Finite Group Databasebeta

← #6598476

Subgroups — #6598476

Order 512.

1944 conjugacy classes of subgroups.

The subgroup lattice has 1398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3348C211yesmaximal, characteristic, complemented
2C2×#3319C211yesmaximal, characteristic
3#38947C211yesmaximal, characteristic, complemented
4#34321C211yesmaximal, characteristic, complemented
5#33117C211yesmaximal, characteristic, complemented
6#33115C211yesmaximal, characteristic, complemented
7#33028C211yesmaximal, characteristic, complemented
8#28659C211yesmaximal, characteristic, complemented
9#28586C211yesmaximal, characteristic, complemented
10#28583C211yesmaximal, characteristic, complemented
11#28203C211yesmaximal, characteristic, complemented
12#28127C211yesmaximal, characteristic, complemented
13#28126C211yesmaximal, characteristic, complemented
14#25462C211yesmaximal, characteristic, complemented
15#25287C211yesmaximal, characteristic, complemented
16#25230C211yesmaximal, characteristic, complemented
17#25214C211yesmaximal, characteristic, complemented
18#25104C211yesmaximal, characteristic, complemented
19#25088C211yesmaximal, characteristic, complemented
20#24688C211yesmaximal, characteristic, complemented
21#24640C211yesmaximal, characteristic, complemented
22#24597C211yesmaximal, characteristic, complemented
23#24584C211yesmaximal, characteristic, complemented
24#24493C211yesmaximal, characteristic, complemented
25#24485C211yesmaximal, characteristic, complemented
26#22702C211yesmaximal, characteristic, complemented
27#22491C211yesmaximal, characteristic, complemented
28#22419C211yesmaximal, characteristic, complemented
29#21507C211yesmaximal, characteristic, complemented
30#21065C211yesmaximal, characteristic, complemented
31#21062C211yesmaximal, characteristic, complemented
32C2×#555C2211yescharacteristic
33C2×#552C2211yescharacteristic
34C2×#546C2211yescharacteristic
35#3348—28no—
36#3319—28no—
37C2×#501C2211yescharacteristic, complemented
38C2×#489C2211yescharacteristic
39C2×#481C2211yescharacteristic, complemented
40C2×#485C2211yescharacteristic
41C2×#485C2211yescharacteristic
42C2×#485C2211yescharacteristic, complemented
43C2×#482C2211yescharacteristic
44C2×#482C2211yescharacteristic
45C2×#475C2211yescharacteristic, complemented
46C2×#478C2211yescharacteristic, complemented
47C2×#474C2211yescharacteristic
48C2×#468C2211yescharacteristic
49C2×#468C2211yescharacteristic, complemented
50C2×#466C2211yescharacteristic
51C2×#465C2211yescharacteristic
52C2×#463C2211yescharacteristic
53C2×#463C2211yescharacteristic
54C2×#449C2211yescharacteristic
55C2×#447C2211yescharacteristic
56C2×#442C2211yescharacteristic
57C2×#440C2211yescharacteristic, complemented
58C2×#435C2211yescharacteristic
59C2×#435C2211yescharacteristic
60C2×#428C2211yescharacteristic, complemented
61C2×#427C2211yescharacteristic
62C2×#417C2211yescharacteristic
63C2×#418C2211yescharacteristic
64C2×#416C2211yescharacteristic
65C22×#102C2211yescharacteristic
66#2861C2211yescharacteristic
67#2707—21no—
68#2707—21no—
69#2697—21no—
70#2697—21no—
71#2621C2211yescharacteristic
72#2620C2211yescharacteristic
73#2566C2211yescharacteristic
74#2545C2211yescharacteristic
75#2504C2211yescharacteristic
76#2499C2211yescharacteristic
77#2480—21no—
78#2480—21no—
