Finite Group Databasebeta

← #29681189

Subgroups — #29681189

Order 15616.

1914 conjugacy classes of subgroups.

The subgroup lattice has 1096 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D61C211yesmaximal, characteristic, complemented
2#525×D61C211yesmaximal, characteristic
3C2×#16839777C212yesmaximal, complemented
4#21448200C211yesmaximal, characteristic, complemented
5#21446122C211yesmaximal, characteristic, complemented
6#21446121C211yesmaximal, characteristic, complemented
7#21446120C212yesmaximal, complemented
8#21446119C211yesmaximal, characteristic, complemented
9#21446118C212yesmaximal, complemented
10#21445527C212yesmaximal, complemented
11C61×#1871C211yesmaximal, characteristic, complemented
12C2×#41×D61C2211yescharacteristic
13C23×C4×D61C2211yescharacteristic
14C22×#11758194C2211yescharacteristic, complemented
15C22×#11758189—21no—
16C2×M16×D61—28no—
17C2×M16×D61—21no—
18C2×M16×D61—21no—
19C2×M16×D61C2212yes—
20C2×M16×D61C2212yescomplemented
21C22×C8×D61—21no—
22#16840275C411yescharacteristic, complemented
23#16840275C411yescharacteristic, complemented
24#16840274C2211yescharacteristic
25#16840273C2211yescharacteristic
26#16840272C411yescharacteristic, complemented
27#16840272C411yescharacteristic, complemented
28#16840271—21no—
29#16840271—21no—
30#16840270—21no—
31#16840269C2211yescharacteristic
32#16840268—21no—
33#123×D61—21no—
34C22⋊Q8×D61C411yescharacteristic, complemented
35C22⋊Q8×D61C411yescharacteristic, complemented
36#121×D61C411yescharacteristic, complemented
37#121×D61C411yescharacteristic, complemented
38#120×D61—21no—
39C4×D4×D61—21no—
40C4×D4×D61—21no—
41C2×#14519734C2212yes—
42#117×D61C2211yescharacteristic
43#16839777—28no—
44C2×#14519705C2212yescomplemented
45C2×#14519704C2212yescomplemented
46C2×#14519703C2212yescomplemented
47#16839624—21no—
48#16839621—21no—
49#16839620—21no—
50#16839617—21no—
51C4×#11758198C2212yescomplemented
52C4×C22⋊Dic61C2211yescharacteristic, complemented
53#16839523C2212yescomplemented
54#16839522C2212yescomplemented
55#16839521C2212yescomplemented
56C22×M16×C61C2211yescharacteristic, complemented
57C61×#525C2211yescharacteristic
58C2×#104×C61C2212yescomplemented
59C4×C22⋊C4×C61C2211yescharacteristic, complemented
60C61×#339C2212yescomplemented
61C24×D61D411yescharacteristic
62C2×#11758226C2×C411yescharacteristic
63C2×#11758222—21no—
64C2×#11758222C2311yescharacteristic
65C2×#11758224—21no—
66C2×#11758224C2×C411yescharacteristic
67#41×D61—24no—
68#41×D61—24no—
69C2×Q8×D61C2×C411yescharacteristic
70C2×D4×D61—21no—
71C2×D4×D61—21no—
72C2×D4×D61—21no—
73C2×D4×D61C2×C411yescharacteristic
74C23×Dic61D411yescharacteristic
75C22×C4×D61—24no—
76C22×C4×D61—24no—
77C22×C4×D61—21no—
78C22×C4×D61C2×C411yescharacteristic
79C22×C4×D61C2×C411yescharacteristic
80C22×C4×D61C2×C411yescharacteristic
81C22×C4×D61C2×C411yescharacteristic
82C22×C4×D61D411yescharacteristic
83C22×C4×D61D411yescharacteristic
84C22×C4×D61D411yescharacteristic
85C22×C4×D61D411yescharacteristic
86C22×C4×D61D411yescharacteristic
87C22×C4×D61D411yescharacteristic
