Finite Group Databasebeta

← #7201325

Subgroups — #7201325

Order 512.

1535 conjugacy classes of subgroups.

The subgroup lattice has 1340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45601C211yesmaximal, characteristic
2#36516C211yesmaximal, characteristic, complemented
3#32985C211yesmaximal, characteristic, complemented
4#32981C211yesmaximal, characteristic, complemented
5#32711C211yesmaximal, characteristic, complemented
6#32709C211yesmaximal, characteristic, complemented
7#32275C211yesmaximal, characteristic, complemented
8#32068C211yesmaximal, characteristic, complemented
9#32064C211yesmaximal, characteristic, complemented
10#31767C211yesmaximal, characteristic, complemented
11#31763C211yesmaximal, characteristic, complemented
12#31679C211yesmaximal, characteristic, complemented
13#31347C211yesmaximal, characteristic, complemented
14#31343C211yesmaximal, characteristic, complemented
15#31045C211yesmaximal, characteristic, complemented
16#31038C211yesmaximal, characteristic, complemented
17#30802C211yesmaximal, characteristic, complemented
18#30798C211yesmaximal, characteristic, complemented
19#27345C211yesmaximal, characteristic, complemented
20#27343C211yesmaximal, characteristic, complemented
21#26811C211yesmaximal, characteristic, complemented
22#26809C211yesmaximal, characteristic, complemented
23#26750C211yesmaximal, characteristic, complemented
24#26748C211yesmaximal, characteristic, complemented
25#26314C211yesmaximal, characteristic, complemented
26#26313C211yesmaximal, characteristic, complemented
27#25712C211yesmaximal, characteristic, complemented
28#24891C211yesmaximal, characteristic, complemented
29#24889C211yesmaximal, characteristic, complemented
30#23981C211yesmaximal, characteristic, complemented
31#23309C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C22×#117C2211yescharacteristic
34C2×#501C2211yescharacteristic, complemented
35C2×#485C2211yescharacteristic
36C2×#485C2211yescharacteristic
37C2×#482C2211yescharacteristic
38C2×#482C2211yescharacteristic
39C2×#479C2211yescharacteristic, complemented
40C2×#452C2211yescharacteristic, complemented
41C2×#417C2211yescharacteristic, complemented
42#2855—21no—
43#2848C2211yescharacteristic
44#2848C2211yescharacteristic
45#2847C2211yescharacteristic
46#2824—21no—
47#2804—21no—
48#2782—21no—
49#2753—21no—
50#2712—21no—
51#2684—21no—
52#2670—21no—
53#2563C2211yescharacteristic
54#2562C2211yescharacteristic
55#2561—21no—
56#2547C2211yescharacteristic
57#2534—21no—
58#2503C2211yescharacteristic
59#2492C2211yescharacteristic
60#2492C2211yescharacteristic
61#2491C2211yescharacteristic
62#2491C2211yescharacteristic
63#2490C2211yescharacteristic
64#2489C2211yescharacteristic
65#2486C2211yescharacteristic
66#2477—21no—
67#2477—21no—
68#2475—21no—
69#2475—21no—
70#2439C2211yescharacteristic
71#2439C2211yescharacteristic
72#2415C2211yescharacteristic
73#2415C2211yescharacteristic
74#2407C2211yescharacteristic
75#2407C2211yescharacteristic
76#2407C2211yescharacteristic
77#2379—21no—
78#2362C2211yescharacteristic
79#2362C2211yescharacteristic
80#2352C2211yescharacteristic
81#2352C2211yescharacteristic
82#2345C2211yescharacteristic
83C4×#123—21no—
84C4×#120C2211yescharacteristic
85#2097C2211yescharacteristic, complemented
86#2092C2211yescharacteristic, complemented
87#2077C2211yescharacteristic
88#2077C2211yescharacteristic
89#2077C2211yescharacteristic
90#2077C2211yescharacteristic, complemented
91#2077C2211yescharacteristic, complemented
92#2076C2211yescharacteristic
93#2076C2211yescharacteristic, complemented
94#2076C2211yescharacteristic, complemented
95#2075C2211yescharacteristic
96#2075C2211yescharacteristic
97#2074C2211yescharacteristic, complemented
98#2073C2211yescharacteristic, complemented
99#2068C2211yescharacteristic, complemented
100#2068C2211yescharacteristic, complemented
101#2065C2211yescharacteristic, complemented
102#2065C2211yescharacteristic, complemented
103#2059C2211yescharacteristic, complemented
