Finite Group Databasebeta

← #29647539

Subgroups — #29647539

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#21448454C211yesmaximal, characteristic, complemented
4#21444393C211yesmaximal, characteristic, complemented
5#21444377C211yesmaximal, characteristic, complemented
6#21444376C211yesmaximal, characteristic, complemented
7#21444364C211yesmaximal, characteristic, complemented
8#21444360C211yesmaximal, characteristic, complemented
9#21444354C211yesmaximal, characteristic, complemented
10#21444348C211yesmaximal, characteristic, complemented
11#21444333C211yesmaximal, characteristic, complemented
12#21444320C211yesmaximal, characteristic, complemented
13#21444307C211yesmaximal, characteristic, complemented
14#327×D61C211yesmaximal, characteristic, complemented
15C61×#1519C211yesmaximal, 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#16839656—21no—
48#16839643—21no—
49#16839638—21no—
50#16839633—21no—
51#16839629C2211yescharacteristic, complemented
52#16839626C2211yescharacteristic, complemented
53#16839625C2211yescharacteristic, complemented
54#16839609C2211yescharacteristic, complemented
55#95×D61C2211yescharacteristic, 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
70C61×#380C2211yescharacteristic, complemented
71C61×#327C2211yescharacteristic
72C61×#327C2211yescharacteristic
73C61×#327C2211yescharacteristic, complemented
74C61×#327C2211yescharacteristic, complemented
75C2×#11758222C2×C411yescharacteristic, complemented
76C2×#11758224—21no—
77C2×#11758224C2×C411yescharacteristic
78C22×C22⋊D61—21no—
79C22×C22⋊D61D411yescharacteristic
80C2×D4×D61—21no—
81C2×D4×D61C2×C411yescharacteristic
82C22×C4×D61—21no—
83C22×C4×D61C2311yescharacteristic
84C2×#11758194—21no—
85C2×#11758189—21no—
86C2×C8×D61—21no—
87#14519776C2×C411yescharacteristic, complemented
88#14519773—21no—
89#14519773C2×C411yescharacteristic, complemented
90#14519772—21no—
91#14519770—21no—
92#14519770—21no—
93#14519768C2×C411yescharacteristic, complemented
94#14519767—21no—
95#14519764—21no—
96#14519764C2×C411yescharacteristic, complemented
97#14519763—21no—
98#14519763—21no—
99#14519762—21no—
100#14519760—21no—
101#14519759—21no—
102#14519759—21no—
103#14519758—21no—
104#14519758—21no—
105#14519758—21no—
106#14519757C2×C411yescharacteristic
107#14519756—21no—
108#14519756C2×C411yescharacteristic, complemented
109#14519756C2311yescharacteristic
110#14519755—21no—
111#14519752C2×C411yescharacteristic
112#14519751—21no—
113#14519751C2×C411yescharacteristic, complemented
114#14519751C2311yescharacteristic
115#14519750—21no—
116#14519750—21no—
117#14519749—21no—
118#14519749—21no—
119#14519749—21no—
120#14519749—21no—
121#14519749—21no—
122#14519749—21no—
123#14519748—21no—
124#14519748—21no—
125#14519748C2×C411yescharacteristic
126#14519748C2×C411yescharacteristic
127#14519746—21no—
128#14519746—21no—
129#14519746—21no—
130#14519745—21no—
131#14519745—21no—
132#14519745—21no—
133#14519742C2×C411yescharacteristic, complemented
134D4×Dic61—21no—
135D4×Dic61—21no—
136D4×Dic61C2×C411yescharacteristic, complemented
137D4×Dic61C2×C411yescharacteristic, complemented
138#14519739C2×C411yescharacteristic, complemented
139C4×C22⋊D61—21no—
140C4×C22⋊D61—21no—
141C4×C22⋊D61—21no—
142C4×C22⋊D61—21no—
143C4×C22⋊D61C2×C411yescharacteristic
144C4×C22⋊D61C2×C411yescharacteristic
145C4×C22⋊D61C2×C411yescharacteristic
146C4×C22⋊D61C2×C411yescharacteristic