88C22×C4×D61C2311yescharacteristic
89C22×C4×D61C2311yescharacteristic
90C2×#11758194—21no—
91C2×#11758194—24no—
92C2×#11758194C2312yes—
93C2×#11758189—28no—
94C2×#11758189—22no—
95C2×#11758189—22no—
96M16×D61—28no—
97M16×D61—28no—
98M16×D61—24no—
99M16×D61—24no—
100M16×D61—24no—
101M16×D61D418yescomplemented
102C22×#92418—21no—
103C2×C8×D61—28no—
104C2×C8×D61—22no—
105C2×C8×D61—22no—
106#14519762—21no—
107#14519762—21no—
108#14519761—21no—
109#14519760—21no—
110#14519759—21no—
111#14519759—21no—
112#14519758—21no—
113#14519757C2×C411yescharacteristic
114#14519757C2×C411yescharacteristic
115#14519756C2×C411yescharacteristic
116#14519756C2×C411yescharacteristic
117#14519755—21no—
118#14519755—21no—
119#14519754—21no—
120#14519754—21no—
121#14519753C2×C411yescharacteristic
122#14519753C2×C411yescharacteristic
123#14519752C2×C411yescharacteristic
124#14519752C2×C411yescharacteristic
125#14519751C2×C411yescharacteristic
126#14519751C2×C411yescharacteristic
127#14519750—21no—
128#14519750—21no—
129#14519749—21no—
130#14519749—21no—
131#14519748C2×C411yescharacteristic
132#14519748C2×C411yescharacteristic
133#14519747—21no—
134#14519747—21no—
135#14519747—21no—
136#14519746—21no—
137#14519745—21no—
138#14519745—21no—
139#14519745—21no—
140C4×D244—21no—
141C4×D244—21no—
142D4×Dic61—21no—
143D4×Dic61—21no—
144#14519739—21no—
145#14519739—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#14519736C2311yescharacteristic
155#14519735C2×C411yescharacteristic
156#14519735C2×C411yescharacteristic
157#14519734—21no—
158#14519734—24no—
159#14519734—24no—
160#14519733—21no—
161C2×#11758196—22no—
162C4⋊C4×D61—21no—
163C4⋊C4×D61—21no—
164C4⋊C4×D61C2×C411yescharacteristic
165C4⋊C4×D61C2×C411yescharacteristic
166C2×C22⋊Dic61—21no—
167C2×#11758198—22no—
168C2×#11758198—22no—
169C22⋊C4×D61—21no—
170C22⋊C4×D61—21no—
171C22⋊C4×D61—21no—
172C22⋊C4×D61—21no—
173C22⋊C4×D61—21no—
174C2×C4×Dic61C2312yes—
175C42×D61—21no—
176#14519705—24no—
177#14519704—24no—
178#14519703—24no—
179#14519684—21no—
180#14519684—22no—
181C2×#41×C61C2311yescharacteristic
182C23×C4×C61C2311yescharacteristic
183C2×M16×C61—21no—
184C2×M16×C61—24no—
185C2×M16×C61C2312yes—
186C22×C8×C61—21no—
187#123×C61—21no—
188C22⋊Q8×C61C2×C411yescharacteristic
189C22⋊Q8×C61C2×C411yescharacteristic
190#121×C61C2×C411yescharacteristic
191#121×C61C2×C411yescharacteristic
192#120×C61—21no—
193C4×D4×C61—21no—
194C4×D4×C61—21no—
195#117×C61C2311yescharacteristic
196C2×C22⋊C4×C61—21no—
197C2×C42×C61C2312yes—
198#104×C61—24no—
199#95×C61—21no—
200C24×C61C2×D411yescharacteristic
201C23×D61—24no—
202C23×D61—21no—
203C23×D61—42no—
204C23×D61—42no—
205C23×D61C22⋊C411yescharacteristic
206C23×D61C22⋊C411yescharacteristic
207C23×D61C22⋊C411yescharacteristic
208C23×D61C22⋊C411yescharacteristic
209C23×D61C2×D411yescharacteristic
210C23×D61C2×D411yescharacteristic
211#41×C61—22no—
212#41×C61—22no—
213C2×Q8×C61C22×C411yescharacteristic
214C2×D4×C61—21no—
215C2×D4×C61—21no—
216C2×D4×C61—21no—
217C2×D4×C61C22×C411yescharacteristic
218C22×C4×C61—22no—
219C22×C4×C61—22no—
220C22×C4×C61—21no—
