Finite Group Databasebeta

← #29647533

Subgroups — #29647533

Order 15616.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459853C211yesmaximal, characteristic
2#21454856C211yesmaximal, characteristic, complemented
3#21448455C211yesmaximal, characteristic, complemented
4#21444396C211yesmaximal, characteristic, complemented
5#21444385C211yesmaximal, characteristic, complemented
6#21444378C211yesmaximal, characteristic, complemented
7#21444374C211yesmaximal, characteristic, complemented
8#21444367C211yesmaximal, characteristic, complemented
9#21444361C211yesmaximal, characteristic, complemented
10#21444346C211yesmaximal, characteristic, complemented
11#21444333C211yesmaximal, characteristic, complemented
12#21444322C211yesmaximal, characteristic, complemented
13#21444309C211yesmaximal, characteristic, complemented
14#327×D61C211yesmaximal, characteristic, complemented
15C61×#1512C211yesmaximal, characteristic, complemented
16#16840477C411yescharacteristic, complemented
17#16840472C411yescharacteristic, complemented
18#16840465C411yescharacteristic, complemented
19#16840465C411yescharacteristic, complemented
20#16840458—21no—
21#16840434C411yescharacteristic, complemented
22#16840405C411yescharacteristic, complemented
23#16840405C411yescharacteristic, complemented
24#16840404—21no—
25#16840404—21no—
26D4×D244—21no—
27D4×D244C411yescharacteristic, complemented
28#16840367—21no—
29#16840351—21no—
30#16840351—21no—
31#16840312C2211yescharacteristic
32#16840275C2211yescharacteristic
33#16840275C2211yescharacteristic
34#121×D61C2211yescharacteristic
35#121×D61C2211yescharacteristic
36#16840236—21no—
37C2×C4×D244C2211yescharacteristic
38#16839839—21no—
39#16839835—21no—
40#16839835—21no—
41#16839827—21no—
42#16839815C2211yescharacteristic, complemented
43#16839724C2211yescharacteristic, complemented
44#16839724C2211yescharacteristic, complemented
45C22⋊C8×D61C2211yescharacteristic, complemented
46C22⋊C8×D61C2211yescharacteristic, complemented
47#16839652—21no—
48#16839647—21no—
49#16839640—21no—
50#16839633—21no—
51#16839630C2211yescharacteristic, complemented
52#16839624C2211yescharacteristic, complemented
53#16839621C2211yescharacteristic, complemented
54#16839609C2211yescharacteristic, complemented
55#95×D61C2211yescharacteristic, complemented
56#16839499C2211yescharacteristic, complemented
57#16839499C2211yescharacteristic, complemented
58#16839497C2211yescharacteristic, complemented
59#16839497C2211yescharacteristic, complemented
60#16839497C2211yescharacteristic, complemented
61#16839497C2211yescharacteristic, complemented
62#16839496C2211yescharacteristic
63#16839496C2211yescharacteristic
64#16839495C2211yescharacteristic, complemented
65#16839495C2211yescharacteristic, complemented
66#16839495C2211yescharacteristic, complemented
67#16839495C2211yescharacteristic, complemented
68C61×#529C2211yescharacteristic
69C61×#432C2211yescharacteristic, complemented
70C61×#382C2211yescharacteristic, complemented
71C61×#328C2211yescharacteristic, complemented
