Finite Group Databasebeta

← #30615600

Subgroups — #30615600

Order 15616.

1986 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519856C211yesmaximal, characteristic, complemented
2C2×#16840752C212yesmaximal, complemented
3C2×D61⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
4#21461807C212yesmaximal, complemented
5#21461806C212yesmaximal, complemented
6#21461805C212yesmaximal, complemented
7#21461804C212yesmaximal, complemented
8#21461504C212yesmaximal, complemented
9#525×D61C211yesmaximal, characteristic
10C22×D61⋊C8C2212yes—
11C2×#14519856—28no—
12C2×#14519856—21no—
13C2×#14519856—21no—
14C2×#14519856C2212yes—
15C2×#14519856C2212yes—
16C22×C4⋊#6923C2212yes—
17C22×C22⋊#6923—21no—
18C22×C4×#6923—21no—
19#16840752—28no—
20C2×#14519840C2214yescomplemented
21C2×#14519839C2214yescomplemented
22C2×#14519834—21no—
23D61⋊(C22⋊C8)—21no—
24D61⋊(C22⋊C8)—21no—
25D61⋊(C22⋊C8)C2212yes—
26D61⋊(C22⋊C8)C2212yes—
27C2×C22⋊#92420—21no—
28#16840635C2214yescomplemented
29#16840635C2214yescomplemented
30C2×#41×D61C2211yescharacteristic
31C23×C4×D61C2211yescharacteristic
32#16840275C411yescharacteristic, complemented
33#16840275C411yescharacteristic, complemented
34#16840274C411yescharacteristic, complemented
35#16840273C411yescharacteristic, complemented
36#16840272C411yescharacteristic, complemented
37#16840272C411yescharacteristic, complemented
38#16840271—21no—
39#16840271—21no—
40#16840270—21no—
41#16840269C411yescharacteristic, complemented
42#16840268—21no—
43#123×D61—21no—
44C22⋊Q8×D61C2211yescharacteristic
45C22⋊Q8×D61C2211yescharacteristic
46#121×D61C2211yescharacteristic
47#121×D61C2211yescharacteristic
48#120×D61—21no—
49C4×D4×D61—21no—
50C4×D4×D61—21no—
51#117×D61C2211yescharacteristic
52C61×#525C411yescharacteristic, complemented
53C23×#6923—22no—
54C2×D61⋊C8—24no—
55C2×D61⋊C8—24no—
56C2×D61⋊C8—22no—
57C2×D61⋊C8C2314yes—
58C22×#92420—22no—
59#14519856—28no—
60#14519856—28no—
61#14519856—24no—
62#14519856—28no—
63#14519856D418yescomplemented
64C2×C4⋊#6923—22no—
65C2×C4⋊#6923—28no—
66C2×C4⋊#6923C2314yes—
67C2×C22⋊#6923—28no—
68C2×C22⋊#6923—22no—
69C2×C22⋊#6923—22no—
70C2×C4×#6923—28no—
71C2×C4×#6923—22no—
72C2×C4×#6923—22no—
73#14519840—28no—
74#14519839—28no—
75#14519834—22no—
76#14519834—22no—
77C22⋊#92420—22no—
78C22⋊#92420—22no—
79C24×D61D411yescharacteristic
80C2×#11758226C2×C411yescharacteristic, complemented
81C2×#11758222—21no—
82C2×#11758222C2×C411yescharacteristic, complemented
83C2×#11758224—21no—
84C2×#11758224C2×C411yescharacteristic, complemented
85#41×D61—24no—
86#41×D61—24no—
87C2×Q8×D61C2311yescharacteristic
88C2×D4×D61—21no—
89C2×D4×D61—21no—
90C2×D4×D61—21no—
91C2×D4×D61C2311yescharacteristic
92C23×Dic61D411yescharacteristic
93C22×C4×D61—24no—
94C22×C4×D61—24no—
95C22×C4×D61—21no—
96C22×C4×D61C2×C411yescharacteristic
97C22×C4×D61C2×C411yescharacteristic
98C22×C4×D61C2×C411yescharacteristic
99C22×C4×D61D411yescharacteristic
100C22×C4×D61D411yescharacteristic
