Finite Group Databasebeta

← #30615705

Subgroups — #30615705

Order 15616.

1954 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519856C211yesmaximal, characteristic, complemented
2C2×#16840759C212yesmaximal, complemented
3C2×#16840733C211yesmaximal, characteristic, complemented
4#21461839C212yesmaximal, complemented
5#21461838C212yesmaximal, complemented
6#21461837C212yesmaximal, complemented
7#21461836C212yesmaximal, complemented
8#21461499C212yesmaximal, complemented
9#525×D61C211yesmaximal, characteristic
10C22×#11758213C2212yes—
11C2×#14519856—28no—
12C2×#14519856—21no—
13C2×#14519856—21no—
14C2×#14519856C2212yes—
15C2×#14519856C2212yescomplemented
16C22×C4⋊#6923—21no—
17C22×C22⋊#6923—21no—
18C22×C4×#6923C2212yescomplemented
19#16840759—28no—
20C2×#14519842C2214yescomplemented
21C2×#14519841C2214yescomplemented
22#16840733—21no—
23#16840733—21no—
24#16840733C2212yescomplemented
25#16840733C2212yescomplemented
26C2×#14519834—21no—
27C2×C22⋊#92420—21no—
28#16840632C2214yescomplemented
29#16840632C2214yescomplemented
30C2×#41×D61C2211yescharacteristic
31C23×C4×D61C2211yescharacteristic
32#16840275C2211yescharacteristic
33#16840275C2211yescharacteristic
34#16840274C411yescharacteristic, complemented
35#16840273C411yescharacteristic, complemented
36#16840272C2211yescharacteristic
37#16840272C2211yescharacteristic
38#16840271—21no—
39#16840271—21no—
40#16840270—21no—
41#16840269C411yescharacteristic, complemented
42#16840268—21no—
43#123×D61—21no—
44C22⋊Q8×D61C411yescharacteristic, complemented
45C22⋊Q8×D61C411yescharacteristic, complemented
46#121×D61C411yescharacteristic, complemented
47#121×D61C411yescharacteristic, complemented
48#120×D61—21no—
49C4×D4×D61—21no—
50C4×D4×D61—21no—
51#117×D61C2211yescharacteristic
52C61×#525C411yescharacteristic, complemented
53C23×#6923—22no—
54C2×#11758213—24no—
55C2×#11758213—24no—
56C2×#11758213—22no—
57C2×#11758213C2314yes—
58C22×#92420—22no—
59#14519856—28no—
60#14519856—28no—
61#14519856—24no—
62#14519856—28no—
63#14519856D418yescomplemented
64C2×C4⋊#6923—28no—
65C2×C4⋊#6923—22no—
66C2×C4⋊#6923—22no—
67C2×C22⋊#6923—28no—
68C2×C22⋊#6923—22no—
69C2×C22⋊#6923—22no—
70C2×C4×#6923—22no—
71C2×C4×#6923—28no—
72C2×C4×#6923C2314yes—
73#14519842—28no—
74#14519841—28no—
75#14519834—22no—
76#14519834—22no—
77C22⋊#92420—22no—
78C22⋊#92420—22no—
79C24×D61D411yescharacteristic
80C2×#11758226C2311yescharacteristic
81C2×#11758222—21no—
82C2×#11758222C2×C411yescharacteristic, complemented
83C2×#11758224—21no—
84C2×#11758224C2311yescharacteristic
85#41×D61—24no—
86#41×D61—24no—
87C2×Q8×D61C2×C411yescharacteristic, complemented
88C2×D4×D61—21no—
89C2×D4×D61—21no—
90C2×D4×D61—21no—
91C2×D4×D61C2×C411yescharacteristic, complemented
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#14519735C2311yescharacteristic
158#14519735C2311yescharacteristic
159#14519734—21no—
160#14519733—21no—
161C4⋊C4×D61—21no—
162C4⋊C4×D61—21no—
163C4⋊C4×D61C2×C411yescharacteristic, complemented
164C4⋊C4×D61C2×C411yescharacteristic, complemented
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—21no—
186C23×D61—42no—
