Finite Group Databasebeta

← #29647532

Subgroups — #29647532

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#21459845C211yesmaximal, characteristic
2#21454850C211yesmaximal, characteristic, complemented
3#21448453C211yesmaximal, characteristic, complemented
4#21444393C211yesmaximal, characteristic, complemented
5#21444385C211yesmaximal, characteristic, complemented
6#21444377C211yesmaximal, characteristic, complemented
7#21444372C211yesmaximal, characteristic, complemented
8#21444364C211yesmaximal, characteristic, complemented
9#21444359C211yesmaximal, characteristic, complemented
10#21444354C211yesmaximal, characteristic, complemented
11#21444346C211yesmaximal, characteristic, complemented
12#21444335C211yesmaximal, characteristic, complemented
13#21444321C211yesmaximal, characteristic, complemented
14#21444311C211yesmaximal, characteristic, complemented
15C2×C61×#327C211yesmaximal, characteristic, complemented
16#16840476C411yescharacteristic, complemented
17#16840467C411yescharacteristic, complemented
18#16840460C411yescharacteristic, complemented
19#16840459C411yescharacteristic, complemented
20#16840455—21no—
21#16840430C411yescharacteristic, complemented
22#16840409C411yescharacteristic, complemented
23#16840406—21no—
24#16840406C411yescharacteristic, complemented
25#16840401—21no—
26D4×C22⋊D61—21no—
27D4×C22⋊D61C411yescharacteristic, complemented
28#16840362—21no—
29#16840350—21no—
30#16840344—21no—
31#16840307C2211yescharacteristic
32#16840293C2211yescharacteristic
33#16840273C2211yescharacteristic
34#16840272C2211yescharacteristic
35#121×D61C2211yescharacteristic
36#16840235—21no—
37C2×C4×C22⋊D61C2211yescharacteristic
38#16839837—21no—
39#16839836—21no—
40#16839833—21no—
41C8×C22⋊D61—21no—
42#16839816C2211yescharacteristic, complemented
43#16839812C2211yescharacteristic, complemented
44#16839726C2211yescharacteristic, complemented
45#16839724C2211yescharacteristic, complemented
46C22⋊C8×D61C2211yescharacteristic, complemented
47#16839651—21no—
48#16839644—21no—
49#16839641—21no—
50#16839635—21no—
51#16839629C2211yescharacteristic, complemented
52#16839626C2211yescharacteristic, complemented
53#16839624C2211yescharacteristic, complemented
54#16839621C2211yescharacteristic, complemented
55C4×C22⋊Dic61C2211yescharacteristic, complemented
56#16839500C2211yescharacteristic, complemented
57#16839500C2211yescharacteristic, complemented
58#16839498C2211yescharacteristic, complemented
59#16839498C2211yescharacteristic, complemented
60#16839497C2211yescharacteristic, complemented
61#16839497C2211yescharacteristic, complemented
62#16839496C2211yescharacteristic
63#16839496C2211yescharacteristic
64#16839496C2211yescharacteristic, complemented
65#16839496C2211yescharacteristic, complemented
66#16839495C2211yescharacteristic, complemented
67#16839495C2211yescharacteristic, complemented
68C2×#121×C61C2211yescharacteristic
69C2×C22⋊C8×C61C2211yescharacteristic, complemented
70C2×#95×C61C2211yescharacteristic, complemented
71C61×#327C2211yescharacteristic
72C61×#327C2211yescharacteristic
73C61×#327C2211yescharacteristic, complemented
74C61×#327C2211yescharacteristic, complemented
75C2×#11758222C2×C411yescharacteristic
76C2×#11758224—21no—
