Finite Group Databasebeta

← #30610856

Subgroups — #30610856

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#21462749C211yesmaximal, characteristic, complemented
2#21462504C211yesmaximal, characteristic, complemented
3#21461180C211yesmaximal, characteristic, complemented
4#21461177C211yesmaximal, characteristic, complemented
5#21461173C211yesmaximal, characteristic, complemented
6#21461159C211yesmaximal, characteristic, complemented
7#21461151C211yesmaximal, characteristic, complemented
8#21461145C211yesmaximal, characteristic, complemented
9#21461137C211yesmaximal, characteristic, complemented
10#21461133C211yesmaximal, characteristic, complemented
11#21461126C211yesmaximal, characteristic, complemented
12#21461119C211yesmaximal, characteristic, complemented
13#21461115C211yesmaximal, characteristic, complemented
14D61⋊(D4⋊C8)C211yesmaximal, characteristic, complemented
15#21459430C211yesmaximal, characteristic
16#16840813—21no—
17#16840792—21no—
18#16840792—21no—
19#16840790—21no—
20#16840787—21no—
21#16840787—21no—
22#16840784C2211yescharacteristic, complemented
23#16840784C2211yescharacteristic, complemented
24#16840781C2211yescharacteristic, complemented
25#16840781C2211yescharacteristic, complemented
26#16840781C2211yescharacteristic, complemented
27#16840780C2211yescharacteristic, complemented
28#16840780C2211yescharacteristic, complemented
29#16840769—21no—
30#16840766C2211yescharacteristic, complemented
31D61⋊(C4⋊C8)C2211yescharacteristic, complemented
32D61⋊(C4⋊C8)C2211yescharacteristic, complemented
33#16840737—21no—
34C4×#11758213C2211yescharacteristic, complemented
35C4×D61⋊C8C2211yescharacteristic, complemented
36#16840612C2211yescharacteristic, complemented
37#16840612C2211yescharacteristic, complemented
38#16840612C2211yescharacteristic, complemented
39#16840612C2211yescharacteristic, complemented
40#16840610C2211yescharacteristic, complemented
41#16840610C2211yescharacteristic, complemented
42#16840610C2211yescharacteristic, complemented
43#16840610C2211yescharacteristic, complemented
44#16840610C2211yescharacteristic, complemented
45#16840610C2211yescharacteristic, complemented
46#16840610C2211yescharacteristic, complemented
47#16840610C2211yescharacteristic, complemented
48D4⋊#92420C2211yescharacteristic
49D4⋊#92420C2211yescharacteristic
50D4⋊#92420C2211yescharacteristic
51D4⋊#92420C2211yescharacteristic
52#16840497C411yescharacteristic
53#16840473C411yescharacteristic
54#16840465C411yescharacteristic
55#16840465C411yescharacteristic
56#16840460—21no—
57#16840439—21no—
58#16840439—21no—
59#16840407C411yescharacteristic
60#16840407C411yescharacteristic
61#16840403—21no—
62D4×D244C411yescharacteristic
63#16840313C2211yescharacteristic
64#16840298—21no—
65#16840297C2211yescharacteristic
66#16840297C2211yescharacteristic
67#16840275—21no—
68#16840275—21no—
69C4×#11758226C2211yescharacteristic
70C4×#11758224C2211yescharacteristic
71C2×#14519739—21no—
72C4×D4×D61C2211yescharacteristic
73C4×D4×D61C2211yescharacteristic
74C61×#554C411yescharacteristic
75C2×#11758213—21no—
76C2×#11758213—21no—
77C2×D61⋊C8—21no—
78C2×D61⋊C8—21no—
79C2×D61⋊C8—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—
94#14519834—21no—
95#14519834—21no—
96#14519834—21no—
97#14519834—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×#11758226D411yescharacteristic
109C2×#11758224C2×C411yescharacteristic
110C22×D244—21no—
111C2×D4×D61C2×C411yescharacteristic
112C2×D4×D61C2×C411yescharacteristic
113C22×C4×D61—21no—
114C22×C4×D61—21no—
115#14519774C2×C411yescharacteristic
116#14519772—21no—
117#14519772—21no—
118#14519772—21no—
119#14519772—21no—
120#14519768—21no—
121#14519766—21no—
122#14519766—21no—
123#14519765C2×C411yescharacteristic
124#14519765C2×C411yescharacteristic
125#14519762—21no—
126#14519762—21no—
127#14519762—21no—