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—22no—
228#11758226—22no—
229Q8×D61—24no—
230#11758224—22no—
231#11758224—22no—
232#11758224—44no—
233D4×D61—24no—
234D4×D61—44no—
235D4×D61—44no—
236D4×D61—42no—
237D4×D61—42no—
238#11758222—24no—
239#11758222—42no—
240#11758222—42no—
241C2×D244—21no—
242C2×D244—21no—
243C2×D244—21no—
244C2×D244C22×C411yescharacteristic
245C2×C4×D61—22no—
246C2×C4×D61—22no—
247C2×C4×D61—24no—
248C2×C4×D61—24no—
249C2×C4×D61—24no—
250C2×C4×D61—24no—
251C2×C4×D61—22no—
252C2×C4×D61—22no—
253C2×C4×D61—24no—
254C2×C4×D61—24no—
255C2×C4×D61—22no—
256C2×C4×D61—22no—
257C2×C4×D61—22no—
258C2×C4×D61—22no—
259C2×C4×D61—22no—
260C2×C4×D61—22no—
261C2×C4×D61—21no—
262C2×C4×D61—21no—
263C2×C4×D61—21no—
264C2×C4×D61—21no—
265C2×C4×D61—21no—
266C2×C4×D61—44no—
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—28no—
293C4×#6923—28no—
294C4×#6923—24no—
295C4×#6923C2×D418yescomplemented
296#11758213—24no—
297#11758213—24no—
298#11758213—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—22no—
345C22×D61—21no—
346C22×D61—21no—
347C22×D61—22no—
348C22×D61—22no—
349C22×D61—22no—
350C22×D61—21no—
351C22×D61—21no—
352C22×D61—22no—
353C22×D61—22no—
354C22×D61—22no—
355C22×D61—22no—
356C22×D61—21no—
357C22×D61—41no—
358C22×D61—41no—
359C22×D61—41no—
360C22×D61—41no—
361C22×D61—41no—
362C22×D61—41no—
363C22×D61—41no—
364C22×D61—48no—
365C22×D61—48no—
366C22×D61—42no—
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×D61C22×D411yescharacteristic
375C2×#6923—28no—
376C2×#6923—416no—
377C2×#6923—44no—
378C2×#6923—44no—
379Q8×C61—22no—
380D4×C61—22no—
381D4×C61—42no—
382D4×C61—42no—
383D4×C61—42no—
384C2×C4×C61—22no—
385C2×C4×C61—22no—
386C2×C4×C61—22no—
387C2×C4×C61—22no—
388C2×C4×C61—22no—
389C2×C4×C61—21no—
390C2×C4×C61—21no—
391C2×C4×C61—21no—
392C2×C4×C61—42no—
393C2×C4×C61C2×C22⋊C411yescharacteristic
394C2×C4×C61C2×C22⋊C411yescharacteristic
395C2×C4×C61C2×C22⋊C411yescharacteristic
396C2×C4×C61C4×D414yes—
397C2×C4×C61C23×C411yescharacteristic
398C22⋊D61—42no—
399C22⋊D61—42no—
400C22⋊D61—42no—
401C22⋊D61—42no—
402C22⋊D61—41no—
403C22⋊D61—41no—
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—41no—
423D244—41no—
424D244—42no—
425C4×D61—21no—
426C4×D61—21no—
427C4×D61—21no—
428C4×D61—21no—
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—22no—
439C4×D61—42no—
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#20979—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#42112yescomplemented
467C22×C61C22×C22⋊C411yescharacteristic
468C2×D61—24no—
469C2×D61—24no—
470C2×D61—21no—
471C2×D61—21no—
472C2×D61—21no—
473C2×D61—21no—
474C2×D61—21no—
475C2×D61—21no—
476C2×D61—21no—
477C2×D61—21no—
478C2×D61—21no—
479C2×D61—42no—
480C2×D61—42no—
481C2×D61—44no—
482C2×D61—44no—
483C2×D61—44no—
484C2×D61—42no—
485C2×D61—42no—
486C2×D61—41no—
487C2×D61—41no—
488C2×D61—41no—
489C2×D61—84no—
490C2×D61#38612yes—
491C2×D61#42112yescomplemented
492C2×D61C2×#12011yescharacteristic
493C2×D61C2×#12311yescharacteristic
494#6923—48no—
495C4×C61—21no—
496C4×C61—21no—
497C4×C61—41no—
498C4×C61—41no—
499C4×C61—41no—
500C4×C61#38612yes—
501C4×C61C2×C4×D412yes—
502Dic61—21no—