77C2×#11758224C2×C411yescharacteristic, complemented
78C22×C22⋊D61—21no—
79C22×C22⋊D61D411yescharacteristic
80C2×D4×D61—21no—
81C2×D4×D61C2×C411yescharacteristic, complemented
82C22×C4×D61C2311yescharacteristic
83C2×#11758194—21no—
84C2×#11758189—21no—
85C2×C8×D61—21no—
86#14519776C2×C411yescharacteristic, complemented
87#14519773—21no—
88#14519773C2×C411yescharacteristic, complemented
89#14519772—21no—
90#14519770—21no—
91#14519770—21no—
92#14519768C2×C411yescharacteristic, complemented
93#14519767—21no—
94#14519764—21no—
95#14519764C2×C411yescharacteristic, complemented
96#14519763—21no—
97#14519763—21no—
98#14519762—21no—
99#14519760—21no—
100#14519759—21no—
101#14519759—21no—
102#14519758—21no—
103#14519758—21no—
104#14519758—21no—
105#14519757C2×C411yescharacteristic, complemented
106#14519756—21no—
107#14519756C2×C411yescharacteristic
108#14519756C2311yescharacteristic
109#14519755—21no—
110#14519752C2×C411yescharacteristic, complemented
111#14519751—21no—
112#14519751C2×C411yescharacteristic
113#14519751C2311yescharacteristic
114#14519750—21no—
115#14519750—21no—
116#14519749—21no—
117#14519749—21no—
118#14519749—21no—
119#14519749—21no—
120#14519749—21no—
121#14519749—21no—
122#14519748—21no—
123#14519748—21no—
124#14519748C2×C411yescharacteristic, complemented
125#14519748C2×C411yescharacteristic, complemented
126#14519746—21no—
127#14519746—21no—
128#14519746—21no—
129#14519745—21no—
130#14519745—21no—
131#14519745—21no—
132#14519742C2×C411yescharacteristic, complemented
133D4×Dic61—21no—
134D4×Dic61—21no—
135D4×Dic61C2×C411yescharacteristic, complemented
136D4×Dic61C2×C411yescharacteristic, complemented
137#14519739C2×C411yescharacteristic, complemented
138C4×C22⋊D61—21no—
139C4×C22⋊D61—21no—
140C4×C22⋊D61—21no—
141C4×C22⋊D61—21no—
142C4×C22⋊D61C2×C411yescharacteristic
143C4×C22⋊D61C2×C411yescharacteristic
144C4×C22⋊D61C2×C411yescharacteristic
145C4×C22⋊D61C2×C411yescharacteristic
146C4×C22⋊D61D411yescharacteristic
147C4×C22⋊D61D411yescharacteristic
148C4×C22⋊D61D411yescharacteristic
149C4×C22⋊D61D411yescharacteristic
150#14519737—21no—
151#14519737—21no—
152#14519737—21no—
153#14519737—21no—
154#14519736C2×C411yescharacteristic
155#14519735C2×C411yescharacteristic, complemented
156#14519733—21no—
157#14519733—21no—
158C2×#11758196—21no—
159C2×#11758196—21no—
160C2×#11758196D411yescharacteristic
161C4⋊C4×D61C2×C411yescharacteristic, complemented
162C2×C22⋊Dic61—21no—
163C2×C22⋊Dic61—21no—
164C2×C22⋊Dic61D411yescharacteristic
165C2×#11758198—21no—
166C2×#11758198—21no—
167C2×#11758198D411yescharacteristic
168C22⋊C4×D61—21no—
169C22⋊C4×D61—21no—
170C2×C4×Dic61—21no—
171C2×C4×Dic61C2311yescharacteristic
172#14519706—21no—
173#14519706—21no—
174C22⋊#92418—21no—
175C22⋊#92418C2311yescharacteristic
176C22⋊#92418C2311yescharacteristic
177#14519689—21no—
178#14519689—21no—
179#14519687—21no—
180C8×Dic61—21no—
181#14519684—21no—
182#14519684—21no—
183#14519684—21no—
184#14519684—21no—
185#14519684C2311yescharacteristic
186#14519684C2311yescharacteristic
187C22×D4×C61—21no—
188C22×D4×C61C2×C411yescharacteristic
189C23×C4×C61—21no—
190C23×C4×C61C2311yescharacteristic
191C22×C8×C61—21no—
192#121×C61—21no—
193#121×C61—21no—
