Finite Group Databasebeta

← #7200480

Subgroups — #7200480

Order 512.

1529 conjugacy classes of subgroups.

The subgroup lattice has 1335 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45623C211yesmaximal, characteristic
2#36516C211yesmaximal, characteristic, complemented
3#32985C211yesmaximal, characteristic, complemented
4#32981C211yesmaximal, characteristic, complemented
5#32710C211yesmaximal, characteristic, complemented
6#32709C211yesmaximal, characteristic, complemented
7#32296C211yesmaximal, characteristic, complemented
8#32002C211yesmaximal, characteristic, complemented
9#31845C211yesmaximal, characteristic, complemented
10#31798C211yesmaximal, characteristic, complemented
11#31779C211yesmaximal, characteristic, complemented
12#31729C211yesmaximal, characteristic, complemented
13#31453C211yesmaximal, characteristic, complemented
14#31375C211yesmaximal, characteristic, complemented
15#31127C211yesmaximal, characteristic, complemented
16#31100C211yesmaximal, characteristic, complemented
17#30706C211yesmaximal, characteristic, complemented
18#30572C211yesmaximal, characteristic, complemented
19#27460C211yesmaximal, characteristic, complemented
20#27412C211yesmaximal, characteristic, complemented
21#27102C211yesmaximal, characteristic, complemented
22#26683C211yesmaximal, characteristic, complemented
23#26646C211yesmaximal, characteristic, complemented
24#26569C211yesmaximal, characteristic, complemented
25#26238C211yesmaximal, characteristic, complemented
26#26208C211yesmaximal, characteristic, complemented
27#25545C211yesmaximal, characteristic, complemented
28#25028C211yesmaximal, characteristic, complemented
29#24945C211yesmaximal, characteristic, complemented
30#24130C211yesmaximal, characteristic, complemented
31#23307C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C22×#117C2211yescharacteristic
34C2×#484C2211yescharacteristic, complemented
35C2×#485C2211yescharacteristic
36C2×#485C2211yescharacteristic
37C2×#482C2211yescharacteristic
38C2×#482C2211yescharacteristic
39C2×#474C2211yescharacteristic, complemented
40C2×#467C2211yescharacteristic, complemented
41C2×#440C2211yescharacteristic, complemented
42#2855—21no—
43#2848C2211yescharacteristic
44#2848C2211yescharacteristic
45#2847C2211yescharacteristic
46#2827—21no—
47#2780—21no—
48#2757—21no—
49#2749—21no—
50#2697—21no—
51#2693—21no—
52#2678—21no—
53#2561—21no—
54#2540C2211yescharacteristic
55#2538C2211yescharacteristic
56#2535C2211yescharacteristic
57#2534—21no—
58#2503C2211yescharacteristic
59#2497C2211yescharacteristic
60#2495C2211yescharacteristic
61#2486C2211yescharacteristic
62#2486C2211yescharacteristic
63#2477—21no—
64#2477—21no—
65#2475—21no—
66#2475—21no—
67#2439C2211yescharacteristic
68#2439C2211yescharacteristic
69#2427C2211yescharacteristic
70#2426C2211yescharacteristic
71#2422C2211yescharacteristic
72#2421C2211yescharacteristic
73#2417C2211yescharacteristic
74#2416C2211yescharacteristic
75#2415C2211yescharacteristic
76#2415C2211yescharacteristic
77#2377—21no—
78#2362C2211yescharacteristic
79#2362C2211yescharacteristic
80#2352C2211yescharacteristic
81#2352C2211yescharacteristic
82#2345C2211yescharacteristic
83C4×#123—21no—
84C4×#120C2211yescharacteristic
85#2101C2211yescharacteristic, complemented
86#2101C2211yescharacteristic, complemented
87#2101C2211yescharacteristic, complemented
88#2096C2211yescharacteristic, complemented
89#2088C2211yescharacteristic, complemented
90#2087C2211yescharacteristic, complemented
91#2086C2211yescharacteristic, complemented
92#2085C2211yescharacteristic, complemented
93#2085C2211yescharacteristic, complemented
94#2083C2211yescharacteristic, complemented
95#2077C2211yescharacteristic
96#2077C2211yescharacteristic, complemented
97#2076C2211yescharacteristic
98#2076C2211yescharacteristic
99#2076C2211yescharacteristic
100#2076C2211yescharacteristic
101#2075C2211yescharacteristic
102#2073C2211yescharacteristic, complemented
103#2068C2211yescharacteristic, complemented
