Finite Group Databasebeta

← #6552664

Subgroups — #6552664

Order 512.

1874 conjugacy classes of subgroups.

The subgroup lattice has 1372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3344C211yesmaximal, characteristic, complemented
2C2×#3314C211yesmaximal, characteristic
3#38947C211yesmaximal, characteristic
4#34484C211yesmaximal, characteristic, complemented
5#29833C211yesmaximal, characteristic, complemented
6#29767C211yesmaximal, characteristic, complemented
7#29764C211yesmaximal, characteristic, complemented
8#28658C211yesmaximal, characteristic, complemented
9#28281C211yesmaximal, characteristic, complemented
10#28133C211yesmaximal, characteristic, complemented
11#28130C211yesmaximal, characteristic, complemented
12#25462C211yesmaximal, characteristic, complemented
13#25287C211yesmaximal, characteristic, complemented
14#25231C211yesmaximal, characteristic, complemented
15#25201C211yesmaximal, characteristic, complemented
16#25105C211yesmaximal, characteristic, complemented
17#25079C211yesmaximal, characteristic, complemented
18#24824C211yesmaximal, characteristic, complemented
19#24765C211yesmaximal, characteristic, complemented
20#24764C211yesmaximal, characteristic, complemented
21#24741C211yesmaximal, characteristic, complemented
22#24588C211yesmaximal, characteristic, complemented
23#24581C211yesmaximal, characteristic, complemented
24#24489C211yesmaximal, characteristic, complemented
25#24477C211yesmaximal, characteristic, complemented
26#23687C211yesmaximal, characteristic, complemented
27#23614C211yesmaximal, characteristic, complemented
28#23610C211yesmaximal, characteristic, complemented
29#22652C211yesmaximal, characteristic, complemented
30#22496C211yesmaximal, characteristic, complemented
31#22424C211yesmaximal, characteristic
32C2×#554C2211yescharacteristic
33C2×#552C2211yescharacteristic
34C2×#546C2211yescharacteristic
35#3344—28no—
36#3314—28no—
37C2×#501C2211yescharacteristic, complemented
38C2×#489C2211yescharacteristic
39C2×#484C2211yescharacteristic
40C2×#484C2211yescharacteristic, complemented
41C2×#485C2211yescharacteristic
42C2×#483C2211yescharacteristic
43C2×#483C2211yescharacteristic, complemented
44C2×#480C2211yescharacteristic
45C2×#479C2211yescharacteristic, complemented
46C2×#475C2211yescharacteristic, complemented
47C2×#474C2211yescharacteristic
48C2×#470C2211yescharacteristic
49C2×#468C2211yescharacteristic
50C2×#467C2211yescharacteristic
51C2×#467C2211yescharacteristic, complemented
52C2×#464C2211yescharacteristic
53C2×#464C2211yescharacteristic
54C2×#462C2211yescharacteristic, complemented
55C2×#452C2211yescharacteristic
56C2×#450C2211yescharacteristic
57C2×#441C2211yescharacteristic, complemented
58C2×#440C2211yescharacteristic
59C2×#435C2211yescharacteristic
60C2×#435C2211yescharacteristic
61C2×#428C2211yescharacteristic
62C22×#106C2211yescharacteristic, complemented
63C2×#424C2211yescharacteristic
64C2×#424C2211yescharacteristic, complemented
65C2×#417C2211yescharacteristic
66C2×#418C2211yescharacteristic
67C2×#416C2211yescharacteristic
68C22×#102C2211yescharacteristic
69#2861C2211yescharacteristic
70#2707—21no—
71#2707—21no—
72#2697—21no—
73#2697—21no—
74#2621C2211yescharacteristic
75#2620C2211yescharacteristic
76#2566C2211yescharacteristic
77#2545C2211yescharacteristic
78#2504C2211yescharacteristic
79#2499C2211yescharacteristic
80#2480—21no—
81#2480—21no—
82#2476—21no—
83#2476—21no—
84#2435C2211yescharacteristic
85#2432C2211yescharacteristic
86#2378—21no—
87#2378—21no—
88#2370—21no—
