Finite Group Databasebeta

← #6564729

Subgroups — #6564729

Order 512.

1869 conjugacy classes of subgroups.

The subgroup lattice has 1371 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3323C211yesmaximal, characteristic
2C2×#3311C211yesmaximal, characteristic
3#37868C211yesmaximal, characteristic, complemented
4#34476C211yesmaximal, characteristic
5#29874C211yesmaximal, characteristic, complemented
6#29726C211yesmaximal, characteristic, complemented
7#29714C211yesmaximal, characteristic, complemented
8#28730C211yesmaximal, characteristic, complemented
9#28583C211yesmaximal, characteristic, complemented
10#28581C211yesmaximal, characteristic, complemented
11#28173C211yesmaximal, characteristic, complemented
12#27654C211yesmaximal, characteristic, complemented
13#27649C211yesmaximal, characteristic, complemented
14#25336C211yesmaximal, characteristic, complemented
15#25328C211yesmaximal, characteristic, complemented
16#25230C211yesmaximal, characteristic, complemented
17#25226C211yesmaximal, characteristic, complemented
18#25220C211yesmaximal, characteristic, complemented
19#25202C211yesmaximal, characteristic, complemented
20#24690C211yesmaximal, characteristic, complemented
21#24680C211yesmaximal, characteristic, complemented
22#24546C211yesmaximal, characteristic, complemented
23#24538C211yesmaximal, characteristic, complemented
24#24538C211yesmaximal, characteristic, complemented
25#24534C211yesmaximal, characteristic, complemented
26#23689C211yesmaximal, characteristic, complemented
27#23634C211yesmaximal, characteristic, complemented
28#23628C211yesmaximal, characteristic, complemented
29#22699C211yesmaximal, characteristic, complemented
30#22504C211yesmaximal, characteristic, complemented
31#22491C211yesmaximal, characteristic, complemented
32C2×#556C2211yescharacteristic
33C2×#552C2211yescharacteristic
34C2×#546C2211yescharacteristic
35#3323—28no—
36#3311—28no—
37C2×#489C2211yescharacteristic
38C2×#488C2211yescharacteristic
39C2×#481C2211yescharacteristic
40C2×#485C2211yescharacteristic
41C2×#485C2211yescharacteristic
42C2×#482C2211yescharacteristic
43C2×#478C2211yescharacteristic
44C2×#476C2211yescharacteristic
45C2×#470C2211yescharacteristic
46C2×#470C2211yescharacteristic
47C2×#468C2211yescharacteristic
48C2×#465C2211yescharacteristic
49C2×#464C2211yescharacteristic
50C2×#464C2211yescharacteristic
51C2×#452C2211yescharacteristic
52C2×#452C2211yescharacteristic
53C2×#450C2211yescharacteristic
54C2×#450C2211yescharacteristic
55C2×#440C2211yescharacteristic
56C2×C4×SD16C2211yescharacteristic
57C2×#436C2211yescharacteristic
58C2×#435C2211yescharacteristic
59C2×#417C2211yescharacteristic
60C2×#418C2211yescharacteristic
61C2×#418C2211yescharacteristic
62C2×#416C2211yescharacteristic
63#2857C2211yescharacteristic
64#2722—21no—
65#2722—21no—
66#2717—21no—
67#2717—21no—
68#2660C2211yescharacteristic, complemented
69#2621C2211yescharacteristic, complemented
70#2567C2211yescharacteristic, complemented
71#2565C2211yescharacteristic, complemented
72#2502C2211yescharacteristic, complemented
73#2499C2211yescharacteristic
74#2499C2211yescharacteristic
75#2499C2211yescharacteristic, complemented
76#2478—21no—
77#2478—21no—
78#2462—21no—
79#2462—21no—
80#2377—21no—
81#2376—21no—
82#2367C2211yescharacteristic
83#2361C2211yescharacteristic
84#2360C2211yescharacteristic
85#2358—21no—
86#2354C2211yescharacteristic
87D4×C4⋊C4C2211yescharacteristic
88#2342—21no—
89#2341C2211yescharacteristic
90D4×C22⋊C4C2211yescharacteristic