101C22×C4×D61D411yescharacteristic
102C22×C4×D61D411yescharacteristic
103C22×C4×D61D411yescharacteristic
104C22×C4×D61D411yescharacteristic
105C22×C4×D61C2311yescharacteristic
106C22×C4×D61C2311yescharacteristic
107C22×C4×D61C2311yescharacteristic
108#14519762—21no—
109#14519762—21no—
110#14519761—21no—
111#14519760—21no—
112#14519759—21no—
113#14519759—21no—
114#14519758—21no—
115#14519757C2×C411yescharacteristic
116#14519757C2×C411yescharacteristic, complemented
117#14519756C2×C411yescharacteristic
118#14519756C2×C411yescharacteristic, complemented
119#14519755—21no—
120#14519755—21no—
121#14519754—21no—
122#14519754—21no—
123#14519753C2×C411yescharacteristic
124#14519753C2×C411yescharacteristic, complemented
125#14519752C2×C411yescharacteristic
126#14519752C2×C411yescharacteristic, complemented
127#14519751C2×C411yescharacteristic
128#14519751C2×C411yescharacteristic, complemented
129#14519750—21no—
130#14519750—21no—
131#14519749—21no—
132#14519749—21no—
133#14519748C2×C411yescharacteristic
134#14519748C2×C411yescharacteristic, complemented
135#14519747—21no—
136#14519747—21no—
137#14519747—21no—
138#14519746—21no—
139#14519745—21no—
140#14519745—21no—
141#14519745—21no—
142C4×D244—21no—
143C4×D244—21no—
144D4×Dic61—21no—
145D4×Dic61—21no—
146#14519739—21no—
147#14519739—21no—
148C4×C22⋊D61—21no—
149C4×C22⋊D61—21no—
150C4×C22⋊D61—21no—
151C4×C22⋊D61—21no—
152#14519737—21no—
153#14519737—21no—
154#14519737—21no—
155#14519737—21no—
156#14519736C2×C411yescharacteristic, complemented
157#14519735C2×C411yescharacteristic, complemented
158#14519735C2×C411yescharacteristic, complemented
159#14519734—21no—
160#14519733—21no—
161C4⋊C4×D61—21no—
162C4⋊C4×D61—21no—
163C4⋊C4×D61C2311yescharacteristic
164C4⋊C4×D61C2311yescharacteristic
165C22⋊C4×D61—21no—
166C22⋊C4×D61—21no—
167C22⋊C4×D61—21no—
168C22⋊C4×D61—21no—
169C22⋊C4×D61—21no—
170C42×D61—21no—
171C2×#41×C61C2×C411yescharacteristic, complemented
172C23×C4×C61C2×C411yescharacteristic
173#123×C61—21no—
174C22⋊Q8×C61C2×C411yescharacteristic
175C22⋊Q8×C61C2×C411yescharacteristic, complemented
176#121×C61C2×C411yescharacteristic
177#121×C61C2×C411yescharacteristic, complemented
178#120×C61—21no—
179C4×D4×C61—21no—
180C4×D4×C61—21no—
181#117×C61C2×C411yescharacteristic, complemented
182C24×C61C22⋊C411yescharacteristic
183C23×D61—22no—
184C23×D61—22no—
185C23×D61—24no—
186C23×D61—21no—
187C23×D61—42no—
188C23×D61C22⋊C411yescharacteristic
189C23×D61C22⋊C411yescharacteristic
190C23×D61C22⋊C411yescharacteristic
191C23×D61C2×D411yescharacteristic
192C23×D61C2×D411yescharacteristic
193C23×D61C2×D411yescharacteristic
194C22×#6923—28no—
195C22×#6923—24no—
196C22×#6923—44no—
197C22×#6923—44no—
198#41×C61—24no—
199C2×Q8×C61C22×C411yescharacteristic
200C2×D4×C61—21no—
201C2×D4×C61—21no—
202C2×D4×C61—21no—
203C2×D4×C61C22×C411yescharacteristic
204C22×C4×C61—24no—
205C22×C4×C61—21no—
206C22×C4×C61C22⋊C411yescharacteristic
207C22×C4×C61C22⋊C411yescharacteristic
