Finite Group Databasebeta

← #29647016

Subgroups — #29647016

Order 15616.

1010 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459423C211yesmaximal, characteristic
2#21454941C211yesmaximal, characteristic, complemented
3#21454461C211yesmaximal, characteristic, complemented
4#21444286C211yesmaximal, characteristic, complemented
5#21444281C211yesmaximal, characteristic, complemented
6#21444280C211yesmaximal, characteristic, complemented
7#21444262C211yesmaximal, characteristic, complemented
8#21444250C211yesmaximal, characteristic, complemented
9#21444242C211yesmaximal, characteristic, complemented
10#21444230C211yesmaximal, characteristic, complemented
11#21444224C211yesmaximal, characteristic, complemented
12#21444216C211yesmaximal, characteristic, complemented
13#21444208C211yesmaximal, characteristic, complemented
14#21444203C211yesmaximal, characteristic, complemented
15C2×C61×D4⋊C8C211yesmaximal, characteristic, complemented
16#16840495C411yescharacteristic
17#16840471C411yescharacteristic
18#16840467C411yescharacteristic
19#16840462C411yescharacteristic
20#16840461—21no—
21#16840460C411yescharacteristic
22#16840441—21no—
23#16840438—21no—
24#16840407C411yescharacteristic
25#16840406C411yescharacteristic
26#16840402—21no—
27D4×C22⋊D61C411yescharacteristic
28#16840309C2211yescharacteristic
29#16840296C2211yescharacteristic
30#16840294C2211yescharacteristic
31#16840292—21no—
32#16840273—21no—
33#16840271—21no—
34C4×#11758222C2211yescharacteristic
35C4×#11758224C2211yescharacteristic
36C2×C4×C22⋊D61—21no—
37C4×D4×D61C2211yescharacteristic
38#16839891—21no—
39#16839833—21no—
40#16839832—21no—
41C8×C22⋊D61—21no—
42#16839821—21no—
43#16839821—21no—
44#16839819C2211yescharacteristic, complemented
45#16839818C2211yescharacteristic, complemented
46#16839814C2211yescharacteristic, complemented
47#16839813C2211yescharacteristic, complemented
48#16839813C2211yescharacteristic, complemented
49#16839813C2211yescharacteristic, complemented
50#16839813C2211yescharacteristic, complemented
51#16839788—21no—
52#16839784C2211yescharacteristic, complemented
53C4⋊C8×D61C2211yescharacteristic, complemented
54#16839728—21no—
55C4×#11758194C2211yescharacteristic, complemented
56#16839494C2211yescharacteristic, complemented
57#16839494C2211yescharacteristic, complemented
58#16839492C2211yescharacteristic, complemented
59#16839492C2211yescharacteristic, complemented
60#16839491C2211yescharacteristic, complemented
61#16839491C2211yescharacteristic, complemented
62D4⋊#92418C2211yescharacteristic
63D4⋊#92418C2211yescharacteristic
64D4⋊#92418C2211yescharacteristic, complemented
65D4⋊#92418C2211yescharacteristic, complemented
66#16839489C2211yescharacteristic, complemented
67#16839489C2211yescharacteristic, complemented