128#14519762—21no—
129#14519762—21no—
130#14519762—21no—
131#14519761—21no—
132#14519761—21no—
133#14519757C2×C411yescharacteristic
134#14519757C2×C411yescharacteristic
135#14519753—21no—
136#14519753—21no—
137#14519752—21no—
138#14519752—21no—
139#14519752—21no—
140#14519752C2×C411yescharacteristic
141#14519752C2×C411yescharacteristic
142#14519752C2×C411yescharacteristic
143#14519752C2×C411yescharacteristic
144#14519751—21no—
145#14519751—21no—
146#14519751—21no—
147#14519747—21no—
148#14519747—21no—
149#14519747—21no—
150#14519747—21no—
151Q8×Dic61D411yescharacteristic
152C4×Dic122C2×C411yescharacteristic
153#14519742C2311yescharacteristic
154C4×D244C2×C411yescharacteristic
155C4×D244C2×C411yescharacteristic
156C4×D244C2×C411yescharacteristic
157C4×D244C2×C411yescharacteristic
158C4×D244C2×C411yescharacteristic
159D4×Dic61C2311yescharacteristic
160#14519739—21no—
161#14519739—21no—
162#14519739—21no—
163#14519739—21no—
164#14519739—21no—
165#14519739—21no—
166#14519739—21no—
167#14519739D411yescharacteristic
168#14519739D411yescharacteristic
169#14519739D411yescharacteristic
170#14519739C2311yescharacteristic
171#14519739C2311yescharacteristic
172C4×C22⋊D61—21no—
173C4×C22⋊D61—21no—
174C4×C22⋊D61—21no—
175#14519737—21no—
176#14519737—21no—
177#14519737—21no—
178#14519735—21no—
179#14519735—21no—
180#14519735C2×C411yescharacteristic
181#14519735D411yescharacteristic
182#14519735D411yescharacteristic
183#14519735D411yescharacteristic
184#14519733—21no—
185C4⋊C4×D61C2×C411yescharacteristic
186C4⋊C4×D61C2×C411yescharacteristic
187C2×#11758198—21no—
188C2×#11758198—21no—
189C22⋊C4×D61—21no—
190C22⋊C4×D61—21no—
191C2×C4×Dic61—21no—
192C42×D61C2311yescharacteristic
193C42×D61C2311yescharacteristic
194C42×D61C2311yescharacteristic
195C4⋊Q8×C61C2×C411yescharacteristic
196#125×C61C2×C411yescharacteristic
197#125×C61C2×C411yescharacteristic
198C22⋊Q8×C61—21no—
199C22⋊Q8×C61—21no—
200C22⋊Q8×C61—21no—
201C4×Q8×C61C2×C411yescharacteristic
202C4×D4×C61C2×C411yescharacteristic
203C4×D4×C61C2×C411yescharacteristic
204C4×D4×C61C2×C411yescharacteristic
205C2×C4⋊C4×C61—21no—
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×C61—21no—
214C2×C22⋊D61—21no—
215C2×C22⋊D61—21no—
216C2×C22⋊D61—21no—
217C22×Dic61—21no—
218C22×Dic61—21no—
219#11758226—42no—
220#11758226—81no—
221#11758226—81no—
222#11758224—22no—
223#11758224—41no—
224D4×D61—22no—
225D4×D61—22no—
226D4×D61—41no—
227D4×D61—41no—
228C2×D244—21no—
229C2×D244—21no—
230C2×D244—21no—
231C2×D244—21no—
232C2×D244—21no—
233C2×D244—21no—
234C2×D244—44no—
235C2×D244C22⋊C411yescharacteristic
236C2×D244C22⋊C411yescharacteristic
237C2×D244C22⋊C411yescharacteristic
238C2×D244C22×C411yescharacteristic
239C2×D244C22×C411yescharacteristic
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—81no—
247C2×C4×D61—81no—
248C2×C4×D61—81no—
249C2×C4×D61—81no—
250C2×C4×D61C22×C411yescharacteristic
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×C4×D61C2×D411yescharacteristic
258C2×C4×D61C2×D411yescharacteristic
259C2×Dic122C22×C411yescharacteristic
260C2×#92420—21no—
261C2×#92420—21no—
262C2×#92420—21no—
263C2×#92420—21no—
264C2×#92420—21no—
265C2×#92420—21no—
266C2×#92420—21no—
267C2×#92420—21no—
268#11758213—42no—
269#11758213—81no—
270D61⋊C8—42no—
271D61⋊C8—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×C61C22⋊C411yescharacteristic
279C4⋊C4×C61C22⋊C411yescharacteristic
280C4⋊C4×C61C22⋊C411yescharacteristic
281C4⋊C4×C61C22×C411yescharacteristic
282C4⋊C4×C61C22×C411yescharacteristic
283C4⋊C4×C61C22×C411yescharacteristic
284C22⋊C4×C61—21no—
285C22⋊C4×C61—21no—
286C22⋊C4×C61—21no—
287C42×C61C22×C411yescharacteristic
288C42×C61C22×C411yescharacteristic
289C42×C61C22×C411yescharacteristic
290C22⋊Dic61—21no—
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#11758198C22⋊C411yescharacteristic
