Finite Group Databasebeta

← #6591631

Subgroups — #6591631

Order 512.

2038 conjugacy classes of subgroups.

The subgroup lattice has 1402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3321C211yesmaximal, characteristic
2C2×#3316C211yesmaximal, characteristic, complemented
3#39489C211yesmaximal, characteristic, complemented
4#34312C211yesmaximal, characteristic, complemented
5#33196C211yesmaximal, characteristic, complemented
6#32919C211yesmaximal, characteristic, complemented
7#32918C211yesmaximal, characteristic, complemented
8#28726C211yesmaximal, characteristic, complemented
9#28256C211yesmaximal, characteristic, complemented
10#27657C211yesmaximal, characteristic, complemented
11#27654C211yesmaximal, characteristic, complemented
12#25336C211yesmaximal, characteristic, complemented
13#25335C211yesmaximal, characteristic, complemented
14#25226C211yesmaximal, characteristic, complemented
15#25221C211yesmaximal, characteristic, complemented
16#25211C211yesmaximal, characteristic, complemented
17#25204C211yesmaximal, characteristic, complemented
18#24831C211yesmaximal, characteristic, complemented
19#24828C211yesmaximal, characteristic, complemented
20#24769C211yesmaximal, characteristic, complemented
21#24767C211yesmaximal, characteristic, complemented
22#24542C211yesmaximal, characteristic, complemented
23#24540C211yesmaximal, characteristic, complemented
24#24534C211yesmaximal, characteristic, complemented
25#24528C211yesmaximal, characteristic, complemented
26#22652C211yesmaximal, characteristic, complemented
27#22497C211yesmaximal, characteristic, complemented
28#22492C211yesmaximal, characteristic, complemented
29#21508C211yesmaximal, characteristic, complemented
30#20652C211yesmaximal, characteristic, complemented
31#20651C211yesmaximal, characteristic, complemented
32C2×#555C2211yescharacteristic
33C2×#554C2211yescharacteristic
34C2×#548C2211yescharacteristic
35C2×#520C2211yescharacteristic
36C2×#519C2211yescharacteristic
37#3321—28no—
38#3316—28no—
39C2×#489C2211yescharacteristic
40C2×#489C2211yescharacteristic
41C2×#481C2211yescharacteristic
42C2×#485C2211yescharacteristic
43C2×#482C2211yescharacteristic
44C2×#483C2211yescharacteristic
45C2×#475C2211yescharacteristic
46C2×#475C2211yescharacteristic
47C2×#470C2211yescharacteristic
48C2×#469C2211yescharacteristic
49C2×#465C2211yescharacteristic
50C2×#465C2211yescharacteristic
51C2×#464C2211yescharacteristic
52C2×#464C2211yescharacteristic
53C2×#464C2211yescharacteristic
54C2×#463C2211yescharacteristic
55C2×#463C2211yescharacteristic
56C2×#452C2211yescharacteristic
57C2×#449C2211yescharacteristic
58C2×#451C2211yescharacteristic
59C2×#448C2211yescharacteristic
60C2×#441C2211yescharacteristic
61C2×#440C2211yescharacteristic
62C2×#435C2211yescharacteristic
63C2×#435C2211yescharacteristic
64C2×#424C2211yescharacteristic
65C2×#424C2211yescharacteristic
66C2×#417C2211yescharacteristic
67C2×#419C2211yescharacteristic
68C2×#416C2211yescharacteristic
69C22×#103C2211yescharacteristic
70#2868C2211yescharacteristic
71#2674—21no—
72#2674—21no—
73#2674—21no—
74#2674—21no—
75#2620C2211yescharacteristic
76#2620C2211yescharacteristic
77#2567C2211yescharacteristic
78#2563C2211yescharacteristic
79#2501C2211yescharacteristic
80#2501C2211yescharacteristic
81#2499C2211yescharacteristic
82#2499C2211yescharacteristic
83#2441—21no—
84#2441—21no—
85#2422—21no—
86#2422—21no—
87#2367—21no—
88#2367C2211yescharacteristic
89#2363—21no—
90#2363C2211yescharacteristic
91#2360—21no—
92#2360C2211yescharacteristic
93#2352—21no—