68C2×C4×D4×C61C2211yescharacteristic
69C2×C4⋊C8×C61C2211yescharacteristic, complemented
70C2×C4×C8×C61C2211yescharacteristic, complemented
71C61×D4⋊C8C2211yescharacteristic
72C61×D4⋊C8C2211yescharacteristic
73C61×D4⋊C8C2211yescharacteristic, complemented
74C61×D4⋊C8C2211yescharacteristic, complemented
75C2×#11758222—21no—
76C2×#11758222D411yescharacteristic
77C2×#11758224C2×C411yescharacteristic
78C22×C22⋊D61—21no—
79C2×D4×D61C2×C411yescharacteristic
80C22×C4×D61—21no—
81C2×#11758194—21no—
82C2×#11758189—21no—
83C2×C8×D61—21no—
84#14519776C2×C411yescharacteristic
85#14519773C2×C411yescharacteristic
86#14519772—21no—
87#14519771—21no—
88#14519770—21no—
89#14519770—21no—
90#14519769C2×C411yescharacteristic
91#14519768C2×C411yescharacteristic
92#14519767—21no—
93#14519765C2×C411yescharacteristic
94#14519764C2×C411yescharacteristic
95#14519763—21no—
96#14519763—21no—
97#14519762—21no—
98#14519761—21no—
99#14519760—21no—
100#14519760—21no—
101#14519760—21no—
102#14519759—21no—
103#14519759—21no—
104#14519758—21no—
105#14519757C2×C411yescharacteristic
106#14519756—21no—
107#14519756—21no—
108#14519756C2×C411yescharacteristic
109#14519755—21no—
110#14519754—21no—
111#14519754—21no—
112#14519752C2×C411yescharacteristic
113#14519751—21no—
114#14519751—21no—
115#14519751C2×C411yescharacteristic
116#14519750—21no—
117#14519750—21no—
118#14519749—21no—
119#14519749—21no—
120#14519748C2×C411yescharacteristic
121#14519748C2×C411yescharacteristic
122#14519747—21no—
123#14519746—21no—
124#14519746—21no—
125#14519745—21no—
126C4×Dic122C2×C411yescharacteristic
127C4×Dic122D411yescharacteristic
128C4×Dic122C2311yescharacteristic
129#14519742C2×C411yescharacteristic
130C4×D244C2×C411yescharacteristic
131C4×D244D411yescharacteristic
132C4×D244C2311yescharacteristic
133D4×Dic61C2×C411yescharacteristic
134D4×Dic61C2×C411yescharacteristic
135#14519739C2×C411yescharacteristic
136C4×C22⋊D61—21no—
137C4×C22⋊D61—21no—
138C4×C22⋊D61—21no—
139C4×C22⋊D61—21no—
140C4×C22⋊D61—21no—
141C4×C22⋊D61—21no—
142C4×C22⋊D61—21no—
143C4×C22⋊D61—21no—
144C4×C22⋊D61—21no—
145C4×C22⋊D61C2×C411yescharacteristic
146C4×C22⋊D61C2×C411yescharacteristic
147C4×C22⋊D61D411yescharacteristic
148C4×C22⋊D61D411yescharacteristic
149#14519737—21no—
150#14519737—21no—
151#14519736—21no—
152#14519736D411yescharacteristic
153#14519735C2×C411yescharacteristic
154#14519734—21no—
155#14519734D411yescharacteristic
156#14519734D411yescharacteristic
157#14519733—21no—
158C2×#11758196—21no—
159C4⋊C4×D61C2×C411yescharacteristic
160C2×C22⋊Dic61—21no—
161C2×#11758198—21no—
162C22⋊C4×D61—21no—
163C2×C4×Dic61—21no—
164C42×D61C2311yescharacteristic
165C42×D61C2311yescharacteristic
166C4⋊#92418C2311yescharacteristic
167C4⋊#92418C2311yescharacteristic
168#14519706—21no—
169#14519706—21no—
170#14519706—21no—
