Finite Group Databasebeta

← #6545113

Subgroups — #6545113

Order 512.

1981 conjugacy classes of subgroups.

The subgroup lattice has 1407 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3312C211yesmaximal, characteristic, complemented
2C2×#3270C211yesmaximal, characteristic
3#38946C211yesmaximal, characteristic
4#34487C211yesmaximal, characteristic, complemented
5#29833C211yesmaximal, characteristic, complemented
6#29728C211yesmaximal, characteristic, complemented
7#29724C211yesmaximal, characteristic, complemented
8#28619C211yesmaximal, characteristic, complemented
9#28255C211yesmaximal, characteristic, complemented
10#28133C211yesmaximal, characteristic, complemented
11#28132C211yesmaximal, characteristic, complemented
12#25379C211yesmaximal, characteristic, complemented
13#25333C211yesmaximal, characteristic, complemented
14#25219C211yesmaximal, characteristic, complemented
15#25203C211yesmaximal, characteristic, complemented
16#25095C211yesmaximal, characteristic, complemented
17#25079C211yesmaximal, characteristic, complemented
18#24769C211yesmaximal, characteristic, complemented
19#24764C211yesmaximal, characteristic, complemented
20#24691C211yesmaximal, characteristic, complemented
21#24641C211yesmaximal, characteristic, complemented
22#24541C211yesmaximal, characteristic, complemented
23#24532C211yesmaximal, characteristic, complemented
24#24369C211yesmaximal, characteristic, complemented
25#24360C211yesmaximal, characteristic, complemented
26#23685C211yesmaximal, characteristic, complemented
27#23545C211yesmaximal, characteristic, complemented
28#23542C211yesmaximal, characteristic, complemented
29#22652C211yesmaximal, characteristic, complemented
30#22496C211yesmaximal, characteristic, complemented
31#22426C211yesmaximal, characteristic
32C22×#137C2211yescharacteristic
33C23×Q16C2211yescharacteristic
34C2×#552C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×#548C2211yescharacteristic
37#3312—28no—
38#3270—28no—
39C2×#497C2211yescharacteristic
40C2×#491C2211yescharacteristic
41C2×#485C2211yescharacteristic
42C2×#483C2211yescharacteristic
43C2×#479C2211yescharacteristic
44C2×#470C2211yescharacteristic
45C2×#470C2211yescharacteristic
46C2×#467C2211yescharacteristic
47C2×#465C2211yescharacteristic
48C2×#464C2211yescharacteristic
49C2×#464C2211yescharacteristic
50C2×#462C2211yescharacteristic
51C2×#462C2211yescharacteristic
52C2×#462C2211yescharacteristic
53C2×#462C2211yescharacteristic
54C2×#462C2211yescharacteristic
55C2×#452C2211yescharacteristic
56C2×#451C2211yescharacteristic
57C2×#451C2211yescharacteristic
58C2×#451C2211yescharacteristic
59C2×#451C2211yescharacteristic
60C2×#448C2211yescharacteristic
61C2×#441C2211yescharacteristic
62C2×#441C2211yescharacteristic
63C2×#435C2211yescharacteristic
64C2×#435C2211yescharacteristic
65C2×#424C2211yescharacteristic
66C2×#424C2211yescharacteristic
67C2×#419C2211yescharacteristic
68C2×#419C2211yescharacteristic
69C2×#416C2211yescharacteristic
70C22×#103C2211yescharacteristic
71#2861C2211yescharacteristic
72#2704—21no—
73#2704—21no—
74#2701—21no—
75#2701—21no—
76#2621C2211yescharacteristic
77#2620C2211yescharacteristic
78#2565C2211yescharacteristic
79#2545C2211yescharacteristic
80#2502C2211yescharacteristic
81#2500C2211yescharacteristic
82#2474—21no—
83#2474—21no—
84#2468—21no—
85#2468—21no—
86#2434C2211yescharacteristic
87#2432C2211yescharacteristic
88#2378—21no—
89#2378—21no—
90#2369—21no—
91#2365C2211yescharacteristic
92#2362C2211yescharacteristic
93#2362C2211yescharacteristic
94#2357—21no—
95#2355C2211yescharacteristic
96#2354C2211yescharacteristic
