Finite Group Databasebeta

← #30610860

Subgroups — #30610860

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#21461179C211yesmaximal, characteristic, complemented
4#21461175C211yesmaximal, characteristic, complemented
5#21461171C211yesmaximal, characteristic, complemented
6#21461159C211yesmaximal, characteristic, complemented
7#21461153C211yesmaximal, characteristic, complemented
8#21461145C211yesmaximal, characteristic, complemented
9#21461135C211yesmaximal, characteristic, complemented
10#21461131C211yesmaximal, characteristic, complemented
11#21461125C211yesmaximal, characteristic, complemented
12#21461119C211yesmaximal, characteristic, complemented
13#21461117C211yesmaximal, characteristic, complemented
14D61⋊(D4⋊C8)C211yesmaximal, characteristic, complemented
15#21459428C211yesmaximal, 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
36Q8⋊#92420C2211yescharacteristic, complemented
37Q8⋊#92420C2211yescharacteristic, complemented
38Q8⋊#92420C2211yescharacteristic, complemented
39Q8⋊#92420C2211yescharacteristic, complemented
40#16840610C2211yescharacteristic
41#16840610C2211yescharacteristic
42#16840610C2211yescharacteristic
43#16840610C2211yescharacteristic
44D4⋊#92420C2211yescharacteristic, complemented
45D4⋊#92420C2211yescharacteristic, complemented
46D4⋊#92420C2211yescharacteristic, complemented
47D4⋊#92420C2211yescharacteristic, complemented
48D4⋊#92420C2211yescharacteristic, complemented
49D4⋊#92420C2211yescharacteristic, complemented
50D4⋊#92420C2211yescharacteristic, complemented
51D4⋊#92420C2211yescharacteristic, complemented
52#16840472C411yescharacteristic
53#16840472C411yescharacteristic
54#16840462—21no—
55#16840462C411yescharacteristic
56#16840462C411yescharacteristic
57#16840440—21no—
58#16840440—21no—
59#16840405—21no—
60#16840405C411yescharacteristic
61#16840405C411yescharacteristic
62#16840397C411yescharacteristic
63#16840310C2211yescharacteristic
64#16840291—21no—
65#16840291C2211yescharacteristic
66#16840291C2211yescharacteristic
67#16840270—21no—
68#16840270—21no—
69C4×#11758226C2211yescharacteristic
70C4×#11758226C2211yescharacteristic
71C4×D4×D61—21no—
72C4×D4×D61C2211yescharacteristic
73C4×D4×D61C2211yescharacteristic
74C61×#559C411yescharacteristic
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×#11758226C2×C411yescharacteristic
108C2×#11758226D411yescharacteristic
109C2×#11758224—21no—
110C2×D4×D61—21no—
111C2×D4×D61C2×C411yescharacteristic
112C2×D4×D61C2×C411yescharacteristic
113C22×C4×D61—21no—
114C22×C4×D61—21no—
115#14519777C2×C411yescharacteristic
116#14519770—21no—
117#14519770—21no—
118#14519770—21no—
119#14519770—21no—
120#14519769—21no—
121#14519769C2×C411yescharacteristic
122#14519769C2×C411yescharacteristic
123#14519764—21no—
124#14519760—21no—
125#14519760—21no—
126#14519759—21no—
127#14519759—21no—
128#14519759—21no—
129#14519759—21no—
130#14519755—21no—
131#14519755—21no—
132#14519755—21no—
133#14519755—21no—
134#14519753—21no—
135#14519753C2×C411yescharacteristic
136#14519753C2×C411yescharacteristic
137#14519750—21no—
138#14519750—21no—
139#14519750—21no—
140#14519750—21no—
141#14519748—21no—
142#14519748—21no—
143#14519748C2×C411yescharacteristic
144#14519748C2×C411yescharacteristic
145#14519748C2×C411yescharacteristic
146#14519748C2×C411yescharacteristic
147#14519747—21no—
148#14519747—21no—
149#14519745—21no—
150#14519745—21no—
151Q8×Dic61D411yescharacteristic
152Q8×Dic61C2311yescharacteristic
153C4×D244—21no—
154C4×D244—21no—
155C4×D244C2×C411yescharacteristic
156C4×D244C2×C411yescharacteristic
157C4×D244C2×C411yescharacteristic
158C4×D244C2×C411yescharacteristic
159C4×D244C2×C411yescharacteristic