194#121×C61C2×C411yescharacteristic
195#121×C61C2×C411yescharacteristic
196#121×C61C2311yescharacteristic
197#121×C61C2311yescharacteristic
198C2×C4⋊C4×C61C2×C411yescharacteristic
199C2×C22⋊C4×C61—21no—
200C22⋊C8×C61—21no—
201C22⋊C8×C61C2311yescharacteristic
202C22⋊C8×C61C2311yescharacteristic
203#95×C61—21no—
204#95×C61C2311yescharacteristic
205#95×C61C2311yescharacteristic
206C24×C61—21no—
207C24×C61C2×D411yescharacteristic
208C23×D61—21no—
209C23×D61C2×D411yescharacteristic
210C2×D4×C61—21no—
211C2×D4×C61—21no—
212C2×D4×C61—21no—
213C2×D4×C61—21no—
214C2×D4×C61—21no—
215C2×D4×C61—81no—
216C2×D4×C61—81no—
217C2×D4×C61—81no—
218C2×D4×C61C22×C411yescharacteristic
219C2×D4×C61C22×C411yescharacteristic
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—42no—
224C22×C4×C61—81no—
225C22×C4×C61—81no—
226C22×C4×C61—81no—
227C22×C4×C61C22×C411yescharacteristic
228C22×C4×C61C22×C411yescharacteristic
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2411yescharacteristic
233C2×C22⋊D61—21no—
234C2×C22⋊D61—21no—
235C2×C22⋊D61—21no—
236C2×C22⋊D61—21no—
237C2×C22⋊D61—21no—
238C2×C22⋊D61—21no—
239C2×C22⋊D61—21no—
240C2×C22⋊D61—21no—
241C2×C22⋊D61—21no—
242C2×C22⋊D61—42no—
243C2×C22⋊D61—44no—
244C2×C22⋊D61C22⋊C411yescharacteristic
245C2×C22⋊D61C22⋊C411yescharacteristic
246C2×C22⋊D61C22⋊C411yescharacteristic
247C2×C22⋊D61C22⋊C411yescharacteristic
248C22×Dic61—21no—
249C22×Dic61—21no—
250C22×Dic61—21no—
251C22×Dic61—21no—
252C22×Dic61—21no—
253C22×Dic61C2×D411yescharacteristic
254C22×Dic61C2×D411yescharacteristic
255C22×Dic61C2×D411yescharacteristic
256#11758224—81no—
257#11758224—81no—
258#11758224—81no—
259D4×D61—81no—
260D4×D61—81no—
261D4×D61—81no—
262#11758222—81no—
263C2×D244—21no—
264C2×D244C22×C411yescharacteristic
265C2×C4×D61—21no—
266C2×C4×D61—21no—
267C2×C4×D61—21no—
268C2×C4×D61—81no—
269C2×C4×D61C22×C411yescharacteristic
270C2×C4×D61C22×C411yescharacteristic
271C2×C4×D61C2×D411yescharacteristic
272C2×C4×D61C2×D411yescharacteristic
273C2×Dic122—21no—
274C2×Dic122C22×C411yescharacteristic
275C2×C8×C61—21no—
276C2×C8×C61—21no—
277C2×C8×C61—81no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61C22×C411yescharacteristic
280C4⋊C4×C61C22×C411yescharacteristic
281C22⋊C4×C61—21no—
282C22⋊C4×C61—21no—
283C22⋊C4×C61—21no—
284C22⋊C4×C61—21no—
285C22⋊Dic61—21no—
286C22⋊Dic61—21no—
287C22⋊Dic61—21no—
288C22⋊Dic61—21no—
289C22⋊Dic61—21no—
290C22⋊Dic61—21no—
291C22⋊Dic61—21no—
292C22⋊Dic61—21no—
293C22⋊Dic61—21no—
294C22⋊Dic61—42no—
295C22⋊Dic61C22⋊C411yescharacteristic
296C22⋊Dic61C22⋊C411yescharacteristic
297C22⋊Dic61C22⋊C411yescharacteristic
298C22⋊Dic61C22⋊C411yescharacteristic
299#11758198—21no—
300#11758198—21no—
301#11758198—21no—
302#11758198—21no—
303#11758198—21no—
304#11758198—21no—
305#11758198—81no—
306#11758198—81no—
307#11758198C22⋊C411yescharacteristic
308#11758198C22⋊C411yescharacteristic
309#11758198C22⋊C411yescharacteristic
310#11758198C22⋊C411yescharacteristic
311C4⋊Dic61—21no—
312C4⋊Dic61—21no—
313C4⋊Dic61C22×C411yescharacteristic
314C4⋊Dic61C22×C411yescharacteristic
315#11758196—21no—
316#11758196—21no—
317#11758196—21no—
318#11758196—21no—
319#11758196—21no—
320#11758196—21no—
321#11758196—81no—
322#11758196—81no—