97Q8×C22⋊C4C2211yescharacteristic
98Q8×C22⋊C4C2211yescharacteristic
99#2332—21no—
100#2332—21no—
101#2331—21no—
102#2323C2211yescharacteristic
103#2323C2211yescharacteristic
104#2319—21no—
105#2311C2211yescharacteristic
106#2310C2211yescharacteristic
107#2310C2211yescharacteristic
108#2310C2211yescharacteristic
109C4×C4⋊Q8C2211yescharacteristic
110C4×C4⋊Q8C2211yescharacteristic
111#2295C2211yescharacteristic
112#2293C2211yescharacteristic
113#2084C2211yescharacteristic
114#2074C2211yescharacteristic
115#2074C2211yescharacteristic
116#2072C2211yescharacteristic
117#2072C2211yescharacteristic
118#2072C2211yescharacteristic
119#2068C2211yescharacteristic
120#2067C2211yescharacteristic
121#2066C2211yescharacteristic
122#2066C2211yescharacteristic
123#2066C2211yescharacteristic
124#2065C2211yescharacteristic
125#2056C2211yescharacteristic
126#2056C2211yescharacteristic
127#2056C2211yescharacteristic
128#2056C2211yescharacteristic
129#2056C2211yescharacteristic
130#2056C2211yescharacteristic
131#2056C2211yescharacteristic
132#2056C2211yescharacteristic
133#2056C2211yescharacteristic
134#2056C2211yescharacteristic
135#2056C2211yescharacteristic
136#2056C2211yescharacteristic
137#2056C2211yescharacteristic
138#2056C2211yescharacteristic
139#2056C2211yescharacteristic
140#2056C2211yescharacteristic
141#2055C2211yescharacteristic
142#2055C2211yescharacteristic
143#2055C2211yescharacteristic
144#2055C2211yescharacteristic
145#2055C2211yescharacteristic
146#2055C2211yescharacteristic
147#2043C2211yescharacteristic
148#2016C2211yescharacteristic
149#2016C2211yescharacteristic
150#2016C2211yescharacteristic
151#2015C2211yescharacteristic
152#2015C2211yescharacteristic
153#1992C2211yescharacteristic
154#1989C2211yescharacteristic
155#1983C2211yescharacteristic
156#1983C2211yescharacteristic
157#1981C2211yescharacteristic
158#1959C2211yescharacteristic
159#1949C2211yescharacteristic
160#1948C2211yescharacteristic
161#1940C2211yescharacteristic
162#1940C2211yescharacteristic
163#1928C2211yescharacteristic
164#1927C2211yescharacteristic
165#1927C2211yescharacteristic
166#1926C2211yescharacteristic
167#1895C2211yescharacteristic
168#1894C2211yescharacteristic
169#1892C2211yescharacteristic
170#1892C2211yescharacteristic
171#1880C2211yescharacteristic
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic
174#1878C2211yescharacteristic
175#1878C2211yescharacteristic
176#1878C2211yescharacteristic
177#1878C2211yescharacteristic
178#1878C2211yescharacteristic
179#1875C2211yescharacteristic
180#1873C2211yescharacteristic
181#1873C2211yescharacteristic
182#1873C2211yescharacteristic
183#1851C2211yescharacteristic
184#1851C2211yescharacteristic
185#1850C2211yescharacteristic
186#1850C2211yescharacteristic
187#1842C2211yescharacteristic
188#1825C2211yescharacteristic
189#1824C2211yescharacteristic
190#1805C2211yescharacteristic
191#1803C2211yescharacteristic
192#1803C2211yescharacteristic
193#1803C2211yescharacteristic
194#1803C2211yescharacteristic
195#1803C2211yescharacteristic
196#1798C2211yescharacteristic
197#1798C2211yescharacteristic
198#1788C2211yescharacteristic
199#1787C2211yescharacteristic
200#1767C2211yescharacteristic
201#1763C2211yescharacteristic
202#1763C2211yescharacteristic
203#1736C2211yescharacteristic
204#1735C2211yescharacteristic
205C22×#41C2311yescharacteristic
206C23×Q8C2311yescharacteristic
207C23×Q8C2311yescharacteristic
208C23×Q8C2311yescharacteristic
209C2×#137—24no—
210C2×#137—42no—
211C2×#137—42no—
212C22×Q16—24no—
213C22×Q16—42no—
214C22×Q16—42no—
215C22×Q16C2311yescharacteristic
216C22×Q16C2311yescharacteristic