72C61×#328C2211yescharacteristic, complemented
73C61×#327C2211yescharacteristic
74C61×#327C2211yescharacteristic
75C2×#11758226C2×C411yescharacteristic
76C2×#11758226C2×C411yescharacteristic, complemented
77C2×#11758222—21no—
78C22×D244—21no—
79C22×D244D411yescharacteristic
80C2×D4×D61—21no—
81C2×D4×D61—21no—
82C2×D4×D61C2×C411yescharacteristic
83C2×D4×D61C2×C411yescharacteristic, complemented
84C22×C4×D61—21no—
85C22×C4×D61C2311yescharacteristic
86C22×C4×D61C2311yescharacteristic
87C2×#11758189—21no—
88C2×#11758189—21no—
89C2×C8×D61—21no—
90C2×C8×D61—21no—
91#14519777C2×C411yescharacteristic, complemented
92#14519774—21no—
93#14519774C2×C411yescharacteristic, complemented
94#14519772—21no—
95#14519772—21no—
96#14519769—21no—
97#14519765—21no—
98#14519763—21no—
99#14519763—21no—
100#14519762—21no—
101#14519762—21no—
102#14519762—21no—
103#14519762—21no—
104#14519759—21no—
105#14519759—21no—
106#14519755—21no—
107#14519755—21no—
108#14519753C2×C411yescharacteristic
109#14519753C2×C411yescharacteristic, complemented
110#14519752—21no—
111#14519752—21no—
112#14519752—21no—
113#14519752—21no—
114#14519752C2×C411yescharacteristic
115#14519752C2×C411yescharacteristic
116#14519752C2×C411yescharacteristic, complemented
117#14519752C2×C411yescharacteristic, complemented
118#14519751—21no—
119#14519751—21no—
120#14519751—21no—
121#14519751C2311yescharacteristic
122#14519751C2311yescharacteristic
123#14519750—21no—
124#14519750—21no—
125#14519750—21no—
126#14519750—21no—
127#14519749—21no—
128#14519749—21no—
129#14519748C2×C411yescharacteristic
130#14519748C2×C411yescharacteristic, complemented
131#14519747—21no—
132#14519747—21no—
133#14519747—21no—
134#14519747—21no—
135#14519747—21no—
136#14519747—21no—
137C4×D244—21no—
138C4×D244—21no—
139C4×D244—21no—
140C4×D244C2×C411yescharacteristic
141C4×D244C2×C411yescharacteristic
142C4×D244C2×C411yescharacteristic
143C4×D244C2×C411yescharacteristic
144C4×D244C2×C411yescharacteristic, complemented
145C4×D244C2×C411yescharacteristic, complemented
146C4×D244D411yescharacteristic
147C4×D244D411yescharacteristic
148C4×D244D411yescharacteristic
149C4×D244D411yescharacteristic
150#14519739—21no—
151#14519739—21no—
152#14519739—21no—
153#14519739—21no—
154#14519737—21no—
155#14519737—21no—
156#14519736—21no—
157#14519735C2×C411yescharacteristic
158#14519735C2×C411yescharacteristic, complemented
159C2×C4⋊Dic61D411yescharacteristic
160C2×#11758196—21no—
161C4⋊C4×D61C2×C411yescharacteristic
162C4⋊C4×D61C2×C411yescharacteristic, complemented
163C2×#11758198—21no—
164C2×#11758198—21no—
165C2×#11758198—21no—
166C2×#11758198D411yescharacteristic
167C2×#11758198D411yescharacteristic
168C22⋊C4×D61—21no—
169C22⋊C4×D61—21no—
170C22⋊C4×D61—21no—
171C22⋊C4×D61—21no—
172C2×C4×Dic61—21no—
173C4⋊#92418—21no—
174C22⋊#92418C2311yescharacteristic
175C22⋊#92418C2311yescharacteristic
176#14519689—21no—
177#14519689—21no—
178#14519689—21no—
179#14519689—21no—
180C4×#92418—21no—
181#14519684—21no—
182#14519684—21no—
183#14519684—21no—
184#14519684—21no—
