Finite Group Databasebeta

← #6598703

Subgroups — #6598703

Order 512.

1961 conjugacy classes of subgroups.

The subgroup lattice has 1379 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3315C211yesmaximal, characteristic, complemented
2C2×#2965C211yesmaximal, characteristic, complemented
3#36404C211yesmaximal, characteristic
4#36375C211yesmaximal, characteristic, complemented
5#33144C211yesmaximal, characteristic, complemented
6#33130C211yesmaximal, characteristic, complemented
7#33059C211yesmaximal, characteristic, complemented
8#28652C211yesmaximal, characteristic, complemented
9#28568C211yesmaximal, characteristic, complemented
10#28564C211yesmaximal, characteristic, complemented
11#28199C211yesmaximal, characteristic, complemented
12#28113C211yesmaximal, characteristic, complemented
13#28106C211yesmaximal, characteristic, complemented
14#25482C211yesmaximal, characteristic, complemented
15#25306C211yesmaximal, characteristic, complemented
16#25256C211yesmaximal, characteristic, complemented
17#25251C211yesmaximal, characteristic, complemented
18#25137C211yesmaximal, characteristic, complemented
19#25129C211yesmaximal, characteristic, complemented
20#24704C211yesmaximal, characteristic, complemented
21#24652C211yesmaximal, characteristic, complemented
22#24604C211yesmaximal, characteristic, complemented
23#24602C211yesmaximal, characteristic, complemented
24#24505C211yesmaximal, characteristic, complemented
25#24505C211yesmaximal, characteristic, complemented
26#22712C211yesmaximal, characteristic, complemented
27#22496C211yesmaximal, characteristic, complemented
28#22420C211yesmaximal, characteristic, complemented
29#21540C211yesmaximal, characteristic, complemented
30#21093C211yesmaximal, characteristic, complemented
31#21083C211yesmaximal, characteristic, complemented
32C2×#552C2211yescharacteristic
33C2×#547C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35#3315—28no—
36C2×#491C2211yescharacteristic
37C2×#484C2211yescharacteristic
38C2×#485C2211yescharacteristic
39C2×#478C2211yescharacteristic
40C2×#470C2211yescharacteristic
41C2×#468C2211yescharacteristic
42C2×#467C2211yescharacteristic
43C2×#462C2211yescharacteristic
44C2×#452C2211yescharacteristic
45C2×#452C2211yescharacteristic
46#2965—28no—
47C2×#446C2211yescharacteristic
48C2×#446C2211yescharacteristic
49C2×#440C2211yescharacteristic
50C2×#436C2211yescharacteristic
51C2×#436C2211yescharacteristic
52C2×#435C2211yescharacteristic
53C2×#435C2211yescharacteristic
54C2×#435C2211yescharacteristic
55C2×#435C2211yescharacteristic
56C2×#431C2211yescharacteristic
57C2×#431C2211yescharacteristic
58C2×#431C2211yescharacteristic
59C2×#417C2211yescharacteristic
60C2×#417C2211yescharacteristic
61C2×#416C2211yescharacteristic
62C2×#416C2211yescharacteristic
63C2×C4×M16C2211yescharacteristic
64C2×C4×M16C2211yescharacteristic
65C22×C4×C8C2211yescharacteristic
66#2857C2211yescharacteristic
67#2855C2211yescharacteristic
68#2855C2211yescharacteristic
69#2855C2211yescharacteristic
70#2855C2211yescharacteristic
71#2851C2211yescharacteristic
72#2584C2211yescharacteristic