94#2352C2211yescharacteristic
95#2351C2211yescharacteristic
96#2341C2211yescharacteristic
97Q8×C22⋊C4C2211yescharacteristic
98#2324—21no—
99#2324C2211yescharacteristic
100#2323—21no—
101#2323C2211yescharacteristic
102#2317C2211yescharacteristic
103#2317C2211yescharacteristic
104C4×#124—21no—
105C4×#124C2211yescharacteristic
106C4×#124C2211yescharacteristic
107#2293—21no—
108#2293C2211yescharacteristic
109C42×Q8C2211yescharacteristic
110#2085C2211yescharacteristic
111#2085C2211yescharacteristic
112#2084C2211yescharacteristic
113#2084C2211yescharacteristic
114#2074C2211yescharacteristic
115#2073C2211yescharacteristic
116#2072C2211yescharacteristic
117#2072C2211yescharacteristic
118#2072C2211yescharacteristic
119#2071C2211yescharacteristic
120#2071C2211yescharacteristic
121#2071C2211yescharacteristic
122#2066C2211yescharacteristic
123#2066C2211yescharacteristic
124#2065C2211yescharacteristic
125#2065C2211yescharacteristic
126#2056C2211yescharacteristic
127#2056C2211yescharacteristic
128#2055C2211yescharacteristic
129#2055C2211yescharacteristic
130#2055C2211yescharacteristic
131#2055C2211yescharacteristic
132#2054C2211yescharacteristic
133#2054C2211yescharacteristic
134#1993C2211yescharacteristic
135#1993C2211yescharacteristic
136#1988C2211yescharacteristic
137#1988C2211yescharacteristic
138#1983C2211yescharacteristic
139#1949C2211yescharacteristic
140#1948C2211yescharacteristic
141#1948C2211yescharacteristic
142#1948C2211yescharacteristic
143#1948C2211yescharacteristic
144#1940C2211yescharacteristic
145#1940C2211yescharacteristic
146#1928C2211yescharacteristic
147#1926C2211yescharacteristic
148#1895C2211yescharacteristic
149#1894C2211yescharacteristic
150#1893C2211yescharacteristic
151#1892C2211yescharacteristic
152#1880C2211yescharacteristic
153#1880C2211yescharacteristic
154#1880C2211yescharacteristic
155#1880C2211yescharacteristic
156#1879C2211yescharacteristic
157#1878C2211yescharacteristic
158#1878C2211yescharacteristic
159#1878C2211yescharacteristic
160#1878C2211yescharacteristic
161#1877C2211yescharacteristic
162#1875C2211yescharacteristic
163#1874C2211yescharacteristic
164#1873C2211yescharacteristic
165#1872C2211yescharacteristic
166#1851C2211yescharacteristic
167#1851C2211yescharacteristic
168#1850C2211yescharacteristic
169#1850C2211yescharacteristic
170#1842C2211yescharacteristic
171#1825C2211yescharacteristic
172#1825C2211yescharacteristic
173#1824C2211yescharacteristic
174#1823C2211yescharacteristic
175#1805C2211yescharacteristic
176#1805C2211yescharacteristic
177#1805C2211yescharacteristic
178#1805C2211yescharacteristic
179#1805C2211yescharacteristic
180#1805C2211yescharacteristic
181#1804C2211yescharacteristic
182#1804C2211yescharacteristic
183#1804C2211yescharacteristic
184#1803C2211yescharacteristic
185#1803C2211yescharacteristic
186#1803C2211yescharacteristic
187#1803C2211yescharacteristic
188#1803C2211yescharacteristic
189#1803C2211yescharacteristic
190#1803C2211yescharacteristic
191#1803C2211yescharacteristic
192#1803C2211yescharacteristic
193#1802C2211yescharacteristic
194#1802C2211yescharacteristic
195#1802C2211yescharacteristic
196#1798C2211yescharacteristic
197#1798C2211yescharacteristic
198#1767C2211yescharacteristic
199#1763C2211yescharacteristic
200#1762C2211yescharacteristic
201#1736C2211yescharacteristic
202#1736C2211yescharacteristic
203#1735C2211yescharacteristic
204C2×#340C2211yescharacteristic
205C22×#41C2311yescharacteristic
206C23×Q8C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×D8C2311yescharacteristic
