Finite Group Databasebeta

← #6561917

Subgroups — #6561917

Order 512.

1618 conjugacy classes of subgroups.

The subgroup lattice has 1333 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38034C211yesmaximal, characteristic
2#34382C211yesmaximal, characteristic, complemented
3#29931C211yesmaximal, characteristic, complemented
4#29919C211yesmaximal, characteristic, complemented
5#29912C211yesmaximal, characteristic, complemented
6#27984C211yesmaximal, characteristic, complemented
7#27872C211yesmaximal, characteristic, complemented
8#27862C211yesmaximal, characteristic, complemented
9#27654C211yesmaximal, characteristic, complemented
10#27594C211yesmaximal, characteristic, complemented
11#27584C211yesmaximal, characteristic, complemented
12#26331C211yesmaximal, characteristic, complemented
13#26324C211yesmaximal, characteristic, complemented
14#26226C211yesmaximal, characteristic, complemented
15#26224C211yesmaximal, characteristic, complemented
16#26214C211yesmaximal, characteristic, complemented
17#26205C211yesmaximal, characteristic, complemented
18#25007C211yesmaximal, characteristic, complemented
19#24993C211yesmaximal, characteristic, complemented
20#24889C211yesmaximal, characteristic, complemented
21#24881C211yesmaximal, characteristic, complemented
22#24878C211yesmaximal, characteristic, complemented
23#24869C211yesmaximal, characteristic, complemented
24#23766C211yesmaximal, characteristic, complemented
25#23632C211yesmaximal, characteristic, complemented
26#23631C211yesmaximal, characteristic, complemented
27#22715C211yesmaximal, characteristic, complemented
28#22712C211yesmaximal, characteristic, complemented
29#22472C211yesmaximal, characteristic, complemented
30#22427C211yesmaximal, characteristic, complemented
31#22419C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#529C2211yescharacteristic
34C2×#481C2211yescharacteristic
35C2×#482C2211yescharacteristic
36C2×#436C2211yescharacteristic
37C2×#435C2211yescharacteristic
38C2×#417C2211yescharacteristic
39C2×#417C2211yescharacteristic
40C2×#418C2211yescharacteristic
41C22×#102C2211yescharacteristic
42#2854C2211yescharacteristic
43#2703—21no—
44#2697—21no—
45#2681—21no—
46#2678—21no—
47#2625C2211yescharacteristic
48#2620C2211yescharacteristic
49#2592C2211yescharacteristic
50#2558—21no—
51#2554—21no—
52#2538C2211yescharacteristic
53#2480—21no—
54#2472—21no—
55#2415C2211yescharacteristic
56#2414C2211yescharacteristic
57#2408C2211yescharacteristic
58#2407C2211yescharacteristic
59#2382—21no—
60#2379—21no—
61#2359—21no—
62#2359—21no—
63#2355C2211yescharacteristic, complemented
64#2355C2211yescharacteristic, complemented
65#2354C2211yescharacteristic
66#2352C2211yescharacteristic
67#2352C2211yescharacteristic
68#2352C2211yescharacteristic
69#2352C2211yescharacteristic, complemented
70D4×C4⋊C4C2211yescharacteristic
71D4×C4⋊C4C2211yescharacteristic, complemented
72#2334—21no—
73#2334—21no—
74#2329—21no—
75#2325—21no—
76#2324C2211yescharacteristic
77#2317C2211yescharacteristic
78#2317C2211yescharacteristic, complemented
79#2314C2211yescharacteristic
80#2314C2211yescharacteristic, complemented
81#2309C2211yescharacteristic
82#2297C2211yescharacteristic
83#2285C2211yescharacteristic, complemented
84C2×#382C2211yescharacteristic, complemented
85#2101C2211yescharacteristic, complemented
86#2101C2211yescharacteristic, complemented
87#2101C2211yescharacteristic, complemented
88#2100C2211yescharacteristic, complemented
89#2099C2211yescharacteristic, complemented
90#2097C2211yescharacteristic, complemented
91#2096C2211yescharacteristic, complemented
92#2095C2211yescharacteristic, complemented
93#2094C2211yescharacteristic
94#2093C2211yescharacteristic
95#2092C2211yescharacteristic
96#2092C2211yescharacteristic
97#2085C2211yescharacteristic, complemented
98#2085C2211yescharacteristic, complemented
99#2084C2211yescharacteristic, complemented
100#2077C2211yescharacteristic, complemented
101#2077C2211yescharacteristic, complemented
102#2074C2211yescharacteristic, complemented
103#2074C2211yescharacteristic, complemented
104#2074C2211yescharacteristic, complemented
105#2074C2211yescharacteristic, complemented
106#2073C2211yescharacteristic
