Finite Group Databasebeta

← #30610857

Subgroups — #30610857

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#21462744C211yesmaximal, characteristic, complemented
2#21462502C211yesmaximal, characteristic, complemented
3#21461180C211yesmaximal, characteristic, complemented
4#21461176C211yesmaximal, characteristic, complemented
5#21461172C211yesmaximal, characteristic, complemented
6#21461160C211yesmaximal, characteristic, complemented
7#21461153C211yesmaximal, characteristic, complemented
8#21461146C211yesmaximal, characteristic, complemented
9#21461136C211yesmaximal, characteristic, complemented
10#21461132C211yesmaximal, characteristic, complemented
11#21461126C211yesmaximal, characteristic, complemented
12#21461120C211yesmaximal, characteristic, complemented
13#21461117C211yesmaximal, characteristic, complemented
14C2×#16840610C211yesmaximal, characteristic, complemented
15#21459430C211yesmaximal, characteristic
16#16840814—21no—
17#16840794—21no—
18#16840793—21no—
19#16840789—21no—
20#16840787—21no—
21#16840786—21no—
22#16840784C2211yescharacteristic, complemented
23#16840783C2211yescharacteristic, complemented
24#16840781C2211yescharacteristic, complemented
25#16840780C2211yescharacteristic, complemented
26#16840779C2211yescharacteristic, complemented
27#16840778C2211yescharacteristic, complemented
28#16840778C2211yescharacteristic, complemented
29#16840768—21no—
30#16840765C2211yescharacteristic, complemented
31D61⋊(C4⋊C8)C2211yescharacteristic, complemented
32C2×C4⋊#92420C2211yescharacteristic, complemented
33#16840735—21no—
34C4×#11758217C2211yescharacteristic, complemented
35C2×C4×#92420C2211yescharacteristic, complemented
36Q8⋊#92420C2211yescharacteristic, complemented
37Q8⋊#92420C2211yescharacteristic, complemented
38Q8⋊#92420C2211yescharacteristic, complemented
39Q8⋊#92420C2211yescharacteristic, complemented
40#16840610C2211yescharacteristic
41#16840610C2211yescharacteristic
42#16840610C2211yescharacteristic
43#16840610C2211yescharacteristic
44#16840610C2211yescharacteristic, complemented
45#16840610C2211yescharacteristic, complemented
46#16840610C2211yescharacteristic, complemented
47#16840610C2211yescharacteristic, complemented
48#16840610C2211yescharacteristic, complemented
49#16840610C2211yescharacteristic, complemented
50#16840610C2211yescharacteristic, complemented
51#16840610C2211yescharacteristic, complemented
52#16840497C411yescharacteristic
53#16840473C411yescharacteristic
54#16840465—21no—
55#16840460C411yescharacteristic
56#16840460C411yescharacteristic
57#16840439—21no—
58#16840439—21no—
59#16840407—21no—
60#16840403C411yescharacteristic
61#16840403C411yescharacteristic
62D4×D244C411yescharacteristic
63#16840313C2211yescharacteristic
64#16840298C2211yescharacteristic
65#16840298C2211yescharacteristic
66#16840297—21no—
67#16840275—21no—
68#16840275—21no—