147C4×C22⋊D61D411yescharacteristic
148C4×C22⋊D61D411yescharacteristic
149C4×C22⋊D61D411yescharacteristic
150C4×C22⋊D61D411yescharacteristic
151#14519737—21no—
152#14519737—21no—
153#14519737—21no—
154#14519737—21no—
155#14519736C2×C411yescharacteristic, complemented
156#14519735C2×C411yescharacteristic
157#14519733—21no—
158#14519733—21no—
159C2×#11758196—21no—
160C2×#11758196D411yescharacteristic
161C4⋊C4×D61C2×C411yescharacteristic
162C2×C22⋊Dic61—21no—
163C2×C22⋊Dic61—21no—
164C2×C22⋊Dic61D411yescharacteristic
165C2×#11758198—21no—
166C2×#11758198D411yescharacteristic
167C22⋊C4×D61—21no—
168C22⋊C4×D61—21no—
169C2×C4×Dic61—21no—
170C2×C4×Dic61C2311yescharacteristic
171#14519706—21no—
172#14519706—21no—
173C22⋊#92418—21no—
174C22⋊#92418C2311yescharacteristic
175C22⋊#92418C2311yescharacteristic
176#14519689—21no—
177#14519689—21no—
178#14519687—21no—
179C8×Dic61—21no—
180#14519684—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, complemented
189C23×C4×C61C2311yescharacteristic
190C22×C8×C61—21no—
191#121×C61—21no—
192#121×C61—21no—
193#121×C61C2×C411yescharacteristic, complemented
194#121×C61C2×C411yescharacteristic, complemented
195#121×C61C2311yescharacteristic
196#121×C61C2311yescharacteristic
197C2×C4⋊C4×C61—21no—
198C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
199C2×C22⋊C4×C61—21no—
200C2×C22⋊C4×C61—21no—
201C22⋊C8×C61—21no—
202C22⋊C8×C61C2311yescharacteristic
203C22⋊C8×C61C2311yescharacteristic
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—81no—
224C22×C4×C61C22×C411yescharacteristic
225C22×C4×C61C22×C411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2411yescharacteristic
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—21no—
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—42no—
240C2×C22⋊D61—44no—
241C2×C22⋊D61C22⋊C411yescharacteristic
242C2×C22⋊D61C22⋊C411yescharacteristic
243C2×C22⋊D61C22⋊C411yescharacteristic
244C2×C22⋊D61C22⋊C411yescharacteristic
245C22×Dic61—21no—
246C22×Dic61—21no—
247C22×Dic61—21no—
248C22×Dic61—21no—
249C22×Dic61—21no—
250C22×Dic61C2×D411yescharacteristic
251C22×Dic61C2×D411yescharacteristic
252C22×Dic61C2×D411yescharacteristic
253#11758224—81no—
254#11758224—81no—
255#11758224—81no—
256D4×D61—81no—
257D4×D61—81no—
258D4×D61—81no—
259#11758222—81no—
260C2×D244—21no—
261C2×D244C22×C411yescharacteristic
262C2×C4×D61—21no—
263C2×C4×D61—21no—
264C2×C4×D61—21no—
265C2×C4×D61—42no—
266C2×C4×D61—81no—
267C2×C4×D61—81no—
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×C61—81no—
280C4⋊C4×C61C22×C411yescharacteristic
281C4⋊C4×C61C22×C411yescharacteristic
282C22⋊C4×C61—21no—
283C22⋊C4×C61—21no—
284C22⋊C4×C61—21no—
285C22⋊C4×C61—21no—
286C22⋊C4×C61—81no—
287C22⋊Dic61—21no—
288C22⋊Dic61—21no—
289C22⋊Dic61—21no—
290C22⋊Dic61—21no—
291C22⋊Dic61—21no—
292C22⋊Dic61—21no—
293C22⋊Dic61—21no—
294C22⋊Dic61—21no—
295C22⋊Dic61—21no—
296C22⋊Dic61—81no—
297C22⋊Dic61C22⋊C411yescharacteristic
298C22⋊Dic61C22⋊C411yescharacteristic
299C22⋊Dic61C22⋊C411yescharacteristic
300C22⋊Dic61C22⋊C411yescharacteristic
301#11758198—21no—
302#11758198—21no—
303#11758198—21no—
304#11758198—21no—
305#11758198—21no—
306#11758198—21no—
307#11758198—42no—
308#11758198C22⋊C411yescharacteristic
309#11758198C22⋊C411yescharacteristic
310#11758198C22⋊C411yescharacteristic
311#11758198C22⋊C411yescharacteristic
312C4⋊Dic61—21no—
313C4⋊Dic61—21no—
