemented
43#16840610C2211yescharacteristic, complemented
44D4⋊#92420C2211yescharacteristic, complemented
45D4⋊#92420C2211yescharacteristic, complemented
46D4⋊#92420C2211yescharacteristic, complemented
47D4⋊#92420C2211yescharacteristic, complemented
48D4⋊#92420C2211yescharacteristic, complemented
49D4⋊#92420C2211yescharacteristic, complemented
50D4⋊#92420C2211yescharacteristic, complemented
51D4⋊#92420C2211yescharacteristic, complemented
52C2×#14519822C411yescharacteristic
53#16840242C411yescharacteristic
54#16840242C411yescharacteristic
55#16840241—21no—
56#16840241C411yescharacteristic
57#16840241C411yescharacteristic
58#16840235—21no—
59#16840235—21no—
60#16840234—21no—
61#16840234C411yescharacteristic
62#16840234C411yescharacteristic
63#16840230C2211yescharacteristic
64#16840230C2211yescharacteristic
65C4×#11758224—21no—
66C4×#11758224C2211yescharacteristic
67C4×#11758224C2211yescharacteristic
68C2×D4×Dic61C2211yescharacteristic
69C2×#14519737—21no—
70C2×#14519737—21no—
71C4×D4×D61—21no—
72C4×D4×D61C2211yescharacteristic
73C4×D4×D61C2211yescharacteristic
74C61×#518C411yescharacteristic
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#14519822—24no—
108#14519822—24no—
109C2×#11758222C2×C411yescharacteristic
110C2×#11758222C2×C411yescharacteristic
111C2×#11758224—21no—
112C2×#11758224C2×C411yescharacteristic
113C2×#11758224C2×C411yescharacteristic
114C22×C22⋊D61—21no—
115C22×C22⋊D61—21no—
116C2×D4×D61—21no—
117C2×D4×D61C2×C411yescharacteristic
118C2×D4×D61C2×C411yescharacteristic
119C23×Dic61—21no—
120C22×C4×D61—21no—
121C22×C4×D61—21no—
122C4×Dic122—21no—
123C4×Dic122C2×C411yescharacteristic
124C4×Dic122C2×C411yescharacteristic
125#14519742C2×C411yescharacteristic
126#14519742D411yescharacteristic
127#14519742D411yescharacteristic
128#14519742C2311yescharacteristic
129C4×D244—21no—
130C4×D244C2×C411yescharacteristic
131C4×D244C2×C411yescharacteristic
132D4×Dic61—21no—
133D4×Dic61—21no—
134D4×Dic61C2×C411yescharacteristic
135D4×Dic61C2×C411yescharacteristic
136D4×Dic61C2311yescharacteristic
137D4×Dic61C2311yescharacteristic
138#14519739C2×C411yescharacteristic
139#14519739D411yescharacteristic
140#14519739D411yescharacteristic
141#14519739C2311yescharacteristic
142C4×C22⋊D61—21no—
143C4×C22⋊D61—21no—
144C4×C22⋊D61—21no—
145C4×C22⋊D61—21no—
146C4×C22⋊D61—21no—
147C4×C22⋊D61—21no—
148C4×C22⋊D61—21no—
149C4×C22⋊D61—21no—
150#14519737—21no—
151#14519737—21no—
152#14519737—21no—
153#14519737—21no—
154#14519737—21no—
155#14519737—21no—
156#14519737—21no—
157#14519737—21no—
158#14519737—21no—
159#14519737—21no—
160#14519737—21no—
161#14519737—21no—
162#14519737—21no—
163#14519737—21no—
164#14519737D411yescharacteristic
165#14519737D411yescharacteristic
166#14519737D411yescharacteristic
167#14519737D411yescharacteristic
168#14519735—21no—
169#14519735C2×C411yescharacteristic
170#14519735C2×C411yescharacteristic
171#14519734—21no—
172#14519734C2×C411yescharacteristic