185#14519684C2311yescharacteristic
186#14519684C2311yescharacteristic
187#126×C61—21no—
188#125×C61C2×C411yescharacteristic, complemented
189#124×C61C2×C411yescharacteristic, complemented
190#123×C61—21no—
191C22⋊Q8×C61C2311yescharacteristic
192#121×C61C2311yescharacteristic
193C4×Q8×C61C2×C411yescharacteristic, complemented
194C4×D4×C61—21no—
195C4×D4×C61C2×C411yescharacteristic, complemented
196#117×C61—21no—
197C2×C4⋊C4×C61—21no—
198C2×C42×C61C2311yescharacteristic
199C4⋊C8×C61—21no—
200C22⋊C8×C61C2311yescharacteristic
201C22⋊C8×C61C2311yescharacteristic
202#97×C61—21no—
203#95×C61—21no—
204#95×C61C2311yescharacteristic
205#95×C61C2311yescharacteristic
206C23×D61—21no—
207C23×D61—21no—
208C23×D61C2×D411yescharacteristic
209C23×D61C2×D411yescharacteristic
210C2×Q8×C61C22×C411yescharacteristic
211C2×D4×C61—21no—
212C2×D4×C61C22×C411yescharacteristic
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2411yescharacteristic
219C2×C22⋊D61—21no—
220C2×C22⋊D61—21no—
221C2×C22⋊D61—21no—
222C2×C22⋊D61—21no—
223C2×C22⋊D61—21no—
224C2×C22⋊D61—21no—
225C22×Dic61—21no—
226C22×Dic61—21no—
227C22×Dic61C2×D411yescharacteristic
228C22×Dic61C2×D411yescharacteristic
229#11758226—81no—
230#11758226—81no—
231D4×D61—81no—
232D4×D61—81no—
233D4×D61—81no—
234D4×D61—81no—
235D4×D61—81no—
236D4×D61—81no—
237#11758222—81no—
238#11758222—81no—
239C2×D244—21no—
240C2×D244—21no—
241C2×D244—21no—
242C2×D244—21no—
243C2×D244—21no—
244C2×D244—21no—
245C2×D244—21no—
246C2×D244—21no—
247C2×D244—42no—
248C2×D244—44no—
249C2×D244C22⋊C411yescharacteristic
250C2×D244C22⋊C411yescharacteristic
251C2×D244C22⋊C411yescharacteristic
252C2×D244C22⋊C411yescharacteristic
253C2×D244C22×C411yescharacteristic
254C2×D244C22×C411yescharacteristic
255C2×C4×D61—21no—
256C2×C4×D61—21no—
257C2×C4×D61—21no—
258C2×C4×D61—21no—
259C2×C4×D61—21no—
260C2×C4×D61—21no—
261C2×C4×D61—42no—
262C2×C4×D61—81no—
263C2×C4×D61—81no—
264C2×C4×D61—81no—
265C2×C4×D61—81no—
266C2×C4×D61C22×C411yescharacteristic
267C2×C4×D61C22×C411yescharacteristic
268C2×C4×D61C22×C411yescharacteristic
269C2×C4×D61C22×C411yescharacteristic
270C2×C4×D61C2×D411yescharacteristic
271C2×C4×D61C2×D411yescharacteristic
272C2×C4×D61C2×D411yescharacteristic
273C2×C4×D61C2×D411yescharacteristic
274C2×Dic122—21no—
275C2×C8×C61—21no—
276C2×C8×C61—21no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61—21no—
280C4⋊C4×C61—21no—
281C4⋊C4×C61—81no—
282C4⋊C4×C61C22×C411yescharacteristic
283C4⋊C4×C61C22×C411yescharacteristic
284C22⋊C4×C61—21no—
285C22⋊C4×C61—21no—
286C22⋊C4×C61—21no—
287C22⋊C4×C61—21no—
288C22⋊C4×C61—21no—
289C42×C61—21no—
290C42×C61C22×C411yescharacteristic
291C42×C61C22×C411yescharacteristic
292C42×C61C2×D411yescharacteristic
293C42×C61C2×D411yescharacteristic
294C22⋊Dic61—21no—
295C22⋊Dic61—21no—
296#11758198—21no—
297#11758198—21no—
298#11758198—21no—
299#11758198—21no—
300#11758198—21no—
301#11758198—21no—
302#11758198—21no—
303#11758198—21no—
304#11758198—21no—
305#11758198—21no—
306#11758198—21no—
307#11758198—21no—
308#11758198—42no—