503Dic61—21no—
504Dic61—41no—
505Dic61—41no—
506Dic61—41no—
507Dic61#38612yes—
508Dic61C2×#12112yes—
509C2×#525—611no—
510C22×#117—611no—
511C2×#421—612no—
512C2×#407—611no—
513#1897—612no—
514#1897—612no—
515#1896—612no—
516#1896—612no—
517#1733—612no—
518C2×C61—22no—
519C2×C61—22no—
520C2×C61—41no—
521C2×C61—81no—
522C2×C61C2×#38611yescharacteristic
523C2×C61C2×#42111yescharacteristic
524C2×C61C2×#42111yescharacteristic
525D61—21no—
526D61—21no—
527D61—22no—
528D61—22no—
529D61—41no—
530D61—81no—
531C22×#41—611no—
532C24×C4—611no—
533C22×M16—612no—
534#525—611no—
535#525—611no—
536#525—611no—
537#525—611no—
538#525—611no—
539#525—611no—
540#525—611no—
541#525—1221no—
542#525—1221no—
543#525—1221no—
544#525—1221no—
545#525#692311yescharacteristic, complemented
546C2×#123—1221no—
547C2×C22⋊Q8—611no—
548C2×C22⋊Q8—611no—
549C2×#121—611no—
550C2×#121—611no—
551C2×#120—1221no—
552C2×C4×D4—1221no—
553C2×C4×D4—1221no—
554C2×#117—612no—
555C2×#117—612no—
556C2×#117—611no—
557C2×#117—1228no—
558C2×#117—1221no—
559C2×#117—1221no—
560C22×C4⋊C4—1221no—
561C22×C22⋊C4—1221no—
562C22×C42—612no—
563#421—1228no—
564C2×#104—614no—
565C2×#104—614no—
566#407—612no—
567#407—612no—
568#407—1221no—
569#407—1221no—
570C2×C22⋊C8—1221no—
571C2×C22⋊C8—1221no—
572#339—614no—
573#339—614no—
574C61#2097911yescharacteristic, complemented, Sylow
575C25—611no—
576C2×#41—611no—
577C2×#41—611no—
578C2×#41—611no—
579C2×#41—1221no—
580C2×#41—1221no—
581C2×#41—1224no—
582C2×#41—1224no—
583C2×#41C2×#692311yescharacteristic, complemented
584C22×Q8—611no—
585C22×D4—611no—
586C22×D4—1221no—
587C22×D4—1221no—
588C22×D4—1221no—
589C23×C4—611no—
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—1224no—
603C23×C4—1224no—
604C23×C4—1221no—
605C23×C4—1222no—
606C23×C4C2×#692311yescharacteristic
607C2×M16—614no—
608C2×M16—1222no—
609C2×M16—1224no—
610C2×M16—1224no—
611C22×C8—1222no—
612#123—21no—
613#123—1221no—
614#123—1221no—
615#123—1221no—
616#123—1221no—
617#123—1221no—
618#123—1221no—
619#123—1221no—
620C22⋊Q8—611no—
621C22⋊Q8—611no—
622C22⋊Q8—611no—
623C22⋊Q8—611no—
624C22⋊Q8—611no—
625C22⋊Q8—611no—
626C22⋊Q8—1221no—
627C22⋊Q8—1221no—
628C22⋊Q8—1221no—
629C22⋊Q8—1221no—
630C22⋊Q8C2×#692311yescharacteristic
631C22⋊Q8C2×#692311yescharacteristic, complemented
632#121—611no—
633#121—611no—
634#121—611no—
635#121—611no—
636#121—611no—
637#121—611no—
638#121—1221no—
639#121—1221no—
640#121—1221no—
641#121—1221no—
642#121C2×#692311yescharacteristic
643#121C2×#692311yescharacteristic, complemented
644#120—21no—
645#120—1221no—
646#120—1221no—
647#120—1221no—
648#120—1221no—
649#120—1221no—
650#120—1221no—
651#120—1221no—
652C4×D4—21no—
653C4×D4—21no—
654C4×D4—1221no—
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—
668#117—618no—
669#117—611no—
670#117—611no—
671#117—611no—
672#117—1221no—
673#117—1228no—
674#117—1221no—
675#117—1224no—
676#117—1228no—
677#117—1228no—
678#117C2×#692311yescharacteristic, complemented
679C2×C4⋊C4—611no—
680C2×C4⋊C4—611no—
681C2×C4⋊C4—1221no—
682C2×C4⋊C4—1221no—
683C2×C4⋊C4—1222no—
684C2×C4⋊C4—1222no—
685C2×C4⋊C4—1228no—
686C2×C22⋊C4—1221no—