160C4×D244C2×C411yescharacteristic
161D4×Dic61—21no—
162D4×Dic61C2311yescharacteristic
163D4×Dic61C2311yescharacteristic
164#14519739—21no—
165#14519739D411yescharacteristic
166#14519739D411yescharacteristic
167#14519739D411yescharacteristic
168#14519739C2311yescharacteristic
169C4×C22⋊D61—21no—
170C4×C22⋊D61—21no—
171C4×C22⋊D61—21no—
172C4×C22⋊D61—21no—
173#14519737—21no—
174#14519737—21no—
175#14519737—21no—
176#14519737—21no—
177#14519735—21no—
178#14519735C2×C411yescharacteristic
179#14519735D411yescharacteristic
180#14519735D411yescharacteristic
181#14519735D411yescharacteristic
182#14519733—21no—
183#14519733—21no—
184C4⋊C4×D61—21no—
185C4⋊C4×D61C2×C411yescharacteristic
186C4⋊C4×D61C2×C411yescharacteristic
187C22⋊C4×D61—21no—
188C22⋊C4×D61—21no—
189C22⋊C4×D61—21no—
190C22⋊C4×D61—21no—
191C42×D61—21no—
192C42×D61C2311yescharacteristic
193C42×D61C2311yescharacteristic
194C42×D61C2311yescharacteristic
195#127×C61C2×C411yescharacteristic
196#124×C61—21no—
197#124×C61C2×C411yescharacteristic
198#124×C61C2×C411yescharacteristic
199#123×C61—21no—
200#123×C61—21no—
201C4×Q8×C61C2×C411yescharacteristic
202C4×Q8×C61C2×C411yescharacteristic
203C4×D4×C61—21no—
204C4×D4×C61C2×C411yescharacteristic
205C4×D4×C61C2×C411yescharacteristic
206C23×D61—21no—
207C23×D61—21no—
208C2×Q8×C61C22⋊C411yescharacteristic
209C2×Q8×C61C22×C411yescharacteristic
210C2×D4×C61—21no—
211C2×D4×C61—21no—
212C2×D4×C61C22×C411yescharacteristic
213C2×D4×C61C22×C411yescharacteristic
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C2×C22⋊D61—21no—
217C2×C22⋊D61—21no—
218C2×C22⋊D61—21no—
219C2×C22⋊D61—21no—
220C2×C22⋊D61—21no—
221C2×C22⋊D61—21no—
222C22×Dic61—21no—
223C22×Dic61—21no—
224#11758226—22no—
225#11758226—42no—
226#11758226—41no—
227#11758224—81no—
228#11758224—81no—
229D4×D61—22no—
230D4×D61—22no—
231D4×D61—41no—
232D4×D61—41no—
233D4×D61—44no—
234C2×D244—21no—
235C2×D244C22⋊C411yescharacteristic
236C2×D244C22⋊C411yescharacteristic
237C2×D244C22⋊C411yescharacteristic
238C2×D244C22×C411yescharacteristic
239C2×C4×D61—21no—
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×Dic122—21no—
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×C61C22⋊C411yescharacteristic
275C4⋊C4×C61C22⋊C411yescharacteristic
276C4⋊C4×C61C22⋊C411yescharacteristic
277C4⋊C4×C61C22×C411yescharacteristic
278C22⋊C4×C61—21no—
279C22⋊C4×C61—21no—
280C22⋊C4×C61—21no—
281C22⋊C4×C61—21no—
282C22⋊C4×C61—21no—
283C22⋊C4×C61—21no—
284C42×C61—21no—
285C42×C61C22×C411yescharacteristic
286C42×C61C22×C411yescharacteristic
287C42×C61C22×C411yescharacteristic
288C22⋊Dic61—21no—
289C22⋊Dic61—21no—
290C22⋊Dic61—21no—
291C22⋊Dic61—21no—
292C22⋊Dic61—21no—
293C22⋊Dic61—21no—
294#11758198—21no—
295#11758198—21no—
296#11758198—21no—
297#11758198—21no—
298#11758198—21no—
299#11758198—21no—
300#11758198—21no—
301#11758198C22⋊C411yescharacteristic
302#11758198C22⋊C411yescharacteristic
303#11758198C22⋊C411yescharacteristic
304#11758198C22⋊C411yescharacteristic
305#11758198C22⋊C411yescharacteristic
306#11758198C22⋊C411yescharacteristic
307C4⋊Dic61—21no—
308C4⋊Dic61—21no—
309C4⋊Dic61C22⋊C411yescharacteristic
310C4⋊Dic61C22⋊C411yescharacteristic
311C4⋊Dic61C22⋊C411yescharacteristic
312C4⋊Dic61C22×C411yescharacteristic
313C4⋊Dic61C22×C411yescharacteristic
314C4⋊Dic61C22×C411yescharacteristic
315#11758196—21no—
316#11758196—21no—
317#11758196—21no—
318#11758196—21no—
319#11758196—21no—
320#11758196—21no—
321#11758196—21no—
322#11758196—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—
333C23×C61—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—21no—
345Q8×C61—21no—
346Q8×C61—41no—
347D4×C61—21no—
348D4×C61—21no—