89#2369C2211yescharacteristic, complemented
90#2362C2211yescharacteristic
91#2362C2211yescharacteristic, complemented
92#2354—21no—
93#2354C2211yescharacteristic
94Q8×C4⋊C4C2211yescharacteristic, complemented
95#2344C2211yescharacteristic
96#2344C2211yescharacteristic, complemented
97#2330—21no—
98#2323—21no—
99#2323—21no—
100#2323C2211yescharacteristic
101#2323C2211yescharacteristic, complemented
102#2319—21no—
103#2316C2211yescharacteristic
104#2316C2211yescharacteristic, complemented
105#2311C2211yescharacteristic
106#2309C2211yescharacteristic
107C4×C4⋊Q8C2211yescharacteristic, complemented
108C4×#124C2211yescharacteristic
109#2295C2211yescharacteristic, complemented
110#2293C2211yescharacteristic
111#2085C2211yescharacteristic, complemented
112#2085C2211yescharacteristic, complemented
113#2085C2211yescharacteristic, complemented
114#2083C2211yescharacteristic, complemented
115#2083C2211yescharacteristic, complemented
116#2074C2211yescharacteristic, complemented
117#2068C2211yescharacteristic, complemented
118#2068C2211yescharacteristic, complemented
119#2068C2211yescharacteristic, complemented
120#2068C2211yescharacteristic, complemented
121#2067C2211yescharacteristic
122#2067C2211yescharacteristic
123#2067C2211yescharacteristic
124#2067C2211yescharacteristic
125#2067C2211yescharacteristic
126#2066C2211yescharacteristic, complemented
127#2066C2211yescharacteristic, complemented
128#2066C2211yescharacteristic, complemented
129#2066C2211yescharacteristic, complemented
130#2066C2211yescharacteristic, complemented
131#2065C2211yescharacteristic
132#2065C2211yescharacteristic
133#2065C2211yescharacteristic
134#2065C2211yescharacteristic
135#2065C2211yescharacteristic
136#2065C2211yescharacteristic
137#2065C2211yescharacteristic
138#2065C2211yescharacteristic
139#2056C2211yescharacteristic, complemented
140#2056C2211yescharacteristic, complemented
141#2056C2211yescharacteristic, complemented
142#2055C2211yescharacteristic
143#2055C2211yescharacteristic
144#2055C2211yescharacteristic
145#2043C2211yescharacteristic, complemented
146#2043C2211yescharacteristic, complemented
147#2042C2211yescharacteristic
148#2042C2211yescharacteristic
149#2042C2211yescharacteristic
150#2015C2211yescharacteristic
151#1992C2211yescharacteristic, complemented
152#1989C2211yescharacteristic, complemented
153#1983C2211yescharacteristic
154#1983C2211yescharacteristic
155#1983C2211yescharacteristic
156#1983C2211yescharacteristic
157#1981C2211yescharacteristic, complemented
158#1959C2211yescharacteristic
159#1949C2211yescharacteristic, complemented
160#1949C2211yescharacteristic, complemented
161#1949C2211yescharacteristic, complemented
162#1947C2211yescharacteristic, complemented
163#1940C2211yescharacteristic, complemented
164#1940C2211yescharacteristic, complemented
165#1928C2211yescharacteristic, complemented
166#1928C2211yescharacteristic, complemented
167#1927C2211yescharacteristic, complemented
168#1926C2211yescharacteristic
169#1926C2211yescharacteristic
170#1926C2211yescharacteristic
171#1926C2211yescharacteristic
172#1925C2211yescharacteristic
173#1894C2211yescharacteristic
174#1894C2211yescharacteristic, complemented
175#1893C2211yescharacteristic
176#1892C2211yescharacteristic
177#1880C2211yescharacteristic
178#1880C2211yescharacteristic
179#1880C2211yescharacteristic
180#1878C2211yescharacteristic, complemented
181#1875C2211yescharacteristic
182#1873C2211yescharacteristic
183#1873C2211yescharacteristic
184#1873C2211yescharacteristic, complemented