213C22×M16C2311yescharacteristic
214C22×M16C2311yescharacteristic
215C23×C8C2311yescharacteristic
216C23×C8C2311yescharacteristic
217#555—24no—
218#555—24no—
219#554—24no—
220#554—24no—
221#548—24no—
222#548D418yes—
223C2×C4⋊Q8—21no—
224C2×C4⋊Q8—21no—
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227C2×#125—21no—
228C2×#124—21no—
229C2×#124—21no—
230C2×#124—21no—
231C2×#124C2311yescharacteristic
232C2×#124C2311yescharacteristic
233C2×#123—21no—
234C2×#123—21no—
235C2×#123—21no—
236C2×#123—21no—
237C2×C22⋊Q8—21no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8C2311yescharacteristic
241C2×C22⋊Q8C2311yescharacteristic
242C2×C22⋊Q8C2311yescharacteristic
243C2×#121—21no—
244C2×#121—21no—
245C2×#121C2311yescharacteristic
246C2×#121C2311yescharacteristic
247C2×#121C2311yescharacteristic
248#520—24no—
249#520—42no—
250#519—24no—
251#519—42no—
252C2×C4×Q8—21no—
253C2×C4×Q8—21no—
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2311yescharacteristic
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2311yescharacteristic
259C2×C4×Q8C2311yescharacteristic
260C2×C4×Q8C2311yescharacteristic
261C2×C4×Q8C2311yescharacteristic
262C2×C4×D4—21no—
263C2×C4×D4—21no—
264C2×C4×D4—21no—
265C2×C4×D4—21no—
266C2×C4×D4C2311yescharacteristic
267C2×C4×D4C2311yescharacteristic
268C2×C4×D4C2311yescharacteristic
269C2×C4×D4C2311yescharacteristic
270C2×#117—21no—
271C2×#117—21no—
272C2×#117—21no—
273C2×#117—21no—
274C2×#117C2311yescharacteristic
275C2×#117C2311yescharacteristic
276C2×#117C2311yescharacteristic
277C2×#117C2311yescharacteristic
278C2×#117C2311yescharacteristic
279C22×C4⋊C4—21no—
280C22×C4⋊C4C2311yescharacteristic
281C22×C4⋊C4C2311yescharacteristic
282C22×C4⋊C4C2311yescharacteristic
283#489—24no—
284#489—24no—
285#485—24no—
286#483—24no—
287#482—24no—
288#481—24no—
289#475—24no—
290#475—24no—
291#470—24no—
292#469—24no—
293#465—24no—
294#465—24no—
295#464—24no—
296#464—24no—
297#464—42no—
298#463—24no—
299#463—42no—
300#452—24no—
301#451—24no—
302#449—24no—
303#448—24no—
304#441—24no—
305#440—24no—
306#435—24no—
307#435—24no—
308C2×#107C2311yescharacteristic
309C2×#106C2311yescharacteristic
310C2×#106C2311yescharacteristic
311C2×#106C2311yescharacteristic
312C2×#106C2311yescharacteristic
313C2×#106C2311yescharacteristic
314#424—42no—
315#424—42no—
316C2×C4⋊C8C2311yescharacteristic
317C2×C4⋊C8C2311yescharacteristic
318C2×C4⋊C8C2311yescharacteristic
319C2×C4⋊C8C2311yescharacteristic
320C2×C4⋊C8C2311yescharacteristic
321C2×C4⋊C8C2311yescharacteristic
322C2×C4⋊C8C2311yescharacteristic
323C2×C4⋊C8C2311yescharacteristic
324C2×C4⋊C8C2311yescharacteristic
325C2×C4⋊C8C2311yescharacteristic
326C2×C4⋊C8C2311yescharacteristic
327C2×C4⋊C8C2311yescharacteristic
328#419—24no—
329#417—24no—
330#416—24no—
331C2×#103—24no—
332C2×#103C2311yescharacteristic
333C2×#103C2311yescharacteristic
334C2×#103C2311yescharacteristic
335C2×#103C2311yescharacteristic
336C2×#103C2311yescharacteristic
337C2×#103C2311yescharacteristic
338C2×#103C2311yescharacteristic
339C2×#103C2311yescharacteristic
340C2×#103C2311yescharacteristic
341C2×#103C2311yescharacteristic
342C2×#103C2311yescharacteristic
343C2×#103C2311yescharacteristic
344C2×#103C2311yescharacteristic
345C2×#103C2311yescharacteristic
346C2×#103C2311yescharacteristic
347C2×#103C2311yescharacteristic
348C2×#103C2311yescharacteristic
349C2×#102C2311yescharacteristic
350C2×#102C2311yescharacteristic
351C2×#102C2311yescharacteristic
352C2×#102C2311yescharacteristic
353C2×#102C2311yescharacteristic
354C2×#102C2311yescharacteristic