687C2×C22⋊C4—1221no—
688C2×C22⋊C4—1221no—
689C2×C22⋊C4—1221no—
690C2×C22⋊C4—1221no—
691C2×C22⋊C4—1222no—
692C2×C22⋊C4—1222no—
693C2×C22⋊C4—1228no—
694C2×C42—614no—
695C2×C42—1221no—
696C2×C42—1228no—
697C2×C42—1222no—
698#104—1228no—
699#104—1228no—
700C22⋊C8—1222no—
701C22⋊C8—1222no—
702C22⋊C8—1222no—
703C22⋊C8—1222no—
704C24—611no—
705C24—611no—
706C24—611no—
707C24—611no—
708C24—611no—
709C24—611no—
710C24—1222no—
711C24—1222no—
712C24—1221no—
713C24—2442no—
714C24—2442no—
715C24C22⋊#692311yescharacteristic
716#41—24no—
717#41—1222no—
718#41—1222no—
719#41—1222no—
720#41—1222no—
721#41—1224no—
722#41—2442no—
723#41—2442no—
724#41—2444no—
725C2×Q8—611no—
726C2×Q8—1221no—
727C2×Q8—1224no—
728C2×Q8C22×#692311yescharacteristic
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—611no—
733C2×D4—1221no—
734C2×D4—1221no—
735C2×D4—1221no—
736C2×D4—1224no—
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—2444no—
801C22×C4—2444no—
802C22×C4—2444no—
803C22×C4C22⋊#692311yescharacteristic
804C22×C4C22⋊#692311yescharacteristic
805C22×C4C22⋊#692311yescharacteristic
806C22×C4C22×#692311yescharacteristic
807C22×C4C22×#692311yescharacteristic
808C22×C4C22×#692311yescharacteristic
809M16—1224no—
810M16—1224no—
811M16—2444no—
812C2×C8—1224no—
813C2×C8—2444no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—611no—
817C4⋊C4—611no—
818C4⋊C4—1221no—
819C4⋊C4—1221no—
820C4⋊C4—1221no—
821C4⋊C4—1221no—
822C4⋊C4—1221no—
823C4⋊C4—1221no—
824C4⋊C4—1228no—
825C4⋊C4—1228no—
826C4⋊C4—1221no—
827C4⋊C4—1221no—
828C4⋊C4C22×#692311yescharacteristic
829C4⋊C4C22×#692311yescharacteristic
830C22⋊C4—21no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—21no—
834C22⋊C4—21no—
835C22⋊C4—1221no—
836C22⋊C4—1221no—
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—1228no—
846C22⋊C4—1228no—
847C22⋊C4—1221no—
848C22⋊C4—1221no—
849C22⋊C4—1221no—
850C22⋊C4—1221no—
851C22⋊C4—1221no—
852C42—21no—
853C42—618no—
854C42—1221no—
855C42—1221no—
856C42—1224no—
857C42—1228no—
858C42—1221no—
859C23—22no—
860C23—22no—
861C23—21no—
862C23—41no—
863C23—611no—
864C23—611no—
865C23—611no—
866C23—612no—
867C23—612no—
868C23—611no—
869C23—1221no—
870C23—1221no—
871C23—1222no—
872C23—1221no—
873C23—1222no—
874C23—1222no—
875C23—1221no—
876C23—1222no—
877C23—1222no—
878C23—1222no—
879C23—1222no—
880C23—1222no—
881C23—1221no—
882C23—2441no—
883C23—2441no—
884C23—2441no—
885C23—2441no—
886C23—2441no—
887C23—2441no—
888C23—2441no—
889C23—2442no—
890C23—2442no—
891C23—2442no—
892C23—2448no—
893C23—2448no—
894C23C2×C22⋊#692311yescharacteristic
895C23C2×C22⋊#692311yescharacteristic
896C23C2×C22⋊#692311yescharacteristic
897Q8—22no—
898Q8—1222no—
899Q8—2442no—
900D4—22no—
901D4—42no—
902D4—42no—
903D4—42no—
904D4—1222no—
905D4—2442no—
906D4—2441no—
907D4—2441no—
908D4—2442no—
909D4—2442no—
910D4—2442no—
911D4—2442no—
912D4—2441no—
913D4—2441no—
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—1222no—
944C2×C4—1222no—
945C2×C4—1221no—
946C2×C4—1221no—
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—2442no—
962C2×C4—2442no—
963C2×C4—2442no—
964C2×C4—2442no—
965C2×C4—24416no—
966C2×C4—2444no—
967C2×C4—2444no—