185#1851C2211yescharacteristic
186#1851C2211yescharacteristic, complemented
187#1850C2211yescharacteristic
188#1850C2211yescharacteristic, complemented
189#1842C2211yescharacteristic, complemented
190#1825C2211yescharacteristic
191#1824C2211yescharacteristic, complemented
192#1805C2211yescharacteristic, complemented
193#1803C2211yescharacteristic, complemented
194#1803C2211yescharacteristic, complemented
195#1802C2211yescharacteristic
196#1798C2211yescharacteristic
197#1798C2211yescharacteristic, complemented
198#1788C2211yescharacteristic
199#1786C2211yescharacteristic
200#1767C2211yescharacteristic, complemented
201#1763C2211yescharacteristic, complemented
202#1762C2211yescharacteristic
203#1736C2211yescharacteristic, complemented
204#1735C2211yescharacteristic
205C22×#41C2311yescharacteristic
206C23×D4C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C23×C8C2311yescharacteristic
214C23×C8C2311yescharacteristic
215#554—24no—
216#554D418yes—
217#552—24no—
218#552—24no—
219#546—24no—
220#546—24no—
221C2×C4⋊Q8C2311yescharacteristic
222C2×C4⋊Q8C2311yescharacteristic
223C2×#126—21no—
224C2×#125—21no—
225C2×#125—21no—
226C2×#125C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#124C2311yescharacteristic
229C2×#124C2311yescharacteristic
230C2×#123—21no—
231C2×#123—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239C2×#121—21no—
240C2×#121C2311yescharacteristic
241C2×#120—21no—
242C2×C4×Q8—21no—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×D4—21no—
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×#117—21no—
251C2×#117—21no—
252C2×#117—21no—
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C22⋊C4—21no—
262#501—24no—
263#489—24no—
264#485—24no—
265#484—24no—
266#484—24no—
267#483—24no—
268#483—24no—
269#480—24no—
270#479—24no—
271#475—24no—
272#474—24no—
273#470—24no—
274#468—24no—
275#467—24no—
276#467—24no—
277#464—24no—
278#464—42no—
279#462—42no—
280#452—24no—
281#450—24no—
282#441—24no—
283#440—24no—
284#435—24no—
285#435—24no—
286#428—24no—
287C2×#107C2311yescharacteristic
288C2×#107C2311yescharacteristic
289C2×#107C2311yescharacteristic
290C2×#107C2311yescharacteristic
291C2×#107C2311yescharacteristic
292C2×#107C2311yescharacteristic
293C2×#106—24no—
294C2×#106C2311yescharacteristic
295C2×#106C2311yescharacteristic
296C2×#106C2311yescharacteristic
297C2×#106C2311yescharacteristic
298C2×#106C2311yescharacteristic
299C2×#106C2311yescharacteristic
300#424—42no—
301#424—42no—
302C2×C4⋊C8C2311yescharacteristic
303C2×C4⋊C8C2311yescharacteristic
304C2×C4⋊C8C2311yescharacteristic
305C2×C4⋊C8C2311yescharacteristic
306C2×C4⋊C8C2311yescharacteristic
307C2×C4⋊C8C2311yescharacteristic
308C2×C4⋊C8C2311yescharacteristic
309C2×C4⋊C8C2311yescharacteristic
310C2×C4⋊C8C2311yescharacteristic
311C2×C4⋊C8C2311yescharacteristic
312C2×C4⋊C8C2311yescharacteristic
313C2×C4⋊C8C2311yescharacteristic
314#418—42no—
315#417—24no—
316#416—42no—
317C2×#103C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
325C2×#103C2311yescharacteristic
326C2×#103C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#103C2311yescharacteristic
329C2×#103C2311yescharacteristic
330C2×#103C2311yescharacteristic
331C2×#103C2311yescharacteristic
332C2×#103C2311yescharacteristic
333C2×#103C2311yescharacteristic
334C2×#103C2311yescharacteristic
335C2×#102—24no—
336C2×#102C2311yescharacteristic
337C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
351C2×C22⋊C8C2311yescharacteristic
352C2×C22⋊C8C2311yescharacteristic
353C2×C22⋊C8C2311yescharacteristic