91#2335—21no—
92#2327C2211yescharacteristic, complemented
93#2326C2211yescharacteristic
94#2324—21no—
95#2324C2211yescharacteristic
96#2321—21no—
97#2319C2211yescharacteristic
98#2317C2211yescharacteristic, complemented
99#2315—21no—
100#2311C2211yescharacteristic
101C4×C22⋊Q8C2211yescharacteristic
102C2×#390C2211yescharacteristic
103#2290C2211yescharacteristic
104#2285C2211yescharacteristic
105#2085C2211yescharacteristic, complemented
106#2085C2211yescharacteristic, complemented
107#2085C2211yescharacteristic, complemented
108#2084C2211yescharacteristic, complemented
109#2084C2211yescharacteristic, complemented
110#2074C2211yescharacteristic, complemented
111#2074C2211yescharacteristic, complemented
112#2074C2211yescharacteristic, complemented
113#2073C2211yescharacteristic
114#2073C2211yescharacteristic
115#2073C2211yescharacteristic
116#2073C2211yescharacteristic
117#2073C2211yescharacteristic
118#2073C2211yescharacteristic
119#2072C2211yescharacteristic, complemented
120#2072C2211yescharacteristic, complemented
121#2071C2211yescharacteristic
122#2071C2211yescharacteristic
123#2071C2211yescharacteristic
124#2071C2211yescharacteristic
125#2071C2211yescharacteristic
126#2071C2211yescharacteristic
127#2071C2211yescharacteristic
128#2071C2211yescharacteristic
129#2068C2211yescharacteristic, complemented
130#2066C2211yescharacteristic, complemented
131#2056C2211yescharacteristic, complemented
132#2056C2211yescharacteristic, complemented
133#2055C2211yescharacteristic
134#2055C2211yescharacteristic
135#2055C2211yescharacteristic
136#2055C2211yescharacteristic
137#2055C2211yescharacteristic
138#2055C2211yescharacteristic
139#2055C2211yescharacteristic
140#2055C2211yescharacteristic
141#2043C2211yescharacteristic, complemented
142#2016C2211yescharacteristic, complemented
143#2013C2211yescharacteristic
144#2013C2211yescharacteristic
145#1992C2211yescharacteristic, complemented
146#1990C2211yescharacteristic, complemented
147#1989C2211yescharacteristic, complemented
148#1988C2211yescharacteristic, complemented
149#1949C2211yescharacteristic, complemented
150#1948C2211yescharacteristic, complemented
151#1948C2211yescharacteristic, complemented
152#1947C2211yescharacteristic, complemented
153#1940C2211yescharacteristic, complemented
154#1939C2211yescharacteristic, complemented
155#1928C2211yescharacteristic, complemented
156#1927C2211yescharacteristic, complemented
157#1927C2211yescharacteristic, complemented
158#1927C2211yescharacteristic, complemented
159#1894C2211yescharacteristic
160#1894C2211yescharacteristic
161#1894C2211yescharacteristic, complemented
162#1892C2211yescharacteristic, complemented
163#1878C2211yescharacteristic, complemented
164#1878C2211yescharacteristic, complemented
165#1878C2211yescharacteristic, complemented
166#1878C2211yescharacteristic, complemented
167#1877C2211yescharacteristic
168#1877C2211yescharacteristic
169#1877C2211yescharacteristic
170#1877C2211yescharacteristic
171#1872C2211yescharacteristic
172#1872C2211yescharacteristic
173#1872C2211yescharacteristic, complemented
174#1872C2211yescharacteristic, complemented
175#1851C2211yescharacteristic
176#1851C2211yescharacteristic
177#1851C2211yescharacteristic, complemented
178#1850C2211yescharacteristic, complemented
179#1832C2211yescharacteristic, complemented
180#1825C2211yescharacteristic
181#1825C2211yescharacteristic
182#1825C2211yescharacteristic, complemented
183#1823C2211yescharacteristic, complemented
184#1805C2211yescharacteristic, complemented