73#2581C2211yescharacteristic
74#2568C2211yescharacteristic
75#2538C2211yescharacteristic
76#2486C2211yescharacteristic
77#2485C2211yescharacteristic
78#2478—21no—
79#2475—21no—
80#2470—21no—
81#2470—21no—
82#2466—21no—
83#2462—21no—
84#2457—21no—
85#2457—21no—
86#2420—21no—
87#2419—21no—
88#2417C2211yescharacteristic
89#2415C2211yescharacteristic
90#2415C2211yescharacteristic
91#2415C2211yescharacteristic
92#2407—21no—
93#2407C2211yescharacteristic
94#2407C2211yescharacteristic
95#2406—21no—
96#2360—21no—
97#2359—21no—
98#2354C2211yescharacteristic
99#2352—21no—
100#2352C2211yescharacteristic
101#2344—21no—
102C4×C22⋊Q8C2211yescharacteristic
103C4×#121C2211yescharacteristic
104#2297C2211yescharacteristic
105#2297C2211yescharacteristic
106#2296C2211yescharacteristic
107C2×#389C2211yescharacteristic
108#2088C2211yescharacteristic
109#2087C2211yescharacteristic
110#2087C2211yescharacteristic
111#2086C2211yescharacteristic
112#2077C2211yescharacteristic
113#2076C2211yescharacteristic
114#2068C2211yescharacteristic
115#2068C2211yescharacteristic
116#2068C2211yescharacteristic
117#2067C2211yescharacteristic
118#2067C2211yescharacteristic
119#2066C2211yescharacteristic
120#2066C2211yescharacteristic
121#2066C2211yescharacteristic
122#2056C2211yescharacteristic
123#2056C2211yescharacteristic
124#2055C2211yescharacteristic
125#2055C2211yescharacteristic
126#2036C2211yescharacteristic
127#2036C2211yescharacteristic
128#2034C2211yescharacteristic
129#2033C2211yescharacteristic
130#2001C2211yescharacteristic
131#2001C2211yescharacteristic
132#1992C2211yescharacteristic
133#1989C2211yescharacteristic
134#1981C2211yescharacteristic
135#1971C2211yescharacteristic
136#1969C2211yescharacteristic
137#1969C2211yescharacteristic
138#1969C2211yescharacteristic
139#1968C2211yescharacteristic
140#1960C2211yescharacteristic
141#1949C2211yescharacteristic
142#1947C2211yescharacteristic
143#1943C2211yescharacteristic
144#1942C2211yescharacteristic
145#1942C2211yescharacteristic
146#1942C2211yescharacteristic
147#1941C2211yescharacteristic
148#1936C2211yescharacteristic
149#1936C2211yescharacteristic
150#1935C2211yescharacteristic
151#1935C2211yescharacteristic
152#1935C2211yescharacteristic
153#1935C2211yescharacteristic
154#1934C2211yescharacteristic
155#1934C2211yescharacteristic
156#1934C2211yescharacteristic
157#1934C2211yescharacteristic
158#1934C2211yescharacteristic
159#1933C2211yescharacteristic
160#1933C2211yescharacteristic
161#1933C2211yescharacteristic
162#1933C2211yescharacteristic
163#1933C2211yescharacteristic
164#1933C2211yescharacteristic
165#1933C2211yescharacteristic
166#1933C2211yescharacteristic
167#1933C2211yescharacteristic
168#1933C2211yescharacteristic
169#1933C2211yescharacteristic
170#1895C2211yescharacteristic
171#1894C2211yescharacteristic
172#1894C2211yescharacteristic
173#1894C2211yescharacteristic
174#1894C2211yescharacteristic
175#1894C2211yescharacteristic
176#1894C2211yescharacteristic
177#1894C2211yescharacteristic
178#1892C2211yescharacteristic
179#1892C2211yescharacteristic
180#1873C2211yescharacteristic