314C4⋊Dic61C22×C411yescharacteristic
315C4⋊Dic61C22×C411yescharacteristic
316#11758196—21no—
317#11758196—21no—
318#11758196—21no—
319#11758196—21no—
320#11758196—21no—
321#11758196—21no—
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—21no—
343C23×C61—21no—
344C23×C61—41no—
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—22no—
355C22×D61—21no—
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×C61C2×C22⋊C411yescharacteristic
387C2×C4×C61C2×C22⋊C411yescharacteristic
388C2×C4×C61C23×C411yescharacteristic
389C2×C4×C61C22×D411yescharacteristic
390C22⋊D61—22no—
391C22⋊D61—22no—
392C22⋊D61—41no—
393C22⋊D61—41no—
394C22⋊D61—42no—
395C22⋊D61—42no—
396C22⋊D61—41no—
397C22⋊D61—41no—
398C22⋊D61—42no—
399C22⋊D61—81no—
400C22⋊D61—81no—
401C22⋊D61—81no—
402C22⋊D61—81no—
403C22⋊D61—81no—
404C2×Dic61—21no—
405C2×Dic61—21no—
406C2×Dic61—21no—
407C2×Dic61—21no—
408C2×Dic61—21no—
409C2×Dic61—41no—
410C2×Dic61—41no—
411C2×Dic61—42no—
412C2×Dic61—41no—
413C2×Dic61—41no—
414C2×Dic61—41no—
415C2×Dic61—41no—
416C2×Dic61—41no—
417C2×Dic61—41no—
418C2×Dic61—81no—
419C2×Dic61—81no—
420C2×Dic61C2×C22⋊C411yescharacteristic
421C2×Dic61C2×C22⋊C411yescharacteristic
422C2×Dic61C2×C22⋊C411yescharacteristic
423C2×Dic61C2×C22⋊C411yescharacteristic
424C2×Dic61C2×C22⋊C411yescharacteristic
425C2×Dic61C2×C22⋊C411yescharacteristic
426D244—41no—
427D244—81no—
428C4×D61—41no—
429C4×D61—41no—
430C4×D61—41no—
431C4×D61—41no—
432C4×D61—81no—
433C4×D61—81no—
434C4×D61—81no—
435C4×D61—84no—
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—21no—
451C22×C61—41no—
452C22×C61—41no—
453C22×C61—41no—
454C22×C61—41no—
455C22×C61—41no—
456C22×C61—41no—
457C22×C61—81no—
458C22×C61—81no—
459C22×C61—162no—
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—42no—
469C2×D61—42no—
470C2×D61—41no—
471C2×D61—41no—
472C2×D61—41no—
473C2×D61—162no—
474C2×D61#42112yes—
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#1519D6111yescharacteristic, complemented
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×#327—611no—
509C2×C61—21no—
510C2×C61—21no—
511C2×C61—41no—
512C2×C61—41no—
513C2×C61—81no—
514C2×C61—81no—
515C2×C61#288311yescharacteristic
516C2×C61#289711yescharacteristic
517C2×C61C2×#42111yescharacteristic
518D61—22no—
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#380C2×D6111yescharacteristic, complemented
562C4×C22⋊C4—611no—
563C2×#95—611no—
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, complemented
590C23×C4—611no—
591C23×C4—1221no—
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, complemented
640#121C4×D6111yescharacteristic, complemented
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—21no—
676C2×C4⋊C4—611no—
677C2×C4⋊C4—611no—
678C2×C4⋊C4—1221no—
679C2×C4⋊C4C4×D6111yescharacteristic, complemented
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—611no—
683C2×C22⋊C4—611no—
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—611no—
704#95—611no—
705#95—1221no—
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—81no—
756C22×C4—611no—
757C22×C4—611no—
758C22×C4—611no—
759C22×C4—611no—
760C22×C4—611no—
761C22×C4—611no—
762C22×C4—611no—
763C22×C4—1221no—
764C22×C4—1221no—
765C22×C4—1221no—
766C22×C4—1221no—
767C22×C4—1221no—
768C22×C4—1221no—
769C22×C4—1221no—
770C22×C4—1221no—
771C22×C4—4881no—
772C22×C4—4881no—
773C22×C4—4881no—
774C22×C4—2442no—
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—81no—