208C22×C4×C61C22⋊C411yescharacteristic
209C22×C4×C61C22×C411yescharacteristic
210C22×C4×C61C22×C411yescharacteristic
211C22×C4×C61C22×C411yescharacteristic
212C2×C22⋊D61—21no—
213C2×C22⋊D61—21no—
214C2×C22⋊D61—21no—
215C2×C22⋊D61—21no—
216C2×C22⋊D61—21no—
217C2×C22⋊D61—21no—
218C2×C22⋊D61—21no—
219C22×Dic61—24no—
220C22×Dic61—21no—
221C22×Dic61C22⋊C411yescharacteristic
222C22×Dic61C22⋊C411yescharacteristic
223C22×Dic61C22⋊C411yescharacteristic
224C22×Dic61C2×D411yescharacteristic
225C22×Dic61C2×D411yescharacteristic
226C22×Dic61C2×D411yescharacteristic
227#11758226—24no—
228Q8×D61—22no—
229Q8×D61—22no—
230#11758224—24no—
231#11758224—44no—
232D4×D61—22no—
233D4×D61—22no—
234D4×D61—44no—
235D4×D61—42no—
236D4×D61—42no—
237D4×D61—44no—
238#11758222—24no—
239#11758222—44no—
240C2×D244—21no—
241C2×D244—21no—
242C2×D244—21no—
243C2×D244C22×C411yescharacteristic
244C2×C4×D61—22no—
245C2×C4×D61—22no—
246C2×C4×D61—24no—
247C2×C4×D61—24no—
248C2×C4×D61—24no—
249C2×C4×D61—24no—
250C2×C4×D61—22no—
251C2×C4×D61—22no—
252C2×C4×D61—24no—
253C2×C4×D61—24no—
254C2×C4×D61—22no—
255C2×C4×D61—22no—
256C2×C4×D61—22no—
257C2×C4×D61—22no—
258C2×C4×D61—22no—
259C2×C4×D61—22no—
260C2×C4×D61—21no—
261C2×C4×D61—21no—
262C2×C4×D61—21no—
263C2×C4×D61—21no—
264C2×C4×D61—21no—
265C2×C4×D61—42no—
266C2×C4×D61—42no—
267C2×C4×D61C22⋊C411yescharacteristic
268C2×C4×D61C22⋊C411yescharacteristic
269C2×C4×D61C22⋊C411yescharacteristic
270C2×C4×D61C22⋊C411yescharacteristic
271C2×C4×D61C22⋊C411yescharacteristic
272C2×C4×D61C22⋊C411yescharacteristic
273C2×C4×D61C22×C411yescharacteristic
274C2×C4×D61C22×C411yescharacteristic
275C2×C4×D61C22×C411yescharacteristic
276C2×C4×D61C2×D411yescharacteristic
277C2×C4×D61C2×D411yescharacteristic
278C2×C4×D61C2×D411yescharacteristic
279C2×C4×D61C2×D411yescharacteristic
280C2×C4×D61C2×D414yes—
281C2×C4×D61C2×D411yescharacteristic
282C2×C4×D61C2×D411yescharacteristic
283C2×C4×D61#4114yes—
284C2×C4×D61C2411yescharacteristic
285C2×Dic122—21no—
286C2×Dic122C22×C411yescharacteristic
287C22⋊#6923—28no—
288C22⋊#6923—28no—
289C2×#92420—24no—
290C2×#92420—44no—
291C4⋊#6923—28no—
292C4⋊#6923—24no—
293C4⋊#6923C2×D418yes—
294C4×#6923—28no—
295C4×#6923—28no—
296D61⋊C8—24no—
297D61⋊C8—24no—
298D61⋊C8—44no—
299C4⋊C4×C61—21no—
300C4⋊C4×C61—21no—
301C4⋊C4×C61C22×C411yescharacteristic
302C4⋊C4×C61C22×C411yescharacteristic
303C22⋊C4×C61—21no—
304C22⋊C4×C61—21no—
305C22⋊C4×C61—21no—
306C22⋊C4×C61—21no—
307C22⋊C4×C61—21no—
308C42×C61—21no—
309C22⋊Dic61—21no—
310C22⋊Dic61—21no—
311C22⋊Dic61—21no—
312C22⋊Dic61—21no—
313C22⋊Dic61—21no—
314#11758198—21no—
315#11758198—21no—
316#11758198—21no—
317#11758198—21no—
318#11758198—21no—
319#11758198—21no—
320#11758198—21no—
321#11758198—21no—
322#11758198—21no—
323#11758198—21no—
324C4⋊Dic61—21no—
325C4⋊Dic61—21no—
326C4⋊Dic61C22×C411yescharacteristic
327C4⋊Dic61C22×C411yescharacteristic
328#11758196—21no—
329#11758196—21no—
330#11758196—21no—
331#11758196—21no—
332#11758196—21no—