968C2×C4—2442no—
969C2×C4C2×C22⋊#692311yescharacteristic
970C2×C4C2×C22⋊#692311yescharacteristic
971C2×C4C2×C22⋊#692311yescharacteristic
972C2×C4D4×#692314yes—
973C2×C4C23×#692311yescharacteristic
974C8—2444no—
975C22—21no—
976C22—21no—
977C22—21no—
978C22—21no—
979C22—21no—
980C22—21no—
981C22—21no—
982C22—44no—
983C22—41no—
984C22—41no—
985C22—41no—
986C22—612no—
987C22—611no—
988C22—612no—
989C22—611no—
990C22—1224no—
991C22—1224no—
992C22—1221no—
993C22—1221no—
994C22—1221no—
995C22—1221no—
996C22—1221no—
997C22—1221no—
998C22—1221no—
999C22—1221no—
1000C22—1221no—
1001C22—4884no—
1002C22—2442no—
1003C22—2442no—
1004C22—2444no—
1005C22—2444no—
1006C22—2444no—
1007C22—2442no—
1008C22—2442no—
1009C22—2441no—
1010C22—2441no—
1011C22—2441no—
1012C22#1684071012yes—
1013C22#1684075912yescomplemented
1014C22C22×C22⋊#692311yescharacteristic
1015C4—21no—
1016C4—21no—
1017C4—41no—
1018C4—41no—
1019C4—41no—
1020C4—612no—
1021C4—612no—
1022C4—1221no—
1023C4—1221no—
1024C4—2448no—
1025C4—2441no—
1026C4—2441no—
1027C4—2441no—
1028C4#1684071012yes—
1029C4C2×D4×#692312yes—
1030C2—22no—
1031C2—22no—
1032C2—41no—
1033C2—81no—
1034C2—1221no—
1035C2—1222no—
1036C2—1221no—
1037C2—1222no—
1038C2—4881no—
1039C2—2441no—
1040C2C2×#1684071011yescharacteristic
1041C2D61⋊#42111yescharacteristic
1042C2C2×#1684075911yescharacteristic
subgroupG/H
centerC22C22×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#20979
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C22×#14519856C2semidirect
2. C2×#16840759C2semidirect
3. C2×#16840733C2semidirect
4. #21461839C2semidirect
5. #21461838C2semidirect
6. #21461837C2semidirect
7. #21461836C2semidirect
8. #21461499C2semidirect
15. C2×#14519856C22semidirect
18. C22×C4×#6923C22semidirect
20. C2×#14519842C22semidirect
21. C2×#14519841C22semidirect
24. #16840733C22semidirect
25. #16840733C22semidirect
28. #16840632C22semidirect
29. #16840632C22semidirect
34. #16840274C4semidirect
35. #16840273C4semidirect
41. #16840269C4semidirect
44. C22⋊Q8×D61C4semidirect
45. C22⋊Q8×D61C4semidirect
46. #121×D61C4semidirect
47. #121×D61C4semidirect
52. C61×#525C4semidirect
63. #14519856D4semidirect
82. C2×#11758222C2×C4semidirect
87. C2×Q8×D61C2×C4semidirect
91. C2×D4×D61C2×C4semidirect
116. #14519757C2×C4semidirect
118. #14519756C2×C4semidirect
124. #14519753C2×C4semidirect
126. #14519752C2×C4semidirect
128. #14519751C2×C4semidirect
134. #14519748C2×C4semidirect
156. #14519736C2×C4semidirect
163. C4⋊C4×D61C2×C4semidirect
164. C4⋊C4×D61C2×C4semidirect
171. C2×#41×C61C2×C4semidirect
175. C22⋊Q8×C61C2×C4semidirect
177. #121×C61C2×C4semidirect
181. #117×C61C2×C4semidirect
295. C4×#6923C2×D4semidirect
466. C22×C61#421semidirect
491. C2×D61#421semidirect
545. #525#6923semidirect
574. C61#20979semidirect
583. C2×#41C2×#6923semidirect
631. C22⋊Q8C2×#6923semidirect
643. #121C2×#6923semidirect
678. #117C2×#6923semidirect
1013. C22#16840759semidirect

Maximal subgroups

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

subgroupindex
C22×#145198562
C2×#168407592
C2×#168407332
#214618392
#214618382
#214618372
#214618362
#214614992
#525×D612
#2097961