Finite Group Databasebeta

← #29680997

Subgroups — #29680997

Order 15616.

1598 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840234C211yesmaximal, characteristic
2C2×#16839801C211yesmaximal, characteristic, complemented
3C2×#16839765C211yesmaximal, characteristic
4C2×#102×D61C211yesmaximal, characteristic
5#21448441C211yesmaximal, characteristic, complemented
6#21446081C211yesmaximal, characteristic, complemented
7#21446080C211yesmaximal, characteristic, complemented
8#21446077C211yesmaximal, characteristic, complemented
9#21446069C211yesmaximal, characteristic, complemented
10#21446068C211yesmaximal, characteristic, complemented
11#21446065C211yesmaximal, characteristic, complemented
12#21446064C211yesmaximal, characteristic, complemented
13#21445534C211yesmaximal, characteristic, complemented
14#21445514C211yesmaximal, characteristic, complemented
15C61×#1864C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19#16840234—24no—
20#16840234—24no—
21C2×C4×D244C2211yescharacteristic
22C2×D4×Dic61C2211yescharacteristic
23C2×#14519739C2211yescharacteristic
24C2×C4×C22⋊D61—21no—
25C2×#14519737—21no—
26C2×#14519735C2211yescharacteristic
27C2×#14519735C2211yescharacteristic
28C2×#14519734C2211yescharacteristic
29C2×C4⋊C4×D61C2211yescharacteristic
30C22×#11758198—21no—
31C2×C22⋊C4×D61—21no—
32#16839801—24no—
33C2×#14519711C2211yescharacteristic, complemented
34C2×#14519710C2211yescharacteristic, complemented
35C2×#14519708C2211yescharacteristic, complemented
36#16839765C418yescomplemented
37C2×#14519699C2211yescharacteristic
38C2×#14519699C2211yescharacteristic
39C2×#14519698C2211yescharacteristic
40C2×#14519698C2211yescharacteristic
41C2×#14519697C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43#102×D61—24no—
44#16839661C2211yescharacteristic, complemented
45#16839660C2211yescharacteristic, complemented
46#16839658C2211yescharacteristic, complemented
47#16839636—21no—
48#16839633—21no—
49#16839631—21no—
50#16839626—21no—
51#16839525C2211yescharacteristic, complemented
52#16839524C2211yescharacteristic, complemented
53#16839524C2211yescharacteristic, complemented
54#16839517C2211yescharacteristic, complemented
55#16839516C2211yescharacteristic, complemented
56#16839516C2211yescharacteristic, complemented
57C2×C4×D4×C61C2211yescharacteristic
58C2×#106×C61C2211yescharacteristic, complemented
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C61×#389C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C61×#336C2211yescharacteristic, complemented
64C24×D61—21no—
65C22×D244C2311yescharacteristic
66C22×C22⋊D61—21no—
67C2×D4×D61—22no—
68C2×D4×D61—22no—
69C2×D4×D61—22no—
70C2×D4×D61C2×C414yes—
71C2×D4×D61D414yes—
72C2×D4×D61Q814yes—
73C23×Dic61—21no—
74C22×C4×D61—21no—
75C22×C4×D61—21no—
76C22×C4×D61—21no—
77C22×C4×D61C2311yescharacteristic
78C2×#11758189—22no—
79C2×#11758189—22no—
80C2×#11758189C2×C414yescomplemented
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83C2×C8×D61—22no—
84C2×C8×D61—22no—
85C2×C8×D61—22no—
86C4×D244—22no—
87C4×D244—22no—
88D4×Dic61—22no—
89D4×Dic61—22no—