333#11758196—21no—
334C4×Dic61—21no—
335C4×Dic61—21no—
336C4×Dic61—21no—
337C23×C61—22no—
338C23×C61—22no—
339C23×C61—21no—
340C23×C61—41no—
341C23×C61C2×C22⋊C411yescharacteristic
342C23×C61C2×C22⋊C411yescharacteristic
343C23×C61C2×C22⋊C411yescharacteristic
344C22×D61—21no—
345C22×D61—21no—
346C22×D61—22no—
347C22×D61—22no—
348C22×D61—22no—
349C22×D61—22no—
350C22×D61—22no—
351C22×D61—21no—
352C22×D61—21no—
353C22×D61—22no—
354C22×D61—22no—
355C22×D61—22no—
356C22×D61—22no—
357C22×D61—22no—
358C22×D61—22no—
359C22×D61—21no—
360C22×D61—41no—
361C22×D61—41no—
362C22×D61—41no—
363C22×D61—48no—
364C22×D61—48no—
365C22×D61—41no—
366C22×D61—41no—
367C22×D61—42no—
368C22×D61—42no—
369C22×D61C2×C22⋊C411yescharacteristic
370C22×D61C2×C22⋊C411yescharacteristic
371C22×D61C2×C22⋊C411yescharacteristic
372C22×D61#12012yes—
373C22×D61#12312yes—
374C22×D61#13514yes—
375C22×D61C22×D411yescharacteristic
376C2×#6923—28no—
377C2×#6923—416no—
378C2×#6923—44no—
379C2×#6923—44no—
380Q8×C61—22no—
381D4×C61—22no—
382D4×C61—42no—
383D4×C61—42no—
384D4×C61—42no—
385C2×C4×C61—22no—
386C2×C4×C61—22no—
387C2×C4×C61—22no—
388C2×C4×C61—22no—
389C2×C4×C61—22no—
390C2×C4×C61—21no—
391C2×C4×C61—21no—
392C2×C4×C61—21no—
393C2×C4×C61—42no—
394C2×C4×C61C2×C22⋊C411yescharacteristic
395C2×C4×C61C2×C22⋊C411yescharacteristic
396C2×C4×C61C2×C22⋊C411yescharacteristic
397C2×C4×C61C4×D414yes—
398C2×C4×C61C23×C411yescharacteristic
399C22⋊D61—42no—
400C22⋊D61—42no—
401C22⋊D61—42no—
402C22⋊D61—42no—
403C22⋊D61—42no—
404C22⋊D61—42no—
405C22⋊D61—42no—
406C2×Dic61—22no—
407C2×Dic61—22no—
408C2×Dic61—22no—
409C2×Dic61—22no—
410C2×Dic61—22no—
411C2×Dic61—21no—
412C2×Dic61—21no—
413C2×Dic61—21no—
414C2×Dic61—42no—
415C2×Dic61C2×C22⋊C411yescharacteristic
416C2×Dic61C2×C22⋊C411yescharacteristic
417C2×Dic61C2×C22⋊C411yescharacteristic
418C2×Dic61#12114yes—
419C2×Dic61C22×D411yescharacteristic
420D244—22no—
421D244—42no—
422D244—42no—
423D244—42no—
424C4×D61—21no—
425C4×D61—21no—
426C4×D61—21no—
427C4×D61—21no—
428C4×D61—22no—
429C4×D61—22no—
430C4×D61—22no—
431C4×D61—22no—
432C4×D61—22no—
433C4×D61—22no—
434C4×D61—22no—
435C4×D61—22no—
436C4×D61—22no—
437C4×D61—22no—
438C4×D61—41no—
439C4×D61—41no—
440C4×D61—42no—
441C4×D61—42no—
442C4×D61—42no—
443C4×D61—42no—
444C4×D61C4×D414yes—
445C4×D61#12012yes—
446C4×D61#12114yes—
447C4×D61#12312yes—
448C4×D61C22×D412yes—
449C4×D61C2×#4112yes—
450Dic122—22no—
451Dic122—42no—
452#92420—44no—
453#20908—611nomaximal, Sylow
454C22×C61—21no—
455C22×C61—21no—
456C22×C61—21no—
457C22×C61—21no—
458C22×C61—21no—
459C22×C61—21no—
460C22×C61—21no—
461C22×C61—44no—
462C22×C61—41no—
463C22×C61—41no—
464C22×C61—41no—
465C22×C61#38612yes—
466C22×C61#41612yescomplemented
467C22×C61C22×C22⋊C411yescharacteristic
468C2×D61—21no—
469C2×D61—21no—
470C2×D61—21no—
471C2×D61—21no—
472C2×D61—24no—
473C2×D61—24no—
474C2×D61—24no—
475C2×D61—24no—
476C2×D61—21no—
477C2×D61—21no—
478C2×D61—21no—
479C2×D61—44no—
480C2×D61—44no—