69C4×#11758226C2211yescharacteristic
70C4×#11758224C2211yescharacteristic
71C2×#14519739C2211yescharacteristic
72C2×#14519739C2211yescharacteristic
73C4×D4×D61—21no—
74C61×#554C411yescharacteristic
75C2×#11758217—21no—
76C2×#11758217—21no—
77C2×D61⋊C8—21no—
78C22×#92420—21no—
79C22×#92420—21no—
80#14519844—21no—
81#14519844—21no—
82#14519844—21no—
83#14519844—21no—
84C4⋊#92420—21no—
85C4⋊#92420—21no—
86C4⋊#92420—21no—
87C4⋊#92420C2311yescharacteristic
88C4⋊#92420C2311yescharacteristic
89C4⋊#92420C2311yescharacteristic
90C4⋊#92420C2311yescharacteristic
91#14519834—21no—
92#14519834—21no—
93#14519834—21no—
94C22⋊#92420—21no—
95C22⋊#92420—21no—
96C22⋊#92420—21no—
97C22⋊#92420—21no—
98#14519832—21no—
99#14519832—21no—
100#14519832—21no—
101C4×#92420—21no—
102C4×#92420—21no—
103C4×#92420C2311yescharacteristic
104C4×#92420C2311yescharacteristic
105C4×#92420C2311yescharacteristic
106C4×#92420C2311yescharacteristic
107C2×#11758226—21no—
108C2×#11758226C2×C411yescharacteristic
109C2×#11758224D411yescharacteristic
110C22×D244C2×C411yescharacteristic
111C22×D244C2×C411yescharacteristic
112C2×D4×D61—21no—
113C22×C4×D61—21no—
114C22×C4×D61—21no—
115#14519774C2×C411yescharacteristic
116#14519772—21no—
117#14519772—21no—
118#14519772—21no—
119#14519772—21no—
120#14519768C2×C411yescharacteristic
121#14519768C2×C411yescharacteristic
122#14519766—21no—
123#14519766C2×C411yescharacteristic
124#14519766C2×C411yescharacteristic
125#14519765—21no—
126#14519762—21no—
127#14519762—21no—
128#14519762—21no—
129#14519762—21no—
130#14519762—21no—
131#14519762—21no—
132#14519761—21no—
133#14519761—21no—
134#14519757—21no—
135#14519753—21no—
136#14519753—21no—
137#14519752—21no—
138#14519752—21no—
139#14519752—21no—
140#14519752—21no—
141#14519752C2×C411yescharacteristic
142#14519752C2×C411yescharacteristic
143#14519751—21no—
144#14519751—21no—
145#14519751C2×C411yescharacteristic
146#14519751C2×C411yescharacteristic
147#14519747—21no—
148#14519747—21no—
149#14519747—21no—
150#14519747—21no—
151Q8×Dic61C2311yescharacteristic
152C4×Dic122C2×C411yescharacteristic
153#14519742D411yescharacteristic
154C4×D244—21no—
155C4×D244—21no—
156C4×D244C2×C411yescharacteristic
157D4×Dic61D411yescharacteristic
158#14519739—21no—
159#14519739—21no—
160#14519739—21no—
161#14519739—21no—
162#14519739—21no—
163#14519739—21no—
164#14519739C2×C411yescharacteristic
165#14519739C2×C411yescharacteristic
166#14519739C2×C411yescharacteristic
167#14519739C2×C411yescharacteristic
168#14519739C2311yescharacteristic
169#14519739C2311yescharacteristic
170#14519739C2311yescharacteristic
171C4×C22⋊D61—21no—
172C4×C22⋊D61—21no—
173C4×C22⋊D61C2×C411yescharacteristic
174C4×C22⋊D61C2×C411yescharacteristic
175#14519737—21no—
176#14519737—21no—
177#14519737D411yescharacteristic
178#14519737D411yescharacteristic
179#14519735—21no—
180#14519735—21no—