217C22×Q16C2311yescharacteristic
218C22×Q16C2311yescharacteristic
219C22×Q16C2311yescharacteristic
220C22×Q16C2311yescharacteristic
221C22×Q16C2311yescharacteristic
222C22×Q16C2311yescharacteristic
223C22×Q16C2311yescharacteristic
224C22×SD16C2311yescharacteristic
225C22×SD16C2311yescharacteristic
226C22×SD16C2311yescharacteristic
227C22×M16C2311yescharacteristic
228C22×M16C2311yescharacteristic
229C23×C8C2311yescharacteristic
230C23×C8C2311yescharacteristic
231#552—24no—
232#552—24no—
233D4×Q8—24no—
234D4×Q8D418yes—
235#548—24no—
236#548—24no—
237C2×C4⋊Q8—21no—
238C2×C4⋊Q8C2311yescharacteristic
239C2×C4⋊Q8C2311yescharacteristic
240C2×C4⋊Q8C2311yescharacteristic
241C2×#126—21no—
242C2×#125—21no—
243C2×#125C2311yescharacteristic
244C2×#124—21no—
245C2×#124C2311yescharacteristic
246C2×#124C2311yescharacteristic
247C2×#123—21no—
248C2×C22⋊Q8—21no—
249C2×C22⋊Q8—21no—
250C2×C22⋊Q8—21no—
251C2×C22⋊Q8C2311yescharacteristic
252C2×C22⋊Q8C2311yescharacteristic
253C2×C22⋊Q8C2311yescharacteristic
254C2×C22⋊Q8C2311yescharacteristic
255C2×C22⋊Q8C2311yescharacteristic
256C2×#121—21no—
257C2×#121C2311yescharacteristic
258C2×C4×Q8C2311yescharacteristic
259C2×C4×Q8C2311yescharacteristic
260C2×C4×Q8C2311yescharacteristic
261C2×C4×Q8C2311yescharacteristic
262C2×C4×Q8C2311yescharacteristic
263C2×C4×Q8C2311yescharacteristic
264C2×C4×Q8C2311yescharacteristic
265C2×C4×D4—21no—
266C2×C4×D4—21no—
267C2×C4×D4C2311yescharacteristic
268C2×#117—21no—
269C2×#117C2311yescharacteristic
270C2×#117C2311yescharacteristic
271C2×#117C2311yescharacteristic
272C2×#117C2311yescharacteristic
273C2×#117C2311yescharacteristic
274C22×C4⋊C4C2311yescharacteristic
275#497—24no—
276#491—24no—
277#485—24no—
278#483—24no—
279#479—24no—
280#470—24no—
281#470—24no—
282#467—24no—
283#465—24no—
284#464—24no—
285#464—42no—
286#462—24no—
287#462—24no—
288#462—42no—
289#462—42no—
290#462—42no—
291#452—24no—
292#451—24no—
293#451—24no—
294#451—24no—
295#451—24no—
296#448—24no—
297#441—24no—
298#441—24no—
299#435—24no—
300#435—24no—
301C2×#107C2311yescharacteristic
302C2×#106C2311yescharacteristic
303C2×#106C2311yescharacteristic
304C2×#106C2311yescharacteristic
305#424—42no—
306#424—42no—
307C2×C4⋊C8C2311yescharacteristic
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
319#419—24no—
320#419—42no—
321#416—42no—
322C2×#103—24no—
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×#103C2311yescharacteristic
336C2×#103C2311yescharacteristic
337C2×#103C2311yescharacteristic
338C2×#103C2311yescharacteristic
339C2×#103C2311yescharacteristic
340C2×#103C2311yescharacteristic
341C2×#103C2311yescharacteristic
342C2×#103C2311yescharacteristic
343C2×#103C2311yescharacteristic
344C2×#103C2311yescharacteristic
345C2×#103C2311yescharacteristic
346C2×#103C2311yescharacteristic
347C2×#103C2311yescharacteristic
348C2×#103C2311yescharacteristic
349C2×#103C2311yescharacteristic
350C2×#102C2311yescharacteristic
351C2×#102C2311yescharacteristic
352C2×#102C2311yescharacteristic
353C2×#102C2311yescharacteristic
354C2×#102C2311yescharacteristic
355C2×C22⋊C8C2311yescharacteristic
356C2×C22⋊C8C2311yescharacteristic
357C2×C22⋊C8C2311yescharacteristic
358C2×C22⋊C8C2311yescharacteristic
359C2×#97C2311yescharacteristic
360C2×#97C2311yescharacteristic
361#398—21no—
362#398—21no—
363#398—21no—
364#398—21no—
365#398—21no—
366#398—21no—
367#397—21no—
368#397—21no—
369#396—21no—
370#396—21no—
371#396—21no—
372#396—21no—
373#395—21no—
374#395—21no—
375#394—21no—
376#394—21no—
377#394—21no—
378#394—21no—
379#394—21no—
380#394—21no—
381#391—21no—
382#391—21no—
383#391—21no—
384#391—21no—
385#391—21no—
386#391—21no—
