Finite Group Databasebeta

← #6465934

Subgroups — #6465934

Order 512.

1958 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×#3181C211yesmaximal, characteristic, complemented
2C2×#3175C211yesmaximal, characteristic, complemented
3#35636C211yesmaximal, characteristic, complemented
4#35573C211yesmaximal, characteristic, complemented
5#28935C211yesmaximal, characteristic, complemented
6#28934C211yesmaximal, characteristic, complemented
7#28931C211yesmaximal, characteristic, complemented
8#28929C211yesmaximal, characteristic, complemented
9#28821C211yesmaximal, characteristic, complemented
10#28492C211yesmaximal, characteristic, complemented
11#28476C211yesmaximal, characteristic, complemented
12#28235C211yesmaximal, characteristic, complemented
13#27796C211yesmaximal, characteristic, complemented
14#27792C211yesmaximal, characteristic, complemented
15#27776C211yesmaximal, characteristic, complemented
16#27774C211yesmaximal, characteristic, complemented
17#25417C211yesmaximal, characteristic, complemented
18#25411C211yesmaximal, characteristic, complemented
19#25388C211yesmaximal, characteristic
20#25386C211yesmaximal, characteristic, complemented
21#23585C211yesmaximal, characteristic, complemented
22#23581C211yesmaximal, characteristic, complemented
23#23571C211yesmaximal, characteristic, complemented
24#23569C211yesmaximal, characteristic, complemented
25#21703C211yesmaximal, characteristic, complemented
26#21542C211yesmaximal, characteristic, complemented
27#21528C211yesmaximal, characteristic, complemented
28#21516C211yesmaximal, characteristic, complemented
29#21509C211yesmaximal, characteristic, complemented
30#20504C211yesmaximal, characteristic, complemented
31#20493C211yesmaximal, characteristic, complemented
32C2×#542C2211yescharacteristic
33C2×#542C2211yescharacteristic
34C2×#533C2211yescharacteristic
35C2×#529C2211yescharacteristic
36#3181—28no—
37#3175—28no—
38C2×#501C2211yescharacteristic
39C2×#500C2211yescharacteristic
40C2×#497C2211yescharacteristic
41C2×#497C2211yescharacteristic
42C2×#495C2211yescharacteristic
43C2×#491C2211yescharacteristic
44C2×#489C2211yescharacteristic
45C2×#489C2211yescharacteristic
46C2×#489C2211yescharacteristic
47C2×#470C2211yescharacteristic
48C2×#468C2211yescharacteristic
49C2×#468C2211yescharacteristic
50C2×#467C2211yescharacteristic
51C2×#467C2211yescharacteristic
52C2×#467C2211yescharacteristic
53C2×#466C2211yescharacteristic
54C2×#465C2211yescharacteristic
55C2×#465C2211yescharacteristic
56C2×#465C2211yescharacteristic
57C2×#462C2211yescharacteristic
58C2×#463C2211yescharacteristic
59C2×#441C2211yescharacteristic
60C2×#441C2211yescharacteristic
61C2×#440C2211yescharacteristic
62C2×#440C2211yescharacteristic
63C2×#440C2211yescharacteristic
64C2×#440C2211yescharacteristic
65C2×C4×Q16C2211yescharacteristic
66C2×C4×Q16C2211yescharacteristic
67C2×C4×SD16C2211yescharacteristic
68C2×C4×SD16C2211yescharacteristic
69C2×C4×D8C2211yescharacteristic
70C2×#435C2211yescharacteristic
71C2×C8×D4C2211yescharacteristic
72C2×#405C2211yescharacteristic
73C22×#97C2211yescharacteristic
74#2610—21no—
75#2604—21no—
76#2602—21no—
77#2601—21no—
78#2564—21no—
79#2558—21no—
80#2557—21no—
81#2556—21no—
82#2553—21no—
83#2551C2211yescharacteristic