323#11758196C22⋊C411yescharacteristic
324#11758196C22⋊C411yescharacteristic
325#11758196C22⋊C411yescharacteristic
326#11758196C22⋊C411yescharacteristic
327C4×Dic61—21no—
328C4×Dic61—21no—
329C4×Dic61—21no—
330C4×Dic61—81no—
331C4×Dic61C22×C411yescharacteristic
332C4×Dic61C22×C411yescharacteristic
333C4×Dic61C2×D411yescharacteristic
334C4×Dic61C2×D411yescharacteristic
335#11758194—81no—
336C2×#92418—21no—
337C2×#92418—21no—
338#11758189—81no—
339C8×D61—81no—
340C23×C61—21no—
341C23×C61—21no—
342C23×C61—22no—
343C23×C61—21no—
344C23×C61—21no—
345C23×C61—41no—
346C23×C61—42no—
347C23×C61—81no—
348C23×C61—81no—
349C23×C61C2×C22⋊C411yescharacteristic
350C23×C61C2×C22⋊C411yescharacteristic
351C23×C61C22×D411yescharacteristic
352C22×D61—21no—
353C22×D61—21no—
354C22×D61—21no—
355C22×D61—41no—
356C22×D61—41no—
357C22×D61—42no—
358C22×D61—81no—
359C22×D61—81no—
360C22×D61C2×C22⋊C411yescharacteristic
361C22×D61C2×C22⋊C411yescharacteristic
362D4×C61—41no—
363D4×C61—41no—
364D4×C61—41no—
365D4×C61—41no—
366D4×C61—41no—
367D4×C61—41no—
368D4×C61—81no—
369D4×C61—81no—
370D4×C61—81no—
371C2×C4×C61—21no—
372C2×C4×C61—21no—
373C2×C4×C61—41no—
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×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61—41no—
384C2×C4×C61—41no—
385C2×C4×C61—81no—
386C2×C4×C61—84no—
387C2×C4×C61C2×C22⋊C411yescharacteristic
388C2×C4×C61C2×C22⋊C411yescharacteristic
389C2×C4×C61C23×C411yescharacteristic
390C2×C4×C61C22×D411yescharacteristic
391C22⋊D61—22no—
392C22⋊D61—22no—
393C22⋊D61—41no—
394C22⋊D61—41no—
395C22⋊D61—42no—
396C22⋊D61—42no—
397C22⋊D61—41no—
398C22⋊D61—41no—
399C22⋊D61—42no—
400C22⋊D61—81no—
401C22⋊D61—81no—
402C22⋊D61—81no—
403C22⋊D61—81no—
404C22⋊D61—81no—
405C2×Dic61—21no—
406C2×Dic61—21no—
407C2×Dic61—21no—
408C2×Dic61—21no—
409C2×Dic61—21no—
410C2×Dic61—41no—
411C2×Dic61—41no—
412C2×Dic61—42no—
413C2×Dic61—41no—
414C2×Dic61—41no—
415C2×Dic61—41no—
416C2×Dic61—41no—
417C2×Dic61—41no—
418C2×Dic61—41no—
419C2×Dic61—81no—
420C2×Dic61—81no—
421C2×Dic61C2×C22⋊C411yescharacteristic
422C2×Dic61C2×C22⋊C411yescharacteristic
423C2×Dic61C2×C22⋊C411yescharacteristic
424C2×Dic61C2×C22⋊C411yescharacteristic
425C2×Dic61C2×C22⋊C411yescharacteristic
426C2×Dic61C2×C22⋊C411yescharacteristic
427D244—41no—
428D244—81no—
429C4×D61—41no—
430C4×D61—41no—
431C4×D61—41no—
432C4×D61—41no—
433C4×D61—81no—
434C4×D61—81no—
435C4×D61—81no—
436Dic122—41no—
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—21no—
446C22×C61—21no—
447C22×C61—21no—
448C22×C61—21no—
449C22×C61—21no—
450C22×C61—42no—
451C22×C61—42no—
452C22×C61—41no—
453C22×C61—41no—
454C22×C61—41no—
455C22×C61—41no—
456C22×C61—41no—
457C22×C61—41no—
458C22×C61—162no—
459C22×C61#42112yes—
460C22×C61C22×C22⋊C411yescharacteristic
461C22×C61#57611yescharacteristic
462C22×C61#57711yescharacteristic
463C2×D61—21no—
464C2×D61—21no—
465C2×D61—21no—
466C2×D61—21no—
467C2×D61—21no—
468C2×D61—21no—
469C2×D61—41no—
470C2×D61—41no—
471C2×D61—41no—
472C2×D61—81no—
473C2×D61—81no—
474C2×D61—162no—
475C4×C61—21no—
476C4×C61—21no—
477C4×C61—21no—
478C4×C61—21no—
479C4×C61—41no—
480C4×C61—41no—
481C4×C61—81no—
482C4×C61—81no—
483Dic61—21no—
484Dic61—21no—
485Dic61—21no—
486Dic61—21no—