104#2066C2211yescharacteristic, complemented
105#2057C2211yescharacteristic, complemented
106#2055C2211yescharacteristic, complemented
107#2042C2211yescharacteristic, complemented
108#2036C2211yescharacteristic
109#2036C2211yescharacteristic
110#2036C2211yescharacteristic
111#2036C2211yescharacteristic
112#2036C2211yescharacteristic
113#2036C2211yescharacteristic
114#2036C2211yescharacteristic
115#2036C2211yescharacteristic
116#2036C2211yescharacteristic, complemented
117#2035C2211yescharacteristic
118#2035C2211yescharacteristic, complemented
119#2035C2211yescharacteristic, complemented
120#2034C2211yescharacteristic
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic
123#2033C2211yescharacteristic, complemented
124#2024C2211yescharacteristic, complemented
125#2015C2211yescharacteristic, complemented
126#2001C2211yescharacteristic
127#2001C2211yescharacteristic
128#2001C2211yescharacteristic
129#2000C2211yescharacteristic
130#2000C2211yescharacteristic
131#2000C2211yescharacteristic
132#2000C2211yescharacteristic, complemented
133#1993C2211yescharacteristic, complemented
134#1983C2211yescharacteristic, complemented
135#1958C2211yescharacteristic, complemented
136#1955C2211yescharacteristic
137#1955C2211yescharacteristic
138#1954C2211yescharacteristic
139#1949C2211yescharacteristic, complemented
140#1947C2211yescharacteristic, complemented
141#1943C2211yescharacteristic, complemented
142#1942C2211yescharacteristic, complemented
143#1936C2211yescharacteristic, complemented
144#1935C2211yescharacteristic, complemented
145#1935C2211yescharacteristic, complemented
146#1933C2211yescharacteristic, complemented
147#1927C2211yescharacteristic, complemented
148#1925C2211yescharacteristic, complemented
149#1924C2211yescharacteristic
150#1924C2211yescharacteristic
151#1924C2211yescharacteristic
152#1924C2211yescharacteristic
153#1923C2211yescharacteristic
154#1923C2211yescharacteristic
155#1921C2211yescharacteristic, complemented
156#1921C2211yescharacteristic, complemented
157#1921C2211yescharacteristic, complemented
158#1920C2211yescharacteristic, complemented
159#1893C2211yescharacteristic, complemented
160#1878C2211yescharacteristic, complemented
161#1878C2211yescharacteristic, complemented
162#1875C2211yescharacteristic
163#1875C2211yescharacteristic
164#1874C2211yescharacteristic
165#1874C2211yescharacteristic
166#1874C2211yescharacteristic, complemented
167#1873C2211yescharacteristic
168#1873C2211yescharacteristic
169#1872C2211yescharacteristic
170#1872C2211yescharacteristic
171#1872C2211yescharacteristic, complemented
172#1869C2211yescharacteristic
173#1869C2211yescharacteristic
174#1869C2211yescharacteristic
175#1865C2211yescharacteristic, complemented
176#1864C2211yescharacteristic, complemented
177#1864C2211yescharacteristic, complemented
178#1863C2211yescharacteristic, complemented
179#1854C2211yescharacteristic
180#1854C2211yescharacteristic
181#1854C2211yescharacteristic
182#1854C2211yescharacteristic
183#1853C2211yescharacteristic
184#1853C2211yescharacteristic
185#1852C2211yescharacteristic
186#1852C2211yescharacteristic
187#1852C2211yescharacteristic, complemented
188#1852C2211yescharacteristic, complemented
189#1847C2211yescharacteristic, complemented
190#1825C2211yescharacteristic
191#1825C2211yescharacteristic
192#1825C2211yescharacteristic
193#1825C2211yescharacteristic
194#1823C2211yescharacteristic, complemented
195#1807C2211yescharacteristic, complemented
196#1805C2211yescharacteristic, complemented
197#1805C2211yescharacteristic, complemented
198#1779C2211yescharacteristic
199#1779C2211yescharacteristic
200C4×#107C2211yescharacteristic, complemented
201#1763C2211yescharacteristic, complemented
202C2×#340C2211yescharacteristic, complemented
203C24×C4C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C23×C8C2311yescharacteristic
207#554—42no—
208#554—42no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×#125—21no—
211C2×#124C2311yescharacteristic
212C2×#123—21no—
213C2×#123—21no—
