Finite Group Databasebeta

← #30610853

Subgroups — #30610853

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#21461179C211yesmaximal, characteristic, complemented
4#21461174C211yesmaximal, characteristic, complemented
5#21461170C211yesmaximal, characteristic, complemented
6#21461158C211yesmaximal, characteristic, complemented
7#21461151C211yesmaximal, characteristic, complemented
8#21461144C211yesmaximal, characteristic, complemented
9#21461134C211yesmaximal, characteristic, complemented
10#21461130C211yesmaximal, characteristic, complemented
11#21461125C211yesmaximal, characteristic, complemented
12#21461118C211yesmaximal, characteristic, complemented
13#21461115C211yesmaximal, characteristic, complemented
14C2×D4⋊#92420C211yesmaximal, characteristic, complemented
15#21459420C211yesmaximal, 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
36#16840612C2211yescharacteristic, complemented
37#16840612C2211yescharacteristic, complemented
38#16840612C2211yescharacteristic, complemented
39#16840612C2211yescharacteristic, complemented
40D4⋊#92420C2211yescharacteristic
41D4⋊#92420C2211yescharacteristic
42D4⋊#92420C2211yescharacteristic
43D4⋊#92420C2211yescharacteristic
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#16840498C411yescharacteristic
53#16840469C411yescharacteristic
54#16840469C411yescharacteristic
55#16840464—21no—
56#16840464C411yescharacteristic
57#16840464C411yescharacteristic
58#16840443—21no—
59#16840443—21no—
60#16840406—21no—
61#16840406C411yescharacteristic
62#16840406C411yescharacteristic
63#16840310C2211yescharacteristic
64#16840293—21no—
65#16840293C2211yescharacteristic
66#16840293C2211yescharacteristic
67#16840268—21no—
68#16840268—21no—
69C4×#11758224C2211yescharacteristic
70C4×#11758224C2211yescharacteristic
71C2×D4×Dic61—21no—
72C2×D4×Dic61C2211yescharacteristic
73C2×D4×Dic61C2211yescharacteristic
74D42×C61C411yescharacteristic
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×#11758224—21no—
108C2×#11758224C2×C411yescharacteristic
109C2×#11758224D411yescharacteristic
110C23×Dic61—21no—
111C23×Dic61—21no—
112#14519777C2×C411yescharacteristic
113#14519770—21no—
114#14519770—21no—
115#14519770—21no—
116#14519770—21no—
117#14519768—21no—
118#14519768C2×C411yescharacteristic
119#14519768C2×C411yescharacteristic
120#14519764—21no—
121#14519764—21no—
122#14519764C2×C411yescharacteristic
123#14519764C2×C411yescharacteristic
124#14519761—21no—
125#14519761—21no—
126#14519758—21no—
127#14519758—21no—
128#14519758—21no—
129#14519758—21no—
130#14519758—21no—
131#14519758—21no—
132#14519756—21no—
133#14519756C2×C411yescharacteristic
134#14519756C2×C411yescharacteristic
135#14519754—21no—
136#14519754—21no—
137#14519754—21no—
138#14519754—21no—
139#14519749—21no—
140#14519749—21no—
141#14519749—21no—
142#14519749—21no—
143#14519748—21no—
144#14519748C2×C411yescharacteristic
145#14519748C2×C411yescharacteristic
146#14519746—21no—
147#14519746—21no—
148C4×Dic122C2×C411yescharacteristic
149C4×Dic122C2×C411yescharacteristic
150#14519742D411yescharacteristic
151#14519742C2311yescharacteristic
152D4×Dic61—21no—
153D4×Dic61—21no—
154D4×Dic61—21no—
155D4×Dic61—21no—
156D4×Dic61—21no—
157D4×Dic61—21no—
158D4×Dic61—21no—
159D4×Dic61—21no—
160D4×Dic61—21no—
161D4×Dic61—21no—
162D4×Dic61—21no—
163D4×Dic61C2×C411yescharacteristic
164D4×Dic61C2×C411yescharacteristic
165D4×Dic61C2×C411yescharacteristic
166D4×Dic61C2×C411yescharacteristic
167D4×Dic61D411yescharacteristic
168D4×Dic61C2311yescharacteristic
169D4×Dic61C2311yescharacteristic
170D4×Dic61C2311yescharacteristic
171C4×C22⋊D61—21no—