79#2476—21no—
80#2476—21no—
81#2435C2211yescharacteristic
82#2432C2211yescharacteristic
83#2369C2211yescharacteristic, complemented
84#2367—21no—
85#2367—21no—
86#2363—21no—
87#2361C2211yescharacteristic
88#2361C2211yescharacteristic, complemented
89#2354C2211yescharacteristic, complemented
90D4×C4⋊C4C2211yescharacteristic
91#2347—21no—
92#2347C2211yescharacteristic
93#2347C2211yescharacteristic, complemented
94#2337—21no—
95#2337—21no—
96#2324C2211yescharacteristic
97#2324C2211yescharacteristic, complemented
98#2311C2211yescharacteristic
99#2309C2211yescharacteristic
100C4×C4⋊Q8C2211yescharacteristic, complemented
101C4×#124C2211yescharacteristic
102C4×#121—21no—
103#2296—21no—
104#2293C2211yescharacteristic
105#2274C2211yescharacteristic
106#2274C2211yescharacteristic, complemented
107C42×D4C2211yescharacteristic, complemented
108#2085C2211yescharacteristic, complemented
109#2085C2211yescharacteristic, complemented
110#2085C2211yescharacteristic, complemented
111#2083C2211yescharacteristic, complemented
112#2073C2211yescharacteristic, complemented
113#2071C2211yescharacteristic, complemented
114#2068C2211yescharacteristic, complemented
115#2068C2211yescharacteristic, complemented
116#2067C2211yescharacteristic
117#2066C2211yescharacteristic, complemented
118#2065C2211yescharacteristic
119#2065C2211yescharacteristic
120#2065C2211yescharacteristic
121#2065C2211yescharacteristic
122#2055C2211yescharacteristic, complemented
123#2054C2211yescharacteristic
124#2054C2211yescharacteristic
125#2054C2211yescharacteristic
126#2043C2211yescharacteristic, complemented
127#2042C2211yescharacteristic
128#2042C2211yescharacteristic
129#2042C2211yescharacteristic
130#2013C2211yescharacteristic, complemented
131#2012C2211yescharacteristic
132#1992C2211yescharacteristic, complemented
133#1989C2211yescharacteristic, complemented
134#1983C2211yescharacteristic
135#1983C2211yescharacteristic
136#1983C2211yescharacteristic
137#1983C2211yescharacteristic
138#1981C2211yescharacteristic, complemented
139#1981C2211yescharacteristic, complemented
140#1959C2211yescharacteristic
141#1949C2211yescharacteristic, complemented
142#1949C2211yescharacteristic, complemented
143#1949C2211yescharacteristic, complemented
144#1948C2211yescharacteristic, complemented
145#1947C2211yescharacteristic, complemented
146#1940C2211yescharacteristic, complemented
147#1940C2211yescharacteristic, complemented
148#1928C2211yescharacteristic, complemented
149#1928C2211yescharacteristic, complemented
150#1928C2211yescharacteristic, complemented
151#1928C2211yescharacteristic, complemented
152#1927C2211yescharacteristic, complemented
153#1927C2211yescharacteristic, complemented
154#1927C2211yescharacteristic, complemented
155#1927C2211yescharacteristic, complemented
156#1927C2211yescharacteristic, complemented
157#1926C2211yescharacteristic
158#1926C2211yescharacteristic
159#1926C2211yescharacteristic
160#1926C2211yescharacteristic
161#1926C2211yescharacteristic
162#1926C2211yescharacteristic
163#1925C2211yescharacteristic
164#1925C2211yescharacteristic
165#1925C2211yescharacteristic
166#1925C2211yescharacteristic
167#1925C2211yescharacteristic
168#1925C2211yescharacteristic
169#1925C2211yescharacteristic
170#1895C2211yescharacteristic
171#1894C2211yescharacteristic