309#11758198—81no—
310#11758198—81no—
311#11758198C22⋊C411yescharacteristic
312#11758198C22⋊C411yescharacteristic
313#11758198C22⋊C411yescharacteristic
314#11758198C22⋊C411yescharacteristic
315#11758198C22⋊C411yescharacteristic
316#11758198C22⋊C411yescharacteristic
317#11758198C22⋊C411yescharacteristic
318#11758198C22⋊C411yescharacteristic
319C4⋊Dic61—21no—
320C4⋊Dic61C22⋊C411yescharacteristic
321C4⋊Dic61C22⋊C411yescharacteristic
322C4⋊Dic61C22⋊C411yescharacteristic
323C4⋊Dic61C22⋊C411yescharacteristic
324C4⋊Dic61C22×C411yescharacteristic
325C4⋊Dic61C22×C411yescharacteristic
326#11758196—21no—
327#11758196—21no—
328#11758196—21no—
329#11758196—21no—
330#11758196—81no—
331C4×Dic61—21no—
332C4×Dic61—21no—
333C4×Dic61—81no—
334C2×#92418—21no—
335C2×#92418—21no—
336#11758189—81no—
337#11758189—81no—
338C8×D61—81no—
339C8×D61—81no—
340C23×C61—21no—
341C23×C61C22×D411yescharacteristic
342C22×D61—21no—
343C22×D61—21no—
344C22×D61—21no—
345C22×D61—21no—
346C22×D61—22no—
347C22×D61—21no—
348C22×D61—21no—
349C22×D61—41no—
350C22×D61—41no—
351C22×D61—41no—
352C22×D61—42no—
353C22×D61—42no—
354C22×D61—81no—
355C22×D61—81no—
356C22×D61—81no—
357C22×D61—81no—
358C22×D61C2×C22⋊C411yescharacteristic
359C22×D61C2×C22⋊C411yescharacteristic
360C22×D61C2×C22⋊C411yescharacteristic
361C22×D61C2×C22⋊C411yescharacteristic
362Q8×C61—41no—
363D4×C61—41no—
364D4×C61—41no—
365D4×C61—41no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61—42no—
374C2×C4×C61—41no—
375C2×C4×C61—41no—
376C2×C4×C61—41no—
377C2×C4×C61—41no—
378C2×C4×C61—41no—
379C2×C4×C61—41no—
380C2×C4×C61C2×C22⋊C411yescharacteristic
381C2×C4×C61C2×C22⋊C411yescharacteristic
382C2×C4×C61C2×C22⋊C411yescharacteristic
383C2×C4×C61C2×C22⋊C411yescharacteristic
384C2×C4×C61C23×C411yescharacteristic
385C2×C4×C61C22×D411yescharacteristic
386C22⋊D61—41no—
387C22⋊D61—41no—
388C22⋊D61—41no—
389C22⋊D61—41no—
390C22⋊D61—81no—
391C22⋊D61—81no—
392C22⋊D61—81no—
393C22⋊D61—81no—
394C2×Dic61—21no—
395C2×Dic61—21no—
396C2×Dic61—41no—
397C2×Dic61—41no—
398C2×Dic61—41no—
399C2×Dic61—41no—
400C2×Dic61—41no—
401C2×Dic61—41no—
402C2×Dic61—41no—
403C2×Dic61—41no—
404C2×Dic61C2×C22⋊C411yescharacteristic
405C2×Dic61C2×C22⋊C411yescharacteristic
406C2×Dic61C2×C22⋊C411yescharacteristic
407C2×Dic61C2×C22⋊C411yescharacteristic
408D244—22no—
409D244—22no—
410D244—41no—
411D244—41no—
412D244—41no—
413D244—41no—
414D244—42no—
415D244—42no—
416D244—42no—
417D244—81no—
418D244—81no—
419D244—81no—
420D244—81no—
421D244—81no—
422C4×D61—41no—
423C4×D61—41no—
424C4×D61—41no—
425C4×D61—41no—
426C4×D61—41no—
427C4×D61—41no—
428C4×D61—41no—
429C4×D61—41no—
430C4×D61—81no—
431C4×D61—81no—
432C4×D61—81no—
433C4×D61—81no—
434C4×D61—81no—
435C4×D61—81no—
436C4×D61—84no—
437Dic122—81no—
438C8×C61—41no—
439C8×C61—41no—
440#92418—41no—
441#92418—41no—
442#17597—611nomaximal, Sylow
443C22×C61—21no—
444C22×C61—21no—
445C22×C61—41no—
446C22×C61—41no—
447C22×C61—41no—
448C22×C61C22×C22⋊C411yescharacteristic
449C22×C61#57611yescharacteristic
450C22×C61#57711yescharacteristic