84#2550C2211yescharacteristic
85#2547C2211yescharacteristic
86#2545—21no—
87#2545C2211yescharacteristic
88#2542C2211yescharacteristic
89#2540C2211yescharacteristic
90#2538C2211yescharacteristic
91#2535C2211yescharacteristic
92#2521—21no—
93#2499—21no—
94#2498—21no—
95#2496—21no—
96#2492C2211yescharacteristic
97#2492C2211yescharacteristic
98#2491C2211yescharacteristic
99#2489C2211yescharacteristic
100#2461—21no—
101#2452—21no—
102#2429C2211yescharacteristic
103#2427C2211yescharacteristic
104#2427C2211yescharacteristic
105#2426C2211yescharacteristic
106#2327C2211yescharacteristic
107#2326C2211yescharacteristic
108#2323C2211yescharacteristic
109#2323C2211yescharacteristic
110C4×C22⋊Q8C2211yescharacteristic
111C4×#121C2211yescharacteristic
112#2290C2211yescharacteristic
113#2276C2211yescharacteristic
114#2275C2211yescharacteristic
115#2059C2211yescharacteristic
116#2058C2211yescharacteristic
117#2057C2211yescharacteristic
118#2057C2211yescharacteristic
119#2043C2211yescharacteristic
120#2042C2211yescharacteristic
121#2042C2211yescharacteristic
122#2042C2211yescharacteristic
123#2036C2211yescharacteristic
124#2036C2211yescharacteristic
125#2036C2211yescharacteristic
126#2036C2211yescharacteristic
127#2035C2211yescharacteristic
128#2034C2211yescharacteristic
129#2034C2211yescharacteristic
130#2033C2211yescharacteristic
131#2025C2211yescharacteristic
132#2024C2211yescharacteristic
133#2024C2211yescharacteristic
134#2024C2211yescharacteristic
135#2016C2211yescharacteristic
136#2015C2211yescharacteristic
137#2015C2211yescharacteristic
138#2012C2211yescharacteristic
139#2001C2211yescharacteristic
140#2001C2211yescharacteristic
141#2001C2211yescharacteristic
142#2001C2211yescharacteristic
143#2000C2211yescharacteristic
144#2000C2211yescharacteristic
145#2000C2211yescharacteristic
146#1999C2211yescharacteristic
147#1983C2211yescharacteristic
148#1981C2211yescharacteristic
149#1973C2211yescharacteristic
150#1973C2211yescharacteristic
151#1971C2211yescharacteristic
152#1969C2211yescharacteristic
153#1969C2211yescharacteristic
154#1968C2211yescharacteristic
155#1958C2211yescharacteristic
156#1956C2211yescharacteristic
157#1949C2211yescharacteristic
158#1947C2211yescharacteristic
159#1944C2211yescharacteristic
160#1941C2211yescharacteristic
161#1936C2211yescharacteristic
162#1935C2211yescharacteristic
163#1935C2211yescharacteristic
164#1935C2211yescharacteristic
165#1928C2211yescharacteristic
166#1928C2211yescharacteristic
167#1927C2211yescharacteristic
168#1925C2211yescharacteristic
169#1893C2211yescharacteristic
170#1892C2211yescharacteristic
171#1892C2211yescharacteristic
172#1892C2211yescharacteristic
173#1879C2211yescharacteristic
174#1878C2211yescharacteristic
175#1878C2211yescharacteristic
176#1877C2211yescharacteristic
177#1847C2211yescharacteristic
178#1809C2211yescharacteristic
179#1808C2211yescharacteristic
180#1805C2211yescharacteristic
181#1802C2211yescharacteristic
182#1776C2211yescharacteristic
183#1776C2211yescharacteristic
184C4×#107C2211yescharacteristic
185#1771C2211yescharacteristic
186#1770C2211yescharacteristic
187#1768C2211yescharacteristic
188#1763C2211yescharacteristic
189#1763C2211yescharacteristic
190#1762C2211yescharacteristic