172#1892C2211yescharacteristic
173#1892C2211yescharacteristic, complemented
174#1879C2211yescharacteristic
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1877C2211yescharacteristic, complemented
178#1877C2211yescharacteristic, complemented
179#1877C2211yescharacteristic, complemented
180#1874C2211yescharacteristic
181#1872C2211yescharacteristic
182#1872C2211yescharacteristic
183#1872C2211yescharacteristic, complemented
184#1851C2211yescharacteristic
185#1851C2211yescharacteristic, complemented
186#1850C2211yescharacteristic
187#1850C2211yescharacteristic, complemented
188#1831C2211yescharacteristic, complemented
189#1825C2211yescharacteristic
190#1823C2211yescharacteristic, complemented
191#1804C2211yescharacteristic, complemented
192#1803C2211yescharacteristic, complemented
193#1802C2211yescharacteristic
194#1798C2211yescharacteristic
195#1798C2211yescharacteristic, complemented
196#1788C2211yescharacteristic
197#1786C2211yescharacteristic
198#1767C2211yescharacteristic, complemented
199#1763C2211yescharacteristic, complemented
200#1762C2211yescharacteristic
201#1736C2211yescharacteristic
202C2×#340C2211yescharacteristic, complemented
203#1729C2211yescharacteristic
204#1729C2211yescharacteristic, complemented
205C22×#41C2311yescharacteristic
206C23×D4C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C23×C8C2311yescharacteristic
214C23×C8C2311yescharacteristic
215#555—24no—
216#555D418yes—
217#552—24no—
218#552—24no—
219#546—24no—
220#546—24no—
221C2×C4⋊Q8C2311yescharacteristic
222C2×C4⋊Q8C2311yescharacteristic
223C2×#126—21no—
224C2×#125—21no—
225C2×#125C2311yescharacteristic
226C2×#124—21no—
227C2×#124—21no—
228C2×#124C2311yescharacteristic
229C2×#124C2311yescharacteristic
230C2×#124C2311yescharacteristic
231C2×#123—21no—
232C2×#123—21no—
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×#121—21no—
237C2×#121—21no—
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#121C2311yescharacteristic
241C2×#120—21no—
242C2×C4×Q8—21no—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×D4—21no—
245C2×C4×D4—21no—
246C2×C4×D4—21no—
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×#117—21no—
253C2×#117—21no—
254C2×#117—21no—
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C22⋊C4—21no—
264C22×C42—21no—
265#501—24no—
266#489—24no—
267#485—24no—
268#485—24no—
269#485—24no—
270#482—24no—
271#482—24no—
272#481—24no—
273#478—24no—
274#475—24no—
275#474—24no—
276#468—24no—
277#468—24no—
278#466—24no—
279#465—24no—
280#463—24no—
281#463—24no—
282#449—24no—
283#447—24no—
284#442—24no—
285#440—24no—
286#435—24no—
287#435—24no—
288#428—24no—
289#427—24no—
290C2×#107C2311yescharacteristic
291C2×#107C2311yescharacteristic
292C2×#107C2311yescharacteristic
293C2×#107C2311yescharacteristic
294C2×#107C2311yescharacteristic
295C2×#107C2311yescharacteristic
296C2×#106C2311yescharacteristic
297C2×#106C2311yescharacteristic
298C2×#106C2311yescharacteristic
299C2×#106C2311yescharacteristic
300C2×#106C2311yescharacteristic
301C2×#106C2311yescharacteristic
302C2×C4⋊C8C2311yescharacteristic
303C2×C4⋊C8C2311yescharacteristic
304C2×C4⋊C8C2311yescharacteristic
305C2×C4⋊C8C2311yescharacteristic
306C2×C4⋊C8C2311yescharacteristic
307C2×C4⋊C8C2311yescharacteristic
308C2×C4⋊C8C2311yescharacteristic
309C2×C4⋊C8C2311yescharacteristic