451C2×D61—21no—
452C2×D61—21no—
453C2×D61—21no—
454C2×D61—21no—
455C2×D61—21no—
456C2×D61—21no—
457C2×D61—21no—
458C2×D61—21no—
459C2×D61—21no—
460C2×D61—21no—
461C2×D61—21no—
462C2×D61—42no—
463C2×D61—42no—
464C2×D61—41no—
465C2×D61—41no—
466C2×D61—41no—
467C2×D61—41no—
468C2×D61—41no—
469C2×D61—41no—
470C2×D61—81no—
471C2×D61—81no—
472C2×D61—162no—
473C2×D61—162no—
474C2×D61#42112yes—
475C4×C61—21no—
476C4×C61—21no—
477C4×C61—21no—
478C4×C61—21no—
479C4×C61—21no—
480C4×C61—21no—
481C4×C61—41no—
482C4×C61—41no—
483C4×C61—41no—
484C4×C61—81no—
485C4×C61—81no—
486Dic61—21no—
487Dic61—21no—
488Dic61—21no—
489Dic61—21no—
490Dic61—41no—
491Dic61—41no—
492Dic61—81no—
493Dic61—81no—
494#3519—611no—
495#2974—611no—
496#2318—611no—
497#1521—611no—
498#1519—611no—
499#1517—611no—
500#1516—611no—
501#1514—611no—
502#1513—611no—
503#1512D6111yescharacteristic, complemented
504#1510—611no—
505#1507—611no—
506#1504—611no—
507#1501—611no—
508C2×#327—611no—
509C2×C61—21no—
510C2×C61—21no—
511C2×C61—81no—
512C2×C61#288311yescharacteristic
513C2×C61#289711yescharacteristic
514C2×C61C2×#42111yescharacteristic
515D61—22no—
516D61—41no—
517D61—41no—
518D61—41no—
519D61—81no—
520D61—81no—
521#555—611no—
522#554—611no—
523#553—611no—
524#553—611no—
525#553—1221no—
526#550—611no—
527#546—611no—
528#546—611no—
529#546—1221no—
530#546—1221no—
531D42—611no—
532D42—1221no—
533#540—1221no—
534#538—1221no—
535#538—1221no—
536#532—611no—
537#529C2×D6111yescharacteristic
538#525—611no—
539#525—611no—
540C2×#121—611no—
541C2×#121—611no—
542#518—1221no—
543C2×C4×D4—611no—
544#436—1221no—
545#435—1221no—
546#435—1221no—
547C8×D4—1221no—
548#432C2×D6111yescharacteristic, complemented
549#431—611no—
550#407—611no—
551#407—611no—
552C2×C22⋊C8—611no—
553C2×C22⋊C8—611no—
554#388—1221no—
555#387—1221no—
556#386—1221no—
557#385—1221no—
558#383—611no—
559#382C2×D6111yescharacteristic, complemented
560#381—611no—
561#380—611no—
562C4×C22⋊C4—611no—
563C2×#95—611no—
564#328—611no—
565#328—611no—
566#328C2×D6111yescharacteristic, complemented
567#328C2×D6111yescharacteristic, complemented
568#327—611no—
569#327—611no—
570#327—611no—
571#327—611no—
572#327—611no—
573#327—611no—
574#327—611no—
575#327—611no—
576#327—611no—
577#327—611no—
578#327C2×D6111yescharacteristic
579#327C2×D6111yescharacteristic
580C61#1759711yescharacteristic, complemented, Sylow
581C2×#41—611no—
582C2×#41—611no—
583C2×#41—1221no—
584C22×D4—611no—
585C22×D4—611no—
586C22×D4—611no—
587C22×D4—1221no—
588C22×D4—1221no—
589C22×D4—1221no—
590C23×C4—611no—
591C23×C4—611no—
592C23×C4—1221no—
593C2×M16—1221no—
594C2×M16—1221no—
595C22×C8—1221no—
596C22×C8—1221no—
597C4⋊Q8—611no—
598#127—611no—
599#127—1221no—
600#126—21no—
601#126—1221no—
602#126—1221no—
603#125—1221no—
604#125C4×D6111yescharacteristic, complemented
605#124—1221no—
606#124—1221no—
607#124—1221no—
608#124C4×D6111yescharacteristic, complemented
609#123—21no—
610#123—1221no—
611#123—1221no—
612#123—1221no—
613#123—1221no—
614#123—1221no—
615#123—1221no—
616C22⋊Q8—611no—