173#14519734C2×C411yescharacteristic
174#14519733—21no—
175#14519733—21no—
176#14519733—21no—
177#14519733—21no—
178C2×C4⋊Dic61C2×C411yescharacteristic
179C2×#11758196—21no—
180C2×#11758196—21no—
181C4⋊C4×D61—21no—
182C4⋊C4×D61C2×C411yescharacteristic
183C4⋊C4×D61C2×C411yescharacteristic
184C2×C22⋊Dic61—21no—
185C2×#11758198—21no—
186C2×#11758198—21no—
187C22⋊C4×D61—21no—
188C22⋊C4×D61—21no—
189C22⋊C4×D61—21no—
190C22⋊C4×D61—21no—
191C2×C4×Dic61—21no—
192C2×C4×Dic61—21no—
193C2×C4×Dic61C2311yescharacteristic
194C42×D61—21no—
195C42×D61C2311yescharacteristic
196C42×D61C2311yescharacteristic
197C22×D4×C61C2×C411yescharacteristic
198C4×D4×C61—21no—
199C4×D4×C61—21no—
200C4×D4×C61C2×C411yescharacteristic
201C4×D4×C61C2×C411yescharacteristic
202C4×D4×C61C2×C411yescharacteristic
203C4×D4×C61C2×C411yescharacteristic
204#117×C61C2×C411yescharacteristic
205#117×C61C2×C411yescharacteristic
206C2×C22⋊C4×C61—21no—
207C2×C22⋊C4×C61—21no—
208C24×C61—21no—
209C23×D61—21no—
210C23×D61—21no—
211C2×D4×C61—22no—
212C2×D4×C61—22no—
213C2×D4×C61—21no—
214C2×D4×C61C22×C411yescharacteristic
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—28no—
222C2×C22⋊D61—28no—
223C2×C22⋊D61—21no—
224C2×C22⋊D61—21no—
225C2×C22⋊D61—21no—
226C2×C22⋊D61—21no—
227C2×C22⋊D61—21no—
228C2×C22⋊D61C22⋊C411yescharacteristic
229C2×C22⋊D61C22⋊C411yescharacteristic
230C22×Dic61—21no—
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61—21no—
234C22×Dic61—21no—
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61—81no—
238C22×Dic61—81no—
239C22×Dic61C2×D411yescharacteristic
240C22×Dic61C2×D411yescharacteristic
241#11758224—28no—
242#11758224—22no—
243#11758224—22no—
244#11758224—22no—
245#11758224M1614yescomplemented
246D4×D61—28no—
247D4×D61—22no—
248D4×D61—22no—
249D4×D61—22no—
250D4×D61M1614yescomplemented
251#11758222—22no—
252#11758222—22no—
253#11758222—22no—
254#11758222—22no—
255C2×D244C22⋊C411yescharacteristic
256C2×D244C22×C411yescharacteristic
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—21no—
264C2×C4×D61—81no—
265C2×C4×D61—81no—
266C2×C4×D61—81no—
267C2×C4×D61—81no—
268C2×C4×D61C22×C411yescharacteristic
269C2×C4×D61C22×C411yescharacteristic
270C2×C4×D61C2×D411yescharacteristic
271C2×C4×D61C2×D411yescharacteristic
272C2×C4×D61C2×D411yescharacteristic
273C2×C4×D61C2×D411yescharacteristic
274C2×Dic122C22⋊C411yescharacteristic
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×C61C22⋊C411yescharacteristic
291C4⋊C4×C61C22⋊C411yescharacteristic
292C4⋊C4×C61C22×C411yescharacteristic
293C4⋊C4×C61C22×C411yescharacteristic
294C22⋊C4×C61—21no—
295C22⋊C4×C61—21no—
296C22⋊C4×C61—21no—
297C22⋊C4×C61—21no—
298C22⋊C4×C61—21no—
299C22⋊C4×C61C22⋊C411yescharacteristic
300C22⋊C4×C61C22⋊C411yescharacteristic
301C42×C61—21no—
302C42×C61C22×C411yescharacteristic
303C42×C61C22×C411yescharacteristic
304C22⋊Dic61—21no—
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#11758198C22⋊C411yescharacteristic