104#2059C2211yescharacteristic, complemented
105#2058C2211yescharacteristic, complemented
106#2057C2211yescharacteristic, complemented
107#2056C2211yescharacteristic, complemented
108#2055C2211yescharacteristic, complemented
109#2036C2211yescharacteristic
110#2036C2211yescharacteristic
111#2036C2211yescharacteristic
112#2036C2211yescharacteristic
113#2036C2211yescharacteristic, complemented
114#2035C2211yescharacteristic
115#2035C2211yescharacteristic
116#2035C2211yescharacteristic
117#2035C2211yescharacteristic
118#2035C2211yescharacteristic
119#2035C2211yescharacteristic, complemented
120#2034C2211yescharacteristic
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic
123#2024C2211yescharacteristic, complemented
124#2024C2211yescharacteristic, complemented
125#2024C2211yescharacteristic, complemented
126#2023C2211yescharacteristic, complemented
127#2001C2211yescharacteristic
128#2001C2211yescharacteristic
129#2001C2211yescharacteristic
130#2000C2211yescharacteristic
131#2000C2211yescharacteristic
132#2000C2211yescharacteristic
133#1993C2211yescharacteristic, complemented
134#1993C2211yescharacteristic, complemented
135#1988C2211yescharacteristic, complemented
136#1988C2211yescharacteristic, complemented
137#1987C2211yescharacteristic, complemented
138#1973C2211yescharacteristic, complemented
139#1971C2211yescharacteristic, complemented
140#1955C2211yescharacteristic
141#1955C2211yescharacteristic
142#1955C2211yescharacteristic
143#1949C2211yescharacteristic, complemented
144#1949C2211yescharacteristic, complemented
145#1936C2211yescharacteristic, complemented
146#1936C2211yescharacteristic, complemented
147#1935C2211yescharacteristic, complemented
148#1935C2211yescharacteristic, complemented
149#1928C2211yescharacteristic, complemented
150#1928C2211yescharacteristic, complemented
151#1927C2211yescharacteristic, complemented
152#1927C2211yescharacteristic, complemented
153#1926C2211yescharacteristic, complemented
154#1925C2211yescharacteristic, complemented
155#1924C2211yescharacteristic
156#1924C2211yescharacteristic
157#1924C2211yescharacteristic
158#1924C2211yescharacteristic
159#1924C2211yescharacteristic
160#1924C2211yescharacteristic
161#1921C2211yescharacteristic, complemented
162#1920C2211yescharacteristic, complemented
163#1919C2211yescharacteristic, complemented
164#1918C2211yescharacteristic, complemented
165#1894C2211yescharacteristic, complemented
166#1880C2211yescharacteristic, complemented
167#1878C2211yescharacteristic, complemented
168#1875C2211yescharacteristic
169#1875C2211yescharacteristic
170#1874C2211yescharacteristic
171#1874C2211yescharacteristic
172#1873C2211yescharacteristic
173#1873C2211yescharacteristic
174#1872C2211yescharacteristic
175#1872C2211yescharacteristic
176#1870C2211yescharacteristic
177#1870C2211yescharacteristic
178#1870C2211yescharacteristic
179#1854C2211yescharacteristic
180#1854C2211yescharacteristic
181#1854C2211yescharacteristic
182#1854C2211yescharacteristic
183#1853C2211yescharacteristic
184#1853C2211yescharacteristic
185#1853C2211yescharacteristic, complemented
186#1852C2211yescharacteristic
187#1852C2211yescharacteristic
188#1852C2211yescharacteristic, complemented
189#1825C2211yescharacteristic
190#1825C2211yescharacteristic
191#1825C2211yescharacteristic
192#1825C2211yescharacteristic
193#1823C2211yescharacteristic, complemented
194#1809C2211yescharacteristic, complemented
195#1809C2211yescharacteristic, complemented
196#1788C2211yescharacteristic, complemented
197#1788C2211yescharacteristic, complemented
198#1779C2211yescharacteristic
199#1779C2211yescharacteristic
200#1776C2211yescharacteristic, complemented
201#1776C2211yescharacteristic, complemented
202#1763C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C24×C4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208#554—42no—
209#554—42no—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#125—21no—
214C2×#125C2311yescharacteristic
215C2×#124—21no—
216C2×#124—21no—
217C2×#124—21no—