481C2×D61—44no—
482C2×D61—42no—
483C2×D61—42no—
484C2×D61—41no—
485C2×D61—41no—
486C2×D61—41no—
487C2×D61—82no—
488C2×D61—82no—
489C2×D61#38612yes—
490C2×D61#41612yescomplemented
491C2×D61C2×#12011yescharacteristic
492C2×D61C2×#12311yescharacteristic
493C2×D61C2×#13512yes—
494C2×D61#57512yes—
495#6923—48no—
496C4×C61—21no—
497C4×C61—21no—
498C4×C61—41no—
499C4×C61—41no—
500C4×C61—41no—
501C4×C61#38612yes—
502C4×C61C2×C4×D412yes—
503Dic61—21no—
504Dic61—21no—
505Dic61—41no—
506Dic61—41no—
507Dic61—41no—
508Dic61#38612yes—
509Dic61C2×#12112yes—
510C2×#525—611no—
511C22×#117—611no—
512C2×#416—612no—
513C22×C22⋊C8—611no—
514#1875—612no—
515#1874—612no—
516#1873—612no—
517#1872—612no—
518#1735—612no—
519C2×C61—22no—
520C2×C61—22no—
521C2×C61—41no—
522C2×C61—81no—
523C2×C61C2×#38611yescharacteristic
524C2×C61C2×#41611yescharacteristic
525C2×C61#289611yescharacteristic
526D61—22no—
527D61—22no—
528D61—41no—
529D61—81no—
530D61#300212yes—
531D61#309112yes—
532C22×#41—611no—
533C24×C4—611no—
534C23×C8—612no—
535#525—611no—
536#525—611no—
537#525—611no—
538#525—611no—
539#525—611no—
540#525—611no—
541#525—611no—
542#525—1221no—
543#525—1221no—
544#525—1221no—
545#525—1221no—
546#525#692311yescharacteristic, complemented
547C2×#123—1221no—
548C2×C22⋊Q8—611no—
549C2×C22⋊Q8—611no—
550C2×#121—611no—
551C2×#121—611no—
552C2×#120—1221no—
553C2×C4×D4—1221no—
554C2×C4×D4—1221no—
555C2×#117—612no—
556C2×#117—611no—
557C2×#117—612no—
558C2×#117—1228no—
559C2×#117—1221no—
560C2×#117—1221no—
561C22×C4⋊C4—612no—
562C22×C22⋊C4—1221no—
563C22×C42—1221no—
564#416—1228no—
565C2×#103—614no—
566C2×#102—614no—
567C2×C22⋊C8—612no—
568C2×C22⋊C8—612no—
569C2×C22⋊C8—1221no—
570C2×C22⋊C8—1221no—
571C2×C22⋊C8—1221no—
572C2×C22⋊C8—1221no—
573#340—614no—
574#340—614no—
575C61#2090811yescharacteristic, complemented, Sylow
576C25—611no—
577C2×#41—611no—
578C2×#41—611no—
579C2×#41—611no—
580C2×#41—1221no—
581C2×#41—1221no—
582C2×#41—1224no—
583C2×#41—1224no—
584C2×#41C2×#692311yescharacteristic, complemented
585C22×Q8—611no—
586C22×D4—611no—
587C22×D4—1221no—
588C22×D4—1221no—
589C22×D4—1221no—
590C23×C4—611no—
591C23×C4—611no—
592C23×C4—611no—
593C23×C4—611no—
594C23×C4—611no—
595C23×C4—611no—
596C23×C4—611no—
597C23×C4—611no—
598C23×C4—611no—
599C23×C4—611no—
600C23×C4—611no—
601C23×C4—611no—
602C23×C4—611no—
603C23×C4—1224no—
604C23×C4—1224no—
605C23×C4—1221no—
606C23×C4—1222no—
607C23×C4C2×#692311yescharacteristic
608C22×C8—614no—
609C22×C8—1222no—
610C22×C8—1224no—
611C22×C8—1222no—
612C22×C8—1224no—
613#123—21no—
614#123—1221no—
615#123—1221no—
616#123—1221no—
617#123—1221no—
618#123—1221no—
619#123—1221no—
620#123—1221no—
621C22⋊Q8—611no—
622C22⋊Q8—611no—
623C22⋊Q8—611no—
624C22⋊Q8—611no—
625C22⋊Q8—611no—
626C22⋊Q8—611no—
627C22⋊Q8—1221no—
628C22⋊Q8—1221no—
629C22⋊Q8—1221no—
630C22⋊Q8—1221no—
631C22⋊Q8C2×#692311yescharacteristic
632C22⋊Q8C2×#692311yescharacteristic, complemented
633#121—611no—
634#121—611no—
635#121—611no—