387#391—21no—
388#391—21no—
389#391—21no—
390#391—21no—
391#391C2311yescharacteristic
392#391C2311yescharacteristic
393#391C2311yescharacteristic
394#391C2311yescharacteristic
395#391C2311yescharacteristic
396#391C2311yescharacteristic
397#391C2311yescharacteristic
398#391C2311yescharacteristic
399#391C2311yescharacteristic
400#391C2311yescharacteristic
401#391C2311yescharacteristic
402#391C2311yescharacteristic
403#391C2311yescharacteristic
404#391C2311yescharacteristic
405#391C2311yescharacteristic
406#390—21no—
407#390D411yescharacteristic
408#390D411yescharacteristic
409#390C2311yescharacteristic
410#390C2311yescharacteristic
411#390C2311yescharacteristic
412#389—21no—
413#389—21no—
414#389—21no—
415#389—21no—
416#389—21no—
417#389—21no—
418#389—21no—
419#389D411yescharacteristic
420#389D411yescharacteristic
421#389C2311yescharacteristic
422#389C2311yescharacteristic
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#388—21no—
435#388—21no—
436#388—21no—
437#388—21no—
438#388—21no—
439#388—21no—
440#388—21no—
441#388D411yescharacteristic
442#388D411yescharacteristic
443#388D411yescharacteristic
444#388D411yescharacteristic
445#387—21no—
446#387—21no—
447#387—21no—
448#387—21no—
449#387—21no—
450#387—21no—
451#387—21no—
452#387—21no—
453#387—21no—
454#387—21no—
455#387—21no—
456#387—21no—
457#386—21no—
458#386—21no—
459#385—21no—
460#385—21no—
461#385—21no—
462#385—21no—
463#385—21no—
464#385—21no—
465#384C2311yescharacteristic
466#384C2311yescharacteristic
467#384C2311yescharacteristic
468#382—21no—
469#382C2311yescharacteristic
470#381—21no—
471#381—21no—
472#381—21no—
473#381—21no—
474#381—21no—
475#381—21no—
476#380—21no—
477#380—21no—
478#380—21no—
479#380—21no—
480#380C2311yescharacteristic
481#380C2311yescharacteristic
482C4×C4⋊C4—21no—
483C4×C4⋊C4—21no—
484C4×C4⋊C4—21no—
485C4×C4⋊C4—21no—
486C4×C4⋊C4—21no—
487C4×C4⋊C4—21no—
488C4×C4⋊C4—21no—
489C4×C4⋊C4—21no—
490C4×C4⋊C4—21no—
491C4×C4⋊C4—21no—
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2311yescharacteristic
496C4×C22⋊C4—21no—
497C4×C22⋊C4—21no—
498C4×C22⋊C4C2311yescharacteristic
499C4×C22⋊C4C2311yescharacteristic
500#376—21no—
501C43C2311yescharacteristic
502#340C2311yescharacteristic
503#340C2311yescharacteristic
504#340C2311yescharacteristic
505#340C2311yescharacteristic
506#340C2311yescharacteristic
507#340C2311yescharacteristic
508#340C2311yescharacteristic
509#340C2311yescharacteristic
510#340C2311yescharacteristic
511#340C2311yescharacteristic
512#340C2311yescharacteristic
513#340C2311yescharacteristic
514#340C2311yescharacteristic
515#340C2311yescharacteristic
516#340C2311yescharacteristic
517#340C2311yescharacteristic
518#336C2311yescharacteristic
519#336C2311yescharacteristic
520#336C2311yescharacteristic
521#336C2311yescharacteristic
522#336C2311yescharacteristic
523#336C2311yescharacteristic
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—41no—
528C2×#41—41no—
529C2×#41—41no—
530C22×Q8—21no—
531C22×Q8—21no—
532C22×Q8—21no—
533C22×Q8—22no—
534C22×Q8—22no—
535C22×Q8—22no—
536C22×Q8—22no—
537C22×Q8—22no—
538C22×Q8—41no—
539C22×Q8—41no—
540C22×Q8—41no—
541C22×Q8—41no—
542C22×Q8—41no—
543C22×Q8—41no—
544C22×Q8—41no—
545C22×Q8—41no—
546C22×Q8—41no—
547C22×Q8—41no—
548C22×Q8—41no—
549C22×Q8C2×D414yes—
550C22×Q8C2×D414yes—
551C22×Q8C2411yescharacteristic
552C22×Q8C2411yescharacteristic
553C22×Q8C2411yescharacteristic
554C22×Q8C2411yescharacteristic
555C22×Q8C2411yescharacteristic
556C22×Q8C2411yescharacteristic
557C22×D4—21no—
558C22×D4—21no—
559C22×D4C2×D411yescharacteristic
560C22×D4C2411yescharacteristic
561C23×C4—21no—