487Dic61—21no—
488Dic61—21no—
489Dic61—41no—
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#1512—611no—
504#1510—611no—
505#1507—611no—
506#1504—611no—
507#1501—611no—
508C2×#327D6111yescharacteristic, complemented
509C2×C61—21no—
510C2×C61—21no—
511C2×C61—22no—
512C2×C61—41no—
513C2×C61—81no—
514C2×C61—81no—
515C2×C61#288311yescharacteristic
516C2×C61#289711yescharacteristic
517C2×C61C2×#42111yescharacteristic
518D61—41no—
519D61—41no—
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#529—611no—
538#525—611no—
539#525—611no—
540C2×#121—611no—
541C2×#121C2×D6111yescharacteristic
542#518—1221no—
543C2×C4×D4—611no—
544#436—1221no—
545#435—1221no—
546#435—1221no—
547C8×D4—1221no—
548#432—611no—
549#431—611no—
550#407—611no—
551#407—611no—
552C2×C22⋊C8—611no—
553C2×C22⋊C8C2×D6111yescharacteristic, complemented
554#388—1221no—
555#387—1221no—
556#386—1221no—
557#385—1221no—
558#383—611no—
559#382—611no—
560#381—611no—
561#380—611no—
562C4×C22⋊C4—611no—
563C2×#95C2×D6111yescharacteristic, complemented
564#328—611no—
565#328—611no—
566#328—611no—
567#328—611no—
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#327C2×D6111yescharacteristic
577#327C2×D6111yescharacteristic
578#327C2×D6111yescharacteristic, complemented
579#327C2×D6111yescharacteristic, complemented
580C61#1759711yescharacteristic, complemented, Sylow
581C2×#41—611no—
582C2×#41—611no—
583C2×#41—1221no—
584C22×D4—21no—
585C22×D4—611no—
586C22×D4—611no—
587C22×D4—1221no—
588C22×D4—1221no—
589C22×D4C4×D6111yescharacteristic
590C23×C4—21no—
591C23×C4—611no—
592C23×C4C22×D6111yescharacteristic
593C2×M16—1221no—
594C2×M16—1221no—
595C22×C8—21no—
596C22×C8—1221no—
597C4⋊Q8—611no—
598#127—611no—
599#127—1221no—
600#126—1221no—
601#126—1221no—
602#126—1221no—
603#125—611no—
604#125—1221no—
605#124—611no—
606#124—1221no—
607#124—1221no—
608#124—1221no—
609#123—1221no—
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—611no—
619C22⋊Q8—1221no—
620C22⋊Q8—1221no—
621#121—21no—
622#121—21no—
623#121—611no—
624#121—611no—
625#121—611no—
626#121—611no—
627#121—611no—
628#121—1221no—
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#121C4×D6111yescharacteristic
640#121C4×D6111yescharacteristic
641#121C22×D6111yescharacteristic
642#121C22×D6111yescharacteristic
643#120—1221no—
644#120—1221no—
645#120—1221no—
646#120—1221no—
647#120—1221no—
648#120—1221no—
649C4×Q8—611no—
650C4×D4—611no—
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×D4—1221no—
671#117—611no—
672#117—611no—
673#117—1221no—
674#117—1221no—
675C2×C4⋊C4—611no—
676C2×C4⋊C4—611no—
677C2×C4⋊C4—1221no—
678C2×C4⋊C4—1221no—
679C2×C4⋊C4C4×D6111yescharacteristic
680C2×C22⋊C4—21no—
681C2×C22⋊C4—611no—
682C2×C22⋊C4—611no—
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—611no—
690C2×C42—1221no—
691C4⋊C8—1221no—
692C4⋊C8—1221no—
693C22⋊C8—21no—
694C22⋊C8—611no—
695C22⋊C8—611no—
696C22⋊C8—1221no—
697C22⋊C8—1221no—
698C22⋊C8—1221no—
699C22⋊C8C22×D6111yescharacteristic
700C22⋊C8C22×D6111yescharacteristic
701#97—1221no—
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—21no—
713C24—611no—
714C24—1221no—
715C24D4×D6111yescharacteristic
716#41—4881no—
717#41—4881no—
718#41—4881no—
719#41—4881no—
720C2×Q8—611no—