172C4×C22⋊D61C2×C411yescharacteristic
173C4×C22⋊D61C2×C411yescharacteristic
174#14519737—21no—
175#14519737D411yescharacteristic
176#14519737D411yescharacteristic
177#14519735C2×C411yescharacteristic
178#14519735D411yescharacteristic
179#14519733—21no—
180#14519733—21no—
181#14519733—21no—
182#14519733D411yescharacteristic
183#14519733D411yescharacteristic
184C2×C4⋊Dic61—21no—
185C2×C4⋊Dic61C2×C411yescharacteristic
186C2×C4⋊Dic61C2×C411yescharacteristic
187C2×C22⋊Dic61—21no—
188C2×C22⋊Dic61—21no—
189C2×C22⋊Dic61—21no—
190C2×C22⋊Dic61—21no—
191C2×C4×Dic61—21no—
192C2×C4×Dic61C2311yescharacteristic
193C2×C4×Dic61C2311yescharacteristic
194C42×D61C2311yescharacteristic
195C22×D4×C61—21no—
196C22×D4×C61C2×C411yescharacteristic
197C22×D4×C61C2×C411yescharacteristic
198#127×C61C2×C411yescharacteristic
199#121×C61—21no—
200#121×C61C2×C411yescharacteristic
201#121×C61C2×C411yescharacteristic
202#120×C61—21no—
203#120×C61—21no—
204C4×D4×C61C2×C411yescharacteristic
205C4×D4×C61C2×C411yescharacteristic
206C24×C61—21no—
207C24×C61—21no—
208C2×D4×C61—22no—
209C2×D4×C61—22no—
210C2×D4×C61—21no—
211C2×D4×C61—21no—
212C2×D4×C61—21no—
213C2×D4×C61—21no—
214C2×D4×C61—21no—
215C2×D4×C61—21no—
216C2×D4×C61—41no—
217C2×D4×C61—41no—
218C2×D4×C61—44no—
219C2×D4×C61C22⋊C411yescharacteristic
220C2×D4×C61C22×C411yescharacteristic
221C2×D4×C61C22×C411yescharacteristic
222C2×D4×C61C22×C411yescharacteristic
223C22×C4×C61—21no—
224C22×C4×C61C22×C411yescharacteristic
225C22×C4×C61C22×C411yescharacteristic
226C2×C22⋊D61—21no—
227C2×C22⋊D61—21no—
228C2×C22⋊D61—21no—
229C2×C22⋊D61C22⋊C411yescharacteristic
230C2×C22⋊D61C22⋊C411yescharacteristic
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61—21no—
234C22×Dic61—21no—
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61—21no—
239C22×Dic61—21no—
240C22×Dic61—21no—
241C22×Dic61—81no—
242C22×Dic61—81no—
243C22×Dic61—81no—
244C22×Dic61—81no—
245C22×Dic61C2×D411yescharacteristic
246C22×Dic61C2×D411yescharacteristic
247C22×Dic61C2×D411yescharacteristic
248C22×Dic61C2×D411yescharacteristic
249#11758224—22no—
250#11758224—41no—
251#11758224—42no—
252#11758224—81no—
253#11758224—81no—
254C2×C4×D61C22×C411yescharacteristic
255C2×C4×D61C2×D411yescharacteristic
256C2×C4×D61C2×D411yescharacteristic
257C2×Dic122—21no—
258C2×Dic122C22⋊C411yescharacteristic
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×C61C22⋊C411yescharacteristic
274C4⋊C4×C61C22×C411yescharacteristic
275C22⋊C4×C61—21no—
276C22⋊C4×C61—21no—
277C22⋊C4×C61—21no—
278C22⋊C4×C61C22⋊C411yescharacteristic
279C22⋊C4×C61C22⋊C411yescharacteristic
280C42×C61C22×C411yescharacteristic
281C22⋊Dic61—21no—
282C22⋊Dic61—21no—
283C22⋊Dic61—21no—
284C22⋊Dic61—21no—
285C22⋊Dic61—21no—
286C22⋊Dic61—21no—
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⋊Dic61C22⋊C411yescharacteristic
297C22⋊Dic61C22⋊C411yescharacteristic
298#11758198—21no—
299#11758198C22⋊C411yescharacteristic
300#11758198C22⋊C411yescharacteristic
301C4⋊Dic61—21no—
302C4⋊Dic61—21no—
303C4⋊Dic61—21no—
304C4⋊Dic61—21no—
305C4⋊Dic61—21no—
306C4⋊Dic61C22⋊C411yescharacteristic
307C4⋊Dic61C22×C411yescharacteristic
308C4⋊Dic61C22×C411yescharacteristic
309C4⋊Dic61C22×C411yescharacteristic
310#11758196—21no—
311#11758196—21no—
312#11758196—21no—
313#11758196—21no—
314#11758196—21no—
315#11758196—21no—
316#11758196C22⋊C411yescharacteristic
317#11758196C22⋊C411yescharacteristic
318#11758196C22⋊C411yescharacteristic
319#11758196C22⋊C411yescharacteristic
320C4×Dic61—21no—
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×C61—21no—
333C23×C61—21no—
334C23×C61—21no—
335C23×C61—42no—
336C23×C61—42no—