310#418—24no—
311#417—24no—
312#416—24no—
313C2×#103C2311yescharacteristic
314C2×#103C2311yescharacteristic
315C2×#103C2311yescharacteristic
316C2×#103C2311yescharacteristic
317C2×#103C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
325C2×#103C2311yescharacteristic
326C2×#103C2311yescharacteristic
327C2×#102—24no—
328C2×#102C2311yescharacteristic
329C2×#102C2311yescharacteristic
330C2×#102C2311yescharacteristic
331C2×#102C2311yescharacteristic
332C2×#102C2311yescharacteristic
333C2×#102C2311yescharacteristic
334C2×#102C2311yescharacteristic
335C2×#102C2311yescharacteristic
336C2×#102C2311yescharacteristic
337C2×#102C2311yescharacteristic
338C2×#102C2311yescharacteristic
339C2×#102C2311yescharacteristic
340C2×#102C2311yescharacteristic
341C2×#102C2311yescharacteristic
342C2×#102C2311yescharacteristic
343C2×#102C2311yescharacteristic
344C2×#102C2311yescharacteristic
345C2×#102C2311yescharacteristic
346C2×C22⋊C8C2311yescharacteristic
347C2×C22⋊C8C2311yescharacteristic
348C2×C22⋊C8C2311yescharacteristic
349C2×C22⋊C8C2311yescharacteristic
350C2×#97C2311yescharacteristic
351C2×#97C2311yescharacteristic
352#398—21no—
353#398—21no—
354#397—21no—
355#397—21no—
356#397—21no—
357#397—21no—
358#397—21no—
359#397—21no—
360#396—21no—
361#396—21no—
362#396—21no—
363#396—21no—
364#396—21no—
365#396—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#394—21no—
370#394—21no—
371#394—21no—
372#391—21no—
373#391—21no—
374#391—21no—
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#391C2311yescharacteristic
378#391C2311yescharacteristic
379#390—21no—
380#390—21no—
381#390—21no—
382#390—21no—
383#390D411yescharacteristic
384#390D411yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#389—21no—
394#389—21no—
395#389—21no—
396#389D411yescharacteristic
397#389D411yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#388—21no—
419#388—21no—
420#388D411yescharacteristic
421#388D411yescharacteristic
422#388D411yescharacteristic
423#388D411yescharacteristic
424#387—21no—
425#387—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#386—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#385—21no—
440#385—21no—
441#385—21no—
442#385—21no—
443#385—21no—
444#384C2311yescharacteristic
445#384C2311yescharacteristic
446#383—21no—
447#383—21no—
448#382C2311yescharacteristic
449#382C2311yescharacteristic
450#380—21no—
451#380—21no—
452#380—21no—
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#379—21no—
456#379—21no—
457#379—21no—
458#379—21no—
459C4×C4⋊C4—21no—
460C4×C4⋊C4—21no—
461C4×C4⋊C4—21no—
462C4×C4⋊C4—21no—
463C4×C4⋊C4—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×C4⋊C4C2311yescharacteristic
472C4×C4⋊C4C2311yescharacteristic
473C4×C4⋊C4C2311yescharacteristic
474C4×C4⋊C4C2311yescharacteristic
475C4×C4⋊C4C2311yescharacteristic
476C4×C4⋊C4C2311yescharacteristic
477C4×C22⋊C4—21no—
478C4×C22⋊C4—21no—
479C4×C22⋊C4—21no—
480C4×C22⋊C4—21no—
481C4×C22⋊C4—21no—
482C4×C22⋊C4—21no—
483C4×C22⋊C4—21no—
484C4×C22⋊C4—21no—
485C4×C22⋊C4—21no—
486C4×C22⋊C4C2311yescharacteristic
487C4×C22⋊C4C2311yescharacteristic
488C43C2311yescharacteristic
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#340C2311yescharacteristic
503#340C2311yescharacteristic
504#340C2311yescharacteristic
505#336C2311yescharacteristic
506#336C2311yescharacteristic