721C2×Q8—1221no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—81no—
728C2×D4—81no—
729C2×D4—81no—
730C2×D4—611no—
731C2×D4—611no—
732C2×D4—611no—
733C2×D4—611no—
734C2×D4—611no—
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—1221no—
744C2×D4—1221no—
745C2×D4—4881no—
746C2×D4—4881no—
747C2×D4—4881no—
748C2×D4—2442no—
749C2×D4—2444no—
750C2×D4C2×C4×D6111yescharacteristic
751C2×D4C2×C4×D6111yescharacteristic
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—42no—
756C22×C4—81no—
757C22×C4—81no—
758C22×C4—81no—
759C22×C4—611no—
760C22×C4—611no—
761C22×C4—611no—
762C22×C4—611no—
763C22×C4—611no—
764C22×C4—611no—
765C22×C4—611no—
766C22×C4—1221no—
767C22×C4—1221no—
768C22×C4—1221no—
769C22×C4—1221no—
770C22×C4—1221no—
771C22×C4—1221no—
772C22×C4—1221no—
773C22×C4—1221no—
774C22×C4—4881no—
775C22×C4C2×C4×D6111yescharacteristic
776C22×C4C2×C4×D6111yescharacteristic
777C22×C4D4×D6111yescharacteristic
778C22×C4D4×D6111yescharacteristic
779C22×C4D4×D6111yescharacteristic
780C22×C4C23×D6111yescharacteristic
781M16—4881no—
782M16—4881no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—81no—
786C2×C8—1221no—
787C2×C8—1221no—
788C2×C8—4881no—
789C4⋊C4—21no—
790C4⋊C4—611no—
791C4⋊C4—611no—
792C4⋊C4—611no—
793C4⋊C4—611no—
794C4⋊C4—611no—
795C4⋊C4—611no—
796C4⋊C4—1221no—
797C4⋊C4—1221no—
798C4⋊C4—1221no—
799C4⋊C4—1221no—
800C4⋊C4—1221no—
801C4⋊C4—1221no—
802C4⋊C4—1221no—
803C4⋊C4—1221no—
804C4⋊C4—4881no—
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—611no—
813C22⋊C4—611no—
814C22⋊C4—611no—
815C22⋊C4—611no—
816C22⋊C4—611no—
817C22⋊C4—611no—
818C22⋊C4—611no—
819C22⋊C4—611no—
820C22⋊C4—1221no—
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—611no—
839C42—611no—
840C42—611no—
841C42—611no—
842C42—1221no—
843C42—1221no—
844C42—1221no—
845C42—4881no—
846C23—22no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—41no—
852C23—42no—
853C23—81no—
854C23—81no—
855C23—611no—
856C23—611no—
857C23—1221no—
858C23—1221no—
859C23—1221no—
860C23—4881no—
861C23—4881no—
862C23—2441no—
863C23—2441no—
864C23—2442no—
865C23C22⋊C4×D6111yescharacteristic
866C23C22⋊C4×D6111yescharacteristic
867C23C2×D4×D6111yescharacteristic
868Q8—4881no—
869Q8—2441no—
870D4—41no—
871D4—41no—
872D4—41no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—81no—
877D4—81no—
878D4—81no—
879D4—1222no—
880D4—1222no—
881D4—4881no—
882D4—4881no—
883D4—4881no—
884D4—4881no—
885D4—4881no—
886D4—4881no—
887D4—2441no—
888D4—2441no—
889D4—2441no—
890D4—2442no—
891D4—2442no—
892D4—2442no—
893D4—2441no—
894D4—2441no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—81no—
910C2×C4—84no—
911C2×C4—611no—
912C2×C4—611no—
913C2×C4—611no—
914C2×C4—611no—
915C2×C4—611no—
916C2×C4—611no—
917C2×C4—1221no—
918C2×C4—1221no—
919C2×C4—1221no—
920C2×C4—1221no—
921C2×C4—1221no—
922C2×C4—4881no—
923C2×C4—4881no—
924C2×C4—4881no—
925C2×C4—4881no—
926C2×C4—4881no—
927C2×C4—2441no—
928C2×C4—2441no—
929C2×C4—2441no—
930C2×C4—2441no—
931C2×C4—2441no—
932C2×C4—2441no—
933C2×C4—2442no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4—2441no—
938C2×C4—2441no—
939C2×C4—2441no—
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—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—42no—