355C2×#102C2311yescharacteristic
356C2×#102C2311yescharacteristic
357C2×#102C2311yescharacteristic
358C2×#102C2311yescharacteristic
359C2×#102C2311yescharacteristic
360C2×C22⋊C8C2311yescharacteristic
361C2×C22⋊C8C2311yescharacteristic
362C2×C22⋊C8C2311yescharacteristic
363C2×C22⋊C8C2311yescharacteristic
364C2×#97C2311yescharacteristic
365C2×#97C2311yescharacteristic
366#399—21no—
367#399—21no—
368#399—21no—
369#399—21no—
370#397—21no—
371#397—21no—
372#397—21no—
373#397—21no—
374#396—21no—
375#396—21no—
376#396—21no—
377#396—21no—
378#395—21no—
379#395—21no—
380#394—21no—
381#394—21no—
382#394—21no—
383#394—21no—
384#393—21no—
385#393—21no—
386#391—21no—
387#391—21no—
388#391C2311yescharacteristic
389#391C2311yescharacteristic
390#391C2311yescharacteristic
391#391C2311yescharacteristic
392#391C2311yescharacteristic
393#390—21no—
394#390—21no—
395#390—21no—
396#390—21no—
397#390D411yescharacteristic
398#390D411yescharacteristic
399#390C2311yescharacteristic
400#390C2311yescharacteristic
401#390C2311yescharacteristic
402#390C2311yescharacteristic
403#390C2311yescharacteristic
404#389—21no—
405#389—21no—
406#389—21no—
407#389—21no—
408#389—21no—
409#389—21no—
410#389—21no—
411#389—21no—
412#389—21no—
413#389—21no—
414#389D411yescharacteristic
415#389D411yescharacteristic
416#389C2311yescharacteristic
417#389C2311yescharacteristic
418#388—21no—
419#388—21no—
420#388—21no—
421#388—21no—
422#388—21no—
423#388—21no—
424#388—21no—
425#388—21no—
426#388—21no—
427#388—21no—
428#388—21no—
429#388D411yescharacteristic
430#388D411yescharacteristic
431#388D411yescharacteristic
432#388D411yescharacteristic
433#387—21no—
434#387—21no—
435#387—21no—
436#387—21no—
437#387—21no—
438#387—21no—
439#387—21no—
440#386—21no—
441#386—21no—
442#386—21no—
443#385—21no—
444#385—21no—
445#385—21no—
446#385—21no—
447#385—21no—
448#385—21no—
449#385—21no—
450#384—21no—
451#384—21no—
452#384C2311yescharacteristic
453#384C2311yescharacteristic
454#384C2311yescharacteristic
455#384C2311yescharacteristic
456#384C2311yescharacteristic
457#384C2311yescharacteristic
458#382—21no—
459#382C2311yescharacteristic
460#382C2311yescharacteristic
461#382C2311yescharacteristic
462#382C2311yescharacteristic
463#380—21no—
464#380—21no—
465#380—21no—
466#380—21no—
467#380C2311yescharacteristic
468#380C2311yescharacteristic
469C4×C4⋊C4—21no—
470C4×C4⋊C4—21no—
471C4×C4⋊C4—21no—
472C4×C4⋊C4—21no—
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⋊C4—21no—
487C4×C22⋊C4C2311yescharacteristic
488C4×C22⋊C4C2311yescharacteristic
489C43—21no—
490C43C2311yescharacteristic
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#340C2311yescharacteristic
506#340C2311yescharacteristic
507#340C2311yescharacteristic
508#340C2311yescharacteristic
509#340C2311yescharacteristic
510#340C2311yescharacteristic
511#340C2311yescharacteristic
512#340C2311yescharacteristic
513#340C2311yescharacteristic
514#340C2311yescharacteristic
515#336C2311yescharacteristic
516#336C2311yescharacteristic
517#336C2311yescharacteristic
518#336C2311yescharacteristic
519#336C2311yescharacteristic
520#336C2311yescharacteristic
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—41no—
525C2×#41—41no—
526C2×#41C2×D414yes—
527C22×Q8—21no—
528C22×Q8—21no—
529C22×Q8—21no—
530C22×Q8—22no—
531C22×Q8—22no—
532C22×Q8—22no—
533C22×Q8—41no—
534C22×Q8—41no—
535C22×Q8C2×D414yes—
536C22×Q8C2411yescharacteristic
537C22×Q8C2411yescharacteristic
538C22×Q8C2411yescharacteristic
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4—21no—
543C22×D4C2×D411yescharacteristic