507#336C2311yescharacteristic
508#336C2311yescharacteristic
509#336C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515C25—21no—
516C2×#41—22no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—41no—
520C2×#41—41no—
521C2×#41—41no—
522C22×Q8—21no—
523C22×Q8C2411yescharacteristic
524C22×Q8C2411yescharacteristic
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—22no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—22no—
531C22×D4—21no—
532C22×D4—22no—
533C22×D4—41no—
534C22×D4—41no—
535C22×D4—41no—
536C22×D4C2×D411yescharacteristic
537C22×D4C2411yescharacteristic
538C22×D4C2411yescharacteristic
539C22×D4C2411yescharacteristic
540C23×C4—21no—
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—21no—
546C23×C4—21no—
547C23×C4—21no—
548C23×C4C2411yescharacteristic
549C23×C4C2411yescharacteristic
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×SD16—41no—
556C2×D8—22no—
557C2×D8—22no—
558C2×D8—22no—
559C2×D8—41no—
560C2×D8—41no—
561C2×D8—41no—
562C2×M16—22no—
563C2×M16—22no—
564C2×M16—22no—
565C2×M16—41no—
566C2×M16—41no—
567C2×M16—41no—
568C22×C8—22no—
569C22×C8—22no—
570C22×C8—22no—
571C22×C8—41no—
572C22×C8—41no—
573C22×C8—41no—
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577C22×C8C2411yescharacteristic
578C22×C8C2411yescharacteristic
579C22×C8C2411yescharacteristic
580C22×C8C2411yescharacteristic
581C22×C8C2411yescharacteristic
582C4⋊Q8—22no—
583C4⋊Q8—41no—
584C4⋊Q8—41no—
585C4⋊Q8C2×D414yes—
586#126—44no—
587#125—22no—
588#125—22no—
589#125—44no—
590#124—28no—
591#124—28no—
592#124—22no—
593#124—22no—
594#124—22no—
595#124—41no—
596#124—41no—
597#124—41no—
598#123—44no—
599#123—44no—
600C22⋊Q8—22no—
601C22⋊Q8—22no—
602C22⋊Q8—22no—
603C22⋊Q8—22no—
604C22⋊Q8—22no—
605C22⋊Q8—22no—
606#121—28no—
607#121—22no—
608#121—22no—
609#121—22no—
610#121—22no—
611#121—44no—
612#121C2×D414yes—
613#121C2×D414yes—
614#120—44no—
615C4×Q8—22no—
616C4×Q8—22no—
617C4×Q8—82no—
618C4×D4—22no—
619C4×D4—22no—
620C4×D4—22no—
621C4×D4—22no—
622C4×D4—41no—
623C4×D4—41no—
624C4×D4—41no—
625C4×D4—82no—
626C4×D4—82no—
627C4×D4—82no—
628C4×D4C2×D414yes—
629C4×D4C2×D414yes—
630C4×D4#4114yes—
631#117—22no—
632#117—22no—
633#117—28no—
634#117—22no—
635#117—22no—
636#117—41no—
637#117—41no—
638#117—41no—
639#117—41no—
640#117—44no—
641#117—82no—
642#117C2×D414yes—
643#117C2×D414yes—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—22no—
646C2×C4⋊C4—22no—
647C2×C4⋊C4—22no—
648C2×C4⋊C4—22no—
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—41no—
669C2×C4⋊C4—41no—
670C2×C4⋊C4C2×D411yescharacteristic
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2×D411yescharacteristic
675C2×C4⋊C4C2×D411yescharacteristic
676C2×C4⋊C4C2×D411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
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—21no—
725C2×C22⋊C4—44no—
726C2×C22⋊C4C2×D411yescharacteristic
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×C22⋊C4C2×D411yescharacteristic
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—21no—
746C2×C42—21no—
747C2×C42—21no—
748C2×C42—21no—
749C2×C42—82no—
750C2×C42C2×D411yescharacteristic
751C2×C42C2×D411yescharacteristic
752C2×C42C2×D411yescharacteristic
753C2×C42C2×D411yescharacteristic
754C2×C42C2411yescharacteristic
755C2×C42C2411yescharacteristic