214C2×#123—21no—
215C2×C22⋊Q8—21no—
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8C2311yescharacteristic
218C2×C22⋊Q8C2311yescharacteristic
219C2×C22⋊Q8C2311yescharacteristic
220C2×C22⋊Q8C2311yescharacteristic
221C2×C22⋊Q8C2311yescharacteristic
222C2×C22⋊Q8C2311yescharacteristic
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×#121—21no—
226C2×#121C2311yescharacteristic
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#120—21no—
231C2×#120D411yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×D4—21no—
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×#117—21no—
240C2×#117—21no—
241C2×#117—42no—
242C2×#117—42no—
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C22⋊C4—21no—
252C22×C42—21no—
253#485—42no—
254#485—42no—
255#484—42no—
256#482—42no—
257#482—42no—
258#474—42no—
259#467—42no—
260#440—42no—
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×#97C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316#400—21no—
317#400—21no—
318#400—21no—
319#400—21no—
320#400—21no—
321#399—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#396—21no—
335#396—21no—
336#396—21no—
337#396—21no—
338#396—21no—
339#396—21no—
340#396—21no—
341#396—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#393—21no—
349#393—21no—
350#392—21no—
351#392—21no—
352#391—21no—
353#391—21no—
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#390—21no—
358#390—21no—
359#390—21no—
360#390—21no—
361#390C2311yescharacteristic
362#389—21no—
363#389—21no—
364#389—21no—
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386D411yescharacteristic
406#386D411yescharacteristic
407#386D411yescharacteristic
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385D411yescharacteristic
416#385D411yescharacteristic
417#385D411yescharacteristic
418#384C2311yescharacteristic
419#383—21no—
420#382C2311yescharacteristic
421#382C2311yescharacteristic
422#382C2311yescharacteristic
423#381—21no—
424#381—21no—
425#381—21no—
426#381—21no—
427#380—21no—
428#380—21no—
429#380—21no—
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#379—21no—
443#379—21no—
444#379D411yescharacteristic
445C4×C4⋊C4—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4C2311yescharacteristic
454C4×C22⋊C4C2311yescharacteristic
455C4×C22⋊C4C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25C2×D411yescharacteristic
491C22×Q8—21no—
492C22×Q8C2411yescharacteristic
493C22×Q8C2411yescharacteristic
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4C2×D411yescharacteristic
499C22×D4C2×D411yescharacteristic
500C22×D4C2×D411yescharacteristic
501C22×D4C2411yescharacteristic
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—41no—
508C23×C4—41no—
509C23×C4—41no—
510C23×C4—41no—
511C23×C4—41no—
512C23×C4—41no—
513C23×C4C2×D411yescharacteristic
514C23×C4C2×D411yescharacteristic
515C23×C4C2×D411yescharacteristic
516C23×C4C2411yescharacteristic
517C23×C4C2411yescharacteristic
518C23×C4C2411yescharacteristic
519C23×C4C2411yescharacteristic
520C2×Q16—41no—
521C2×Q16—41no—
522C2×Q16—41no—
523C2×SD16—41no—
524C2×SD16—41no—
525C2×SD16—41no—
526C22×C8—41no—
527C22×C8—41no—
528C22×C8—41no—
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C4⋊Q8—22no—
538C4⋊Q8—41no—
539#125—44no—
540#124—41no—
541#124—41no—
542#123—44no—
543#123—82no—
544#123—82no—
545C22⋊Q8—22no—
546C22⋊Q8—41no—
547C22⋊Q8—41no—
548C22⋊Q8—41no—
549C22⋊Q8—41no—
550C22⋊Q8—41no—
551C22⋊Q8—41no—
552C22⋊Q8—41no—
553C22⋊Q8—44no—
554C22⋊Q8—44no—
555C22⋊Q8—41no—
556C22⋊Q8—41no—
557C22⋊Q8—41no—
558C22⋊Q8—41no—
559C22⋊Q8—41no—
560C22⋊Q8—41no—
561C22⋊Q8—41no—
562C22⋊Q8—41no—
563#121—44no—
564#121—41no—
565#121—41no—
566#121—41no—
567#121—41no—
568#121—41no—
569#121—41no—
570#121—41no—
571#121—41no—
572#120—42no—
573#120—82no—
574C4×Q8—22no—
575C4×Q8—41no—
576C4×Q8—41no—
577C4×Q8—41no—
578C4×D4—41no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4—41no—
583C4×D4—41no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—44no—
587#117—22no—
588#117—22no—
589#117—22no—