185#1804C2211yescharacteristic
186#1804C2211yescharacteristic
187#1803C2211yescharacteristic, complemented
188#1803C2211yescharacteristic, complemented
189#1803C2211yescharacteristic, complemented
190#1803C2211yescharacteristic, complemented
191#1803C2211yescharacteristic, complemented
192#1802C2211yescharacteristic
193#1802C2211yescharacteristic
194#1798C2211yescharacteristic, complemented
195#1797C2211yescharacteristic
196#1768C2211yescharacteristic, complemented
197#1763C2211yescharacteristic, complemented
198C4×#103C2211yescharacteristic, complemented
199#1736C2211yescharacteristic
200#1736C2211yescharacteristic
201#1736C2211yescharacteristic, complemented
202C2×#340C2211yescharacteristic, complemented
203#1729C2211yescharacteristic, complemented
204#1728C2211yescharacteristic
205C22×#41C2311yescharacteristic
206C23×D4C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×M16C2311yescharacteristic
214C22×M16C2311yescharacteristic
215C22×M16C2311yescharacteristic
216C23×C8C2311yescharacteristic
217#556—24no—
218#556—24no—
219#552—24no—
220#552—24no—
221#546—24no—
222#546D418yes—
223C2×C4⋊Q8C2311yescharacteristic
224C2×C4⋊Q8C2311yescharacteristic
225C2×#126—21no—
226C2×#126—21no—
227C2×#126—21no—
228C2×#125—21no—
229C2×#125C2311yescharacteristic
230C2×#124—21no—
231C2×#124C2311yescharacteristic
232C2×#123—21no—
233C2×#123—21no—
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239C2×#121—21no—
240C2×#121C2311yescharacteristic
241C2×#120—21no—
242C2×C4×Q8—21no—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×D4—21no—
248C2×C4×D4—21no—
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×#117—21no—
254C2×#117—21no—
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C22⋊C4—21no—
263C22×C22⋊C4—21no—
264C22×C22⋊C4—21no—
265C22×C22⋊C4—21no—
266C22×C42C2311yescharacteristic
267#489—24no—
268#488—24no—
269#485—24no—
270#485—24no—
271#482—24no—
272#481—24no—
273#478—24no—
274#476—24no—
275#470—24no—
276#470—24no—
277#468—24no—
278#465—24no—
279#464—24no—
280#464—24no—
281#452—24no—
282#452—24no—
283#450—24no—
284#450—24no—
285#440—24no—
286C4×SD16—24no—
287#436—24no—
288#435—24no—
289C2×#107C2311yescharacteristic
290C2×#107C2311yescharacteristic
291C2×#106C2311yescharacteristic
292C2×#106C2311yescharacteristic
293C2×#106C2311yescharacteristic
294C2×#106C2311yescharacteristic
295C2×C4⋊C8C2311yescharacteristic
296C2×C4⋊C8C2311yescharacteristic
297C2×C4⋊C8C2311yescharacteristic
298C2×C4⋊C8C2311yescharacteristic
299C2×C4⋊C8C2311yescharacteristic
300C2×C4⋊C8C2311yescharacteristic
301C2×C4⋊C8C2311yescharacteristic
302C2×C4⋊C8C2311yescharacteristic
303#418—24no—
304#418—24no—
305#417—24no—
306#416—24no—
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#103C2311yescharacteristic
312C2×#103C2311yescharacteristic
313C2×#103C2311yescharacteristic
314C2×#103C2311yescharacteristic
315C2×#103C2311yescharacteristic
316C2×#103C2311yescharacteristic
317C2×#103C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×#102C2311yescharacteristic
327C2×#102C2311yescharacteristic
328C2×#102C2311yescharacteristic
329C2×#102C2311yescharacteristic
330C2×#102C2311yescharacteristic
331C2×#102C2311yescharacteristic
332C2×#102C2311yescharacteristic
333C2×#102C2311yescharacteristic
334C2×#102C2311yescharacteristic
335C2×C22⋊C8C2311yescharacteristic
336C2×C22⋊C8C2311yescharacteristic
337C2×C22⋊C8C2311yescharacteristic
338C2×C22⋊C8C2311yescharacteristic
339C2×#97C2311yescharacteristic
340C2×C4×C8C2311yescharacteristic
341#398—21no—