221C22×C4×C61—22no—
222C22×C4×C61C22×C411yescharacteristic
223C22×C4×C61C22×C411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2411yescharacteristic
228C2×C22⋊D61—21no—
229C2×C22⋊D61—21no—
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—21no—
233C2×C22⋊D61—21no—
234C2×C22⋊D61—21no—
235C22×Dic61—24no—
236C22×Dic61—21no—
237C22×Dic61—22no—
238C22×Dic61C22⋊C411yescharacteristic
239C22×Dic61C22⋊C411yescharacteristic
240C22×Dic61C22⋊C411yescharacteristic
241C22×Dic61C22⋊C411yescharacteristic
242C22×Dic61C2×D411yescharacteristic
243C22×Dic61C2×D411yescharacteristic
244#11758226—24no—
245Q8×D61—24no—
246#11758224—24no—
247#11758224—44no—
248D4×D61—24no—
249D4×D61—44no—
250D4×D61—44no—
251D4×D61—44no—
252#11758222—22no—
253#11758222—22no—
254#11758222—42no—
255#11758222—42no—
256C2×D244—21no—
257C2×D244—21no—
258C2×D244—21no—
259C2×D244C22×C411yescharacteristic
260C2×C4×D61—24no—
261C2×C4×D61—22no—
262C2×C4×D61—22no—
263C2×C4×D61—24no—
264C2×C4×D61—24no—
265C2×C4×D61—24no—
266C2×C4×D61—24no—
267C2×C4×D61—24no—
268C2×C4×D61—22no—
269C2×C4×D61—22no—
270C2×C4×D61—22no—
271C2×C4×D61—22no—
272C2×C4×D61—22no—
273C2×C4×D61—22no—
274C2×C4×D61—22no—
275C2×C4×D61—22no—
276C2×C4×D61—21no—
277C2×C4×D61—21no—
278C2×C4×D61—21no—
279C2×C4×D61—21no—
280C2×C4×D61—21no—
281C2×C4×D61—42no—
282C2×C4×D61—42no—
283C2×C4×D61C22⋊C411yescharacteristic
284C2×C4×D61C22⋊C411yescharacteristic
285C2×C4×D61C22⋊C411yescharacteristic
286C2×C4×D61C22⋊C411yescharacteristic
287C2×C4×D61C22⋊C411yescharacteristic
288C2×C4×D61C22⋊C411yescharacteristic
289C2×C4×D61C22⋊C411yescharacteristic
290C2×C4×D61C22⋊C411yescharacteristic
291C2×C4×D61C22×C411yescharacteristic
292C2×C4×D61C22×C411yescharacteristic
293C2×C4×D61C22×C411yescharacteristic
294C2×C4×D61C22×C411yescharacteristic
295C2×C4×D61C2×D411yescharacteristic
296C2×C4×D61C2×D411yescharacteristic
297C2×C4×D61C2×D414yes—
298C2×C4×D61C2×D411yescharacteristic
299C2×C4×D61C2×D411yescharacteristic
300C2×C4×D61#4114yes—
301C2×Dic122—21no—
302C2×Dic122C22×C411yescharacteristic
303M16×C61—24no—
304M16×C61—22no—
305M16×C61C2×D414yescomplemented
306C2×C8×C61—24no—
307C2×C8×C61—22no—
308C4⋊C4×C61—21no—
309C4⋊C4×C61—21no—
310C4⋊C4×C61C22×C411yescharacteristic
311C4⋊C4×C61C22×C411yescharacteristic
312C22⋊C4×C61—21no—
313C22⋊C4×C61—21no—
314C22⋊C4×C61—21no—
315C22⋊C4×C61—21no—
316C22⋊C4×C61—21no—
317C22⋊C4×C61—42no—
318C42×C61—21no—
319C42×C61—22no—
320C42×C61—22no—
321C22⋊Dic61—21no—
322C22⋊Dic61—21no—
323C22⋊Dic61—21no—
324C22⋊Dic61—21no—
325C22⋊Dic61—21no—
326C22⋊Dic61—42no—
327#11758198—21no—
328#11758198—21no—
329#11758198—21no—
330#11758198—21no—
331#11758198—21no—
332#11758198—21no—
333#11758198—21no—
334#11758198—21no—
335#11758198—21no—
336#11758198—21no—
337#11758198—44no—
338#11758198—44no—
339C4⋊Dic61—21no—
340C4⋊Dic61—21no—
341C4⋊Dic61C22×C411yescharacteristic
342C4⋊Dic61C22×C411yescharacteristic
343#11758196—21no—
344#11758196—21no—
345#11758196—21no—
346#11758196—21no—
347#11758196—21no—
348#11758196—21no—
349#11758196—44no—
350C4×Dic61—21no—
351C4×Dic61—21no—
352C4×Dic61—21no—