218C2×#123—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8C2311yescharacteristic
222C2×C22⋊Q8C2311yescharacteristic
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#120—21no—
232C2×#120D411yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×D4—21no—
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×#117—21no—
239C2×#117—21no—
240C2×#117—42no—
241C2×#117—42no—
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C22⋊C4—21no—
250C22×C42—21no—
251#501—42no—
252#485—42no—
253#485—42no—
254#482—42no—
255#482—42no—
256#479—42no—
257#452—42no—
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275#417—42no—
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×#97C2311yescharacteristic
314#400—21no—
315#400—21no—
316#400—21no—
317#400—21no—
318#400—21no—
319#400—21no—
320#398—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#396—21no—
329#396—21no—
330#394—21no—
331#394—21no—
332#394—21no—
333#394—21no—
334#394—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#393—21no—
340#393—21no—
341#393—21no—
342#393—21no—
343#393—21no—
344#393—21no—
345#393—21no—
346#393—21no—
347#392—21no—
348#392—21no—
349#392—21no—
350#391—21no—
351#391—21no—
352#391—21no—
353#391—21no—
354#391—21no—
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#390—21no—
361#390—21no—
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#389—21no—
366#389—21no—
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386D411yescharacteristic
404#386D411yescharacteristic
405#386D411yescharacteristic
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385D411yescharacteristic
416#385D411yescharacteristic
417#385D411yescharacteristic
418#382—21no—
419#382—21no—
420#382C2311yescharacteristic
421#382C2311yescharacteristic
422#381—21no—
423#381—21no—
424#381—21no—
425#380—21no—
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#379—21no—
441#379—21no—
442#379D411yescharacteristic
443C4×C4⋊C4—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4C2311yescharacteristic
454C4×C22⋊C4C2311yescharacteristic
455C4×C22⋊C4C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25C2×D411yescharacteristic
491C2×#41—41no—
492C2×#41—41no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C22×Q8—21no—
498C22×Q8—21no—
499C22×Q8—21no—
500C22×Q8C2411yescharacteristic
501C22×Q8C2411yescharacteristic
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4C2×D411yescharacteristic
507C22×D4C2×D411yescharacteristic
508C22×D4C2×D411yescharacteristic
509C22×D4C2411yescharacteristic
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—41no—
515C23×C4—41no—
516C23×C4—41no—
517C23×C4—41no—
518C23×C4—41no—
519C23×C4—41no—
520C23×C4C2×D411yescharacteristic
521C23×C4C2×D411yescharacteristic
522C23×C4C2×D411yescharacteristic
523C23×C4C2411yescharacteristic
524C23×C4C2411yescharacteristic
525C23×C4C2411yescharacteristic
526C23×C4C2411yescharacteristic
527C2×Q16—41no—
528C2×Q16—41no—
529C2×Q16—41no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×M16—41no—
534C2×M16—41no—
535C2×M16—41no—
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C4⋊Q8—22no—
545C4⋊Q8—41no—
546C4⋊Q8—41no—
547C4⋊Q8—41no—
548C4⋊Q8—41no—
549C4⋊Q8—41no—
550#125—41no—
551#125—41no—
552#125—44no—
553#124—44no—
554#124—82no—
555#124—82no—
556#123—44no—
557C22⋊Q8—22no—
558C22⋊Q8—41no—
559C22⋊Q8—41no—
560C22⋊Q8—41no—
561C22⋊Q8—41no—
562C22⋊Q8—41no—
563C22⋊Q8—41no—
564C22⋊Q8—41no—
565C22⋊Q8—44no—
566C22⋊Q8—44no—
567C22⋊Q8—41no—
568C22⋊Q8—41no—
569C22⋊Q8—41no—
570C22⋊Q8—41no—
571C22⋊Q8—41no—
572C22⋊Q8—41no—
573#121—41no—
574#121—41no—
575#121—41no—
576#121—41no—
577#121—41no—
578#121—41no—
579#120—42no—
580#120—82no—
581C4×Q8—22no—
582C4×Q8—41no—
583C4×D4—41no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—41no—
587C4×D4—41no—
588C4×D4—41no—
589C4×D4—44no—
590#117—22no—
591#117—22no—
592#117—22no—
593#117—22no—
594#117—41no—
595#117—41no—
596#117—41no—
597#117—41no—
598#117—44no—
599#117—44no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—41no—
624C2×C4⋊C4—41no—
