Finite Group Databasebeta

← #6552646

Subgroups — #6552646

Order 512.

1922 conjugacy classes of subgroups.

The subgroup lattice has 1408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3346C211yesmaximal, characteristic, complemented
2C2×#3309C211yesmaximal, characteristic
3#38952C211yesmaximal, characteristic, complemented
4#34483C211yesmaximal, characteristic, complemented
5#29824C211yesmaximal, characteristic, complemented
6#29769C211yesmaximal, characteristic, complemented
7#29767C211yesmaximal, characteristic, complemented
8#28661C211yesmaximal, characteristic, complemented
9#28287C211yesmaximal, characteristic, complemented
10#28129C211yesmaximal, characteristic, complemented
11#28127C211yesmaximal, characteristic, complemented
12#25467C211yesmaximal, characteristic, complemented
13#25291C211yesmaximal, characteristic, complemented
14#25221C211yesmaximal, characteristic, complemented
15#25200C211yesmaximal, characteristic, complemented
16#25104C211yesmaximal, characteristic, complemented
17#25085C211yesmaximal, characteristic, complemented
18#24833C211yesmaximal, characteristic, complemented
19#24767C211yesmaximal, characteristic, complemented
20#24763C211yesmaximal, characteristic, complemented
21#24749C211yesmaximal, characteristic, complemented
22#24592C211yesmaximal, characteristic, complemented
23#24576C211yesmaximal, characteristic, complemented
24#24489C211yesmaximal, characteristic, complemented
25#24485C211yesmaximal, characteristic, complemented
26#23683C211yesmaximal, characteristic, complemented
27#23616C211yesmaximal, characteristic, complemented
28#23611C211yesmaximal, characteristic, complemented
29#22652C211yesmaximal, characteristic, complemented
30#22497C211yesmaximal, characteristic, complemented
31#22422C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C2×#553C2211yescharacteristic
34C2×#550C2211yescharacteristic
35#3346—28no—
36#3309—28no—
37C2×#501C2211yescharacteristic
38C2×#490C2211yescharacteristic
39C2×#484C2211yescharacteristic
40C2×#481C2211yescharacteristic
41C2×#485C2211yescharacteristic
42C2×#482C2211yescharacteristic
43C2×#480C2211yescharacteristic
44C2×#480C2211yescharacteristic
45C2×#479C2211yescharacteristic
46C2×#479C2211yescharacteristic
47C2×#474C2211yescharacteristic
48C2×#469C2211yescharacteristic
49C2×#468C2211yescharacteristic
50C2×#466C2211yescharacteristic
51C2×#465C2211yescharacteristic
52C2×#463C2211yescharacteristic
53C2×#463C2211yescharacteristic
54C2×#459C2211yescharacteristic
55C2×#449C2211yescharacteristic
56C2×#449C2211yescharacteristic
57C2×#440C2211yescharacteristic
58C2×#440C2211yescharacteristic
59C2×#435C2211yescharacteristic
60C2×#435C2211yescharacteristic
61C2×#428C2211yescharacteristic
62C22×#107C2211yescharacteristic
63C2×#424C2211yescharacteristic
64C2×#424C2211yescharacteristic
65C2×#417C2211yescharacteristic
66C2×#417C2211yescharacteristic
67C2×#416C2211yescharacteristic
68C2×#416C2211yescharacteristic
69#2858C2211yescharacteristic
70#2672—21no—
71#2672—21no—
72#2672—21no—
73#2672—21no—
74#2620C2211yescharacteristic
75#2620C2211yescharacteristic
76#2567C2211yescharacteristic
77#2548C2211yescharacteristic
78#2501C2211yescharacteristic