791C4⋊C4—611no—
792C4⋊C4—611no—
793C4⋊C4—611no—
794C4⋊C4—611no—
795C4⋊C4—611no—
796C4⋊C4—611no—
797C4⋊C4—1221no—
798C4⋊C4—1221no—
799C4⋊C4—1221no—
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—81no—
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—1221no—
836C22⋊C4—4881no—
837C22⋊C4—2442no—
838C42—611no—
839C42—611no—
840C42—611no—
841C42—611no—
842C42—1221no—
843C42—1221no—
844C42—1221no—
845C42—4881no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—41no—
851C23—41no—
852C23—42no—
853C23—81no—
854C23—81no—
855C23—611no—
856C23—611no—
857C23—1222no—
858C23—1221no—
859C23—1221no—
860C23—1221no—
861C23—4881no—
862C23—4881no—
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—611no—
911C2×C4—611no—
912C2×C4—611no—
913C2×C4—611no—
914C2×C4—611no—
915C2×C4—611no—
916C2×C4—1221no—
917C2×C4—1221no—
918C2×C4—1221no—
919C2×C4—1221no—
920C2×C4—1221no—
921C2×C4—4881no—
922C2×C4—4881no—
923C2×C4—4881no—
924C2×C4—4884no—
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—21no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—81no—
963C22—81no—
964C22—162no—
965C22—612no—
966C22—1221no—
967C22—1221no—
968C22—1221no—
969C22—1221no—
970C22—1221no—
971C22—9762no—
972C22—2442no—
973C22—2442no—
974C22—2441no—
975C22—2441no—
976C22—2441no—
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—41no—
1002C2—41no—
1003C2—81no—
1004C2—81no—
1005C2—1222no—
1006C2—4881no—
1007C2—2441no—
1008C2#2145427711yescharacteristic
1009C2#2145434011yescharacteristic
1010C2#421×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1519C2
socleC22×C61C22×C22⋊C4
prime radical#21459845C2
cosocleC22×C4×C61C24
hypercenter#1519D61
hypocenterC61#17597
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1519

Complements

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

NH ≅ G/Ntype
2. #21454850C2semidirect
3. #21448454C2semidirect
4. #21444393C2semidirect
5. #21444377C2semidirect
6. #21444376C2semidirect
7. #21444364C2semidirect
8. #21444360C2semidirect
9. #21444354C2semidirect
10. #21444348C2semidirect
11. #21444333C2semidirect
12. #21444320C2semidirect
13. #21444307C2semidirect
14. #327×D61C2semidirect
15. C61×#1519C2semidirect
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. #16839625C22semidirect
54. #16839609C22semidirect
55. #95×D61C22semidirect
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. C61×#380C22semidirect
73. C61×#327C22semidirect
74. C61×#327C22semidirect
75. C2×#11758222C2×C4semidirect
87. #14519776C2×C4semidirect
89. #14519773C2×C4semidirect
93. #14519768C2×C4semidirect
96. #14519764C2×C4semidirect
108. #14519756C2×C4semidirect
113. #14519751C2×C4semidirect
133. #14519742C2×C4semidirect
136. D4×Dic61C2×C4semidirect
137. D4×Dic61C2×C4semidirect
138. #14519739C2×C4semidirect
155. #14519736C2×C4semidirect
188. C22×D4×C61C2×C4semidirect
193. #121×C61C2×C4semidirect
194. #121×C61C2×C4semidirect
198. C2×C4⋊C4×C61C2×C4semidirect
498. #1519D61semidirect
553. C2×C22⋊C8C2×D61semidirect
561. #380C2×D61semidirect
578. #327C2×D61semidirect
579. #327C2×D61semidirect
580. C61#17597semidirect
589. C22×D4C4×D61semidirect
639. #121C4×D61semidirect
640. #121C4×D61semidirect
679. C2×C4⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214598452
#214548502
#214484542
#214443932
#214443772
#214443762
#214443642
#214443602
#214443542
#214443482
#214443332
#214443202
#214443072
#327×D612
C61×#15192
#1759761