636#121—611no—
637#121—611no—
638#121—611no—
639#121—1221no—
640#121—1221no—
641#121—1221no—
642#121—1221no—
643#121C2×#692311yescharacteristic
644#121C2×#692311yescharacteristic, complemented
645#120—21no—
646#120—1221no—
647#120—1221no—
648#120—1221no—
649#120—1221no—
650#120—1221no—
651#120—1221no—
652#120—1221no—
653C4×D4—21no—
654C4×D4—21no—
655C4×D4—1221no—
656C4×D4—1221no—
657C4×D4—1221no—
658C4×D4—1221no—
659C4×D4—1221no—
660C4×D4—1221no—
661C4×D4—1221no—
662C4×D4—1221no—
663C4×D4—1221no—
664C4×D4—1221no—
665C4×D4—1221no—
666C4×D4—1221no—
667C4×D4—1221no—
668C4×D4—1221no—
669#117—618no—
670#117—611no—
671#117—611no—
672#117—611no—
673#117—1221no—
674#117—1221no—
675#117—1228no—
676#117—1224no—
677#117—1228no—
678#117—1228no—
679#117C2×#692311yescharacteristic, complemented
680C2×C4⋊C4—614no—
681C2×C4⋊C4—611no—
682C2×C4⋊C4—611no—
683C2×C4⋊C4—1221no—
684C2×C4⋊C4—1221no—
685C2×C4⋊C4—1228no—
686C2×C4⋊C4—1222no—
687C2×C22⋊C4—1221no—
688C2×C22⋊C4—1221no—
689C2×C22⋊C4—1221no—
690C2×C22⋊C4—1221no—
691C2×C22⋊C4—1221no—
692C2×C22⋊C4—1222no—
693C2×C22⋊C4—1222no—
694C2×C22⋊C4—1228no—
695C2×C42—1221no—
696C2×C42—1222no—
697C2×C42—1222no—
698C2×C42—1228no—
699#103—1228no—
700#102—1228no—
701C22⋊C8—1222no—
702C22⋊C8—1222no—
703C22⋊C8—1222no—
704C22⋊C8—1222no—
705C24—611no—
706C24—611no—
707C24—611no—
708C24—611no—
709C24—611no—
710C24—611no—
711C24—1222no—
712C24—1222no—
713C24—1224no—
714C24—1221no—
715C24—2442no—
716C24C22⋊#692311yescharacteristic
717#41—24no—
718#41—1224no—
719#41—1224no—
720#41—1224no—
721#41—2444no—
722#41—2444no—
723C2×Q8—611no—
724C2×Q8—1221no—
725C2×Q8—1222no—
726C2×Q8—1222no—
727C2×Q8C22×#692311yescharacteristic
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—611no—
732C2×D4—1221no—
733C2×D4—1221no—
734C2×D4—1221no—
735C2×D4—1222no—
736C2×D4—1222no—
737C2×D4—1221no—
738C2×D4—1221no—
739C2×D4—1221no—
740C2×D4—1221no—
741C2×D4—1221no—
742C2×D4—1221no—
743C2×D4—1221no—
744C2×D4—2442no—
745C2×D4—2442no—
746C2×D4—2444no—
747C2×D4—2444no—
748C2×D4C22×#692311yescharacteristic
749C22×C4—24no—
750C22×C4—21no—
751C22×C4—611no—
752C22×C4—611no—
753C22×C4—611no—
754C22×C4—614no—
755C22×C4—614no—
756C22×C4—611no—
757C22×C4—611no—
758C22×C4—611no—
759C22×C4—611no—
760C22×C4—611no—
761C22×C4—611no—
762C22×C4—611no—
763C22×C4—611no—
764C22×C4—611no—
765C22×C4—611no—
766C22×C4—611no—
767C22×C4—611no—
768C22×C4—611no—
769C22×C4—611no—
770C22×C4—611no—
771C22×C4—611no—
772C22×C4—611no—
773C22×C4—611no—
774C22×C4—611no—
775C22×C4—1222no—
776C22×C4—1222no—
777C22×C4—1222no—
778C22×C4—1222no—
779C22×C4—1224no—
780C22×C4—1224no—
781C22×C4—1224no—
782C22×C4—1222no—
783C22×C4—1222no—
784C22×C4—1224no—
785C22×C4—1224no—
786C22×C4—1222no—
787C22×C4—1222no—
788C22×C4—1221no—
789C22×C4—1222no—
790C22×C4—1222no—
791C22×C4—1221no—
792C22×C4—1221no—
793C22×C4—1221no—
794C22×C4—1224no—
795C22×C4—1221no—
796C22×C4—1224no—
797C22×C4—1224no—
798C22×C4—1228no—
799C22×C4—1221no—
800C22×C4—2442no—