590#117—22no—
591#117—41no—
592#117—41no—
593#117—41no—
594#117—41no—
595#117—44no—
596#117—44no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—41no—
626C2×C4⋊C4—41no—
627C2×C4⋊C4—41no—
628C2×C4⋊C4—41no—
629C2×C4⋊C4—41no—
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—44no—
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—44no—
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705#107—22no—
706#107—22no—
707#107—22no—
708#107—22no—
709#107—41no—
710#107—41no—
711#107—41no—
712#107—41no—
713#107—41no—
714#106—41no—
715#106—41no—
716#106—41no—
717#106—41no—
718#106—41no—
719C4⋊C8—41no—
720C4⋊C8—41no—
721C4⋊C8—41no—
722#103—22no—
723#103—22no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#103—41no—
730#103—41no—
731#103—41no—
732#103—41no—
733#103—41no—
734#103—41no—
735#102—22no—
736#102—22no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742C22⋊C8—41no—
743C22⋊C8—41no—
744C22⋊C8—41no—
745C22⋊C8—41no—
746C22⋊C8—41no—
747C22⋊C8—41no—
748C22⋊C8—41no—
749C22⋊C8—41no—
750C22⋊C8—41no—
751C22⋊C8—41no—
752C22⋊C8—41no—
753C22⋊C8—41no—
754C22⋊C8—41no—
755C22⋊C8—41no—
756C22⋊C8—41no—
757#97—41no—
758#97—41no—
759C4×C8—41no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801C24—22no—
802C24—21no—
803C24—41no—
804C24—41no—
805C24—41no—
806C24—41no—
807C24—41no—
808C24—41no—
809C24C22×D411yescharacteristic
810C24C22×D411yescharacteristic
811C24C22×D411yescharacteristic
812C24C22×D411yescharacteristic
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—42no—
826C2×Q8—81no—
827C2×Q8—81no—
828C2×D4—22no—
829C2×D4—22no—
830C2×D4—22no—
831C2×D4—22no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—41no—
839C2×D4—41no—
840C2×D4—41no—
841C2×D4—41no—
842C2×D4—41no—
843C2×D4—42no—
844C2×D4—42no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—81no—
848C2×D4—81no—
849C2×D4—81no—
850C2×D4—81no—
851C2×D4—81no—
852C2×D4—81no—
853C2×D4—81no—
854C2×D4—81no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—24no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—41no—
896C22×C4—41no—
897C22×C4—41no—
898C22×C4—41no—
899C22×C4—41no—
900C22×C4—41no—
901C22×C4—41no—
902C22×C4—41no—
903C22×C4—41no—
904C22×C4—42no—
905C22×C4—44no—
906C22×C4—44no—
907C22×C4—44no—
908C22×C4—44no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C2511yescharacteristic
933Q16—82no—
934SD16—44no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—82no—
960C4⋊C4—24no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—41no—
986C4⋊C4—41no—
987C4⋊C4—41no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4H(5,𝔽2)12yes—
1013C4⋊C4H(5,𝔽2)12yes—
1014C22⋊C4—22no—
1015C22⋊C4—41no—
1016C22⋊C4—41no—
1017C22⋊C4—41no—
1018C22⋊C4—41no—
1019C22⋊C4—41no—
1020C22⋊C4—41no—
1021C22⋊C4—41no—
1022C22⋊C4—41no—
1023C22⋊C4—41no—
1024C22⋊C4—41no—
1025C22⋊C4—41no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—42no—
1066C42—42no—
1067C42—42no—
1068C42—42no—
1069C42—42no—
1070C42—81no—
1071C42—81no—
1072C42—81no—
1073C42—81no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—44no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—82no—
1109C23—82no—
1110C23—82no—
1111C23—82no—
1112C23—82no—
1113C23—82no—
1114C23#57512yes—
1115C23#57812yes—
1116C23C23×D411yescharacteristic
1117Q8—41no—
1118Q8—41no—
1119Q8—41no—
1120Q8—41no—
1121Q8—41no—
1122Q8—41no—
1123Q8—41no—
1124Q8—41no—
1125Q8—162no—
1126D4—44no—
1127D4—41no—
1128D4—41no—
1129D4—41no—
1130D4—41no—
1131D4—82no—
1132D4—82no—
1133D4—162no—
1134D4—162no—
1135D4—162no—
1136D4—162no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—44no—
1170C2×C4—44no—
1171C2×C4—44no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—84no—
1232C2×C4—84no—
1233C2×C4—162no—
1234C2×C4—162no—
1235C2×C4—162no—
1236C2×C4C2×H(5,𝔽2)11yescharacteristic
1237C2×C4C2×H(5,𝔽2)11yescharacteristic
1238C2×C4#58511yescharacteristic
1239C2×C4#58511yescharacteristic
1240C2×C4#58511yescharacteristic
1241C2×C4#58511yescharacteristic
1242C8—41no—
1243C8—41no—
1244C8—41no—
1245C8—41no—
1246C8—41no—
1247C8—41no—