562C23×C4—21no—
563C23×C4—21no—
564C23×C4—21no—
565C23×C4—21no—
566C23×C4C2411yescharacteristic
567C23×C4C2411yescharacteristic
568#137—416no—
569C2×Q16—22no—
570C2×Q16—22no—
571C2×Q16—22no—
572C2×Q16—22no—
573C2×Q16—22no—
574C2×Q16—22no—
575C2×Q16—22no—
576C2×Q16—22no—
577C2×Q16—22no—
578C2×Q16—22no—
579C2×Q16—22no—
580C2×Q16—22no—
581C2×Q16—22no—
582C2×Q16—22no—
583C2×Q16—41no—
584C2×Q16—41no—
585C2×Q16—41no—
586C2×Q16—41no—
587C2×Q16—41no—
588C2×Q16—41no—
589C2×Q16—41no—
590C2×Q16—41no—
591C2×Q16—41no—
592C2×Q16—41no—
593C2×Q16—41no—
594C2×Q16—41no—
595C2×Q16—41no—
596C2×Q16—416no—
597C2×SD16—22no—
598C2×SD16—22no—
599C2×SD16—22no—
600C2×SD16—22no—
601C2×SD16—41no—
602C2×SD16—41no—
603C2×SD16—41no—
604C2×SD16—41no—
605C2×SD16—41no—
606C2×M16—22no—
607C2×M16—22no—
608C2×M16—22no—
609C2×M16—41no—
610C2×M16—41no—
611C2×M16—41no—
612C22×C8—22no—
613C22×C8—22no—
614C22×C8—22no—
615C22×C8—41no—
616C22×C8—41no—
617C22×C8—41no—
618C22×C8C2411yescharacteristic
619C22×C8C2411yescharacteristic
620C22×C8C2411yescharacteristic
621C22×C8C2411yescharacteristic
622C22×C8C2411yescharacteristic
623C22×C8C2411yescharacteristic
624C22×C8C2411yescharacteristic
625C22×C8C2411yescharacteristic
626C4⋊Q8—28no—
627C4⋊Q8—22no—
628C4⋊Q8—22no—
629C4⋊Q8—41no—
630C4⋊Q8—41no—
631C4⋊Q8—41no—
632C4⋊Q8C2×D414yes—
633#126—44no—
634#125—22no—
635#125—22no—
636#125—44no—
637#124—22no—
638#124—22no—
639#124—41no—
640#124—41no—
641#124—44no—
642#123—44no—
643C22⋊Q8—22no—
644C22⋊Q8—22no—
645C22⋊Q8—28no—
646C22⋊Q8—28no—
647C22⋊Q8—22no—
648C22⋊Q8—22no—
649C22⋊Q8—22no—
650C22⋊Q8—22no—
651C22⋊Q8—22no—
652C22⋊Q8—22no—
653C22⋊Q8—44no—
654C22⋊Q8C2×D414yes—
655C22⋊Q8C2×D414yes—
656#121—22no—
657#121—22no—
658#121—44no—
659C4×Q8—22no—
660C4×Q8—22no—
661C4×Q8—22no—
662C4×Q8—22no—
663C4×Q8—22no—
664C4×Q8—41no—
665C4×Q8—41no—
666C4×Q8—41no—
667C4×Q8—41no—
668C4×Q8—41no—
669C4×Q8—41no—
670C4×Q8—41no—
671C4×Q8—41no—
672C4×Q8C2×D414yes—
673C4×D4—28no—
674C4×D4—44no—
675C4×D4C2×D414yes—
676C4×D4#4114yes—
677#117—22no—
678#117—22no—
679#117—41no—
680#117—41no—
681#117—41no—
682#117—41no—
683#117—44no—
684#117—41no—
685#117—41no—
686#117—41no—
687#117—41no—
688C2×C4⋊C4—21no—
689C2×C4⋊C4—21no—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C4⋊C4—21no—
693C2×C4⋊C4—22no—
694C2×C4⋊C4—22no—
695C2×C4⋊C4—21no—
696C2×C4⋊C4—21no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—21no—
700C2×C4⋊C4—21no—
701C2×C4⋊C4—21no—
702C2×C4⋊C4—21no—
703C2×C4⋊C4—21no—
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4—21no—
707C2×C4⋊C4—21no—
708C2×C4⋊C4—21no—
709C2×C4⋊C4—21no—
710C2×C4⋊C4—21no—
711C2×C4⋊C4—21no—
712C2×C4⋊C4—21no—
713C2×C4⋊C4—21no—
714C2×C4⋊C4—21no—
715C2×C4⋊C4—21no—
716C2×C4⋊C4—21no—
717C2×C4⋊C4—21no—
718C2×C4⋊C4—21no—
719C2×C4⋊C4C2×D411yescharacteristic
720C2×C4⋊C4C2×D411yescharacteristic
721C2×C4⋊C4C2×D411yescharacteristic
722C2×C4⋊C4C2×D411yescharacteristic
723C2×C4⋊C4C2×D411yescharacteristic
724C2×C4⋊C4C2×D411yescharacteristic
725C2×C4⋊C4C2×D411yescharacteristic
726C2×C4⋊C4C2411yescharacteristic
727C2×C4⋊C4C2411yescharacteristic
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2411yescharacteristic
731C2×C4⋊C4C2411yescharacteristic
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2411yescharacteristic
735C2×C22⋊C4—21no—
736C2×C22⋊C4—21no—
737C2×C22⋊C4—21no—
738C2×C22⋊C4—21no—
739C2×C22⋊C4—21no—
740C2×C22⋊C4—21no—
741C2×C22⋊C4—21no—
742C2×C22⋊C4—21no—
743C2×C22⋊C4—21no—
744C2×C22⋊C4—21no—
745C2×C22⋊C4—21no—
746C2×C22⋊C4—21no—
747C2×C22⋊C4—21no—
748C2×C22⋊C4—21no—
749C2×C22⋊C4—21no—
750C2×C22⋊C4—21no—
751C2×C22⋊C4—21no—
752C2×C22⋊C4—21no—
753C2×C22⋊C4—21no—