315#11758198C22⋊C411yescharacteristic
316#11758198C22⋊C411yescharacteristic
317#11758198C22⋊C411yescharacteristic
318C4⋊Dic61—21no—
319C4⋊Dic61C22×C411yescharacteristic
320C4⋊Dic61C22×C411yescharacteristic
321#11758196—21no—
322#11758196—21no—
323#11758196—21no—
324#11758196—21no—
325#11758196—21no—
326#11758196—21no—
327#11758196C22⋊C411yescharacteristic
328#11758196C22⋊C411yescharacteristic
329#11758196C22⋊C411yescharacteristic
330#11758196C22⋊C411yescharacteristic
331C4×Dic61—21no—
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—24no—
346C23×C61—21no—
347C23×C61—21no—
348C23×C61—81no—
349C23×C61—81no—
350C23×C61C2×C22⋊C411yescharacteristic
351C22×D61—21no—
352C22×D61—24no—
353C22×D61—24no—
354C22×D61—81no—
355C22×D61—81no—
356C22×D61—81no—
357C22×D61—81no—
358C22×D61C2×C22⋊C411yescharacteristic
359C22×D61C2×C22⋊C411yescharacteristic
360D4×C61—24no—
361D4×C61—21no—
362D4×C61—21no—
363D4×C61C2×M1612yes—
364D4×C61C2×M1612yes—
365C2×C4×C61—21no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—81no—
370C2×C4×C61—81no—
371C2×C4×C61—81no—
372C2×C4×C61—81no—
373C2×C4×C61C2×C22⋊C411yescharacteristic
374C2×C4×C61C2×C22⋊C411yescharacteristic
375C2×C4×C61C2×C22⋊C411yescharacteristic
376C2×C4×C61C2×C22⋊C411yescharacteristic
377C2×C4×C61C2×C22⋊C411yescharacteristic
378C2×C4×C61C23×C411yescharacteristic
379C22⋊D61—24no—
380C22⋊D61—24no—
381C22⋊D61—24no—
382C22⋊D61—22no—
383C22⋊D61—24no—
384C22⋊D61—22no—
385C22⋊D61—24no—
386C2×Dic61—24no—
387C2×Dic61—21no—
388C2×Dic61—21no—
389C2×Dic61—21no—
390C2×Dic61—24no—
391C2×Dic61—21no—
392C2×Dic61—21no—
393C2×Dic61—41no—
394C2×Dic61—41no—
395C2×Dic61—41no—
396C2×Dic61—41no—
397C2×Dic61—41no—
398C2×Dic61—81no—
399C2×Dic61—81no—
400C2×Dic61—81no—
401C2×Dic61C2×C22⋊C411yescharacteristic
402C2×Dic61C2×C22⋊C411yescharacteristic
403C2×Dic61C2×C22⋊C411yescharacteristic
404C2×Dic61C2×C22⋊C411yescharacteristic
405C2×Dic61C22×D411yescharacteristic
406C2×Dic61C22×D411yescharacteristic
407D244—22no—
408D244—21no—
409D244C2×M1612yes—
410C4×D61—24no—
411C4×D61—21no—
412C4×D61—21no—
413C4×D61—21no—
414C4×D61—21no—
415C4×D61—21no—
416C4×D61—21no—
417C4×D61—41no—
418C4×D61—41no—
419C4×D61—41no—
420C4×D61—41no—
421C4×D61—81no—
422C4×D61—81no—
423C4×D61—81no—
424C4×D61—81no—
425C4×D61—81no—
426C4×D61C2×M1612yes—
427C4×D61C2×M1612yes—
428Dic122—21no—
429Dic122—22no—
430Dic122C2×M1612yes—
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—22no—
441C22×C61—22no—
442C22×C61—21no—
443C22×C61—21no—
444C22×C61—21no—
445C22×C61—41no—
446C22×C61—41no—
447C22×C61—41no—
448C22×C61—41no—
449C22×C61—84no—
450C22×C61C22×C22⋊C411yescharacteristic
451C2×D61—21no—
452C2×D61—21no—
453C2×D61—21no—
454C2×D61—22no—
455C2×D61—21no—
456C2×D61—21no—
457C2×D61—41no—
458C2×D61—41no—
459C2×D61—84no—
460C2×D61—84no—
461C2×D61#40712yes—
462C4×C61—21no—
463C4×C61—21no—
464C4×C61—21no—
465C4×C61—21no—
466C4×C61—21no—
467C4×C61—41no—
468C4×C61—41no—