354C2×#97C2311yescharacteristic
355C2×#97C2311yescharacteristic
356#398—21no—
357#398—21no—
358#397—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#396—21no—
368#396—21no—
369#396—21no—
370#394—21no—
371#394—21no—
372#394—21no—
373#394—21no—
374#394—21no—
375#394—21no—
376#391—21no—
377#391—21no—
378#391—21no—
379#391C2311yescharacteristic
380#391C2311yescharacteristic
381#391C2311yescharacteristic
382#391C2311yescharacteristic
383#391C2311yescharacteristic
384#391C2311yescharacteristic
385#390—21no—
386#390—21no—
387#390—21no—
388#390D411yescharacteristic
389#390D411yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#389—21no—
397#389—21no—
398#389—21no—
399#389—21no—
400#389—21no—
401#389—21no—
402#389—21no—
403#389—21no—
404#389—21no—
405#389—21no—
406#389D411yescharacteristic
407#389D411yescharacteristic
408#389C2311yescharacteristic
409#389C2311yescharacteristic
410#389C2311yescharacteristic
411#389C2311yescharacteristic
412#389C2311yescharacteristic
413#389C2311yescharacteristic
414#389C2311yescharacteristic
415#389C2311yescharacteristic
416#388—21no—
417#388—21no—
418#388—21no—
419#388—21no—
420#388—21no—
421#388—21no—
422#388—21no—
423#388—21no—
424#388—21no—
425#388—21no—
426#388—21no—
427#388—21no—
428#388—21no—
429#388—21no—
430#388—21no—
431#388—21no—
432#388—21no—
433#388—21no—
434#388D411yescharacteristic
435#388D411yescharacteristic
436#388D411yescharacteristic
437#388D411yescharacteristic
438#387—21no—
439#387—21no—
440#387—21no—
441#387—21no—
442#387—21no—
443#387—21no—
444#387—21no—
445#387—21no—
446#387—21no—
447#387—21no—
448#387—21no—
449#387—21no—
450#386—21no—
451#386—21no—
452#386—21no—
453#386—21no—
454#385—21no—
455#385—21no—
456#385—21no—
457#385—21no—
458#384—21no—
459#384C2311yescharacteristic
460#384C2311yescharacteristic
461#382C2311yescharacteristic
462#382C2311yescharacteristic
463#381—21no—
464#381—21no—
465#380—21no—
466#380—21no—
467#380—21no—
468#380—21no—
469#380—21no—
470#380—21no—
471#380C2311yescharacteristic
472#380C2311yescharacteristic
473#379—21no—
474#379—21no—
475#379—21no—
476#379—21no—
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⋊C4—21no—
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2311yescharacteristic
490C4×C22⋊C4—21no—
491C4×C22⋊C4—21no—
492C4×C22⋊C4C2311yescharacteristic
493C4×C22⋊C4C2311yescharacteristic
494#376—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
518C25—21no—
519C2×#41—22no—
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—41no—
523C2×#41—41no—
524C2×#41—41no—
525C22×Q8—21no—
526C22×Q8C2411yescharacteristic
527C22×Q8C2411yescharacteristic
528C22×Q8C2411yescharacteristic
529C22×D4—22no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—22no—
533C22×D4—21no—
534C22×D4—22no—
535C22×D4—41no—
536C22×D4—41no—
537C22×D4—41no—
538C22×D4C2×D411yescharacteristic
539C22×D4C2411yescharacteristic
540C22×D4C2411yescharacteristic
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—21no—
546C23×C4C2411yescharacteristic
547C23×C4C2411yescharacteristic
548C2×Q16—22no—
549C2×Q16—22no—
550C2×Q16—22no—
551C2×Q16—41no—
552C2×Q16—41no—
553C2×Q16—41no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—41no—
558C2×SD16—41no—
559C2×SD16—41no—
560C2×M16—22no—
561C2×M16—22no—
562C2×M16—22no—
563C2×M16—41no—
564C2×M16—41no—
565C2×M16—41no—
566C22×C8—22no—
567C22×C8—22no—
568C22×C8—22no—
569C22×C8—41no—
570C22×C8—41no—
571C22×C8—41no—
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577C22×C8C2411yescharacteristic
578C22×C8C2411yescharacteristic