171#14519706—21no—
172#14519706—21no—
173#14519706—21no—
174C22⋊#92418—21no—
175#14519689—21no—
176#14519689—21no—
177#14519689—21no—
178#14519689—21no—
179#14519689—21no—
180#14519689—21no—
181#14519688—21no—
182#14519688—21no—
183#14519687—21no—
184C4×#92418C2311yescharacteristic
185C4×#92418C2311yescharacteristic
186C8×Dic61—21no—
187C22×D4×C61C2×C411yescharacteristic
188C23×C4×C61—21no—
189C22×C8×C61—21no—
190C22×C8×C61—21no—
191C4×D4×C61—21no—
192C4×D4×C61—21no—
193C4×D4×C61C2×C411yescharacteristic
194C4×D4×C61C2×C411yescharacteristic
195C4×D4×C61C2311yescharacteristic
196C4×D4×C61C2311yescharacteristic
197C2×C4⋊C4×C61C2×C411yescharacteristic
198C2×C22⋊C4×C61—21no—
199C2×C42×C61C2311yescharacteristic
200C4⋊C8×C61—21no—
201C4⋊C8×C61C2311yescharacteristic
202C4⋊C8×C61C2311yescharacteristic
203C4×C8×C61—21no—
204C4×C8×C61C2311yescharacteristic
205C4×C8×C61C2311yescharacteristic
206C24×C61—21no—
207C23×D61—21no—
208C2×D4×C61—22no—
209C2×D4×C61—21no—
210C2×D4×C61—41no—
211C2×D4×C61C22×C411yescharacteristic
212C2×D4×C61C22×C411yescharacteristic
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—81no—
219C22×C4×C61—81no—
220C22×C4×C61C22×C411yescharacteristic
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C2×C22⋊D61—21no—
224C2×C22⋊D61—21no—
225C2×C22⋊D61—21no—
226C2×C22⋊D61—21no—
227C2×C22⋊D61—21no—
228C2×C22⋊D61—21no—
229C2×C22⋊D61—21no—
230C2×C22⋊D61—44no—
231C2×C22⋊D61C22⋊C411yescharacteristic
232C2×C22⋊D61C22⋊C411yescharacteristic
233C22×Dic61—21no—
234C22×Dic61—21no—
235C22×Dic61—21no—
236#11758224—22no—
237#11758224—41no—
238D4×D61—22no—
239D4×D61—41no—
240#11758222—42no—
241#11758222—81no—
242#11758222—81no—
243C2×D244—21no—
244C2×D244C22⋊C411yescharacteristic
245C2×D244C22×C411yescharacteristic
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—81no—
250C2×C4×D61—81no—
251C2×C4×D61C22×C411yescharacteristic
252C2×C4×D61C22×C411yescharacteristic
253C2×C4×D61C2×D411yescharacteristic
254C2×C4×D61C2×D411yescharacteristic
255C2×C4×D61C2×D411yescharacteristic
256C2×C4×D61C2×D411yescharacteristic
257C2×Dic122—21no—
258C2×Dic122C22⋊C411yescharacteristic
259C2×Dic122C22×C411yescharacteristic
260C2×C8×C61—21no—
261C2×C8×C61—21no—
262C2×C8×C61—21no—
263C2×C8×C61—21no—
264C2×C8×C61—42no—
265C2×C8×C61—81no—
266C4⋊C4×C61—21no—
267C4⋊C4×C61C22×C411yescharacteristic
268C4⋊C4×C61C22×C411yescharacteristic
269C22⋊C4×C61—21no—
270C22⋊C4×C61—21no—
271C22⋊C4×C61—21no—
272C22⋊C4×C61—21no—
273C42×C61C22×C411yescharacteristic
274C42×C61C2×D411yescharacteristic
275C42×C61C2×D411yescharacteristic
276C42×C61C2411yescharacteristic
277C22⋊Dic61—21no—
278C22⋊Dic61—21no—
279C22⋊Dic61—21no—
280C22⋊Dic61—21no—
281C22⋊Dic61—21no—
282C22⋊Dic61—21no—
283C22⋊Dic61—21no—
284C22⋊Dic61C22⋊C411yescharacteristic
285C22⋊Dic61C22⋊C411yescharacteristic