349D4×C61—21no—
350D4×C61—21no—
351D4×C61—42no—
352D4×C61—81no—
353C2×C4×C61—21no—
354C2×C4×C61—21no—
355C2×C4×C61—81no—
356C2×C4×C61—81no—
357C2×C4×C61C2×C22⋊C411yescharacteristic
358C2×C4×C61C2×C22⋊C411yescharacteristic
359C2×C4×C61C2×C22⋊C411yescharacteristic
360C2×C4×C61C2×C22⋊C411yescharacteristic
361C2×C4×C61C2×C22⋊C411yescharacteristic
362C2×C4×C61C2×C22⋊C411yescharacteristic
363C2×C4×C61C23×C411yescharacteristic
364C22⋊D61—42no—
365C22⋊D61—42no—
366C22⋊D61—42no—
367C22⋊D61—42no—
368C22⋊D61—81no—
369C22⋊D61—81no—
370C2×Dic61—21no—
371C2×Dic61—21no—
372C2×Dic61—21no—
373C2×Dic61—41no—
374C2×Dic61—41no—
375C2×Dic61—41no—
376C2×Dic61—41no—
377C2×Dic61C2×C22⋊C411yescharacteristic
378C2×Dic61C2×C22⋊C411yescharacteristic
379C2×Dic61C2×C22⋊C411yescharacteristic
380C2×Dic61C22×D411yescharacteristic
381C2×Dic61C22×D411yescharacteristic
382D244—22no—
383D244—22no—
384D244—21no—
385D244—41no—
386D244—42no—
387D244#13112yes—
388C4×D61—22no—
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—21no—
401C4×D61—41no—
402C4×D61—41no—
403C4×D61—42no—
404C4×D61—42no—
405C4×D61—41no—
406C4×D61—41no—
407C4×D61—81no—
408C4×D61—81no—
409C4×D61—81no—
410C4×D61—81no—
411Dic122—81no—
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—41no—
422C22×C61—41no—
423C22×C61—41no—
424C22×C61—41no—
425C22×C61—41no—
426C22×C61—41no—
427C22×C61C22×C22⋊C411yescharacteristic
428C2×D61—21no—
429C2×D61—21no—
430C2×D61—21no—
431C2×D61—21no—
432C2×D61—22no—
433C2×D61—21no—
434C2×D61—21no—
435C2×D61—21no—
436C2×D61—21no—
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×C61C2×#13111yescharacteristic
451C4×C61#56811yescharacteristic
452Dic61—21no—
453Dic61—21no—
454Dic61—21no—
455Dic61—21no—
456Dic61—41no—
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—81no—
477C2×C61—81no—
478C2×C61#288011yescharacteristic
479C2×C61#289711yescharacteristic
480C2×C61C2×#42111yescharacteristic
481D61—22no—
482D61—41no—
483D61—41no—
484D61—42no—
485#559#692311yescharacteristic
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—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⋊Q8—611no—
559#127C2×#692311yescharacteristic
560#126—1221no—
561#126—1221no—
562#126—1221no—
563#126—1221no—
564#125—611no—
565#125—611no—
566#125—1221no—
567#124—21no—
568#124—1221no—
569#124C2×#692311yescharacteristic
570#124C2×#692311yescharacteristic
571#123—21no—
572#123—21no—
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×Q8C2×#692311yescharacteristic
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—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×D4—1221no—
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—611no—
639C2×C4⋊C4—611no—
640C2×C4⋊C4—1221no—
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—1221no—
684C2×Q8C22⋊#692311yescharacteristic
685C2×Q8C22×#692311yescharacteristic
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—611no—
689C2×D4—611no—
690C2×D4—611no—
691C2×D4—611no—
692C2×D4—1221no—
693C2×D4—1221no—
694C2×D4—1221no—
695C2×D4—1222no—
696C2×D4—1222no—
697C2×D4—1221no—
698C2×D4—1221no—
699C2×D4—1221no—
700C2×D4—1221no—
701C2×D4—2441no—
702C2×D4—2441no—
703C2×D4—2444no—
704C2×D4C22×#692311yescharacteristic
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—611no—
716C22×C4—611no—
717C22×C4—1221no—
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—611no—
745C4⋊C4—611no—
746C4⋊C4—611no—
747C4⋊C4—611no—
748C4⋊C4—611no—
749C4⋊C4—611no—
750C4⋊C4—1221no—
751C4⋊C4—1221no—
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⋊C4C22⋊#692311yescharacteristic
761C4⋊C4C22⋊#692311yescharacteristic
762C4⋊C4C22⋊#692311yescharacteristic
763C4⋊C4C22×#692311yescharacteristic
764C22⋊C4—21no—