90#14519739—22no—
91#14519739—22no—
92C4×C22⋊D61—28no—
93#14519737—28no—
94#14519735—22no—
95#14519735—22no—
96#14519735C2×C414yescomplemented
97#14519735D414yes—
98#14519734—22no—
99#14519734—22no—
100C2×C4⋊Dic61—21no—
101C2×C4⋊Dic61C2311yescharacteristic
102C2×C4⋊Dic61C2311yescharacteristic
103C2×C4⋊Dic61C2311yescharacteristic
104C2×#11758196—21no—
105C2×#11758196—21no—
106C2×#11758196—21no—
107C2×#11758196D411yescharacteristic
108C2×#11758196D411yescharacteristic
109C4⋊C4×D61—22no—
110C4⋊C4×D61—22no—
111C2×C22⋊Dic61—21no—
112C2×#11758198—28no—
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198D411yescharacteristic
118C2×#11758198D411yescharacteristic
119C22⋊C4×D61—28no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61—21no—
122C2×C4×Dic61C2311yescharacteristic
123#14519711—22no—
124#14519710—22no—
125#14519708—22no—
126#14519699—22no—
127#14519699C2×C414yescomplemented
128#14519698—22no—
129#14519698C2×C414yescomplemented
130#14519697—22no—
131#14519697C2×C414yescomplemented
132#14519684—21no—
133#14519684—21no—
134#14519684—21no—
135C22×D4×C61C2311yescharacteristic
136C23×C4×C61—21no—
137C22×C8×C61C2311yescharacteristic
138C22×C8×C61C2311yescharacteristic
139C4×D4×C61—22no—
140C4×D4×C61—22no—
141C2×C4⋊C4×C61—21no—
142C2×C4⋊C4×C61C2311yescharacteristic
143C2×C4⋊C4×C61C2311yescharacteristic
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C22⋊C4×C61—21no—
146C2×C42×C61C2311yescharacteristic
147#106×C61—22no—
148#102×C61—22no—
149#102×C61C2×C414yescomplemented
150#95×C61—21no—
151C24×C61—21no—
152C23×D61—21no—
153C23×D61—24no—
154C23×D61—24no—
155C23×D61—24no—
156C23×D61—81no—
157C23×D61—81no—
158C23×D61—81no—
159C23×D61—81no—
160C23×D61C2×D411yescharacteristic
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61C22×C412yes—
165C2×D4×C61C2×D412yes—
166C2×D4×C61C2×Q812yes—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—24no—
170C22×C4×C61—21no—
171C22×C4×C61—81no—
172C22×C4×C61—81no—
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2411yescharacteristic
176C2×C22⋊D61—24no—
177C2×C22⋊D61—24no—
178C2×C22⋊D61—24no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61—24no—
182C22×Dic61—21no—
183C22×Dic61—81no—
184C22×Dic61—81no—
185C22×Dic61C2×D411yescharacteristic
186C22×Dic61C2×D411yescharacteristic
187C22×Dic61C2×D411yescharacteristic
188D4×D61—28no—
189D4×D61—28no—
190D4×D61—28no—
191D4×D61C4⋊C4116yescomplemented
192C2×D244—21no—
193C2×D244—21no—
194C2×D244—21no—
195C2×D244C22×C412yes—
196C2×D244C2×D412yes—
197C2×D244C2×Q812yes—
198C2×C4×D61—24no—
199C2×C4×D61—24no—
200C2×C4×D61—42no—
201C2×C4×D61—81no—
202C2×C4×D61—81no—
203C2×C4×D61—81no—
204C2×C4×D61—81no—
205C2×C4×D61—81no—
206C2×C4×D61—81no—
207C2×C4×D61C22×C412yes—
208C2×C4×D61C2×D412yes—
209C2×C4×D61C2×D412yes—
210C2×C4×D61C2×Q812yes—
211C2×C4×D61#4112yes—
212C2×C4×D61#4112yes—
213C2×C8×C61—21no—
214C2×C8×C61—21no—
215C2×C8×C61—21no—
216C2×C8×C61—21no—
217C2×C8×C61—21no—
218C2×C8×C61C22×C412yes—
219C4⋊C4×C61—21no—
220C4⋊C4×C61—21no—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—81no—
