Finite Group Databasebeta

← #30610771

Subgroups — #30610771

Order 15616.

890 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462741C211yesmaximal, characteristic, complemented
2#21462630C211yesmaximal, characteristic, complemented
3#21461183C211yesmaximal, characteristic, complemented
4#21461177C211yesmaximal, characteristic, complemented
5#21461173C211yesmaximal, characteristic, complemented
6#21461169C211yesmaximal, characteristic, complemented
7#21461163C211yesmaximal, characteristic, complemented
8#21461156C211yesmaximal, characteristic, complemented
9#21461152C211yesmaximal, characteristic, complemented
10#21461149C211yesmaximal, characteristic, complemented
11#21461143C211yesmaximal, characteristic, complemented
12#21461137C211yesmaximal, characteristic, complemented
13#21461133C211yesmaximal, characteristic, complemented
14#21461129C211yesmaximal, characteristic, complemented
15#21459253C211yesmaximal, characteristic
16#16840814—21no—
17#16840814—21no—
18#16840795—21no—
19#16840795—21no—
20#16840794—21no—
21#16840794—21no—
22#16840792—21no—
23#16840792—21no—
24#16840784C2211yescharacteristic
25#16840783C2211yescharacteristic
26#16840781C2211yescharacteristic
27#16840781C2211yescharacteristic
28#16840780C2211yescharacteristic
29#16840779C2211yescharacteristic
30#16840766C2211yescharacteristic
31#16840765C2211yescharacteristic
32D61⋊(C4⋊C8)C2211yescharacteristic
33C4×#11758213C2211yescharacteristic
34C4×#11758217C2211yescharacteristic
35C4×D61⋊C8C2211yescharacteristic
36#16840612C2211yescharacteristic
37#16840612C2211yescharacteristic
38#16840612C2211yescharacteristic
39#16840612C2211yescharacteristic
40#16840612C2211yescharacteristic
41#16840612C2211yescharacteristic
42#16840612C2211yescharacteristic
43#16840612C2211yescharacteristic
44#16840612C2211yescharacteristic
45#16840612C2211yescharacteristic
46#16840612C2211yescharacteristic
47#16840612C2211yescharacteristic
48#16840610C2211yescharacteristic
49#16840610C2211yescharacteristic
50#16840610C2211yescharacteristic
51#16840610C2211yescharacteristic
52#16840386—21no—
53#16840386C411yescharacteristic
54#16840386C411yescharacteristic
55#16840375—21no—
56#16840375C411yescharacteristic
57#16840375C411yescharacteristic
58#16840361—21no—
59#16840361—21no—
60#16840343C411yescharacteristic
61#16840338C411yescharacteristic
62#16840338C411yescharacteristic
63#16840317—21no—
64#16840317C2211yescharacteristic
65#16840317C2211yescharacteristic
66#16840298—21no—
67#16840298—21no—
68#16840297—21no—
69#16840297C2211yescharacteristic
70#16840297C2211yescharacteristic
71#16840230C2211yescharacteristic
72#16840230C2211yescharacteristic
73C2×#14519742C2211yescharacteristic
74C61×#544C411yescharacteristic
75C2×#11758213—21no—
76C2×#11758213—21no—
77C2×#11758217—21no—
78C2×#11758217—21no—
79C2×D61⋊C8—21no—
80C2×D61⋊C8—21no—
81#14519844—21no—
82#14519844—21no—
83#14519844—21no—
84#14519844—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—
95C22⋊#92420—21no—
96C22⋊#92420—21no—
97#14519832—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×#11758222C2×C411yescharacteristic
108C2×#11758222C2×C411yescharacteristic