181#1873C2211yescharacteristic
182#1873C2211yescharacteristic
183#1872C2211yescharacteristic
184#1854C2211yescharacteristic
185#1854C2211yescharacteristic
186#1854C2211yescharacteristic
187#1852C2211yescharacteristic
188#1836C2211yescharacteristic
189#1825C2211yescharacteristic
190#1824C2211yescharacteristic
191#1809C2211yescharacteristic
192#1809C2211yescharacteristic
193#1808C2211yescharacteristic
194#1804C2211yescharacteristic
195#1803C2211yescharacteristic
196#1788C2211yescharacteristic
197#1788C2211yescharacteristic
198#1776C2211yescharacteristic
199#1763C2211yescharacteristic
200#1762C2211yescharacteristic
201#1736C2211yescharacteristic
202#1736C2211yescharacteristic
203#1735C2211yescharacteristic
204#1735C2211yescharacteristic
205C22×#41D411yescharacteristic
206C22×#41C2311yescharacteristic
207C22×#41C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C22×M16C2311yescharacteristic
214C22×M16C2311yescharacteristic
215C23×C8C2311yescharacteristic
216C23×C8C2311yescharacteristic
217#552—24no—
218#552—24no—
219#547—24no—
220#547—24no—
221C2×C4⋊Q8C2311yescharacteristic
222C2×#126—21no—
223C2×#125—21no—
224C2×#125C2311yescharacteristic
225C2×#123—21no—
226C2×#123—21no—
227C2×#123—21no—
228C2×#123—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×#121—21no—
238C2×#121C2311yescharacteristic
239C4×#41—24no—
240C4×#41—24no—
241C2×C4×Q8D411yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×D4—21no—
245C2×C4×D4D411yescharacteristic
246C2×C4×D4D411yescharacteristic
247C2×C4×D4D411yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×#117—21no—
253C2×#117D411yescharacteristic
254C2×#117D411yescharacteristic
255C2×#117D411yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C22×C4⋊C4—21no—
261C22×C4⋊C4—21no—
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C42C2311yescharacteristic
265C22×C42C2311yescharacteristic
266C22×C42C2311yescharacteristic
267#491—24no—
268#485—24no—
269#484—24no—
270#478—24no—
271#470—24no—
272#468—24no—
273#467—24no—
274#462—24no—
275#452—24no—
276#452—24no—
277#446—24no—
278#446—24no—
279#440—24no—
280#436—24no—
281#436—24no—
282#435—24no—
283#435—24no—
284#435—24no—
285#435D418yescomplemented
286#431—24no—
287#431—24no—
288#431—24no—
289C2×#107C2311yescharacteristic
290C2×#107C2311yescharacteristic
291C2×#107C2311yescharacteristic
292C2×#107C2311yescharacteristic
293C2×#107C2311yescharacteristic
294C2×#107C2311yescharacteristic
295C2×#106C2311yescharacteristic
296C2×#106C2311yescharacteristic
297C2×#106C2311yescharacteristic
298C2×C4⋊C8C2311yescharacteristic
299C2×C4⋊C8C2311yescharacteristic
300C2×C4⋊C8C2311yescharacteristic
301C2×C4⋊C8C2311yescharacteristic
302C2×C4⋊C8C2311yescharacteristic
303C2×C4⋊C8C2311yescharacteristic
304#417—24no—
305#417—24no—
306#416—24no—
307#416—24no—
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#103C2311yescharacteristic
312C2×#103C2311yescharacteristic
313C2×#103C2311yescharacteristic
314C2×#103C2311yescharacteristic
315C2×#103C2311yescharacteristic
316C2×#103C2311yescharacteristic
317C2×#103C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