286#11758198—21no—
287#11758198—21no—
288#11758198—21no—
289#11758198—21no—
290#11758198—21no—
291#11758198—21no—
292#11758198—21no—
293#11758198—21no—
294#11758198C22⋊C411yescharacteristic
295#11758198C22⋊C411yescharacteristic
296#11758198C22⋊C411yescharacteristic
297#11758198C22⋊C411yescharacteristic
298C4⋊Dic61—21no—
299C4⋊Dic61—21no—
300C4⋊Dic61C22⋊C411yescharacteristic
301C4⋊Dic61C22⋊C411yescharacteristic
302C4⋊Dic61C22×C411yescharacteristic
303C4⋊Dic61C22×C411yescharacteristic
304#11758196—21no—
305#11758196—21no—
306#11758196—21no—
307#11758196—21no—
308#11758196—21no—
309#11758196—21no—
310#11758196—21no—
311#11758196—21no—
312#11758196C22⋊C411yescharacteristic
313#11758196C22⋊C411yescharacteristic
314#11758196C22⋊C411yescharacteristic
315#11758196C22⋊C411yescharacteristic
316C4×Dic61—21no—
317C4×Dic61—21no—
318C4×Dic61—21no—
319C4×Dic61C22×C411yescharacteristic
320C4×Dic61C22×C411yescharacteristic
321C4×Dic61C2×D411yescharacteristic
322C4×Dic61C2×D411yescharacteristic
323C4×Dic61C2×D411yescharacteristic
324C4×Dic61C2×D411yescharacteristic
325#11758194—42no—
326C2×#92418—21no—
327C2×#92418—21no—
328C2×#92418—21no—
329C2×#92418—21no—
330#11758189—81no—
331C8×D61—81no—
332C23×C61—21no—
333C23×C61—21no—
334C23×C61—42no—
335C23×C61—42no—
336C23×C61—81no—
337C23×C61C2×C22⋊C411yescharacteristic
338C22×D61—21no—
339C22×D61—42no—
340C22×D61—42no—
341C22×D61—81no—
342C22×D61C2×C22⋊C411yescharacteristic
343C22×D61C2×C22⋊C411yescharacteristic
344D4×C61—21no—
345D4×C61—21no—
346D4×C61—21no—
347D4×C61—42no—
348D4×C61#13112yes—
349C2×C4×C61—22no—
350C2×C4×C61—21no—
351C2×C4×C61—21no—
352C2×C4×C61—21no—
353C2×C4×C61—21no—
354C2×C4×C61—21no—
355C2×C4×C61—21no—
356C2×C4×C61—41no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—81no—
361C2×C4×C61—81no—
362C2×C4×C61—81no—
363C2×C4×C61C2×C22⋊C411yescharacteristic
364C2×C4×C61C2×C22⋊C411yescharacteristic
365C2×C4×C61C2×C22⋊C411yescharacteristic
366C2×C4×C61C23×C411yescharacteristic
367C2×C4×C61C22×D411yescharacteristic
368C2×C4×C61C22×D411yescharacteristic
369C22⋊D61—22no—
370C22⋊D61—22no—
371C22⋊D61—42no—
372C22⋊D61—42no—
373C22⋊D61—42no—
374C22⋊D61—42no—
375C22⋊D61—42no—
376C22⋊D61—81no—
377C22⋊D61—81no—
378C2×Dic61—21no—
379C2×Dic61—21no—
380C2×Dic61—21no—
381C2×Dic61—42no—
382C2×Dic61—42no—
383C2×Dic61—81no—
384C2×Dic61C2×C22⋊C411yescharacteristic
385C2×Dic61C2×C22⋊C411yescharacteristic
386C2×Dic61C2×C22⋊C411yescharacteristic
387C2×Dic61C2×C22⋊C411yescharacteristic
388C2×Dic61C2×C22⋊C411yescharacteristic
389C2×Dic61C2×C22⋊C411yescharacteristic
390D244—21no—
391D244—21no—
392D244—41no—
393D244—81no—
394C4×D61—21no—
395C4×D61—21no—
396C4×D61—21no—
397C4×D61—21no—
398C4×D61—21no—
399C4×D61—21no—
400C4×D61—21no—
401C4×D61—21no—
402C4×D61—41no—
403C4×D61—41no—
404C4×D61—41no—