107#2073C2211yescharacteristic
108#2073C2211yescharacteristic
109#2073C2211yescharacteristic
110#2073C2211yescharacteristic
111#2073C2211yescharacteristic
112#2073C2211yescharacteristic
113#2073C2211yescharacteristic
114#2072C2211yescharacteristic, complemented
115#2071C2211yescharacteristic
116#2071C2211yescharacteristic
117#2071C2211yescharacteristic
118#2071C2211yescharacteristic
119#2036C2211yescharacteristic, complemented
120#2036C2211yescharacteristic, complemented
121#2034C2211yescharacteristic
122#2033C2211yescharacteristic
123#2033C2211yescharacteristic
124#2033C2211yescharacteristic
125#1985C2211yescharacteristic, complemented
126#1984C2211yescharacteristic, complemented
127#1983C2211yescharacteristic
128#1983C2211yescharacteristic
129#1959C2211yescharacteristic
130#1958C2211yescharacteristic
131#1949C2211yescharacteristic, complemented
132#1948C2211yescharacteristic, complemented
133#1947C2211yescharacteristic, complemented
134#1947C2211yescharacteristic, complemented
135#1928C2211yescharacteristic, complemented
136#1927C2211yescharacteristic, complemented
137#1927C2211yescharacteristic, complemented
138#1927C2211yescharacteristic, complemented
139#1926C2211yescharacteristic
140#1926C2211yescharacteristic
141#1926C2211yescharacteristic
142#1926C2211yescharacteristic
143#1925C2211yescharacteristic
144#1925C2211yescharacteristic
145#1925C2211yescharacteristic
146#1925C2211yescharacteristic
147#1921C2211yescharacteristic, complemented
148#1921C2211yescharacteristic, complemented
149#1921C2211yescharacteristic, complemented
150#1918C2211yescharacteristic, complemented
151#1895C2211yescharacteristic
152#1895C2211yescharacteristic
153#1894C2211yescharacteristic
154#1892C2211yescharacteristic
155#1875C2211yescharacteristic
156#1874C2211yescharacteristic
157#1874C2211yescharacteristic
158#1874C2211yescharacteristic
159#1873C2211yescharacteristic
160#1873C2211yescharacteristic, complemented
161#1872C2211yescharacteristic
162#1872C2211yescharacteristic, complemented
163#1870C2211yescharacteristic
164#1870C2211yescharacteristic, complemented
165#1870C2211yescharacteristic, complemented
166#1869C2211yescharacteristic
167#1854C2211yescharacteristic
168#1854C2211yescharacteristic
169#1854C2211yescharacteristic
170#1854C2211yescharacteristic, complemented
171#1854C2211yescharacteristic, complemented
172#1853C2211yescharacteristic
173#1853C2211yescharacteristic, complemented
174#1852C2211yescharacteristic, complemented
175#1836C2211yescharacteristic, complemented
176#1834C2211yescharacteristic, complemented
177#1825C2211yescharacteristic, complemented
178#1823C2211yescharacteristic, complemented
179#1818C2211yescharacteristic
180#1817C2211yescharacteristic, complemented
181#1809C2211yescharacteristic
182#1809C2211yescharacteristic, complemented
183#1809C2211yescharacteristic, complemented
184#1808C2211yescharacteristic
185#1804C2211yescharacteristic
186#1802C2211yescharacteristic
187#1798C2211yescharacteristic, complemented
188#1788C2211yescharacteristic
189#1788C2211yescharacteristic
190#1786C2211yescharacteristic
191#1786C2211yescharacteristic
192#1776C2211yescharacteristic, complemented
193C4×#106C2211yescharacteristic, complemented
194#1762C2211yescharacteristic
195C4×#102C2211yescharacteristic
196#1750C2211yescharacteristic, complemented
197#1736C2211yescharacteristic
198#1736C2211yescharacteristic, complemented
199#1736C2211yescharacteristic, complemented
200#1735C2211yescharacteristic
201#1729C2211yescharacteristic
202#1728C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#546—24no—
210#546—24no—
211#529—24no—
212#529—24no—
213C2×#126D411yescharacteristic
214C2×#126D411yescharacteristic
215C2×#125D411yescharacteristic
216C2×#124D411yescharacteristic
217C2×#124C2311yescharacteristic
218C2×#123—21no—
219C2×#123—21no—
220C2×#123D411yescharacteristic
221C2×#123D411yescharacteristic
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8D411yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×#121—21no—
227C2×#121D411yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#120—21no—
232C2×#120—21no—
233C2×C4×Q8C2311yescharacteristic
234C2×C4×D4—21no—
235C2×C4×D4—21no—