79#2501C2211yescharacteristic
80#2454—21no—
81#2454—21no—
82#2445—21no—
83#2445—21no—
84#2432C2211yescharacteristic
85#2432C2211yescharacteristic
86#2383—21no—
87#2377—21no—
88#2370C2211yescharacteristic
89#2363C2211yescharacteristic
90#2361C2211yescharacteristic
91#2359—21no—
92#2354—21no—
93#2352C2211yescharacteristic
94#2349C2211yescharacteristic
95#2347C2211yescharacteristic
96#2344C2211yescharacteristic
97#2335—21no—
98#2334—21no—
99#2324—21no—
100#2324C2211yescharacteristic
101#2324C2211yescharacteristic
102#2318—21no—
103#2317C2211yescharacteristic
104#2316C2211yescharacteristic
105#2311C2211yescharacteristic
106#2311C2211yescharacteristic
107C4×C4⋊Q8C2211yescharacteristic
108C4×#125C2211yescharacteristic
109#2293C2211yescharacteristic
110#2293C2211yescharacteristic
111#2084C2211yescharacteristic
112#2083C2211yescharacteristic
113#2083C2211yescharacteristic
114#2083C2211yescharacteristic
115#2083C2211yescharacteristic
116#2071C2211yescharacteristic
117#2068C2211yescharacteristic
118#2068C2211yescharacteristic
119#2068C2211yescharacteristic
120#2068C2211yescharacteristic
121#2068C2211yescharacteristic
122#2068C2211yescharacteristic
123#2068C2211yescharacteristic
124#2067C2211yescharacteristic
125#2067C2211yescharacteristic
126#2067C2211yescharacteristic
127#2067C2211yescharacteristic
128#2067C2211yescharacteristic
129#2067C2211yescharacteristic
130#2067C2211yescharacteristic
131#2067C2211yescharacteristic
132#2067C2211yescharacteristic
133#2066C2211yescharacteristic
134#2066C2211yescharacteristic
135#2066C2211yescharacteristic
136#2065C2211yescharacteristic
137#2065C2211yescharacteristic
138#2065C2211yescharacteristic
139#2055C2211yescharacteristic
140#2055C2211yescharacteristic
141#2054C2211yescharacteristic
142#2054C2211yescharacteristic
143#2054C2211yescharacteristic
144#2054C2211yescharacteristic
145#2043C2211yescharacteristic
146#2042C2211yescharacteristic
147#2042C2211yescharacteristic
148#2042C2211yescharacteristic
149#2042C2211yescharacteristic
150#2013C2211yescharacteristic
151#1993C2211yescharacteristic
152#1988C2211yescharacteristic
153#1983C2211yescharacteristic
154#1983C2211yescharacteristic
155#1982C2211yescharacteristic
156#1981C2211yescharacteristic
157#1981C2211yescharacteristic
158#1961C2211yescharacteristic
159#1948C2211yescharacteristic
160#1948C2211yescharacteristic
161#1947C2211yescharacteristic
162#1947C2211yescharacteristic
163#1940C2211yescharacteristic
164#1940C2211yescharacteristic
165#1928C2211yescharacteristic
166#1927C2211yescharacteristic
167#1926C2211yescharacteristic
168#1926C2211yescharacteristic
169#1926C2211yescharacteristic
170#1925C2211yescharacteristic
171#1925C2211yescharacteristic
172#1925C2211yescharacteristic
173#1895C2211yescharacteristic
174#1894C2211yescharacteristic
175#1893C2211yescharacteristic
176#1892C2211yescharacteristic
177#1879C2211yescharacteristic
178#1879C2211yescharacteristic
179#1877C2211yescharacteristic
180#1877C2211yescharacteristic
181#1875C2211yescharacteristic
182#1874C2211yescharacteristic
183#1873C2211yescharacteristic
184#1872C2211yescharacteristic
185#1851C2211yescharacteristic
186#1851C2211yescharacteristic
187#1850C2211yescharacteristic