405C4×D61—41no—
406C4×D61—81no—
407C4×D61—81no—
408Dic122—21no—
409Dic122—21no—
410Dic122—41no—
411Dic122—81no—
412C8×C61—41no—
413C8×C61—41no—
414C8×C61—41no—
415C8×C61—41no—
416#92418—41no—
417#92418—41no—
418#92418—41no—
419#92418—41no—
420#17521—611nomaximal, Sylow
421C22×C61—21no—
422C22×C61—21no—
423C22×C61—22no—
424C22×C61—41no—
425C22×C61—41no—
426C22×C61—41no—
427C22×C61—41no—
428C22×C61—41no—
429C22×C61—84no—
430C22×C61#42112yes—
431C22×C61C22×C22⋊C411yescharacteristic
432C2×D61—21no—
433C2×D61—21no—
434C2×D61—21no—
435C2×D61—21no—
436C2×D61—21no—
437C2×D61—21no—
438C2×D61—41no—
439C2×D61—41no—
440C2×D61—41no—
441C2×D61—84no—
442C4×C61—21no—
443C4×C61—21no—
444C4×C61—21no—
445C4×C61—21no—
446C4×C61—41no—
447C4×C61—41no—
448C4×C61C2×#13111yescharacteristic
449C4×C61#56811yescharacteristic
450C4×C61#57611yescharacteristic
451C4×C61#57711yescharacteristic
452Dic61—21no—
453Dic61—21no—
454Dic61—21no—
455Dic61—21no—
456Dic61—21no—
457Dic61—21no—
458Dic61—41no—
459Dic61—41no—
460Dic61—41no—
461#3481—611no—
462#2990—611no—
463#2922—611no—
464#1496—611no—
465#1495—611no—
466#1494—611no—
467#1490—611no—
468#1488—611no—
469#1486—611no—
470#1483—611no—
471#1482—611no—
472#1480—611no—
473#1478—611no—
474#1477—611no—
475C2×D4⋊C8D6111yescharacteristic, complemented
476C2×C61—22no—
477C2×C61—42no—
478C2×C61—81no—
479C2×C61#288011yescharacteristic
480C2×C61#289711yescharacteristic
481C2×C61C2×#42111yescharacteristic
482D61—41no—
483D61—41no—
484D61—81no—
485#559—611no—
486#554—611no—
487#554—611no—
488#553—611no—
489#553—611no—
490#553—1221no—
491#551—1221no—
492#551—1221no—
493#546—611no—
494#546—611no—
495#546—1221no—
496D42—611no—
497#532—611no—
498#529—611no—
499#529—611no—
500#529—1221no—
501#525—1221no—
502#525—1221no—
503C4×#41—611no—
504C4×#41—611no—
505C2×C4×D4—611no—
506C2×C4×D4—1221no—
507C2×C4×D4C2×D6111yescharacteristic
508#446—1221no—
509#435—1221no—
510#435—1221no—
511C8×D4—1221no—
512#433—1221no—
513#433—1221no—
514#432—611no—
515#432—611no—
516#431—611no—
517#431—611no—
518#431—611no—
519#431—611no—
520#431—611no—
521#424—1221no—
522#423—611no—
523C2×C4⋊C8—611no—
524C2×C4⋊C8C2×D6111yescharacteristic, complemented
525#408—1221no—
526C4×M16—611no—
527C2×C4×C8C2×D6111yescharacteristic, complemented
528Q8⋊C8—611no—
529Q8⋊C8—611no—
530Q8⋊C8—611no—
531Q8⋊C8—611no—
532D4⋊C8—611no—
533D4⋊C8—611no—
534D4⋊C8—611no—
535D4⋊C8—611no—
536D4⋊C8—611no—
537D4⋊C8—611no—
538D4⋊C8—611no—
539D4⋊C8—611no—
540D4⋊C8C2×D6111yescharacteristic
541D4⋊C8C2×D6111yescharacteristic
542D4⋊C8C2×D6111yescharacteristic, complemented
543D4⋊C8C2×D6111yescharacteristic, complemented
544C61#1752111yescharacteristic, complemented, Sylow
545C2×#41—611no—
546C2×#41—611no—
547C2×#41—1221no—
548C22×D4—611no—
549C22×D4—1221no—
550C22×D4C4×D6111yescharacteristic