191#1762C2211yescharacteristic
192C4×#103C2211yescharacteristic
193C4×#103C2211yescharacteristic
194C4×#103C2211yescharacteristic
195C4×#103C2211yescharacteristic
196C4×#102C2211yescharacteristic
197C4×#102C2211yescharacteristic
198#1753C2211yescharacteristic
199#1752C2211yescharacteristic
200#1752C2211yescharacteristic
201C8×C22⋊C4C2211yescharacteristic
202#1750C2211yescharacteristic
203C4×C22⋊C8C2211yescharacteristic
204#1726C2211yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×M16C2311yescharacteristic
215C23×C8C2311yescharacteristic
216C23×C8C2311yescharacteristic
217C23×C8C2311yescharacteristic
218#542—24no—
219#542—24no—
220#542—42no—
221#542—42no—
222#533—24no—
223#533—42no—
224C2×C4⋊Q8—21no—
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2311yescharacteristic
229C2×C4⋊Q8C2311yescharacteristic
230#529—24no—
231#529—42no—
232C2×#126—21no—
233C2×#126—21no—
234C2×#126—21no—
235C2×#125—21no—
236C2×#125C2311yescharacteristic
237C2×#124—21no—
238C2×#124—21no—
239C2×#124—21no—
240C2×#124C2311yescharacteristic
241C2×#124C2311yescharacteristic
242C2×#124C2311yescharacteristic
243C2×#124C2311yescharacteristic
244C2×#123—21no—
245C2×#123—21no—
246C2×#123—21no—
247C2×C22⋊Q8—21no—
248C2×C22⋊Q8—21no—
249C2×C22⋊Q8—21no—
250C2×C22⋊Q8C2311yescharacteristic
251C2×C22⋊Q8C2311yescharacteristic
252C2×C22⋊Q8C2311yescharacteristic
253C2×C22⋊Q8C2311yescharacteristic
254C2×C22⋊Q8C2311yescharacteristic
255C2×C22⋊Q8C2311yescharacteristic
256C2×C22⋊Q8C2311yescharacteristic
257C2×C22⋊Q8C2311yescharacteristic
258C2×#121C2311yescharacteristic
259C2×#121C2311yescharacteristic
260C2×#121C2311yescharacteristic
261C2×#121C2311yescharacteristic
262C2×C4×Q8—21no—
263C2×C4×Q8C2311yescharacteristic
264C2×C4×Q8C2311yescharacteristic
265C2×C4×Q8C2311yescharacteristic
266C2×C4×Q8C2311yescharacteristic
267C2×C4×Q8C2311yescharacteristic
268C2×C4×Q8C2311yescharacteristic
269C2×C4×D4—21no—
270C2×C4×D4—21no—
271C2×C4×D4C2311yescharacteristic
272C2×C4×D4C2311yescharacteristic
273C2×C4×D4C2311yescharacteristic
274C2×C4×D4C2311yescharacteristic
275C2×C4×D4C2311yescharacteristic
276C2×#117—21no—
277C2×#117—21no—
278C2×#117C2311yescharacteristic
279C22×C42C2311yescharacteristic
280#501—24no—
281#500—24no—
282#497—24no—
283#497—24no—
284#495—24no—
285#491—24no—
286#489—24no—
287#489—24no—
288#489—24no—
289#470—24no—
290#468—24no—
291#468—24no—
292#467—24no—
293#467—24no—
294#467—24no—
295#466—24no—
296#465—24no—
297#465—24no—
298#465—24no—
299#463—24no—
300#462—24no—
301#441—24no—
302#441—24no—
303#440—24no—
304#440—24no—
305#440—24no—
306#440D418yescomplemented
307C4×Q16—24no—
308C4×Q16—42no—
309C4×SD16—24no—
310C4×SD16—42no—
311C4×D8—24no—
312#435—24no—
313C8×D4—24no—
314C2×#107C2311yescharacteristic
315C2×#107C2311yescharacteristic
316C2×#107C2311yescharacteristic
317C2×#107C2311yescharacteristic
318C2×#107C2311yescharacteristic
319C2×#107C2311yescharacteristic
320C2×#107C2311yescharacteristic
321C2×#106C2311yescharacteristic
322C2×#106C2311yescharacteristic
323C2×#106C2311yescharacteristic
324C2×#106C2311yescharacteristic
325C2×C4⋊C8C2311yescharacteristic
326C2×C4⋊C8C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#103C2311yescharacteristic
329C2×#103C2311yescharacteristic