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×#117—21no—
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
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×C42C2311yescharacteristic
253#482—42no—
254#481—42no—
255#436—24no—
256#435—24no—
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271#418—42no—
272#417—42no—
273#417—42no—
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#102—42no—
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
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×#97C2311yescharacteristic
308C2×C4×C8C2311yescharacteristic
309#400—21no—
310#398—21no—
311#397—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#396—21no—
316#396—21no—
317#396—21no—
318#396—21no—
319#394—21no—
320#394—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#394—21no—
325#393—21no—
326#392—21no—
327#392—21no—
328#392—21no—
329#391—21no—
330#391—21no—
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#390—21no—
335#390—21no—
336#390—21no—
337#390—21no—
338#390—21no—
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#389—21no—
346#389—21no—
347#389—21no—
348#389—21no—
349#389—21no—
350#389—21no—
351#389—21no—
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#388—21no—
356#388—21no—
357#388—21no—
358#388—21no—
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#386—21no—
385#386—21no—
386#386—21no—
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#384C2311yescharacteristic
404#384C2311yescharacteristic
405#384C2311yescharacteristic
406#384C2311yescharacteristic
407#384C2311yescharacteristic
408#382—21no—
409#382—21no—
410#382—21no—
411#382C2311yescharacteristic
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#382C2311yescharacteristic
417#380—21no—
418#380—21no—
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#379—21no—
429#379—21no—
430#379—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C2×#95—21no—
449C2×#95—21no—
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
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#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C22×Q8C2×D411yescharacteristic
498C22×Q8C2411yescharacteristic
499C22×D4—22no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—22no—
506C22×D4—22no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4C2×D411yescharacteristic
511C22×D4C2×D411yescharacteristic
512C22×D4C2×D411yescharacteristic
513C22×D4C2411yescharacteristic
514C22×D4C2411yescharacteristic
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4C2×D411yescharacteristic
522C23×C4C2×D411yescharacteristic
523C23×C4C2411yescharacteristic
524C23×C4C2411yescharacteristic
525C23×C4C2411yescharacteristic
526C2×M16—22no—
527C2×M16—22no—
528C2×M16—22no—
529C2×M16—41no—
530C2×M16—41no—
531C2×M16—41no—
532C2×M16—41no—
533C2×M16—41no—
534C2×M16—41no—
535C22×C8—22no—
536C22×C8—41no—
537C22×C8—41no—
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546#126—24no—
547#126—24no—
548#125—24no—
549#124—24no—
550#124—22no—
551#124—22no—
552#123—24no—
553#123—24no—
554#123—44no—
555#123—82no—
556C22⋊Q8—24no—
557C22⋊Q8—22no—
558C22⋊Q8—22no—
559C22⋊Q8—41no—
560C22⋊Q8—41no—
561C22⋊Q8—82no—
562#121—24no—
563#121—22no—
564#121—22no—
565#121—22no—
566#121—41no—
567#121—44no—
568#121—41no—
569#121—41no—
570#120—44no—
571#120—82no—
572C4×Q8—22no—
573C4×Q8—22no—
574C4×D4—22no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—82no—
581C4×D4—82no—
582C4×D4#4114yes—
583C4×D4#4114yes—
584#117—22no—
585#117—22no—
586#117—22no—
587#117—22no—
588#117—41no—
589#117—41no—
590#117—41no—
591#117—41no—
592#117—41no—
593#117—41no—
594#117—41no—
595#117—41no—
596#117—82no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
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—41no—
617C2×C4⋊C4—41no—
618C2×C4⋊C4—41no—
619C2×C4⋊C4—41no—
620C2×C4⋊C4—41no—
621C2×C4⋊C4—41no—
622C2×C4⋊C4—41no—
623C2×C4⋊C4—41no—
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
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—21no—
680C2×C22⋊C4—44no—
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×C42—22no—
692C2×C42—22no—
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—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42C2×D411yescharacteristic