307#11758198C22⋊C411yescharacteristic
308#11758198C22⋊C411yescharacteristic
309#11758198C22⋊C411yescharacteristic
310#11758198C22⋊C411yescharacteristic
311#11758198C22⋊C411yescharacteristic
312C4⋊Dic61—21no—
313C4⋊Dic61—21no—
314C4⋊Dic61C22⋊C411yescharacteristic
315C4⋊Dic61C22⋊C411yescharacteristic
316C4⋊Dic61C22⋊C411yescharacteristic
317C4⋊Dic61C22×C411yescharacteristic
318#11758196—21no—
319#11758196—21no—
320#11758196—21no—
321#11758196—21no—
322C4×Dic61—21no—
323C4×Dic61—21no—
324C4×Dic61—21no—
325C4×Dic61C2×D411yescharacteristic
326C4×Dic61C2×D411yescharacteristic
327C4×Dic61C2×D411yescharacteristic
328C4×Dic61C2×D411yescharacteristic
329C4×Dic61C2×D411yescharacteristic
330C4×Dic61C2×D411yescharacteristic
331C4×Dic61C2411yescharacteristic
332C23×C61—21no—
333C22×D61—21no—
334C22×D61—21no—
335C22×D61—42no—
336C22×D61—42no—
337C22×D61—42no—
338C22×D61—42no—
339C22×D61—81no—
340C22×D61—81no—
341C22×D61C2×C22⋊C411yescharacteristic
342C22×D61C2×C22⋊C411yescharacteristic
343C22×D61C2×C22⋊C411yescharacteristic
344Q8×C61—41no—
345Q8×C61—81no—
346D4×C61—21no—
347D4×C61#13112yes—
348C2×C4×C61—21no—
349C2×C4×C61—21no—
350C2×C4×C61—21no—
351C2×C4×C61—42no—
352C2×C4×C61—81no—
353C2×C4×C61—81no—
354C2×C4×C61C2×C22⋊C411yescharacteristic
355C2×C4×C61C2×C22⋊C411yescharacteristic
356C2×C4×C61C2×C22⋊C411yescharacteristic
357C2×C4×C61C2×C22⋊C411yescharacteristic
358C2×C4×C61C2×C22⋊C411yescharacteristic
359C2×C4×C61C2×C22⋊C411yescharacteristic
360C2×C4×C61C23×C411yescharacteristic
361C22⋊D61—42no—
362C22⋊D61—42no—
363C22⋊D61—42no—
364C2×Dic61—21no—
365C2×Dic61—21no—
366C2×Dic61—42no—
367C2×Dic61—41no—
368C2×Dic61—41no—
369C2×Dic61C2×C22⋊C411yescharacteristic
370C2×Dic61C2×C22⋊C411yescharacteristic
371C2×Dic61C2×C22⋊C411yescharacteristic
372C2×Dic61C22×D411yescharacteristic
373C2×Dic61C22×D411yescharacteristic
374D244—22no—
375D244—22no—
376D244—21no—
377D244—21no—
378D244—21no—
379D244—21no—
380D244—41no—
381D244—42no—
382D244—42no—
383D244—42no—
384D244—81no—
385D244—81no—
386D244—81no—
387C4×D61—22no—
388C4×D61—21no—
389C4×D61—21no—
390C4×D61—21no—
391C4×D61—21no—
392C4×D61—21no—
393C4×D61—21no—
394C4×D61—21no—
395C4×D61—21no—
396C4×D61—21no—
397C4×D61—21no—
398C4×D61—21no—
399C4×D61—21no—
400C4×D61—41no—
401C4×D61—41no—
402C4×D61—41no—
403C4×D61—41no—
404C4×D61—41no—
405C4×D61—41no—
406C4×D61—81no—
407C4×D61—81no—
408C4×D61—81no—
409C4×D61—81no—
410Dic122—21no—
411Dic122—21no—
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—22no—
422C22×C61—41no—
423C22×C61—41no—
424C22×C61C22×C22⋊C411yescharacteristic
425C2×D61—21no—
426C2×D61—21no—
427C2×D61—21no—
428C2×D61—21no—
429C2×D61—21no—
430C2×D61—21no—
431C2×D61—21no—
432C2×D61—21no—
433C2×D61—41no—
434C2×D61—41no—
435C2×D61—41no—
436C2×D61—41no—
437C2×D61—41no—
438C2×D61—41no—
439C2×D61—84no—
440C2×D61—84no—
441C2×D61#42112yes—
442C4×C61—21no—
443C4×C61—21no—
444C4×C61—21no—
445C4×C61—21no—
446C4×C61—21no—
447C4×C61—21no—
448C4×C61—41no—
449C4×C61—41no—
450C4×C61—41no—
451C4×C61C2×#13111yescharacteristic
452C4×C61#56811yescharacteristic
453Dic61—21no—
454Dic61—21no—
455Dic61—21no—
456Dic61—21no—
457Dic61—41no—
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—42no—
477C2×C61#288011yescharacteristic
478C2×C61#289711yescharacteristic
479C2×C61C2×#42111yescharacteristic
480D61—22no—
481D61—41no—
482D61—41no—
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—1221no—
565#125C2×#692311yescharacteristic
566#125C2×#692311yescharacteristic
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—21no—
582C22⋊Q8—611no—
583C22⋊Q8—611no—
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×Q8C2×#692311yescharacteristic
604C4×D4—611no—
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—1221no—
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×D4—1221no—
628C4×D4C2×#692311yescharacteristic