342#398—21no—
343#398—21no—
344#398—21no—
345#398—21no—
346#398—21no—
347#398—21no—
348#398—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#397—21no—
354#397—21no—
355#397—21no—
356#397—21no—
357#395—21no—
358#395—21no—
359#395—21no—
360#395—21no—
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#390—21no—
370#390—21no—
371#390—21no—
372#390—21no—
373#390—21no—
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#389—21no—
381#389—21no—
382#389—21no—
383#389—21no—
384#389—21no—
385#389—21no—
386#389—21no—
387#389—21no—
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388D411yescharacteristic
401#388D411yescharacteristic
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387D411yescharacteristic
417#387D411yescharacteristic
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386D411yescharacteristic
425#386D411yescharacteristic
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#385D411yescharacteristic
440#385D411yescharacteristic
441#384C2311yescharacteristic
442#384C2311yescharacteristic
443#384C2311yescharacteristic
444#384C2311yescharacteristic
445#384C2311yescharacteristic
446#384C2311yescharacteristic
447#382C2311yescharacteristic
448#382C2311yescharacteristic
449#382C2311yescharacteristic
450#382C2311yescharacteristic
451#381—21no—
452#380—21no—
453#380—21no—
454#380—21no—
455#380—21no—
456#380—21no—
457#380—21no—
458#380—21no—
459#380—21no—
460#380—21no—
461#380C2311yescharacteristic
462#380C2311yescharacteristic
463#379—21no—
464C4×C4⋊C4—21no—
465C4×C4⋊C4—21no—
466C4×C4⋊C4—21no—
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
470C4×C4⋊C4C2311yescharacteristic
471C4×C22⋊C4—21no—
472C4×C22⋊C4—21no—
473C4×C22⋊C4—21no—
474C4×C22⋊C4—21no—
475C4×C22⋊C4C2311yescharacteristic
476C4×C22⋊C4C2311yescharacteristic
477#376C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#340C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#340C2311yescharacteristic
497#340C2311yescharacteristic
498#340C2311yescharacteristic
499#340C2311yescharacteristic
500#340C2311yescharacteristic
501#340C2311yescharacteristic
502#336C2311yescharacteristic
503#336C2311yescharacteristic
504#336C2311yescharacteristic
505#336C2311yescharacteristic
506#336C2311yescharacteristic
507#336C2311yescharacteristic
508#336C2311yescharacteristic
509#336C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512C25—21no—
513C2×#41—22no—
514C2×#41—41no—
515C2×#41—41no—
516C2×#41—41no—
517C2×#41—41no—
518C2×#41C2×D414yes—
519C22×Q8—21no—
520C22×Q8C2411yescharacteristic
521C22×Q8C2411yescharacteristic
522C22×Q8C2411yescharacteristic
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—22no—
527C22×D4—41no—
528C22×D4—41no—
529C22×D4—41no—
530C22×D4—41no—
531C22×D4C2×D414yes—
532C22×D4C2×D411yescharacteristic
533C22×D4C2411yescharacteristic
534C22×D4C2411yescharacteristic
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4C2×D411yescharacteristic
543C23×C4C2×D411yescharacteristic
544C23×C4C2411yescharacteristic
545C23×C4C2411yescharacteristic
546C2×Q16—22no—
547C2×Q16—22no—
548C2×Q16—41no—
549C2×Q16—41no—
550C2×Q16—41no—
551C2×Q16—41no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—41no—
557C2×SD16—41no—
558C2×SD16—41no—
559C2×SD16—41no—
560C2×SD16—41no—
561C2×SD16—41no—
562C2×SD16—41no—
563C2×SD16—41no—
564C2×M16—22no—
565C2×M16—22no—
566C2×M16—22no—
567C2×M16—41no—
568C2×M16—41no—
569C2×M16—41no—
570C2×M16—41no—
571C2×M16—41no—
572C2×M16—41no—
573C22×C8—22no—
574C22×C8—41no—
575C22×C8—41no—
576C22×C8C2411yescharacteristic