188#1850C2211yescharacteristic
189#1842C2211yescharacteristic
190#1824C2211yescharacteristic
191#1823C2211yescharacteristic
192#1805C2211yescharacteristic
193#1805C2211yescharacteristic
194#1802C2211yescharacteristic
195#1802C2211yescharacteristic
196#1798C2211yescharacteristic
197#1798C2211yescharacteristic
198#1788C2211yescharacteristic
199#1788C2211yescharacteristic
200#1767C2211yescharacteristic
201#1763C2211yescharacteristic
202#1763C2211yescharacteristic
203#1736C2211yescharacteristic
204C2×#340C2211yescharacteristic
205C22×#41C2311yescharacteristic
206C22×#41C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C23×C8C2311yescharacteristic
214C23×C8C2311yescharacteristic
215#554—24no—
216#554—24no—
217#553—24no—
218#553D418yes—
219#550—24no—
220#550—24no—
221C2×C4⋊Q8C2311yescharacteristic
222C2×C4⋊Q8C2311yescharacteristic
223C2×#127—21no—
224C2×#127C2311yescharacteristic
225C2×#126—21no—
226C2×#125—21no—
227C2×#125C2311yescharacteristic
228C2×#124—21no—
229C2×#124—21no—
230C2×#124C2311yescharacteristic
231C2×#124C2311yescharacteristic
232C2×#123—21no—
233C2×#123—21no—
234C2×#123—21no—
235C2×#123—21no—
236C2×#123—21no—
237C2×C22⋊Q8—21no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8C2311yescharacteristic
240C2×C22⋊Q8C2311yescharacteristic
241C2×#121—21no—
242C2×#121—21no—
243C2×#121—21no—
244C2×#121C2311yescharacteristic
245C2×#121C2311yescharacteristic
246C2×#121C2311yescharacteristic
247C2×#121C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×D4—21no—
251C2×C4×D4—21no—
252C2×C4×D4—21no—
253C2×C4×D4—21no—
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×#117—21no—
259C2×#117—21no—
260C2×#117C2311yescharacteristic
261C2×#117C2311yescharacteristic
262C2×#117C2311yescharacteristic
263C2×#117C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2311yescharacteristic
268#501—24no—
269#490—24no—
270#485—24no—
271#484—24no—
272#482—24no—
273#481—24no—
274#480—24no—
275#480—24no—
276#479—24no—
277#479—24no—
278#474—24no—
279#469—24no—
280#468—24no—
281#466—24no—
282#465—24no—
283#463—42no—
284#463—42no—
285#459—24no—
286#449—24no—
287#449—24no—
288#440—24no—
289#440—24no—
290#435—24no—
291#435—24no—
292#428—24no—
293C2×#107—24no—
294C2×#107C2311yescharacteristic
295C2×#107C2311yescharacteristic
296C2×#107C2311yescharacteristic
297C2×#107C2311yescharacteristic
298C2×#107C2311yescharacteristic
299C2×#107C2311yescharacteristic
300C2×#107C2311yescharacteristic
301C2×#107C2311yescharacteristic
302C2×#106C2311yescharacteristic
303C2×#106C2311yescharacteristic
304C2×#106C2311yescharacteristic
305C2×#106C2311yescharacteristic
306#424—42no—
307#424—42no—
308C2×C4⋊C8C2311yescharacteristic
309C2×C4⋊C8C2311yescharacteristic
310C2×C4⋊C8C2311yescharacteristic
311C2×C4⋊C8C2311yescharacteristic
312C2×C4⋊C8C2311yescharacteristic
313C2×C4⋊C8C2311yescharacteristic
314C2×C4⋊C8C2311yescharacteristic
315C2×C4⋊C8C2311yescharacteristic
316C2×C4⋊C8C2311yescharacteristic
317C2×C4⋊C8C2311yescharacteristic
318C2×C4⋊C8C2311yescharacteristic
319C2×C4⋊C8C2311yescharacteristic
320#417—24no—
321#417—42no—
322#416—24no—
323#416—42no—
324C2×#103C2311yescharacteristic
325C2×#103C2311yescharacteristic