705C2×C42C2×D411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710#107—41no—
711#107—41no—
712#107—41no—
713#107—41no—
714#107—41no—
715#107—41no—
716#106—41no—
717#106—41no—
718#106—41no—
719#106—41no—
720#106—41no—
721#106—41no—
722C4⋊C8—22no—
723C4⋊C8—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#102—22no—
733#102—22no—
734#102—22no—
735#102—22no—
736#102—22no—
737#102—22no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748C22⋊C8—22no—
749C22⋊C8—22no—
750C22⋊C8—22no—
751C22⋊C8—22no—
752C22⋊C8—41no—
753C22⋊C8—41no—
754C22⋊C8—41no—
755C22⋊C8—41no—
756#97—22no—
757C4×C8—22no—
758#95—21no—
759#95—21no—
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—
795C24—21no—
796C24—21no—
797C24—42no—
798C24—42no—
799C24—81no—
800C24—81no—
801C24—81no—
802C24—81no—
803C24—81no—
804C24C22×D411yescharacteristic
805C24C22×D411yescharacteristic
806C24C22×D411yescharacteristic
807#41—44no—
808#41—44no—
809#41—82no—
810#41—82no—
811C2×Q8—22no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—41no—
819C2×Q8—41no—
820C2×D4—22no—
821C2×D4—22no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—44no—
834C2×D4—44no—
835C2×D4—41no—
836C2×D4—41no—
837C2×D4—41no—
838C2×D4—41no—
839C2×D4—41no—
840C2×D4—41no—
841C2×D4—42no—
842C2×D4—42no—
843C2×D4—42no—
844C2×D4—42no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—82no—
848C2×D4—82no—
849C2×D4—81no—
850C2×D4—81no—
851C2×D4—81no—
852C2×D4—81no—
853C2×D4—81no—
854C2×D4—81no—
855C2×D4—81no—
856C2×D4—81no—
857C2×D4—81no—
858C2×D4#12314yes—
859C2×D4H(5,𝔽2)12yes—
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—22no—
869C22×C4—22no—
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—41no—
891C22×C4—41no—
892C22×C4—41no—
893C22×C4—41no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—81no—
900C22×C4—81no—
901C22×C4—81no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C2×#4112yes—
924C22×C4C2×#4112yes—
925C22×C4C2×#4112yes—
926C22×C4C2×#4112yes—
927C22×C4C2511yescharacteristic
928M16—82no—
929M16—82no—
930M16—82no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
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—82no—
956C4⋊C4—22no—
957C4⋊C4—22no—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—22no—
962C4⋊C4—22no—
963C4⋊C4—22no—
964C4⋊C4—22no—
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—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
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#12314yes—
1011C22⋊C4—22no—
1012C22⋊C4—22no—
1013C22⋊C4—22no—
1014C22⋊C4—22no—
1015C22⋊C4—22no—
1016C22⋊C4—22no—
1017C22⋊C4—22no—
1018C22⋊C4—22no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
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#12314yes—
1053C22⋊C4#12314yes—
1054C42—22no—
1055C42—22no—
1056C42—21no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—81no—
1063C42—81no—
1064C42—81no—
1065C42—81no—
1066C42—81no—
1067C42—81no—
1068C42—81no—
1069C42—81no—
1070C42—81no—
1071C42—81no—
1072C42—81no—
1073C42C2×#4112yes—
1074C42C2×#4112yes—
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—22no—
1093C23—21no—
1094C23—21no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—84no—
1109C23—84no—
1110C23—162no—
1111C23—162no—
1112C23—162no—
1113C23—162no—
1114C23—162no—
1115C23C2×#12312yes—
1116C23C2×#12312yes—
1117C23C23×D411yescharacteristic
1118Q8—41no—
1119Q8—41no—
1120Q8—41no—
1121Q8—41no—
1122Q8—82no—
1123D4—22no—
1124D4—22no—
1125D4—44no—
1126D4—44no—
1127D4—41no—
1128D4—41no—
1129D4—41no—
1130D4—41no—
1131D4—41no—
1132D4—41no—
1133D4—84no—
1134D4—82no—
1135D4—84no—
1136D4—162no—
1137D4—162no—
1138D4—162no—
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—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
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—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—44no—
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—84no—
1224C2×C4—82no—
1225C2×C4—162no—
1226C2×C4—162no—
1227C2×C4—162no—
1228C2×C4—162no—
1229C2×C4—162no—
1230C2×C4C2×#12312yes—
1231C2×C4C2×#12312yes—
1232C2×C4C2×#12312yes—
1233C2×C4C2×#12312yes—
1234C2×C4C22×#4111yescharacteristic
1235C2×C4C22×#4111yescharacteristic