756C2×C42C2411yescharacteristic
757C2×C42C2411yescharacteristic
758C2×C42C2411yescharacteristic
759#107—22no—
760#107—22no—
761#107—22no—
762#107—22no—
763#107—22no—
764#107—22no—
765#106—22no—
766#106—22no—
767#106—22no—
768#106—22no—
769#106—22no—
770#106—22no—
771C4⋊C8—22no—
772C4⋊C8—22no—
773C4⋊C8—22no—
774C4⋊C8—41no—
775C4⋊C8—41no—
776C4⋊C8—41no—
777C4⋊C8—41no—
778C4⋊C8—41no—
779#103—22no—
780#103—22no—
781#103—22no—
782#103—22no—
783#103—22no—
784#103—22no—
785#103—22no—
786#103—22no—
787#103—22no—
788#103—41no—
789#103—41no—
790#103—41no—
791#103—41no—
792#103—41no—
793#102—22no—
794#102—22no—
795#102—22no—
796#102—22no—
797#102—22no—
798#102—22no—
799#102—22no—
800#102—22no—
801#102—22no—
802#102—22no—
803#102—22no—
804#102—22no—
805#102—22no—
806#102—22no—
807#102—41no—
808#102—41no—
809#102—41no—
810#102#4114yes—
811C22⋊C8—22no—
812C22⋊C8—22no—
813C22⋊C8—22no—
814C22⋊C8—22no—
815#97—22no—
816#97—22no—
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#95—21no—
834#95—21no—
835#95—21no—
836#95—21no—
837#95—21no—
838#95—21no—
839#95—21no—
840#95—21no—
841#95—21no—
842#95—21no—
843#95—21no—
844#95C2×D411yescharacteristic
845#95C2×D411yescharacteristic
846#95C2×D411yescharacteristic
847#95C2×D411yescharacteristic
848#95C2×D411yescharacteristic
849#95C2×D411yescharacteristic
850C24—21no—
851C24—21no—
852C24—21no—
853C24—42no—
854C24—42no—
855C24—81no—
856C24—81no—
857C24—81no—
858C24—81no—
859C24—81no—
860C24C22×D411yescharacteristic
861C24C22×D411yescharacteristic
862#41—44no—
863#41—44no—
864#41—82no—
865#41—82no—
866C2×Q8—24no—
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—21no—
876C2×Q8—21no—
877C2×Q8—21no—
878C2×Q8—21no—
879C2×Q8—81no—
880C2×Q8—81no—
881C2×D4—24no—
882C2×D4—24no—
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—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—21no—
898C2×D4—21no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—41no—
902C2×D4—41no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—42no—
906C2×D4—42no—
907C2×D4—42no—
908C2×D4—82no—
909C2×D4—82no—
910C2×D4—81no—
911C2×D4—81no—
912C2×D4—81no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4—81no—
917C2×D4—81no—
918C2×D4#12114yes—
919C2×D4C22×D412yes—
920C2×D4C2×#4112yes—
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—21no—
933C22×C4—24no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—42no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4—81no—
961C22×C4—81no—
962C22×C4—81no—
963C22×C4—81no—
964C22×C4—81no—
965C22×C4—81no—
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C22×D411yescharacteristic
973C22×C4C22×D411yescharacteristic
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C22×D411yescharacteristic
977C22×C4C22×D411yescharacteristic
978C22×C4C22×D412yes—
979C22×C4C22×D412yes—
980C22×C4C2×#4112yes—
981C22×C4C2×#4112yes—
982C22×C4C2511yescharacteristic
983SD16—44no—
984SD16—82no—
985D8—44no—
986D8—82no—
987M16—44no—
988M16—82no—
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—21no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—44no—
1013C2×C8—82no—
1014C2×C8C2×#4112yes—
1015C4⋊C4—24no—
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—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—41no—
1035C4⋊C4—41no—
1036C4⋊C4—41no—
1037C4⋊C4—41no—
1038C4⋊C4—41no—