353C4×Dic61—22no—
354C4×Dic61—22no—
355#11758194—24no—
356#11758194—22no—
357#11758194C2×D414yescomplemented
358C2×#92418—24no—
359C2×#92418—22no—
360#11758189—28no—
361#11758189—28no—
362C8×D61—28no—
363C8×D61—28no—
364C23×C61—22no—
365C23×C61—22no—
366C23×C61—21no—
367C23×C61—41no—
368C23×C61C2×C22⋊C411yescharacteristic
369C23×C61C2×C22⋊C411yescharacteristic
370C23×C61C22×D411yescharacteristic
371C22×D61—22no—
372C22×D61—22no—
373C22×D61—22no—
374C22×D61—22no—
375C22×D61—22no—
376C22×D61—22no—
377C22×D61—22no—
378C22×D61—22no—
379C22×D61—22no—
380C22×D61—22no—
381C22×D61—21no—
382C22×D61—41no—
383C22×D61—41no—
384C22×D61—41no—
385C22×D61—41no—
386C22×D61—41no—
387C22×D61—41no—
388C22×D61—41no—
389C22×D61—416no—
390C22×D61—42no—
391C22×D61—42no—
392C22×D61—42no—
393C22×D61C2×C22⋊C411yescharacteristic
394C22×D61C2×C22⋊C411yescharacteristic
395C22×D61C2×C22⋊C411yescharacteristic
396C22×D61C2×C22⋊C411yescharacteristic
397C22×D61#12114yes—
398Q8×C61—22no—
399D4×C61—22no—
400D4×C61—42no—
401D4×C61—42no—
402D4×C61—42no—
403C2×C4×C61—22no—
404C2×C4×C61—22no—
405C2×C4×C61—22no—
406C2×C4×C61—21no—
407C2×C4×C61—21no—
408C2×C4×C61—21no—
409C2×C4×C61—21no—
410C2×C4×C61—21no—
411C2×C4×C61—21no—
412C2×C4×C61—21no—
413C2×C4×C61—41no—
414C2×C4×C61—41no—
415C2×C4×C61—42no—
416C2×C4×C61—42no—
417C2×C4×C61—42no—
418C2×C4×C61C2×C22⋊C411yescharacteristic
419C2×C4×C61C2×C22⋊C411yescharacteristic
420C2×C4×C61C23×C411yescharacteristic
421C2×C4×C61C22×D412yes—
422C2×C4×C61C22×D411yescharacteristic
423C2×C4×C61C2×#4112yes—
424C22⋊D61—42no—
425C22⋊D61—42no—
426C22⋊D61—42no—
427C22⋊D61—42no—
428C22⋊D61—42no—
429C22⋊D61—42no—
430C22⋊D61—42no—
431C2×Dic61—22no—
432C2×Dic61—22no—
433C2×Dic61—22no—
434C2×Dic61—22no—
435C2×Dic61—22no—
436C2×Dic61—21no—
437C2×Dic61—21no—
438C2×Dic61—21no—
439C2×Dic61—42no—
440C2×Dic61—42no—
441C2×Dic61—42no—
442C2×Dic61—42no—
443C2×Dic61C2×C22⋊C411yescharacteristic
444C2×Dic61C2×C22⋊C411yescharacteristic
445C2×Dic61C2×C22⋊C411yescharacteristic
446C2×Dic61C2×C22⋊C411yescharacteristic
447C2×Dic61#12114yes—
448D244—22no—
449D244—42no—
450D244—42no—
451D244—42no—
452C4×D61—22no—
453C4×D61—22no—
454C4×D61—22no—
455C4×D61—22no—
456C4×D61—22no—
457C4×D61—22no—
458C4×D61—21no—
459C4×D61—21no—
460C4×D61—21no—
461C4×D61—21no—
462C4×D61—22no—
463C4×D61—22no—
464C4×D61—22no—
465C4×D61—22no—
466C4×D61—42no—
467C4×D61—42no—
468C4×D61—42no—
469C4×D61—41no—
470C4×D61—41no—
471C4×D61—42no—
472C4×D61C4×D414yes—
473C4×D61C4×D414yes—
474C4×D61#12012yes—
475C4×D61#12012yes—
476C4×D61#12312yes—
477C4×D61#12312yes—
478Dic122—22no—
479Dic122—42no—
480C8×C61—24no—
481#92418—24no—
482#20902—611nomaximal, Sylow
483C22×C61—21no—
484C22×C61—21no—
485C22×C61—21no—
486C22×C61—21no—
487C22×C61—21no—
488C22×C61—21no—
489C22×C61—21no—
490C22×C61—44no—
491C22×C61—41no—
492C22×C61—41no—
493C22×C61—41no—
494C22×C61#42112yescomplemented
495C22×C61C22×C22⋊C411yescharacteristic
496C22×C61C2×#12112yes—
497C2×D61—28no—
498C2×D61—21no—
499C2×D61—21no—
500C2×D61—21no—
501C2×D61—21no—
502C2×D61—21no—
503C2×D61—21no—
504C2×D61—21no—