577C22×C8C2411yescharacteristic
578C22×C8C2411yescharacteristic
579C22×C8C2411yescharacteristic
580C22×C8C2411yescharacteristic
581C22×C8C2411yescharacteristic
582C22×C8C2411yescharacteristic
583C22×C8C2411yescharacteristic
584C4⋊Q8—22no—
585C4⋊Q8—22no—
586C4⋊Q8—41no—
587C4⋊Q8—41no—
588#126—44no—
589#126—44no—
590#126—44no—
591#125—22no—
592#125—22no—
593#125—44no—
594#124—22no—
595#124—44no—
596#124C2×D414yes—
597#123—28no—
598#123—44no—
599C22⋊Q8—22no—
600C22⋊Q8—22no—
601C22⋊Q8—22no—
602C22⋊Q8—22no—
603C22⋊Q8—22no—
604C22⋊Q8—22no—
605C22⋊Q8—22no—
606C22⋊Q8—22no—
607C22⋊Q8—22no—
608C22⋊Q8C2×D414yes—
609#121—22no—
610#121—28no—
611#121C2×D414yes—
612#120—28no—
613C4×Q8—22no—
614C4×Q8—22no—
615C4×Q8—22no—
616C4×Q8—22no—
617C4×Q8—41no—
618C4×Q8—41no—
619C4×Q8—41no—
620C4×Q8—41no—
621C4×Q8—44no—
622C4×D4—22no—
623C4×D4—41no—
624C4×D4—41no—
625C4×D4—41no—
626C4×D4—41no—
627C4×D4—82no—
628C4×D4—82no—
629C4×D4C2×D414yes—
630C4×D4C2×D414yes—
631C4×D4#4114yes—
632#117—22no—
633#117—22no—
634#117—22no—
635#117—22no—
636#117—22no—
637#117—22no—
638#117—41no—
639#117—41no—
640#117—44no—
641#117—82no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—22no—
644C2×C4⋊C4—22no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—41no—
676C2×C4⋊C4—41no—
677C2×C4⋊C4—41no—
678C2×C4⋊C4—41no—
679C2×C4⋊C4C2×D411yescharacteristic
680C2×C4⋊C4C2×D411yescharacteristic
681C2×C4⋊C4C2×D411yescharacteristic
682C2×C4⋊C4C2×D411yescharacteristic
683C2×C4⋊C4C2×D411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
693C2×C4⋊C4C2411yescharacteristic
694C2×C4⋊C4C2411yescharacteristic
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—28no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—82no—
725C2×C22⋊C4—82no—
726C2×C22⋊C4—82no—
727C2×C22⋊C4C2×D411yescharacteristic
728C2×C22⋊C4C2×D411yescharacteristic
729C2×C22⋊C4C2×D411yescharacteristic
730C2×C22⋊C4C2×D411yescharacteristic
731C2×C22⋊C4C2×D411yescharacteristic
732C2×C22⋊C4C2×D411yescharacteristic
733C2×C22⋊C4C2×D411yescharacteristic
734C2×C22⋊C4C2×D411yescharacteristic
735C2×C42—21no—
736C2×C42—21no—
737C2×C42—21no—
738C2×C42—21no—
739C2×C42—21no—
740C2×C42—21no—
741C2×C42—21no—
742C2×C42—21no—
743C2×C42—21no—
744C2×C42—21no—
745C2×C42—41no—
746C2×C42—41no—
747C2×C42C2×D411yescharacteristic
748C2×C42C2×D411yescharacteristic
749C2×C42C2411yescharacteristic
750C2×C42C2411yescharacteristic
751C2×C42C2411yescharacteristic
752C2×C42C2411yescharacteristic
753C2×C42C2411yescharacteristic
754#107—22no—
755#107—22no—
756#106—22no—
757#106—22no—
758#106—22no—
759#106—22no—
760C4⋊C8—22no—
761C4⋊C8—22no—
762C4⋊C8—41no—
763C4⋊C8—41no—
764C4⋊C8—41no—
765C4⋊C8—41no—
766C4⋊C8—41no—
767C4⋊C8—41no—
768#103—22no—
769#103—22no—
770#103—22no—
771#103—22no—
772#103—22no—
773#103—22no—
774#103—22no—
775#103—22no—
776#103—41no—
777#103—41no—
778#103—41no—
779#103—41no—
780#103—41no—
781#103—41no—
782#103—41no—
783#103—41no—
784#102—22no—
785#102—22no—
786#102—22no—
787#102—22no—
788#102—22no—
789#102—22no—
790#102—22no—
791#102—22no—
792#102—22no—
793#102—22no—
794#102—22no—
795#102—22no—
796C22⋊C8—22no—
797C22⋊C8—22no—
798C22⋊C8—22no—
799C22⋊C8—22no—
800#97—22no—
801C4×C8—22no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837#95C2×D411yescharacteristic
838#95C2×D411yescharacteristic
839#95C2×D411yescharacteristic
840#95C2×D411yescharacteristic
841#95C2×D411yescharacteristic
842#95C2×D411yescharacteristic
843C24—21no—
844C24—21no—
845C24—24no—
846C24—42no—
847C24—42no—
848C24—81no—
849C24—81no—
850C24—81no—
851C24—81no—