224C4⋊C4×C61C22×C412yes—
225C4⋊C4×C61C2×D412yes—
226C22⋊C4×C61—24no—
227C42×C61—21no—
228C42×C61—21no—
229C22⋊Dic61—24no—
230#11758198—24no—
231#11758198—24no—
232#11758198—24no—
233#11758198—22no—
234#11758198—24no—
235#11758198—22no—
236C4⋊Dic61—21no—
237C4⋊Dic61—21no—
238C4⋊Dic61—21no—
239C4⋊Dic61—21no—
240C4⋊Dic61—81no—
241C4⋊Dic61C22×C412yes—
242C4⋊Dic61C2×D412yes—
243#11758196—22no—
244#11758196—22no—
245#11758196—42no—
246#11758196—81no—
247#11758196—81no—
248C4×Dic61—21no—
249C4×Dic61—21no—
250C4×Dic61—24no—
251C4×Dic61—24no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418—21no—
257C2×#92418C22×C412yes—
258#11758189—28no—
259C8×D61—44no—
260C23×C61—22no—
261C23×C61—22no—
262C23×C61—22no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61C22×D411yescharacteristic
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—21no—
271C22×D61—21no—
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—22no—
275C22×D61—216no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61—84no—
281C22×D61—84no—
282C22×D61—84no—
283C22×D61—84no—
284C22×D61—84no—
285C22×D61—84no—
286C22×D61C4×D412yes—
287C22×D61#12012yes—
288C22×D61C22⋊Q812yes—
289D4×C61—22no—
290D4×C61—22no—
291D4×C61—22no—
292D4×C61C2×C4⋊C414yes—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—84no—
309C2×C4×C61C23×C411yescharacteristic
310C2×C4×C61C22×D411yescharacteristic
311C2×C4×C61C22×D411yescharacteristic
312C2×C4×C61C22×Q811yescharacteristic
313C2×C4×C61C2×#4111yescharacteristic
314C2×C4×C61C2×#4111yescharacteristic
315C22⋊D61—216no—
316C2×Dic61—22no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—22no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—84no—
332C2×Dic61C4×D412yes—
333C2×Dic61#12012yes—
334C2×Dic61C22⋊Q812yes—
335D244—22no—
336D244—22no—
337D244—22no—
338D244C2×C4⋊C414yes—
339C4×D61—84no—
340C4×D61—84no—
341C4×D61—84no—
342C4×D61C2×C4⋊C414yes—
343C4×D61C4×D414yes—
344C4×D61C22⋊Q814yes—
345C4×D61#12314yes—
346C8×C61—22no—
347C8×C61—41no—
348#92418—22no—
349#92418—41no—
350#20876—611nomaximal, Sylow
351C22×C61—24no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61—42no—
358C22×C61C2×C4×D411yescharacteristic
359C22×C61C2×#12011yescharacteristic
360C22×C61C2×C22⋊Q811yescharacteristic
361C22×C61#57611yescharacteristic
362C22×C61#57611yescharacteristic
363C22×C61#57711yescharacteristic
364C22×C61#57711yescharacteristic
365C2×D61—22no—
366C2×D61—22no—
367C2×D61—22no—
368C2×D61—22no—
369C2×D61—22no—
370C2×D61—22no—
371C2×D61—24no—
372C2×D61—42no—
373C2×D61—42no—
374C2×D61—42no—
375C2×D61—42no—
376C2×D61—42no—
377C2×D61—42no—
378C2×D61—816no—
379C2×D61#38514yes—
380C4×C61—42no—
381C4×C61—41no—
382C4×C61—42no—
383C4×C61—41no—
384C4×C61—81no—
385C4×C61C22×C4⋊C411yescharacteristic
386C4×C61C2×C4×D411yescharacteristic
387C4×C61C2×C22⋊Q811yescharacteristic
388C4×C61C2×#12311yescharacteristic
389Dic61—42no—
390Dic61—42no—
391Dic61—41no—
392Dic61—41no—
393Dic61—81no—
394Dic61#38514yes—
395C2×#518—611no—
396C2×#428—611no—
397C2×#418—611no—
398C22×#102—611no—
399#2317—611no—
400#1864—611no—
401#1864—611no—
402#1864—611no—