325C2×#103C2311yescharacteristic
326C2×#103C2311yescharacteristic
327C2×#102C2311yescharacteristic
328C2×#102C2311yescharacteristic
329C2×#102C2311yescharacteristic
330C2×#102C2311yescharacteristic
331C2×#102C2311yescharacteristic
332C2×#102C2311yescharacteristic
333C2×#102C2311yescharacteristic
334C2×C22⋊C8C2311yescharacteristic
335C2×C22⋊C8C2311yescharacteristic
336C2×C22⋊C8C2311yescharacteristic
337C2×C22⋊C8C2311yescharacteristic
338C2×C22⋊C8C2311yescharacteristic
339C2×C22⋊C8C2311yescharacteristic
340C4×M16—24no—
341C4×M16—24no—
342C2×#97C2311yescharacteristic
343C2×#97C2311yescharacteristic
344C2×#97C2311yescharacteristic
345C2×#97C2311yescharacteristic
346C2×C4×C8—24no—
347C2×C4×C8C2311yescharacteristic
348C2×C4×C8C2311yescharacteristic
349C2×C4×C8C2311yescharacteristic
350C2×C4×C8C2311yescharacteristic
351C2×C4×C8C2311yescharacteristic
352C2×C4×C8C2311yescharacteristic
353#400—21no—
354#400—21no—
355#400—21no—
356#398—21no—
357#398—21no—
358#398—21no—
359#397—21no—
360#397—21no—
361#397—21no—
362#397—21no—
363#397—21no—
364#396—21no—
365#396—21no—
366#396—21no—
367#395—21no—
368#395—21no—
369#394—21no—
370#394—21no—
371#394—21no—
372#394—21no—
373#394—21no—
374#394—21no—
375#392—21no—
376#392—21no—
377#391—21no—
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#391C2311yescharacteristic
381#391C2311yescharacteristic
382#391C2311yescharacteristic
383#391C2311yescharacteristic
384#391C2311yescharacteristic
385#391C2311yescharacteristic
386#391C2311yescharacteristic
387#390—21no—
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#389—21no—
392#389—21no—
393#389—21no—
394#389—21no—
395#389—21no—
396#389—21no—
397#389—21no—
398#389—21no—
399#389—21no—
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#389C2311yescharacteristic
407#389C2311yescharacteristic
408#389C2311yescharacteristic
409#389C2311yescharacteristic
410#389C2311yescharacteristic
411#389C2311yescharacteristic
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#388—21no—
419#388—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#387—21no—
427#387—21no—
428#387—21no—
429#387—21no—
430#387—21no—
431#387—21no—
432#387—21no—
433#387—21no—
434#387—21no—
435#386—21no—
436#386—21no—
437#386—21no—
438#386—21no—
439#386—21no—
440#386—21no—
441#386—21no—
442#386—21no—
443#386—21no—
444#385—21no—
445#385—21no—
446#385—21no—
447#385—21no—
448#385—21no—
449#385—21no—
450#385—21no—
451#385—21no—
452#385—21no—
453#385—21no—
454#385—21no—
455#384C2311yescharacteristic
456#382—21no—
457#382C2311yescharacteristic
458#381—21no—
459#381—21no—
460#381—21no—
461#381—21no—
462#381—21no—
463#380—21no—
464#380—21no—
465#380—21no—
466#380—21no—
467#380C2311yescharacteristic
468#380C2311yescharacteristic
469#380C2311yescharacteristic
470#380C2311yescharacteristic
471#380C2311yescharacteristic
472#380C2311yescharacteristic
473#380C2311yescharacteristic
474#380C2311yescharacteristic
475C4×C4⋊C4—21no—
476C4×C4⋊C4—21no—
477C4×C4⋊C4—21no—
478C4×C4⋊C4—21no—
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
488C2×#95—21no—