337C23×C61—42no—
338C23×C61—42no—
339C23×C61—81no—
340C23×C61—81no—
341C23×C61C2×C22⋊C411yescharacteristic
342C23×C61C2×C22⋊C411yescharacteristic
343C22×D61C2×C22⋊C411yescharacteristic
344D4×C61—22no—
345D4×C61—21no—
346D4×C61—21no—
347D4×C61—21no—
348D4×C61—21no—
349D4×C61—21no—
350D4×C61—42no—
351D4×C61—42no—
352D4×C61—42no—
353D4×C61—42no—
354D4×C61—42no—
355D4×C61—81no—
356D4×C61#13112yes—
357C2×C4×C61—21no—
358C2×C4×C61—21no—
359C2×C4×C61—21no—
360C2×C4×C61—21no—
361C2×C4×C61—21no—
362C2×C4×C61—42no—
363C2×C4×C61C2×C22⋊C411yescharacteristic
364C2×C4×C61C2×C22⋊C411yescharacteristic
365C2×C4×C61C2×C22⋊C411yescharacteristic
366C2×C4×C61C2×C22⋊C411yescharacteristic
367C2×C4×C61C23×C411yescharacteristic
368C22⋊D61—22no—
369C22⋊D61—41no—
370C22⋊D61—42no—
371C22⋊D61—81no—
372C22⋊D61—81no—
373C2×Dic61—22no—
374C2×Dic61—21no—
375C2×Dic61—21no—
376C2×Dic61—21no—
377C2×Dic61—21no—
378C2×Dic61—21no—
379C2×Dic61—21no—
380C2×Dic61—21no—
381C2×Dic61—21no—
382C2×Dic61—41no—
383C2×Dic61—42no—
384C2×Dic61—41no—
385C2×Dic61—41no—
386C2×Dic61—41no—
387C2×Dic61—41no—
388C2×Dic61—41no—
389C2×Dic61—41no—
390C2×Dic61—81no—
391C2×Dic61—81no—
392C2×Dic61—81no—
393C2×Dic61—81no—
394C2×Dic61—81no—
395C2×Dic61—81no—
396C2×Dic61C2×C22⋊C411yescharacteristic
397C2×Dic61C2×C22⋊C411yescharacteristic
398C2×Dic61C2×C22⋊C411yescharacteristic
399C2×Dic61C2×C22⋊C411yescharacteristic
400C2×Dic61C2×C22⋊C411yescharacteristic
401C2×Dic61C22×D411yescharacteristic
402C2×Dic61C22×D411yescharacteristic
403C4×D61—21no—
404C4×D61—21no—
405C4×D61—21no—
406C4×D61—21no—
407C4×D61—41no—
408Dic122—21no—
409Dic122—21no—
410Dic122—41no—
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—21no—
422C22×C61—21no—
423C22×C61—22no—
424C22×C61—21no—
425C22×C61—21no—
426C22×C61—21no—
427C22×C61—41no—
428C22×C61—41no—
429C22×C61—41no—
430C22×C61—41no—
431C22×C61—41no—
432C22×C61—41no—
433C22×C61—41no—
434C22×C61—41no—
435C22×C61—84no—
436C22×C61—84no—
437C22×C61#42112yes—
438C22×C61C22×C22⋊C411yescharacteristic
439C2×D61—21no—
440C2×D61—21no—
441C2×D61—21no—
442C4×C61—21no—
443C4×C61—21no—
444C4×C61—21no—
445C4×C61—21no—
446C4×C61—41no—
447C4×C61C2×#13111yescharacteristic
448C4×C61#56811yescharacteristic
449Dic61—21no—
450Dic61—21no—
451Dic61—21no—
452Dic61—21no—
453Dic61—21no—
454Dic61—21no—
455Dic61—41no—
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—22no—
477C2×C61—41no—
478C2×C61—42no—
479C2×C61—81no—
480C2×C61—81no—
481C2×C61#288011yescharacteristic
482C2×C61#289711yescharacteristic
483C2×C61C2×#42111yescharacteristic
484D61—41no—
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#692311yescharacteristic
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—21no—
549C22×D4C2×#692311yescharacteristic
550C22×D4C2×#692311yescharacteristic
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—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—21no—
587#121—611no—
588#121—611no—
589#121—1221no—
590#121—1221no—
591#121—1221no—
592#121—1221no—
593#121—1221no—
594#121C2×#692311yescharacteristic
595#121C2×#692311yescharacteristic
596#120—21no—
597#120—21no—
598#120—1221no—
599#120—1221no—
600C4×Q8—611no—
601C4×Q8—611no—
602C4×Q8—611no—
603C4×Q8—611no—
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—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×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—21no—
677C24—21no—
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—22no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—41no—
695C2×D4—41no—
696C2×D4—44no—
697C2×D4—611no—
698C2×D4—611no—
699C2×D4—1221no—
700C2×D4—1221no—
701C2×D4—1221no—