544C22×D4C2411yescharacteristic
545C22×D4C2411yescharacteristic
546C23×C4—21no—
547C23×C4—21no—
548C23×C4—21no—
549C23×C4—21no—
550C23×C4—21no—
551C23×C4—21no—
552C23×C4—21no—
553C23×C4—21no—
554C23×C4C2411yescharacteristic
555C23×C4C2411yescharacteristic
556C2×Q16—22no—
557C2×Q16—22no—
558C2×Q16—22no—
559C2×Q16—22no—
560C2×Q16—41no—
561C2×Q16—41no—
562C2×SD16—22no—
563C2×SD16—22no—
564C2×SD16—22no—
565C2×SD16—22no—
566C2×SD16—22no—
567C2×SD16—41no—
568C2×SD16—41no—
569C2×SD16—41no—
570C2×SD16—41no—
571C2×D8—22no—
572C2×D8—41no—
573C2×D8—41no—
574C2×M16—22no—
575C2×M16—22no—
576C2×M16—41no—
577C2×M16—41no—
578C2×M16—41no—
579C2×M16—41no—
580C22×C8—22no—
581C22×C8—22no—
582C22×C8—41no—
583C22×C8—41no—
584C22×C8—41no—
585C22×C8—41no—
586C22×C8C2411yescharacteristic
587C22×C8C2411yescharacteristic
588C22×C8C2411yescharacteristic
589C22×C8C2411yescharacteristic
590C22×C8C2411yescharacteristic
591C22×C8C2411yescharacteristic
592C22×C8C2411yescharacteristic
593C22×C8C2411yescharacteristic
594C4⋊Q8—22no—
595C4⋊Q8—22no—
596C4⋊Q8—22no—
597C4⋊Q8—22no—
598C4⋊Q8—82no—
599C4⋊Q8—82no—
600#125—44no—
601#124—28no—
602#124—22no—
603#124—22no—
604#124—22no—
605#124—44no—
606#124—44no—
607#124C2×D414yes—
608#123—82no—
609#123—82no—
610#123—82no—
611#123—82no—
612C22⋊Q8—22no—
613C22⋊Q8—28no—
614C22⋊Q8—22no—
615C22⋊Q8—22no—
616C22⋊Q8—22no—
617C22⋊Q8—22no—
618C22⋊Q8—44no—
619C22⋊Q8—44no—
620C22⋊Q8C2×D414yes—
621#121—28no—
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—22no—
627#121—44no—
628#121C2×D414yes—
629C4×Q8—22no—
630C4×Q8—22no—
631C4×Q8—22no—
632C4×Q8—22no—
633C4×Q8—22no—
634C4×Q8—22no—
635C4×Q8—22no—
636C4×Q8—22no—
637C4×Q8—22no—
638C4×Q8—22no—
639C4×Q8—41no—
640C4×Q8—41no—
641C4×Q8—41no—
642C4×Q8—41no—
643C4×Q8—44no—
644C4×Q8—44no—
645C4×Q8C2×D414yes—
646C4×Q8#4114yes—
647C4×D4—28no—
648C4×D4—22no—
649C4×D4—22no—
650C4×D4—22no—
651C4×D4—22no—
652C4×D4—22no—
653C4×D4—44no—
654C4×D4—41no—
655C4×D4—44no—
656C4×D4—44no—
657C4×D4C2×D414yes—
658C4×D4#4114yes—
659#117—22no—
660#117—22no—
661#117—22no—
662#117—22no—
663#117—22no—
664#117—22no—
665#117—22no—
666#117—22no—
667#117—22no—
668#117—44no—
669#117—44no—
670#117—44no—
671#117—41no—
672#117—44no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—21no—
682C2×C4⋊C4—21no—
683C2×C4⋊C4—21no—
684C2×C4⋊C4—21no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—21no—
688C2×C4⋊C4—21no—
689C2×C4⋊C4—21no—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C4⋊C4—21no—
693C2×C4⋊C4—21no—
694C2×C4⋊C4—21no—
695C2×C4⋊C4—21no—
696C2×C4⋊C4—21no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—21no—
700C2×C4⋊C4—21no—
701C2×C4⋊C4—21no—
702C2×C4⋊C4—21no—
703C2×C4⋊C4—21no—
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4—21no—
707C2×C4⋊C4—21no—
708C2×C4⋊C4—41no—
709C2×C4⋊C4—44no—
710C2×C4⋊C4C2×D411yescharacteristic
711C2×C4⋊C4C2×D411yescharacteristic
712C2×C4⋊C4C2×D411yescharacteristic
713C2×C4⋊C4C2×D411yescharacteristic
714C2×C4⋊C4C2×D411yescharacteristic
715C2×C4⋊C4C2×D411yescharacteristic
716C2×C4⋊C4C2×D411yescharacteristic
717C2×C4⋊C4C2411yescharacteristic
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2411yescharacteristic
721C2×C4⋊C4C2411yescharacteristic
722C2×C4⋊C4C2411yescharacteristic
723C2×C4⋊C4C2411yescharacteristic
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2411yescharacteristic
726C2×C4⋊C4C2411yescharacteristic
727C2×C4⋊C4C2411yescharacteristic
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—21no—
733C2×C22⋊C4—21no—
734C2×C22⋊C4—21no—
735C2×C22⋊C4—21no—
736C2×C22⋊C4—21no—