617C22⋊Q8—611no—
618C22⋊Q8—1221no—
619C22⋊Q8—1221no—
620C22⋊Q8C22×D6111yescharacteristic
621#121—611no—
622#121—611no—
623#121—611no—
624#121—611no—
625#121—611no—
626#121—611no—
627#121—611no—
628#121—611no—
629#121—1221no—
630#121—1221no—
631#121—1221no—
632#121—1221no—
633#121—1221no—
634#121—1221no—
635#121—1221no—
636#121—1221no—
637#121—1221no—
638#121—1221no—
639#121—1221no—
640#121—1221no—
641#121—1221no—
642#121C22×D6111yescharacteristic
643#120—1221no—
644#120—1221no—
645#120—1221no—
646#120—1221no—
647#120—1221no—
648#120—1221no—
649C4×Q8C4×D6111yescharacteristic, complemented
650C4×D4—21no—
651C4×D4—611no—
652C4×D4—611no—
653C4×D4—611no—
654C4×D4—611no—
655C4×D4—611no—
656C4×D4—611no—
657C4×D4—611no—
658C4×D4—611no—
659C4×D4—611no—
660C4×D4—611no—
661C4×D4—1221no—
662C4×D4—1221no—
663C4×D4—1221no—
664C4×D4—1221no—
665C4×D4—1221no—
666C4×D4—1221no—
667C4×D4—1221no—
668C4×D4—1221no—
669C4×D4—1221no—
670C4×D4C4×D6111yescharacteristic, complemented
671#117—21no—
672#117—611no—
673#117—611no—
674#117—1221no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—611no—
677C2×C4⋊C4—611no—
678C2×C4⋊C4—611no—
679C2×C4⋊C4—1221no—
680C2×C22⋊C4—611no—
681C2×C22⋊C4—611no—
682C2×C22⋊C4—1221no—
683C2×C22⋊C4—1221no—
684C2×C22⋊C4—1221no—
685C2×C22⋊C4—1221no—
686C2×C22⋊C4—1221no—
687C2×C22⋊C4—1221no—
688C2×C22⋊C4—1221no—
689C2×C42—1221no—
690C2×C42C22×D6111yescharacteristic
691C4⋊C8—21no—
692C4⋊C8—1221no—
693C22⋊C8—611no—
694C22⋊C8—611no—
695C22⋊C8—1221no—
696C22⋊C8—1221no—
697C22⋊C8—1221no—
698C22⋊C8—1221no—
699C22⋊C8C22×D6111yescharacteristic
700C22⋊C8C22×D6111yescharacteristic
701#97—21no—
702C4×C8—1221no—
703#95—21no—
704#95—611no—
705#95—611no—
706#95—1221no—
707#95—1221no—
708#95—1221no—
709#95—1221no—
710#95C22×D6111yescharacteristic
711#95C22×D6111yescharacteristic
712C24—611no—
713C24—611no—
714C24—1221no—
715C24—1221no—
716#41—4881no—
717#41—4881no—
718#41—4881no—
719#41—4881no—
720C2×Q8—1221no—
721C2×Q8C2×C4×D6111yescharacteristic
722C2×D4—21no—
723C2×D4—611no—
724C2×D4—611no—
725C2×D4—611no—
726C2×D4—611no—
727C2×D4—611no—
728C2×D4—611no—
729C2×D4—1221no—
730C2×D4—1221no—
731C2×D4—1221no—
732C2×D4—1221no—
733C2×D4—1221no—
734C2×D4—1221no—
735C2×D4—1221no—
736C2×D4—1221no—
737C2×D4—1221no—
738C2×D4—1221no—
739C2×D4—1221no—
740C2×D4—1221no—
741C2×D4—1221no—
742C2×D4—1221no—
743C2×D4—4881no—
744C2×D4—4881no—
745C2×D4—4881no—
746C2×D4—4881no—
747C2×D4—4881no—
748C2×D4—4881no—
749C2×D4—2442no—
750C2×D4—2444no—
751C2×D4C2×C4×D6111yescharacteristic
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—611no—
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—1221no—
766C22×C4—1221no—
767C22×C4—1221no—
768C22×C4—1221no—
769C22×C4—1221no—
770C22×C4—1221no—
771C22×C4—1221no—
772C22×C4—1221no—
773C22×C4—4881no—
774C22×C4—4881no—
775C22×C4—4881no—
776C22×C4—4881no—
777C22×C4—2442no—
778C22×C4D4×D6111yescharacteristic
779C22×C4D4×D6111yescharacteristic
780C22×C4C23×D6111yescharacteristic
781M16—4881no—
782M16—4881no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—1221no—