551C23×C4—21no—
552C23×C4—1221no—
553C2×M16—1221no—
554C2×M16—1221no—
555C22×C8—21no—
556C22×C8—21no—
557C22×C8—1221no—
558C4⋊Q8—611no—
559#127—611no—
560#126—1221no—
561#126—1221no—
562#126—1221no—
563#126—1221no—
564#125—611no—
565#125—611no—
566#125—1221no—
567#124—611no—
568#124—611no—
569#124—1221no—
570#124—1221no—
571#123—1221no—
572#123—1221no—
573#123—1221no—
574#123—1221no—
575#123—1221no—
576#123—1221no—
577#123—1221no—
578#123—1221no—
579C22⋊Q8—611no—
580C22⋊Q8—611no—
581C22⋊Q8—1221no—
582C22⋊Q8—1221no—
583C22⋊Q8—1221no—
584C22⋊Q8—1221no—
585C22⋊Q8—1221no—
586#121—611no—
587#121—611no—
588#121—611no—
589#121—611no—
590#121—1221no—
591#121—1221no—
592#121—1221no—
593#121—1221no—
594#121—1221no—
595#121—1221no—
596#120—1221no—
597#120—1221no—
598#120—1221no—
599#120—1221no—
600C4×Q8—611no—
601C4×Q8—611no—
602C4×Q8—611no—
603C4×Q8—611no—
604C4×D4—21no—
605C4×D4—21no—
606C4×D4—611no—
607C4×D4—611no—
608C4×D4—611no—
609C4×D4—611no—
610C4×D4—611no—
611C4×D4—611no—
612C4×D4—611no—
613C4×D4—611no—
614C4×D4—611no—
615C4×D4—611no—
616C4×D4—1221no—
617C4×D4—1221no—
618C4×D4—1221no—
619C4×D4—1221no—
620C4×D4—1221no—
621C4×D4—1221no—
622C4×D4—1221no—
623C4×D4—1221no—
624C4×D4—1221no—
625C4×D4—1221no—
626C4×D4—1221no—
627C4×D4C4×D6111yescharacteristic
628C4×D4C4×D6111yescharacteristic
629C4×D4C22×D6111yescharacteristic
630C4×D4C22×D6111yescharacteristic
631#117—611no—
632#117—611no—
633#117—611no—
634#117—611no—
635#117—1221no—
636#117—1221no—
637#117—1221no—
638C2×C4⋊C4—611no—
639C2×C4⋊C4—1221no—
640C2×C4⋊C4C4×D6111yescharacteristic
641C2×C22⋊C4—21no—
642C2×C22⋊C4—1221no—
643C2×C22⋊C4—1221no—
644C2×C22⋊C4—1221no—
645C2×C42—611no—
646C2×C42—611no—
647C2×C42—1221no—
648C2×C42C22×D6111yescharacteristic
649C4⋊C8—21no—
650C4⋊C8—611no—
651C4⋊C8—611no—
652C4⋊C8—1221no—
653C4⋊C8—1221no—
654C4⋊C8—1221no—
655C4⋊C8—1221no—
656C4⋊C8—1221no—
657C4⋊C8—1221no—
658C4⋊C8C22×D6111yescharacteristic
659C4⋊C8C22×D6111yescharacteristic
660C22⋊C8—1221no—
661C22⋊C8—1221no—
662C22⋊C8—1221no—
663C22⋊C8—1221no—
664C22⋊C8—1221no—
665C22⋊C8—1221no—
666C22⋊C8—1221no—
667#97—1221no—
668#97—1221no—
669#97—1221no—
670C4×C8—21no—
671C4×C8—611no—
672C4×C8—611no—
673C4×C8—1221no—
674C4×C8C22×D6111yescharacteristic
675C4×C8C22×D6111yescharacteristic
676C24—21no—
677C24—1221no—
678#41—1222no—
679#41—4881no—
680#41—4881no—
681#41—2442no—
682#41—2441no—
683C2×Q8—611no—
684C2×Q8—611no—
685C2×Q8—1221no—
686C2×D4—22no—
687C2×D4—21no—
688C2×D4—41no—
689C2×D4—611no—
690C2×D4—611no—
691C2×D4—611no—
692C2×D4—611no—
693C2×D4—1221no—
694C2×D4—1221no—
695C2×D4—1221no—
696C2×D4—1221no—
697C2×D4—1222no—
698C2×D4—1221no—
699C2×D4—1221no—
700C2×D4—1221no—
701C2×D4—1221no—
702C2×D4—2441no—
703C2×D4—2444no—
704C2×D4C2×C4×D6111yescharacteristic