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#340C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#340C2311yescharacteristic
497#340C2311yescharacteristic
498#340C2311yescharacteristic
499#340C2311yescharacteristic
500#340C2311yescharacteristic
501#340C2311yescharacteristic
502#340C2311yescharacteristic
503#340C2311yescharacteristic
504#340C2311yescharacteristic
505#340C2311yescharacteristic
506#340C2311yescharacteristic
507#340C2311yescharacteristic
508#340C2311yescharacteristic
509#340C2311yescharacteristic
510#340C2311yescharacteristic
511#340C2311yescharacteristic
512#340C2311yescharacteristic
513#340C2311yescharacteristic
514#340C2311yescharacteristic
515C2×#41—24no—
516C2×#41—22no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—42no—
523C2×#41—42no—
524C2×#41—41no—
525C2×#41—41no—
526C2×#41—41no—
527C2×#41—41no—
528C2×#41—41no—
529C2×#41—41no—
530C22×Q8C2×D411yescharacteristic
531C22×Q8C2411yescharacteristic
532C22×Q8C2411yescharacteristic
533C22×Q8C2411yescharacteristic
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—21no—
537C22×D4C2×D411yescharacteristic
538C22×D4C2×D411yescharacteristic
539C22×D4C2×D411yescharacteristic
540C22×D4C2411yescharacteristic
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—21no—
546C23×C4C2×D411yescharacteristic
547C23×C4C2×D411yescharacteristic
548C23×C4C2×D411yescharacteristic
549C23×C4C2×D411yescharacteristic
550C23×C4C2×D411yescharacteristic
551C23×C4C2×D411yescharacteristic
552C23×C4C2411yescharacteristic
553C23×C4C2411yescharacteristic
554C23×C4C2411yescharacteristic
555C2×Q16—22no—
556C2×Q16—22no—
557C2×Q16—41no—
558C2×Q16—41no—
559C2×Q16—41no—
560C2×Q16—41no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—41no—
564C2×M16—22no—
565C2×M16—22no—
566C2×M16—22no—
567C2×M16—22no—
568C2×M16—22no—
569C2×M16—41no—
570C2×M16—41no—
571C2×M16—41no—
572C2×M16—41no—
573C2×M16—41no—
574C2×M16—41no—
575C2×M16C2×D414yes—
576C22×C8—22no—
577C22×C8—22no—
578C22×C8—41no—
579C22×C8—41no—
580C22×C8—41no—
581C22×C8C2×D414yes—
582C22×C8C2411yescharacteristic
583C22×C8C2411yescharacteristic
584C22×C8C2411yescharacteristic
585C22×C8C2411yescharacteristic
586C22×C8C2411yescharacteristic
587C22×C8C2411yescharacteristic
588C22×C8C2411yescharacteristic
589C22×C8C2411yescharacteristic
590C4⋊Q8—22no—
591C4⋊Q8—22no—
592#126—44no—
593#125—22no—
594#125—22no—
595#125—44no—
596#123—44no—
597#123—44no—
598#123—44no—
599#123—44no—
600C22⋊Q8—22no—
601C22⋊Q8—22no—
602C22⋊Q8—22no—
603C22⋊Q8—22no—
604C22⋊Q8—22no—
605C22⋊Q8—22no—
606C22⋊Q8—22no—
607C22⋊Q8—22no—
608C22⋊Q8—22no—
609C22⋊Q8—41no—
610C22⋊Q8—44no—
611C22⋊Q8—41no—
612C22⋊Q8—41no—
613C22⋊Q8—41no—
614C22⋊Q8—41no—
615#121—22no—
616#121—41no—
617#121—44no—
618C4×Q8—24no—
619C4×Q8—22no—
620C4×Q8—22no—
621C4×Q8—22no—
622C4×Q8—22no—
623C4×D4—24no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—22no—
628C4×D4—24no—
629C4×D4—24no—
630C4×D4—22no—
631C4×D4—22no—
632C4×D4—44no—
633C4×D4C2×D414yes—
634C4×D4#4114yes—
635#117—24no—
636#117—24no—
637#117—24no—
638#117—22no—
639#117—22no—
640#117—22no—
641#117—41no—
642#117—44no—
643#117—41no—
644#117—41no—
645#117—41no—
646#117—41no—
647C2×C4⋊C4—22no—