1236C2×C4C2×H(5,𝔽2)11yescharacteristic
1237C2×C4#58511yescharacteristic
1238C2×C4#58511yescharacteristic
1239C2×C4#58511yescharacteristic
1240C8—41no—
1241C8—41no—
1242C8—41no—
1243C8—41no—
1244C8—41no—
1245C8—41no—
1246C8—41no—
1247C8—41no—
1248C22—22no—
1249C22—22no—
1250C22—22no—
1251C22—22no—
1252C22—22no—
1253C22—22no—
1254C22—41no—
1255C22—41no—
1256C22—41no—
1257C22—41no—
1258C22—41no—
1259C22—41no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—42no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22—42no—
1269C22—41no—
1270C22—42no—
1271C22—41no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—168no—
1284C22C22×#12311yescharacteristic
1285C22#348811yescharacteristic
1286C22#350011yescharacteristic
1287C22#358411yescharacteristic
1288C22#358511yescharacteristic
1289C22#358511yescharacteristic
1290C22#358611yescharacteristic
1291C4—22no—
1292C4—22no—
1293C4—22no—
1294C4—22no—
1295C4—41no—
1296C4—41no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—41no—
1301C4—41no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4#351311yescharacteristic
1317C4#351311yescharacteristic
1318C4#352111yescharacteristic
1319C4#352111yescharacteristic
1320C2—42no—
1321C2—42no—
1322C2—81no—
1323C2—82no—
1324C2—161no—
1325C2#3597611yescharacteristic
1326C2#6051711yescharacteristic
1327C2#6052311yescharacteristic
1328C2#6204711yescharacteristic
1329C2#6208711yescharacteristic
1330C2#6257311yescharacteristic
1331C2#6261211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#38034C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#529 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34382C2semidirect
3. #29931C2semidirect
4. #29919C2semidirect
5. #29912C2semidirect
6. #27984C2semidirect
7. #27872C2semidirect
8. #27862C2semidirect
9. #27654C2semidirect
10. #27594C2semidirect
11. #27584C2semidirect
12. #26331C2semidirect
13. #26324C2semidirect
14. #26226C2semidirect
15. #26224C2semidirect
16. #26214C2semidirect
17. #26205C2semidirect
18. #25007C2semidirect
19. #24993C2semidirect
20. #24889C2semidirect
21. #24881C2semidirect
22. #24878C2semidirect
23. #24869C2semidirect
24. #23766C2semidirect
25. #23632C2semidirect
26. #23631C2semidirect
27. #22715C2semidirect
28. #22712C2semidirect
29. #22472C2semidirect
30. #22427C2semidirect
31. #22419C2semidirect
63. #2355C22semidirect
64. #2355C22semidirect
69. #2352C22semidirect
71. D4×C4⋊C4C22semidirect
78. #2317C22semidirect
80. #2314C22semidirect
83. #2285C22semidirect
84. C2×#382C22semidirect
85. #2101C22semidirect
86. #2101C22semidirect
87. #2101C22semidirect
88. #2100C22semidirect
89. #2099C22semidirect
90. #2097C22semidirect
91. #2096C22semidirect
92. #2095C22semidirect
97. #2085C22semidirect
98. #2085C22semidirect
99. #2084C22semidirect
100. #2077C22semidirect
101. #2077C22semidirect
102. #2074C22semidirect
103. #2074C22semidirect
104. #2074C22semidirect
105. #2074C22semidirect
114. #2072C22semidirect
119. #2036C22semidirect
120. #2036C22semidirect
125. #1985C22semidirect
126. #1984C22semidirect
131. #1949C22semidirect
132. #1948C22semidirect
133. #1947C22semidirect
134. #1947C22semidirect
135. #1928C22semidirect
136. #1927C22semidirect
137. #1927C22semidirect
138. #1927C22semidirect
147. #1921C22semidirect
148. #1921C22semidirect
149. #1921C22semidirect
150. #1918C22semidirect
160. #1873C22semidirect
162. #1872C22semidirect
164. #1870C22semidirect
165. #1870C22semidirect
170. #1854C22semidirect
171. #1854C22semidirect
173. #1853C22semidirect
174. #1852C22semidirect
175. #1836C22semidirect
176. #1834C22semidirect
177. #1825C22semidirect
178. #1823C22semidirect
180. #1817C22semidirect
182. #1809C22semidirect
183. #1809C22semidirect
187. #1798C22semidirect
192. #1776C22semidirect
193. C4×#106C22semidirect
196. #1750C22semidirect
198. #1736C22semidirect
199. #1736C22semidirect
202. #1728C22semidirect

Maximal subgroups

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

subgroupindex
#380342
#343822
#299312
#299192
#299122
#279842
#278722
#278622
#276542
#275942
#275842
#263312
#263242
#262262
#262242
#262142
#262052
#250072
#249932
#248892
#248812
#248782
#248692
#237662
#236322
#236312
#227152
#227122
#224722
#224272
#224192