801C22×C4—2442no—
802C22×C4—2444no—
803C22×C4—2444no—
804C22×C4C22⋊#692311yescharacteristic
805C22×C4C22⋊#692311yescharacteristic
806C22×C4C22⋊#692311yescharacteristic
807C22×C4C22×#692311yescharacteristic
808C22×C4C22×#692311yescharacteristic
809C22×C4C22×#692311yescharacteristic
810C2×C8—1224no—
811C2×C8—1224no—
812C2×C8—1224no—
813C2×C8—2444no—
814C2×C8—2444no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—618no—
818C4⋊C4—611no—
819C4⋊C4—611no—
820C4⋊C4—1221no—
821C4⋊C4—1221no—
822C4⋊C4—1221no—
823C4⋊C4—1221no—
824C4⋊C4—1221no—
825C4⋊C4—1221no—
826C4⋊C4—1224no—
827C4⋊C4—1228no—
828C4⋊C4—1221no—
829C4⋊C4—1221no—
830C4⋊C4C22×#692311yescharacteristic
831C4⋊C4C22×#692311yescharacteristic
832C22⋊C4—21no—
833C22⋊C4—21no—
834C22⋊C4—21no—
835C22⋊C4—21no—
836C22⋊C4—21no—
837C22⋊C4—1221no—
838C22⋊C4—1221no—
839C22⋊C4—1221no—
840C22⋊C4—1221no—
841C22⋊C4—1221no—
842C22⋊C4—1221no—
843C22⋊C4—1221no—
844C22⋊C4—1221no—
845C22⋊C4—1221no—
846C22⋊C4—1221no—
847C22⋊C4—1228no—
848C22⋊C4—1228no—
849C22⋊C4—1221no—
850C22⋊C4—1221no—
851C22⋊C4—1221no—
852C22⋊C4—1221no—
853C22⋊C4—1221no—
854C42—21no—
855C42—1221no—
856C42—1221no—
857C42—1228no—
858C42—1228no—
859C42—1221no—
860C23—22no—
861C23—22no—
862C23—21no—
863C23—41no—
864C23—611no—
865C23—612no—
866C23—612no—
867C23—614no—
868C23—611no—
869C23—611no—
870C23—611no—
871C23—1221no—
872C23—1221no—
873C23—1222no—
874C23—1222no—
875C23—1222no—
876C23—1221no—
877C23—1222no—
878C23—1221no—
879C23—1222no—
880C23—1222no—
881C23—1222no—
882C23—1222no—
883C23—1222no—
884C23—1222no—
885C23—1222no—
886C23—1221no—
887C23—2441no—
888C23—2441no—
889C23—2441no—
890C23—2441no—
891C23—2441no—
892C23—2442no—
893C23—2442no—
894C23—2448no—
895C23—2448no—
896C23C2×C22⋊#692311yescharacteristic
897C23C2×C22⋊#692311yescharacteristic
898C23C2×C22⋊#692311yescharacteristic
899Q8—22no—
900Q8—1222no—
901Q8—2442no—
902D4—22no—
903D4—42no—
904D4—42no—
905D4—42no—
906D4—1222no—
907D4—2442no—
908D4—2442no—
909D4—2442no—
910D4—2442no—
911D4—2442no—
912D4—2442no—
913D4—2442no—
914D4—2442no—
915D4—2442no—
916D4—2442no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—42no—
926C2×C4—614no—
927C2×C4—611no—
928C2×C4—611no—
929C2×C4—612no—
930C2×C4—614no—
931C2×C4—612no—
932C2×C4—614no—
933C2×C4—612no—
934C2×C4—612no—
935C2×C4—611no—
936C2×C4—611no—
937C2×C4—1222no—
938C2×C4—1222no—
939C2×C4—1222no—
940C2×C4—1222no—
941C2×C4—1221no—
942C2×C4—1221no—
943C2×C4—1221no—
944C2×C4—1221no—
945C2×C4—1222no—
946C2×C4—1222no—
947C2×C4—1222no—
948C2×C4—1222no—
949C2×C4—1222no—
950C2×C4—1222no—
951C2×C4—1222no—
952C2×C4—1222no—
953C2×C4—1222no—
954C2×C4—1222no—
955C2×C4—1222no—
956C2×C4—1228no—
957C2×C4—1221no—
958C2×C4—1221no—
959C2×C4—1221no—
960C2×C4—2442no—
961C2×C4—2441no—
962C2×C4—2441no—
963C2×C4—2442no—
964C2×C4—2442no—
965C2×C4—2442no—
966C2×C4—2444no—
967C2×C4—2444no—
968C2×C4—24416no—
969C2×C4—2442no—
970C2×C4C2×C22⋊#692311yescharacteristic
971C2×C4C2×C22⋊#692311yescharacteristic