181#14519735—21no—
182#14519735C2×C411yescharacteristic
183#14519735D411yescharacteristic
184#14519733D411yescharacteristic
185#14519733D411yescharacteristic
186C4⋊C4×D61—21no—
187C2×#11758198—21no—
188C2×#11758198—21no—
189C22⋊C4×D61—21no—
190C22⋊C4×D61—21no—
191C2×C4×Dic61C2311yescharacteristic
192C2×C4×Dic61C2311yescharacteristic
193C42×D61—21no—
194C42×D61C2311yescharacteristic
195C4⋊Q8×C61C2×C411yescharacteristic
196#125×C61—21no—
197C22⋊Q8×C61—21no—
198C22⋊Q8×C61—21no—
199C22⋊Q8×C61C2×C411yescharacteristic
200C22⋊Q8×C61C2×C411yescharacteristic
201C4×Q8×C61C2×C411yescharacteristic
202C4×D4×C61—21no—
203C4×D4×C61C2×C411yescharacteristic
204C2×C4⋊C4×C61C2×C411yescharacteristic
205C2×C4⋊C4×C61C2×C411yescharacteristic
206C23×D61—21no—
207C23×D61—21no—
208C2×Q8×C61—21no—
209C2×Q8×C61C22×C411yescharacteristic
210C2×D4×C61C22⋊C411yescharacteristic
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61C22×C411yescharacteristic
214C22×C4×C61C22×C411yescharacteristic
215C2×C22⋊D61—21no—
216C2×C22⋊D61—21no—
217C2×C22⋊D61C22⋊C411yescharacteristic
218C2×C22⋊D61C22⋊C411yescharacteristic
219C22×Dic61C2×D411yescharacteristic
220C22×Dic61C2×D411yescharacteristic
221C22×Dic61C2×D411yescharacteristic
222C22×Dic61C2×D411yescharacteristic
223#11758226—22no—
224#11758226—41no—
225#11758226—81no—
226#11758226—81no—
227#11758224—42no—
228D4×D61—44no—
229C2×D244—22no—
230C2×D244—22no—
231C2×D244—21no—
232C2×D244—21no—
233C2×D244—21no—
234C2×D244—21no—
235C2×D244—21no—
236C2×D244—21no—
237C2×D244—21no—
238C2×D244—41no—
239C2×D244—41no—
240C2×D244C22×C411yescharacteristic
241C2×D244C22×C411yescharacteristic
242C2×D244C22×C411yescharacteristic
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×C4×D61—21no—
252C2×C4×D61—81no—
253C2×C4×D61—81no—
254C2×C4×D61—81no—
255C2×C4×D61—81no—
256C2×C4×D61C22×C411yescharacteristic
257C2×C4×D61C2×D411yescharacteristic
258C2×C4×D61C2×D411yescharacteristic
259C2×Dic122C22⋊C411yescharacteristic
260#11758217—42no—
261#11758217—81no—
262C2×#92420—21no—
263C2×#92420—21no—
264C2×#92420—21no—
265C2×#92420—21no—
266C2×#92420—21no—
267C2×#92420—21no—
268C2×#92420—21no—
269C2×#92420—21no—
270C2×#92420—42no—
271C2×#92420—81no—
272D61⋊C8—81no—
273C4⋊C4×C61—21no—
274C4⋊C4×C61—21no—
275C4⋊C4×C61—21no—
276C4⋊C4×C61—21no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61C22⋊C411yescharacteristic
280C4⋊C4×C61C22×C411yescharacteristic
281C4⋊C4×C61C22×C411yescharacteristic
282C4⋊C4×C61C22×C411yescharacteristic
283C22⋊C4×C61—21no—
284C22⋊C4×C61—21no—
285C22⋊C4×C61C22⋊C411yescharacteristic
286C22⋊C4×C61C22⋊C411yescharacteristic
287C42×C61—21no—
288C42×C61C22×C411yescharacteristic
289C22⋊Dic61C22⋊C411yescharacteristic
290C22⋊Dic61C22⋊C411yescharacteristic
291#11758198—21no—
292#11758198—21no—
293#11758198—21no—
294#11758198—21no—
295#11758198—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#11758198C22⋊C411yescharacteristic