326C2×#103C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#103C2311yescharacteristic
329C2×#103C2311yescharacteristic
330C2×#103C2311yescharacteristic
331C2×#103C2311yescharacteristic
332C2×#103C2311yescharacteristic
333C2×#103C2311yescharacteristic
334C2×#103C2311yescharacteristic
335C2×#103C2311yescharacteristic
336C2×#103C2311yescharacteristic
337C2×#103C2311yescharacteristic
338C2×#102C2311yescharacteristic
339C2×#102C2311yescharacteristic
340C2×#102C2311yescharacteristic
341C2×#102C2311yescharacteristic
342C2×#102C2311yescharacteristic
343C2×#102C2311yescharacteristic
344C2×#102C2311yescharacteristic
345C2×#102C2311yescharacteristic
346C2×#102C2311yescharacteristic
347C2×#102C2311yescharacteristic
348C2×#102C2311yescharacteristic
349C2×#102C2311yescharacteristic
350C2×#102C2311yescharacteristic
351C2×#102C2311yescharacteristic
352C2×#102C2311yescharacteristic
353C2×#102C2311yescharacteristic
354C2×#102C2311yescharacteristic
355C2×#102C2311yescharacteristic
356C2×C22⋊C8C2311yescharacteristic
357C2×C22⋊C8C2311yescharacteristic
358C2×C22⋊C8C2311yescharacteristic
359C2×C22⋊C8C2311yescharacteristic
360C2×#97C2311yescharacteristic
361C2×#97C2311yescharacteristic
362#399—21no—
363#399—21no—
364#399—21no—
365#399—21no—
366#396—21no—
367#396—21no—
368#396—21no—
369#396—21no—
370#395—21no—
371#395—21no—
372#394—21no—
373#394—21no—
374#394—21no—
375#394—21no—
376#394—21no—
377#394—21no—
378#394—21no—
379#394—21no—
380#394—21no—
381#394—21no—
382#391C2311yescharacteristic
383#391C2311yescharacteristic
384#391C2311yescharacteristic
385#391C2311yescharacteristic
386#390—21no—
387#390—21no—
388#390—21no—
389#390—21no—
390#390—21no—
391#390—21no—
392#390—21no—
393#390D411yescharacteristic
394#390D411yescharacteristic
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#390C2311yescharacteristic
400#390C2311yescharacteristic
401#390C2311yescharacteristic
402#390C2311yescharacteristic
403#389—21no—
404#389—21no—
405#389—21no—
406#389—21no—
407#389—21no—
408#389—21no—
409#389—21no—
410#389D411yescharacteristic
411#389D411yescharacteristic
412#389C2311yescharacteristic
413#389C2311yescharacteristic
414#389C2311yescharacteristic
415#389C2311yescharacteristic
416#389C2311yescharacteristic
417#389C2311yescharacteristic
418#389C2311yescharacteristic
419#389C2311yescharacteristic
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#386—21no—
444#386—21no—
445#386—21no—
446#386—21no—
447#386—21no—
448#386—21no—
449#385—21no—
450#385—21no—
451#385—21no—
452#385—21no—
453#385—21no—
454#385—21no—
455#385—21no—
456#385—21no—
457#385—21no—
458#385—21no—
459#385—21no—
460#384—21no—
461#384C2311yescharacteristic
462#384C2311yescharacteristic
463#384C2311yescharacteristic
464#383—21no—
465#382—21no—
466#382C2311yescharacteristic
467#381—21no—
468#380—21no—
469#380—21no—
470#380—21no—
471#380—21no—
472#380—21no—
473#380—21no—
474#380—21no—
475#380C2311yescharacteristic
476#380C2311yescharacteristic
477C4×C4⋊C4—21no—
478C4×C4⋊C4—21no—
479C4×C4⋊C4—21no—
480C4×C4⋊C4—21no—
481C4×C4⋊C4—21no—
482C4×C4⋊C4—21no—
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2311yescharacteristic
489C4×C22⋊C4—21no—
490C4×C22⋊C4—21no—
491C4×C22⋊C4—21no—
492C4×C22⋊C4C2311yescharacteristic