505C2×D61—21no—
506C2×D61—21no—
507C2×D61—44no—
508C2×D61—44no—
509C2×D61—44no—
510C2×D61—44no—
511C2×D61—44no—
512C2×D61—41no—
513C2×D61—41no—
514C2×D61—41no—
515C2×D61—84no—
516C2×D61#38612yes—
517C2×D61#38612yes—
518C2×D61#42112yescomplemented
519C4×C61—21no—
520C4×C61—21no—
521C4×C61—41no—
522C4×C61—41no—
523C4×C61—41no—
524C4×C61—82no—
525C4×C61C2×C4×D412yes—
526C4×C61C2×#12011yescharacteristic
527C4×C61C2×#12311yescharacteristic
528Dic61—21no—
529Dic61—21no—
530Dic61—41no—
531Dic61—41no—
532Dic61—41no—
533Dic61—82no—
534Dic61#38612yes—
535Dic61#38612yes—
536C23×M16—611no—
537C2×#525—611no—
538C2×#421—612no—
539#2280—611no—
540#1871—612no—
541#1871—611no—
542#1871—612no—
543#1871—611no—
544#1871—611no—
545#1871D6111yescharacteristic, complemented
546#1733—612no—
547C2×C61—22no—
548C2×C61—22no—
549C2×C61—41no—
550C2×C61—81no—
551C2×C61C2×#38611yescharacteristic
552C2×C61C2×#42111yescharacteristic
553C2×C61C2×#42111yescharacteristic
554D61—22no—
555D61—22no—
556D61—22no—
557D61—41no—
558D61—81no—
559C22×#41—611no—
560C24×C4—611no—
561C22×M16—612no—
562C22×M16—611no—
563C22×M16—612no—
564C22×M16—1221no—
565C22×M16—1228no—
566C22×M16—1221no—
567C22×M16—1221no—
568C22×M16C2×D6111yescharacteristic, complemented
569C23×C8—1221no—
570#525—611no—
571#525—611no—
572#525—611no—
573#525—611no—
574#525—611no—
575#525—611no—
576#525—611no—
577#525—1221no—
578#525—1221no—
579#525—1221no—
580#525—1221no—
581#525C2×D6111yescharacteristic
582C2×#123—1221no—
583C2×C22⋊Q8—611no—
584C2×C22⋊Q8—611no—
585C2×#121—611no—
586C2×#121—611no—
587C2×#120—1221no—
588C2×C4×D4—1221no—
589C2×C4×D4—1221no—
590C2×#117—612no—
591C2×#117—611no—
592#421—1228no—
593C2×#104—612no—
594C2×#104—612no—
595C2×#104—612no—
596C2×#104C2×D6112yescomplemented
597#381—1221no—
598#380—1221no—
599#380—1221no—
600#379—1221no—
601C4×C22⋊C4—611no—
602C4×C22⋊C4—612no—
603C4×C22⋊C4C2×D6111yescharacteristic, complemented
604#339—612no—
605#339—612no—
606#339—612no—
607#339C2×D6112yescomplemented
608C61#2090211yescharacteristic, complemented, Sylow
609C25—611no—
610C2×#41—611no—
611C2×#41—611no—
612C2×#41—611no—
613C2×#41—1221no—
614C2×#41—1221no—
615C2×#41—1224no—
616C2×#41—1224no—
617C2×#41C22×D6111yescharacteristic
618C22×Q8—611no—
619C22×D4—611no—
620C22×D4—1221no—
621C22×D4—1221no—
622C22×D4—1221no—
623C23×C4—611no—
624C23×C4—611no—
625C23×C4—611no—
626C23×C4—611no—
627C23×C4—611no—
628C23×C4—611no—
629C23×C4—611no—
630C23×C4—611no—
631C23×C4—611no—
632C23×C4—611no—
633C23×C4—611no—
634C23×C4—611no—
635C23×C4—611no—
636C23×C4—1224no—
637C23×C4—1224no—
638C23×C4—1221no—
639C23×C4C22×D6111yescharacteristic
640C2×M16—21no—
641C2×M16—24no—
642C2×M16—612no—
643C2×M16—618no—
644C2×M16—1222no—
645C2×M16—1222no—
646C2×M16—1228no—
647C2×M16—1224no—
648C2×M16—1224no—
649C2×M16—1228no—
650C2×M16—1228no—
651C2×M16—1224no—
652C2×M16—1221no—
653C2×M16—1224no—
654C2×M16C22×D6112yes—
655C22×C8—21no—
656C22×C8—1222no—
657C22×C8—1222no—
658C22×C8—1228no—
659C22×C8—1221no—
660#123—21no—
661#123—1221no—
662#123—1221no—
663#123—1221no—
664#123—1221no—