852C24C22×D411yescharacteristic
853C24C22×D411yescharacteristic
854#41—44no—
855#41—44no—
856#41—82no—
857#41—82no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—42no—
876C2×Q8—81no—
877C2×Q8—81no—
878C2×Q8C22×D412yes—
879C2×D4—24no—
880C2×D4—24no—
881C2×D4—24no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—41no—
895C2×D4—41no—
896C2×D4—82no—
897C2×D4—82no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4#12114yes—
905C2×D4C22×D412yes—
906C2×D4C22×D412yes—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—24no—
918C22×C4—24no—
919C22×C4—22no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—41no—
933C22×C4—41no—
934C22×C4—41no—
935C22×C4—41no—
936C22×C4—41no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D412yes—
968C22×C4C22×D412yes—
969C22×C4C22×D411yescharacteristic
970C22×C4C2×#4112yes—
971C22×C4C2×#4112yes—
972C22×C4C2511yescharacteristic
973Q16—82no—
974Q16—82no—
975SD16—44no—
976SD16—44no—
977SD16—82no—
978SD16—82no—
979M16—82no—
980M16—82no—
981M16—82no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—82no—
1007C4⋊C4—24no—
1008C4⋊C4—22no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—41no—
1031C4⋊C4—41no—
1032C4⋊C4—41no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4—81no—
1054C4⋊C4—81no—
1055C4⋊C4—81no—
1056C4⋊C4—81no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C4⋊C4—81no—
1060C4⋊C4—81no—
1061C4⋊C4—81no—
1062C4⋊C4—81no—
1063C4⋊C4#12114yes—
1064C4⋊C4C22×D412yes—
1065C22⋊C4—24no—
1066C22⋊C4—24no—
1067C22⋊C4—24no—
1068C22⋊C4—24no—
1069C22⋊C4—24no—
1070C22⋊C4—22no—
1071C22⋊C4—41no—
1072C22⋊C4—41no—
1073C22⋊C4—41no—
1074C22⋊C4—41no—
1075C22⋊C4—41no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4#12114yes—
1100C22⋊C4#12114yes—
1101C42—21no—
1102C42—21no—
1103C42—21no—
1104C42—21no—
1105C42—21no—
1106C42—21no—
1107C42—21no—
1108C42—21no—
1109C42—41no—
1110C42—41no—
1111C42—42no—
1112C42—42no—
1113C42—42no—
1114C42—42no—
1115C42—42no—
1116C42—42no—
1117C42—81no—
1118C42—81no—
1119C42—81no—
1120C42—81no—
1121C42C22×D412yes—
1122C42C2×#4112yes—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—21no—
1135C23—22no—
1136C23—22no—
1137C23—48no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—84no—
1151C23—84no—
1152C23—162no—
1153C23—162no—
1154C23—162no—
1155C23—162no—
1156C23C2×#12112yes—
1157C23C2×#12112yes—
1158C23C23×D411yescharacteristic
1159Q8—22no—
1160Q8—22no—
1161Q8—41no—
1162Q8—41no—
1163Q8—41no—
1164Q8—41no—
1165Q8—41no—
1166Q8—41no—
1167Q8—41no—
1168Q8—41no—
1169Q8—41no—
1170Q8—41no—
1171Q8—84no—
1172D4—22no—
1173D4—22no—
1174D4—22no—
1175D4—22no—
1176D4—44no—
1177D4—41no—
1178D4—41no—
1179D4—41no—
1180D4—41no—
1181D4—84no—
1182D4—84no—
1183D4—84no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—82no—
1266C2×C4—84no—
1267C2×C4—84no—
1268C2×C4—82no—
1269C2×C4—84no—
1270C2×C4—162no—
1271C2×C4—162no—
1272C2×C4—162no—
1273C2×C4—162no—
1274C2×C4C2×#12112yes—
1275C2×C4C2×#12112yes—
1276C2×C4C2×#12112yes—
1277C2×C4C2×#12112yes—
1278C2×C4#57712yes—
1279C2×C4C23×D411yescharacteristic
1280C2×C4C22×#4111yescharacteristic
1281C2×C4#58511yescharacteristic
1282C2×C4#58511yescharacteristic
1283C2×C4#58511yescharacteristic
1284C2×C4#58511yescharacteristic
1285C8—41no—
1286C8—41no—
1287C8—41no—
1288C8—41no—
1289C8—41no—
1290C8—41no—
1291C8—41no—
1292C8—41no—
1293C22—22no—
1294C22—22no—
1295C22—22no—
1296C22—22no—
1297C22—22no—
1298C22—22no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—42no—
1308C22—42no—
1309C22—42no—
1310C22—42no—
1311C22—42no—