786C2×C8—1221no—
787C2×C8—4881no—
788C2×C8—4881no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—81no—
794C4⋊C4—611no—
795C4⋊C4—611no—
796C4⋊C4—611no—
797C4⋊C4—611no—
798C4⋊C4—611no—
799C4⋊C4—611no—
800C4⋊C4—1221no—
801C4⋊C4—1221no—
802C4⋊C4—1221no—
803C4⋊C4—1221no—
804C4⋊C4—1221no—
805C4⋊C4—4881no—
806C4⋊C4C2×C4×D6111yescharacteristic
807C4⋊C4C2×C4×D6111yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—611no—
814C22⋊C4—611no—
815C22⋊C4—611no—
816C22⋊C4—611no—
817C22⋊C4—611no—
818C22⋊C4—611no—
819C22⋊C4—611no—
820C22⋊C4—611no—
821C22⋊C4—1221no—
822C22⋊C4—1221no—
823C22⋊C4—1221no—
824C22⋊C4—1221no—
825C22⋊C4—1221no—
826C22⋊C4—1221no—
827C22⋊C4—1221no—
828C22⋊C4—1221no—
829C22⋊C4—1221no—
830C22⋊C4—1221no—
831C22⋊C4—1221no—
832C22⋊C4—1221no—
833C22⋊C4—1221no—
834C22⋊C4—1221no—
835C22⋊C4—4881no—
836C22⋊C4—4881no—
837C22⋊C4—2442no—
838C42—21no—
839C42—1221no—
840C42—1221no—
841C42—4881no—
842C42C2×C4×D6111yescharacteristic
843C42C2×C4×D6111yescharacteristic
844C42D4×D6111yescharacteristic
845C42D4×D6111yescharacteristic
846C23—21no—
847C23—611no—
848C23—611no—
849C23—611no—
850C23—611no—
851C23—1222no—
852C23—1221no—
853C23—1221no—
854C23—1221no—
855C23—1221no—
856C23—1221no—
857C23—1221no—
858C23—4881no—
859C23—4881no—
860C23—4881no—
861C23—4881no—
862C23—2441no—
863C23—2441no—
864C23—2441no—
865C23—2442no—
866C23—2442no—
867C23C2×D4×D6111yescharacteristic
868Q8—41no—
869Q8—4881no—
870D4—41no—
871D4—41no—
872D4—41no—
873D4—1222no—
874D4—1222no—
875D4—4881no—
876D4—4881no—
877D4—4881no—
878D4—4881no—
879D4—4881no—
880D4—4881no—
881D4—4881no—
882D4—4881no—
883D4—4881no—
884D4—2441no—
885D4—2441no—
886D4—2441no—
887D4—2441no—
888D4—2442no—
889D4—2442no—
890D4—2442no—
891D4—2441no—
892D4—2441no—
893D4—2441no—
894D4—2441no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—42no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—611no—
910C2×C4—611no—
911C2×C4—611no—
912C2×C4—611no—
913C2×C4—1221no—
914C2×C4—1221no—
915C2×C4—4881no—
916C2×C4—4881no—
917C2×C4—4881no—
918C2×C4—4881no—
919C2×C4—4881no—
920C2×C4—4881no—
921C2×C4—4884no—
922C2×C4—2441no—
923C2×C4—2441no—
924C2×C4—2441no—
925C2×C4—2441no—
926C2×C4—2441no—
927C2×C4—2441no—
928C2×C4—2441no—
929C2×C4—2441no—
930C2×C4—2441no—
931C2×C4—2441no—
932C2×C4—2441no—
933C2×C4—2441no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4—2441no—
938C2×C4C22⋊C4×D6111yescharacteristic
939C2×C4C22⋊C4×D6111yescharacteristic
940C2×C4C22⋊C4×D6111yescharacteristic
941C2×C4C22⋊C4×D6111yescharacteristic
942C2×C4C22×C4×D6111yescharacteristic
943C2×C4C2×D4×D6111yescharacteristic
944C8—41no—
945C8—41no—
946C8—2441no—
947C8—2441no—
948C22—21no—
949C22—21no—
950C22—41no—
951C22—41no—
952C22—41no—
953C22—612no—
954C22—1221no—
955C22—1221no—
956C22—1221no—
957C22—1221no—
958C22—1221no—
959C22—1221no—
960C22—1221no—
961C22—1221no—
962C22—1221no—
963C22—1221no—
964C22—1221no—
965C22—9762no—
966C22—9762no—
967C22—4881no—
968C22—4881no—
969C22—2442no—
970C22—2442no—
971C22—2441no—
972C22—2441no—
973C22—2441no—
974C22—2441no—