1248C8—41no—
1249C8—41no—
1250C22—22no—
1251C22—22no—
1252C22—22no—
1253C22—22no—
1254C22—22no—
1255C22—22no—
1256C22—41no—
1257C22—41no—
1258C22—41no—
1259C22—41no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22—41no—
1269C22—41no—
1270C22—41no—
1271C22—41no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—41no—
1277C22—41no—
1278C22—88no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22#348411yescharacteristic
1287C22#348511yescharacteristic
1288C22#348511yescharacteristic
1289C22C2×#57511yescharacteristic
1290C22C2×#57811yescharacteristic
1291C22#358411yescharacteristic
1292C22#358511yescharacteristic
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—41no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—41no—
1301C4—41no—
1302C4—41no—
1303C4—42no—
1304C4—42no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4#352911yescharacteristic
1319C4#353911yescharacteristic
1320C4#353911yescharacteristic
1321C4#354011yescharacteristic
1322C2—42no—
1323C2—42no—
1324C2—81no—
1325C2—81no—
1326C2—161no—
1327C2#4544011yescharacteristic
1328C2#6160311yescharacteristic
1329C2#6161411yescharacteristic
1330C2#6171411yescharacteristic
1331C2#6173211yescharacteristic
1332C2#6175411yescharacteristic
1333C2#6177111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#45623C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#120 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #36516C2semidirect
3. #32985C2semidirect
4. #32981C2semidirect
5. #32710C2semidirect
6. #32709C2semidirect
7. #32296C2semidirect
8. #32002C2semidirect
9. #31845C2semidirect
10. #31798C2semidirect
11. #31779C2semidirect
12. #31729C2semidirect
13. #31453C2semidirect
14. #31375C2semidirect
15. #31127C2semidirect
16. #31100C2semidirect
17. #30706C2semidirect
18. #30572C2semidirect
19. #27460C2semidirect
20. #27412C2semidirect
21. #27102C2semidirect
22. #26683C2semidirect
23. #26646C2semidirect
24. #26569C2semidirect
25. #26238C2semidirect
26. #26208C2semidirect
27. #25545C2semidirect
28. #25028C2semidirect
29. #24945C2semidirect
30. #24130C2semidirect
31. #23307C2semidirect
34. C2×#484C22semidirect
39. C2×#474C22semidirect
40. C2×#467C22semidirect
41. C2×#440C22semidirect
85. #2101C22semidirect
86. #2101C22semidirect
87. #2101C22semidirect
88. #2096C22semidirect
89. #2088C22semidirect
90. #2087C22semidirect
91. #2086C22semidirect
92. #2085C22semidirect
93. #2085C22semidirect
94. #2083C22semidirect
96. #2077C22semidirect
102. #2073C22semidirect
103. #2068C22semidirect
104. #2066C22semidirect
105. #2057C22semidirect
106. #2055C22semidirect
107. #2042C22semidirect
116. #2036C22semidirect
118. #2035C22semidirect
119. #2035C22semidirect
123. #2033C22semidirect
124. #2024C22semidirect
125. #2015C22semidirect
132. #2000C22semidirect
133. #1993C22semidirect
134. #1983C22semidirect
135. #1958C22semidirect
139. #1949C22semidirect
140. #1947C22semidirect
141. #1943C22semidirect
142. #1942C22semidirect
143. #1936C22semidirect
144. #1935C22semidirect
145. #1935C22semidirect
146. #1933C22semidirect
147. #1927C22semidirect
148. #1925C22semidirect
155. #1921C22semidirect
156. #1921C22semidirect
157. #1921C22semidirect
158. #1920C22semidirect
159. #1893C22semidirect
160. #1878C22semidirect
161. #1878C22semidirect
166. #1874C22semidirect
171. #1872C22semidirect
175. #1865C22semidirect
176. #1864C22semidirect
177. #1864C22semidirect
178. #1863C22semidirect
187. #1852C22semidirect
188. #1852C22semidirect
189. #1847C22semidirect
194. #1823C22semidirect
195. #1807C22semidirect
196. #1805C22semidirect
197. #1805C22semidirect
200. C4×#107C22semidirect
201. #1763C22semidirect
202. C2×#340C22semidirect

Maximal subgroups

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

subgroupindex
#456232
#365162
#329852
#329812
#327102
#327092
#322962
#320022
#318452
#317982
#317792
#317292
#314532
#313752
#311272
#311002
#307062
#305722
#274602
#274122
#271022
#266832
#266462
#265692
#262382
#262082
#255452
#250282
#249452
#241302
#233072