705C2×D4C2×C4×D6111yescharacteristic
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—81no—
712C22×C4—81no—
713C22×C4—611no—
714C22×C4—611no—
715C22×C4—611no—
716C22×C4—611no—
717C22×C4—611no—
718C22×C4—611no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—4881no—
726C22×C4—4881no—
727C22×C4C2×C4×D6111yescharacteristic
728C22×C4D4×D6111yescharacteristic
729C22×C4D4×D6111yescharacteristic
730M16—4881no—
731M16—2442no—
732C2×C8—21no—
733C2×C8—21no—
734C2×C8—21no—
735C2×C8—21no—
736C2×C8—42no—
737C2×C8—81no—
738C2×C8—1221no—
739C2×C8—1221no—
740C2×C8—1221no—
741C2×C8—1221no—
742C2×C8—4881no—
743C4⋊C4—21no—
744C4⋊C4—611no—
745C4⋊C4—611no—
746C4⋊C4—611no—
747C4⋊C4—611no—
748C4⋊C4—611no—
749C4⋊C4—611no—
750C4⋊C4—611no—
751C4⋊C4—611no—
752C4⋊C4—1221no—
753C4⋊C4—1221no—
754C4⋊C4—1221no—
755C4⋊C4—1221no—
756C4⋊C4—1221no—
757C4⋊C4—1221no—
758C4⋊C4—1221no—
759C4⋊C4—1221no—
760C4⋊C4—1221no—
761C4⋊C4—1221no—
762C4⋊C4C2×C4×D6111yescharacteristic
763C4⋊C4C2×C4×D6111yescharacteristic
764C22⋊C4—21no—
765C22⋊C4—21no—
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—611no—
769C22⋊C4—611no—
770C22⋊C4—611no—
771C22⋊C4—611no—
772C22⋊C4—611no—
773C22⋊C4—611no—
774C22⋊C4—1221no—
775C22⋊C4—1221no—
776C22⋊C4—1221no—
777C22⋊C4—1221no—
778C22⋊C4—1221no—
779C22⋊C4—1221no—
780C22⋊C4—1221no—
781C22⋊C4—1221no—
782C22⋊C4—1221no—
783C22⋊C4—1221no—
784C22⋊C4—1221no—
785C22⋊C4—1221no—
786C22⋊C4—1221no—
787C22⋊C4—1221no—
788C22⋊C4—1221no—
789C42—611no—
790C42—611no—
791C42—611no—
792C42—611no—
793C42—611no—
794C42—611no—
795C42—1221no—
796C42—1221no—
797C42—1221no—
798C42C2×C4×D6111yescharacteristic
799C42D4×D6111yescharacteristic
800C42D4×D6111yescharacteristic
801C42C23×D6111yescharacteristic
802C23—21no—
803C23—21no—
804C23—42no—
805C23—42no—
806C23—81no—
807C23—611no—
808C23—611no—
809C23—1221no—
810C23—4881no—
811C23—2442no—
812C23—2442no—
813C23C22⋊C4×D6111yescharacteristic
814Q8—1221no—
815Q8—1221no—
816Q8—4881no—
817Q8—2441no—
818D4—21no—
819D4—21no—
820D4—21no—
821D4—42no—
822D4—1222no—
823D4—1222no—
824D4—1221no—
825D4—1221no—
826D4—4881no—
827D4—4881no—
828D4—4881no—
829D4—2441no—
830D4—2442no—
831D4—2442no—
832D4—2442no—
833D4—2442no—
834D4—2442no—
835D4#1451978312yes—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—81no—
848C2×C4—81no—
849C2×C4—81no—
850C2×C4—611no—
851C2×C4—611no—
852C2×C4—611no—
853C2×C4—611no—
854C2×C4—611no—
855C2×C4—611no—
856C2×C4—1221no—
857C2×C4—1221no—
858C2×C4—1221no—
859C2×C4—1221no—
860C2×C4—1221no—
861C2×C4—1221no—
862C2×C4—1221no—
863C2×C4—1221no—
864C2×C4—1221no—
865C2×C4—1221no—
866C2×C4—1221no—
867C2×C4—4881no—
868C2×C4—4881no—
869C2×C4—4881no—
870C2×C4—2441no—
871C2×C4—2441no—
872C2×C4—2442no—
873C2×C4—2442no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4C22⋊C4×D6111yescharacteristic