330C2×#103C2311yescharacteristic
331C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
348C2×#102C2311yescharacteristic
349C2×#102C2311yescharacteristic
350C2×#102C2311yescharacteristic
351C2×#102C2311yescharacteristic
352C2×#102C2311yescharacteristic
353C2×#102C2311yescharacteristic
354C2×#102C2311yescharacteristic
355C2×#102C2311yescharacteristic
356C2×#102C2311yescharacteristic
357C2×C22⋊C8C2311yescharacteristic
358C2×C22⋊C8C2311yescharacteristic
359C2×C22⋊C8C2311yescharacteristic
360C2×C22⋊C8C2311yescharacteristic
361#405—24no—
362C2×#97—24no—
363C2×#97C2311yescharacteristic
364C2×#97C2311yescharacteristic
365C2×#97C2311yescharacteristic
366C2×#97C2311yescharacteristic
367C2×#97C2311yescharacteristic
368C2×#97C2311yescharacteristic
369C2×#97C2311yescharacteristic
370C2×C4×C8C2311yescharacteristic
371C2×C4×C8C2311yescharacteristic
372C2×C4×C8C2311yescharacteristic
373C2×C4×C8C2311yescharacteristic
374C2×C4×C8C2311yescharacteristic
375#400—21no—
376#400—21no—
377#400—21no—
378#399—21no—
379#399—21no—
380#399—21no—
381#398—21no—
382#398—21no—
383#397—21no—
384#397—21no—
385#397—21no—
386#397—21no—
387#397—21no—
388#397—21no—
389#396—21no—
390#396—21no—
391#396—21no—
392#396—21no—
393#396—21no—
394#396—21no—
395#395—21no—
396#395—21no—
397#395—21no—
398#394—21no—
399#394—21no—
400#394—21no—
401#394—21no—
402#393—21no—
403#393—21no—
404#393—21no—
405#392—21no—
406#392—21no—
407#391—21no—
408#391—21no—
409#391—21no—
410#391C2311yescharacteristic
411#391C2311yescharacteristic
412#391C2311yescharacteristic
413#391C2311yescharacteristic
414#391C2311yescharacteristic
415#391C2311yescharacteristic
416#390—21no—
417#390—21no—
418#390—21no—
419#390—21no—
420#390—21no—
421#390C2311yescharacteristic
422#390C2311yescharacteristic
423#389—21no—
424#389—21no—
425#389—21no—
426#389—21no—
427#389—21no—
428#389—21no—
429#389C2311yescharacteristic
430#389C2311yescharacteristic
431#389C2311yescharacteristic
432#389C2311yescharacteristic
433#388—21no—
434#388—21no—
435#388—21no—
436#388—21no—
437#388—21no—
438#388—21no—
439#388—21no—
440#388—21no—
441#388—21no—
442#388—21no—
443#388—21no—
444#388—21no—
445#388—21no—
446#388—21no—
447#388—21no—
448#388D411yescharacteristic
449#388D411yescharacteristic
450#387—21no—
451#387—21no—
452#387—21no—
453#387—21no—
454#387—21no—
455#387—21no—
456#387—21no—
457#387D411yescharacteristic
458#387D411yescharacteristic
459#386—21no—
460#386—21no—
461#386—21no—
462#386—21no—
463#386—21no—
464#386D411yescharacteristic
465#386D411yescharacteristic
466#385—21no—
467#385—21no—
468#385—21no—
469#385D411yescharacteristic
470#385D411yescharacteristic
471#384—21no—
472#384C2311yescharacteristic
473#382—21no—
474#382C2311yescharacteristic
475#380—21no—
476#380—21no—
477#380—21no—
478#380—21no—
479#380C2311yescharacteristic
480#380C2311yescharacteristic
481#380C2311yescharacteristic
482#380C2311yescharacteristic
483C4×C4⋊C4—21no—
484C4×C4⋊C4—21no—
485C4×C4⋊C4—21no—
486C4×C4⋊C4—21no—
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2311yescharacteristic
494C4×C22⋊C4—21no—
495C4×C22⋊C4—21no—
496C4×C22⋊C4—21no—
497C4×C22⋊C4—21no—
498C4×C22⋊C4—21no—
499C4×C22⋊C4C2311yescharacteristic
500C4×C22⋊C4C2311yescharacteristic
501#376—21no—
502#376C2311yescharacteristic