665#123—1221no—
666#123—1221no—
667#123—1221no—
668C22⋊Q8—611no—
669C22⋊Q8—611no—
670C22⋊Q8—611no—
671C22⋊Q8—611no—
672C22⋊Q8—611no—
673C22⋊Q8—611no—
674C22⋊Q8—1221no—
675C22⋊Q8—1221no—
676C22⋊Q8—1221no—
677C22⋊Q8—1221no—
678C22⋊Q8C4×D6111yescharacteristic
679C22⋊Q8C4×D6111yescharacteristic
680#121—611no—
681#121—611no—
682#121—611no—
683#121—611no—
684#121—611no—
685#121—611no—
686#121—1221no—
687#121—1221no—
688#121—1221no—
689#121—1221no—
690#121C4×D6111yescharacteristic
691#121C4×D6111yescharacteristic
692#120—21no—
693#120—1221no—
694#120—1221no—
695#120—1221no—
696#120—1221no—
697#120—1221no—
698#120—1221no—
699#120—1221no—
700C4×D4—21no—
701C4×D4—21no—
702C4×D4—1221no—
703C4×D4—1221no—
704C4×D4—1221no—
705C4×D4—1221no—
706C4×D4—1221no—
707C4×D4—1221no—
708C4×D4—1221no—
709C4×D4—1221no—
710C4×D4—1221no—
711C4×D4—1221no—
712C4×D4—1221no—
713C4×D4—1221no—
714C4×D4—1221no—
715C4×D4—1221no—
716#117—611no—
717#117—611no—
718#117—611no—
719#117—1221no—
720#117—1224no—
721#117—1224no—
722#117—1221no—
723#117C22×D6111yescharacteristic
724C2×C4⋊C4—611no—
725C2×C4⋊C4—611no—
726C2×C4⋊C4—1221no—
727C2×C4⋊C4—1221no—
728C2×C4⋊C4—1222no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—1221no—
731C2×C22⋊C4—1221no—
732C2×C22⋊C4—1221no—
733C2×C22⋊C4—1221no—
734C2×C22⋊C4—1221no—
735C2×C22⋊C4—1222no—
736C2×C22⋊C4—1222no—
737C2×C22⋊C4—1221no—
738C2×C42—612no—
739C2×C42—1221no—
740C2×C42C22×D6112yes—
741#104—24no—
742#104—1224no—
743#104—1224no—
744#104—1224no—
745#95—21no—
746#95—1222no—
747#95—1221no—
748C24—611no—
749C24—611no—
750C24—611no—
751C24—611no—
752C24—611no—
753C24—611no—
754C24—1224no—
755C24—1221no—
756C24—2442no—
757C24—2442no—
758C24D4×D6111yescharacteristic
759#41—22no—
760#41—22no—
761#41—1224no—
762#41—1224no—
763#41—1222no—
764#41—1222no—
765#41—2442no—
766#41—2442no—
767#41—2444no—
768C2×Q8—611no—
769C2×Q8—1221no—
770C2×Q8—1224no—
771C2×Q8C2×C4×D6111yescharacteristic
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—611no—
776C2×D4—1221no—
777C2×D4—1221no—
778C2×D4—1221no—
779C2×D4—1224no—
780C2×D4—1221no—
781C2×D4—1221no—
782C2×D4—1221no—
783C2×D4—1221no—
784C2×D4—1221no—
785C2×D4—1221no—
786C2×D4—1221no—
787C2×D4—2444no—
788C2×D4—2444no—
789C2×D4—2444no—
790C2×D4C2×C4×D6111yescharacteristic
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—21no—
794C22×C4—22no—
795C22×C4—611no—
796C22×C4—611no—
797C22×C4—611no—
798C22×C4—614no—
799C22×C4—611no—
800C22×C4—611no—
801C22×C4—614no—
802C22×C4—611no—
803C22×C4—611no—
804C22×C4—611no—
805C22×C4—611no—
806C22×C4—611no—
807C22×C4—611no—
808C22×C4—611no—
809C22×C4—611no—
810C22×C4—611no—
811C22×C4—611no—
812C22×C4—611no—
813C22×C4—611no—
814C22×C4—611no—
815C22×C4—611no—
816C22×C4—611no—
817C22×C4—611no—
818C22×C4—611no—
819C22×C4—1222no—
820C22×C4—1222no—
821C22×C4—1222no—
822C22×C4—1222no—
823C22×C4—1224no—
824C22×C4—1224no—
825C22×C4—1224no—
826C22×C4—1224no—
827C22×C4—1224no—
828C22×C4—1222no—
829C22×C4—1222no—
830C22×C4—1222no—
831C22×C4—1222no—
832C22×C4—1221no—
833C22×C4—1224no—
834C22×C4—1221no—
835C22×C4—1221no—
836C22×C4—1221no—