648C2×C4⋊C4—22no—
649C2×C4⋊C4—22no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—41no—
679C2×C4⋊C4—44no—
680C2×C4⋊C4—44no—
681C2×C4⋊C4C2×D411yescharacteristic
682C2×C4⋊C4C2×D411yescharacteristic
683C2×C4⋊C4C2×D411yescharacteristic
684C2×C4⋊C4C2×D411yescharacteristic
685C2×C4⋊C4C2×D411yescharacteristic
686C2×C4⋊C4C2×D411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
693C2×C4⋊C4C2411yescharacteristic
694C2×C4⋊C4C2411yescharacteristic
695C2×C4⋊C4C2411yescharacteristic
696C2×C4⋊C4C2411yescharacteristic
697C2×C4⋊C4C2411yescharacteristic
698C2×C4⋊C4C2411yescharacteristic
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4C2×D411yescharacteristic
727C2×C22⋊C4C2×D411yescharacteristic
728C2×C22⋊C4C2×D411yescharacteristic
729C2×C22⋊C4C2×D411yescharacteristic
730C2×C22⋊C4C2×D411yescharacteristic
731C2×C22⋊C4C2×D411yescharacteristic
732C2×C42—22no—
733C2×C42—22no—
734C2×C42—22no—
735C2×C42—22no—
736C2×C42—22no—
737C2×C42—22no—
738C2×C42—21no—
739C2×C42—21no—
740C2×C42—21no—
741C2×C42—21no—
742C2×C42—21no—
743C2×C42—21no—
744C2×C42—21no—
745C2×C42C2×D411yescharacteristic
746C2×C42C2×D411yescharacteristic
747C2×C42C2×D411yescharacteristic
748C2×C42C2×D411yescharacteristic
749C2×C42C2×D411yescharacteristic
750C2×C42C2×D411yescharacteristic
751C2×C42C2411yescharacteristic
752C2×C42C2411yescharacteristic
753C2×C42C2411yescharacteristic
754C2×C42C2411yescharacteristic
755#107—22no—
756#107—22no—
757#107—22no—
758#107—41no—
759#107—41no—
760#107—41no—
761#106—22no—
762#106—41no—
763#106—41no—
764C4⋊C8—22no—
765C4⋊C8—22no—
766C4⋊C8—22no—
767C4⋊C8—22no—
768C4⋊C8—22no—
769C4⋊C8C2×D414yes—
770#103—22no—
771#103—22no—
772#103—22no—
773#103—22no—
774#103—22no—
775#103—22no—
776#103—22no—
777#103—22no—
778#103—22no—
779#103—22no—
780#103—22no—
781#103—22no—
782#103—41no—
783#103—41no—
784#103—41no—
785#103—41no—
786#103—41no—
787#103—41no—
788#103—41no—
789#102—22no—
790#102—22no—
791#102—22no—
792#102—22no—
793#102—22no—
794#102—41no—
795#102#4114yescomplemented
796C22⋊C8—22no—
797C22⋊C8—22no—
798C22⋊C8—22no—
799C22⋊C8—22no—
800C22⋊C8C2×D414yes—
801C22⋊C8C2×D414yes—
802#97—22no—
803#97—22no—
804#97—22no—
805#97C2×D414yes—
806C4×C8—22no—
807C4×C8—22no—
808C4×C8—22no—
809C4×C8—22no—
810C4×C8—22no—
811C4×C8—22no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95—21no—
836#95—21no—
837#95—21no—
838#95—21no—
839#95—21no—
840#95—21no—
841#95—21no—
842#95—21no—
843#95—21no—
844#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—
854C24—21no—
855C24C22×D411yescharacteristic
856C24C22×D411yescharacteristic
857C24C22×D411yescharacteristic
858#41—416no—
859#41—44no—
860#41—44no—
861#41—44no—
862#41—44no—
863#41—82no—
864#41—82no—
865#41—82no—
866#41—82no—
867C2×Q8—22no—
868C2×Q8—22no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—21no—
876C2×Q8—21no—
877C2×Q8—21no—
878C2×Q8—21no—
879C2×Q8—21no—
880C2×Q8—21no—
881C2×Q8—21no—
882C2×Q8—21no—
883C2×Q8—21no—
884C2×Q8—21no—
885C2×Q8—21no—
886C2×Q8—21no—
887C2×Q8—41no—
888C2×D4—22no—
889C2×D4—22no—
890C2×D4—22no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—41no—
897C2×D4—41no—