503C2×#95—21no—
504#340C2311yescharacteristic
505#340C2311yescharacteristic
506#340C2311yescharacteristic
507#340C2311yescharacteristic
508#340C2311yescharacteristic
509#340C2311yescharacteristic
510#340C2311yescharacteristic
511#340C2311yescharacteristic
512#340C2311yescharacteristic
513#340C2311yescharacteristic
514#340C2311yescharacteristic
515#340C2311yescharacteristic
516#340C2311yescharacteristic
517#340C2311yescharacteristic
518#336C2311yescharacteristic
519#336C2311yescharacteristic
520#336C2311yescharacteristic
521#336C2311yescharacteristic
522#336C2311yescharacteristic
523#336C2311yescharacteristic
524C22×Q8—21no—
525C22×Q8—21no—
526C22×Q8—21no—
527C22×Q8C2411yescharacteristic
528C22×Q8C2411yescharacteristic
529C22×Q8C2411yescharacteristic
530C22×Q8C2411yescharacteristic
531C22×D4—21no—
532C22×D4—21no—
533C22×D4—21no—
534C22×D4—21no—
535C22×D4C2×D411yescharacteristic
536C22×D4C2411yescharacteristic
537C22×D4C2411yescharacteristic
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4C2×D411yescharacteristic
543C23×C4C2×D411yescharacteristic
544C23×C4C2411yescharacteristic
545C23×C4C2411yescharacteristic
546C2×Q16—22no—
547C2×Q16—22no—
548C2×Q16—22no—
549C2×Q16—22no—
550C2×Q16—22no—
551C2×Q16—22no—
552C2×Q16—22no—
553C2×Q16—22no—
554C2×Q16—41no—
555C2×Q16—41no—
556C2×Q16—41no—
557C2×Q16—41no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—22no—
564C2×SD16—22no—
565C2×SD16—22no—
566C2×SD16—41no—
567C2×SD16—41no—
568C2×SD16—41no—
569C2×SD16C2×D414yes—
570C2×D8—22no—
571C2×D8—22no—
572C2×D8—41no—
573C2×M16—22no—
574C2×M16—22no—
575C2×M16—22no—
576C22×C8—22no—
577C22×C8—22no—
578C22×C8—22no—
579C22×C8—22no—
580C22×C8—22no—
581C22×C8—22no—
582C22×C8—22no—
583C22×C8—41no—
584C22×C8—41no—
585C22×C8C2411yescharacteristic
586C22×C8C2411yescharacteristic
587C22×C8C2411yescharacteristic
588C22×C8C2411yescharacteristic
589C22×C8C2411yescharacteristic
590C22×C8C2411yescharacteristic
591C22×C8C2411yescharacteristic
592C22×C8C2411yescharacteristic
593C4⋊Q8—22no—
594C4⋊Q8—22no—
595C4⋊Q8—22no—
596C4⋊Q8—22no—
597C4⋊Q8—22no—
598C4⋊Q8—22no—
599C4⋊Q8—41no—
600C4⋊Q8—41no—
601C4⋊Q8—41no—
602C4⋊Q8—41no—
603C4⋊Q8—82no—
604#126—44no—
605#126—44no—
606#126—44no—
607#125—22no—
608#125—41no—
609#125—44no—
610#124—22no—
611#124—22no—
612#124—22no—
613#124—22no—
614#124—22no—
615#124—44no—
616#124—41no—
617#124—41no—
618#124—41no—
619#124—44no—
620#124—82no—
621#123—44no—
622#123—44no—
623#123—44no—
624C22⋊Q8—22no—
625C22⋊Q8—22no—
626C22⋊Q8—22no—
627C22⋊Q8—22no—
628C22⋊Q8—22no—
629C22⋊Q8—22no—
630C22⋊Q8—22no—
631C22⋊Q8—22no—
632C22⋊Q8—44no—
633C22⋊Q8—41no—
634C22⋊Q8—41no—
635C22⋊Q8—41no—
636C22⋊Q8—41no—
637C22⋊Q8—41no—
638C22⋊Q8—41no—
639C22⋊Q8—41no—
640C22⋊Q8—41no—
641C22⋊Q8—44no—
642C22⋊Q8—44no—
643#121—22no—
644#121—22no—
645#121—22no—
646#121—22no—
647#121—41no—
648#121—41no—
649#121—41no—
650#121—41no—
651C4×Q8—22no—
652C4×Q8—22no—
653C4×Q8—22no—
654C4×Q8—22no—
655C4×Q8—22no—
656C4×Q8—22no—
657C4×Q8—22no—
658C4×Q8—22no—
659C4×Q8—22no—
660C4×Q8—22no—
661C4×Q8—44no—
662C4×Q8—41no—
663C4×Q8C2×D414yes—
664C4×D4—22no—
665C4×D4—22no—
666C4×D4—22no—
667C4×D4—22no—
668C4×D4—22no—
669C4×D4—22no—
670C4×D4—22no—
671C4×D4—22no—
672C4×D4—41no—
673C4×D4—44no—
674C4×D4—82no—