737C2×C22⋊C4—21no—
738C2×C22⋊C4—21no—
739C2×C22⋊C4—21no—
740C2×C22⋊C4—21no—
741C2×C22⋊C4—21no—
742C2×C22⋊C4—21no—
743C2×C22⋊C4—21no—
744C2×C22⋊C4—21no—
745C2×C22⋊C4—21no—
746C2×C22⋊C4—21no—
747C2×C22⋊C4—21no—
748C2×C22⋊C4—21no—
749C2×C22⋊C4—21no—
750C2×C22⋊C4—21no—
751C2×C22⋊C4—21no—
752C2×C22⋊C4—21no—
753C2×C22⋊C4—21no—
754C2×C22⋊C4—21no—
755C2×C22⋊C4—21no—
756C2×C22⋊C4C2×D411yescharacteristic
757C2×C22⋊C4C2×D411yescharacteristic
758C2×C22⋊C4C2×D411yescharacteristic
759C2×C22⋊C4C2×D411yescharacteristic
760C2×C22⋊C4C2×D411yescharacteristic
761C2×C22⋊C4C2×D411yescharacteristic
762C2×C22⋊C4C2×D411yescharacteristic
763C2×C22⋊C4C2×D411yescharacteristic
764C2×C22⋊C4C2×D411yescharacteristic
765C2×C22⋊C4C2×D411yescharacteristic
766C2×C42—21no—
767C2×C42—21no—
768C2×C42—21no—
769C2×C42—21no—
770C2×C42—21no—
771C2×C42—21no—
772C2×C42—21no—
773C2×C42—21no—
774C2×C42—21no—
775C2×C42—21no—
776C2×C42—21no—
777C2×C42—21no—
778C2×C42—21no—
779C2×C42—21no—
780C2×C42C2×D411yescharacteristic
781C2×C42C2×D411yescharacteristic
782C2×C42C2×D411yescharacteristic
783C2×C42C2×D411yescharacteristic
784C2×C42C2411yescharacteristic
785C2×C42C2411yescharacteristic
786C2×C42C2411yescharacteristic
787C2×C42C2411yescharacteristic
788C2×C42C2411yescharacteristic
789#107—22no—
790#106—22no—
791#106—22no—
792#106—22no—
793#106—22no—
794#106—22no—
795C4⋊C8—22no—
796C4⋊C8—22no—
797C4⋊C8—22no—
798C4⋊C8—22no—
799C4⋊C8—22no—
800C4⋊C8—22no—
801C4⋊C8—41no—
802C4⋊C8—41no—
803C4⋊C8—41no—
804C4⋊C8—41no—
805C4⋊C8—41no—
806C4⋊C8—41no—
807#103—22no—
808#103—22no—
809#103—22no—
810#103—22no—
811#103—22no—
812#103—22no—
813#103—22no—
814#103—22no—
815#103—22no—
816#103—22no—
817#103—22no—
818#103—22no—
819#103—22no—
820#103—22no—
821#103—41no—
822#103—41no—
823#103—41no—
824#102—22no—
825#102—22no—
826#102—22no—
827#102—22no—
828#102—22no—
829#102—22no—
830#102—22no—
831#102—22no—
832#102—41no—
833#102—41no—
834#102—41no—
835C22⋊C8—22no—
836C22⋊C8—22no—
837C22⋊C8—22no—
838C22⋊C8—22no—
839#97—22no—
840#97—22no—
841#95—21no—
842#95—21no—
843#95—21no—
844#95—21no—
845#95—21no—
846#95—21no—
847#95—21no—
848#95—21no—
849#95—21no—
850#95—21no—
851#95—21no—
852#95—21no—
853#95—21no—
854#95—21no—
855#95—21no—
856#95—21no—
857#95—21no—
858#95—21no—
859#95—21no—
860#95—21no—
861#95—21no—
862#95—21no—
863#95—21no—
864#95—21no—
865#95—21no—
866#95C2×D411yescharacteristic
867#95C2×D411yescharacteristic
868#95C2×D411yescharacteristic
869#95C2×D411yescharacteristic
870#95C2×D411yescharacteristic
871#95C2×D411yescharacteristic
872C24—21no—
873C24—21no—
874C24C22×D411yescharacteristic
875C24C22×D411yescharacteristic
876#41—28no—
877#41—44no—
878#41—44no—
879#41—44no—
880C2×Q8—24no—
881C2×Q8—21no—
882C2×Q8—21no—
883C2×Q8—21no—
884C2×Q8—21no—
885C2×Q8—28no—
886C2×Q8—21no—
887C2×Q8—21no—
888C2×Q8—21no—
889C2×Q8—21no—
890C2×Q8—21no—
891C2×Q8—21no—
892C2×Q8—21no—
893C2×Q8—21no—
894C2×Q8—21no—
895C2×Q8—21no—
896C2×Q8—42no—
897C2×Q8—42no—
898C2×Q8—44no—
899C2×Q8—44no—
900C2×Q8—44no—
901C2×Q8—42no—
902C2×Q8—42no—
903C2×Q8—81no—
904C2×Q8—81no—
905C2×Q8—81no—
906C2×Q8—81no—
907C2×Q8C22×D412yes—
908C2×Q8C22×D412yes—
909C2×Q8C2×#4112yes—
910C2×Q82−1+412yes—
911C2×D4—24no—
912C2×D4—24no—
913C2×D4—21no—
914C2×D4—21no—
915C2×D4—21no—
916C2×D4—21no—
917C2×D4—21no—
918C2×D4—21no—
919C2×D4—21no—
920C2×D4—21no—
921C2×D4—21no—
922C2×D4—21no—
923C2×D4—21no—
924C2×D4—41no—
925C2×D4—41no—
926C2×D4—42no—
927C2×D4—42no—
928C2×D4—42no—
929C2×D4—42no—
930C2×D4—81no—
931C2×D4—81no—
932C2×D4—81no—
933C2×D4—81no—
934C2×D4—81no—
935C2×D4—81no—