898C2×D4—41no—
899C2×D4—41no—
900C2×D4—41no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—42no—
906C2×D4—42no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4#12114yes—
911C2×D4C2×#4112yes—
912C22×C4—22no—
913C22×C4—22no—
914C22×C4—22no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—22no—
924C22×C4—22no—
925C22×C4—22no—
926C22×C4—21no—
927C22×C4—22no—
928C22×C4—22no—
929C22×C4—22no—
930C22×C4—22no—
931C22×C4—22no—
932C22×C4—22no—
933C22×C4—22no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—41no—
955C22×C4—41no—
956C22×C4—41no—
957C22×C4—41no—
958C22×C4—41no—
959C22×C4—42no—
960C22×C4—42no—
961C22×C4—42no—
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—81no—
972C22×C4—81no—
973C22×C4—81no—
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C22×D411yescharacteristic
977C22×C4C22×D411yescharacteristic
978C22×C4C22×D411yescharacteristic
979C22×C4C22×D411yescharacteristic
980C22×C4C22×D411yescharacteristic
981C22×C4C22×D411yescharacteristic
982C22×C4C22×D412yes—
983C22×C4C22×D412yes—
984C22×C4C22×D411yescharacteristic
985C22×C4C22×D411yescharacteristic
986C22×C4C22×D411yescharacteristic
987C22×C4C2×#4112yes—
988C22×C4C2×#4112yes—
989C22×C4C2511yescharacteristic
990Q16—82no—
991Q16—82no—
992SD16—44no—
993M16—44no—
994M16—44no—
995M16—44no—
996M16—44no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—44no—
1017C2×C8—44no—
1018C2×C8C22×D412yes—
1019C2×C8C22×D412yes—
1020C2×C8C22×D412yes—
1021C2×C8C22×D412yes—
1022C2×C8C2×#4112yes—
1023C4⋊C4—22no—
1024C4⋊C4—22no—
1025C4⋊C4—22no—
1026C4⋊C4—22no—
1027C4⋊C4—22no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
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—42no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—42no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
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—81no—
1075C4⋊C4—81no—
1076C4⋊C4—81no—
1077C4⋊C4—81no—
1078C4⋊C4—81no—
1079C4⋊C4#12114yes—
1080C4⋊C4C2×#4112yes—
1081C22⋊C4—22no—
1082C22⋊C4—22no—
1083C22⋊C4—22no—
1084C22⋊C4—22no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—42no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C22⋊C4#12114yes—
1113C22⋊C4#12114yes—
1114C42—22no—
1115C42—22no—
1116C42—22no—
1117C42—22no—
1118C42—22no—
1119C42—22no—
1120C42—21no—
1121C42—21no—
1122C42—21no—
1123C42—21no—
1124C42—21no—
1125C42—21no—
1126C42—42no—
1127C42—42no—
1128C42—42no—
1129C42—42no—
1130C42—81no—
1131C42—81no—
1132C42—81no—
1133C42C22×D412yes—
1134C42C2×#4112yes—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—22no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23C2×#12112yes—
1162C23C2×#12112yes—
1163C23C23×D411yescharacteristic
1164Q8—44no—
1165Q8—41no—
1166Q8—41no—
1167Q8—41no—
1168Q8—41no—
1169Q8—41no—
1170Q8—41no—
1171Q8—41no—
1172Q8—41no—
1173Q8—41no—
1174Q8—41no—
1175Q8—41no—
1176Q8—41no—
1177D4—22no—
1178D4—22no—
1179D4—44no—
1180D4—44no—
1181D4—44no—
1182D4—41no—
1183D4—41no—
1184D4—84no—
1185D4—84no—
1186D4—84no—
1187C2×C4—28no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—22no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—44no—