675C4×D4C2×D414yes—
676#117—22no—
677#117—22no—
678#117—44no—
679#117—44no—
680C2×C4⋊C4—21no—
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—21no—
709C2×C4⋊C4C2×D411yescharacteristic
710C2×C4⋊C4C2×D411yescharacteristic
711C2×C4⋊C4C2×D411yescharacteristic
712C2×C4⋊C4C2×D411yescharacteristic
713C2×C4⋊C4C2×D411yescharacteristic
714C2×C4⋊C4C2411yescharacteristic
715C2×C4⋊C4C2411yescharacteristic
716C2×C4⋊C4C2411yescharacteristic
717C2×C4⋊C4C2411yescharacteristic
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2411yescharacteristic
721C2×C4⋊C4C2411yescharacteristic
722C2×C4⋊C4C2411yescharacteristic
723C2×C4⋊C4C2411yescharacteristic
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
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×C42—21no—
765C2×C42—22no—
766C2×C42—22no—
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×C42C2×D411yescharacteristic
779C2×C42C2×D411yescharacteristic
780C2×C42C2411yescharacteristic
781C2×C42C2411yescharacteristic
782C2×C42C2411yescharacteristic
783C2×C42C2411yescharacteristic
784C2×C42C2411yescharacteristic
785#107—22no—
786#107—22no—
787#107—22no—
788#107—22no—
789#107—22no—
790#107—41no—
791#107C2×D414yes—
792#106—22no—
793#106—22no—
794#106—41no—
795#106#4114yes—
796C4⋊C8—22no—
797C4⋊C8#4114yes—
798#103—22no—
799#103—22no—
800#103—22no—
801#103—22no—
802#103—22no—
803#103—22no—
804#103—22no—
805#103—22no—
806#103—22no—
807#103—22no—
808#103—22no—
809#103—22no—
810#103—22no—
811#103—22no—
812#103—22no—
813#103—22no—
814#103—41no—
815#103—41no—
816#103—41no—
817#103C2×D414yes—
818#102—22no—
819#102—22no—
820#102—22no—
821#102—22no—
822#102—22no—
823#102—22no—
824#102—22no—
825#102—22no—
826#102—41no—
827#102C2×D414yes—
828C22⋊C8—22no—
829C22⋊C8—22no—
830C22⋊C8—22no—
831C22⋊C8—22no—
832#97—22no—
833#97—22no—
834#97—22no—
835#97—22no—
836#97—41no—
837#97C2×D414yes—
838#97#4114yes—
839C4×C8—22no—
840C4×C8—22no—
841C4×C8—22no—
842C4×C8—22no—
843C4×C8—22no—
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#95—21no—
867#95—21no—
868#95—21no—
869#95—21no—
870#95—21no—
871#95—21no—
872#95C2×D411yescharacteristic
873#95C2×D411yescharacteristic
874#95C2×D411yescharacteristic
875#95C2×D411yescharacteristic
876#95C2×D411yescharacteristic
877#95C2×D411yescharacteristic
878#95C2×D411yescharacteristic
879#95C2×D411yescharacteristic
880#95C2×D411yescharacteristic
881#95C2×D411yescharacteristic
882C24—21no—
883C24—21no—
884C24C22×D411yescharacteristic
885C24C22×D411yescharacteristic
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—21no—
897C2×Q8—21no—
898C2×Q8—21no—
899C2×Q8—21no—
900C2×Q8—21no—
901C2×Q8—21no—
902C2×Q8—21no—
903C2×Q8—21no—
904C2×Q8—21no—
905C2×Q8—21no—
906C2×Q8—21no—
907C2×Q8—21no—
908C2×Q8—21no—
909C2×Q8—42no—
910C2×Q8—42no—
911C2×Q8—42no—
912C2×Q8—42no—
913C2×Q8—81no—
914C2×Q8—81no—
915C2×Q8—81no—
916C2×Q8—81no—
917C2×Q8—81no—
918C2×Q8C22×D412yes—
919C2×D4—22no—
920C2×D4—22no—
921C2×D4—21no—
922C2×D4—21no—
923C2×D4—21no—
924C2×D4—21no—
925C2×D4—21no—
926C2×D4—21no—
927C2×D4—21no—
928C2×D4—21no—
929C2×D4—21no—
930C2×D4—21no—
931C2×D4—21no—
932C2×D4—41no—
933C2×D4—42no—
934C2×D4—42no—
935C2×D4—42no—
936C2×D4—42no—
937C2×D4—42no—
938C2×D4—42no—
939C2×D4—81no—
940C2×D4—81no—
941C2×D4—81no—
942C2×D4—81no—