109C22×Dic122C2×C411yescharacteristic
110#14519777—21no—
111#14519777C2×C411yescharacteristic
112#14519777C2×C411yescharacteristic
113#14519772—21no—
114#14519772—21no—
115#14519772—21no—
116#14519772—21no—
117#14519772—21no—
118#14519772—21no—
119#14519772—21no—
120#14519772—21no—
121#14519768—21no—
122#14519768—21no—
123#14519768—21no—
124#14519768—21no—
125#14519768—21no—
126#14519768—21no—
127#14519766—21no—
128#14519766—21no—
129#14519765—21no—
130#14519765C2×C411yescharacteristic
131#14519765C2×C411yescharacteristic
132#14519762—21no—
133#14519762—21no—
134#14519762—21no—
135#14519762—21no—
136#14519761—21no—
137#14519761—21no—
138#14519761—21no—
139#14519761—21no—
140#14519757—21no—
141#14519757—21no—
142#14519757—21no—
143#14519757C2×C411yescharacteristic
144#14519757C2×C411yescharacteristic
145#14519757C2×C411yescharacteristic
146#14519757C2×C411yescharacteristic
147#14519757C2×C411yescharacteristic
148#14519757C2×C411yescharacteristic
149#14519753—21no—
150#14519753—21no—
151#14519753—21no—
152#14519753—21no—
153#14519752—21no—
154#14519752C2×C411yescharacteristic
155#14519752C2×C411yescharacteristic
156#14519751—21no—
157#14519751—21no—
158Q8×Dic61—21no—
159Q8×Dic61—21no—
160#14519742—21no—
161#14519742—21no—
162#14519742C2×C411yescharacteristic
163#14519742C2×C411yescharacteristic
164#14519742C2×C411yescharacteristic
165#14519742D411yescharacteristic
166#14519742D411yescharacteristic
167#14519742C2311yescharacteristic
168#14519742C2311yescharacteristic
169#14519742C2311yescharacteristic
170#14519739—21no—
171#14519739—21no—
172#14519739C2×C411yescharacteristic
173#14519739D411yescharacteristic
174#14519739D411yescharacteristic
175#14519739C2311yescharacteristic
176#14519737—21no—
177#14519737—21no—
178#14519737D411yescharacteristic
179#14519737D411yescharacteristic
180#14519737D411yescharacteristic
181#14519737D411yescharacteristic
182#14519735—21no—
183#14519735—21no—
184#14519735—21no—
185#14519735—21no—
186#14519734—21no—
187#14519734C2×C411yescharacteristic
188#14519734C2×C411yescharacteristic
189C2×#11758196—21no—
190C2×C4×Dic61—21no—
191C2×C4×Dic61C2311yescharacteristic
192C42×D61—21no—
193C42×D61C2311yescharacteristic
194C42×D61C2311yescharacteristic
195C4⋊Q8×C61—21no—
196C4⋊Q8×C61C2×C411yescharacteristic
197C4⋊Q8×C61C2×C411yescharacteristic
198#125×C61—21no—
199#125×C61C2×C411yescharacteristic
200#125×C61C2×C411yescharacteristic
201C22⋊Q8×C61—21no—
202C22⋊Q8×C61—21no—
203#117×C61C2×C411yescharacteristic
204#117×C61C2×C411yescharacteristic
205C2×C4⋊C4×C61C2×C411yescharacteristic
206C2×Q8×C61—21no—
207C2×Q8×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61C22×C411yescharacteristic
210C2×C22⋊D61—21no—
211C2×C22⋊D61C22⋊C411yescharacteristic
212C2×C22⋊D61C22⋊C411yescharacteristic
213C22×Dic61—21no—
214C22×Dic61C2×D411yescharacteristic
215C22×Dic61C2×D411yescharacteristic
216#11758222—42no—
217#11758222—42no—
218C2×D244—21no—
219C2×D244—21no—
220C2×D244C22⋊C411yescharacteristic
221C2×D244C22×C411yescharacteristic
222C2×C4×D61—21no—
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61C22×C411yescharacteristic
226C2×C4×D61C22×C411yescharacteristic
227C2×C4×D61C2×D411yescharacteristic