403#1864D6111yescharacteristic, complemented
404#1862—611no—
405#1862—611no—
406#1862—611no—
407#1862—611no—
408#1735—611no—
409#1729—611no—
410C2×C61—44no—
411C2×C61C2×#38511yescharacteristic
412C2×C61#294611yescharacteristic
413C2×C61#294611yescharacteristic
414C2×C61#300811yescharacteristic
415C2×C61#300911yescharacteristic
416C2×C61#308111yescharacteristic
417C2×C61#308111yescharacteristic
418D61—24no—
419D61—44no—
420C23×D4—611no—
421C22×M16—611no—
422C23×C8—611no—
423#518—1224no—
424#518—1224no—
425C2×C4×D4—611no—
426C2×C4×D4—611no—
427C2×C4×D4—611no—
428C2×C4×D4—1221no—
429C2×C4×D4—1221no—
430C2×C4×D4C2×D6111yescharacteristic
431C2×#117—611no—
432C2×#117—611no—
433C2×#117—611no—
434C22×C4⋊C4—611no—
435C22×C22⋊C4—1221no—
436C22×C22⋊C4—1221no—
437#428—1224no—
438C2×#107—611no—
439C2×#107—611no—
440C2×#106—611no—
441C2×#106C2×D6111yescharacteristic, complemented
442#418—618no—
443C2×#102—611no—
444C2×#102—611no—
445C2×#102—611no—
446C2×#102—611no—
447C2×#102—611no—
448C2×#102—611no—
449C2×#102—1224no—
450C2×#102C2×D6111yescharacteristic
451C2×#102C2×D6111yescharacteristic
452#389—611no—
453#389—611no—
454#389—611no—
455#389C2×D6111yescharacteristic, complemented
456#385—1221no—
457#385—1221no—
458#384—1221no—
459#382—1221no—
460#340—611no—
461#340—611no—
462#340—611no—
463#340C2×D6111yescharacteristic, complemented
464#336—611no—
465#336—611no—
466#336—611no—
467#336C2×D6111yescharacteristic, complemented
468C61#2087611yescharacteristic, complemented, Sylow
469C25—1221no—
470C22×D4—614no—
471C22×D4—614no—
472C22×D4—614no—
473C22×D4—611no—
474C22×D4—1222no—
475C22×D4—1222no—
476C22×D4—1222no—
477C22×D4—1221no—
478C22×D4C22×D6111yescharacteristic
479C23×C4—21no—
480C23×C4—611no—
481C23×C4—1221no—
482C23×C4—1221no—
483C23×C4—1221no—
484C23×C4—1221no—
485C2×M16—614no—
486C2×M16—1222no—
487C2×M16—1222no—
488C22×C8—611no—
489C22×C8—611no—
490C22×C8—1222no—
491C22×C8—1222no—
492C22×C8—1222no—
493C22×C8C22×D6111yescharacteristic
494C22×C8C22×D6111yescharacteristic
495C4×D4—22no—
496C4×D4—22no—
497C4×D4—1222no—
498C4×D4—1222no—
499C4×D4—1228no—
500C4×D4—1222no—
501C4×D4—1222no—
502C4×D4—1228no—
503C4×D4—1222no—
504C4×D4—1222no—
505#117—614no—
506#117—614no—
507#117—1222no—
508#117—1222no—
509#117—1222no—
510#117—1222no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4—611no—
514C2×C4⋊C4—611no—
515C2×C4⋊C4—611no—
516C2×C4⋊C4—611no—
517C2×C4⋊C4—1222no—
518C2×C4⋊C4—1222no—
519C2×C4⋊C4—1221no—
520C2×C4⋊C4—1221no—
521C2×C4⋊C4—1221no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4C22×D6111yescharacteristic
524C2×C4⋊C4C22×D6111yescharacteristic
525C2×C4⋊C4C22×D6111yescharacteristic
526C2×C22⋊C4—21no—
527C2×C22⋊C4—611no—
528C2×C22⋊C4—611no—
529C2×C22⋊C4—1228no—
530C2×C22⋊C4—1221no—
531C2×C22⋊C4—1221no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1228no—
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—1221no—
536C2×C42—611no—
537C2×C42—1221no—
538C2×C42—1221no—
539C2×C42C22×D6111yescharacteristic
540#107—1222no—
541#107—1222no—
542#106—22no—
543#106—1222no—
544#102—22no—