1224C2×C4—44no—
1225C2×C4—44no—
1226C2×C4—44no—
1227C2×C4—44no—
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—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—84no—
1277C2×C4—84no—
1278C2×C4—84no—
1279C2×C4—84no—
1280C2×C4—84no—
1281C2×C4C2×#12112yes—
1282C2×C4C2×#12112yes—
1283C2×C4C2×#12112yes—
1284C2×C4C2×#12112yes—
1285C2×C4#57512yes—
1286C2×C4#57512yes—
1287C2×C4#57812yes—
1288C2×C4C23×D411yescharacteristic
1289C2×C4C22×#4111yescharacteristic
1290C2×C4C22×#4111yescharacteristic
1291C2×C4#58511yescharacteristic
1292C2×C4#58511yescharacteristic
1293C2×C4#58511yescharacteristic
1294C8—22no—
1295C8—22no—
1296C8—22no—
1297C8—22no—
1298C8—22no—
1299C8—41no—
1300C8—41no—
1301C8—41no—
1302C22—22no—
1303C22—22no—
1304C22—22no—
1305C22—22no—
1306C22—22no—
1307C22—22no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—41no—
1317C22—42no—
1318C22—41no—
1319C22—42no—
1320C22—41no—
1321C22—41no—
1322C22—41no—
1323C22—41no—
1324C22—41no—
1325C22—42no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22C22×#12111yescharacteristic
1331C22D4×#4111yescharacteristic
1332C22#350011yescharacteristic
1333C22C2×#57511yescharacteristic
1334C22C2×#57511yescharacteristic
1335C22C2×#57811yescharacteristic
1336C22#358411yescharacteristic
1337C4—22no—
1338C4—22no—
1339C4—22no—
1340C4—22no—
1341C4—22no—
1342C4—22no—
1343C4—22no—
1344C4—42no—
1345C4—41no—
1346C4—41no—
1347C4—41no—
1348C4—41no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4—81no—
1363C4D4×#4111yescharacteristic
1364C4#347511yescharacteristic
1365C4#348511yescharacteristic
1366C4#352111yescharacteristic
1367C2—42no—
1368C2—42no—
1369C2—81no—
1370C2—82no—
1371C2#3621811yescharacteristic
1372C2#6044411yescharacteristic
1373C2#6045911yescharacteristic
1374C2#6144211yescharacteristic
1375C2#6144711yescharacteristic
1376C2#6254511yescharacteristic
1377C2#6254911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36404C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×#41 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3315C2semidirect
2. C2×#2965C2semidirect
4. #36375C2semidirect
5. #33144C2semidirect
6. #33130C2semidirect
7. #33059C2semidirect
8. #28652C2semidirect
9. #28568C2semidirect
10. #28564C2semidirect
11. #28199C2semidirect
12. #28113C2semidirect
13. #28106C2semidirect
14. #25482C2semidirect
15. #25306C2semidirect
16. #25256C2semidirect
17. #25251C2semidirect
18. #25137C2semidirect
19. #25129C2semidirect
20. #24704C2semidirect
21. #24652C2semidirect
22. #24604C2semidirect
23. #24602C2semidirect
24. #24505C2semidirect
25. #24505C2semidirect
26. #22712C2semidirect
27. #22496C2semidirect
28. #22420C2semidirect
29. #21540C2semidirect
30. #21093C2semidirect
31. #21083C2semidirect
285. #435D4semidirect
795. #102#41semidirect

Maximal subgroups

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

subgroupindex
C2×#33152
C2×#29652
#364042
#363752
#331442
#331302
#330592
#286522
#285682
#285642
#281992
#281132
#281062
#254822
#253062
#252562
#252512
#251372
#251292
#247042
#246522
#246042
#246022
#245052
#227122
#224962
#224202
#215402
#210932
#210832