493C4×C22⋊C4C2311yescharacteristic
494C2×#95—21no—
495C43C2311yescharacteristic
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#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515#336C2311yescharacteristic
516#336C2311yescharacteristic
517#336C2311yescharacteristic
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—41no—
525C2×#41—41no—
526C2×#41—41no—
527C2×#41—41no—
528C2×#41—41no—
529C2×#41—41no—
530C22×Q8—21no—
531C22×Q8C2411yescharacteristic
532C22×Q8C2411yescharacteristic
533C22×D4—21no—
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4C2×D411yescharacteristic
542C22×D4C2411yescharacteristic
543C22×D4C2411yescharacteristic
544C22×D4C2411yescharacteristic
545C23×C4—21no—
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×SD16—22no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—41no—
561C2×SD16—41no—
562C2×D8—22no—
563C2×D8—22no—
564C2×D8—41no—
565C2×D8—41no—
566C2×D8—41no—
567C2×D8—41no—
568C2×M16—22no—
569C2×M16—22no—
570C2×M16—22no—
571C2×M16—41no—
572C2×M16—41no—
573C2×M16—41no—
574C22×C8—22no—
575C22×C8—22no—
576C22×C8—22no—
577C22×C8—41no—
578C22×C8—41no—
579C22×C8—41no—
580C22×C8C2411yescharacteristic
581C22×C8C2411yescharacteristic
582C22×C8C2411yescharacteristic
583C22×C8C2411yescharacteristic
584C22×C8C2411yescharacteristic
585C22×C8C2411yescharacteristic
586C22×C8C2411yescharacteristic
587C22×C8C2411yescharacteristic
588C4⋊Q8—22no—
589C4⋊Q8—22no—
590C4⋊Q8—22no—
591C4⋊Q8—41no—
592#127—22no—
593#127—22no—
594#127—44no—
595#126—28no—
596#125—22no—
597#125—44no—
598#125C2×D414yes—
599#124—41no—
600#124—41no—
601#124—41no—
602#124—41no—
603#124—82no—
604#124—82no—
605#123—28no—
606#123—82no—
607#123—82no—
608#123—82no—
609#123—82no—
610C22⋊Q8—22no—
611C22⋊Q8—22no—
612C22⋊Q8—22no—
613C22⋊Q8—22no—
614C22⋊Q8—44no—
615C22⋊Q8—44no—
616#121—28no—
617#121—22no—
618#121—22no—
619#121—22no—
620#121—22no—
621#121—22no—
622#121—22no—
623#121—44no—
624#121—44no—
625#121C2×D414yes—
626#121C2×D414yes—
627C4×Q8—22no—
628C4×Q8—22no—
629C4×Q8—22no—
630C4×Q8—22no—
631C4×D4—28no—
632C4×D4—22no—
633C4×D4—41no—
634C4×D4—41no—
635C4×D4—41no—
636C4×D4—41no—
637C4×D4—44no—
638C4×D4—44no—
639C4×D4—82no—
640C4×D4C2×D414yes—
641C4×D4C2×D414yes—
642C4×D4#4114yes—
643#117—22no—
644#117—41no—
645#117—41no—
646#117—41no—
647#117—41no—
648#117—41no—
649#117—41no—
650#117—82no—
651#117—82no—
652#117C2×D414yes—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—22no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—22no—
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—21no—
679C2×C4⋊C4—21no—
680C2×C4⋊C4—21no—
681C2×C4⋊C4—21no—
682C2×C4⋊C4—21no—
683C2×C4⋊C4—21no—
684C2×C4⋊C4—21no—
685C2×C4⋊C4—41no—
686C2×C4⋊C4—41no—
687C2×C4⋊C4C2×D414yes—
688C2×C4⋊C4C2×D411yescharacteristic
689C2×C4⋊C4C2×D411yescharacteristic
690C2×C4⋊C4C2×D411yescharacteristic
691C2×C4⋊C4C2×D411yescharacteristic
692C2×C4⋊C4C2×D411yescharacteristic
693C2×C4⋊C4C2×D411yescharacteristic
694C2×C4⋊C4C2×D411yescharacteristic
695C2×C4⋊C4C2411yescharacteristic
696C2×C4⋊C4C2411yescharacteristic
697C2×C4⋊C4C2411yescharacteristic
698C2×C4⋊C4C2411yescharacteristic
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2411yescharacteristic