936C2×D4#12114yes—
937C2×D4C22×D412yes—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—24no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—24no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—42no—
965C22×C4—42no—
966C22×C4—42no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—81no—
975C22×C4—81no—
976C22×C4—81no—
977C22×C4—81no—
978C22×C4—81no—
979C22×C4—81no—
980C22×C4—81no—
981C22×C4—81no—
982C22×C4—81no—
983C22×C4—81no—
984C22×C4C22×D411yescharacteristic
985C22×C4C22×D411yescharacteristic
986C22×C4C22×D411yescharacteristic
987C22×C4C22×D411yescharacteristic
988C22×C4C22×D411yescharacteristic
989C22×C4C22×D411yescharacteristic
990C22×C4C22×D411yescharacteristic
991C22×C4C22×D411yescharacteristic
992C22×C4C22×D411yescharacteristic
993C22×C4C22×D412yes—
994C22×C4C22×D412yes—
995C22×C4C22×D411yescharacteristic
996C22×C4C22×D411yescharacteristic
997C22×C4C22×D411yescharacteristic
998C22×C4C2×#4112yes—
999C22×C4C2×#4112yes—
1000C22×C4C2511yescharacteristic
1001Q16—44no—
1002Q16—82no—
1003SD16—44no—
1004SD16—82no—
1005SD16—82no—
1006D8—82no—
1007M16—82no—
1008M16—82no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—21no—
1027C2×C8—21no—
1028C2×C8—21no—
1029C2×C8—21no—
1030C2×C8—21no—
1031C2×C8—21no—
1032C2×C8—21no—
1033C2×C8—82no—
1034C2×C8—82no—
1035C4⋊C4—24no—
1036C4⋊C4—24no—
1037C4⋊C4—24no—
1038C4⋊C4—22no—
1039C4⋊C4—22no—
1040C4⋊C4—22no—
1041C4⋊C4—22no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—21no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—21no—
1058C4⋊C4—21no—
1059C4⋊C4—21no—
1060C4⋊C4—21no—
1061C4⋊C4—21no—
1062C4⋊C4—41no—
1063C4⋊C4—41no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—42no—
1078C4⋊C4—42no—
1079C4⋊C4—42no—
1080C4⋊C4—42no—
1081C4⋊C4—81no—
1082C4⋊C4—81no—
1083C4⋊C4—81no—
1084C4⋊C4—81no—
1085C4⋊C4—81no—
1086C4⋊C4—81no—
1087C4⋊C4—81no—
1088C4⋊C4—81no—
1089C4⋊C4—81no—
1090C4⋊C4—81no—
1091C4⋊C4#12114yes—
1092C4⋊C4C22×D412yes—
1093C4⋊C4C2×#4112yes—
1094C22⋊C4—24no—
1095C22⋊C4—24no—
1096C22⋊C4—24no—
1097C22⋊C4—24no—
1098C22⋊C4—22no—
1099C22⋊C4—22no—
1100C22⋊C4—22no—
1101C22⋊C4—22no—
1102C22⋊C4—22no—
1103C22⋊C4—22no—
1104C22⋊C4—41no—
1105C22⋊C4—41no—
1106C22⋊C4—42no—
1107C22⋊C4—42no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—42no—
1113C22⋊C4—42no—
1114C22⋊C4—42no—
1115C22⋊C4—42no—
1116C22⋊C4—42no—
1117C22⋊C4—42no—
1118C22⋊C4—42no—
1119C22⋊C4—42no—
1120C22⋊C4—42no—
1121C22⋊C4—81no—
1122C22⋊C4—81no—
1123C22⋊C4—81no—
1124C22⋊C4—81no—
1125C22⋊C4—81no—
1126C22⋊C4—81no—
1127C22⋊C4—81no—
1128C22⋊C4—81no—
1129C22⋊C4—81no—
1130C22⋊C4#12114yes—
1131C22⋊C4#12114yes—
1132C42—24no—
1133C42—24no—
1134C42—22no—
1135C42—21no—
1136C42—21no—
1137C42—21no—
1138C42—21no—
1139C42—21no—
1140C42—21no—
1141C42—41no—
1142C42—41no—
1143C42—41no—
1144C42—42no—
1145C42—42no—
1146C42—42no—
1147C42—42no—
1148C42—42no—
1149C42—42no—
1150C42—42no—
1151C42—42no—
1152C42—42no—
1153C42—81no—
1154C42—81no—
1155C42—81no—
1156C42C22×D412yes—
1157C42C2×#4112yes—
1158C42C2×#4112yes—
1159C42H(5,𝔽2)12yes—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—21no—
1165C23—21no—
1166C23—21no—
1167C23—21no—
1168C23—21no—
1169C23—21no—
1170C23—21no—
1171C23—21no—
1172C23—22no—
1173C23—41no—
1174C23—41no—
1175C23—41no—
1176C23—41no—
1177C23—41no—
1178C23—41no—
1179C23—41no—
1180C23—41no—
1181C23—41no—
1182C23—41no—
1183C23—41no—
1184C23—41no—
1185C23—41no—
1186C23C2×#12112yes—
1187C23C2×#12112yes—
1188C23C23×D411yescharacteristic
1189Q8—22no—
1190Q8—22no—
1191Q8—22no—
1192Q8—22no—
1193Q8—22no—
1194Q8—48no—
1195Q8—41no—
1196Q8—41no—