228C2×C4×D61C2×D411yescharacteristic
229C2×C4×D61C2×D411yescharacteristic
230C2×C4×D61C2×D411yescharacteristic
231C2×Dic122—21no—
232C2×Dic122—42no—
233C2×Dic122C22⋊C411yescharacteristic
234C2×Dic122C22×C411yescharacteristic
235C2×Dic122C22×C411yescharacteristic
236C2×Dic122C22×C411yescharacteristic
237#11758217—42no—
238#11758217—81no—
239C2×#92420—21no—
240C2×#92420—21no—
241C2×#92420—21no—
242C2×#92420—21no—
243C2×#92420—21no—
244C2×#92420—21no—
245C2×#92420—21no—
246C2×#92420—21no—
247#11758213—42no—
248#11758213—81no—
249D61⋊C8—42no—
250D61⋊C8—81no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61C22⋊C411yescharacteristic
259C4⋊C4×C61C22⋊C411yescharacteristic
260C4⋊C4×C61C22×C411yescharacteristic
261C4⋊C4×C61C22×C411yescharacteristic
262C4⋊C4×C61C22×C411yescharacteristic
263C4⋊C4×C61C22×C411yescharacteristic
264C22⋊C4×C61—21no—
265C22⋊C4×C61C22⋊C411yescharacteristic
266C22⋊C4×C61C22⋊C411yescharacteristic
267C42×C61—21no—
268C42×C61C22×C411yescharacteristic
269C42×C61C22×C411yescharacteristic
270#11758198—21no—
271#11758198—21no—
272#11758198—21no—
273#11758198—21no—
274#11758198—21no—
275#11758198—21no—
276#11758198—21no—
277#11758198—21no—
278#11758198—21no—
279#11758198—21no—
280#11758198—21no—
281#11758198—21no—
282#11758198—21no—
283#11758198—21no—
284#11758198C22⋊C411yescharacteristic
285#11758198C22⋊C411yescharacteristic
286#11758198C22⋊C411yescharacteristic
287#11758198C22⋊C411yescharacteristic
288C4⋊Dic61—21no—
289C4⋊Dic61—21no—
290C4⋊Dic61—21no—
291C4⋊Dic61—21no—
292C4⋊Dic61—21no—
293C4⋊Dic61—21no—
294C4⋊Dic61—21no—
295C4⋊Dic61—21no—
296C4⋊Dic61—21no—
297C4⋊Dic61—21no—
298#11758196—21no—
299#11758196—21no—
300#11758196—21no—
301#11758196—21no—
302#11758196—21no—
303#11758196—21no—
304#11758196C22⋊C411yescharacteristic
305#11758196C22⋊C411yescharacteristic
306#11758196C22⋊C411yescharacteristic
307#11758196C22⋊C411yescharacteristic
308C4×Dic61—21no—
309C4×Dic61—21no—
310C4×Dic61—21no—
311C4×Dic61—21no—
312C4×Dic61—21no—
313C4×Dic61—21no—
314C4×Dic61C22×C411yescharacteristic
315C4×Dic61C2×D411yescharacteristic
316C4×Dic61C2×D411yescharacteristic
317C4×Dic61C2×D411yescharacteristic
318C4×Dic61C2×D411yescharacteristic
319C4×Dic61C2×D411yescharacteristic
320C4×Dic61C2×D411yescharacteristic
321C4×Dic61C2411yescharacteristic
322C23×C61C2×C22⋊C411yescharacteristic
323C22×D61—21no—
324C22×D61C2×C22⋊C411yescharacteristic
325C22×D61C2×C22⋊C411yescharacteristic
326Q8×C61—81no—
327Q8×C61—81no—
328C2×C4×C61—22no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—81no—
334C2×C4×C61C2×C22⋊C411yescharacteristic
335C2×C4×C61C2×C22⋊C411yescharacteristic
336C2×C4×C61C2×C22⋊C411yescharacteristic
337C2×C4×C61C2×C22⋊C411yescharacteristic
338C2×C4×C61C2×C22⋊C411yescharacteristic
339C2×C4×C61C23×C411yescharacteristic
340C22⋊D61—41no—
341C22⋊D61—41no—
342C22⋊D61—42no—
343C2×Dic61—21no—
344C2×Dic61—21no—
345C2×Dic61—21no—
346C2×Dic61—21no—
347C2×Dic61—21no—
348C2×Dic61—41no—
349C2×Dic61—42no—
350C2×Dic61C2×C22⋊C411yescharacteristic
351C2×Dic61C2×C22⋊C411yescharacteristic
352C2×Dic61C2×C22⋊C411yescharacteristic
353C2×Dic61C2×C22⋊C411yescharacteristic
354C2×Dic61C22×D411yescharacteristic