625C2×C4⋊C4—41no—
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—44no—
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—44no—
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703#107—22no—
704#107—22no—
705#107—41no—
706#107—41no—
707#107—41no—
708#107—41no—
709#107—41no—
710#106—22no—
711#106—22no—
712#106—41no—
713#106—41no—
714#106—41no—
715#106—41no—
716#106—41no—
717C4⋊C8—41no—
718C4⋊C8—41no—
719C4⋊C8—41no—
720#103—22no—
721#103—22no—
722#103—41no—
723#103—41no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#103—41no—
730#103—41no—
731#103—41no—
732#103—41no—
733#102—22no—
734#102—22no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740C22⋊C8—41no—
741C22⋊C8—41no—
742C22⋊C8—41no—
743C22⋊C8—41no—
744C22⋊C8—41no—
745C22⋊C8—41no—
746C22⋊C8—41no—
747C22⋊C8—41no—
748C22⋊C8—41no—
749C22⋊C8—41no—
750C22⋊C8—41no—
751C22⋊C8—41no—
752C22⋊C8—41no—
753C22⋊C8—41no—
754C22⋊C8—41no—
755#97—41no—
756#97—41no—
757#97—41no—
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—
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801C24—22no—
802C24—21no—
803C24—41no—
804C24—41no—
805C24—41no—
806C24—41no—
807C24—41no—
808C24—41no—
809C24C22×D411yescharacteristic
810C24C22×D411yescharacteristic
811C24C22×D411yescharacteristic
812C24C22×D411yescharacteristic
813#41—44no—
814#41—82no—
815#41—82no—
816#41—82no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—42no—
830C2×Q8—42no—
831C2×Q8—81no—
832C2×Q8—81no—
833C2×Q8—81no—
834C2×Q8—81no—
835C2×Q8—81no—
836C2×Q8—81no—
837C2×Q8—81no—
838C2×D4—22no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—41no—
846C2×D4—41no—
847C2×D4—41no—
848C2×D4—41no—
849C2×D4—41no—
850C2×D4—41no—
851C2×D4—41no—
852C2×D4—41no—
853C2×D4—42no—
854C2×D4—42no—
855C2×D4—42no—
856C2×D4—81no—
857C2×D4—81no—
858C2×D4—81no—
859C2×D4—81no—
860C2×D4—81no—
861C2×D4—81no—
862C2×D4—81no—
863C2×D4—81no—
864C2×D4—81no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—24no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—41no—
906C22×C4—41no—
907C22×C4—41no—
908C22×C4—41no—
909C22×C4—41no—
910C22×C4—41no—
911C22×C4—41no—
912C22×C4—41no—
913C22×C4—41no—
914C22×C4—42no—
915C22×C4—44no—
916C22×C4—44no—
917C22×C4—44no—
918C22×C4—44no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C2511yescharacteristic
940Q16—82no—
941SD16—82no—
942M16—82no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C4⋊C4—24no—
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—21no—
992C4⋊C4—41no—
993C4⋊C4—41no—
994C4⋊C4—41no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4H(5,𝔽2)12yes—
1015C4⋊C4H(5,𝔽2)12yes—
1016C22⋊C4—22no—
1017C22⋊C4—41no—
1018C22⋊C4—41no—
1019C22⋊C4—41no—
1020C22⋊C4—41no—
1021C22⋊C4—41no—
1022C22⋊C4—41no—
1023C22⋊C4—41no—
1024C22⋊C4—41no—
1025C22⋊C4—41no—
1026C22⋊C4—41no—
1027C22⋊C4—41no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—42no—
1069C42—42no—
1070C42—42no—
1071C42—42no—
1072C42—42no—
1073C42—42no—
1074C42—81no—
1075C42—81no—
1076C42—81no—
1077C42—81no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—44no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—82no—
1114C23—82no—
1115C23—82no—
1116C23—82no—
1117C23—82no—
1118C23—82no—
1119C23#57512yes—
1120C23C23×D411yescharacteristic
1121Q8—41no—
1122Q8—41no—
1123Q8—41no—
1124Q8—41no—
1125Q8—41no—
1126Q8—41no—
1127Q8—41no—
1128Q8—41no—
1129Q8—162no—
1130Q8—162no—
1131Q8—162no—
1132D4—44no—
1133D4—41no—
1134D4—41no—
1135D4—41no—
1136D4—41no—
1137D4—82no—
1138D4—82no—
1139D4—84no—
1140D4—162no—
1141D4—162no—
1142D4—162no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—22no—
1157C2×C4—22no—
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—44no—
1176C2×C4—44no—
1177C2×C4—44no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—84no—
1238C2×C4—84no—
1239C2×C4—84no—
1240C2×C4—162no—
1241C2×C4C2×H(5,𝔽2)11yescharacteristic
1242C2×C4C2×H(5,𝔽2)11yescharacteristic
1243C2×C4#58511yescharacteristic
1244C2×C4#58511yescharacteristic
1245C2×C4#58511yescharacteristic
1246C2×C4#58511yescharacteristic