877C2×C4C22⋊C4×D6111yescharacteristic
878C2×C4C22⋊C4×D6111yescharacteristic
879C2×C4C22×C4×D6111yescharacteristic
880C2×C4C2×D4×D6111yescharacteristic
881C2×C4C2×D4×D6111yescharacteristic
882C8—41no—
883C8—41no—
884C8—41no—
885C8—41no—
886C8—2441no—
887C8—2441no—
888C8—2441no—
889C8—2441no—
890C22—21no—
891C22—21no—
892C22—22no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—84no—
899C22—1221no—
900C22—1221no—
901C22—1221no—
902C22—1221no—
903C22—1221no—
904C22—1221no—
905C22—4884no—
906C22—2441no—
907C22—2441no—
908C22—2441no—
909C22#1683977712yes—
910C22C2×C22⋊C4×D6111yescharacteristic
911C4—21no—
912C4—21no—
913C4—21no—
914C4—21no—
915C4—41no—
916C4—41no—
917C4—1221no—
918C4—1221no—
919C4—1221no—
920C4—1221no—
921C4—1221no—
922C4—1221no—
923C4—2441no—
924C4—2441no—
925C4—2441no—
926C4C2×#1451978311yescharacteristic
927C4#1684052811yescharacteristic
928C4#1684056311yescharacteristic
929C4#1684056811yescharacteristic
930C2—22no—
931C2—42no—
932C2—81no—
933C2—4881no—
934C2—2441no—
935C2—2441no—
936C2#2145426511yescharacteristic
937C2#2145434011yescharacteristic
938C2C2×#1683977711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC2×C61×D4⋊C8C2
socleC22×C61C22×C22⋊C4
prime radical#21459423C2
cosocleC42×C61C24
hypercenterC2×D4⋊C8D61
hypocenterC61#17521
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #21454941C2semidirect
3. #21454461C2semidirect
4. #21444286C2semidirect
5. #21444281C2semidirect
6. #21444280C2semidirect
7. #21444262C2semidirect
8. #21444250C2semidirect
9. #21444242C2semidirect
10. #21444230C2semidirect
11. #21444224C2semidirect
12. #21444216C2semidirect
13. #21444208C2semidirect
14. #21444203C2semidirect
15. C2×C61×D4⋊C8C2semidirect
44. #16839819C22semidirect
45. #16839818C22semidirect
46. #16839814C22semidirect
47. #16839813C22semidirect
48. #16839813C22semidirect
49. #16839813C22semidirect
50. #16839813C22semidirect
52. #16839784C22semidirect
53. C4⋊C8×D61C22semidirect
55. C4×#11758194C22semidirect
56. #16839494C22semidirect
57. #16839494C22semidirect
58. #16839492C22semidirect
59. #16839492C22semidirect
60. #16839491C22semidirect
61. #16839491C22semidirect
64. D4⋊#92418C22semidirect
65. D4⋊#92418C22semidirect
66. #16839489C22semidirect
67. #16839489C22semidirect
69. C2×C4⋊C8×C61C22semidirect
70. C2×C4×C8×C61C22semidirect
73. C61×D4⋊C8C22semidirect
74. C61×D4⋊C8C22semidirect
475. C2×D4⋊C8D61semidirect
524. C2×C4⋊C8C2×D61semidirect
527. C2×C4×C8C2×D61semidirect
542. D4⋊C8C2×D61semidirect
543. D4⋊C8C2×D61semidirect
544. C61#17521semidirect

Maximal subgroups

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

subgroupindex
#214594232
#214549412
#214544612
#214442862
#214442812
#214442802
#214442622
#214442502
#214442422
#214442302
#214442242
#214442162
#214442082
#214442032
C2×C61×D4⋊C82
#1752161