754C2×C22⋊C4—21no—
755C2×C22⋊C4—21no—
756C2×C22⋊C4C2×D411yescharacteristic
757C2×C22⋊C4C2×D411yescharacteristic
758C2×C22⋊C4C2×D411yescharacteristic
759C2×C22⋊C4C2×D411yescharacteristic
760C2×C22⋊C4C2×D411yescharacteristic
761C2×C22⋊C4C2×D411yescharacteristic
762C2×C22⋊C4C2×D411yescharacteristic
763C2×C22⋊C4C2×D411yescharacteristic
764C2×C22⋊C4C2×D411yescharacteristic
765C2×C22⋊C4C2×D411yescharacteristic
766C2×C42—21no—
767C2×C42—21no—
768C2×C42—21no—
769C2×C42—21no—
770C2×C42—21no—
771C2×C42—21no—
772C2×C42—21no—
773C2×C42—21no—
774C2×C42—21no—
775C2×C42—21no—
776C2×C42—21no—
777C2×C42—21no—
778C2×C42—21no—
779C2×C42C2×D411yescharacteristic
780C2×C42C2×D411yescharacteristic
781C2×C42C2×D411yescharacteristic
782C2×C42C2×D411yescharacteristic
783C2×C42C2411yescharacteristic
784C2×C42C2411yescharacteristic
785C2×C42C2411yescharacteristic
786C2×C42C2411yescharacteristic
787C2×C42C2411yescharacteristic
788#107—22no—
789#106—22no—
790#106—22no—
791#106—22no—
792C4⋊C8—22no—
793C4⋊C8—22no—
794C4⋊C8—22no—
795C4⋊C8—22no—
796C4⋊C8—22no—
797C4⋊C8—41no—
798C4⋊C8—41no—
799C4⋊C8—41no—
800C4⋊C8—41no—
801C4⋊C8—41no—
802C4⋊C8—41no—
803C4⋊C8—41no—
804#103—22no—
805#103—22no—
806#103—22no—
807#103—22no—
808#103—22no—
809#103—22no—
810#103—22no—
811#103—22no—
812#103—22no—
813#103—22no—
814#103—22no—
815#103—22no—
816#103—22no—
817#103—22no—
818#103—22no—
819#103—22no—
820#103—22no—
821#103—22no—
822#103—22no—
823#103—41no—
824#103—41no—
825#103—41no—
826#103—41no—
827#103—41no—
828#103—41no—
829#103—41no—
830#103—41no—
831#102—22no—
832#102—41no—
833#102—41no—
834#102—41no—
835#102—41no—
836C22⋊C8—22no—
837C22⋊C8—22no—
838C22⋊C8—22no—
839C22⋊C8—22no—
840#97—22no—
841#97—22no—
842#95—21no—
843#95—21no—
844#95—21no—
845#95—21no—
846#95—21no—
847#95—21no—
848#95—21no—
849#95—21no—
850#95—21no—
851#95—21no—
852#95—21no—
853#95—21no—
854#95—21no—
855#95—21no—
856#95—21no—
857#95—21no—
858#95—21no—
859#95—21no—
860#95—21no—
861#95—21no—
862#95—21no—
863#95—21no—
864#95—21no—
865#95—21no—
866#95—21no—
867#95—21no—
868#95—21no—
869#95—21no—
870#95—21no—
871#95—21no—
872#95—21no—
873#95—21no—
874#95—21no—
875#95—21no—
876#95—21no—
877#95—21no—
878#95—21no—
879#95—21no—
880#95—21no—
881#95C2×D411yescharacteristic
882#95C2×D411yescharacteristic
883#95C2×D411yescharacteristic
884#95C2×D411yescharacteristic
885#95C2×D411yescharacteristic
886#95C2×D411yescharacteristic
887C24—21no—
888C24C22×D411yescharacteristic
889C24C22×D411yescharacteristic
890#41—44no—
891#41—44no—
892#41—82no—
893#41—82no—
894C2×Q8—24no—
895C2×Q8—24no—
896C2×Q8—21no—
897C2×Q8—21no—
898C2×Q8—21no—
899C2×Q8—21no—
900C2×Q8—21no—
901C2×Q8—21no—
902C2×Q8—21no—
903C2×Q8—21no—
904C2×Q8—21no—
905C2×Q8—21no—
906C2×Q8—21no—
907C2×Q8—21no—
908C2×Q8—21no—
909C2×Q8—21no—
910C2×Q8—21no—
911C2×Q8—21no—
912C2×Q8—21no—
913C2×Q8—21no—
914C2×Q8—21no—
915C2×Q8—21no—
916C2×Q8—21no—
917C2×Q8—21no—
918C2×Q8—21no—
919C2×Q8—21no—
920C2×Q8—21no—
921C2×Q8—21no—
922C2×Q8—21no—
923C2×Q8—21no—
924C2×Q8—21no—
925C2×Q8—21no—
926C2×Q8—21no—
927C2×Q8—21no—
928C2×Q8—42no—
929C2×Q8—44no—
930C2×Q8—44no—
931C2×Q8—44no—
932C2×Q8—44no—
933C2×Q8—44no—
934C2×Q8—44no—
935C2×Q8—42no—
936C2×Q8—81no—
937C2×Q8—81no—
938C2×Q8—81no—
939C2×Q8—81no—
940C2×Q8—81no—
941C2×Q8—82no—
942C2×Q8—82no—
943C2×Q8—82no—
944C2×Q8—82no—
945C2×Q8—82no—
946C2×Q8—82no—
947C2×Q8C22×D412yes—
948C2×Q8C22×D412yes—
949C2×Q8C22×D412yes—
950C2×Q8H(5,𝔽2)12yes—
951C2×D4—21no—
952C2×D4—21no—
953C2×D4—21no—
954C2×D4—21no—
955C2×D4—21no—
956C2×D4—21no—
957C2×D4—41no—
958C2×D4—41no—
959C2×D4—42no—
960C2×D4—42no—
961C2×D4—42no—
962C2×D4—81no—
963C2×D4—81no—
964C2×D4—81no—