975C22—2441no—
976C22—2441no—
977C22C2×C22⋊C4×D6111yescharacteristic
978C22#1684056611yescharacteristic
979C22#1684057111yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—41no—
987C4—41no—
988C4—41no—
989C4—81no—
990C4—81no—
991C4—1221no—
992C4—1221no—
993C4—1221no—
994C4—1221no—
995C4—4881no—
996C4—4881no—
997C4—2441no—
998C4—2441no—
999C2—21no—
1000C2—21no—
1001C2—81no—
1002C2—1222no—
1003C2—4881no—
1004C2—4881no—
1005C2—2441no—
1006C2—2441no—
1007C2—2441no—
1008C2#2145427811yescharacteristic
1009C2#2145434311yescharacteristic
1010C2#421×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1512C2
socleC22×C61C22×C22⋊C4
prime radical#21459853C2
cosocleC22×C4×C61C24
hypercenter#1512D61
hypocenterC61#17597
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1512

Complements

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

NH ≅ G/Ntype
2. #21454856C2semidirect
3. #21448455C2semidirect
4. #21444396C2semidirect
5. #21444385C2semidirect
6. #21444378C2semidirect
7. #21444374C2semidirect
8. #21444367C2semidirect
9. #21444361C2semidirect
10. #21444346C2semidirect
11. #21444333C2semidirect
12. #21444322C2semidirect
13. #21444309C2semidirect
14. #327×D61C2semidirect
15. C61×#1512C2semidirect
16. #16840477C4semidirect
17. #16840472C4semidirect
18. #16840465C4semidirect
19. #16840465C4semidirect
21. #16840434C4semidirect
22. #16840405C4semidirect
23. #16840405C4semidirect
27. D4×D244C4semidirect
42. #16839815C22semidirect
43. #16839724C22semidirect
44. #16839724C22semidirect
45. C22⋊C8×D61C22semidirect
46. C22⋊C8×D61C22semidirect
51. #16839630C22semidirect
52. #16839624C22semidirect
53. #16839621C22semidirect
54. #16839609C22semidirect
55. #95×D61C22semidirect
56. #16839499C22semidirect
57. #16839499C22semidirect
58. #16839497C22semidirect
59. #16839497C22semidirect
60. #16839497C22semidirect
61. #16839497C22semidirect
64. #16839495C22semidirect
65. #16839495C22semidirect
66. #16839495C22semidirect
67. #16839495C22semidirect
69. C61×#432C22semidirect
70. C61×#382C22semidirect
71. C61×#328C22semidirect
72. C61×#328C22semidirect
76. C2×#11758226C2×C4semidirect
83. C2×D4×D61C2×C4semidirect
91. #14519777C2×C4semidirect
93. #14519774C2×C4semidirect
109. #14519753C2×C4semidirect
116. #14519752C2×C4semidirect
117. #14519752C2×C4semidirect
130. #14519748C2×C4semidirect
144. C4×D244C2×C4semidirect
145. C4×D244C2×C4semidirect
158. #14519735C2×C4semidirect
162. C4⋊C4×D61C2×C4semidirect
188. #125×C61C2×C4semidirect
189. #124×C61C2×C4semidirect
193. C4×Q8×C61C2×C4semidirect
195. C4×D4×C61C2×C4semidirect
503. #1512D61semidirect
548. #432C2×D61semidirect
559. #382C2×D61semidirect
566. #328C2×D61semidirect
567. #328C2×D61semidirect
580. C61#17597semidirect
604. #125C4×D61semidirect
608. #124C4×D61semidirect
649. C4×Q8C4×D61semidirect
670. C4×D4C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214598532
#214548562
#214484552
#214443962
#214443852
#214443782
#214443742
#214443672
#214443612
#214443462
#214443332
#214443222
#214443092
#327×D612
C61×#15122
#1759761