309#11758198C22⋊C411yescharacteristic
310C4⋊Dic61—21no—
311C4⋊Dic61—21no—
312C4⋊Dic61—21no—
313C4⋊Dic61C22⋊C411yescharacteristic
314C4⋊Dic61C22×C411yescharacteristic
315#11758196—21no—
316#11758196—21no—
317#11758196C22⋊C411yescharacteristic
318#11758196C22⋊C411yescharacteristic
319#11758196C22⋊C411yescharacteristic
320#11758196C22⋊C411yescharacteristic
321C4×Dic61—21no—
322C4×Dic61—21no—
323C4×Dic61C22×C411yescharacteristic
324C4×Dic61C22×C411yescharacteristic
325C4×Dic61C2×D411yescharacteristic
326C4×Dic61C2×D411yescharacteristic
327C4×Dic61C2×D411yescharacteristic
328C4×Dic61C2×D411yescharacteristic
329C4×Dic61C2×D411yescharacteristic
330C4×Dic61C2×D411yescharacteristic
331C4×Dic61C2411yescharacteristic
332C23×C61C2×C22⋊C411yescharacteristic
333C23×C61C2×C22⋊C411yescharacteristic
334C22×D61—21no—
335C22×D61—21no—
336C22×D61—21no—
337C22×D61—42no—
338C22×D61—42no—
339C22×D61—42no—
340C22×D61—42no—
341C22×D61—81no—
342C22×D61—81no—
343C22×D61C2×C22⋊C411yescharacteristic
344Q8×C61—21no—
345Q8×C61—21no—
346Q8×C61—81no—
347D4×C61—22no—
348C2×C4×C61—21no—
349C2×C4×C61—21no—
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—81no—
357C2×C4×C61—81no—
358C2×C4×C61C2×C22⋊C411yescharacteristic
359C2×C4×C61C2×C22⋊C411yescharacteristic
360C2×C4×C61C2×C22⋊C411yescharacteristic
361C2×C4×C61C2×C22⋊C411yescharacteristic
362C2×C4×C61C23×C411yescharacteristic
363C22⋊D61—22no—
364C22⋊D61—41no—
365C22⋊D61—42no—
366C22⋊D61—42no—
367C2×Dic61—22no—
368C2×Dic61—21no—
369C2×Dic61—21no—
370C2×Dic61—21no—
371C2×Dic61—21no—
372C2×Dic61—21no—
373C2×Dic61—41no—
374C2×Dic61C2×C22⋊C411yescharacteristic
375C2×Dic61C2×C22⋊C411yescharacteristic
376C2×Dic61C2×C22⋊C411yescharacteristic
377C2×Dic61C2×C22⋊C411yescharacteristic
378C2×Dic61C2×C22⋊C411yescharacteristic
379C2×Dic61C22×D411yescharacteristic
380C2×Dic61C22×D411yescharacteristic
381D244—21no—
382D244—21no—
383D244—21no—
384D244—21no—
385D244—21no—
386D244—42no—
387D244—42no—
388D244—42no—
389D244—42no—
390D244—81no—
391D244—81no—
392D244—81no—
393D244#13112yes—
394C4×D61—21no—
395C4×D61—21no—
396C4×D61—21no—
397C4×D61—21no—
398C4×D61—41no—
399C4×D61—42no—
400C4×D61—42no—
401C4×D61—41no—
402C4×D61—41no—
403C4×D61—41no—
404C4×D61—41no—
405C4×D61—41no—
406C4×D61—41no—
407C4×D61—81no—
408C4×D61—81no—
409C4×D61—81no—
410C4×D61—81no—
411Dic122—41no—
412#92420—41no—
413#92420—41no—
414#92420—41no—
415#92420—41no—
416#92420—41no—
417#92420—41no—
418#92420—41no—
419#92420—41no—
420#17521—611nomaximal, Sylow
421C22×C61—21no—
422C22×C61—21no—
423C22×C61—21no—
424C22×C61—21no—
425C22×C61—21no—
426C22×C61#42112yes—
427C22×C61C22×C22⋊C411yescharacteristic
428C2×D61—21no—
429C2×D61—22no—
430C2×D61—21no—
431C2×D61—21no—
432C2×D61—41no—
433C2×D61—41no—
434C2×D61—41no—
435C2×D61—41no—
436C2×D61—41no—
437C2×D61—41no—
438C2×D61—41no—