629C4×D4C2×#692311yescharacteristic
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—21no—
639C2×C4⋊C4—611no—
640C2×C4⋊C4—611no—
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—2441no—
682#41—2442no—
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—1221no—
692C2×D4—1221no—
693C2×D4—1221no—
694C2×D4—1221no—
695C2×D4—1221no—
696C2×D4—1221no—
697C2×D4—1222no—
698C2×D4—1222no—
699C2×D4—1221no—
700C2×D4—1221no—
701C2×D4—1221no—
702C2×D4—2444no—
703C2×D4—2441no—
704C2×D4—2441no—
705C2×D4C22×#692311yescharacteristic
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—611no—
710C22×C4—611no—
711C22×C4—611no—
712C22×C4—611no—
713C22×C4—611no—
714C22×C4—611no—
715C22×C4—611no—
716C22×C4—611no—
717C22×C4—611no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—4881no—
727C22×C4—4881no—
728C22×C4—4881no—
729C22×C4—4881no—
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—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⋊C4C22⋊#692311yescharacteristic
759C4⋊C4C22⋊#692311yescharacteristic
760C4⋊C4C22⋊#692311yescharacteristic
761C4⋊C4C22×#692311yescharacteristic
762C4⋊C4C22×#692311yescharacteristic
763C4⋊C4C22×#692311yescharacteristic
764C22⋊C4—21no—
765C22⋊C4—21no—
766C22⋊C4—21no—
767C22⋊C4—611no—
768C22⋊C4—611no—
769C22⋊C4—611no—
770C22⋊C4—611no—
771C22⋊C4—611no—
772C22⋊C4—611no—
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⋊C4—1221no—
788C22⋊C4—1221no—
789C42—611no—
790C42—611no—
791C42—611no—
792C42—611no—
793C42—611no—
794C42—611no—
795C42—611no—
796C42—1221no—
797C42—1221no—
798C42—1221no—
799C42C22×#692311yescharacteristic
800C42C22×#692311yescharacteristic
801C42C22×#692311yescharacteristic
802C23—21no—
803C23—611no—
804C23—611no—
805C23—611no—
806C23—1221no—
807C23—1221no—
808C23—4881no—
809C23—4881no—
810C23—2442no—
811C23—2442no—
812C23—2442no—
813C23—2442no—
814Q8—41no—
815Q8—81no—
816Q8—1221no—
817Q8—1221no—
818D4—21no—
819D4—1222no—
820D4—1222no—
821D4—1221no—
822D4—1221no—
823D4—1221no—
824D4—1221no—
825D4—4881no—
826D4—4881no—
827D4—4881no—
828D4—2441no—
829D4—2442no—
830D4—2442no—
831D4—2442no—
832D4—2442no—
833D4—2442no—
834D4—2442no—
835D4#1451986512yes—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—42no—
840C2×C4—81no—
841C2×C4—81no—
842C2×C4—611no—
843C2×C4—611no—
844C2×C4—611no—
845C2×C4—611no—
846C2×C4—611no—
847C2×C4—1221no—
848C2×C4—1221no—
849C2×C4—1221no—
850C2×C4—1221no—
851C2×C4—1221no—
852C2×C4—1221no—
853C2×C4—1222no—
854C2×C4—1221no—
855C2×C4—1221no—
856C2×C4—1221no—
857C2×C4—1221no—
858C2×C4—1221no—
859C2×C4—1221no—
860C2×C4—1221no—
861C2×C4—1221no—
862C2×C4—4881no—
863C2×C4—4881no—
864C2×C4—4881no—
865C2×C4—4881no—
866C2×C4—2441no—
867C2×C4—2441no—
868C2×C4—2441no—
869C2×C4—2441no—
870C2×C4—2441no—
871C2×C4—2441no—
872C2×C4—2441no—
873C2×C4—2441no—
874C2×C4—2442no—
875C2×C4C2×C22⋊#692311yescharacteristic
876C2×C4C2×C22⋊#692311yescharacteristic
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—22no—
891C22—41no—
892C22—41no—
893C22—612no—
894C22—1221no—
895C22—1221no—
896C22—1221no—
897C22—1221no—
898C22—1221no—
899C22—1221no—
900C22—1221no—
901C22—1221no—
902C22—4884no—
903C22—4884no—
904C22—2441no—
905C22—2441no—
906C22—2441no—
907C22—2441no—
908C22—2441no—
909C22—2441no—
910C22C22×C22⋊#692311yescharacteristic
911C4—21no—
912C4—21no—
913C4—21no—
914C4—21no—
915C4—21no—
916C4—21no—
917C4—41no—
918C4—41no—
919C4—41no—
920C4—611no—
921C4—611no—
922C4—1221no—
923C4—1221no—
924C4—1221no—
925C4—1221no—
926C4—2441no—
927C4—2441no—
928C4C2×#1451986511yescharacteristic
929C4#1684084211yescharacteristic
930C2—42no—
931C2—1222no—
932C2—4881no—
933C2—4881no—
934C2—2441no—
935C2—2441no—
936C2#2146240811yescharacteristic
937C2#2146244011yescharacteristic
938C2D61⋊#42111yescharacteristic
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×Q8 ◁ #554