837C22×C4—1224no—
838C22×C4—1221no—
839C22×C4—1222no—
840C22×C4—1222no—
841C22×C4—1221no—
842C22×C4—1222no—
843C22×C4—2442no—
844C22×C4—2442no—
845C22×C4C2×C4×D6111yescharacteristic
846C22×C4C2×C4×D6111yescharacteristic
847C22×C4D4×D6111yescharacteristic
848C22×C4D4×D6111yescharacteristic
849C22×C4D4×D6111yescharacteristic
850C22×C4C23×D6111yescharacteristic
851M16—24no—
852M16—22no—
853M16—614no—
854M16—1228no—
855M16—1228no—
856M16—1224no—
857M16—1222no—
858M16D4×D6114yescomplemented
859C2×C8—24no—
860C2×C8—22no—
861C2×C8—1228no—
862C2×C8—1228no—
863C2×C8—1224no—
864C2×C8—1222no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—611no—
868C4⋊C4—611no—
869C4⋊C4—1221no—
870C4⋊C4—1221no—
871C4⋊C4—1221no—
872C4⋊C4—1221no—
873C4⋊C4—1221no—
874C4⋊C4—1221no—
875C4⋊C4—1221no—
876C4⋊C4—1221no—
877C4⋊C4—2444no—
878C4⋊C4C2×C4×D6111yescharacteristic
879C4⋊C4C2×C4×D6111yescharacteristic
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—21no—
885C22⋊C4—42no—
886C22⋊C4—1221no—
887C22⋊C4—1221no—
888C22⋊C4—1221no—
889C22⋊C4—1221no—
890C22⋊C4—1221no—
891C22⋊C4—1221no—
892C22⋊C4—1221no—
893C22⋊C4—1221no—
894C22⋊C4—1221no—
895C22⋊C4—1221no—
896C22⋊C4—1221no—
897C22⋊C4—1221no—
898C22⋊C4—1221no—
899C22⋊C4—1221no—
900C22⋊C4—1221no—
901C22⋊C4—2444no—
902C22⋊C4—2444no—
903C22⋊C4—2442no—
904C42—21no—
905C42—22no—
906C42—22no—
907C42—1221no—
908C42—1221no—
909C42—1221no—
910C42—1222no—
911C42—1222no—
912C23—22no—
913C23—22no—
914C23—21no—
915C23—41no—
916C23—611no—
917C23—611no—
918C23—611no—
919C23—614no—
920C23—611no—
921C23—1222no—
922C23—1222no—
923C23—1222no—
924C23—1222no—
925C23—1222no—
926C23—1222no—
927C23—1222no—
928C23—1222no—
929C23—1222no—
930C23—1222no—
931C23—1221no—
932C23—2441no—
933C23—2441no—
934C23—2441no—
935C23—2441no—
936C23—2441no—
937C23—2441no—
938C23—2441no—
939C23—2442no—
940C23—2442no—
941C23—2442no—
942C23—24416no—
943C23C22⋊C4×D6111yescharacteristic
944C23C22⋊C4×D6111yescharacteristic
945C23C2×D4×D6111yescharacteristic
946Q8—22no—
947Q8—1222no—
948Q8—2442no—
949D4—22no—
950D4—42no—
951D4—42no—
952D4—42no—
953D4—1222no—
954D4—2442no—
955D4—2442no—
956D4—2442no—
957D4—2442no—
958D4—2442no—
959D4—2442no—
960D4—2442no—
961D4—2442no—
962D4—2442no—
963D4—2442no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—42no—
979C2×C4—611no—
980C2×C4—611no—
981C2×C4—614no—
982C2×C4—614no—
983C2×C4—614no—
984C2×C4—612no—
985C2×C4—612no—
986C2×C4—612no—
987C2×C4—612no—
988C2×C4—611no—
989C2×C4—611no—
990C2×C4—1222no—
991C2×C4—1222no—
992C2×C4—1222no—
993C2×C4—1222no—
994C2×C4—1222no—
995C2×C4—1222no—
996C2×C4—1222no—
997C2×C4—1222no—
998C2×C4—1222no—
999C2×C4—1222no—
1000C2×C4—1222no—
1001C2×C4—1222no—
1002C2×C4—1222no—
1003C2×C4—1222no—
1004C2×C4—1222no—
1005C2×C4—1221no—
1006C2×C4—1221no—
1007C2×C4—1221no—
1008C2×C4—1221no—
1009C2×C4—1221no—
1010C2×C4—1221no—
1011C2×C4—1221no—
1012C2×C4—2442no—
1013C2×C4—2442no—
1014C2×C4—2442no—
1015C2×C4—2442no—
1016C2×C4—2442no—
1017C2×C4—2442no—
1018C2×C4—2442no—
1019C2×C4—2442no—
1020C2×C4—2441no—
1021C2×C4—2441no—
1022C2×C4C22⋊C4×D6111yescharacteristic