469C4×C61C22×M1611yescharacteristic
470C4×C61C22×M1611yescharacteristic
471Dic61—21no—
472Dic61—22no—
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—42no—
497C2×C61—42no—
498C2×C61—41no—
499C2×C61C2×#40711yescharacteristic
500C2×C61#289711yescharacteristic
501C2×C61#290111yescharacteristic
502D61—22no—
503D61—41no—
504D61—42no—
505C2×H(5,𝔽2)—611no—
506#520—611no—
507#520—611no—
508#520—611no—
509#520—611no—
510#520—1221no—
511#518—611no—
512#518—611no—
513#518—1221no—
514#518—1221no—
515#518—1221no—
516#518#692311yescharacteristic
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—611no—
571C2×#41—1221no—
572C22×D4—611no—
573C22×D4—611no—
574C22×D4—1221no—
575C22×D4—1221no—
576C22×D4—1221no—
577C22×D4C2×#692311yescharacteristic
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—611no—
592C4×Q8—611no—
593C4×Q8—1221no—
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—1221no—
611C4×D4—1221no—
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×D4C2×#692311yescharacteristic
636C4×D4C2×#692311yescharacteristic
637C4×D4C2×#692311yescharacteristic
638C4×D4C2×#692311yescharacteristic
639#117—611no—
640#117—611no—
641#117—611no—
642#117—611no—
643#117—1221no—
644#117—1221no—
645#117—1221no—
646#117—1221no—
647#117—1221no—
648#117—1221no—
649#117C2×#692311yescharacteristic
650#117C2×#692311yescharacteristic
651C2×C4⋊C4—611no—
652C2×C4⋊C4—611no—
653C2×C4⋊C4—611no—
654C2×C4⋊C4—1221no—
655C2×C4⋊C4—1221no—
656C2×C4⋊C4—1221no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
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—21no—
699C24—1221no—
700C24—1221no—
701#41—614no—
702#41—1222no—
703#41—1222no—
704#41—1222no—
705#41—1222no—
706#41—1222no—
707#41—1222no—
708#41—1228no—
709#41—1222no—
710C2×Q8—611no—
711C2×Q8—611no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—21no—
715C2×D4—614no—
716C2×D4—611no—
717C2×D4—611no—
718C2×D4—611no—
719C2×D4—611no—
720C2×D4—1222no—
721C2×D4—1221no—
722C2×D4—1221no—
723C2×D4—1222no—
724C2×D4—1228no—
725C2×D4—1221no—
726C2×D4—1221no—
727C2×D4—1228no—
728C2×D4—1228no—
729C2×D4—1221no—
730C2×D4—1222no—
731C2×D4C22×#692311yescharacteristic
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—611no—
781C4⋊C4—611no—
782C4⋊C4—611no—
783C4⋊C4—611no—
784C4⋊C4—611no—
785C4⋊C4—611no—
786C4⋊C4—1221no—
787C4⋊C4—1221no—
788C4⋊C4—1221no—
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—21no—
800C22⋊C4—21no—
801C22⋊C4—21no—
802C22⋊C4—611no—
803C22⋊C4—611no—
804C22⋊C4—611no—
805C22⋊C4—611no—
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—611no—
820C42—611no—
821C42—611no—
822C42—611no—
823C42—611no—
824C42—611no—
825C42—611no—
826C42—611no—
827C42—1221no—
828C42—1221no—
829C42—1221no—
830C42—1221no—
831C42—1221no—
832C42—1221no—
833C42C22×#692311yescharacteristic
834C42C22×#692311yescharacteristic
835C23—24no—
836C23—21no—
837C23—21no—
838C23—81no—
839C23—81no—
840C23—611no—
841C23—611no—
842C23—1224no—
843C23—1224no—