439C2×D61—41no—
440C2×D61—84no—
441C2×D61—84no—
442C4×C61—21no—
443C4×C61—21no—
444C4×C61—21no—
445C4×C61—21no—
446C4×C61—41no—
447C4×C61—41no—
448C4×C61—41no—
449C4×C61—41no—
450C4×C61C2×#13111yescharacteristic
451C4×C61#56811yescharacteristic
452Dic61—21no—
453Dic61—21no—
454Dic61—21no—
455Dic61—21no—
456Dic61—21no—
457Dic61—21no—
458Dic61—41no—
459Dic61#57611yescharacteristic
460Dic61#57711yescharacteristic
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⋊C8—611no—
476C2×C61—22no—
477C2×C61—41no—
478C2×C61#288011yescharacteristic
479C2×C61#289711yescharacteristic
480C2×C61C2×#42111yescharacteristic
481D61—41no—
482D61—42no—
483D61—81no—
484D61—81no—
485#559—611no—
486#554—611no—
487#554#692311yescharacteristic
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—611no—
507C2×C4×D4—1221no—
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⋊C8—611no—
525#408—1221no—
526C4×M16—611no—
527C2×C4×C8—611no—
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⋊C8—611no—
541D4⋊C8—611no—
542D4⋊C8—611no—
543D4⋊C8—611no—
544C61#1752111yescharacteristic, complemented, Sylow
545C2×#41—611no—
546C2×#41—611no—
547C2×#41—1221no—
548C22×D4—611no—
549C22×D4—611no—
550C22×D4—1221no—
551C23×C4—1221no—
552C23×C4—1221no—
553C2×M16—1221no—
554C2×M16—1221no—
555C22×C8—1221no—
556C22×C8—1221no—
557C22×C8—1221no—
558C4⋊Q8C2×#692311yescharacteristic
559#127—611no—
560#126—1221no—
561#126—1221no—
562#126—1221no—
563#126—1221no—
564#125—21no—
565#125—611no—
566#125—611no—
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—21no—
580C22⋊Q8—21no—
581C22⋊Q8—1221no—
582C22⋊Q8—1221no—
583C22⋊Q8—1221no—
584C22⋊Q8C2×#692311yescharacteristic
585C22⋊Q8C2×#692311yescharacteristic
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×Q8C2×#692311yescharacteristic
604C4×D4—21no—
605C4×D4—611no—
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—611no—
617C4×D4—611no—
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×D4—1221no—
628C4×D4—1221no—
629C4×D4—1221no—
630C4×D4C2×#692311yescharacteristic
631#117—611no—
632#117—611no—
633#117—611no—
634#117—611no—
635#117—1221no—
636#117—1221no—
637#117—1221no—
638C2×C4⋊C4—1221no—
639C2×C4⋊C4C2×#692311yescharacteristic
640C2×C4⋊C4C2×#692311yescharacteristic
641C2×C22⋊C4—1221no—
642C2×C22⋊C4—1221no—
643C2×C22⋊C4—1221no—
644C2×C22⋊C4—1221no—
645C2×C42—611no—
646C2×C42—611no—
647C2×C42—611no—
648C2×C42—1221no—
649C4⋊C8—611no—
650C4⋊C8—611no—
651C4⋊C8—611no—
652C4⋊C8—611no—
653C4⋊C8—1221no—
654C4⋊C8—1221no—
655C4⋊C8—1221no—
656C4⋊C8—1221no—
657C4⋊C8—1221no—
658C4⋊C8—1221no—
659C4⋊C8—1221no—
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—611no—
671C4×C8—611no—
672C4×C8—611no—
673C4×C8—611no—
674C4×C8—1221no—
675C4×C8—1221no—
676C24—1221no—
677C24—1221no—
678#41—1222no—
679#41—4881no—
680#41—4881no—
681#41—2442no—
682#41—2441no—
683C2×Q8—21no—
684C2×Q8—611no—