1023C2×C4C22⋊C4×D6111yescharacteristic
1024C2×C4C22×C4×D6111yescharacteristic
1025C2×C4C2×D4×D6112yes—
1026C2×C4C2×D4×D6111yescharacteristic
1027C2×C4#41×D6112yes—
1028C8—24no—
1029C8—1224no—
1030C22—21no—
1031C22—21no—
1032C22—21no—
1033C22—21no—
1034C22—21no—
1035C22—21no—
1036C22—21no—
1037C22—44no—
1038C22—41no—
1039C22—41no—
1040C22—41no—
1041C22—612no—
1042C22—612no—
1043C22—612no—
1044C22—1228no—
1045C22—1221no—
1046C22—1221no—
1047C22—1221no—
1048C22—1221no—
1049C22—1221no—
1050C22—1221no—
1051C22—1221no—
1052C22—1221no—
1053C22—1221no—
1054C22—4884no—
1055C22—2444no—
1056C22—2444no—
1057C22—2444no—
1058C22—2444no—
1059C22—2444no—
1060C22—2441no—
1061C22—2441no—
1062C22—2441no—
1063C22#1683977712yescomplemented
1064C22C2×C22⋊C4×D6111yescharacteristic
1065C22#121×D6112yes—
1066C4—21no—
1067C4—21no—
1068C4—41no—
1069C4—41no—
1070C4—41no—
1071C4—82no—
1072C4—612no—
1073C4—612no—
1074C4—1221no—
1075C4—1221no—
1076C4—4882no—
1077C4—2441no—
1078C4—2441no—
1079C4—2441no—
1080C4C4×D4×D6112yes—
1081C4#120×D6111yescharacteristic
1082C4#123×D6111yescharacteristic
1083C2—22no—
1084C2—22no—
1085C2—41no—
1086C2—81no—
1087C2—1222no—
1088C2—1222no—
1089C2—1222no—
1090C2—4881no—
1091C2—2441no—
1092C2#386×D6111yescharacteristic
1093C2#421×D6111yescharacteristic
1094C2C2×#1683977711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1871C2
socleC22×C61C22×C22⋊C4
prime radical#525×D61C2
cosocleC22×C4×C61C24
hypercenter#1871D61
hypocenterC61#20902
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1871

Complements

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

NH ≅ G/Ntype
1. C22×M16×D61C2semidirect
3. C2×#16839777C2semidirect
4. #21448200C2semidirect
5. #21446122C2semidirect
6. #21446121C2semidirect
7. #21446120C2semidirect
8. #21446119C2semidirect
9. #21446118C2semidirect
10. #21445527C2semidirect
11. C61×#1871C2semidirect
14. C22×#11758194C22semidirect
20. C2×M16×D61C22semidirect
22. #16840275C4semidirect
23. #16840275C4semidirect
26. #16840272C4semidirect
27. #16840272C4semidirect
34. C22⋊Q8×D61C4semidirect
35. C22⋊Q8×D61C4semidirect
36. #121×D61C4semidirect
37. #121×D61C4semidirect
44. C2×#14519705C22semidirect
45. C2×#14519704C22semidirect
46. C2×#14519703C22semidirect
51. C4×#11758198C22semidirect
52. C4×C22⋊Dic61C22semidirect
53. #16839523C22semidirect
54. #16839522C22semidirect
55. #16839521C22semidirect
56. C22×M16×C61C22semidirect
58. C2×#104×C61C22semidirect
59. C4×C22⋊C4×C61C22semidirect
60. C61×#339C22semidirect
101. M16×D61D4semidirect
305. M16×C61C2×D4semidirect
357. #11758194C2×D4semidirect
494. C22×C61#421semidirect
518. C2×D61#421semidirect
545. #1871D61semidirect
568. C22×M16C2×D61semidirect
596. C2×#104C2×D61semidirect
603. C4×C22⋊C4C2×D61semidirect
607. #339C2×D61semidirect
608. C61#20902semidirect
858. M16D4×D61semidirect
1063. C22#16839777semidirect

Maximal subgroups

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

subgroupindex
C22×M16×D612
#525×D612
C2×#168397772
#214482002
#214461222
#214461212
#214461202
#214461192
#214461182
#214455272
C61×#18712
#2090261