765C22⋊C4—21no—
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—611no—
771C22⋊C4—611no—
772C22⋊C4—611no—
773C22⋊C4—611no—
774C22⋊C4—611no—
775C22⋊C4—611no—
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—21no—
790C42—611no—
791C42—611no—
792C42—611no—
793C42—611no—
794C42—611no—
795C42—611no—
796C42—611no—
797C42—1221no—
798C42—1221no—
799C42C22×#692311yescharacteristic
800C42C22×#692311yescharacteristic
801C42C22×#692311yescharacteristic
802C23—21no—
803C23—21no—
804C23—611no—
805C23—611no—
806C23—611no—
807C23—1221no—
808C23—4881no—
809C23—4881no—
810C23—2442no—
811C23—2442no—
812C23—2442no—
813C23—2442no—
814Q8—21no—
815Q8—21no—
816Q8—41no—
817Q8—4881no—
818D4—21no—
819D4—21no—
820D4—21no—
821D4—21no—
822D4—42no—
823D4—81no—
824D4—612no—
825D4—1222no—
826D4—1222no—
827D4—1221no—
828D4—4881no—
829D4—4881no—
830D4—2441no—
831D4—2442no—
832D4—2442no—
833D4—2442no—
834D4—2442no—
835D4—2442no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—81no—
839C2×C4—81no—
840C2×C4—611no—
841C2×C4—611no—
842C2×C4—611no—
843C2×C4—611no—
844C2×C4—611no—
845C2×C4—1221no—
846C2×C4—1221no—
847C2×C4—1221no—
848C2×C4—1221no—
849C2×C4—1221no—
850C2×C4—1221no—
851C2×C4—1222no—
852C2×C4—1221no—
853C2×C4—1221no—
854C2×C4—1221no—
855C2×C4—1221no—
856C2×C4—1221no—
857C2×C4—1221no—
858C2×C4—1221no—
859C2×C4—1221no—
860C2×C4—1221no—
861C2×C4—4881no—
862C2×C4—4881no—
863C2×C4—4881no—
864C2×C4—4881no—
865C2×C4—2441no—
866C2×C4—2441no—
867C2×C4—2442no—
868C2×C4—2441no—
869C2×C4—2441no—
870C2×C4—2442no—
871C2×C4—2441no—
872C2×C4—2441no—
873C2×C4—2441no—
874C2×C4—2441no—
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—41no—
891C22—41no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—612no—
897C22—1221no—
898C22—1221no—
899C22—1221no—
900C22—1221no—
901C22—1222no—
902C22—1221no—
903C22—1221no—
904C22—1221no—
905C22—1221no—
906C22—4884no—
907C22—4884no—
908C22—2441no—
909C22—2441no—
910C22C22×C22⋊#692311yescharacteristic
911C4—21no—
912C4—21no—
913C4—21no—
914C4—21no—
915C4—21no—
916C4—21no—
917C4—41no—
918C4—41no—
919C4—611no—
920C4—611no—
921C4—1221no—
922C4—1221no—
923C4—1221no—
924C4—1221no—
925C4—2441no—
926C4—2441no—
927C4—2441no—
928C4D61⋊#13111yescharacteristic
929C4#1684084111yescharacteristic
930C2—81no—
931C2—81no—
932C2—1222no—
933C2—2441no—
934C2—2441no—
935C2—2442no—
936C2#2146241011yescharacteristic
937C2#2146244011yescharacteristic
938C2D61⋊#42111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#559C4
socleC22×C61C22×C22⋊C4
prime radical#21459428C2
cosocleC4×Dic61C24
hypercenter#559#6923
hypocenterC61#17521
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #559

Complements

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

NH ≅ G/Ntype
1. #21462749C2semidirect
2. #21462504C2semidirect
3. #21461179C2semidirect
4. #21461175C2semidirect
5. #21461171C2semidirect
6. #21461159C2semidirect
7. #21461153C2semidirect
8. #21461145C2semidirect
9. #21461135C2semidirect
10. #21461131C2semidirect
11. #21461125C2semidirect
12. #21461119C2semidirect
13. #21461117C2semidirect
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. Q8⋊#92420C22semidirect
37. Q8⋊#92420C22semidirect
38. Q8⋊#92420C22semidirect
39. Q8⋊#92420C22semidirect
44. D4⋊#92420C22semidirect
45. D4⋊#92420C22semidirect
46. D4⋊#92420C22semidirect
47. D4⋊#92420C22semidirect
48. D4⋊#92420C22semidirect
49. D4⋊#92420C22semidirect
50. D4⋊#92420C22semidirect
51. D4⋊#92420C22semidirect
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
#214611792
#214611752
#214611712
#214611592
#214611532
#214611452
#214611352
#214611312
#214611252
#214611192
#214611172
D61⋊(D4⋊C8)2
#214594282
#1752161