685C2×Q8C22×#692311yescharacteristic
686C2×D4—611no—
687C2×D4—611no—
688C2×D4—611no—
689C2×D4—611no—
690C2×D4—611no—
691C2×D4—1222no—
692C2×D4—1222no—
693C2×D4—1221no—
694C2×D4—1221no—
695C2×D4—1221no—
696C2×D4—1221no—
697C2×D4—1221no—
698C2×D4—1221no—
699C2×D4—1221no—
700C2×D4—1221no—
701C2×D4—1221no—
702C2×D4—2441no—
703C2×D4—2441no—
704C2×D4—2444no—
705C2×D4C22⋊#692311yescharacteristic
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—611no—
709C22×C4—611no—
710C22×C4—611no—
711C22×C4—611no—
712C22×C4—611no—
713C22×C4—611no—
714C22×C4—611no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—4881no—
725C22×C4—4881no—
726C22×C4—4881no—
727C22×C4—4881no—
728C22×C4C22×#692311yescharacteristic
729C22×C4C22×#692311yescharacteristic
730M16—4881no—
731M16—2442no—
732C2×C8—1221no—
733C2×C8—1221no—
734C2×C8—1221no—
735C2×C8—1221no—
736C2×C8—1221no—
737C2×C8—1221no—
738C2×C8—1221no—
739C2×C8—1221no—
740C2×C8—4881no—
741C2×C8—4881no—
742C2×C8—2442no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—611no—
750C4⋊C4—611no—
751C4⋊C4—611no—
752C4⋊C4—611no—
753C4⋊C4—611no—
754C4⋊C4—611no—
755C4⋊C4—1221no—
756C4⋊C4—1221no—
757C4⋊C4—1221no—
758C4⋊C4—1221no—
759C4⋊C4—1221no—
760C4⋊C4C22⋊#692311yescharacteristic
761C4⋊C4C22×#692311yescharacteristic
762C4⋊C4C22×#692311yescharacteristic
763C4⋊C4C22×#692311yescharacteristic
764C22⋊C4—21no—
765C22⋊C4—21no—
766C22⋊C4—611no—
767C22⋊C4—611no—
768C22⋊C4—611no—
769C22⋊C4—611no—
770C22⋊C4—1221no—
771C22⋊C4—1221no—
772C22⋊C4—1221no—
773C22⋊C4—1221no—
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⋊C4C22⋊#692311yescharacteristic
788C22⋊C4C22⋊#692311yescharacteristic
789C42—21no—
790C42—611no—
791C42—611no—
792C42—611no—
793C42—611no—
794C42—611no—
795C42—611no—
796C42—611no—
797C42—611no—
798C42—611no—
799C42—1221no—
800C42—1221no—
801C42C22×#692311yescharacteristic
802C23—611no—
803C23—1221no—
804C23—1221no—
805C23—1221no—
806C23—4881no—
807C23—4881no—
808C23—2442no—
809C23—2442no—
810C23—2442no—
811C23—2442no—
812C23C2×C22⋊#692311yescharacteristic
813C23C2×C22⋊#692311yescharacteristic
814Q8—21no—
815Q8—21no—
816Q8—81no—
817Q8—2441no—
818D4—22no—
819D4—612no—
820D4—1222no—
821D4—1221no—
822D4—1221no—
823D4—1221no—
824D4—1221no—
825D4—1221no—
826D4—4881no—
827D4—4881no—
828D4—4881no—
829D4—2442no—
830D4—2442no—
831D4—2442no—
832D4—2442no—
833D4—2441no—
834D4—2442no—
835D4—2442no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—81no—
845C2×C4—81no—
846C2×C4—611no—
847C2×C4—611no—
848C2×C4—611no—
849C2×C4—611no—
850C2×C4—611no—
851C2×C4—611no—
852C2×C4—611no—
853C2×C4—1221no—
854C2×C4—1221no—
855C2×C4—1221no—
856C2×C4—1221no—
857C2×C4—1221no—
858C2×C4—1221no—
859C2×C4—1222no—
860C2×C4—1221no—
861C2×C4—1221no—
862C2×C4—1221no—
863C2×C4—4881no—
864C2×C4—4881no—
865C2×C4—4881no—
866C2×C4—4881no—
867C2×C4—2441no—
868C2×C4—2442no—
869C2×C4—2441no—