355C2×Dic61C22×D411yescharacteristic
356D244—22no—
357D244—41no—
358D244—81no—
359D244—81no—
360C4×D61—22no—
361C4×D61—22no—
362C4×D61—21no—
363C4×D61—21no—
364C4×D61—21no—
365C4×D61—21no—
366C4×D61—41no—
367C4×D61—41no—
368C4×D61—42no—
369C4×D61—41no—
370C4×D61—41no—
371C4×D61—81no—
372Dic122—22no—
373Dic122—22no—
374Dic122—22no—
375Dic122—41no—
376Dic122—42no—
377#92420—22no—
378#92420—41no—
379#92420—41no—
380#92420—41no—
381#92420—41no—
382#92420—41no—
383#92420—41no—
384#92420—41no—
385#17506—611nomaximal, Sylow
386C22×C61—21no—
387C22×C61—21no—
388C22×C61—21no—
389C22×C61C22×C22⋊C411yescharacteristic
390C2×D61—21no—
391C2×D61—21no—
392C2×D61—21no—
393C2×D61—21no—
394C2×D61—21no—
395C2×D61—21no—
396C2×D61—41no—
397C2×D61—41no—
398C2×D61—41no—
399C4×C61—21no—
400C4×C61—21no—
401C4×C61—21no—
402C4×C61—21no—
403C4×C61—21no—
404C4×C61—41no—
405C4×C61—41no—
406C4×C61—41no—
407C4×C61—41no—
408C4×C61#56812yes—
409Dic61—21no—
410Dic61—21no—
411Dic61—21no—
412Dic61—21no—
413Dic61—21no—
414Dic61—41no—
415Dic61—41no—
416Dic61—41no—
417Dic61#57711yescharacteristic
418Dic61#57811yescharacteristic
419#3461—611no—
420#2989—611no—
421#2965—611no—
422#1497—611no—
423#1495—611no—
424#1494—611no—
425#1493—611no—
426#1491—611no—
427#1489—611no—
428#1488—611no—
429#1487—611no—
430#1485—611no—
431#1483—611no—
432#1482—611no—
433#1481—611no—
434C2×C61—41no—
435C2×C61#287911yescharacteristic
436C2×C61#289811yescharacteristic
437C2×C61#290111yescharacteristic
438D61—41no—
439D61—41no—
440D61—81no—
441#544#692311yescharacteristic
442#542—611no—
443#542—611no—
444#542—1221no—
445#541—611no—
446#541—611no—
447#541—1221no—
448#539—1221no—
449#539—1221no—
450#537—611no—
451#536—611no—
452#536—611no—
453#533—611no—
454#533—611no—
455#533—1221no—
456#529—611no—
457#529—611no—
458#529—1221no—
459#529—1221no—
460#529—1221no—
461C4×#41—611no—
462C4×#41—611no—
463C2×C4×Q8—611no—
464#446—1221no—
465#446—1221no—
466#436—1221no—
467#436—1221no—
468#435—1221no—
469#435—1221no—
470#435—1221no—
471#435—1221no—
472#432—611no—
473#432—611no—
474#431—611no—
475#431—611no—
476#431—611no—
477#431—611no—
478#423—611no—
479#423—611no—
480C2×C4⋊C8—611no—
481C4×M16—611no—
482C4×M16—611no—
483C2×C4×C8—611no—
484Q8⋊C8—611no—
485Q8⋊C8—611no—
486Q8⋊C8—611no—
487Q8⋊C8—611no—
488Q8⋊C8—611no—
489Q8⋊C8—611no—
490Q8⋊C8—611no—
491Q8⋊C8—611no—
492Q8⋊C8—611no—
493Q8⋊C8—611no—
494Q8⋊C8—611no—
495Q8⋊C8—611no—
496D4⋊C8—611no—
497D4⋊C8—611no—
498D4⋊C8—611no—
499D4⋊C8—611no—
500C61#1750611yescharacteristic, complemented, Sylow
501C2×#41—611no—
502C2×#41—611no—
503C22×Q8—611no—
504C2×M16—1221no—
505C2×M16—1221no—
506C2×M16—1221no—
507C2×M16—1221no—
508C22×C8—1221no—
509C22×C8—1221no—
510C4⋊Q8—21no—
511C4⋊Q8—611no—
512C4⋊Q8—611no—
513C4⋊Q8—1221no—
514C4⋊Q8C2×#692311yescharacteristic
515C4⋊Q8C2×#692311yescharacteristic
516#126—1221no—
517#126—1221no—
518#126—1221no—
519#126—1221no—
520#126—1221no—
521#126—1221no—
522#126—1221no—
523#126—1221no—
524#125—21no—
525#125—1221no—
526#125—1221no—
527#125—1221no—
528#125—1221no—
529#125—1221no—
530#125—1221no—
531#125C2×#692311yescharacteristic
532#125C2×#692311yescharacteristic