545#102—614no—
546#102—614no—
547#102—614no—
548#102—1222no—
549#102—1222no—
550#102—1222no—
551#102C4×D6114yescomplemented
552#95—21no—
553#95—1221no—
554#95—1221no—
555#95—1221no—
556C24—21no—
557C24—611no—
558C24—1224no—
559C24—1224no—
560C24—1224no—
561C24—1221no—
562C24—4881no—
563C24—4881no—
564C24—4881no—
565C24—4881no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—6116no—
570C2×D4—612no—
571C2×D4—612no—
572C2×D4—612no—
573C2×D4—1228no—
574C2×D4—1228no—
575C2×D4—1228no—
576C2×D4—1224no—
577C2×D4—1224no—
578C2×D4—1224no—
579C2×D4—1221no—
580C2×D4—1221no—
581C2×D4—1221no—
582C2×D4C2×C4×D6112yes—
583C2×D4D4×D6112yes—
584C2×D4Q8×D6112yes—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—24no—
588C22×C4—21no—
589C22×C4—81no—
590C22×C4—81no—
591C22×C4—611no—
592C22×C4—612no—
593C22×C4—612no—
594C22×C4—612no—
595C22×C4—612no—
596C22×C4—612no—
597C22×C4—612no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—1224no—
601C22×C4—1224no—
602C22×C4—1224no—
603C22×C4—1221no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—4881no—
607C22×C4—4881no—
608C22×C4—4881no—
609C22×C4—4881no—
610C22×C4—4881no—
611C22×C4—4881no—
612C22×C4—4881no—
613C22×C4—4881no—
614C22×C4—2442no—
615C22×C4D4×D6111yescharacteristic
616C22×C4D4×D6111yescharacteristic
617C22×C4C23×D6111yescharacteristic
618M16—1228no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—612no—
625C2×C8—1221no—
626C2×C8—1221no—
627C2×C8—1221no—
628C2×C8—1221no—
629C2×C8—1221no—
630C2×C8—2444no—
631C2×C8C2×C4×D6112yes—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—81no—
637C4⋊C4—612no—
638C4⋊C4—612no—
639C4⋊C4—1222no—
640C4⋊C4—1222no—
641C4⋊C4—1221no—
642C4⋊C4—1221no—
643C4⋊C4—1221no—
644C4⋊C4—1221no—
645C4⋊C4—4881no—
646C4⋊C4—4881no—
647C4⋊C4—4881no—
648C4⋊C4—2442no—
649C4⋊C4C2×C4×D6112yes—
650C4⋊C4D4×D6112yes—
651C22⋊C4—24no—
652C22⋊C4—1222no—
653C22⋊C4—1222no—
654C22⋊C4—1224no—
655C22⋊C4—1224no—
656C22⋊C4—1224no—
657C22⋊C4—1224no—
658C22⋊C4—1224no—
659C42—21no—
660C42—21no—
661C42—1224no—
662C42—1224no—
663C42—1221no—
664C42—1221no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—612no—
673C23—612no—
674C23—612no—
675C23—12216no—
676C23—1221no—
677C23—1221no—
678C23—1221no—
679C23—1221no—
680C23—1222no—
681C23—1222no—
682C23—1222no—
683C23—4884no—
684C23—4884no—
685C23—4884no—
686C23—4884no—
687C23—4884no—
688C23—4884no—
689C23—2441no—
690C23—2441no—
691C23—2441no—
692C23—2441no—
693C23C2×D4×D6111yescharacteristic
694D4—22no—
695D4—22no—
696D4—22no—
697D4—614no—
698D4—12216no—
699D4—1222no—
700D4—1222no—
701D4—1222no—
702D4C4⋊C4×D6114yes—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—84no—
719C2×C4—612no—
720C2×C4—612no—
721C2×C4—612no—
722C2×C4—614no—
723C2×C4—614no—
724C2×C4—614no—
725C2×C4—614no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—1221no—
729C2×C4—1221no—
730C2×C4—1221no—
731C2×C4—1221no—
732C2×C4—1221no—
733C2×C4—1221no—
734C2×C4—4884no—
735C2×C4—4884no—
736C2×C4—4884no—
737C2×C4—4884no—
738C2×C4—2441no—
739C2×C4—2441no—
740C2×C4—2441no—
741C2×C4—2441no—
742C2×C4—2441no—
743C2×C4—2441no—