1312C22—42no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—168no—
1322C22C22×#12111yescharacteristic
1323C22#348511yescharacteristic
1324C22#350011yescharacteristic
1325C22C2×#57711yescharacteristic
1326C22#358511yescharacteristic
1327C22#358611yescharacteristic
1328C22#358611yescharacteristic
1329C4—22no—
1330C4—22no—
1331C4—22no—
1332C4—22no—
1333C4—22no—
1334C4—42no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—41no—
1342C4—42no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4#348511yescharacteristic
1356C4#348511yescharacteristic
1357C4#352111yescharacteristic
1358C4#352111yescharacteristic
1359C2—42no—
1360C2—42no—
1361C2—82no—
1362C2—82no—
1363C2#3600911yescharacteristic
1364C2#6042511yescharacteristic
1365C2#6042911yescharacteristic
1366C2#6175511yescharacteristic
1367C2#6178011yescharacteristic
1368C2#6257111yescharacteristic
1369C2#6260811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#546C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #37868C2semidirect
5. #29874C2semidirect
6. #29726C2semidirect
7. #29714C2semidirect
8. #28730C2semidirect
9. #28583C2semidirect
10. #28581C2semidirect
11. #28173C2semidirect
12. #27654C2semidirect
13. #27649C2semidirect
14. #25336C2semidirect
15. #25328C2semidirect
16. #25230C2semidirect
17. #25226C2semidirect
18. #25220C2semidirect
19. #25202C2semidirect
20. #24690C2semidirect
21. #24680C2semidirect
22. #24546C2semidirect
23. #24538C2semidirect
24. #24538C2semidirect
25. #24534C2semidirect
26. #23689C2semidirect
27. #23634C2semidirect
28. #23628C2semidirect
29. #22699C2semidirect
30. #22504C2semidirect
31. #22491C2semidirect
68. #2660C22semidirect
69. #2621C22semidirect
70. #2567C22semidirect
71. #2565C22semidirect
72. #2502C22semidirect
75. #2499C22semidirect
92. #2327C22semidirect
98. #2317C22semidirect
105. #2085C22semidirect
106. #2085C22semidirect
107. #2085C22semidirect
108. #2084C22semidirect
109. #2084C22semidirect
110. #2074C22semidirect
111. #2074C22semidirect
112. #2074C22semidirect
119. #2072C22semidirect
120. #2072C22semidirect
129. #2068C22semidirect
130. #2066C22semidirect
131. #2056C22semidirect
132. #2056C22semidirect
141. #2043C22semidirect
142. #2016C22semidirect
145. #1992C22semidirect
146. #1990C22semidirect
147. #1989C22semidirect
148. #1988C22semidirect
149. #1949C22semidirect
150. #1948C22semidirect
151. #1948C22semidirect
152. #1947C22semidirect
153. #1940C22semidirect
154. #1939C22semidirect
155. #1928C22semidirect
156. #1927C22semidirect
157. #1927C22semidirect
158. #1927C22semidirect
161. #1894C22semidirect
162. #1892C22semidirect
163. #1878C22semidirect
164. #1878C22semidirect
165. #1878C22semidirect
166. #1878C22semidirect
173. #1872C22semidirect
174. #1872C22semidirect
177. #1851C22semidirect
178. #1850C22semidirect
179. #1832C22semidirect
182. #1825C22semidirect
183. #1823C22semidirect
184. #1805C22semidirect
187. #1803C22semidirect
188. #1803C22semidirect
189. #1803C22semidirect
190. #1803C22semidirect
191. #1803C22semidirect
194. #1798C22semidirect
196. #1768C22semidirect
197. #1763C22semidirect
198. C4×#103C22semidirect
201. #1736C22semidirect
202. C2×#340C22semidirect
203. #1729C22semidirect

Maximal subgroups

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

subgroupindex
C2×#33232
C2×#33112
#378682
#344762
#298742
#297262
#297142
#287302
#285832
#285812
#281732
#276542
#276492
#253362
#253282
#252302
#252262
#252202
#252022
#246902
#246802
#245462
#245382
#245342
#236892
#236342
#236282
#226992
#225042
#224912