579C22×C8C2411yescharacteristic
580C4⋊Q8—22no—
581C4⋊Q8—41no—
582C4⋊Q8—41no—
583C4⋊Q8C2×D414yes—
584#126—44no—
585#125—28no—
586#125—22no—
587#125—22no—
588#125—44no—
589#124—22no—
590#124—22no—
591#124—22no—
592#124—41no—
593#124—41no—
594#124—41no—
595#123—44no—
596#123—44no—
597C22⋊Q8—22no—
598C22⋊Q8—22no—
599C22⋊Q8—28no—
600C22⋊Q8—28no—
601C22⋊Q8—22no—
602C22⋊Q8—22no—
603C22⋊Q8—22no—
604C22⋊Q8—22no—
605C22⋊Q8—22no—
606C22⋊Q8—22no—
607C22⋊Q8C2×D414yes—
608C22⋊Q8C2×D414yes—
609#121—22no—
610#121—22no—
611#121—44no—
612#120—44no—
613C4×Q8—22no—
614C4×Q8—22no—
615C4×Q8—22no—
616C4×Q8—41no—
617C4×Q8—41no—
618C4×Q8—41no—
619C4×Q8—41no—
620C4×Q8—82no—
621C4×Q8C2×D414yes—
622C4×D4—28no—
623C4×D4—22no—
624C4×D4—22no—
625C4×D4C2×D414yes—
626C4×D4#4114yes—
627#117—22no—
628#117—22no—
629#117—41no—
630#117—41no—
631#117—41no—
632#117—41no—
633#117—44no—
634#117—41no—
635#117—41no—
636#117—41no—
637#117—41no—
638#117—82no—
639#117—82no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—22no—
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⋊C4C2×D414yes—
674C2×C4⋊C4C2×D414yes—
675C2×C4⋊C4C2×D411yescharacteristic
676C2×C4⋊C4C2×D411yescharacteristic
677C2×C4⋊C4C2×D411yescharacteristic
678C2×C4⋊C4C2×D411yescharacteristic
679C2×C4⋊C4C2×D411yescharacteristic
680C2×C4⋊C4C2×D411yescharacteristic
681C2×C4⋊C4C2×D411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
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—44no—
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C22⋊C4C2×D411yescharacteristic
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×C22⋊C4C2×D411yescharacteristic
733C2×C22⋊C4C2×D411yescharacteristic
734C2×C42—21no—
735C2×C42—21no—
736C2×C42—21no—
737C2×C42—21no—
738C2×C42—21no—
739C2×C42—21no—
740C2×C42—21no—
741C2×C42—21no—
742C2×C42—21no—
743C2×C42—21no—
744C2×C42—21no—
745C2×C42—21no—
746C2×C42C2×D411yescharacteristic
747C2×C42C2×D411yescharacteristic
748C2×C42C2×D411yescharacteristic
749C2×C42C2×D411yescharacteristic
750C2×C42C2411yescharacteristic
751C2×C42C2411yescharacteristic
752C2×C42C2411yescharacteristic
753C2×C42C2411yescharacteristic
754C2×C42C2411yescharacteristic
755#107—22no—
756#107—22no—
757#107—22no—
758#107—22no—
759#107—22no—
760#107—22no—
761#106—22no—
762#106—22no—
763#106—22no—
764#106—22no—
765#106—22no—
766#106—22no—
767C4⋊C8—22no—
768C4⋊C8—22no—
769C4⋊C8—22no—
770C4⋊C8—22no—
771C4⋊C8—22no—
772C4⋊C8—41no—
773C4⋊C8—41no—
774C4⋊C8—41no—
775C4⋊C8—41no—
776C4⋊C8—41no—
777C4⋊C8—41no—
778C4⋊C8—41no—
779#103—22no—
780#103—22no—
781#103—22no—
782#103—22no—
783#103—22no—
784#103—22no—
785#103—22no—
786#103—22no—
787#103—22no—
788#103—22no—
789#103—22no—
790#103—41no—
791#103—41no—
792#103—41no—
793#103—41no—
794#103—41no—
795#103—41no—
796#103—41no—
797#102—22no—
798#102—22no—
799#102—22no—
800#102—22no—
801#102—22no—
802#102—22no—
803#102—22no—
804#102—22no—
805#102—22no—
806#102—41no—
807#102—41no—
808#102—41no—
809#102—41no—
810#102—41no—
811C22⋊C8—22no—
812C22⋊C8—22no—
813C22⋊C8—22no—
814C22⋊C8—22no—
815#97—22no—
816#97—22no—
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#95C2×D411yescharacteristic
849#95C2×D411yescharacteristic
850#95C2×D411yescharacteristic
851#95C2×D411yescharacteristic
852#95C2×D411yescharacteristic
853#95C2×D411yescharacteristic
854C24—21no—
855C24—21no—
856C24—42no—
857C24—42no—
858C24—81no—
859C24—81no—
860C24—81no—
861C24—81no—
862C24—81no—
863C24C22×D411yescharacteristic
864C24C22×D411yescharacteristic
865#41—44no—
866#41—44no—
867#41—82no—
868#41—82no—
869C2×Q8—24no—