943C2×D4—81no—
944C2×D4—81no—
945C2×D4C22×D412yes—
946C22×C4—22no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—22no—
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—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—22no—
966C22×C4—24no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—41no—
977C22×C4—41no—
978C22×C4—41no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—42no—
982C22×C4—81no—
983C22×C4—81no—
984C22×C4—81no—
985C22×C4—81no—
986C22×C4—81no—
987C22×C4—81no—
988C22×C4—81no—
989C22×C4—81no—
990C22×C4C22×D411yescharacteristic
991C22×C4C22×D411yescharacteristic
992C22×C4C22×D411yescharacteristic
993C22×C4C22×D411yescharacteristic
994C22×C4C22×D411yescharacteristic
995C22×C4C22×D411yescharacteristic
996C22×C4C22×D411yescharacteristic
997C22×C4C22×D411yescharacteristic
998C22×C4C22×D411yescharacteristic
999C22×C4C22×D411yescharacteristic
1000C22×C4C22×D411yescharacteristic
1001C22×C4C22×D411yescharacteristic
1002C22×C4C2511yescharacteristic
1003Q16—44no—
1004Q16—44no—
1005Q16—44no—
1006Q16—44no—
1007SD16—28no—
1008SD16—44no—
1009SD16—44no—
1010SD16—44no—
1011D8—44no—
1012M16—44no—
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—44no—
1031C2×C8—44no—
1032C2×C8—44no—
1033C2×C8C22×D412yes—
1034C2×C8C22×D412yes—
1035C2×C8C2×#4112yes—
1036C2×C8C2×#4112yes—
1037C2×C8C2×#4112yes—
1038C2×C8C2×#4112yes—
1039C2×C8C2×#4112yes—
1040C4⋊C4—22no—
1041C4⋊C4—24no—
1042C4⋊C4—22no—
1043C4⋊C4—22no—
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—41no—
1061C4⋊C4—41no—
1062C4⋊C4—42no—
1063C4⋊C4—42no—
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—42no—
1082C4⋊C4—42no—
1083C4⋊C4—42no—
1084C4⋊C4—42no—
1085C4⋊C4—81no—
1086C4⋊C4—81no—
1087C4⋊C4—81no—
1088C4⋊C4—81no—
1089C4⋊C4—81no—
1090C4⋊C4C22×D412yes—
1091C4⋊C4C22×D412yes—
1092C4⋊C4C2×#4112yes—
1093C4⋊C4C2×#4112yes—
1094C22⋊C4—22no—
1095C22⋊C4—22no—
1096C22⋊C4—22no—
1097C22⋊C4—24no—
1098C22⋊C4—22no—
1099C22⋊C4—22no—
1100C22⋊C4—41no—
1101C22⋊C4—41no—
1102C22⋊C4—41no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
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—42no—
1122C22⋊C4—42no—
1123C22⋊C4—42no—
1124C22⋊C4—42no—
1125C22⋊C4—42no—
1126C22⋊C4—42no—
1127C22⋊C4—42no—
1128C22⋊C4—81no—
1129C22⋊C4—81no—
1130C22⋊C4—81no—
1131C22⋊C4—81no—
1132C22⋊C4—81no—
1133C22⋊C4—81no—
1134C42—22no—
1135C42—22no—
1136C42—24no—
1137C42—21no—
1138C42—21no—
1139C42—21no—
1140C42—21no—
1141C42—21no—
1142C42—21no—
1143C42—42no—
1144C42—42no—
1145C42—42no—
1146C42—42no—
1147C42—42no—
1148C42—81no—
1149C42—81no—
1150C42—81no—
1151C42—81no—
1152C42—81no—
1153C42—81no—
1154C42C22×D412yes—
1155C42C2×#4112yes—
1156C42C2×#4112yes—
1157C42H(5,𝔽2)12yes—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—21no—
1165C23—21no—
1166C23—21no—
1167C23—21no—
1168C23—21no—
1169C23—22no—
1170C23—21no—
1171C23—21no—
1172C23—41no—
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#57812yes—
1186C23C23×D411yescharacteristic
1187Q8—22no—
1188Q8—22no—
1189Q8—41no—
1190Q8—41no—
1191Q8—41no—
1192Q8—41no—
1193Q8—41no—
1194Q8—41no—
1195Q8—41no—
1196Q8—41no—
1197Q8—41no—
1198Q8—41no—
1199Q8—41no—
1200Q8—41no—
1201Q8—41no—
1202Q8—41no—
1203Q8—84no—
1204Q8—162no—
1205Q8—162no—
1206D4—22no—
1207D4—22no—
1208D4—44no—