870C2×C4—2441no—
871C2×C4—2441no—
872C2×C4—2441no—
873C2×C4—2441no—
874C2×C4—2441no—
875C2×C4—2442no—
876C2×C4—2441no—
877C2×C4C2×C22⋊#692311yescharacteristic
878C2×C4C2×C22⋊#692311yescharacteristic
879C2×C4C2×C22⋊#692311yescharacteristic
880C2×C4C2×C22⋊#692311yescharacteristic
881C2×C4C23×#692311yescharacteristic
882C8—2441no—
883C8—2441no—
884C8—2441no—
885C8—2441no—
886C8—2441no—
887C8—2441no—
888C8—2441no—
889C8—2441no—
890C22—21no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—21no—
895C22—1221no—
896C22—1222no—
897C22—1221no—
898C22—1221no—
899C22—4884no—
900C22—4884no—
901C22—2441no—
902C22—2441no—
903C22—2441no—
904C22—2441no—
905C22—2441no—
906C22—2441no—
907C22—2441no—
908C22—2441no—
909C22#1684076112yes—
910C22C22×C22⋊#692311yescharacteristic
911C4—21no—
912C4—21no—
913C4—21no—
914C4—21no—
915C4—41no—
916C4—41no—
917C4—41no—
918C4—41no—
919C4—611no—
920C4—611no—
921C4—1221no—
922C4—1221no—
923C4—1221no—
924C4—1221no—
925C4—1221no—
926C4—1221no—
927C4—2441no—
928C4D61⋊#13111yescharacteristic
929C4#1684084111yescharacteristic
930C2—22no—
931C2—41no—
932C2—4881no—
933C2—4881no—
934C2—2441no—
935C2—2442no—
936C2#2146240911yescharacteristic
937C2#2146244011yescharacteristic
938C2C2×#1684076111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#554C4
socleC22×C61C22×C22⋊C4
prime radical#21459430C2
cosocleC4×Dic61C24
hypercenter#554#6923
hypocenterC61#17521
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #554

Complements

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

NH ≅ G/Ntype
1. #21462744C2semidirect
2. #21462502C2semidirect
3. #21461180C2semidirect
4. #21461176C2semidirect
5. #21461172C2semidirect
6. #21461160C2semidirect
7. #21461153C2semidirect
8. #21461146C2semidirect
9. #21461136C2semidirect
10. #21461132C2semidirect
11. #21461126C2semidirect
12. #21461120C2semidirect
13. #21461117C2semidirect
14. C2×#16840610C2semidirect
22. #16840784C22semidirect
23. #16840783C22semidirect
24. #16840781C22semidirect
25. #16840780C22semidirect
26. #16840779C22semidirect
27. #16840778C22semidirect
28. #16840778C22semidirect
30. #16840765C22semidirect
31. D61⋊(C4⋊C8)C22semidirect
32. C2×C4⋊#92420C22semidirect
34. C4×#11758217C22semidirect
35. C2×C4×#92420C22semidirect
36. Q8⋊#92420C22semidirect
37. Q8⋊#92420C22semidirect
38. Q8⋊#92420C22semidirect
39. Q8⋊#92420C22semidirect
44. #16840610C22semidirect
45. #16840610C22semidirect
46. #16840610C22semidirect
47. #16840610C22semidirect
48. #16840610C22semidirect
49. #16840610C22semidirect
50. #16840610C22semidirect
51. #16840610C22semidirect
544. C61#17521semidirect

Maximal subgroups

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

subgroupindex
#214627442
#214625022
#214611802
#214611762
#214611722
#214611602
#214611532
#214611462
#214611362
#214611322
#214611262
#214611202
#214611172
C2×#168406102
#214594302
#1752161