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—81no—
888C2×Q8—81no—
889C2×Q8C22×D412yes—
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—44no—
902C2×D4—44no—
903C2×D4—41no—
904C2×D4—41no—
905C2×D4—42no—
906C2×D4—42no—
907C2×D4—42no—
908C2×D4—42no—
909C2×D4—42no—
910C2×D4—82no—
911C2×D4—82no—
912C2×D4—81no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4#12114yes—
917C2×D42−1+412yes—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—24no—
931C22×C4—24no—
932C22×C4—21no—
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—42no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D412yes—
968C22×C4C22×D412yes—
969C22×C4C2×#4112yes—
970C22×C4C2×#4112yes—
971C22×C4C2511yescharacteristic
972Q16—44no—
973Q16—82no—
974SD16—44no—
975SD16—82no—
976M16—44no—
977M16—82no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—44no—
1002C2×C8—82no—
1003C2×C8H(5,𝔽2)12yes—
1004C4⋊C4—24no—
1005C4⋊C4—24no—
1006C4⋊C4—24no—
1007C4⋊C4—24no—
1008C4⋊C4—24no—
1009C4⋊C4—24no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—41no—
1030C4⋊C4—41no—
1031C4⋊C4—41no—
1032C4⋊C4—41no—
1033C4⋊C4—41no—
1034C4⋊C4—41no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4—81no—
1054C4⋊C4—81no—
1055C4⋊C4—81no—
1056C4⋊C4—81no—
1057C4⋊C4—81no—
1058C4⋊C4#12114yes—
1059C4⋊C4C22×D412yes—
1060C4⋊C4C22×D412yes—
1061C4⋊C4C22×D412yes—
1062C22⋊C4—24no—
1063C22⋊C4—24no—
1064C22⋊C4—41no—
1065C22⋊C4—41no—
1066C22⋊C4—41no—
1067C22⋊C4—41no—
1068C22⋊C4—41no—
1069C22⋊C4—41no—
1070C22⋊C4—41no—
1071C22⋊C4—41no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4#12114yes—
1101C22⋊C4#12114yes—
1102C42—24no—
1103C42—21no—
1104C42—21no—
1105C42—21no—
1106C42—21no—
1107C42—21no—
1108C42—21no—
1109C42—21no—
1110C42—21no—
1111C42—41no—
1112C42—41no—
1113C42—41no—
1114C42—41no—
1115C42—42no—
1116C42—42no—
1117C42—42no—
1118C42—42no—
1119C42—42no—
1120C42—81no—
1121C42—81no—
1122C42—81no—
1123C42—81no—
1124C42—81no—
1125C42—81no—
1126C42C22×D412yes—
1127C42C2×#4112yes—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—21no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—22no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—84no—
1155C23—84no—
1156C23—162no—
1157C23—162no—
1158C23—162no—
1159C23—162no—
1160C23—162no—
1161C23C2×#12112yes—
1162C23C2×#12112yes—
1163C23C23×D411yescharacteristic
1164Q8—22no—
1165Q8—22no—
1166Q8—41no—
1167Q8—41no—
1168Q8—41no—
1169Q8—41no—
1170Q8—41no—
1171Q8—41no—
1172Q8—41no—
1173Q8—41no—
1174Q8—41no—
1175Q8—41no—
1176Q8—84no—
1177D4—22no—
1178D4—22no—
1179D4—44no—
1180D4—41no—
1181D4—41no—
1182D4—41no—
1183D4—41no—
1184D4—41no—
1185D4—41no—
1186D4—84no—
1187D4—84no—
1188D4—162no—
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—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
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—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—84no—
1272C2×C4—84no—
1273C2×C4—84no—
1274C2×C4—84no—
1275C2×C4—162no—
1276C2×C4C2×#12112yes—
1277C2×C4C2×#12112yes—
1278C2×C4C2×#12112yes—
1279C2×C4C2×#12112yes—
1280C2×C4C23×D411yescharacteristic
1281C2×C4C22×#4111yescharacteristic
1282C2×C4C2×H(5,𝔽2)11yescharacteristic
1283C2×C4C2×2−1+411yescharacteristic
1284C2×C4#58511yescharacteristic
1285C2×C4#58511yescharacteristic
1286C8—22no—
1287C8—41no—
1288C8—41no—
1289C8—41no—
1290C8—41no—
1291C8—41no—
1292C8—41no—
1293C8—41no—
1294C22—22no—
1295C22—22no—
1296C22—22no—
1297C22—22no—
1298C22—22no—
1299C22—22no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—42no—
1309C22—42no—