702C2×D4C22⋊#692311yescharacteristic
703C2×D4C22×#692311yescharacteristic
704C2×D4C22×#692311yescharacteristic
705C2×D4C22×#692311yescharacteristic
706C22×C4—21no—
707C22×C4—611no—
708C22×C4—611no—
709C22×C4—611no—
710C22×C4—611no—
711C22×C4—611no—
712C22×C4—611no—
713C22×C4—611no—
714C22×C4—1221no—
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—611no—
744C4⋊C4—611no—
745C4⋊C4—611no—
746C4⋊C4—611no—
747C4⋊C4—611no—
748C4⋊C4—611no—
749C4⋊C4—611no—
750C4⋊C4—611no—
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⋊C4—1221no—
761C4⋊C4—1221no—
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—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—611no—
790C42—611no—
791C42—611no—
792C42—611no—
793C42—611no—
794C42—611no—
795C42—611no—
796C42—611no—
797C42—611no—
798C42—1221no—
799C42—1221no—
800C42—1221no—
801C42C22×#692311yescharacteristic
802C23—21no—
803C23—21no—
804C23—21no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—81no—
810C23—81no—
811C23—611no—
812C23C2×C22⋊#692311yescharacteristic
813C23C2×C22⋊#692311yescharacteristic
814Q8—1221no—
815Q8—1221no—
816Q8—4881no—
817Q8—2441no—
818D4—22no—
819D4—21no—
820D4—21no—
821D4—21no—
822D4—21no—
823D4—21no—
824D4—42no—
825D4—42no—
826D4—42no—
827D4—42no—
828D4—42no—
829D4—81no—
830D4—1222no—
831D4—4881no—
832D4—4881no—
833D4—2441no—
834D4—2442no—
835D4#1451986412yes—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—42no—
842C2×C4—611no—
843C2×C4—611no—
844C2×C4—611no—
845C2×C4—611no—
846C2×C4—611no—
847C2×C4—611no—
848C2×C4—611no—
849C2×C4—1221no—
850C2×C4—1221no—
851C2×C4—1221no—
852C2×C4—1221no—
853C2×C4—1221no—
854C2×C4—1221no—
855C2×C4—1222no—
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—4881no—
867C2×C4—4881no—
868C2×C4—2441no—
869C2×C4—2441no—
870C2×C4—2441no—
871C2×C4—2441no—
872C2×C4—2441no—
873C2×C4—2441no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4—2442no—
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—22no—
894C22—21no—
895C22—21no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—84no—
905C22—84no—
906C22—1221no—
907C22—1221no—
908C22—1221no—
909C22#1684076012yes—
910C22C22×C22⋊#692311yescharacteristic
911C4—21no—
912C4—21no—
913C4—21no—
914C4—21no—
915C4—41no—
916C4—611no—
917C4—611no—
918C4—1221no—
919C4—1221no—
920C4—1221no—
921C4—1221no—
922C4—1221no—
923C4—1221no—
924C4—2441no—
925C4—2441no—
926C4—2441no—
927C4—2441no—
928C4C2×#1451986411yescharacteristic
929C4#1684084011yescharacteristic
930C2—22no—
931C2—41no—
932C2—42no—
933C2—81no—
934C2—81no—
935C2—2441no—
936C2#2146240711yescharacteristic
937C2#2146244011yescharacteristic
938C2C2×#1684076011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingD42×C61C4
socleC22×C61C22×C22⋊C4
prime radical#21459420C2
cosocleC4×Dic61C24
hypercenterD42#6923
hypocenterC61#17521
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #21462744C2semidirect
2. #21462502C2semidirect
3. #21461179C2semidirect
4. #21461174C2semidirect
5. #21461170C2semidirect
6. #21461158C2semidirect
7. #21461151C2semidirect
8. #21461144C2semidirect
9. #21461134C2semidirect
10. #21461130C2semidirect
11. #21461125C2semidirect
12. #21461118C2semidirect
13. #21461115C2semidirect
14. C2×D4⋊#92420C2semidirect
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. #16840612C22semidirect
37. #16840612C22semidirect
38. #16840612C22semidirect
39. #16840612C22semidirect
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
#214627442
#214625022
#214611792
#214611742
#214611702
#214611582
#214611512
#214611442
#214611342
#214611302
#214611252
#214611182
#214611152
C2×D4⋊#924202
#214594202
#1752161