972C2×C4C2×C22⋊#692311yescharacteristic
973C2×C4D4×#692314yes—
974C2×C4C23×#692311yescharacteristic
975C8—2444no—
976C22—21no—
977C22—21no—
978C22—21no—
979C22—21no—
980C22—21no—
981C22—21no—
982C22—21no—
983C22—44no—
984C22—41no—
985C22—41no—
986C22—41no—
987C22—612no—
988C22—612no—
989C22—611no—
990C22—611no—
991C22—612no—
992C22—612no—
993C22—1224no—
994C22—1224no—
995C22—1224no—
996C22—1224no—
997C22—1221no—
998C22—1221no—
999C22—1221no—
1000C22—1221no—
1001C22—1221no—
1002C22—1221no—
1003C22—1221no—
1004C22—4882no—
1005C22—4882no—
1006C22—2444no—
1007C22—2444no—
1008C22—2442no—
1009C22—2442no—
1010C22—2444no—
1011C22—2441no—
1012C22—2441no—
1013C22—2441no—
1014C22#1684071012yes—
1015C22#1684075212yescomplemented
1016C22C22×C22⋊#692311yescharacteristic
1017C4—21no—
1018C4—21no—
1019C4—41no—
1020C4—41no—
1021C4—41no—
1022C4—612no—
1023C4—612no—
1024C4—1221no—
1025C4—1221no—
1026C4—2448no—
1027C4—2441no—
1028C4—2441no—
1029C4—2441no—
1030C4#1684071012yes—
1031C4C2×D4×#692312yes—
1032C2—22no—
1033C2—22no—
1034C2—41no—
1035C2—81no—
1036C2—612no—
1037C2—612no—
1038C2—1222no—
1039C2—1222no—
1040C2—4881no—
1041C2—2441no—
1042C2C2×#1684071011yescharacteristic
1043C2C2×#1684075211yescharacteristic
1044C2#2146243911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#525C4
socleC22×C61C22×C22⋊C4
prime radical#525×D61C2
cosocleC2×C4×D61C24
hypercenter#525#6923
hypocenterC61#20908
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C22×#14519856C2semidirect
2. C2×#16840752C2semidirect
3. C2×D61⋊(C22⋊C8)C2semidirect
4. #21461807C2semidirect
5. #21461806C2semidirect
6. #21461805C2semidirect
7. #21461804C2semidirect
8. #21461504C2semidirect
20. C2×#14519840C22semidirect
21. C2×#14519839C22semidirect
28. #16840635C22semidirect
29. #16840635C22semidirect
32. #16840275C4semidirect
33. #16840275C4semidirect
34. #16840274C4semidirect
35. #16840273C4semidirect
36. #16840272C4semidirect
37. #16840272C4semidirect
41. #16840269C4semidirect
52. C61×#525C4semidirect
63. #14519856D4semidirect
80. C2×#11758226C2×C4semidirect
82. C2×#11758222C2×C4semidirect
84. C2×#11758224C2×C4semidirect
116. #14519757C2×C4semidirect
118. #14519756C2×C4semidirect
124. #14519753C2×C4semidirect
126. #14519752C2×C4semidirect
128. #14519751C2×C4semidirect
134. #14519748C2×C4semidirect
156. #14519736C2×C4semidirect
157. #14519735C2×C4semidirect
158. #14519735C2×C4semidirect
171. C2×#41×C61C2×C4semidirect
175. C22⋊Q8×C61C2×C4semidirect
177. #121×C61C2×C4semidirect
181. #117×C61C2×C4semidirect
466. C22×C61#416semidirect
490. C2×D61#416semidirect
546. #525#6923semidirect
575. C61#20908semidirect
584. C2×#41C2×#6923semidirect
632. C22⋊Q8C2×#6923semidirect
644. #121C2×#6923semidirect
679. #117C2×#6923semidirect
1015. C22#16840752semidirect

Maximal subgroups

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

subgroupindex
C22×#145198562
C2×#168407522
C2×D61⋊(C22⋊C8)2
#214618072
#214618062
#214618052
#214618042
#214615042
#525×D612
#2090861