533#124—611no—
534#124—611no—
535#124—1221no—
536#124—1221no—
537#124—1221no—
538#123—1221no—
539#123—1221no—
540#123—1221no—
541#123—1221no—
542#123—1221no—
543#123—1221no—
544#123—1221no—
545#123—1221no—
546C22⋊Q8—21no—
547C22⋊Q8—21no—
548C22⋊Q8—611no—
549C22⋊Q8—611no—
550C22⋊Q8—611no—
551C22⋊Q8—611no—
552C22⋊Q8—611no—
553C22⋊Q8—611no—
554C22⋊Q8—1221no—
555C22⋊Q8—1221no—
556C22⋊Q8—1221no—
557C22⋊Q8—1221no—
558C22⋊Q8—1221no—
559C22⋊Q8—1221no—
560C22⋊Q8—1221no—
561#121—611no—
562#121—611no—
563#121—1221no—
564#121—1221no—
565#121—1221no—
566C4×Q8—611no—
567C4×Q8—611no—
568C4×Q8—611no—
569C4×Q8—611no—
570C4×Q8—611no—
571C4×Q8—611no—
572C4×Q8—611no—
573C4×Q8—611no—
574C4×Q8—1221no—
575C4×Q8—1221no—
576C4×Q8—1221no—
577C4×Q8—1221no—
578C4×D4—611no—
579C4×D4—611no—
580C4×D4—611no—
581C4×D4—611no—
582C4×D4—611no—
583C4×D4—611no—
584C4×D4—611no—
585C4×D4—611no—
586C4×D4—1221no—
587C4×D4—1221no—
588C4×D4—1221no—
589C4×D4—1221no—
590#117—611no—
591#117—611no—
592#117—1221no—
593#117—1221no—
594#117—1221no—
595#117—1221no—
596#117—1221no—
597#117C2×#692311yescharacteristic
598#117C2×#692311yescharacteristic
599C2×C4⋊C4—1221no—
600C2×C4⋊C4C2×#692311yescharacteristic
601C2×C42—611no—
602C2×C42—611no—
603C2×C42—611no—
604C2×C42—1221no—
605C2×C42—1221no—
606C4⋊C8—611no—
607C4⋊C8—611no—
608C4⋊C8—611no—
609C4⋊C8—611no—
610C4⋊C8—1221no—
611C4⋊C8—1221no—
612C4⋊C8—1221no—
613C4⋊C8—1221no—
614C4⋊C8—1221no—
615C4⋊C8—1221no—
616C22⋊C8—1221no—
617C22⋊C8—1221no—
618C22⋊C8—1221no—
619C22⋊C8—1221no—
620C22⋊C8—1221no—
621C22⋊C8—1221no—
622#97—1221no—
623#97—1221no—
624#97—1221no—
625#97—1221no—
626C4×C8—611no—
627C4×C8—611no—
628C4×C8—611no—
629C4×C8—611no—
630C4×C8—1221no—
631C4×C8—1221no—
632#41—2442no—
633#41—2442no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—611no—
637C2×Q8—611no—
638C2×Q8—611no—
639C2×Q8—611no—
640C2×Q8—1221no—
641C2×Q8—2442no—
642C2×D4—611no—
643C2×D4—611no—
644C2×D4—611no—
645C2×D4—611no—
646C2×D4—1221no—
647C2×D4—1221no—
648C2×D4—1221no—
649C22×C4—21no—
650C22×C4—611no—
651C22×C4—611no—
652C22×C4—611no—
653C22×C4—611no—
654C22×C4—611no—
655C22×C4—611no—
656C22×C4—611no—
657C22×C4—611no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4—1221no—
661C22×C4—1221no—
662C22×C4C22×#692311yescharacteristic
663M16—4881no—
664M16—4881no—
665M16—2442no—
666M16—2442no—
667C2×C8—1221no—
668C2×C8—1221no—
669C2×C8—1221no—
670C2×C8—1221no—
671C2×C8—1221no—
672C2×C8—1221no—
673C2×C8—1221no—
674C2×C8—1221no—
675C2×C8—4881no—
676C2×C8—2442no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—611no—
685C4⋊C4—611no—
686C4⋊C4—611no—
687C4⋊C4—611no—
688C4⋊C4—1221no—
689C4⋊C4—1221no—
690C4⋊C4—1221no—
691C4⋊C4—1221no—
692C4⋊C4—1221no—
693C4⋊C4—1221no—
694C4⋊C4—1221no—
695C4⋊C4—1221no—
696C4⋊C4—1221no—
697C4⋊C4—1221no—
698C4⋊C4—1221no—
699C4⋊C4—1221no—
700C4⋊C4—1221no—
701C4⋊C4—1221no—
702C4⋊C4—1221no—
703C4⋊C4—1221no—
704C4⋊C4C22⋊#692311yescharacteristic
705C4⋊C4C22⋊#692311yescharacteristic
706C4⋊C4C22×#692311yescharacteristic
707C4⋊C4C22×#692311yescharacteristic
708C4⋊C4C22×#692311yescharacteristic
709C4⋊C4C22×#692311yescharacteristic
710C22⋊C4—21no—
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—1221no—