Complements

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

NH ≅ G/Ntype
1. #21462749C2semidirect
2. #21462504C2semidirect
3. #21461180C2semidirect
4. #21461177C2semidirect
5. #21461173C2semidirect
6. #21461159C2semidirect
7. #21461151C2semidirect
8. #21461145C2semidirect
9. #21461137C2semidirect
10. #21461133C2semidirect
11. #21461126C2semidirect
12. #21461119C2semidirect
13. #21461115C2semidirect
14. D61⋊(D4⋊C8)C2semidirect
22. #16840784C22semidirect
23. #16840784C22semidirect
24. #16840781C22semidirect
25. #16840781C22semidirect
26. #16840781C22semidirect
27. #16840780C22semidirect
28. #16840780C22semidirect
30. #16840766C22semidirect
31. D61⋊(C4⋊C8)C22semidirect
32. D61⋊(C4⋊C8)C22semidirect
34. C4×#11758213C22semidirect
35. C4×D61⋊C8C22semidirect
36. #16840612C22semidirect
37. #16840612C22semidirect
38. #16840612C22semidirect
39. #16840612C22semidirect
40. #16840610C22semidirect
41. #16840610C22semidirect
42. #16840610C22semidirect
43. #16840610C22semidirect
44. #16840610C22semidirect
45. #16840610C22semidirect
46. #16840610C22semidirect
47. #16840610C22semidirect
544. C61#17521semidirect

Maximal subgroups

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

subgroupindex
#214627492
#214625042
#214611802
#214611772
#214611732
#214611592
#214611512
#214611452
#214611372
#214611332
#214611262
#214611192
#214611152
D61⋊(D4⋊C8)2
#214594302
#1752161