1039C4⋊C4—41no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—81no—
1053C4⋊C4—81no—
1054C4⋊C4—81no—
1055C4⋊C4—81no—
1056C4⋊C4—81no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C4⋊C4#12114yes—
1060C4⋊C4C22×D412yes—
1061C4⋊C4C22×D412yes—
1062C4⋊C4C22×D412yes—
1063C4⋊C4C2×#4112yes—
1064C22⋊C4—24no—
1065C22⋊C4—24no—
1066C22⋊C4—24no—
1067C22⋊C4—24no—
1068C22⋊C4—24no—
1069C22⋊C4—41no—
1070C22⋊C4—41no—
1071C22⋊C4—41no—
1072C22⋊C4—41no—
1073C22⋊C4—41no—
1074C22⋊C4—41no—
1075C22⋊C4—41no—
1076C22⋊C4—41no—
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—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
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—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4#12114yes—
1110C22⋊C4#12114yes—
1111C42—24no—
1112C42—24no—
1113C42—21no—
1114C42—21no—
1115C42—21no—
1116C42—21no—
1117C42—21no—
1118C42—21no—
1119C42—21no—
1120C42—21no—
1121C42—41no—
1122C42—41no—
1123C42—41no—
1124C42—41no—
1125C42—42no—
1126C42—42no—
1127C42—42no—
1128C42—81no—
1129C42—81no—
1130C42—81no—
1131C42—81no—
1132C42—81no—
1133C42—81no—
1134C42—81no—
1135C42—81no—
1136C42C22×D412yes—
1137C42C2×#4112yes—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—22no—
1151C23—22no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—84no—
1172C23—84no—
1173C23—162no—
1174C23—162no—
1175C23—162no—
1176C23—162no—
1177C23—162no—
1178C23C2×#12112yes—
1179C23C2×#12112yes—
1180C23C23×D411yescharacteristic
1181Q8—41no—
1182Q8—41no—
1183Q8—41no—
1184Q8—41no—
1185Q8—41no—
1186Q8—41no—
1187Q8—41no—
1188Q8—41no—
1189Q8—84no—
1190D4—22no—
1191D4—22no—
1192D4—22no—
1193D4—22no—
1194D4—44no—
1195D4—41no—
1196D4—41no—
1197D4—41no—
1198D4—41no—
1199D4—41no—
1200D4—41no—
1201D4—41no—
1202D4—41no—
1203D4—84no—
1204D4—84no—
1205D4—84no—
1206D4—84no—
1207D4—162no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—22no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—48no—
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—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—84no—
1289C2×C4—84no—
1290C2×C4—84no—
1291C2×C4—84no—
1292C2×C4—162no—
1293C2×C4—162no—
1294C2×C4—162no—
1295C2×C4C2×#12112yes—
1296C2×C4C2×#12112yes—
1297C2×C4C2×#12112yes—
1298C2×C4C2×#12112yes—
1299C2×C4C23×D411yescharacteristic
1300C2×C4C22×#4111yescharacteristic
1301C2×C4C22×#4111yescharacteristic
1302C2×C4#58511yescharacteristic
1303C2×C4#58511yescharacteristic
1304C2×C4#58511yescharacteristic
1305C8—22no—
1306C8—41no—
1307C8—41no—
1308C8—41no—
1309C8—41no—
1310C8—41no—
1311C8—41no—
1312C8—41no—
1313C22—22no—
1314C22—22no—
1315C22—22no—
1316C22—22no—
1317C22—22no—
1318C22—22no—
1319C22—41no—
1320C22—41no—
1321C22—41no—
1322C22—41no—
1323C22—41no—
1324C22—41no—
1325C22—41no—
1326C22—41no—
1327C22—42no—
1328C22—42no—
1329C22—42no—
1330C22—42no—
1331C22—42no—
1332C22—42no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—168no—
1349C22C22×#12111yescharacteristic
1350C22D4×#4111yescharacteristic
1351C22#348511yescharacteristic
1352C22#358411yescharacteristic
1353C22#358511yescharacteristic
1354C22#358511yescharacteristic
1355C22#358611yescharacteristic
1356C4—22no—
1357C4—22no—
1358C4—22no—
1359C4—22no—
1360C4—42no—
1361C4—42no—
1362C4—42no—
1363C4—41no—
1364C4—42no—
1365C4—41no—
1366C4—41no—
1367C4—41no—
1368C4—41no—
1369C4—41no—