956C22—42no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—162no—
964C22—1221no—
965C22—1221no—
966C22—1221no—
967C22—1221no—
968C22—1221no—
969C22—1221no—
970C22—9762no—
971C22—4881no—
972C22—4881no—
973C22—2441no—
974C22—2441no—
975C22—2441no—
976C22#1683977712yes—
977C22C2×C22⋊C4×D6111yescharacteristic
978C22#1684056311yescharacteristic
979C22#1684056811yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—41no—
985C4—41no—
986C4—81no—
987C4—81no—
988C4—1221no—
989C4—1221no—
990C4—1221no—
991C4—1221no—
992C4—1221no—
993C4—1221no—
994C4—4881no—
995C4—4881no—
996C4—2441no—
997C4—2441no—
998C4—2441no—
999C2—21no—
1000C2—21no—
1001C2—22no—
1002C2—41no—
1003C2—81no—
1004C2—81no—
1005C2—4881no—
1006C2—2441no—
1007C2—2441no—
1008C2#2145427711yescharacteristic
1009C2#2145434011yescharacteristic
1010C2C2×#1683977711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#327C2
socleC22×C61C22×C22⋊C4
prime radical#21459845C2
cosocleC22×C4×C61C24
hypercenterC2×#327D61
hypocenterC61#17597
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. #21454850C2semidirect
3. #21448453C2semidirect
4. #21444393C2semidirect
5. #21444385C2semidirect
6. #21444377C2semidirect
7. #21444372C2semidirect
8. #21444364C2semidirect
9. #21444359C2semidirect
10. #21444354C2semidirect
11. #21444346C2semidirect
12. #21444335C2semidirect
13. #21444321C2semidirect
14. #21444311C2semidirect
15. C2×C61×#327C2semidirect
16. #16840476C4semidirect
17. #16840467C4semidirect
18. #16840460C4semidirect
19. #16840459C4semidirect
21. #16840430C4semidirect
22. #16840409C4semidirect
24. #16840406C4semidirect
27. D4×C22⋊D61C4semidirect
42. #16839816C22semidirect
43. #16839812C22semidirect
44. #16839726C22semidirect
45. #16839724C22semidirect
46. C22⋊C8×D61C22semidirect
51. #16839629C22semidirect
52. #16839626C22semidirect
53. #16839624C22semidirect
54. #16839621C22semidirect
55. C4×C22⋊Dic61C22semidirect
56. #16839500C22semidirect
57. #16839500C22semidirect
58. #16839498C22semidirect
59. #16839498C22semidirect
60. #16839497C22semidirect
61. #16839497C22semidirect
64. #16839496C22semidirect
65. #16839496C22semidirect
66. #16839495C22semidirect
67. #16839495C22semidirect
69. C2×C22⋊C8×C61C22semidirect
70. C2×#95×C61C22semidirect
73. C61×#327C22semidirect
74. C61×#327C22semidirect
77. C2×#11758224C2×C4semidirect
81. C2×D4×D61C2×C4semidirect
86. #14519776C2×C4semidirect
88. #14519773C2×C4semidirect
92. #14519768C2×C4semidirect
95. #14519764C2×C4semidirect
105. #14519757C2×C4semidirect
110. #14519752C2×C4semidirect
124. #14519748C2×C4semidirect
125. #14519748C2×C4semidirect
132. #14519742C2×C4semidirect
135. D4×Dic61C2×C4semidirect
136. D4×Dic61C2×C4semidirect
137. #14519739C2×C4semidirect
155. #14519735C2×C4semidirect
161. C4⋊C4×D61C2×C4semidirect
508. C2×#327D61semidirect
553. C2×C22⋊C8C2×D61semidirect
563. C2×#95C2×D61semidirect
578. #327C2×D61semidirect
579. #327C2×D61semidirect
580. C61#17597semidirect

Maximal subgroups

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

subgroupindex
#214598452
#214548502
#214484532
#214443932
#214443852
#214443772
#214443722
#214443642
#214443592
#214443542
#214443462
#214443352
#214443212
#214443112
C2×C61×#3272
#1759761