725C22⋊C4—1221no—
726C22⋊C4—1221no—
727C22⋊C4—1221no—
728C22⋊C4—1221no—
729C22⋊C4C22⋊#692311yescharacteristic
730C22⋊C4C22⋊#692311yescharacteristic
731C42—21no—
732C42—611no—
733C42—611no—
734C42—611no—
735C42—611no—
736C42—611no—
737C42—611no—
738C42—611no—
739C42—611no—
740C42—1221no—
741C42—1221no—
742C42—1221no—
743C42—1221no—
744C42—1221no—
745C42—1221no—
746C42C22×#692311yescharacteristic
747C42C22×#692311yescharacteristic
748C23—611no—
749C23—611no—
750C23—1221no—
751C23C2×C22⋊#692311yescharacteristic
752Q8—81no—
753Q8—81no—
754Q8—1222no—
755Q8—1222no—
756Q8—1222no—
757Q8—2441no—
758Q8—2442no—
759D4—1222no—
760D4—4881no—
761D4—4881no—
762D4—2441no—
763D4—2441no—
764D4—2441no—
765D4—2442no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—81no—
772C2×C4—611no—
773C2×C4—611no—
774C2×C4—611no—
775C2×C4—611no—
776C2×C4—611no—
777C2×C4—611no—
778C2×C4—1221no—
779C2×C4—1221no—
780C2×C4—1221no—
781C2×C4—1221no—
782C2×C4—1221no—
783C2×C4—1221no—
784C2×C4—1222no—
785C2×C4—1222no—
786C2×C4—1221no—
787C2×C4—1221no—
788C2×C4—1221no—
789C2×C4—4881no—
790C2×C4—2441no—
791C2×C4—2441no—
792C2×C4—2442no—
793C2×C4—2441no—
794C2×C4—2441no—
795C2×C4—2441no—
796C2×C4—2442no—
797C2×C4C2×C22⋊#692311yescharacteristic
798C2×C4C2×C22⋊#692311yescharacteristic
799C2×C4C2×C22⋊#692311yescharacteristic
800C2×C4C2×C22⋊#692311yescharacteristic
801C2×C4C2×C22⋊#692311yescharacteristic
802C2×C4C23×#692311yescharacteristic
803C8—1222no—
804C8—2441no—
805C8—2441no—
806C8—2441no—
807C8—2441no—
808C8—2441no—
809C8—2441no—
810C8—2441no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—1221no—
815C22—1221no—
816C22—1221no—
817C22—1221no—
818C22—1221no—
819C22—1221no—
820C22—2441no—
821C22—2441no—
822C22—2441no—
823C22C22×C22⋊#692311yescharacteristic
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—21no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—41no—
833C4—611no—
834C4—611no—
835C4—1221no—
836C4—1221no—
837C4—1221no—
838C4—1221no—
839C4—1221no—
840C4—2441no—
841C4—2441no—
842C4—2441no—
843C4#1684084212yes—
844C2—41no—
845C2—4881no—
846C2—2441no—
847C2—2441no—
848C2#2146240611yescharacteristic
849C2#2146244111yescharacteristic
850C2#2146244911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#544C4
socleC22×C61C22×C22⋊C4
prime radical#16840343C4
cosocleC4×Dic61C24
hypercenter#544#6923
hypocenterC61#17506
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #544

Complements

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

NH ≅ G/Ntype
1. #21462741C2semidirect
2. #21462630C2semidirect
3. #21461183C2semidirect
4. #21461177C2semidirect
5. #21461173C2semidirect
6. #21461169C2semidirect
7. #21461163C2semidirect
8. #21461156C2semidirect
9. #21461152C2semidirect
10. #21461149C2semidirect
11. #21461143C2semidirect
12. #21461137C2semidirect
13. #21461133C2semidirect
14. #21461129C2semidirect
500. C61#17506semidirect

Maximal subgroups

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

subgroupindex
#214627412
#214626302
#214611832
#214611772
#214611732
#214611692
#214611632
#214611562
#214611522
#214611492
#214611432
#214611372
#214611332
#214611292
#214592532
#1750661