1370C4—41no—
1371C4—41no—
1372C4—81no—
1373C4—81no—
1374C4—81no—
1375C4—81no—
1376C4—81no—
1377C4—81no—
1378C4—81no—
1379C4—81no—
1380C4—81no—
1381C4D4×#4111yescharacteristic
1382C4#347511yescharacteristic
1383C4#350011yescharacteristic
1384C4#352111yescharacteristic
1385C2—42no—
1386C2—42no—
1387C2—82no—
1388C2—82no—
1389C2—161no—
1390C2#3621811yescharacteristic
1391C2#6042511yescharacteristic
1392C2#6043011yescharacteristic
1393C2#6150611yescharacteristic
1394C2#6152811yescharacteristic
1395C2#6179911yescharacteristic
1396C2#6180411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3319C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2293 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3348C2semidirect
3. #38947C2semidirect
4. #34321C2semidirect
5. #33117C2semidirect
6. #33115C2semidirect
7. #33028C2semidirect
8. #28659C2semidirect
9. #28586C2semidirect
10. #28583C2semidirect
11. #28203C2semidirect
12. #28127C2semidirect
13. #28126C2semidirect
14. #25462C2semidirect
15. #25287C2semidirect
16. #25230C2semidirect
17. #25214C2semidirect
18. #25104C2semidirect
19. #25088C2semidirect
20. #24688C2semidirect
21. #24640C2semidirect
22. #24597C2semidirect
23. #24584C2semidirect
24. #24493C2semidirect
25. #24485C2semidirect
26. #22702C2semidirect
27. #22491C2semidirect
28. #22419C2semidirect
29. #21507C2semidirect
30. #21065C2semidirect
31. #21062C2semidirect
37. C2×#501C22semidirect
39. C2×#481C22semidirect
42. C2×#485C22semidirect
45. C2×#475C22semidirect
46. C2×#478C22semidirect
49. C2×#468C22semidirect
57. C2×#440C22semidirect
60. C2×#428C22semidirect
83. #2369C22semidirect
88. #2361C22semidirect
89. #2354C22semidirect
93. #2347C22semidirect
97. #2324C22semidirect
100. C4×C4⋊Q8C22semidirect
106. #2274C22semidirect
107. C42×D4C22semidirect
108. #2085C22semidirect
109. #2085C22semidirect
110. #2085C22semidirect
111. #2083C22semidirect
112. #2073C22semidirect
113. #2071C22semidirect
114. #2068C22semidirect
115. #2068C22semidirect
117. #2066C22semidirect
122. #2055C22semidirect
126. #2043C22semidirect
130. #2013C22semidirect
132. #1992C22semidirect
133. #1989C22semidirect
138. #1981C22semidirect
139. #1981C22semidirect
141. #1949C22semidirect
142. #1949C22semidirect
143. #1949C22semidirect
144. #1948C22semidirect
145. #1947C22semidirect
146. #1940C22semidirect
147. #1940C22semidirect
148. #1928C22semidirect
149. #1928C22semidirect
150. #1928C22semidirect
151. #1928C22semidirect
152. #1927C22semidirect
153. #1927C22semidirect
154. #1927C22semidirect
155. #1927C22semidirect
156. #1927C22semidirect
173. #1892C22semidirect
177. #1877C22semidirect
178. #1877C22semidirect
179. #1877C22semidirect
183. #1872C22semidirect
185. #1851C22semidirect
187. #1850C22semidirect
188. #1831C22semidirect
190. #1823C22semidirect
191. #1804C22semidirect
192. #1803C22semidirect
195. #1798C22semidirect
198. #1767C22semidirect
199. #1763C22semidirect
202. C2×#340C22semidirect
204. #1729C22semidirect

Maximal subgroups

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

subgroupindex
C2×#33482
C2×#33192
#389472
#343212
#331172
#331152
#330282
#286592
#285862
#285832
#282032
#281272
#281262
#254622
#252872
#252302
#252142
#251042
#250882
#246882
#246402
#245972
#245842
#244932
#244852
#227022
#224912
#224192
#215072
#210652
#210622