844C23—1221no—
845C23—4881no—
846C23—4881no—
847C23—4881no—
848C23—4881no—
849C23C2×C22⋊#692311yescharacteristic
850Q8—612no—
851Q8—1222no—
852Q8—1221no—
853D4—24no—
854D4—21no—
855D4—21no—
856D4—612no—
857D4—1222no—
858D4—1222no—
859D4—1224no—
860D4—1222no—
861D4—1224no—
862D4—1224no—
863D4—1224no—
864D4—1224no—
865D4—1221no—
866D4D61⋊M1612yes—
867D4D61⋊M1612yes—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—81no—
873C2×C4—81no—
874C2×C4—81no—
875C2×C4—81no—
876C2×C4—611no—
877C2×C4—611no—
878C2×C4—612no—
879C2×C4—612no—
880C2×C4—611no—
881C2×C4—611no—
882C2×C4—611no—
883C2×C4—611no—
884C2×C4—1221no—
885C2×C4—1221no—
886C2×C4—1221no—
887C2×C4—1221no—
888C2×C4—1224no—
889C2×C4—1221no—
890C2×C4—1221no—
891C2×C4—1224no—
892C2×C4—1224no—
893C2×C4—1221no—
894C2×C4—1221no—
895C2×C4—1221no—
896C2×C4—1221no—
897C2×C4—1221no—
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—22no—
932C22—21no—
933C22—21no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—84no—
939C22—612no—
940C22—1221no—
941C22—1221no—
942C22—1222no—
943C22—1221no—
944C22—1221no—
945C22—1221no—
946C22—4884no—
947C22—4884no—
948C22—2441no—
949C22—2441no—
950C22C22×C22⋊#692311yescharacteristic
951C4—21no—
952C4—21no—
953C4—21no—
954C4—21no—
955C4—21no—
956C4—41no—
957C4—41no—
958C4—612no—
959C4—611no—
960C4—611no—
961C4—1221no—
962C4—1222no—
963C4—1221no—
964C4—1221no—
965C4—1221no—
966C4—2441no—
967C4—2441no—
968C4C2×D61⋊M1611yescharacteristic
969C4C2×D61⋊M1611yescharacteristic
970C2—41no—
971C2—42no—
972C2—42no—
973C2—1222no—
974C2—2441no—
975C2—2442no—
976C2D61⋊#40711yescharacteristic
977C2#2146244011yescharacteristic
978C2#2146244911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#518C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519822C4
cosocleC4×Dic61C24
hypercenter#518#6923
hypocenterC61#17453
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #21462741C2semidirect
2. #21462630C2semidirect
3. #21461159C2semidirect
4. #21461158C2semidirect
5. #21461156C2semidirect
6. #21461155C2semidirect
7. #21461152C2semidirect
8. #21461151C2semidirect
9. #21461145C2semidirect
10. #21461144C2semidirect
11. #21461119C2semidirect
12. #21461115C2semidirect
13. #21461111C2semidirect
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. #16840612C22semidirect
37. #16840612C22semidirect
38. #16840612C22semidirect
39. #16840612C22semidirect
40. #16840610C22semidirect
41. #16840610C22semidirect
42. #16840610C22semidirect
43. #16840610C22semidirect
44. D4⋊#92420C22semidirect
45. D4⋊#92420C22semidirect
46. D4⋊#92420C22semidirect
47. D4⋊#92420C22semidirect
48. D4⋊#92420C22semidirect
49. D4⋊#92420C22semidirect
50. D4⋊#92420C22semidirect
51. D4⋊#92420C22semidirect
245. #11758224M16semidirect
250. 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
#214611592
#214611582
#214611562
#214611552
#214611522
#214611512
#214611452
#214611442
#214611192
#214611152
#214611112
D61⋊(D4⋊C8)2
#214590232
#1745361