701C2×C4⋊C4C2411yescharacteristic
702C2×C4⋊C4C2411yescharacteristic
703C2×C4⋊C4C2411yescharacteristic
704C2×C4⋊C4C2411yescharacteristic
705C2×C4⋊C4C2411yescharacteristic
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⋊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⋊C4C2×D411yescharacteristic
740C2×C22⋊C4C2×D411yescharacteristic
741C2×C22⋊C4C2×D411yescharacteristic
742C2×C22⋊C4C2×D411yescharacteristic
743C2×C22⋊C4C2×D411yescharacteristic
744C2×C22⋊C4C2×D411yescharacteristic
745C2×C22⋊C4C2×D411yescharacteristic
746C2×C22⋊C4C2×D411yescharacteristic
747C2×C22⋊C4C2×D411yescharacteristic
748C2×C22⋊C4C2×D411yescharacteristic
749C2×C42—21no—
750C2×C42—21no—
751C2×C42—21no—
752C2×C42—21no—
753C2×C42—21no—
754C2×C42—21no—
755C2×C42—21no—
756C2×C42—21no—
757C2×C42—21no—
758C2×C42C2×D411yescharacteristic
759C2×C42C2×D411yescharacteristic
760C2×C42C2×D411yescharacteristic
761C2×C42C2×D411yescharacteristic
762C2×C42C2411yescharacteristic
763C2×C42C2411yescharacteristic
764C2×C42C2411yescharacteristic
765C2×C42C2411yescharacteristic
766C2×C42C2411yescharacteristic
767#107—22no—
768#107—22no—
769#107—22no—
770#107—22no—
771#107—22no—
772#107—22no—
773#107—22no—
774#107—22no—
775#106—22no—
776#106—22no—
777#106—22no—
778#106—22no—
779C4⋊C8—22no—
780C4⋊C8—22no—
781C4⋊C8—22no—
782C4⋊C8—22no—
783C4⋊C8—22no—
784C4⋊C8—41no—
785C4⋊C8—41no—
786C4⋊C8—41no—
787C4⋊C8—41no—
788C4⋊C8—41no—
789C4⋊C8—41no—
790C4⋊C8—41no—
791#103—22no—
792#103—22no—
793#103—22no—
794#103—22no—
795#103—22no—
796#103—22no—
797#103—22no—
798#103—22no—
799#103—41no—
800#103—41no—
801#103—41no—
802#103—41no—
803#103—41no—
804#103—41no—
805#102—22no—
806#102—22no—
807#102—22no—
808#102—22no—
809#102—22no—
810#102—22no—
811#102—22no—
812#102—22no—
813#102—22no—
814#102—22no—
815#102—22no—
816#102—22no—
817#102—41no—
818#102—41no—
819#102—41no—
820#102—41no—
821#102—41no—
822#102—41no—
823C22⋊C8—22no—
824C22⋊C8—22no—
825C22⋊C8—22no—
826C22⋊C8—22no—
827#97—22no—
828#97—22no—
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—
854#95C2×D411yescharacteristic
855#95C2×D411yescharacteristic
856#95C2×D411yescharacteristic
857#95C2×D411yescharacteristic
858#95C2×D411yescharacteristic
859#95C2×D411yescharacteristic
860C24—21no—
861C24—21no—
862C24—21no—
863C24C22×D411yescharacteristic
864C24C22×D411yescharacteristic
865#41—44no—
866#41—44no—
867#41—44no—
868#41—44no—
869#41—82no—
870#41—82no—
871#41—82no—
872#41—82no—
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—42no—
885C2×Q8—81no—
886C2×Q8—81no—
887C2×Q82−1+412yes—
888C2×D4—24no—
889C2×D4—24no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—21no—
898C2×D4—21no—
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—21no—
906C2×D4—21no—
907C2×D4—41no—
908C2×D4—41no—
909C2×D4—42no—
910C2×D4—42no—
911C2×D4—42no—
912C2×D4—42no—
913C2×D4—42no—
914C2×D4—42no—
915C2×D4—42no—
916C2×D4—42no—
917C2×D4—42no—
918C2×D4—42no—
919C2×D4—81no—
920C2×D4—81no—
921C2×D4—81no—
922C2×D4—81no—
923C2×D4—81no—
924C2×D4—81no—
925C2×D4—81no—
926C2×D4—81no—
927C2×D4—81no—
928C2×D4—81no—
929C2×D4—81no—
930C2×D4—81no—
931C2×D4#12114yes—
932C2×D4C22×D412yes—
933C22×C4—21no—
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—24no—