965C2×D4#12114yes—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—24no—
980C22×C4—24no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—42no—
992C22×C4—42no—
993C22×C4—42no—
994C22×C4—42no—
995C22×C4—42no—
996C22×C4—81no—
997C22×C4—81no—
998C22×C4—81no—
999C22×C4—81no—
1000C22×C4—81no—
1001C22×C4—81no—
1002C22×C4—81no—
1003C22×C4—81no—
1004C22×C4C22×D411yescharacteristic
1005C22×C4C22×D411yescharacteristic
1006C22×C4C22×D411yescharacteristic
1007C22×C4C22×D411yescharacteristic
1008C22×C4C22×D411yescharacteristic
1009C22×C4C22×D411yescharacteristic
1010C22×C4C22×D411yescharacteristic
1011C22×C4C22×D411yescharacteristic
1012C22×C4C22×D411yescharacteristic
1013C22×C4C22×D411yescharacteristic
1014C22×C4C22×D411yescharacteristic
1015C22×C4C22×D412yes—
1016C22×C4C22×D412yes—
1017C22×C4C22×D411yescharacteristic
1018C22×C4C2×#4112yes—
1019C22×C4C2×#4112yes—
1020C22×C4C2511yescharacteristic
1021Q16—28no—
1022Q16—44no—
1023Q16—44no—
1024Q16—44no—
1025Q16—44no—
1026Q16—44no—
1027Q16—82no—
1028Q16—82no—
1029Q16—82no—
1030SD16—44no—
1031SD16—44no—
1032SD16—82no—
1033M16—44no—
1034M16—82no—
1035C2×C8—21no—
1036C2×C8—21no—
1037C2×C8—21no—
1038C2×C8—21no—
1039C2×C8—21no—
1040C2×C8—21no—
1041C2×C8—21no—
1042C2×C8—21no—
1043C2×C8—21no—
1044C2×C8—21no—
1045C2×C8—21no—
1046C2×C8—21no—
1047C2×C8—21no—
1048C2×C8—21no—
1049C2×C8—21no—
1050C2×C8—21no—
1051C2×C8—21no—
1052C2×C8—21no—
1053C2×C8—21no—
1054C2×C8—21no—
1055C2×C8—21no—
1056C2×C8—21no—
1057C2×C8—21no—
1058C2×C8—44no—
1059C2×C8—82no—
1060C2×C8H(5,𝔽2)12yes—
1061C4⋊C4—24no—
1062C4⋊C4—24no—
1063C4⋊C4—24no—
1064C4⋊C4—24no—
1065C4⋊C4—24no—
1066C4⋊C4—21no—
1067C4⋊C4—21no—
1068C4⋊C4—21no—
1069C4⋊C4—21no—
1070C4⋊C4—21no—
1071C4⋊C4—21no—
1072C4⋊C4—21no—
1073C4⋊C4—21no—
1074C4⋊C4—21no—
1075C4⋊C4—21no—
1076C4⋊C4—21no—
1077C4⋊C4—21no—
1078C4⋊C4—21no—
1079C4⋊C4—21no—
1080C4⋊C4—21no—
1081C4⋊C4—21no—
1082C4⋊C4—21no—
1083C4⋊C4—41no—
1084C4⋊C4—41no—
1085C4⋊C4—41no—
1086C4⋊C4—41no—
1087C4⋊C4—41no—
1088C4⋊C4—41no—
1089C4⋊C4—42no—
1090C4⋊C4—42no—
1091C4⋊C4—42no—
1092C4⋊C4—42no—
1093C4⋊C4—42no—
1094C4⋊C4—42no—
1095C4⋊C4—42no—
1096C4⋊C4—42no—
1097C4⋊C4—42no—
1098C4⋊C4—42no—
1099C4⋊C4—42no—
1100C4⋊C4—42no—
1101C4⋊C4—81no—
1102C4⋊C4—81no—
1103C4⋊C4—81no—
1104C4⋊C4—81no—
1105C4⋊C4—81no—
1106C4⋊C4—81no—
1107C4⋊C4—81no—
1108C4⋊C4—81no—
1109C4⋊C4—81no—
1110C4⋊C4—81no—
1111C4⋊C4—81no—
1112C4⋊C4—81no—
1113C4⋊C4#12114yes—
1114C4⋊C4C22×D412yes—
1115C22⋊C4—24no—
1116C22⋊C4—24no—
1117C22⋊C4—22no—
1118C22⋊C4—22no—
1119C22⋊C4—41no—
1120C22⋊C4—41no—
1121C22⋊C4—41no—
1122C22⋊C4—41no—
1123C22⋊C4—41no—
1124C22⋊C4—41no—
1125C22⋊C4—42no—
1126C22⋊C4—42no—
1127C22⋊C4—42no—
1128C22⋊C4—42no—
1129C22⋊C4—42no—
1130C22⋊C4—42no—
1131C22⋊C4—42no—
1132C22⋊C4—42no—
1133C22⋊C4—42no—
1134C22⋊C4—81no—
1135C22⋊C4—81no—
1136C22⋊C4—81no—
1137C22⋊C4—81no—
1138C22⋊C4—81no—
1139C22⋊C4—81no—
1140C22⋊C4—81no—
1141C22⋊C4—81no—
1142C22⋊C4—81no—
1143C22⋊C4—81no—
1144C22⋊C4#12114yes—
1145C22⋊C4#12114yes—
1146C42—24no—
1147C42—22no—
1148C42—21no—
1149C42—21no—
1150C42—21no—
1151C42—21no—
1152C42—21no—
1153C42—21no—
1154C42—21no—
1155C42—21no—
1156C42—41no—
1157C42—41no—
1158C42—41no—
1159C42—42no—
1160C42—42no—
1161C42—42no—
1162C42—42no—
1163C42—81no—
1164C42—81no—
1165C42—81no—
1166C42—81no—
1167C42—81no—
1168C42—81no—
1169C42—81no—
1170C42—81no—
1171C42C22×D412yes—
1172C42C2×#4112yes—
1173C23—21no—
1174C23—21no—
1175C23—21no—
1176C23—21no—
1177C23—21no—
1178C23—21no—
1179C23—21no—
1180C23—21no—
1181C23—21no—
1182C23—21no—
1183C23—21no—
1184C23—21no—
1185C23—41no—
1186C23—41no—
1187C23—41no—
1188C23—41no—
1189C23—41no—
1190C23—41no—