1247C8—41no—
1248C8—41no—
1249C8—41no—
1250C8—41no—
1251C8—41no—
1252C8—41no—
1253C8—41no—
1254C8—41no—
1255C22—22no—
1256C22—22no—
1257C22—22no—
1258C22—41no—
1259C22—41no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22—41no—
1269C22—41no—
1270C22—41no—
1271C22—41no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—41no—
1280C22—41no—
1281C22—41no—
1282C22—41no—
1283C22—88no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22#348411yescharacteristic
1292C22#348511yescharacteristic
1293C22#348511yescharacteristic
1294C22C2×#57511yescharacteristic
1295C22#358511yescharacteristic
1296C22#358611yescharacteristic
1297C22#358611yescharacteristic
1298C4—41no—
1299C4—41no—
1300C4—41no—
1301C4—41no—
1302C4—41no—
1303C4—41no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—42no—
1309C4—42no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4#352911yescharacteristic
1324C4#354011yescharacteristic
1325C4#354011yescharacteristic
1326C4#354011yescharacteristic
1327C2—42no—
1328C2—81no—
1329C2—81no—
1330C2—81no—
1331C2—161no—
1332C2#4544211yescharacteristic
1333C2#6157811yescharacteristic
1334C2#6164711yescharacteristic
1335C2#6171411yescharacteristic
1336C2#6171511yescharacteristic
1337C2#6178011yescharacteristic
1338C2#6178111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#45601C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#120 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #36516C2semidirect
3. #32985C2semidirect
4. #32981C2semidirect
5. #32711C2semidirect
6. #32709C2semidirect
7. #32275C2semidirect
8. #32068C2semidirect
9. #32064C2semidirect
10. #31767C2semidirect
11. #31763C2semidirect
12. #31679C2semidirect
13. #31347C2semidirect
14. #31343C2semidirect
15. #31045C2semidirect
16. #31038C2semidirect
17. #30802C2semidirect
18. #30798C2semidirect
19. #27345C2semidirect
20. #27343C2semidirect
21. #26811C2semidirect
22. #26809C2semidirect
23. #26750C2semidirect
24. #26748C2semidirect
25. #26314C2semidirect
26. #26313C2semidirect
27. #25712C2semidirect
28. #24891C2semidirect
29. #24889C2semidirect
30. #23981C2semidirect
31. #23309C2semidirect
34. C2×#501C22semidirect
39. C2×#479C22semidirect
40. C2×#452C22semidirect
41. C2×#417C22semidirect
85. #2097C22semidirect
86. #2092C22semidirect
90. #2077C22semidirect
91. #2077C22semidirect
93. #2076C22semidirect
94. #2076C22semidirect
97. #2074C22semidirect
98. #2073C22semidirect
99. #2068C22semidirect
100. #2068C22semidirect
101. #2065C22semidirect
102. #2065C22semidirect
103. #2059C22semidirect
104. #2059C22semidirect
105. #2058C22semidirect
106. #2057C22semidirect
107. #2056C22semidirect
108. #2055C22semidirect
113. #2036C22semidirect
119. #2035C22semidirect
123. #2024C22semidirect
124. #2024C22semidirect
125. #2024C22semidirect
126. #2023C22semidirect
133. #1993C22semidirect
134. #1993C22semidirect
135. #1988C22semidirect
136. #1988C22semidirect
137. #1987C22semidirect
138. #1973C22semidirect
139. #1971C22semidirect
143. #1949C22semidirect
144. #1949C22semidirect
145. #1936C22semidirect
146. #1936C22semidirect
147. #1935C22semidirect
148. #1935C22semidirect
149. #1928C22semidirect
150. #1928C22semidirect
151. #1927C22semidirect
152. #1927C22semidirect
153. #1926C22semidirect
154. #1925C22semidirect
161. #1921C22semidirect
162. #1920C22semidirect
163. #1919C22semidirect
164. #1918C22semidirect
165. #1894C22semidirect
166. #1880C22semidirect
167. #1878C22semidirect
185. #1853C22semidirect
188. #1852C22semidirect
193. #1823C22semidirect
194. #1809C22semidirect
195. #1809C22semidirect
196. #1788C22semidirect
197. #1788C22semidirect
200. #1776C22semidirect
201. #1776C22semidirect
202. #1763C22semidirect

Maximal subgroups

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

subgroupindex
#456012
#365162
#329852
#329812
#327112
#327092
#322752
#320682
#320642
#317672
#317632
#316792
#313472
#313432
#310452
#310382
#308022
#307982
#273452
#273432
#268112
#268092
#267502
#267482
#263142
#263132
#257122
#248912
#248892
#239812
#233092