946C22×C4—24no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—42no—
957C22×C4—42no—
958C22×C4—42no—
959C22×C4—42no—
960C22×C4—42no—
961C22×C4—42no—
962C22×C4—81no—
963C22×C4—81no—
964C22×C4—81no—
965C22×C4—81no—
966C22×C4—81no—
967C22×C4—81no—
968C22×C4—81no—
969C22×C4—81no—
970C22×C4—81no—
971C22×C4—81no—
972C22×C4—81no—
973C22×C4—81no—
974C22×C4—81no—
975C22×C4—81no—
976C22×C4—81no—
977C22×C4—81no—
978C22×C4—81no—
979C22×C4—81no—
980C22×C4—81no—
981C22×C4C22×D411yescharacteristic
982C22×C4C22×D411yescharacteristic
983C22×C4C22×D411yescharacteristic
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×D412yes—
993C22×C4C22×D412yes—
994C22×C4C22×D411yescharacteristic
995C22×C4C2×#4112yes—
996C22×C4C2×#4112yes—
997C22×C4C2511yescharacteristic
998SD16—44no—
999SD16—44no—
1000D8—82no—
1001D8—82no—
1002M16—44no—
1003M16—82no—
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—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—44no—
1028C2×C8—82no—
1029C2×C8H(5,𝔽2)12yes—
1030C4⋊C4—24no—
1031C4⋊C4—24no—
1032C4⋊C4—24no—
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—21no—
1052C4⋊C4—41no—
1053C4⋊C4—41no—
1054C4⋊C4—41no—
1055C4⋊C4—41no—
1056C4⋊C4—41no—
1057C4⋊C4—41no—
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—81no—
1071C4⋊C4—81no—
1072C4⋊C4—81no—
1073C4⋊C4—81no—
1074C4⋊C4—81no—
1075C4⋊C4—81no—
1076C4⋊C4—81no—
1077C4⋊C4—81no—
1078C4⋊C4—81no—
1079C4⋊C4—81no—
1080C4⋊C4—81no—
1081C4⋊C4—81no—
1082C4⋊C4#12114yes—
1083C4⋊C4C22×D412yes—
1084C4⋊C4C22×D412yes—
1085C4⋊C4C22×D412yes—
1086C22⋊C4—24no—
1087C22⋊C4—24no—
1088C22⋊C4—24no—
1089C22⋊C4—24no—
1090C22⋊C4—22no—
1091C22⋊C4—22no—
1092C22⋊C4—41no—
1093C22⋊C4—41no—
1094C22⋊C4—41no—
1095C22⋊C4—41no—
1096C22⋊C4—41no—
1097C22⋊C4—41no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
1106C22⋊C4—42no—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C22⋊C4—81no—
1114C22⋊C4—81no—
1115C22⋊C4—81no—
1116C22⋊C4—81no—
1117C22⋊C4—81no—
1118C22⋊C4—81no—
1119C22⋊C4—81no—
1120C22⋊C4—81no—
1121C22⋊C4—81no—
1122C22⋊C4—81no—
1123C22⋊C4—81no—
1124C22⋊C4—81no—
1125C22⋊C4—81no—
1126C22⋊C4—81no—
1127C22⋊C4#12114yes—
1128C22⋊C4#12114yes—
1129C42—24no—
1130C42—22no—
1131C42—21no—
1132C42—21no—
1133C42—21no—
1134C42—21no—
1135C42—21no—
1136C42—21no—
1137C42—21no—
1138C42—21no—
1139C42—41no—
1140C42—41no—
1141C42—41no—
1142C42—42no—
1143C42—42no—
1144C42—42no—
1145C42—81no—
1146C42—81no—
1147C42—81no—
1148C42—81no—
1149C42—81no—
1150C42C22×D412yes—
1151C42C2×#4112yes—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—22no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
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—
1185C23C2×#12112yes—
1186C23C2×#12112yes—
1187C23C23×D411yescharacteristic
1188Q8—22no—
1189Q8—22no—
1190Q8—41no—
1191Q8—41no—
1192Q8—41no—
1193Q8—41no—
1194Q8—41no—
1195Q8—41no—
1196Q8—162no—
1197D4—22no—
1198D4—22no—
1199D4—44no—
1200D4—41no—
1201D4—41no—
1202D4—41no—
1203D4—41no—
1204D4—41no—
1205D4—41no—
1206D4—41no—
1207D4—41no—
1208D4—41no—
1209D4—41no—
1210D4—84no—
1211D4—84no—
1212D4—84no—
1213D4—84no—
1214D4—84no—
1215D4—162no—
1216D4—162no—
1217D4—162no—
1218C2×C4—21no—
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—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—21no—