1191C23—41no—
1192C23C2×#12112yes—
1193C23C2×#12112yes—
1194C23C23×D411yescharacteristic
1195Q8—22no—
1196Q8—22no—
1197Q8—22no—
1198Q8—22no—
1199Q8—22no—
1200Q8—22no—
1201Q8—22no—
1202Q8—22no—
1203Q8—41no—
1204Q8—41no—
1205Q8—41no—
1206Q8—41no—
1207Q8—41no—
1208Q8—41no—
1209Q8—41no—
1210Q8—41no—
1211Q8—41no—
1212Q8—41no—
1213Q8—41no—
1214Q8—41no—
1215Q8—41no—
1216Q8—41no—
1217Q8—41no—
1218Q8—41no—
1219Q8—84no—
1220Q8—84no—
1221Q8—84no—
1222D4—44no—
1223D4—41no—
1224D4—41no—
1225D4—41no—
1226D4—41no—
1227D4—84no—
1228D4—84no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—21no—
1263C2×C4—22no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
1307C2×C4—41no—
1308C2×C4—41no—
1309C2×C4—41no—
1310C2×C4—41no—
1311C2×C4—41no—
1312C2×C4—41no—
1313C2×C4—84no—
1314C2×C4—84no—
1315C2×C4—84no—
1316C2×C4—84no—
1317C2×C4—84no—
1318C2×C4C2×#12112yes—
1319C2×C4C2×#12112yes—
1320C2×C4C2×#12112yes—
1321C2×C4C2×#12112yes—
1322C2×C4#57812yes—
1323C2×C4C23×D411yescharacteristic
1324C2×C4C22×#4111yescharacteristic
1325C2×C4C2×H(5,𝔽2)11yescharacteristic
1326C2×C4C2×H(5,𝔽2)11yescharacteristic
1327C2×C4#58511yescharacteristic
1328C2×C4#58511yescharacteristic
1329C8—22no—
1330C8—41no—
1331C8—41no—
1332C8—41no—
1333C8—41no—
1334C8—41no—
1335C8—41no—
1336C8—41no—
1337C22—22no—
1338C22—22no—
1339C22—22no—
1340C22—22no—
1341C22—22no—
1342C22—22no—
1343C22—41no—
1344C22—41no—
1345C22—41no—
1346C22—41no—
1347C22—41no—
1348C22—41no—
1349C22—41no—
1350C22—41no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—81no—
1356C22—81no—
1357C22—81no—
1358C22C22×#12111yescharacteristic
1359C22#348811yescharacteristic
1360C22#349611yescharacteristic
1361C22C2×#57811yescharacteristic
1362C22#358611yescharacteristic
1363C22#358611yescharacteristic
1364C22#358611yescharacteristic
1365C4—22no—
1366C4—22no—
1367C4—22no—
1368C4—22no—
1369C4—22no—
1370C4—42no—
1371C4—41no—
1372C4—41no—
1373C4—41no—
1374C4—41no—
1375C4—41no—
1376C4—41no—
1377C4—41no—
1378C4—42no—
1379C4—42no—
1380C4—42no—
1381C4—42no—
1382C4—81no—
1383C4—81no—
1384C4—81no—
1385C4—81no—
1386C4—81no—
1387C4—81no—
1388C4—81no—
1389C4—81no—
1390C4—81no—
1391C4—81no—
1392C4#348411yescharacteristic
1393C4#348511yescharacteristic
1394C4#351311yescharacteristic
1395C4#351411yescharacteristic
1396C2—42no—
1397C2—42no—
1398C2—161no—
1399C2#3576111yescharacteristic
1400C2#6042411yescharacteristic
1401C2#6043211yescharacteristic
1402C2#6201011yescharacteristic
1403C2#6208611yescharacteristic
1404C2#6233511yescharacteristic
1405C2#6235011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#548C22
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×#3312C2semidirect
4. #34487C2semidirect
5. #29833C2semidirect
6. #29728C2semidirect
7. #29724C2semidirect
8. #28619C2semidirect
9. #28255C2semidirect
10. #28133C2semidirect
11. #28132C2semidirect
12. #25379C2semidirect
13. #25333C2semidirect
14. #25219C2semidirect
15. #25203C2semidirect
16. #25095C2semidirect
17. #25079C2semidirect
18. #24769C2semidirect
19. #24764C2semidirect
20. #24691C2semidirect
21. #24641C2semidirect
22. #24541C2semidirect
23. #24532C2semidirect
24. #24369C2semidirect
25. #24360C2semidirect
26. #23685C2semidirect
27. #23545C2semidirect
28. #23542C2semidirect
29. #22652C2semidirect
30. #22496C2semidirect

Maximal subgroups

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

subgroupindex
C2×#33122
C2×#32702
#389462
#344872
#298332
#297282
#297242
#286192
#282552
#281332
#281322
#253792
#253332
#252192
#252032
#250952
#250792
#247692
#247642
#246912
#246412
#245412
#245322
#243692
#243602
#236852
#235452
#235422
#226522
#224962
#224262