1310C22—42no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—168no—
1323C22C22×#12111yescharacteristic
1324C22#348911yescharacteristic
1325C22#349611yescharacteristic
1326C22#358411yescharacteristic
1327C22#358511yescharacteristic
1328C22#358611yescharacteristic
1329C22#358611yescharacteristic
1330C4—22no—
1331C4—22no—
1332C4—22no—
1333C4—22no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—41no—
1342C4—41no—
1343C4—41no—
1344C4—41no—
1345C4—42no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4#348811yescharacteristic
1357C4#348911yescharacteristic
1358C4#352011yescharacteristic
1359C4#352111yescharacteristic
1360C2—42no—
1361C2—42no—
1362C2—82no—
1363C2—161no—
1364C2#3582111yescharacteristic
1365C2#6042411yescharacteristic
1366C2#6043011yescharacteristic
1367C2#6217211yescharacteristic
1368C2#6222811yescharacteristic
1369C2#6233811yescharacteristic
1370C2#6235211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#546C22
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×#3344C2semidirect
4. #34484C2semidirect
5. #29833C2semidirect
6. #29767C2semidirect
7. #29764C2semidirect
8. #28658C2semidirect
9. #28281C2semidirect
10. #28133C2semidirect
11. #28130C2semidirect
12. #25462C2semidirect
13. #25287C2semidirect
14. #25231C2semidirect
15. #25201C2semidirect
16. #25105C2semidirect
17. #25079C2semidirect
18. #24824C2semidirect
19. #24765C2semidirect
20. #24764C2semidirect
21. #24741C2semidirect
22. #24588C2semidirect
23. #24581C2semidirect
24. #24489C2semidirect
25. #24477C2semidirect
26. #23687C2semidirect
27. #23614C2semidirect
28. #23610C2semidirect
29. #22652C2semidirect
30. #22496C2semidirect
37. C2×#501C22semidirect
40. C2×#484C22semidirect
43. C2×#483C22semidirect
45. C2×#479C22semidirect
46. C2×#475C22semidirect
51. C2×#467C22semidirect
54. C2×#462C22semidirect
57. C2×#441C22semidirect
62. C22×#106C22semidirect
64. C2×#424C22semidirect
89. #2369C22semidirect
91. #2362C22semidirect
94. Q8×C4⋊C4C22semidirect
96. #2344C22semidirect
101. #2323C22semidirect
104. #2316C22semidirect
107. C4×C4⋊Q8C22semidirect
109. #2295C22semidirect
111. #2085C22semidirect
112. #2085C22semidirect
113. #2085C22semidirect
114. #2083C22semidirect
115. #2083C22semidirect
116. #2074C22semidirect
117. #2068C22semidirect
118. #2068C22semidirect
119. #2068C22semidirect
120. #2068C22semidirect
126. #2066C22semidirect
127. #2066C22semidirect
128. #2066C22semidirect
129. #2066C22semidirect
130. #2066C22semidirect
139. #2056C22semidirect
140. #2056C22semidirect
141. #2056C22semidirect
145. #2043C22semidirect
146. #2043C22semidirect
151. #1992C22semidirect
152. #1989C22semidirect
157. #1981C22semidirect
159. #1949C22semidirect
160. #1949C22semidirect
161. #1949C22semidirect
162. #1947C22semidirect
163. #1940C22semidirect
164. #1940C22semidirect
165. #1928C22semidirect
166. #1928C22semidirect
167. #1927C22semidirect
174. #1894C22semidirect
180. #1878C22semidirect
184. #1873C22semidirect
186. #1851C22semidirect
188. #1850C22semidirect
189. #1842C22semidirect
191. #1824C22semidirect
192. #1805C22semidirect
193. #1803C22semidirect
194. #1803C22semidirect
197. #1798C22semidirect
200. #1767C22semidirect
201. #1763C22semidirect
203. #1736C22semidirect

Maximal subgroups

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

subgroupindex
C2×#33442
C2×#33142
#389472
#344842
#298332
#297672
#297642
#286582
#282812
#281332
#281302
#254622
#252872
#252312
#252012
#251052
#250792
#248242
#247652
#247642
#247412
#245882
#245812
#244892
#244772
#236872
#236142
#236102
#226522
#224962
#224242