1251C2×C4—22no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
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—84no—
1297C2×C4—84no—
1298C2×C4—84no—
1299C2×C4—84no—
1300C2×C4—162no—
1301C2×C4—162no—
1302C2×C4—162no—
1303C2×C4—162no—
1304C2×C4—162no—
1305C2×C4C2×#12112yes—
1306C2×C4C2×#12112yes—
1307C2×C4C2×#12112yes—
1308C2×C4C2×#12112yes—
1309C2×C4#57612yes—
1310C2×C4C23×D411yescharacteristic
1311C2×C4C22×#4111yescharacteristic
1312C2×C4C2×H(5,𝔽2)11yescharacteristic
1313C2×C4C2×2−1+411yescharacteristic
1314C2×C4#58511yescharacteristic
1315C2×C4#58511yescharacteristic
1316C8—22no—
1317C8—41no—
1318C8—41no—
1319C8—41no—
1320C8—41no—
1321C8—41no—
1322C8—41no—
1323C8—41no—
1324C22—22no—
1325C22—22no—
1326C22—22no—
1327C22—22no—
1328C22—22no—
1329C22—22no—
1330C22—41no—
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—41no—
1335C22—41no—
1336C22—41no—
1337C22—41no—
1338C22—42no—
1339C22—42no—
1340C22—42no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—81no—
1356C22—81no—
1357C22—81no—
1358C22—81no—
1359C22C22×#12111yescharacteristic
1360C22#348911yescharacteristic
1361C22#349611yescharacteristic
1362C22C2×#57611yescharacteristic
1363C22#358511yescharacteristic
1364C22#358611yescharacteristic
1365C22#358611yescharacteristic
1366C4—22no—
1367C4—22no—
1368C4—22no—
1369C4—22no—
1370C4—22no—
1371C4—42no—
1372C4—42no—
1373C4—42no—
1374C4—41no—
1375C4—41no—
1376C4—41no—
1377C4—41no—
1378C4—41no—
1379C4—41no—
1380C4—41no—
1381C4—42no—
1382C4—81no—
1383C4—81no—
1384C4—81no—
1385C4—81no—
1386C4—81no—
1387C4—81no—
1388C4—81no—
1389C4—81no—
1390C4—81no—
1391C4#348811yescharacteristic
1392C4#348911yescharacteristic
1393C4#352011yescharacteristic
1394C4#352111yescharacteristic
1395C2—42no—
1396C2—42no—
1397C2—82no—
1398C2—161no—
1399C2—161no—
1400C2#3582111yescharacteristic
1401C2#6042711yescharacteristic
1402C2#6042811yescharacteristic
1403C2#6217011yescharacteristic
1404C2#6222611yescharacteristic
1405C2#6233811yescharacteristic
1406C2#6235311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3309C2
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
1. C2×#3346C2semidirect
3. #38952C2semidirect
4. #34483C2semidirect
5. #29824C2semidirect
6. #29769C2semidirect
7. #29767C2semidirect
8. #28661C2semidirect
9. #28287C2semidirect
10. #28129C2semidirect
11. #28127C2semidirect
12. #25467C2semidirect
13. #25291C2semidirect
14. #25221C2semidirect
15. #25200C2semidirect
16. #25104C2semidirect
17. #25085C2semidirect
18. #24833C2semidirect
19. #24767C2semidirect
20. #24763C2semidirect
21. #24749C2semidirect
22. #24592C2semidirect
23. #24576C2semidirect
24. #24489C2semidirect
25. #24485C2semidirect
26. #23683C2semidirect
27. #23616C2semidirect
28. #23611C2semidirect
29. #22652C2semidirect
30. #22497C2semidirect
31. #22422C2semidirect

Maximal subgroups

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

subgroupindex
C2×#33462
C2×#33092
#389522
#344832
#298242
#297692
#297672
#286612
#282872
#281292
#281272
#254672
#252912
#252212
#252002
#251042
#250852
#248332
#247672
#247632
#247492
#245922
#245762
#244892
#244852
#236832
#236162
#236112
#226522
#224972
#224222