1209D4—41no—
1210D4—41no—
1211D4—41no—
1212D4—41no—
1213D4—41no—
1214D4—41no—
1215D4—84no—
1216D4—84no—
1217D4—162no—
1218D4—162no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—44no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—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—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—82no—
1303C2×C4—84no—
1304C2×C4—162no—
1305C2×C4—162no—
1306C2×C4—162no—
1307C2×C4#53212yes—
1308C2×C4#53212yes—
1309C2×C4D4212yes—
1310C2×C4D4212yes—
1311C2×C4C23×D411yescharacteristic
1312C2×C4C22×#4111yescharacteristic
1313C2×C4C22×#4111yescharacteristic
1314C2×C4C22×#4111yescharacteristic
1315C2×C4C2×H(5,𝔽2)11yescharacteristic
1316C2×C4#58511yescharacteristic
1317C8—22no—
1318C8—22no—
1319C8—22no—
1320C8—22no—
1321C8—41no—
1322C8—41no—
1323C8—41no—
1324C8#53214yes—
1325C22—22no—
1326C22—22no—
1327C22—22no—
1328C22—41no—
1329C22—41no—
1330C22—41no—
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—41no—
1335C22—41no—
1336C22—41no—
1337C22—42no—
1338C22—42no—
1339C22—41no—
1340C22—42no—
1341C22—41no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22C2×#53211yescharacteristic
1354C22C2×D4211yescharacteristic
1355C22D4×#4111yescharacteristic
1356C22C2×#57811yescharacteristic
1357C22#358411yescharacteristic
1358C22#358511yescharacteristic
1359C22#358611yescharacteristic
1360C4—22no—
1361C4—22no—
1362C4—22no—
1363C4—22no—
1364C4—41no—
1365C4—42no—
1366C4—41no—
1367C4—42no—
1368C4—41no—
1369C4—41no—
1370C4—42no—
1371C4—41no—
1372C4—41no—
1373C4—42no—
1374C4—42no—
1375C4—41no—
1376C4—41no—
1377C4—81no—
1378C4—81no—
1379C4—81no—
1380C4—81no—
1381C4—81no—
1382C4—81no—
1383C4—81no—
1384C4—81no—
1385C4—81no—
1386C4C2×#53211yescharacteristic
1387C4#346011yescharacteristic
1388C4D4×#4111yescharacteristic
1389C4#348311yescharacteristic
1390C2—42no—
1391C2—81no—
1392C2—82no—
1393C2—161no—
1394C2#3492511yescharacteristic
1395C2#6070811yescharacteristic
1396C2#6072711yescharacteristic
1397C2#6107411yescharacteristic
1398C2#6107611yescharacteristic
1399C2#6152411yescharacteristic
1400C2#6152811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#25388C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3181C2semidirect
2. C2×#3175C2semidirect
3. #35636C2semidirect
4. #35573C2semidirect
5. #28935C2semidirect
6. #28934C2semidirect
7. #28931C2semidirect
8. #28929C2semidirect
9. #28821C2semidirect
10. #28492C2semidirect
11. #28476C2semidirect
12. #28235C2semidirect
13. #27796C2semidirect
14. #27792C2semidirect
15. #27776C2semidirect
16. #27774C2semidirect
17. #25417C2semidirect
18. #25411C2semidirect
20. #25386C2semidirect
21. #23585C2semidirect
22. #23581C2semidirect
23. #23571C2semidirect
24. #23569C2semidirect
25. #21703C2semidirect
26. #21542C2semidirect
27. #21528C2semidirect
28. #21516C2semidirect
29. #21509C2semidirect
30. #20504C2semidirect
31. #20493C2semidirect
306. #440D4semidirect

Maximal subgroups

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

subgroupindex
C2×#31812
C2×#31752
#356362
#355732
#289352
#289342
#289312
#289292
#288212
#284922
#284762
#282352
#277962
#277922
#277762
#277742
#254172
#254112
#253882
#253862
#235852
#235812
#235712
#235692
#217032
#215422
#215282
#215162
#215092
#205042
#204932