1197Q8—41no—
1198Q8—41no—
1199Q8—41no—
1200Q8—41no—
1201Q8—162no—
1202Q8—162no—
1203Q8#54714yes—
1204D4—22no—
1205D4—22no—
1206D4—44no—
1207D4—48no—
1208D4—41no—
1209D4—41no—
1210D4—41no—
1211D4—41no—
1212D4—41no—
1213D4—41no—
1214D4—84no—
1215D4—162no—
1216D4—162no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—22no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—22no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—48no—
1261C2×C4—48no—
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—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—84no—
1299C2×C4—162no—
1300C2×C4—162no—
1301C2×C4—162no—
1302C2×C4—162no—
1303C2×C4—162no—
1304C2×C4C2×#12112yes—
1305C2×C4C2×#12112yes—
1306C2×C4C2×#12112yes—
1307C2×C4C2×#12112yes—
1308C2×C4#54612yes—
1309C2×C4#54612yes—
1310C2×C4#57712yes—
1311C2×C4C23×D411yescharacteristic
1312C2×C4C22×#4111yescharacteristic
1313C2×C4C22×#4111yescharacteristic
1314C2×C4C2×H(5,𝔽2)11yescharacteristic
1315C2×C4C2×2−1+411yescharacteristic
1316C2×C4#58511yescharacteristic
1317C8—41no—
1318C8—41no—
1319C8—41no—
1320C8—41no—
1321C8—41no—
1322C8—41no—
1323C8—41no—
1324C8—41no—
1325C22—22no—
1326C22—22no—
1327C22—22no—
1328C22—22no—
1329C22—22no—
1330C22—22no—
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—41no—
1335C22—41no—
1336C22—41no—
1337C22—41no—
1338C22—41no—
1339C22—42no—
1340C22—42no—
1341C22—42no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22C22×#12111yescharacteristic
1354C22C2×#54611yescharacteristic
1355C22#348911yescharacteristic
1356C22C2×#57711yescharacteristic
1357C22#358511yescharacteristic
1358C22#358611yescharacteristic
1359C22#358611yescharacteristic
1360C4—22no—
1361C4—22no—
1362C4—22no—
1363C4—22no—
1364C4—22no—
1365C4—22no—
1366C4—24no—
1367C4—22no—
1368C4—42no—
1369C4—41no—
1370C4—41no—
1371C4—41no—
1372C4—41no—
1373C4—41no—
1374C4—42no—
1375C4—42no—
1376C4—81no—
1377C4—81no—
1378C4—81no—
1379C4—81no—
1380C4—81no—
1381C4—81no—
1382C4—81no—
1383C4—81no—
1384C4—81no—
1385C4—81no—
1386C4C2×#54711yescharacteristic
1387C4#347511yescharacteristic
1388C4#349611yescharacteristic
1389C4#352011yescharacteristic
1390C2—42no—
1391C2—42no—
1392C2—82no—
1393C2—161no—
1394C2#3615311yescharacteristic
1395C2#6042711yescharacteristic
1396C2#6043111yescharacteristic
1397C2#6120211yescharacteristic
1398C2#6122211yescharacteristic
1399C2#6215711yescharacteristic
1400C2#6223011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3321C2
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
2. C2×#3316C2semidirect
3. #39489C2semidirect
4. #34312C2semidirect
5. #33196C2semidirect
6. #32919C2semidirect
7. #32918C2semidirect
8. #28726C2semidirect
9. #28256C2semidirect
10. #27657C2semidirect
11. #27654C2semidirect
12. #25336C2semidirect
13. #25335C2semidirect
14. #25226C2semidirect
15. #25221C2semidirect
16. #25211C2semidirect
17. #25204C2semidirect
18. #24831C2semidirect
19. #24828C2semidirect
20. #24769C2semidirect
21. #24767C2semidirect
22. #24542C2semidirect
23. #24540C2semidirect
24. #24534C2semidirect
25. #24528C2semidirect
26. #22652C2semidirect
27. #22497C2semidirect
28. #22492C2semidirect
29. #21508C2semidirect
30. #20652C2semidirect
31. #20651C2semidirect

Maximal subgroups

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

subgroupindex
C2×#33212
C2×#33162
#394892
#343122
#331962
#329192
#329182
#287262
#282562
#276572
#276542
#253362
#253352
#252262
#252212
#252112
#252042
#248312
#248282
#247692
#247672
#245422
#245402
#245342
#245282
#226522
#224972
#224922
#215082
#206522
#206512