744C2×C4—2441no—
745C2×C4C22×C4×D6111yescharacteristic
746C2×C4C2×D4×D6111yescharacteristic
747C2×C4C2×D4×D6111yescharacteristic
748C2×C4C2×Q8×D6111yescharacteristic
749C2×C4#41×D6111yescharacteristic
750C2×C4#41×D6111yescharacteristic
751C8—22no—
752C8—41no—
753C8—1222no—
754C8—2441no—
755C22—24no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—614no—
763C22—1222no—
764C22—1222no—
765C22—1222no—
766C22—1222no—
767C22—1222no—
768C22—1222no—
769C22—1224no—
770C22—48816no—
771C22—2442no—
772C22—2442no—
773C22—2442no—
774C22—2442no—
775C22—2442no—
776C22—2442no—
777C22C4×D4×D6111yescharacteristic
778C22#120×D6111yescharacteristic
779C22C22⋊Q8×D6111yescharacteristic
780C22#1684056411yescharacteristic
781C22#1684056611yescharacteristic
782C22#1684056811yescharacteristic
783C22#1684057211yescharacteristic
784C4—42no—
785C4—41no—
786C4—41no—
787C4—42no—
788C4—81no—
789C4—614no—
790C4—4881no—
791C4—2442no—
792C4—2441no—
793C4—2442no—
794C4—2441no—
795C4C2×C4⋊C4×D6111yescharacteristic
796C4C4×D4×D6111yescharacteristic
797C4C22⋊Q8×D6111yescharacteristic
798C4#123×D6111yescharacteristic
799C2—44no—
800C2—1224no—
801C2—2444no—
802C2#385×D6111yescharacteristic
803C2#2145464611yescharacteristic
804C2#2145464811yescharacteristic
805C2#2145508411yescharacteristic
806C2#2145509111yescharacteristic
807C2#2145564511yescharacteristic
808C2#2145564711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1864C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
cosocleC22×C4×C61C24
hypercenter#1864D61
hypocenterC61#20876
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1864

Complements

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

NH ≅ G/Ntype
2. C2×#16839801C2semidirect
5. #21448441C2semidirect
6. #21446081C2semidirect
7. #21446080C2semidirect
8. #21446077C2semidirect
9. #21446069C2semidirect
10. #21446068C2semidirect
11. #21446065C2semidirect
12. #21446064C2semidirect
13. #21445534C2semidirect
14. #21445514C2semidirect
15. C61×#1864C2semidirect
33. C2×#14519711C22semidirect
34. C2×#14519710C22semidirect
35. C2×#14519708C22semidirect
36. #16839765C4semidirect
44. #16839661C22semidirect
45. #16839660C22semidirect
46. #16839658C22semidirect
51. #16839525C22semidirect
52. #16839524C22semidirect
53. #16839524C22semidirect
54. #16839517C22semidirect
55. #16839516C22semidirect
56. #16839516C22semidirect
58. C2×#106×C61C22semidirect
61. C61×#389C22semidirect
62. C61×#340C22semidirect
63. C61×#336C22semidirect
80. C2×#11758189C2×C4semidirect
96. #14519735C2×C4semidirect
127. #14519699C2×C4semidirect
129. #14519698C2×C4semidirect
131. #14519697C2×C4semidirect
149. #102×C61C2×C4semidirect
191. D4×D61C4⋊C4semidirect
403. #1864D61semidirect
441. C2×#106C2×D61semidirect
455. #389C2×D61semidirect
463. #340C2×D61semidirect
467. #336C2×D61semidirect
468. C61#20876semidirect
551. #102C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402342
C2×#168398012
C2×#168397652
C2×#102×D612
#214484412
#214460812
#214460802
#214460772
#214460692
#214460682
#214460652
#214460642
#214455342
#214455142
C61×#18642
#2087661